id	sid	tid	token	lemma	pos
37681	1	1	THE	the	DT
37681	1	2	TEACHING	teaching	NN
37681	1	3	OF	of	IN
37681	1	4	GEOMETRY	GEOMETRY	NNP
37681	1	5	BY	by	IN
37681	1	6	DAVID	david	NN
37681	1	7	EUGENE	EUGENE	NNP
37681	1	8	SMITH	SMITH	NNP
37681	1	9	GINN	GINN	NNP
37681	1	10	AND	and	CC
37681	1	11	COMPANY	COMPANY	NNP
37681	1	12	BOSTON	BOSTON	NNP
37681	1	13	·	·	NFP
37681	1	14	NEW	NEW	NNP
37681	1	15	YORK	YORK	NNP
37681	1	16	·	·	NFP
37681	1	17	CHICAGO	CHICAGO	NNP
37681	1	18	·	·	NFP
37681	1	19	LONDON	LONDON	NNP
37681	1	20	COPYRIGHT	COPYRIGHT	NNP
37681	1	21	,	,	,
37681	1	22	1911	1911	CD
37681	1	23	,	,	,
37681	1	24	BY	by	IN
37681	1	25	DAVID	DAVID	NNP
37681	1	26	EUGENE	EUGENE	NNS
37681	1	27	SMITH	SMITH	NNP
37681	1	28	ALL	all	DT
37681	1	29	RIGHTS	right	NNS
37681	1	30	RESERVED	reserve	VBD
37681	1	31	911.6	911.6	CD
37681	1	32	The	the	DT
37681	1	33	Athenæum	Athenæum	NNP
37681	1	34	Press	Press	NNP
37681	1	35	GINN	GINN	NNP
37681	1	36	AND	and	CC
37681	1	37	COMPANY	COMPANY	NNP
37681	1	38	·	·	NFP
37681	1	39	PROPRIETORS	PROPRIETORS	NNP
37681	1	40	BOSTON	BOSTON	NNP
37681	1	41	·	·	NFP
37681	1	42	U.S.A.	U.S.A.	NNP
37681	2	1	PREFACE	preface	VB
37681	2	2	A	a	DT
37681	2	3	book	book	NN
37681	2	4	upon	upon	IN
37681	2	5	the	the	DT
37681	2	6	teaching	teaching	NN
37681	2	7	of	of	IN
37681	2	8	geometry	geometry	NN
37681	2	9	may	may	MD
37681	2	10	be	be	VB
37681	2	11	planned	plan	VBN
37681	2	12	in	in	IN
37681	2	13	divers	diver	NNS
37681	2	14	ways	way	NNS
37681	2	15	.	.	.
37681	3	1	It	-PRON-	PRP
37681	3	2	may	may	MD
37681	3	3	be	be	VB
37681	3	4	written	write	VBN
37681	3	5	to	to	TO
37681	3	6	exploit	exploit	VB
37681	3	7	a	a	DT
37681	3	8	new	new	JJ
37681	3	9	theory	theory	NN
37681	3	10	of	of	IN
37681	3	11	geometry	geometry	NN
37681	3	12	,	,	,
37681	3	13	or	or	CC
37681	3	14	a	a	DT
37681	3	15	new	new	JJ
37681	3	16	method	method	NN
37681	3	17	of	of	IN
37681	3	18	presenting	present	VBG
37681	3	19	the	the	DT
37681	3	20	science	science	NN
37681	3	21	as	as	IN
37681	3	22	we	-PRON-	PRP
37681	3	23	already	already	RB
37681	3	24	have	have	VBP
37681	3	25	it	-PRON-	PRP
37681	3	26	.	.	.
37681	4	1	On	on	IN
37681	4	2	the	the	DT
37681	4	3	other	other	JJ
37681	4	4	hand	hand	NN
37681	4	5	,	,	,
37681	4	6	it	-PRON-	PRP
37681	4	7	may	may	MD
37681	4	8	be	be	VB
37681	4	9	ultraconservative	ultraconservative	JJ
37681	4	10	,	,	,
37681	4	11	making	make	VBG
37681	4	12	a	a	DT
37681	4	13	plea	plea	NN
37681	4	14	for	for	IN
37681	4	15	the	the	DT
37681	4	16	ancient	ancient	JJ
37681	4	17	teaching	teaching	NN
37681	4	18	and	and	CC
37681	4	19	the	the	DT
37681	4	20	ancient	ancient	JJ
37681	4	21	geometry	geometry	NN
37681	4	22	.	.	.
37681	5	1	It	-PRON-	PRP
37681	5	2	may	may	MD
37681	5	3	be	be	VB
37681	5	4	prepared	prepare	VBN
37681	5	5	for	for	IN
37681	5	6	the	the	DT
37681	5	7	purpose	purpose	NN
37681	5	8	of	of	IN
37681	5	9	setting	set	VBG
37681	5	10	forth	forth	RP
37681	5	11	the	the	DT
37681	5	12	work	work	NN
37681	5	13	as	as	IN
37681	5	14	it	-PRON-	PRP
37681	5	15	now	now	RB
37681	5	16	is	be	VBZ
37681	5	17	,	,	,
37681	5	18	or	or	CC
37681	5	19	with	with	IN
37681	5	20	the	the	DT
37681	5	21	tempting	tempting	JJ
37681	5	22	but	but	CC
37681	5	23	dangerous	dangerous	JJ
37681	5	24	idea	idea	NN
37681	5	25	of	of	IN
37681	5	26	prophecy	prophecy	NN
37681	5	27	.	.	.
37681	6	1	It	-PRON-	PRP
37681	6	2	may	may	MD
37681	6	3	appeal	appeal	VB
37681	6	4	to	to	IN
37681	6	5	the	the	DT
37681	6	6	iconoclast	iconoclast	NN
37681	6	7	by	by	IN
37681	6	8	its	-PRON-	PRP$
37681	6	9	spirit	spirit	NN
37681	6	10	of	of	IN
37681	6	11	destruction	destruction	NN
37681	6	12	,	,	,
37681	6	13	or	or	CC
37681	6	14	to	to	IN
37681	6	15	the	the	DT
37681	6	16	disciples	disciple	NNS
37681	6	17	of	of	IN
37681	6	18	_	_	NNP
37681	6	19	laissez	laissez	NNP
37681	6	20	faire	faire	NN
37681	6	21	_	_	NNP
37681	6	22	by	by	IN
37681	6	23	its	-PRON-	PRP$
37681	6	24	spirit	spirit	NN
37681	6	25	of	of	IN
37681	6	26	conserving	conserve	VBG
37681	6	27	what	what	WP
37681	6	28	the	the	DT
37681	6	29	past	past	NN
37681	6	30	has	have	VBZ
37681	6	31	bequeathed	bequeath	VBN
37681	6	32	.	.	.
37681	7	1	It	-PRON-	PRP
37681	7	2	may	may	MD
37681	7	3	be	be	VB
37681	7	4	written	write	VBN
37681	7	5	for	for	IN
37681	7	6	the	the	DT
37681	7	7	few	few	JJ
37681	7	8	who	who	WP
37681	7	9	always	always	RB
37681	7	10	lead	lead	VBP
37681	7	11	,	,	,
37681	7	12	or	or	CC
37681	7	13	think	think	VBP
37681	7	14	they	-PRON-	PRP
37681	7	15	lead	lead	VBP
37681	7	16	,	,	,
37681	7	17	or	or	CC
37681	7	18	for	for	IN
37681	7	19	the	the	DT
37681	7	20	many	many	JJ
37681	7	21	who	who	WP
37681	7	22	are	be	VBP
37681	7	23	ranked	rank	VBN
37681	7	24	by	by	IN
37681	7	25	the	the	DT
37681	7	26	few	few	JJ
37681	7	27	as	as	IN
37681	7	28	followers	follower	NNS
37681	7	29	.	.	.
37681	8	1	And	and	CC
37681	8	2	in	in	IN
37681	8	3	view	view	NN
37681	8	4	of	of	IN
37681	8	5	these	these	DT
37681	8	6	varied	varied	JJ
37681	8	7	pathways	pathway	NNS
37681	8	8	into	into	IN
37681	8	9	the	the	DT
37681	8	10	joint	joint	JJ
37681	8	11	domain	domain	NN
37681	8	12	of	of	IN
37681	8	13	geometry	geometry	NN
37681	8	14	and	and	CC
37681	8	15	education	education	NN
37681	8	16	,	,	,
37681	8	17	a	a	DT
37681	8	18	writer	writer	NN
37681	8	19	may	may	MD
37681	8	20	well	well	RB
37681	8	21	afford	afford	VB
37681	8	22	to	to	TO
37681	8	23	pause	pause	VB
37681	8	24	before	before	IN
37681	8	25	he	-PRON-	PRP
37681	8	26	sets	set	VBZ
37681	8	27	his	-PRON-	PRP$
37681	8	28	pen	pen	NN
37681	8	29	to	to	IN
37681	8	30	paper	paper	NN
37681	8	31	,	,	,
37681	8	32	and	and	CC
37681	8	33	to	to	TO
37681	8	34	decide	decide	VB
37681	8	35	with	with	IN
37681	8	36	care	care	VB
37681	8	37	the	the	DT
37681	8	38	route	route	NN
37681	8	39	that	that	IN
37681	8	40	he	-PRON-	PRP
37681	8	41	will	will	MD
37681	8	42	take	take	VB
37681	8	43	.	.	.
37681	9	1	At	at	IN
37681	9	2	present	present	NN
37681	9	3	in	in	IN
37681	9	4	America	America	NNP
37681	9	5	we	-PRON-	PRP
37681	9	6	have	have	VBP
37681	9	7	a	a	DT
37681	9	8	fairly	fairly	RB
37681	9	9	well	well	RB
37681	9	10	-	-	HYPH
37681	9	11	defined	define	VBN
37681	9	12	body	body	NN
37681	9	13	of	of	IN
37681	9	14	matter	matter	NN
37681	9	15	in	in	IN
37681	9	16	geometry	geometry	NN
37681	9	17	,	,	,
37681	9	18	and	and	CC
37681	9	19	this	this	DT
37681	9	20	occupies	occupy	VBZ
37681	9	21	a	a	DT
37681	9	22	fairly	fairly	RB
37681	9	23	well	well	RB
37681	9	24	-	-	HYPH
37681	9	25	defined	define	VBN
37681	9	26	place	place	NN
37681	9	27	in	in	IN
37681	9	28	the	the	DT
37681	9	29	curriculum	curriculum	NN
37681	9	30	.	.	.
37681	10	1	There	there	EX
37681	10	2	are	be	VBP
37681	10	3	not	not	RB
37681	10	4	wanting	want	VBG
37681	10	5	many	many	JJ
37681	10	6	earnest	earnest	JJ
37681	10	7	teachers	teacher	NNS
37681	10	8	who	who	WP
37681	10	9	would	would	MD
37681	10	10	change	change	VB
37681	10	11	both	both	CC
37681	10	12	the	the	DT
37681	10	13	matter	matter	NN
37681	10	14	and	and	CC
37681	10	15	the	the	DT
37681	10	16	place	place	NN
37681	10	17	in	in	IN
37681	10	18	a	a	DT
37681	10	19	very	very	RB
37681	10	20	radical	radical	JJ
37681	10	21	fashion	fashion	NN
37681	10	22	.	.	.
37681	11	1	There	there	EX
37681	11	2	are	be	VBP
37681	11	3	not	not	RB
37681	11	4	wanting	want	VBG
37681	11	5	others	other	NNS
37681	11	6	,	,	,
37681	11	7	also	also	RB
37681	11	8	many	many	JJ
37681	11	9	in	in	IN
37681	11	10	number	number	NN
37681	11	11	,	,	,
37681	11	12	who	who	WP
37681	11	13	are	be	VBP
37681	11	14	content	content	JJ
37681	11	15	with	with	IN
37681	11	16	things	thing	NNS
37681	11	17	as	as	IN
37681	11	18	they	-PRON-	PRP
37681	11	19	find	find	VBP
37681	11	20	them	-PRON-	PRP
37681	11	21	.	.	.
37681	12	1	But	but	CC
37681	12	2	by	by	IN
37681	12	3	far	far	RB
37681	12	4	the	the	DT
37681	12	5	largest	large	JJS
37681	12	6	part	part	NN
37681	12	7	of	of	IN
37681	12	8	the	the	DT
37681	12	9	teaching	teaching	NN
37681	12	10	body	body	NN
37681	12	11	is	be	VBZ
37681	12	12	of	of	IN
37681	12	13	a	a	DT
37681	12	14	mind	mind	NN
37681	12	15	to	to	TO
37681	12	16	welcome	welcome	VB
37681	12	17	the	the	DT
37681	12	18	natural	natural	JJ
37681	12	19	and	and	CC
37681	12	20	gradual	gradual	JJ
37681	12	21	evolution	evolution	NN
37681	12	22	of	of	IN
37681	12	23	geometry	geometry	NN
37681	12	24	toward	toward	IN
37681	12	25	better	well	JJR
37681	12	26	things	thing	NNS
37681	12	27	,	,	,
37681	12	28	contributing	contribute	VBG
37681	12	29	to	to	IN
37681	12	30	this	this	DT
37681	12	31	evolution	evolution	NN
37681	12	32	as	as	RB
37681	12	33	much	much	RB
37681	12	34	as	as	IN
37681	12	35	it	-PRON-	PRP
37681	12	36	can	can	MD
37681	12	37	,	,	,
37681	12	38	glad	glad	JJ
37681	12	39	to	to	TO
37681	12	40	know	know	VB
37681	12	41	the	the	DT
37681	12	42	best	good	JJS
37681	12	43	that	that	IN
37681	12	44	others	other	NNS
37681	12	45	have	have	VBP
37681	12	46	to	to	TO
37681	12	47	offer	offer	VB
37681	12	48	,	,	,
37681	12	49	receptive	receptive	VB
37681	12	50	of	of	IN
37681	12	51	ideas	idea	NNS
37681	12	52	that	that	WDT
37681	12	53	make	make	VBP
37681	12	54	for	for	IN
37681	12	55	better	well	JJR
37681	12	56	teaching	teaching	NN
37681	12	57	,	,	,
37681	12	58	but	but	CC
37681	12	59	out	out	IN
37681	12	60	of	of	IN
37681	12	61	sympathy	sympathy	NN
37681	12	62	with	with	IN
37681	12	63	either	either	CC
37681	12	64	the	the	DT
37681	12	65	extreme	extreme	NN
37681	12	66	of	of	IN
37681	12	67	revolution	revolution	NN
37681	12	68	or	or	CC
37681	12	69	the	the	DT
37681	12	70	extreme	extreme	NN
37681	12	71	of	of	IN
37681	12	72	stagnation	stagnation	NN
37681	12	73	.	.	.
37681	13	1	It	-PRON-	PRP
37681	13	2	is	be	VBZ
37681	13	3	for	for	IN
37681	13	4	this	this	DT
37681	13	5	larger	large	JJR
37681	13	6	class	class	NN
37681	13	7	,	,	,
37681	13	8	the	the	DT
37681	13	9	great	great	JJ
37681	13	10	body	body	NN
37681	13	11	of	of	IN
37681	13	12	progressive	progressive	JJ
37681	13	13	teachers	teacher	NNS
37681	13	14	,	,	,
37681	13	15	that	that	IN
37681	13	16	this	this	DT
37681	13	17	book	book	NN
37681	13	18	is	be	VBZ
37681	13	19	written	write	VBN
37681	13	20	.	.	.
37681	14	1	It	-PRON-	PRP
37681	14	2	stands	stand	VBZ
37681	14	3	for	for	IN
37681	14	4	vitalizing	vitalize	VBG
37681	14	5	geometry	geometry	NN
37681	14	6	in	in	IN
37681	14	7	every	every	DT
37681	14	8	legitimate	legitimate	JJ
37681	14	9	way	way	NN
37681	14	10	;	;	:
37681	14	11	for	for	IN
37681	14	12	improving	improve	VBG
37681	14	13	the	the	DT
37681	14	14	subject	subject	JJ
37681	14	15	matter	matter	NN
37681	14	16	in	in	IN
37681	14	17	such	such	JJ
37681	14	18	manner	manner	NN
37681	14	19	as	as	IN
37681	14	20	not	not	RB
37681	14	21	to	to	TO
37681	14	22	destroy	destroy	VB
37681	14	23	the	the	DT
37681	14	24	pupil	pupil	NN
37681	14	25	's	's	POS
37681	14	26	interest	interest	NN
37681	14	27	;	;	:
37681	14	28	for	for	IN
37681	14	29	so	so	RB
37681	14	30	teaching	teach	VBG
37681	14	31	geometry	geometry	NN
37681	14	32	as	as	IN
37681	14	33	to	to	TO
37681	14	34	make	make	VB
37681	14	35	it	-PRON-	PRP
37681	14	36	appeal	appeal	VB
37681	14	37	to	to	IN
37681	14	38	pupils	pupil	NNS
37681	14	39	as	as	RB
37681	14	40	strongly	strongly	RB
37681	14	41	as	as	IN
37681	14	42	any	any	DT
37681	14	43	other	other	JJ
37681	14	44	subject	subject	NN
37681	14	45	in	in	IN
37681	14	46	the	the	DT
37681	14	47	curriculum	curriculum	NN
37681	14	48	;	;	:
37681	14	49	but	but	CC
37681	14	50	for	for	IN
37681	14	51	the	the	DT
37681	14	52	recognition	recognition	NN
37681	14	53	of	of	IN
37681	14	54	geometry	geometry	NN
37681	14	55	for	for	IN
37681	14	56	geometry	geometry	NN
37681	14	57	's	's	POS
37681	14	58	sake	sake	NN
37681	14	59	and	and	CC
37681	14	60	not	not	RB
37681	14	61	for	for	IN
37681	14	62	the	the	DT
37681	14	63	sake	sake	NN
37681	14	64	of	of	IN
37681	14	65	a	a	DT
37681	14	66	fancied	fancied	JJ
37681	14	67	utility	utility	NN
37681	14	68	that	that	WDT
37681	14	69	hardly	hardly	RB
37681	14	70	exists	exist	VBZ
37681	14	71	.	.	.
37681	15	1	Expressing	express	VBG
37681	15	2	full	full	JJ
37681	15	3	appreciation	appreciation	NN
37681	15	4	of	of	IN
37681	15	5	the	the	DT
37681	15	6	desirability	desirability	NN
37681	15	7	of	of	IN
37681	15	8	establishing	establish	VBG
37681	15	9	a	a	DT
37681	15	10	motive	motive	NN
37681	15	11	for	for	IN
37681	15	12	all	all	DT
37681	15	13	studies	study	NNS
37681	15	14	,	,	,
37681	15	15	so	so	IN
37681	15	16	as	as	IN
37681	15	17	to	to	TO
37681	15	18	have	have	VB
37681	15	19	the	the	DT
37681	15	20	work	work	NN
37681	15	21	proceed	proceed	VB
37681	15	22	with	with	IN
37681	15	23	interest	interest	NN
37681	15	24	and	and	CC
37681	15	25	vigor	vigor	NN
37681	15	26	,	,	,
37681	15	27	it	-PRON-	PRP
37681	15	28	does	do	VBZ
37681	15	29	not	not	RB
37681	15	30	hesitate	hesitate	VB
37681	15	31	to	to	TO
37681	15	32	express	express	VB
37681	15	33	doubt	doubt	NN
37681	15	34	as	as	IN
37681	15	35	to	to	IN
37681	15	36	certain	certain	JJ
37681	15	37	motives	motive	NNS
37681	15	38	that	that	WDT
37681	15	39	have	have	VBP
37681	15	40	been	be	VBN
37681	15	41	exploited	exploit	VBN
37681	15	42	,	,	,
37681	15	43	nor	nor	CC
37681	15	44	to	to	TO
37681	15	45	stand	stand	VB
37681	15	46	for	for	IN
37681	15	47	such	such	PDT
37681	15	48	a	a	DT
37681	15	49	genuine	genuine	JJ
37681	15	50	,	,	,
37681	15	51	thought	think	VBN
37681	15	52	-	-	HYPH
37681	15	53	compelling	compel	VBG
37681	15	54	development	development	NN
37681	15	55	of	of	IN
37681	15	56	the	the	DT
37681	15	57	science	science	NN
37681	15	58	as	as	IN
37681	15	59	is	be	VBZ
37681	15	60	in	in	IN
37681	15	61	harmony	harmony	NN
37681	15	62	with	with	IN
37681	15	63	the	the	DT
37681	15	64	mental	mental	JJ
37681	15	65	powers	power	NNS
37681	15	66	of	of	IN
37681	15	67	the	the	DT
37681	15	68	pupils	pupil	NNS
37681	15	69	in	in	IN
37681	15	70	the	the	DT
37681	15	71	American	american	JJ
37681	15	72	high	high	JJ
37681	15	73	school	school	NN
37681	15	74	.	.	.
37681	16	1	For	for	IN
37681	16	2	this	this	DT
37681	16	3	class	class	NN
37681	16	4	of	of	IN
37681	16	5	teachers	teacher	NNS
37681	16	6	the	the	DT
37681	16	7	author	author	NN
37681	16	8	hopes	hope	VBZ
37681	16	9	that	that	IN
37681	16	10	the	the	DT
37681	16	11	book	book	NN
37681	16	12	will	will	MD
37681	16	13	prove	prove	VB
37681	16	14	of	of	IN
37681	16	15	service	service	NN
37681	16	16	,	,	,
37681	16	17	and	and	CC
37681	16	18	that	that	IN
37681	16	19	through	through	IN
37681	16	20	its	-PRON-	PRP$
37681	16	21	perusal	perusal	NN
37681	16	22	they	-PRON-	PRP
37681	16	23	will	will	MD
37681	16	24	come	come	VB
37681	16	25	to	to	TO
37681	16	26	admire	admire	VB
37681	16	27	the	the	DT
37681	16	28	subject	subject	NN
37681	16	29	more	more	RBR
37681	16	30	and	and	CC
37681	16	31	more	more	RBR
37681	16	32	,	,	,
37681	16	33	and	and	CC
37681	16	34	to	to	TO
37681	16	35	teach	teach	VB
37681	16	36	it	-PRON-	PRP
37681	16	37	with	with	IN
37681	16	38	greater	great	JJR
37681	16	39	interest	interest	NN
37681	16	40	.	.	.
37681	17	1	It	-PRON-	PRP
37681	17	2	offers	offer	VBZ
37681	17	3	no	no	DT
37681	17	4	panacea	panacea	NN
37681	17	5	,	,	,
37681	17	6	it	-PRON-	PRP
37681	17	7	champions	champion	VBZ
37681	17	8	no	no	DT
37681	17	9	single	single	JJ
37681	17	10	method	method	NN
37681	17	11	,	,	,
37681	17	12	but	but	CC
37681	17	13	it	-PRON-	PRP
37681	17	14	seeks	seek	VBZ
37681	17	15	to	to	TO
37681	17	16	set	set	VB
37681	17	17	forth	forth	RP
37681	17	18	plainly	plainly	RB
37681	17	19	the	the	DT
37681	17	20	reasons	reason	NNS
37681	17	21	for	for	IN
37681	17	22	teaching	teach	VBG
37681	17	23	a	a	DT
37681	17	24	geometry	geometry	NN
37681	17	25	of	of	IN
37681	17	26	the	the	DT
37681	17	27	kind	kind	NN
37681	17	28	that	that	WDT
37681	17	29	we	-PRON-	PRP
37681	17	30	have	have	VBP
37681	17	31	inherited	inherit	VBN
37681	17	32	,	,	,
37681	17	33	and	and	CC
37681	17	34	for	for	IN
37681	17	35	hoping	hope	VBG
37681	17	36	for	for	IN
37681	17	37	a	a	DT
37681	17	38	gradual	gradual	JJ
37681	17	39	but	but	CC
37681	17	40	definite	definite	JJ
37681	17	41	improvement	improvement	NN
37681	17	42	in	in	IN
37681	17	43	the	the	DT
37681	17	44	science	science	NN
37681	17	45	and	and	CC
37681	17	46	in	in	IN
37681	17	47	the	the	DT
37681	17	48	methods	method	NNS
37681	17	49	of	of	IN
37681	17	50	its	-PRON-	PRP$
37681	17	51	presentation	presentation	NN
37681	17	52	.	.	.
37681	18	1	DAVID	DAVID	NNP
37681	18	2	EUGENE	EUGENE	NNP
37681	18	3	SMITH	SMITH	NNP
37681	18	4	CONTENTS	CONTENTS	NNP
37681	18	5	CHAPTER	chapter	NN
37681	18	6	PAGE	page	NN
37681	18	7	I.	i.	NN
37681	19	1	CERTAIN	certain	JJ
37681	19	2	QUESTIONS	QUESTIONS	NNP
37681	19	3	NOW	now	RB
37681	19	4	AT	at	IN
37681	19	5	ISSUE	ISSUE	NNP
37681	19	6	1	1	CD
37681	19	7	II	ii	CD
37681	19	8	.	.	.
37681	20	1	WHY	why	WRB
37681	20	2	GEOMETRY	GEOMETRY	NNP
37681	20	3	IS	be	VBZ
37681	20	4	STUDIED	STUDIED	NNP
37681	20	5	7	7	CD
37681	20	6	III	iii	CD
37681	20	7	.	.	.
37681	21	1	A	a	DT
37681	21	2	BRIEF	brief	NN
37681	21	3	HISTORY	history	NN
37681	21	4	OF	of	IN
37681	21	5	GEOMETRY	GEOMETRY	NNP
37681	21	6	26	26	CD
37681	21	7	IV	IV	NNP
37681	21	8	.	.	.
37681	22	1	DEVELOPMENT	development	NN
37681	22	2	OF	of	IN
37681	22	3	THE	the	DT
37681	22	4	TEACHING	teaching	NN
37681	22	5	OF	of	IN
37681	22	6	GEOMETRY	GEOMETRY	NNP
37681	22	7	40	40	CD
37681	22	8	V.	v.	NN
37681	22	9	EUCLID	EUCLID	NNP
37681	22	10	47	47	CD
37681	22	11	VI	VI	NNP
37681	22	12	.	.	.
37681	23	1	EFFORTS	EFFORTS	NNP
37681	23	2	AT	at	IN
37681	23	3	IMPROVING	improve	VBG
37681	23	4	EUCLID	EUCLID	NNP
37681	23	5	57	57	CD
37681	23	6	VII	vii	NN
37681	23	7	.	.	.
37681	24	1	THE	the	DT
37681	24	2	TEXTBOOK	TEXTBOOK	NNP
37681	24	3	IN	in	IN
37681	24	4	GEOMETRY	GEOMETRY	NNP
37681	24	5	70	70	CD
37681	24	6	VIII	viii	NN
37681	24	7	.	.	.
37681	25	1	THE	the	DT
37681	25	2	RELATION	relation	NN
37681	25	3	OF	of	IN
37681	25	4	ALGEBRA	ALGEBRA	NNP
37681	25	5	TO	to	IN
37681	25	6	GEOMETRY	GEOMETRY	NNP
37681	25	7	84	84	CD
37681	25	8	IX	ix	NN
37681	25	9	.	.	.
37681	26	1	THE	the	DT
37681	26	2	INTRODUCTION	introduction	NN
37681	26	3	TO	to	IN
37681	26	4	GEOMETRY	GEOMETRY	NNP
37681	26	5	93	93	CD
37681	26	6	X.	x.	NN
37681	27	1	THE	the	DT
37681	27	2	CONDUCT	conduct	NN
37681	27	3	OF	of	IN
37681	27	4	A	a	DT
37681	27	5	CLASS	class	NN
37681	27	6	IN	in	IN
37681	27	7	GEOMETRY	GEOMETRY	NNP
37681	27	8	108	108	CD
37681	27	9	XI	XI	NNP
37681	27	10	.	.	.
37681	28	1	THE	the	DT
37681	28	2	AXIOMS	axiom	NNS
37681	28	3	AND	and	CC
37681	28	4	POSTULATES	postulate	NNS
37681	28	5	116	116	CD
37681	28	6	XII	xii	NN
37681	28	7	.	.	.
37681	29	1	THE	the	DT
37681	29	2	DEFINITIONS	definition	NNS
37681	29	3	OF	of	IN
37681	29	4	GEOMETRY	GEOMETRY	NNP
37681	29	5	132	132	CD
37681	29	6	XIII	xiii	NN
37681	29	7	.	.	.
37681	30	1	HOW	how	WRB
37681	30	2	TO	to	TO
37681	30	3	ATTACK	attack	VB
37681	30	4	THE	the	DT
37681	30	5	EXERCISES	exercise	NNS
37681	30	6	160	160	CD
37681	30	7	XIV	xiv	NN
37681	30	8	.	.	.
37681	31	1	BOOK	book	IN
37681	31	2	I	-PRON-	PRP
37681	31	3	AND	and	CC
37681	31	4	ITS	its	PRP$
37681	31	5	PROPOSITIONS	propositions	NN
37681	31	6	165	165	CD
37681	31	7	XV	XV	NNP
37681	31	8	.	.	.
37681	32	1	THE	the	DT
37681	32	2	LEADING	lead	VBG
37681	32	3	PROPOSITIONS	proposition	NNS
37681	32	4	OF	of	IN
37681	32	5	BOOK	BOOK	NNP
37681	32	6	II	II	NNP
37681	32	7	201	201	CD
37681	32	8	XVI	XVI	NNP
37681	32	9	.	.	.
37681	33	1	THE	the	DT
37681	33	2	LEADING	lead	VBG
37681	33	3	PROPOSITIONS	proposition	NNS
37681	33	4	OF	of	IN
37681	33	5	BOOK	book	NN
37681	33	6	III	iii	CD
37681	33	7	227	227	CD
37681	33	8	XVII	XVII	NNS
37681	33	9	.	.	.
37681	34	1	THE	the	DT
37681	34	2	LEADING	lead	VBG
37681	34	3	PROPOSITIONS	proposition	NNS
37681	34	4	OF	of	IN
37681	34	5	BOOK	BOOK	NNP
37681	34	6	IV	IV	NNP
37681	34	7	252	252	CD
37681	34	8	XVIII	xviii	NN
37681	34	9	.	.	.
37681	35	1	THE	the	DT
37681	35	2	LEADING	lead	VBG
37681	35	3	PROPOSITIONS	proposition	NNS
37681	35	4	OF	of	IN
37681	35	5	BOOK	book	NN
37681	35	6	V	v	NN
37681	35	7	269	269	CD
37681	35	8	XIX	xix	NN
37681	35	9	.	.	.
37681	36	1	THE	the	DT
37681	36	2	LEADING	lead	VBG
37681	36	3	PROPOSITIONS	proposition	NNS
37681	36	4	OF	of	IN
37681	36	5	BOOK	BOOK	NNP
37681	36	6	VI	VI	NNP
37681	36	7	289	289	CD
37681	36	8	XX	XX	NNS
37681	36	9	.	.	.
37681	37	1	THE	the	DT
37681	37	2	LEADING	lead	VBG
37681	37	3	PROPOSITIONS	proposition	NNS
37681	37	4	OF	of	IN
37681	37	5	BOOK	BOOK	NNP
37681	37	6	VII	vii	NN
37681	37	7	303	303	CD
37681	37	8	XXI	XXI	NNP
37681	37	9	.	.	.
37681	38	1	THE	the	DT
37681	38	2	LEADING	lead	VBG
37681	38	3	PROPOSITIONS	proposition	NNS
37681	38	4	OF	of	IN
37681	38	5	BOOK	BOOK	NNS
37681	38	6	VIII	viii	NN
37681	38	7	321	321	CD
37681	38	8	INDEX	index	NN
37681	38	9	335	335	CD
37681	38	10	THE	the	DT
37681	38	11	TEACHING	teaching	NN
37681	38	12	OF	of	IN
37681	38	13	GEOMETRY	GEOMETRY	NNP
37681	38	14	CHAPTER	CHAPTER	NNP
37681	38	15	I	-PRON-	PRP
37681	38	16	CERTAIN	CERTAIN	NNP
37681	38	17	QUESTIONS	QUESTIONS	NNP
37681	38	18	NOW	now	RB
37681	38	19	AT	at	IN
37681	38	20	ISSUE	ISSUE	NNP
37681	38	21	It	-PRON-	PRP
37681	38	22	is	be	VBZ
37681	38	23	commonly	commonly	RB
37681	38	24	said	say	VBN
37681	38	25	at	at	IN
37681	38	26	the	the	DT
37681	38	27	present	present	JJ
37681	38	28	time	time	NN
37681	38	29	that	that	IN
37681	38	30	the	the	DT
37681	38	31	opening	opening	NN
37681	38	32	of	of	IN
37681	38	33	the	the	DT
37681	38	34	twentieth	twentieth	JJ
37681	38	35	century	century	NN
37681	38	36	is	be	VBZ
37681	38	37	a	a	DT
37681	38	38	period	period	NN
37681	38	39	of	of	IN
37681	38	40	unusual	unusual	JJ
37681	38	41	advancement	advancement	NN
37681	38	42	in	in	IN
37681	38	43	all	all	DT
37681	38	44	that	that	WDT
37681	38	45	has	have	VBZ
37681	38	46	to	to	TO
37681	38	47	do	do	VB
37681	38	48	with	with	IN
37681	38	49	the	the	DT
37681	38	50	school	school	NN
37681	38	51	.	.	.
37681	39	1	It	-PRON-	PRP
37681	39	2	would	would	MD
37681	39	3	be	be	VB
37681	39	4	pleasant	pleasant	JJ
37681	39	5	to	to	TO
37681	39	6	feel	feel	VB
37681	39	7	that	that	IN
37681	39	8	we	-PRON-	PRP
37681	39	9	are	be	VBP
37681	39	10	living	live	VBG
37681	39	11	in	in	IN
37681	39	12	such	such	PDT
37681	39	13	an	an	DT
37681	39	14	age	age	NN
37681	39	15	,	,	,
37681	39	16	but	but	CC
37681	39	17	it	-PRON-	PRP
37681	39	18	is	be	VBZ
37681	39	19	doubtful	doubtful	JJ
37681	39	20	if	if	IN
37681	39	21	the	the	DT
37681	39	22	future	future	JJ
37681	39	23	historian	historian	NN
37681	39	24	of	of	IN
37681	39	25	education	education	NN
37681	39	26	will	will	MD
37681	39	27	find	find	VB
37681	39	28	this	this	DT
37681	39	29	to	to	TO
37681	39	30	be	be	VB
37681	39	31	the	the	DT
37681	39	32	case	case	NN
37681	39	33	,	,	,
37681	39	34	or	or	CC
37681	39	35	that	that	IN
37681	39	36	biographers	biographer	NNS
37681	39	37	will	will	MD
37681	39	38	rank	rank	VB
37681	39	39	the	the	DT
37681	39	40	leaders	leader	NNS
37681	39	41	of	of	IN
37681	39	42	our	-PRON-	PRP$
37681	39	43	generation	generation	NN
37681	39	44	relatively	relatively	RB
37681	39	45	as	as	RB
37681	39	46	high	high	JJ
37681	39	47	as	as	IN
37681	39	48	many	many	JJ
37681	39	49	who	who	WP
37681	39	50	have	have	VBP
37681	39	51	passed	pass	VBN
37681	39	52	away	away	RP
37681	39	53	,	,	,
37681	39	54	or	or	CC
37681	39	55	that	that	IN
37681	39	56	any	any	DT
37681	39	57	great	great	JJ
37681	39	58	movements	movement	NNS
37681	39	59	of	of	IN
37681	39	60	the	the	DT
37681	39	61	present	present	NN
37681	39	62	will	will	MD
37681	39	63	be	be	VB
37681	39	64	found	find	VBN
37681	39	65	that	that	DT
37681	39	66	measure	measure	NN
37681	39	67	up	up	RP
37681	39	68	to	to	IN
37681	39	69	certain	certain	JJ
37681	39	70	ones	one	NNS
37681	39	71	that	that	WDT
37681	39	72	the	the	DT
37681	39	73	world	world	NN
37681	39	74	now	now	RB
37681	39	75	recognizes	recognize	VBZ
37681	39	76	as	as	IN
37681	39	77	epoch	epoch	NN
37681	39	78	-	-	HYPH
37681	39	79	making	making	NN
37681	39	80	.	.	.
37681	40	1	Every	every	DT
37681	40	2	generation	generation	NN
37681	40	3	since	since	IN
37681	40	4	the	the	DT
37681	40	5	invention	invention	NN
37681	40	6	of	of	IN
37681	40	7	printing	printing	NN
37681	40	8	has	have	VBZ
37681	40	9	been	be	VBN
37681	40	10	a	a	DT
37681	40	11	period	period	NN
37681	40	12	of	of	IN
37681	40	13	agitation	agitation	NN
37681	40	14	in	in	IN
37681	40	15	educational	educational	JJ
37681	40	16	matters	matter	NNS
37681	40	17	,	,	,
37681	40	18	but	but	CC
37681	40	19	out	out	IN
37681	40	20	of	of	IN
37681	40	21	all	all	PDT
37681	40	22	the	the	DT
37681	40	23	noise	noise	NN
37681	40	24	and	and	CC
37681	40	25	self	self	NN
37681	40	26	-	-	HYPH
37681	40	27	assertion	assertion	NN
37681	40	28	,	,	,
37681	40	29	out	out	IN
37681	40	30	of	of	IN
37681	40	31	all	all	PDT
37681	40	32	the	the	DT
37681	40	33	pretense	pretense	NN
37681	40	34	of	of	IN
37681	40	35	the	the	DT
37681	40	36	chronic	chronic	JJ
37681	40	37	revolutionist	revolutionist	NN
37681	40	38	,	,	,
37681	40	39	out	out	IN
37681	40	40	of	of	IN
37681	40	41	all	all	PDT
37681	40	42	the	the	DT
37681	40	43	sham	sham	NN
37681	40	44	that	that	WDT
37681	40	45	leads	lead	VBZ
37681	40	46	to	to	IN
37681	40	47	dogmatism	dogmatism	NN
37681	40	48	,	,	,
37681	40	49	so	so	RB
37681	40	50	little	little	JJ
37681	40	51	is	be	VBZ
37681	40	52	remembered	remember	VBN
37681	40	53	that	that	IN
37681	40	54	we	-PRON-	PRP
37681	40	55	are	be	VBP
37681	40	56	apt	apt	JJ
37681	40	57	to	to	TO
37681	40	58	feel	feel	VB
37681	40	59	that	that	IN
37681	40	60	the	the	DT
37681	40	61	past	past	NN
37681	40	62	had	have	VBD
37681	40	63	no	no	DT
37681	40	64	problems	problem	NNS
37681	40	65	and	and	CC
37681	40	66	was	be	VBD
37681	40	67	content	content	NN
37681	40	68	simply	simply	RB
37681	40	69	to	to	TO
37681	40	70	accept	accept	VB
37681	40	71	its	-PRON-	PRP$
37681	40	72	inheritance	inheritance	NN
37681	40	73	.	.	.
37681	41	1	In	in	IN
37681	41	2	one	one	CD
37681	41	3	sense	sense	NN
37681	41	4	it	-PRON-	PRP
37681	41	5	is	be	VBZ
37681	41	6	not	not	RB
37681	41	7	a	a	DT
37681	41	8	misfortune	misfortune	NN
37681	41	9	thus	thus	RB
37681	41	10	to	to	TO
37681	41	11	be	be	VB
37681	41	12	blinded	blind	VBN
37681	41	13	by	by	IN
37681	41	14	the	the	DT
37681	41	15	dust	dust	NN
37681	41	16	of	of	IN
37681	41	17	present	present	JJ
37681	41	18	agitation	agitation	NN
37681	41	19	and	and	CC
37681	41	20	to	to	TO
37681	41	21	be	be	VB
37681	41	22	deafened	deafen	VBN
37681	41	23	by	by	IN
37681	41	24	the	the	DT
37681	41	25	noisy	noisy	JJ
37681	41	26	clamor	clamor	NN
37681	41	27	of	of	IN
37681	41	28	the	the	DT
37681	41	29	agitator	agitator	NN
37681	41	30	,	,	,
37681	41	31	since	since	IN
37681	41	32	it	-PRON-	PRP
37681	41	33	stirs	stir	VBZ
37681	41	34	us	-PRON-	PRP
37681	41	35	to	to	IN
37681	41	36	action	action	NN
37681	41	37	at	at	IN
37681	41	38	finding	find	VBG
37681	41	39	ourselves	-PRON-	PRP
37681	41	40	in	in	IN
37681	41	41	the	the	DT
37681	41	42	midst	midst	NN
37681	41	43	of	of	IN
37681	41	44	the	the	DT
37681	41	45	skirmish	skirmish	NN
37681	41	46	;	;	:
37681	41	47	but	but	CC
37681	41	48	in	in	IN
37681	41	49	another	another	DT
37681	41	50	sense	sense	NN
37681	41	51	it	-PRON-	PRP
37681	41	52	is	be	VBZ
37681	41	53	detrimental	detrimental	JJ
37681	41	54	to	to	IN
37681	41	55	our	-PRON-	PRP$
37681	41	56	progress	progress	NN
37681	41	57	,	,	,
37681	41	58	since	since	IN
37681	41	59	we	-PRON-	PRP
37681	41	60	thereby	thereby	RB
37681	41	61	tend	tend	VBP
37681	41	62	to	to	TO
37681	41	63	lose	lose	VB
37681	41	64	the	the	DT
37681	41	65	idea	idea	NN
37681	41	66	of	of	IN
37681	41	67	perspective	perspective	NN
37681	41	68	,	,	,
37681	41	69	and	and	CC
37681	41	70	the	the	DT
37681	41	71	coin	coin	NN
37681	41	72	comes	come	VBZ
37681	41	73	to	to	TO
37681	41	74	appear	appear	VB
37681	41	75	to	to	IN
37681	41	76	our	-PRON-	PRP$
37681	41	77	vision	vision	NN
37681	41	78	as	as	RB
37681	41	79	large	large	JJ
37681	41	80	as	as	IN
37681	41	81	the	the	DT
37681	41	82	moon	moon	NN
37681	41	83	.	.	.
37681	42	1	In	in	IN
37681	42	2	considering	consider	VBG
37681	42	3	a	a	DT
37681	42	4	question	question	NN
37681	42	5	like	like	IN
37681	42	6	the	the	DT
37681	42	7	teaching	teaching	NN
37681	42	8	of	of	IN
37681	42	9	geometry	geometry	NN
37681	42	10	,	,	,
37681	42	11	we	-PRON-	PRP
37681	42	12	at	at	IN
37681	42	13	once	once	RB
37681	42	14	find	find	VBP
37681	42	15	ourselves	-PRON-	PRP
37681	42	16	in	in	IN
37681	42	17	the	the	DT
37681	42	18	midst	midst	NN
37681	42	19	of	of	IN
37681	42	20	a	a	DT
37681	42	21	skirmish	skirmish	NN
37681	42	22	of	of	IN
37681	42	23	this	this	DT
37681	42	24	nature	nature	NN
37681	42	25	.	.	.
37681	43	1	If	if	IN
37681	43	2	we	-PRON-	PRP
37681	43	3	join	join	VBP
37681	43	4	thoughtlessly	thoughtlessly	RB
37681	43	5	in	in	IN
37681	43	6	the	the	DT
37681	43	7	noise	noise	NN
37681	43	8	,	,	,
37681	43	9	we	-PRON-	PRP
37681	43	10	may	may	MD
37681	43	11	easily	easily	RB
37681	43	12	persuade	persuade	VB
37681	43	13	ourselves	-PRON-	PRP
37681	43	14	that	that	IN
37681	43	15	we	-PRON-	PRP
37681	43	16	are	be	VBP
37681	43	17	waging	wage	VBG
37681	43	18	a	a	DT
37681	43	19	mighty	mighty	JJ
37681	43	20	battle	battle	NN
37681	43	21	,	,	,
37681	43	22	fighting	fight	VBG
37681	43	23	for	for	IN
37681	43	24	some	some	DT
37681	43	25	stupendous	stupendous	JJ
37681	43	26	principle	principle	NN
37681	43	27	,	,	,
37681	43	28	doing	do	VBG
37681	43	29	deeds	deed	NNS
37681	43	30	of	of	IN
37681	43	31	great	great	JJ
37681	43	32	valor	valor	NN
37681	43	33	and	and	CC
37681	43	34	of	of	IN
37681	43	35	personal	personal	JJ
37681	43	36	sacrifice	sacrifice	NN
37681	43	37	.	.	.
37681	44	1	If	if	IN
37681	44	2	,	,	,
37681	44	3	on	on	IN
37681	44	4	the	the	DT
37681	44	5	other	other	JJ
37681	44	6	hand	hand	NN
37681	44	7	,	,	,
37681	44	8	we	-PRON-	PRP
37681	44	9	stand	stand	VBP
37681	44	10	aloof	aloof	NN
37681	44	11	and	and	CC
37681	44	12	think	think	VB
37681	44	13	of	of	IN
37681	44	14	the	the	DT
37681	44	15	present	present	JJ
37681	44	16	movement	movement	NN
37681	44	17	as	as	IN
37681	44	18	merely	merely	RB
37681	44	19	a	a	DT
37681	44	20	chronic	chronic	JJ
37681	44	21	effervescence	effervescence	NN
37681	44	22	,	,	,
37681	44	23	fostered	foster	VBN
37681	44	24	by	by	IN
37681	44	25	the	the	DT
37681	44	26	professional	professional	JJ
37681	44	27	educator	educator	NN
37681	44	28	at	at	IN
37681	44	29	the	the	DT
37681	44	30	expense	expense	NN
37681	44	31	of	of	IN
37681	44	32	the	the	DT
37681	44	33	practical	practical	JJ
37681	44	34	teacher	teacher	NN
37681	44	35	,	,	,
37681	44	36	we	-PRON-	PRP
37681	44	37	are	be	VBP
37681	44	38	equally	equally	RB
37681	44	39	shortsighted	shortsighted	JJ
37681	44	40	.	.	.
37681	45	1	Sir	Sir	NNP
37681	45	2	Conan	Conan	NNP
37681	45	3	Doyle	Doyle	NNP
37681	45	4	expressed	express	VBD
37681	45	5	this	this	DT
37681	45	6	sentiment	sentiment	NN
37681	45	7	most	most	RBS
37681	45	8	delightfully	delightfully	RB
37681	45	9	in	in	IN
37681	45	10	these	these	DT
37681	45	11	words	word	NNS
37681	45	12	:	:	:
37681	45	13	The	the	DT
37681	45	14	dead	dead	NNS
37681	45	15	are	be	VBP
37681	45	16	such	such	JJ
37681	45	17	good	good	JJ
37681	45	18	company	company	NN
37681	45	19	that	that	IN
37681	45	20	one	one	PRP
37681	45	21	may	may	MD
37681	45	22	come	come	VB
37681	45	23	to	to	TO
37681	45	24	think	think	VB
37681	45	25	too	too	RB
37681	45	26	little	little	JJ
37681	45	27	of	of	IN
37681	45	28	the	the	DT
37681	45	29	living	living	NN
37681	45	30	.	.	.
37681	46	1	It	-PRON-	PRP
37681	46	2	is	be	VBZ
37681	46	3	a	a	DT
37681	46	4	real	real	JJ
37681	46	5	and	and	CC
37681	46	6	pressing	press	VBG
37681	46	7	danger	danger	NN
37681	46	8	with	with	IN
37681	46	9	many	many	JJ
37681	46	10	of	of	IN
37681	46	11	us	-PRON-	PRP
37681	46	12	that	that	IN
37681	46	13	we	-PRON-	PRP
37681	46	14	should	should	MD
37681	46	15	never	never	RB
37681	46	16	find	find	VB
37681	46	17	our	-PRON-	PRP$
37681	46	18	own	own	JJ
37681	46	19	thoughts	thought	NNS
37681	46	20	and	and	CC
37681	46	21	our	-PRON-	PRP$
37681	46	22	own	own	JJ
37681	46	23	souls	soul	NNS
37681	46	24	,	,	,
37681	46	25	but	but	CC
37681	46	26	be	be	VB
37681	46	27	ever	ever	RB
37681	46	28	obsessed	obsess	VBN
37681	46	29	by	by	IN
37681	46	30	the	the	DT
37681	46	31	dead	dead	NN
37681	46	32	.	.	.
37681	47	1	In	in	IN
37681	47	2	every	every	DT
37681	47	3	generation	generation	NN
37681	47	4	it	-PRON-	PRP
37681	47	5	behooves	behoove	VBZ
37681	47	6	the	the	DT
37681	47	7	open	open	JJ
37681	47	8	-	-	HYPH
37681	47	9	minded	minded	JJ
37681	47	10	,	,	,
37681	47	11	earnest	earnest	JJ
37681	47	12	,	,	,
37681	47	13	progressive	progressive	JJ
37681	47	14	teacher	teacher	NN
37681	47	15	to	to	TO
37681	47	16	seek	seek	VB
37681	47	17	for	for	IN
37681	47	18	the	the	DT
37681	47	19	best	good	JJS
37681	47	20	in	in	IN
37681	47	21	the	the	DT
37681	47	22	way	way	NN
37681	47	23	of	of	IN
37681	47	24	improvement	improvement	NN
37681	47	25	,	,	,
37681	47	26	to	to	TO
37681	47	27	endeavor	endeavor	VB
37681	47	28	to	to	TO
37681	47	29	sift	sift	VB
37681	47	30	the	the	DT
37681	47	31	few	few	JJ
37681	47	32	grains	grain	NNS
37681	47	33	of	of	IN
37681	47	34	gold	gold	NN
37681	47	35	out	out	IN
37681	47	36	of	of	IN
37681	47	37	the	the	DT
37681	47	38	common	common	JJ
37681	47	39	dust	dust	NN
37681	47	40	,	,	,
37681	47	41	to	to	TO
37681	47	42	weigh	weigh	VB
37681	47	43	the	the	DT
37681	47	44	values	value	NNS
37681	47	45	of	of	IN
37681	47	46	proposed	propose	VBN
37681	47	47	reforms	reform	NNS
37681	47	48	,	,	,
37681	47	49	and	and	CC
37681	47	50	to	to	TO
37681	47	51	put	put	VB
37681	47	52	forth	forth	RP
37681	47	53	his	-PRON-	PRP$
37681	47	54	efforts	effort	NNS
37681	47	55	to	to	TO
37681	47	56	know	know	VB
37681	47	57	and	and	CC
37681	47	58	to	to	TO
37681	47	59	use	use	VB
37681	47	60	the	the	DT
37681	47	61	best	good	JJS
37681	47	62	that	that	IN
37681	47	63	the	the	DT
37681	47	64	science	science	NN
37681	47	65	of	of	IN
37681	47	66	education	education	NN
37681	47	67	has	have	VBZ
37681	47	68	to	to	TO
37681	47	69	offer	offer	VB
37681	47	70	.	.	.
37681	48	1	This	this	DT
37681	48	2	has	have	VBZ
37681	48	3	been	be	VBN
37681	48	4	the	the	DT
37681	48	5	attitude	attitude	NN
37681	48	6	of	of	IN
37681	48	7	mind	mind	NN
37681	48	8	of	of	IN
37681	48	9	the	the	DT
37681	48	10	real	real	JJ
37681	48	11	leaders	leader	NNS
37681	48	12	in	in	IN
37681	48	13	the	the	DT
37681	48	14	school	school	NN
37681	48	15	life	life	NN
37681	48	16	of	of	IN
37681	48	17	the	the	DT
37681	48	18	past	past	NN
37681	48	19	,	,	,
37681	48	20	and	and	CC
37681	48	21	it	-PRON-	PRP
37681	48	22	will	will	MD
37681	48	23	be	be	VB
37681	48	24	that	that	DT
37681	48	25	of	of	IN
37681	48	26	the	the	DT
37681	48	27	leaders	leader	NNS
37681	48	28	of	of	IN
37681	48	29	the	the	DT
37681	48	30	future	future	NN
37681	48	31	.	.	.
37681	49	1	With	with	IN
37681	49	2	these	these	DT
37681	49	3	remarks	remark	NNS
37681	49	4	to	to	TO
37681	49	5	guide	guide	VB
37681	49	6	us	-PRON-	PRP
37681	49	7	,	,	,
37681	49	8	it	-PRON-	PRP
37681	49	9	is	be	VBZ
37681	49	10	now	now	RB
37681	49	11	proposed	propose	VBN
37681	49	12	to	to	TO
37681	49	13	take	take	VB
37681	49	14	up	up	RP
37681	49	15	the	the	DT
37681	49	16	issues	issue	NNS
37681	49	17	of	of	IN
37681	49	18	the	the	DT
37681	49	19	present	present	JJ
37681	49	20	day	day	NN
37681	49	21	in	in	IN
37681	49	22	the	the	DT
37681	49	23	teaching	teaching	NN
37681	49	24	of	of	IN
37681	49	25	geometry	geometry	NN
37681	49	26	,	,	,
37681	49	27	in	in	IN
37681	49	28	order	order	NN
37681	49	29	that	that	IN
37681	49	30	we	-PRON-	PRP
37681	49	31	may	may	MD
37681	49	32	consider	consider	VB
37681	49	33	them	-PRON-	PRP
37681	49	34	calmly	calmly	RB
37681	49	35	and	and	CC
37681	49	36	dispassionately	dispassionately	RB
37681	49	37	,	,	,
37681	49	38	and	and	CC
37681	49	39	may	may	MD
37681	49	40	see	see	VB
37681	49	41	where	where	WRB
37681	49	42	the	the	DT
37681	49	43	opportunities	opportunity	NNS
37681	49	44	for	for	IN
37681	49	45	improvement	improvement	NN
37681	49	46	lie	lie	NN
37681	49	47	.	.	.
37681	50	1	At	at	IN
37681	50	2	the	the	DT
37681	50	3	present	present	JJ
37681	50	4	time	time	NN
37681	50	5	,	,	,
37681	50	6	in	in	IN
37681	50	7	the	the	DT
37681	50	8	educational	educational	JJ
37681	50	9	circles	circle	NNS
37681	50	10	of	of	IN
37681	50	11	the	the	DT
37681	50	12	United	United	NNP
37681	50	13	States	States	NNP
37681	50	14	,	,	,
37681	50	15	questions	question	NNS
37681	50	16	of	of	IN
37681	50	17	the	the	DT
37681	50	18	following	following	JJ
37681	50	19	type	type	NN
37681	50	20	are	be	VBP
37681	50	21	causing	cause	VBG
37681	50	22	the	the	DT
37681	50	23	chief	chief	JJ
37681	50	24	discussion	discussion	NN
37681	50	25	among	among	IN
37681	50	26	teachers	teacher	NNS
37681	50	27	of	of	IN
37681	50	28	geometry	geometry	NN
37681	50	29	:	:	:
37681	50	30	1	1	CD
37681	50	31	.	.	.
37681	51	1	Shall	Shall	MD
37681	51	2	geometry	geometry	NN
37681	51	3	continue	continue	VB
37681	51	4	to	to	TO
37681	51	5	be	be	VB
37681	51	6	taught	teach	VBN
37681	51	7	as	as	IN
37681	51	8	an	an	DT
37681	51	9	application	application	NN
37681	51	10	of	of	IN
37681	51	11	logic	logic	NN
37681	51	12	,	,	,
37681	51	13	or	or	CC
37681	51	14	shall	shall	MD
37681	51	15	it	-PRON-	PRP
37681	51	16	be	be	VB
37681	51	17	treated	treat	VBN
37681	51	18	solely	solely	RB
37681	51	19	with	with	IN
37681	51	20	reference	reference	NN
37681	51	21	to	to	IN
37681	51	22	its	-PRON-	PRP$
37681	51	23	applications	application	NNS
37681	51	24	?	?	.
37681	52	1	2	2	LS
37681	52	2	.	.	.
37681	53	1	If	if	IN
37681	53	2	the	the	DT
37681	53	3	latter	latter	NN
37681	53	4	is	be	VBZ
37681	53	5	the	the	DT
37681	53	6	purpose	purpose	NN
37681	53	7	in	in	IN
37681	53	8	view	view	NN
37681	53	9	,	,	,
37681	53	10	shall	shall	MD
37681	53	11	the	the	DT
37681	53	12	propositions	proposition	NNS
37681	53	13	of	of	IN
37681	53	14	geometry	geometry	NN
37681	53	15	be	be	VB
37681	53	16	limited	limit	VBN
37681	53	17	to	to	IN
37681	53	18	those	those	DT
37681	53	19	that	that	WDT
37681	53	20	offer	offer	VBP
37681	53	21	an	an	DT
37681	53	22	opportunity	opportunity	NN
37681	53	23	for	for	IN
37681	53	24	real	real	JJ
37681	53	25	application	application	NN
37681	53	26	,	,	,
37681	53	27	thus	thus	RB
37681	53	28	contracting	contract	VBG
37681	53	29	the	the	DT
37681	53	30	whole	whole	JJ
37681	53	31	subject	subject	NN
37681	53	32	to	to	IN
37681	53	33	very	very	RB
37681	53	34	narrow	narrow	JJ
37681	53	35	dimensions	dimension	NNS
37681	53	36	?	?	.
37681	54	1	3	3	LS
37681	54	2	.	.	.
37681	55	1	Shall	Shall	MD
37681	55	2	a	a	DT
37681	55	3	subject	subject	NN
37681	55	4	called	call	VBN
37681	55	5	geometry	geometry	NN
37681	55	6	be	be	VB
37681	55	7	extended	extend	VBN
37681	55	8	over	over	IN
37681	55	9	several	several	JJ
37681	55	10	years	year	NNS
37681	55	11	,	,	,
37681	55	12	as	as	IN
37681	55	13	is	be	VBZ
37681	55	14	the	the	DT
37681	55	15	case	case	NN
37681	55	16	in	in	IN
37681	55	17	Europe,[1	Europe,[1	NNP
37681	55	18	]	]	-RRB-
37681	55	19	or	or	CC
37681	55	20	shall	shall	MD
37681	55	21	the	the	DT
37681	55	22	name	name	NN
37681	55	23	be	be	VB
37681	55	24	applied	apply	VBN
37681	55	25	only	only	RB
37681	55	26	to	to	IN
37681	55	27	serious	serious	JJ
37681	55	28	demonstrative	demonstrative	JJ
37681	55	29	geometry[2	geometry[2	''
37681	55	30	]	]	-RRB-
37681	55	31	as	as	IN
37681	55	32	given	give	VBN
37681	55	33	in	in	IN
37681	55	34	the	the	DT
37681	55	35	second	second	JJ
37681	55	36	year	year	NN
37681	55	37	of	of	IN
37681	55	38	the	the	DT
37681	55	39	four	four	CD
37681	55	40	-	-	HYPH
37681	55	41	year	year	NN
37681	55	42	high	high	JJ
37681	55	43	school	school	NN
37681	55	44	course	course	NN
37681	55	45	in	in	IN
37681	55	46	the	the	DT
37681	55	47	United	United	NNP
37681	55	48	States	States	NNP
37681	55	49	at	at	IN
37681	55	50	present	present	NN
37681	55	51	?	?	.
37681	56	1	4	4	LS
37681	56	2	.	.	.
37681	57	1	Shall	Shall	MD
37681	57	2	geometry	geometry	NN
37681	57	3	be	be	VB
37681	57	4	taught	teach	VBN
37681	57	5	by	by	IN
37681	57	6	itself	-PRON-	PRP
37681	57	7	,	,	,
37681	57	8	or	or	CC
37681	57	9	shall	shall	MD
37681	57	10	it	-PRON-	PRP
37681	57	11	be	be	VB
37681	57	12	either	either	CC
37681	57	13	mixed	mix	VBN
37681	57	14	with	with	IN
37681	57	15	algebra	algebra	NN
37681	57	16	(	(	-LRB-
37681	57	17	say	say	VB
37681	57	18	a	a	DT
37681	57	19	day	day	NN
37681	57	20	of	of	IN
37681	57	21	one	one	CD
37681	57	22	subject	subject	NN
37681	57	23	followed	follow	VBN
37681	57	24	by	by	IN
37681	57	25	a	a	DT
37681	57	26	day	day	NN
37681	57	27	of	of	IN
37681	57	28	the	the	DT
37681	57	29	other	other	JJ
37681	57	30	)	)	-RRB-
37681	57	31	or	or	CC
37681	57	32	fused	fuse	VBN
37681	57	33	with	with	IN
37681	57	34	it	-PRON-	PRP
37681	57	35	in	in	IN
37681	57	36	the	the	DT
37681	57	37	form	form	NN
37681	57	38	of	of	IN
37681	57	39	a	a	DT
37681	57	40	combined	combine	VBN
37681	57	41	mathematics	mathematic	NNS
37681	57	42	?	?	.
37681	58	1	5	5	CD
37681	58	2	.	.	.
37681	59	1	Shall	Shall	MD
37681	59	2	a	a	DT
37681	59	3	textbook	textbook	NN
37681	59	4	be	be	VB
37681	59	5	used	use	VBN
37681	59	6	in	in	IN
37681	59	7	which	which	WDT
37681	59	8	the	the	DT
37681	59	9	basal	basal	NN
37681	59	10	propositions	proposition	NNS
37681	59	11	are	be	VBP
37681	59	12	proved	prove	VBN
37681	59	13	in	in	IN
37681	59	14	full	full	JJ
37681	59	15	,	,	,
37681	59	16	the	the	DT
37681	59	17	exercises	exercise	NNS
37681	59	18	furnishing	furnish	VBG
37681	59	19	the	the	DT
37681	59	20	opportunity	opportunity	NN
37681	59	21	for	for	IN
37681	59	22	original	original	JJ
37681	59	23	work	work	NN
37681	59	24	and	and	CC
37681	59	25	being	be	VBG
37681	59	26	looked	look	VBN
37681	59	27	upon	upon	IN
37681	59	28	as	as	IN
37681	59	29	the	the	DT
37681	59	30	most	most	RBS
37681	59	31	important	important	JJ
37681	59	32	feature	feature	NN
37681	59	33	,	,	,
37681	59	34	or	or	CC
37681	59	35	shall	shall	MD
37681	59	36	one	one	PRP
37681	59	37	be	be	VB
37681	59	38	employed	employ	VBN
37681	59	39	in	in	IN
37681	59	40	which	which	WDT
37681	59	41	the	the	DT
37681	59	42	pupil	pupil	NN
37681	59	43	is	be	VBZ
37681	59	44	expected	expect	VBN
37681	59	45	to	to	TO
37681	59	46	invent	invent	VB
37681	59	47	the	the	DT
37681	59	48	proofs	proof	NNS
37681	59	49	for	for	IN
37681	59	50	the	the	DT
37681	59	51	basal	basal	NN
37681	59	52	propositions	proposition	NNS
37681	59	53	as	as	RB
37681	59	54	well	well	RB
37681	59	55	as	as	IN
37681	59	56	for	for	IN
37681	59	57	the	the	DT
37681	59	58	exercises	exercise	NNS
37681	59	59	?	?	.
37681	60	1	6	6	CD
37681	60	2	.	.	.
37681	61	1	Shall	Shall	MD
37681	61	2	the	the	DT
37681	61	3	terminology	terminology	NN
37681	61	4	and	and	CC
37681	61	5	the	the	DT
37681	61	6	spirit	spirit	NN
37681	61	7	of	of	IN
37681	61	8	a	a	DT
37681	61	9	modified	modify	VBN
37681	61	10	Euclid	Euclid	NNP
37681	61	11	and	and	CC
37681	61	12	Legendre	Legendre	NNP
37681	61	13	prevail	prevail	VB
37681	61	14	in	in	IN
37681	61	15	the	the	DT
37681	61	16	future	future	NN
37681	61	17	as	as	IN
37681	61	18	they	-PRON-	PRP
37681	61	19	have	have	VBP
37681	61	20	in	in	IN
37681	61	21	the	the	DT
37681	61	22	past	past	NN
37681	61	23	,	,	,
37681	61	24	or	or	CC
37681	61	25	shall	shall	MD
37681	61	26	there	there	EX
37681	61	27	be	be	VB
37681	61	28	a	a	DT
37681	61	29	revolution	revolution	NN
37681	61	30	in	in	IN
37681	61	31	the	the	DT
37681	61	32	use	use	NN
37681	61	33	of	of	IN
37681	61	34	terms	term	NNS
37681	61	35	and	and	CC
37681	61	36	in	in	IN
37681	61	37	the	the	DT
37681	61	38	general	general	JJ
37681	61	39	statements	statement	NNS
37681	61	40	of	of	IN
37681	61	41	the	the	DT
37681	61	42	propositions	proposition	NNS
37681	61	43	?	?	.
37681	62	1	7	7	LS
37681	62	2	.	.	.
37681	63	1	Shall	Shall	MD
37681	63	2	geometry	geometry	NN
37681	63	3	be	be	VB
37681	63	4	made	make	VBN
37681	63	5	a	a	DT
37681	63	6	strong	strong	JJ
37681	63	7	elective	elective	JJ
37681	63	8	subject	subject	NN
37681	63	9	,	,	,
37681	63	10	to	to	TO
37681	63	11	be	be	VB
37681	63	12	taken	take	VBN
37681	63	13	only	only	RB
37681	63	14	by	by	IN
37681	63	15	those	those	DT
37681	63	16	whose	whose	WP$
37681	63	17	minds	mind	NNS
37681	63	18	are	be	VBP
37681	63	19	capable	capable	JJ
37681	63	20	of	of	IN
37681	63	21	serious	serious	JJ
37681	63	22	work	work	NN
37681	63	23	?	?	.
37681	64	1	Shall	Shall	MD
37681	64	2	it	-PRON-	PRP
37681	64	3	be	be	VB
37681	64	4	a	a	DT
37681	64	5	required	require	VBN
37681	64	6	subject	subject	NN
37681	64	7	,	,	,
37681	64	8	diluted	dilute	VBN
37681	64	9	to	to	IN
37681	64	10	the	the	DT
37681	64	11	comprehension	comprehension	NN
37681	64	12	of	of	IN
37681	64	13	the	the	DT
37681	64	14	weakest	weak	JJS
37681	64	15	minds	mind	NNS
37681	64	16	?	?	.
37681	65	1	Or	or	CC
37681	65	2	is	be	VBZ
37681	65	3	it	-PRON-	PRP
37681	65	4	now	now	RB
37681	65	5	,	,	,
37681	65	6	by	by	IN
37681	65	7	proper	proper	JJ
37681	65	8	teaching	teaching	NN
37681	65	9	,	,	,
37681	65	10	as	as	IN
37681	65	11	suitable	suitable	JJ
37681	65	12	for	for	IN
37681	65	13	all	all	DT
37681	65	14	pupils	pupil	NNS
37681	65	15	as	as	IN
37681	65	16	is	be	VBZ
37681	65	17	any	any	DT
37681	65	18	other	other	JJ
37681	65	19	required	require	VBN
37681	65	20	subject	subject	NN
37681	65	21	in	in	IN
37681	65	22	the	the	DT
37681	65	23	school	school	NN
37681	65	24	curriculum	curriculum	NN
37681	65	25	?	?	.
37681	66	1	And	and	CC
37681	66	2	in	in	IN
37681	66	3	any	any	DT
37681	66	4	case	case	NN
37681	66	5	,	,	,
37681	66	6	will	will	MD
37681	66	7	the	the	DT
37681	66	8	various	various	JJ
37681	66	9	distinct	distinct	JJ
37681	66	10	types	type	NNS
37681	66	11	of	of	IN
37681	66	12	high	high	JJ
37681	66	13	schools	school	NNS
37681	66	14	now	now	RB
37681	66	15	arising	arise	VBG
37681	66	16	call	call	NN
37681	66	17	for	for	IN
37681	66	18	distinct	distinct	JJ
37681	66	19	types	type	NNS
37681	66	20	of	of	IN
37681	66	21	geometry	geometry	NN
37681	66	22	?	?	.
37681	67	1	This	this	DT
37681	67	2	brief	brief	JJ
37681	67	3	list	list	NN
37681	67	4	might	may	MD
37681	67	5	easily	easily	RB
37681	67	6	be	be	VB
37681	67	7	amplified	amplify	VBN
37681	67	8	,	,	,
37681	67	9	but	but	CC
37681	67	10	it	-PRON-	PRP
37681	67	11	is	be	VBZ
37681	67	12	sufficiently	sufficiently	RB
37681	67	13	extended	extend	VBN
37681	67	14	to	to	TO
37681	67	15	set	set	VB
37681	67	16	forth	forth	RP
37681	67	17	the	the	DT
37681	67	18	trend	trend	NN
37681	67	19	of	of	IN
37681	67	20	thought	thought	NN
37681	67	21	at	at	IN
37681	67	22	the	the	DT
37681	67	23	present	present	JJ
37681	67	24	time	time	NN
37681	67	25	,	,	,
37681	67	26	and	and	CC
37681	67	27	to	to	TO
37681	67	28	show	show	VB
37681	67	29	that	that	IN
37681	67	30	the	the	DT
37681	67	31	questions	question	NNS
37681	67	32	before	before	IN
37681	67	33	the	the	DT
37681	67	34	teachers	teacher	NNS
37681	67	35	of	of	IN
37681	67	36	geometry	geometry	NN
37681	67	37	are	be	VBP
37681	67	38	neither	neither	RB
37681	67	39	particularly	particularly	RB
37681	67	40	novel	novel	JJ
37681	67	41	nor	nor	CC
37681	67	42	particularly	particularly	RB
37681	67	43	serious	serious	JJ
37681	67	44	.	.	.
37681	68	1	These	these	DT
37681	68	2	questions	question	NNS
37681	68	3	and	and	CC
37681	68	4	others	other	NNS
37681	68	5	of	of	IN
37681	68	6	similar	similar	JJ
37681	68	7	nature	nature	NN
37681	68	8	are	be	VBP
37681	68	9	really	really	RB
37681	68	10	side	side	JJ
37681	68	11	issues	issue	NNS
37681	68	12	of	of	IN
37681	68	13	two	two	CD
37681	68	14	larger	large	JJR
37681	68	15	questions	question	NNS
37681	68	16	of	of	IN
37681	68	17	far	far	RB
37681	68	18	greater	great	JJR
37681	68	19	significance	significance	NN
37681	68	20	:	:	:
37681	68	21	(	(	-LRB-
37681	68	22	1	1	LS
37681	68	23	)	)	-RRB-
37681	68	24	Are	be	VBP
37681	68	25	the	the	DT
37681	68	26	reasons	reason	NNS
37681	68	27	for	for	IN
37681	68	28	teaching	teach	VBG
37681	68	29	demonstrative	demonstrative	JJ
37681	68	30	geometry	geometry	NN
37681	68	31	such	such	JJ
37681	68	32	that	that	IN
37681	68	33	it	-PRON-	PRP
37681	68	34	should	should	MD
37681	68	35	be	be	VB
37681	68	36	a	a	DT
37681	68	37	required	require	VBN
37681	68	38	subject	subject	NN
37681	68	39	,	,	,
37681	68	40	or	or	CC
37681	68	41	at	at	IN
37681	68	42	least	least	JJS
37681	68	43	a	a	DT
37681	68	44	subject	subject	NN
37681	68	45	that	that	WDT
37681	68	46	is	be	VBZ
37681	68	47	strongly	strongly	RB
37681	68	48	recommended	recommend	VBN
37681	68	49	to	to	IN
37681	68	50	all	all	DT
37681	68	51	,	,	,
37681	68	52	whatever	whatever	WDT
37681	68	53	the	the	DT
37681	68	54	type	type	NN
37681	68	55	of	of	IN
37681	68	56	high	high	JJ
37681	68	57	school	school	NN
37681	68	58	?	?	.
37681	69	1	(	(	-LRB-
37681	69	2	2	2	LS
37681	69	3	)	)	-RRB-
37681	69	4	If	if	IN
37681	69	5	so	so	RB
37681	69	6	,	,	,
37681	69	7	how	how	WRB
37681	69	8	can	can	MD
37681	69	9	it	-PRON-	PRP
37681	69	10	be	be	VB
37681	69	11	made	make	VBN
37681	69	12	interesting	interesting	JJ
37681	69	13	?	?	.
37681	70	1	The	the	DT
37681	70	2	present	present	JJ
37681	70	3	work	work	NN
37681	70	4	is	be	VBZ
37681	70	5	written	write	VBN
37681	70	6	with	with	IN
37681	70	7	these	these	DT
37681	70	8	two	two	CD
37681	70	9	larger	large	JJR
37681	70	10	questions	question	NNS
37681	70	11	in	in	IN
37681	70	12	mind	mind	NN
37681	70	13	,	,	,
37681	70	14	although	although	IN
37681	70	15	it	-PRON-	PRP
37681	70	16	considers	consider	VBZ
37681	70	17	from	from	IN
37681	70	18	time	time	NN
37681	70	19	to	to	IN
37681	70	20	time	time	NN
37681	70	21	the	the	DT
37681	70	22	minor	minor	JJ
37681	70	23	ones	one	NNS
37681	70	24	already	already	RB
37681	70	25	mentioned	mention	VBN
37681	70	26	,	,	,
37681	70	27	together	together	RB
37681	70	28	with	with	IN
37681	70	29	others	other	NNS
37681	70	30	of	of	IN
37681	70	31	a	a	DT
37681	70	32	similar	similar	JJ
37681	70	33	nature	nature	NN
37681	70	34	.	.	.
37681	71	1	It	-PRON-	PRP
37681	71	2	recognizes	recognize	VBZ
37681	71	3	that	that	IN
37681	71	4	the	the	DT
37681	71	5	recent	recent	JJ
37681	71	6	growth	growth	NN
37681	71	7	in	in	IN
37681	71	8	popular	popular	JJ
37681	71	9	education	education	NN
37681	71	10	has	have	VBZ
37681	71	11	brought	bring	VBN
37681	71	12	into	into	IN
37681	71	13	the	the	DT
37681	71	14	high	high	JJ
37681	71	15	school	school	NN
37681	71	16	a	a	DT
37681	71	17	less	less	RBR
37681	71	18	carefully	carefully	RB
37681	71	19	selected	select	VBN
37681	71	20	type	type	NN
37681	71	21	of	of	IN
37681	71	22	mind	mind	NN
37681	71	23	than	than	IN
37681	71	24	was	be	VBD
37681	71	25	formerly	formerly	RB
37681	71	26	the	the	DT
37681	71	27	case	case	NN
37681	71	28	,	,	,
37681	71	29	and	and	CC
37681	71	30	that	that	IN
37681	71	31	for	for	IN
37681	71	32	this	this	DT
37681	71	33	type	type	NN
37681	71	34	a	a	DT
37681	71	35	different	different	JJ
37681	71	36	kind	kind	NN
37681	71	37	of	of	IN
37681	71	38	mathematical	mathematical	JJ
37681	71	39	training	training	NN
37681	71	40	will	will	MD
37681	71	41	naturally	naturally	RB
37681	71	42	be	be	VB
37681	71	43	developed	develop	VBN
37681	71	44	.	.	.
37681	72	1	It	-PRON-	PRP
37681	72	2	proceeds	proceed	VBZ
37681	72	3	upon	upon	IN
37681	72	4	the	the	DT
37681	72	5	theory	theory	NN
37681	72	6	,	,	,
37681	72	7	however	however	RB
37681	72	8	,	,	,
37681	72	9	that	that	IN
37681	72	10	for	for	IN
37681	72	11	the	the	DT
37681	72	12	normal	normal	JJ
37681	72	13	mind,--for	mind,--for	IN
37681	72	14	the	the	DT
37681	72	15	boy	boy	NN
37681	72	16	or	or	CC
37681	72	17	girl	girl	NN
37681	72	18	who	who	WP
37681	72	19	is	be	VBZ
37681	72	20	preparing	prepare	VBG
37681	72	21	to	to	TO
37681	72	22	win	win	VB
37681	72	23	out	out	RP
37681	72	24	in	in	IN
37681	72	25	the	the	DT
37681	72	26	long	long	JJ
37681	72	27	run,--geometry	run,--geometry	NN
37681	72	28	will	will	MD
37681	72	29	continue	continue	VB
37681	72	30	to	to	TO
37681	72	31	be	be	VB
37681	72	32	taught	teach	VBN
37681	72	33	as	as	IN
37681	72	34	demonstrative	demonstrative	JJ
37681	72	35	geometry	geometry	NN
37681	72	36	,	,	,
37681	72	37	as	as	IN
37681	72	38	a	a	DT
37681	72	39	vigorous	vigorous	JJ
37681	72	40	thought	thought	NN
37681	72	41	-	-	HYPH
37681	72	42	compelling	compel	VBG
37681	72	43	subject	subject	NN
37681	72	44	,	,	,
37681	72	45	and	and	CC
37681	72	46	along	along	IN
37681	72	47	the	the	DT
37681	72	48	general	general	JJ
37681	72	49	lines	line	NNS
37681	72	50	that	that	WDT
37681	72	51	the	the	DT
37681	72	52	experience	experience	NN
37681	72	53	of	of	IN
37681	72	54	the	the	DT
37681	72	55	world	world	NN
37681	72	56	has	have	VBZ
37681	72	57	shown	show	VBN
37681	72	58	to	to	TO
37681	72	59	be	be	VB
37681	72	60	the	the	DT
37681	72	61	best	good	JJS
37681	72	62	.	.	.
37681	73	1	Soft	soft	JJ
37681	73	2	mathematics	mathematics	NN
37681	73	3	is	be	VBZ
37681	73	4	not	not	RB
37681	73	5	interesting	interesting	JJ
37681	73	6	to	to	IN
37681	73	7	this	this	DT
37681	73	8	normal	normal	JJ
37681	73	9	mind	mind	NN
37681	73	10	,	,	,
37681	73	11	and	and	CC
37681	73	12	a	a	DT
37681	73	13	sham	sham	JJ
37681	73	14	treatment	treatment	NN
37681	73	15	will	will	MD
37681	73	16	never	never	RB
37681	73	17	appeal	appeal	VB
37681	73	18	to	to	IN
37681	73	19	the	the	DT
37681	73	20	pupil	pupil	NN
37681	73	21	;	;	:
37681	73	22	and	and	CC
37681	73	23	this	this	DT
37681	73	24	book	book	NN
37681	73	25	is	be	VBZ
37681	73	26	written	write	VBN
37681	73	27	for	for	IN
37681	73	28	teachers	teacher	NNS
37681	73	29	who	who	WP
37681	73	30	believe	believe	VBP
37681	73	31	in	in	IN
37681	73	32	this	this	DT
37681	73	33	principle	principle	NN
37681	73	34	,	,	,
37681	73	35	who	who	WP
37681	73	36	believe	believe	VBP
37681	73	37	in	in	IN
37681	73	38	geometry	geometry	NN
37681	73	39	for	for	IN
37681	73	40	the	the	DT
37681	73	41	sake	sake	NN
37681	73	42	of	of	IN
37681	73	43	geometry	geometry	NN
37681	73	44	,	,	,
37681	73	45	and	and	CC
37681	73	46	who	who	WP
37681	73	47	earnestly	earnestly	RB
37681	73	48	seek	seek	VBP
37681	73	49	to	to	TO
37681	73	50	make	make	VB
37681	73	51	the	the	DT
37681	73	52	subject	subject	NN
37681	73	53	so	so	RB
37681	73	54	interesting	interesting	JJ
37681	73	55	that	that	IN
37681	73	56	pupils	pupil	NNS
37681	73	57	will	will	MD
37681	73	58	wish	wish	VB
37681	73	59	to	to	TO
37681	73	60	study	study	VB
37681	73	61	it	-PRON-	PRP
37681	73	62	whether	whether	IN
37681	73	63	it	-PRON-	PRP
37681	73	64	is	be	VBZ
37681	73	65	required	require	VBN
37681	73	66	or	or	CC
37681	73	67	elective	elective	JJ
37681	73	68	.	.	.
37681	74	1	The	the	DT
37681	74	2	work	work	NN
37681	74	3	stands	stand	VBZ
37681	74	4	for	for	IN
37681	74	5	the	the	DT
37681	74	6	great	great	JJ
37681	74	7	basal	basal	NN
37681	74	8	propositions	proposition	NNS
37681	74	9	that	that	WDT
37681	74	10	have	have	VBP
37681	74	11	come	come	VBN
37681	74	12	down	down	RP
37681	74	13	to	to	IN
37681	74	14	us	-PRON-	PRP
37681	74	15	,	,	,
37681	74	16	as	as	IN
37681	74	17	logically	logically	RB
37681	74	18	arranged	arrange	VBN
37681	74	19	and	and	CC
37681	74	20	as	as	RB
37681	74	21	scientifically	scientifically	RB
37681	74	22	proved	prove	VBN
37681	74	23	as	as	IN
37681	74	24	the	the	DT
37681	74	25	powers	power	NNS
37681	74	26	of	of	IN
37681	74	27	the	the	DT
37681	74	28	pupils	pupil	NNS
37681	74	29	in	in	IN
37681	74	30	the	the	DT
37681	74	31	American	american	JJ
37681	74	32	high	high	JJ
37681	74	33	school	school	NN
37681	74	34	will	will	MD
37681	74	35	permit	permit	VB
37681	74	36	;	;	:
37681	74	37	and	and	CC
37681	74	38	it	-PRON-	PRP
37681	74	39	seeks	seek	VBZ
37681	74	40	to	to	TO
37681	74	41	tell	tell	VB
37681	74	42	the	the	DT
37681	74	43	story	story	NN
37681	74	44	of	of	IN
37681	74	45	these	these	DT
37681	74	46	propositions	proposition	NNS
37681	74	47	and	and	CC
37681	74	48	to	to	TO
37681	74	49	show	show	VB
37681	74	50	their	-PRON-	PRP$
37681	74	51	possible	possible	JJ
37681	74	52	and	and	CC
37681	74	53	their	-PRON-	PRP$
37681	74	54	probable	probable	JJ
37681	74	55	applications	application	NNS
37681	74	56	in	in	IN
37681	74	57	such	such	PDT
37681	74	58	a	a	DT
37681	74	59	way	way	NN
37681	74	60	as	as	IN
37681	74	61	to	to	TO
37681	74	62	furnish	furnish	VB
37681	74	63	teachers	teacher	NNS
37681	74	64	with	with	IN
37681	74	65	a	a	DT
37681	74	66	fund	fund	NN
37681	74	67	of	of	IN
37681	74	68	interesting	interesting	JJ
37681	74	69	material	material	NN
37681	74	70	with	with	IN
37681	74	71	which	which	WDT
37681	74	72	to	to	TO
37681	74	73	supplement	supplement	VB
37681	74	74	the	the	DT
37681	74	75	book	book	NN
37681	74	76	work	work	NN
37681	74	77	of	of	IN
37681	74	78	their	-PRON-	PRP$
37681	74	79	classes	class	NNS
37681	74	80	.	.	.
37681	75	1	After	after	RB
37681	75	2	all	all	RB
37681	75	3	,	,	,
37681	75	4	the	the	DT
37681	75	5	problem	problem	NN
37681	75	6	of	of	IN
37681	75	7	teaching	teach	VBG
37681	75	8	any	any	DT
37681	75	9	subject	subject	NN
37681	75	10	comes	come	VBZ
37681	75	11	down	down	RP
37681	75	12	to	to	IN
37681	75	13	this	this	DT
37681	75	14	:	:	:
37681	75	15	Get	get	VB
37681	75	16	a	a	DT
37681	75	17	subject	subject	JJ
37681	75	18	worth	worth	JJ
37681	75	19	teaching	teaching	NN
37681	75	20	and	and	CC
37681	75	21	then	then	RB
37681	75	22	make	make	VB
37681	75	23	every	every	DT
37681	75	24	minute	minute	NN
37681	75	25	of	of	IN
37681	75	26	it	-PRON-	PRP
37681	75	27	interesting	interesting	JJ
37681	75	28	.	.	.
37681	76	1	Pupils	pupil	NNS
37681	76	2	do	do	VBP
37681	76	3	not	not	RB
37681	76	4	object	object	VB
37681	76	5	to	to	TO
37681	76	6	work	work	VB
37681	76	7	if	if	IN
37681	76	8	they	-PRON-	PRP
37681	76	9	like	like	VBP
37681	76	10	a	a	DT
37681	76	11	subject	subject	NN
37681	76	12	,	,	,
37681	76	13	but	but	CC
37681	76	14	they	-PRON-	PRP
37681	76	15	do	do	VBP
37681	76	16	object	object	NN
37681	76	17	to	to	IN
37681	76	18	aimless	aimless	JJ
37681	76	19	and	and	CC
37681	76	20	uninteresting	uninteresting	JJ
37681	76	21	tasks	task	NNS
37681	76	22	.	.	.
37681	77	1	Geometry	geometry	NN
37681	77	2	is	be	VBZ
37681	77	3	particularly	particularly	RB
37681	77	4	fortunate	fortunate	JJ
37681	77	5	in	in	IN
37681	77	6	that	that	DT
37681	77	7	the	the	DT
37681	77	8	feeling	feeling	NN
37681	77	9	of	of	IN
37681	77	10	accomplishment	accomplishment	NN
37681	77	11	comes	come	VBZ
37681	77	12	with	with	IN
37681	77	13	every	every	DT
37681	77	14	proposition	proposition	NN
37681	77	15	proved	prove	VBN
37681	77	16	;	;	:
37681	77	17	and	and	CC
37681	77	18	,	,	,
37681	77	19	given	give	VBN
37681	77	20	a	a	DT
37681	77	21	class	class	NN
37681	77	22	of	of	IN
37681	77	23	fair	fair	JJ
37681	77	24	intelligence	intelligence	NN
37681	77	25	,	,	,
37681	77	26	a	a	DT
37681	77	27	teacher	teacher	NN
37681	77	28	must	must	MD
37681	77	29	be	be	VB
37681	77	30	lacking	lack	VBG
37681	77	31	in	in	IN
37681	77	32	knowledge	knowledge	NN
37681	77	33	and	and	CC
37681	77	34	enthusiasm	enthusiasm	NN
37681	77	35	who	who	WP
37681	77	36	can	can	MD
37681	77	37	not	not	RB
37681	77	38	foster	foster	VB
37681	77	39	an	an	DT
37681	77	40	interest	interest	NN
37681	77	41	that	that	WDT
37681	77	42	will	will	MD
37681	77	43	make	make	VB
37681	77	44	geometry	geometry	NN
37681	77	45	stand	stand	VB
37681	77	46	forth	forth	RB
37681	77	47	as	as	IN
37681	77	48	the	the	DT
37681	77	49	subject	subject	NN
37681	77	50	that	that	WDT
37681	77	51	brings	bring	VBZ
37681	77	52	the	the	DT
37681	77	53	most	most	JJS
37681	77	54	pleasure	pleasure	NN
37681	77	55	,	,	,
37681	77	56	and	and	CC
37681	77	57	that	that	DT
37681	77	58	seems	seem	VBZ
37681	77	59	the	the	DT
37681	77	60	most	most	RBS
37681	77	61	profitable	profitable	JJ
37681	77	62	of	of	IN
37681	77	63	all	all	DT
37681	77	64	that	that	WDT
37681	77	65	are	be	VBP
37681	77	66	studied	study	VBN
37681	77	67	in	in	IN
37681	77	68	the	the	DT
37681	77	69	first	first	JJ
37681	77	70	years	year	NNS
37681	77	71	of	of	IN
37681	77	72	the	the	DT
37681	77	73	high	high	JJ
37681	77	74	school	school	NN
37681	77	75	.	.	.
37681	78	1	Continually	continually	RB
37681	78	2	to	to	TO
37681	78	3	advance	advance	VB
37681	78	4	,	,	,
37681	78	5	continually	continually	RB
37681	78	6	to	to	TO
37681	78	7	attempt	attempt	VB
37681	78	8	to	to	TO
37681	78	9	make	make	VB
37681	78	10	mathematics	mathematic	NNS
37681	78	11	fascinating	fascinating	JJ
37681	78	12	,	,	,
37681	78	13	always	always	RB
37681	78	14	to	to	TO
37681	78	15	conserve	conserve	VB
37681	78	16	the	the	DT
37681	78	17	best	good	JJS
37681	78	18	of	of	IN
37681	78	19	the	the	DT
37681	78	20	old	old	JJ
37681	78	21	and	and	CC
37681	78	22	to	to	TO
37681	78	23	sift	sift	VB
37681	78	24	out	out	RP
37681	78	25	and	and	CC
37681	78	26	use	use	VB
37681	78	27	the	the	DT
37681	78	28	best	good	JJS
37681	78	29	of	of	IN
37681	78	30	the	the	DT
37681	78	31	new	new	JJ
37681	78	32	,	,	,
37681	78	33	to	to	TO
37681	78	34	believe	believe	VB
37681	78	35	that	that	IN
37681	78	36	"	"	``
37681	78	37	mankind	mankind	NN
37681	78	38	is	be	VBZ
37681	78	39	better	well	RBR
37681	78	40	served	serve	VBN
37681	78	41	by	by	IN
37681	78	42	nature	nature	NN
37681	78	43	's	's	POS
37681	78	44	quiet	quiet	JJ
37681	78	45	and	and	CC
37681	78	46	progressive	progressive	JJ
37681	78	47	changes	change	NNS
37681	78	48	than	than	IN
37681	78	49	by	by	IN
37681	78	50	earthquakes,"[3	earthquakes,"[3	NN
37681	78	51	]	]	-RRB-
37681	78	52	to	to	TO
37681	78	53	believe	believe	VB
37681	78	54	that	that	DT
37681	78	55	geometry	geometry	NN
37681	78	56	as	as	IN
37681	78	57	geometry	geometry	NN
37681	78	58	is	be	VBZ
37681	78	59	so	so	RB
37681	78	60	valuable	valuable	JJ
37681	78	61	and	and	CC
37681	78	62	so	so	RB
37681	78	63	interesting	interesting	JJ
37681	78	64	that	that	IN
37681	78	65	the	the	DT
37681	78	66	normal	normal	JJ
37681	78	67	mind	mind	NN
37681	78	68	may	may	MD
37681	78	69	rightly	rightly	RB
37681	78	70	demand	demand	VB
37681	78	71	it,--this	it,--this	CD
37681	78	72	is	be	VBZ
37681	78	73	to	to	TO
37681	78	74	ally	ally	VB
37681	78	75	ourselves	-PRON-	PRP
37681	78	76	with	with	IN
37681	78	77	progress	progress	NN
37681	78	78	.	.	.
37681	79	1	Continually	continually	RB
37681	79	2	to	to	TO
37681	79	3	destroy	destroy	VB
37681	79	4	,	,	,
37681	79	5	continually	continually	RB
37681	79	6	to	to	TO
37681	79	7	follow	follow	VB
37681	79	8	strange	strange	JJ
37681	79	9	gods	god	NNS
37681	79	10	,	,	,
37681	79	11	always	always	RB
37681	79	12	to	to	TO
37681	79	13	decry	decry	VB
37681	79	14	the	the	DT
37681	79	15	best	good	JJS
37681	79	16	of	of	IN
37681	79	17	the	the	DT
37681	79	18	old	old	JJ
37681	79	19	,	,	,
37681	79	20	and	and	CC
37681	79	21	to	to	TO
37681	79	22	have	have	VB
37681	79	23	no	no	DT
37681	79	24	well	well	RB
37681	79	25	-	-	HYPH
37681	79	26	considered	consider	VBN
37681	79	27	aim	aim	NN
37681	79	28	in	in	IN
37681	79	29	the	the	DT
37681	79	30	teaching	teaching	NN
37681	79	31	of	of	IN
37681	79	32	a	a	DT
37681	79	33	subject,--this	subject,--this	NNP
37681	79	34	is	be	VBZ
37681	79	35	to	to	TO
37681	79	36	join	join	VB
37681	79	37	the	the	DT
37681	79	38	forces	force	NNS
37681	79	39	of	of	IN
37681	79	40	reaction	reaction	NN
37681	79	41	,	,	,
37681	79	42	to	to	TO
37681	79	43	waste	waste	VB
37681	79	44	our	-PRON-	PRP$
37681	79	45	time	time	NN
37681	79	46	,	,	,
37681	79	47	to	to	TO
37681	79	48	be	be	VB
37681	79	49	recreant	recreant	JJ
37681	79	50	to	to	IN
37681	79	51	our	-PRON-	PRP$
37681	79	52	trust	trust	NN
37681	79	53	,	,	,
37681	79	54	to	to	TO
37681	79	55	blind	blind	VB
37681	79	56	ourselves	-PRON-	PRP
37681	79	57	to	to	IN
37681	79	58	the	the	DT
37681	79	59	failures	failure	NNS
37681	79	60	of	of	IN
37681	79	61	the	the	DT
37681	79	62	past	past	NN
37681	79	63	,	,	,
37681	79	64	and	and	CC
37681	79	65	to	to	TO
37681	79	66	confess	confess	VB
37681	79	67	our	-PRON-	PRP$
37681	79	68	weakness	weakness	NN
37681	79	69	as	as	IN
37681	79	70	teachers	teacher	NNS
37681	79	71	.	.	.
37681	80	1	It	-PRON-	PRP
37681	80	2	is	be	VBZ
37681	80	3	with	with	IN
37681	80	4	the	the	DT
37681	80	5	desire	desire	NN
37681	80	6	to	to	TO
37681	80	7	aid	aid	VB
37681	80	8	in	in	IN
37681	80	9	the	the	DT
37681	80	10	progressive	progressive	JJ
37681	80	11	movement	movement	NN
37681	80	12	,	,	,
37681	80	13	to	to	TO
37681	80	14	assist	assist	VB
37681	80	15	those	those	DT
37681	80	16	who	who	WP
37681	80	17	believe	believe	VBP
37681	80	18	that	that	IN
37681	80	19	real	real	JJ
37681	80	20	geometry	geometry	NN
37681	80	21	should	should	MD
37681	80	22	be	be	VB
37681	80	23	recommended	recommend	VBN
37681	80	24	to	to	IN
37681	80	25	all	all	DT
37681	80	26	,	,	,
37681	80	27	and	and	CC
37681	80	28	to	to	TO
37681	80	29	show	show	VB
37681	80	30	that	that	IN
37681	80	31	geometry	geometry	NN
37681	80	32	is	be	VBZ
37681	80	33	both	both	CC
37681	80	34	attractive	attractive	JJ
37681	80	35	and	and	CC
37681	80	36	valuable	valuable	JJ
37681	80	37	that	that	IN
37681	80	38	this	this	DT
37681	80	39	book	book	NN
37681	80	40	is	be	VBZ
37681	80	41	written	write	VBN
37681	80	42	.	.	.
37681	81	1	FOOTNOTES	footnote	NNS
37681	81	2	:	:	:
37681	81	3	[	[	-LRB-
37681	81	4	1	1	CD
37681	81	5	]	]	-RRB-
37681	81	6	And	and	CC
37681	81	7	really	really	RB
37681	81	8	,	,	,
37681	81	9	though	though	IN
37681	81	10	not	not	RB
37681	81	11	nominally	nominally	RB
37681	81	12	,	,	,
37681	81	13	in	in	IN
37681	81	14	the	the	DT
37681	81	15	United	United	NNP
37681	81	16	States	States	NNP
37681	81	17	,	,	,
37681	81	18	where	where	WRB
37681	81	19	the	the	DT
37681	81	20	first	first	JJ
37681	81	21	concepts	concept	NNS
37681	81	22	are	be	VBP
37681	81	23	found	find	VBN
37681	81	24	in	in	IN
37681	81	25	the	the	DT
37681	81	26	kindergarten	kindergarten	NN
37681	81	27	,	,	,
37681	81	28	and	and	CC
37681	81	29	where	where	WRB
37681	81	30	an	an	DT
37681	81	31	excellent	excellent	JJ
37681	81	32	course	course	NN
37681	81	33	in	in	IN
37681	81	34	mensuration	mensuration	NN
37681	81	35	is	be	VBZ
37681	81	36	given	give	VBN
37681	81	37	in	in	IN
37681	81	38	any	any	DT
37681	81	39	of	of	IN
37681	81	40	our	-PRON-	PRP$
37681	81	41	better	well	JJR
37681	81	42	class	class	NN
37681	81	43	of	of	IN
37681	81	44	arithmetics	arithmetic	NNS
37681	81	45	.	.	.
37681	82	1	That	that	IN
37681	82	2	we	-PRON-	PRP
37681	82	3	are	be	VBP
37681	82	4	wise	wise	JJ
37681	82	5	in	in	IN
37681	82	6	not	not	RB
37681	82	7	attempting	attempt	VBG
37681	82	8	serious	serious	JJ
37681	82	9	demonstrative	demonstrative	JJ
37681	82	10	geometry	geometry	NN
37681	82	11	much	much	RB
37681	82	12	earlier	early	RBR
37681	82	13	seems	seem	VBZ
37681	82	14	to	to	TO
37681	82	15	be	be	VB
37681	82	16	generally	generally	RB
37681	82	17	conceded	concede	VBN
37681	82	18	.	.	.
37681	83	1	[	[	-LRB-
37681	83	2	2	2	LS
37681	83	3	]	]	-RRB-
37681	83	4	The	the	DT
37681	83	5	third	third	JJ
37681	83	6	stage	stage	NN
37681	83	7	of	of	IN
37681	83	8	geometry	geometry	NN
37681	83	9	as	as	IN
37681	83	10	defined	define	VBN
37681	83	11	in	in	IN
37681	83	12	the	the	DT
37681	83	13	recent	recent	JJ
37681	83	14	circular	circular	JJ
37681	83	15	(	(	-LRB-
37681	83	16	No	no	UH
37681	83	17	.	.	.
37681	84	1	711	711	CD
37681	84	2	)	)	-RRB-
37681	84	3	of	of	IN
37681	84	4	the	the	DT
37681	84	5	British	British	NNP
37681	84	6	Board	Board	NNP
37681	84	7	of	of	IN
37681	84	8	Education	Education	NNP
37681	84	9	,	,	,
37681	84	10	London	London	NNP
37681	84	11	,	,	,
37681	84	12	1909	1909	CD
37681	84	13	.	.	.
37681	85	1	[	[	-LRB-
37681	85	2	3	3	LS
37681	85	3	]	]	-RRB-
37681	85	4	The	the	DT
37681	85	5	closing	close	VBG
37681	85	6	words	word	NNS
37681	85	7	of	of	IN
37681	85	8	a	a	DT
37681	85	9	sensible	sensible	JJ
37681	85	10	review	review	NN
37681	85	11	of	of	IN
37681	85	12	the	the	DT
37681	85	13	British	British	NNP
37681	85	14	Board	Board	NNP
37681	85	15	of	of	IN
37681	85	16	Education	Education	NNP
37681	85	17	circular	circular	JJ
37681	85	18	(	(	-LRB-
37681	85	19	No	no	UH
37681	85	20	.	.	.
37681	86	1	711	711	CD
37681	86	2	)	)	-RRB-
37681	86	3	,	,	,
37681	86	4	on	on	IN
37681	86	5	"	"	``
37681	86	6	The	the	DT
37681	86	7	Teaching	Teaching	NNP
37681	86	8	of	of	IN
37681	86	9	Geometry	Geometry	NNP
37681	86	10	"	"	''
37681	86	11	(	(	-LRB-
37681	86	12	London	London	NNP
37681	86	13	,	,	,
37681	86	14	1909	1909	CD
37681	86	15	)	)	-RRB-
37681	86	16	,	,	,
37681	86	17	by	by	IN
37681	86	18	H.	H.	NNP
37681	86	19	S.	S.	NNP
37681	86	20	Hall	Hall	NNP
37681	86	21	in	in	IN
37681	86	22	the	the	DT
37681	86	23	_	_	NNP
37681	86	24	School	School	NNP
37681	86	25	World	World	NNP
37681	86	26	_	_	NNP
37681	86	27	,	,	,
37681	86	28	1909	1909	CD
37681	86	29	,	,	,
37681	86	30	p.	p.	NN
37681	86	31	222	222	CD
37681	86	32	.	.	.
37681	87	1	CHAPTER	CHAPTER	NNP
37681	87	2	II	ii	CD
37681	87	3	WHY	why	WRB
37681	87	4	GEOMETRY	GEOMETRY	NNP
37681	87	5	IS	be	VBZ
37681	87	6	STUDIED	study	VBN
37681	87	7	With	with	IN
37681	87	8	geometry	geometry	NN
37681	87	9	,	,	,
37681	87	10	as	as	IN
37681	87	11	with	with	IN
37681	87	12	other	other	JJ
37681	87	13	subjects	subject	NNS
37681	87	14	,	,	,
37681	87	15	it	-PRON-	PRP
37681	87	16	is	be	VBZ
37681	87	17	easier	easy	JJR
37681	87	18	to	to	TO
37681	87	19	set	set	VB
37681	87	20	forth	forth	RP
37681	87	21	what	what	WP
37681	87	22	are	be	VBP
37681	87	23	not	not	RB
37681	87	24	the	the	DT
37681	87	25	reasons	reason	NNS
37681	87	26	for	for	IN
37681	87	27	studying	study	VBG
37681	87	28	it	-PRON-	PRP
37681	87	29	than	than	IN
37681	87	30	to	to	TO
37681	87	31	proceed	proceed	VB
37681	87	32	positively	positively	RB
37681	87	33	and	and	CC
37681	87	34	enumerate	enumerate	VB
37681	87	35	the	the	DT
37681	87	36	advantages	advantage	NNS
37681	87	37	.	.	.
37681	88	1	Although	although	IN
37681	88	2	such	such	PDT
37681	88	3	a	a	DT
37681	88	4	negative	negative	JJ
37681	88	5	course	course	NN
37681	88	6	is	be	VBZ
37681	88	7	not	not	RB
37681	88	8	satisfying	satisfy	VBG
37681	88	9	to	to	IN
37681	88	10	the	the	DT
37681	88	11	mind	mind	NN
37681	88	12	as	as	IN
37681	88	13	a	a	DT
37681	88	14	finality	finality	NN
37681	88	15	,	,	,
37681	88	16	it	-PRON-	PRP
37681	88	17	possesses	possess	VBZ
37681	88	18	definite	definite	JJ
37681	88	19	advantages	advantage	NNS
37681	88	20	in	in	IN
37681	88	21	the	the	DT
37681	88	22	beginning	beginning	NN
37681	88	23	of	of	IN
37681	88	24	such	such	PDT
37681	88	25	a	a	DT
37681	88	26	discussion	discussion	NN
37681	88	27	as	as	IN
37681	88	28	this	this	DT
37681	88	29	.	.	.
37681	89	1	Whenever	whenever	WRB
37681	89	2	false	false	JJ
37681	89	3	prophets	prophet	NNS
37681	89	4	arise	arise	VBP
37681	89	5	,	,	,
37681	89	6	and	and	CC
37681	89	7	with	with	IN
37681	89	8	an	an	DT
37681	89	9	attitude	attitude	NN
37681	89	10	of	of	IN
37681	89	11	pained	pain	VBN
37681	89	12	superiority	superiority	NN
37681	89	13	proclaim	proclaim	VBP
37681	89	14	unworthy	unworthy	JJ
37681	89	15	aims	aim	NNS
37681	89	16	in	in	IN
37681	89	17	human	human	JJ
37681	89	18	life	life	NN
37681	89	19	,	,	,
37681	89	20	it	-PRON-	PRP
37681	89	21	is	be	VBZ
37681	89	22	well	well	JJ
37681	89	23	to	to	TO
37681	89	24	show	show	VB
37681	89	25	the	the	DT
37681	89	26	fallacy	fallacy	NN
37681	89	27	of	of	IN
37681	89	28	their	-PRON-	PRP$
37681	89	29	position	position	NN
37681	89	30	before	before	IN
37681	89	31	proceeding	proceed	VBG
37681	89	32	to	to	IN
37681	89	33	a	a	DT
37681	89	34	constructive	constructive	JJ
37681	89	35	philosophy	philosophy	NN
37681	89	36	.	.	.
37681	90	1	Taking	take	VBG
37681	90	2	for	for	IN
37681	90	3	a	a	DT
37681	90	4	moment	moment	NN
37681	90	5	this	this	DT
37681	90	6	negative	negative	JJ
37681	90	7	course	course	NN
37681	90	8	,	,	,
37681	90	9	let	let	VB
37681	90	10	us	-PRON-	PRP
37681	90	11	inquire	inquire	VB
37681	90	12	as	as	IN
37681	90	13	to	to	IN
37681	90	14	what	what	WP
37681	90	15	are	be	VBP
37681	90	16	not	not	RB
37681	90	17	the	the	DT
37681	90	18	reasons	reason	NNS
37681	90	19	for	for	IN
37681	90	20	studying	study	VBG
37681	90	21	geometry	geometry	NN
37681	90	22	,	,	,
37681	90	23	or	or	CC
37681	90	24	,	,	,
37681	90	25	to	to	TO
37681	90	26	be	be	VB
37681	90	27	more	more	RBR
37681	90	28	emphatic	emphatic	JJ
37681	90	29	,	,	,
37681	90	30	as	as	IN
37681	90	31	to	to	IN
37681	90	32	what	what	WP
37681	90	33	are	be	VBP
37681	90	34	not	not	RB
37681	90	35	the	the	DT
37681	90	36	worthy	worthy	JJ
37681	90	37	reasons	reason	NNS
37681	90	38	.	.	.
37681	91	1	In	in	IN
37681	91	2	view	view	NN
37681	91	3	of	of	IN
37681	91	4	a	a	DT
37681	91	5	periodic	periodic	JJ
37681	91	6	activity	activity	NN
37681	91	7	in	in	IN
37681	91	8	favor	favor	NN
37681	91	9	of	of	IN
37681	91	10	the	the	DT
37681	91	11	utilities	utility	NNS
37681	91	12	of	of	IN
37681	91	13	geometry	geometry	NN
37681	91	14	,	,	,
37681	91	15	it	-PRON-	PRP
37681	91	16	is	be	VBZ
37681	91	17	well	well	JJ
37681	91	18	to	to	TO
37681	91	19	understand	understand	VB
37681	91	20	,	,	,
37681	91	21	in	in	IN
37681	91	22	the	the	DT
37681	91	23	first	first	JJ
37681	91	24	place	place	NN
37681	91	25	,	,	,
37681	91	26	that	that	DT
37681	91	27	geometry	geometry	NN
37681	91	28	is	be	VBZ
37681	91	29	not	not	RB
37681	91	30	studied	study	VBN
37681	91	31	,	,	,
37681	91	32	and	and	CC
37681	91	33	never	never	RB
37681	91	34	has	have	VBZ
37681	91	35	been	be	VBN
37681	91	36	studied	study	VBN
37681	91	37	,	,	,
37681	91	38	because	because	IN
37681	91	39	of	of	IN
37681	91	40	its	-PRON-	PRP$
37681	91	41	positive	positive	JJ
37681	91	42	utility	utility	NN
37681	91	43	in	in	IN
37681	91	44	commercial	commercial	JJ
37681	91	45	life	life	NN
37681	91	46	or	or	CC
37681	91	47	even	even	RB
37681	91	48	in	in	IN
37681	91	49	the	the	DT
37681	91	50	workshop	workshop	NN
37681	91	51	.	.	.
37681	92	1	In	in	IN
37681	92	2	America	America	NNP
37681	92	3	we	-PRON-	PRP
37681	92	4	commonly	commonly	RB
37681	92	5	allow	allow	VBP
37681	92	6	at	at	IN
37681	92	7	least	least	JJS
37681	92	8	a	a	DT
37681	92	9	year	year	NN
37681	92	10	to	to	IN
37681	92	11	plane	plane	NN
37681	92	12	geometry	geometry	NN
37681	92	13	and	and	CC
37681	92	14	a	a	DT
37681	92	15	half	half	JJ
37681	92	16	year	year	NN
37681	92	17	to	to	IN
37681	92	18	solid	solid	JJ
37681	92	19	geometry	geometry	NN
37681	92	20	;	;	:
37681	92	21	but	but	CC
37681	92	22	all	all	DT
37681	92	23	of	of	IN
37681	92	24	the	the	DT
37681	92	25	facts	fact	NNS
37681	92	26	that	that	WDT
37681	92	27	a	a	DT
37681	92	28	skilled	skilled	JJ
37681	92	29	mechanic	mechanic	NN
37681	92	30	or	or	CC
37681	92	31	an	an	DT
37681	92	32	engineer	engineer	NN
37681	92	33	would	would	MD
37681	92	34	ever	ever	RB
37681	92	35	need	need	VB
37681	92	36	could	could	MD
37681	92	37	be	be	VB
37681	92	38	taught	teach	VBN
37681	92	39	in	in	IN
37681	92	40	a	a	DT
37681	92	41	few	few	JJ
37681	92	42	lessons	lesson	NNS
37681	92	43	.	.	.
37681	93	1	All	all	PDT
37681	93	2	the	the	DT
37681	93	3	rest	rest	NN
37681	93	4	is	be	VBZ
37681	93	5	either	either	CC
37681	93	6	obvious	obvious	JJ
37681	93	7	or	or	CC
37681	93	8	is	be	VBZ
37681	93	9	commercially	commercially	RB
37681	93	10	and	and	CC
37681	93	11	technically	technically	RB
37681	93	12	useless	useless	JJ
37681	93	13	.	.	.
37681	94	1	We	-PRON-	PRP
37681	94	2	prove	prove	VBP
37681	94	3	,	,	,
37681	94	4	for	for	IN
37681	94	5	example	example	NN
37681	94	6	,	,	,
37681	94	7	that	that	IN
37681	94	8	the	the	DT
37681	94	9	angles	angle	NNS
37681	94	10	opposite	opposite	IN
37681	94	11	the	the	DT
37681	94	12	equal	equal	JJ
37681	94	13	sides	side	NNS
37681	94	14	of	of	IN
37681	94	15	a	a	DT
37681	94	16	triangle	triangle	NN
37681	94	17	are	be	VBP
37681	94	18	equal	equal	JJ
37681	94	19	,	,	,
37681	94	20	a	a	DT
37681	94	21	fact	fact	NN
37681	94	22	that	that	WDT
37681	94	23	is	be	VBZ
37681	94	24	probably	probably	RB
37681	94	25	quite	quite	RB
37681	94	26	as	as	RB
37681	94	27	obvious	obvious	JJ
37681	94	28	as	as	IN
37681	94	29	the	the	DT
37681	94	30	postulate	postulate	NN
37681	94	31	that	that	WDT
37681	94	32	but	but	CC
37681	94	33	one	one	CD
37681	94	34	line	line	NN
37681	94	35	can	can	MD
37681	94	36	be	be	VB
37681	94	37	drawn	draw	VBN
37681	94	38	through	through	IN
37681	94	39	a	a	DT
37681	94	40	given	give	VBN
37681	94	41	point	point	NN
37681	94	42	parallel	parallel	NN
37681	94	43	to	to	IN
37681	94	44	a	a	DT
37681	94	45	given	give	VBN
37681	94	46	line	line	NN
37681	94	47	.	.	.
37681	95	1	We	-PRON-	PRP
37681	95	2	then	then	RB
37681	95	3	prove	prove	VBP
37681	95	4	,	,	,
37681	95	5	sometimes	sometimes	RB
37681	95	6	by	by	IN
37681	95	7	the	the	DT
37681	95	8	unsatisfactory	unsatisfactory	JJ
37681	95	9	process	process	NN
37681	95	10	of	of	IN
37681	95	11	_	_	NNP
37681	95	12	reductio	reductio	NN
37681	95	13	ad	ad	NN
37681	95	14	absurdum	absurdum	NN
37681	95	15	_	_	NNP
37681	95	16	,	,	,
37681	95	17	the	the	DT
37681	95	18	converse	converse	NN
37681	95	19	of	of	IN
37681	95	20	this	this	DT
37681	95	21	proposition,--a	proposition,--a	NNP
37681	95	22	fact	fact	NN
37681	95	23	that	that	WDT
37681	95	24	is	be	VBZ
37681	95	25	as	as	RB
37681	95	26	obvious	obvious	JJ
37681	95	27	as	as	IN
37681	95	28	most	most	JJS
37681	95	29	other	other	JJ
37681	95	30	facts	fact	NNS
37681	95	31	that	that	WDT
37681	95	32	come	come	VBP
37681	95	33	to	to	IN
37681	95	34	our	-PRON-	PRP$
37681	95	35	consciousness	consciousness	NN
37681	95	36	,	,	,
37681	95	37	at	at	IN
37681	95	38	least	least	JJS
37681	95	39	after	after	IN
37681	95	40	the	the	DT
37681	95	41	preceding	precede	VBG
37681	95	42	proposition	proposition	NN
37681	95	43	has	have	VBZ
37681	95	44	been	be	VBN
37681	95	45	proved	prove	VBN
37681	95	46	.	.	.
37681	96	1	And	and	CC
37681	96	2	these	these	DT
37681	96	3	two	two	CD
37681	96	4	theorems	theorem	NNS
37681	96	5	are	be	VBP
37681	96	6	perfectly	perfectly	RB
37681	96	7	fair	fair	JJ
37681	96	8	types	type	NNS
37681	96	9	of	of	IN
37681	96	10	upwards	upward	NNS
37681	96	11	of	of	IN
37681	96	12	one	one	CD
37681	96	13	hundred	hundred	CD
37681	96	14	sixty	sixty	CD
37681	96	15	or	or	CC
37681	96	16	seventy	seventy	CD
37681	96	17	propositions	proposition	NNS
37681	96	18	comprising	comprise	VBG
37681	96	19	Euclid	Euclid	NNP
37681	96	20	's	's	POS
37681	96	21	books	book	NNS
37681	96	22	on	on	IN
37681	96	23	plane	plane	NN
37681	96	24	geometry	geometry	NN
37681	96	25	.	.	.
37681	97	1	They	-PRON-	PRP
37681	97	2	are	be	VBP
37681	97	3	generally	generally	RB
37681	97	4	not	not	RB
37681	97	5	useful	useful	JJ
37681	97	6	in	in	IN
37681	97	7	daily	daily	JJ
37681	97	8	life	life	NN
37681	97	9	,	,	,
37681	97	10	and	and	CC
37681	97	11	they	-PRON-	PRP
37681	97	12	were	be	VBD
37681	97	13	never	never	RB
37681	97	14	intended	intend	VBN
37681	97	15	to	to	TO
37681	97	16	be	be	VB
37681	97	17	so	so	RB
37681	97	18	.	.	.
37681	98	1	There	there	EX
37681	98	2	is	be	VBZ
37681	98	3	an	an	DT
37681	98	4	oft	oft	RB
37681	98	5	-	-	HYPH
37681	98	6	repeated	repeat	VBN
37681	98	7	but	but	CC
37681	98	8	not	not	RB
37681	98	9	well	well	RB
37681	98	10	-	-	HYPH
37681	98	11	authenticated	authenticate	VBN
37681	98	12	story	story	NN
37681	98	13	of	of	IN
37681	98	14	Euclid	Euclid	NNP
37681	98	15	that	that	WDT
37681	98	16	illustrates	illustrate	VBZ
37681	98	17	the	the	DT
37681	98	18	feeling	feeling	NN
37681	98	19	of	of	IN
37681	98	20	the	the	DT
37681	98	21	founders	founder	NNS
37681	98	22	of	of	IN
37681	98	23	geometry	geometry	NN
37681	98	24	as	as	RB
37681	98	25	well	well	RB
37681	98	26	as	as	IN
37681	98	27	of	of	IN
37681	98	28	its	-PRON-	PRP$
37681	98	29	most	most	RBS
37681	98	30	worthy	worthy	JJ
37681	98	31	teachers	teacher	NNS
37681	98	32	.	.	.
37681	99	1	A	a	DT
37681	99	2	Greek	greek	JJ
37681	99	3	writer	writer	NN
37681	99	4	,	,	,
37681	99	5	Stobæus	Stobæus	NNP
37681	99	6	,	,	,
37681	99	7	relates	relate	VBZ
37681	99	8	the	the	DT
37681	99	9	story	story	NN
37681	99	10	in	in	IN
37681	99	11	these	these	DT
37681	99	12	words	word	NNS
37681	99	13	:	:	:
37681	99	14	Some	some	DT
37681	99	15	one	one	NN
37681	99	16	who	who	WP
37681	99	17	had	have	VBD
37681	99	18	begun	begin	VBN
37681	99	19	to	to	TO
37681	99	20	read	read	VB
37681	99	21	geometry	geometry	NN
37681	99	22	with	with	IN
37681	99	23	Euclid	Euclid	NNP
37681	99	24	,	,	,
37681	99	25	when	when	WRB
37681	99	26	he	-PRON-	PRP
37681	99	27	had	have	VBD
37681	99	28	learned	learn	VBN
37681	99	29	the	the	DT
37681	99	30	first	first	JJ
37681	99	31	theorem	theorem	NN
37681	99	32	,	,	,
37681	99	33	asked	ask	VBD
37681	99	34	,	,	,
37681	99	35	"	"	``
37681	99	36	But	but	CC
37681	99	37	what	what	WP
37681	99	38	shall	shall	MD
37681	99	39	I	-PRON-	PRP
37681	99	40	get	get	VB
37681	99	41	by	by	IN
37681	99	42	learning	learn	VBG
37681	99	43	these	these	DT
37681	99	44	things	thing	NNS
37681	99	45	?	?	.
37681	99	46	"	"	''
37681	100	1	Euclid	Euclid	NNP
37681	100	2	called	call	VBD
37681	100	3	his	-PRON-	PRP$
37681	100	4	slave	slave	NN
37681	100	5	and	and	CC
37681	100	6	said	say	VBD
37681	100	7	,	,	,
37681	100	8	"	"	``
37681	100	9	Give	give	VB
37681	100	10	him	-PRON-	PRP
37681	100	11	three	three	CD
37681	100	12	obols	obol	NNS
37681	100	13	,	,	,
37681	100	14	since	since	IN
37681	100	15	he	-PRON-	PRP
37681	100	16	must	must	MD
37681	100	17	make	make	VB
37681	100	18	gain	gain	NN
37681	100	19	out	out	IN
37681	100	20	of	of	IN
37681	100	21	what	what	WP
37681	100	22	he	-PRON-	PRP
37681	100	23	learns	learn	VBZ
37681	100	24	.	.	.
37681	100	25	"	"	''
37681	101	1	Whether	whether	IN
37681	101	2	true	true	JJ
37681	101	3	or	or	CC
37681	101	4	not	not	RB
37681	101	5	,	,	,
37681	101	6	the	the	DT
37681	101	7	story	story	NN
37681	101	8	expresses	express	VBZ
37681	101	9	the	the	DT
37681	101	10	sentiment	sentiment	NN
37681	101	11	that	that	WDT
37681	101	12	runs	run	VBZ
37681	101	13	through	through	IN
37681	101	14	Euclid	Euclid	NNP
37681	101	15	's	's	POS
37681	101	16	work	work	NN
37681	101	17	,	,	,
37681	101	18	and	and	CC
37681	101	19	not	not	RB
37681	101	20	improbably	improbably	RB
37681	101	21	we	-PRON-	PRP
37681	101	22	have	have	VBP
37681	101	23	here	here	RB
37681	101	24	a	a	DT
37681	101	25	bit	bit	NN
37681	101	26	of	of	IN
37681	101	27	real	real	JJ
37681	101	28	biography,--practically	biography,--practically	RB
37681	101	29	all	all	DT
37681	101	30	of	of	IN
37681	101	31	the	the	DT
37681	101	32	personal	personal	JJ
37681	101	33	Euclid	Euclid	NNP
37681	101	34	that	that	WDT
37681	101	35	has	have	VBZ
37681	101	36	come	come	VBN
37681	101	37	down	down	RP
37681	101	38	to	to	IN
37681	101	39	us	-PRON-	PRP
37681	101	40	from	from	IN
37681	101	41	the	the	DT
37681	101	42	world	world	NN
37681	101	43	's	's	POS
37681	101	44	first	first	JJ
37681	101	45	great	great	JJ
37681	101	46	textbook	textbook	NN
37681	101	47	maker	maker	NN
37681	101	48	.	.	.
37681	102	1	It	-PRON-	PRP
37681	102	2	is	be	VBZ
37681	102	3	well	well	RB
37681	102	4	that	that	IN
37681	102	5	we	-PRON-	PRP
37681	102	6	read	read	VBP
37681	102	7	the	the	DT
37681	102	8	story	story	NN
37681	102	9	occasionally	occasionally	RB
37681	102	10	,	,	,
37681	102	11	and	and	CC
37681	102	12	also	also	RB
37681	102	13	such	such	JJ
37681	102	14	words	word	NNS
37681	102	15	as	as	IN
37681	102	16	the	the	DT
37681	102	17	following	follow	VBG
37681	102	18	,	,	,
37681	102	19	recently	recently	RB
37681	102	20	uttered[4	uttered[4	NNPS
37681	102	21	]	]	-RRB-
37681	102	22	by	by	IN
37681	102	23	Sir	Sir	NNP
37681	102	24	Conan	Conan	NNP
37681	102	25	Doyle,--words	doyle,--word	VBZ
37681	102	26	bearing	bear	VBG
37681	102	27	the	the	DT
37681	102	28	same	same	JJ
37681	102	29	lesson	lesson	NN
37681	102	30	,	,	,
37681	102	31	although	although	IN
37681	102	32	upon	upon	IN
37681	102	33	a	a	DT
37681	102	34	different	different	JJ
37681	102	35	theme	theme	NN
37681	102	36	:	:	:
37681	102	37	In	in	IN
37681	102	38	the	the	DT
37681	102	39	present	present	JJ
37681	102	40	utilitarian	utilitarian	JJ
37681	102	41	age	age	NN
37681	102	42	one	one	CD
37681	102	43	frequently	frequently	RB
37681	102	44	hears	hear	VBZ
37681	102	45	the	the	DT
37681	102	46	question	question	NN
37681	102	47	asked	ask	VBD
37681	102	48	,	,	,
37681	102	49	"	"	``
37681	102	50	What	what	WP
37681	102	51	is	be	VBZ
37681	102	52	the	the	DT
37681	102	53	use	use	NN
37681	102	54	of	of	IN
37681	102	55	it	-PRON-	PRP
37681	102	56	all	all	DT
37681	102	57	?	?	.
37681	102	58	"	"	''
37681	103	1	as	as	IN
37681	103	2	if	if	IN
37681	103	3	every	every	DT
37681	103	4	noble	noble	JJ
37681	103	5	deed	deed	NN
37681	103	6	was	be	VBD
37681	103	7	not	not	RB
37681	103	8	its	-PRON-	PRP$
37681	103	9	own	own	JJ
37681	103	10	justification	justification	NN
37681	103	11	.	.	.
37681	104	1	As	as	IN
37681	104	2	if	if	IN
37681	104	3	every	every	DT
37681	104	4	action	action	NN
37681	104	5	which	which	WDT
37681	104	6	makes	make	VBZ
37681	104	7	for	for	IN
37681	104	8	self	self	NN
37681	104	9	-	-	HYPH
37681	104	10	denial	denial	NN
37681	104	11	,	,	,
37681	104	12	for	for	IN
37681	104	13	hardihood	hardihood	NN
37681	104	14	,	,	,
37681	104	15	and	and	CC
37681	104	16	for	for	IN
37681	104	17	endurance	endurance	NN
37681	104	18	was	be	VBD
37681	104	19	not	not	RB
37681	104	20	in	in	IN
37681	104	21	itself	-PRON-	PRP
37681	104	22	a	a	DT
37681	104	23	most	most	RBS
37681	104	24	precious	precious	JJ
37681	104	25	lesson	lesson	NN
37681	104	26	to	to	IN
37681	104	27	mankind	mankind	NN
37681	104	28	.	.	.
37681	105	1	That	that	IN
37681	105	2	people	people	NNS
37681	105	3	can	can	MD
37681	105	4	be	be	VB
37681	105	5	found	find	VBN
37681	105	6	to	to	TO
37681	105	7	ask	ask	VB
37681	105	8	such	such	PDT
37681	105	9	a	a	DT
37681	105	10	question	question	NN
37681	105	11	shows	show	VBZ
37681	105	12	how	how	WRB
37681	105	13	far	far	RB
37681	105	14	materialism	materialism	NN
37681	105	15	has	have	VBZ
37681	105	16	gone	go	VBN
37681	105	17	,	,	,
37681	105	18	and	and	CC
37681	105	19	how	how	WRB
37681	105	20	needful	needful	JJ
37681	105	21	it	-PRON-	PRP
37681	105	22	is	be	VBZ
37681	105	23	that	that	IN
37681	105	24	we	-PRON-	PRP
37681	105	25	insist	insist	VBP
37681	105	26	upon	upon	IN
37681	105	27	the	the	DT
37681	105	28	value	value	NN
37681	105	29	of	of	IN
37681	105	30	all	all	DT
37681	105	31	that	that	WDT
37681	105	32	is	be	VBZ
37681	105	33	nobler	noble	JJR
37681	105	34	and	and	CC
37681	105	35	higher	high	JJR
37681	105	36	in	in	IN
37681	105	37	life	life	NN
37681	105	38	.	.	.
37681	106	1	An	an	DT
37681	106	2	American	american	JJ
37681	106	3	statesman	statesman	NN
37681	106	4	and	and	CC
37681	106	5	jurist	jurist	NN
37681	106	6	,	,	,
37681	106	7	speaking	speak	VBG
37681	106	8	upon	upon	IN
37681	106	9	a	a	DT
37681	106	10	similar	similar	JJ
37681	106	11	occasion[5	occasion[5	.
37681	106	12	]	]	-RRB-
37681	106	13	,	,	,
37681	106	14	gave	give	VBD
37681	106	15	utterance	utterance	NN
37681	106	16	to	to	IN
37681	106	17	the	the	DT
37681	106	18	same	same	JJ
37681	106	19	sentiments	sentiment	NNS
37681	106	20	in	in	IN
37681	106	21	these	these	DT
37681	106	22	words	word	NNS
37681	106	23	:	:	:
37681	106	24	When	when	WRB
37681	106	25	the	the	DT
37681	106	26	time	time	NN
37681	106	27	comes	come	VBZ
37681	106	28	that	that	IN
37681	106	29	knowledge	knowledge	NN
37681	106	30	will	will	MD
37681	106	31	not	not	RB
37681	106	32	be	be	VB
37681	106	33	sought	seek	VBN
37681	106	34	for	for	IN
37681	106	35	its	-PRON-	PRP$
37681	106	36	own	own	JJ
37681	106	37	sake	sake	NN
37681	106	38	,	,	,
37681	106	39	and	and	CC
37681	106	40	men	man	NNS
37681	106	41	will	will	MD
37681	106	42	not	not	RB
37681	106	43	press	press	VB
37681	106	44	forward	forward	RB
37681	106	45	simply	simply	RB
37681	106	46	in	in	IN
37681	106	47	a	a	DT
37681	106	48	desire	desire	NN
37681	106	49	of	of	IN
37681	106	50	achievement	achievement	NN
37681	106	51	,	,	,
37681	106	52	without	without	IN
37681	106	53	hope	hope	NN
37681	106	54	of	of	IN
37681	106	55	gain	gain	NN
37681	106	56	,	,	,
37681	106	57	to	to	TO
37681	106	58	extend	extend	VB
37681	106	59	the	the	DT
37681	106	60	limits	limit	NNS
37681	106	61	of	of	IN
37681	106	62	human	human	JJ
37681	106	63	knowledge	knowledge	NN
37681	106	64	and	and	CC
37681	106	65	information	information	NN
37681	106	66	,	,	,
37681	106	67	then	then	RB
37681	106	68	,	,	,
37681	106	69	indeed	indeed	RB
37681	106	70	,	,	,
37681	106	71	will	will	MD
37681	106	72	the	the	DT
37681	106	73	race	race	NN
37681	106	74	enter	enter	VB
37681	106	75	upon	upon	IN
37681	106	76	its	-PRON-	PRP$
37681	106	77	decadence	decadence	NN
37681	106	78	.	.	.
37681	107	1	There	there	EX
37681	107	2	have	have	VBP
37681	107	3	not	not	RB
37681	107	4	been	be	VBN
37681	107	5	wanting	want	VBG
37681	107	6	,	,	,
37681	107	7	however	however	RB
37681	107	8	,	,	,
37681	107	9	in	in	IN
37681	107	10	every	every	DT
37681	107	11	age	age	NN
37681	107	12	,	,	,
37681	107	13	those	those	DT
37681	107	14	whose	whose	WP$
37681	107	15	zeal	zeal	NN
37681	107	16	is	be	VBZ
37681	107	17	in	in	IN
37681	107	18	inverse	inverse	JJ
37681	107	19	proportion	proportion	NN
37681	107	20	to	to	IN
37681	107	21	their	-PRON-	PRP$
37681	107	22	experience	experience	NN
37681	107	23	,	,	,
37681	107	24	who	who	WP
37681	107	25	were	be	VBD
37681	107	26	possessed	possess	VBN
37681	107	27	with	with	IN
37681	107	28	the	the	DT
37681	107	29	idea	idea	NN
37681	107	30	that	that	IN
37681	107	31	it	-PRON-	PRP
37681	107	32	is	be	VBZ
37681	107	33	the	the	DT
37681	107	34	duty	duty	NN
37681	107	35	of	of	IN
37681	107	36	the	the	DT
37681	107	37	schools	school	NNS
37681	107	38	to	to	TO
37681	107	39	make	make	VB
37681	107	40	geometry	geometry	NN
37681	107	41	practical	practical	JJ
37681	107	42	.	.	.
37681	108	1	We	-PRON-	PRP
37681	108	2	have	have	VBP
37681	108	3	them	-PRON-	PRP
37681	108	4	to	to	IN
37681	108	5	-	-	HYPH
37681	108	6	day	day	NN
37681	108	7	,	,	,
37681	108	8	and	and	CC
37681	108	9	the	the	DT
37681	108	10	world	world	NN
37681	108	11	had	have	VBD
37681	108	12	them	-PRON-	PRP
37681	108	13	yesterday	yesterday	NN
37681	108	14	,	,	,
37681	108	15	and	and	CC
37681	108	16	the	the	DT
37681	108	17	future	future	NN
37681	108	18	shall	shall	MD
37681	108	19	see	see	VB
37681	108	20	them	-PRON-	PRP
37681	108	21	as	as	RB
37681	108	22	active	active	JJ
37681	108	23	as	as	IN
37681	108	24	ever	ever	RB
37681	108	25	.	.	.
37681	109	1	These	these	DT
37681	109	2	people	people	NNS
37681	109	3	do	do	VBP
37681	109	4	good	good	NN
37681	109	5	to	to	IN
37681	109	6	the	the	DT
37681	109	7	world	world	NN
37681	109	8	,	,	,
37681	109	9	and	and	CC
37681	109	10	their	-PRON-	PRP$
37681	109	11	labors	labor	NNS
37681	109	12	should	should	MD
37681	109	13	always	always	RB
37681	109	14	be	be	VB
37681	109	15	welcome	welcome	JJ
37681	109	16	,	,	,
37681	109	17	for	for	IN
37681	109	18	out	out	IN
37681	109	19	of	of	IN
37681	109	20	the	the	DT
37681	109	21	myriad	myriad	NN
37681	109	22	of	of	IN
37681	109	23	suggestions	suggestion	NNS
37681	109	24	that	that	IN
37681	109	25	they	-PRON-	PRP
37681	109	26	make	make	VBP
37681	109	27	a	a	DT
37681	109	28	few	few	JJ
37681	109	29	have	have	VBP
37681	109	30	value	value	NN
37681	109	31	,	,	,
37681	109	32	and	and	CC
37681	109	33	these	these	DT
37681	109	34	are	be	VBP
37681	109	35	helpful	helpful	JJ
37681	109	36	both	both	DT
37681	109	37	to	to	IN
37681	109	38	the	the	DT
37681	109	39	mathematician	mathematician	NN
37681	109	40	and	and	CC
37681	109	41	the	the	DT
37681	109	42	artisan	artisan	NNP
37681	109	43	.	.	.
37681	110	1	Not	not	RB
37681	110	2	infrequently	infrequently	RB
37681	110	3	they	-PRON-	PRP
37681	110	4	have	have	VBP
37681	110	5	contributed	contribute	VBN
37681	110	6	material	material	NN
37681	110	7	that	that	WDT
37681	110	8	serves	serve	VBZ
37681	110	9	to	to	TO
37681	110	10	make	make	VB
37681	110	11	geometry	geometry	NN
37681	110	12	somewhat	somewhat	RB
37681	110	13	more	more	RBR
37681	110	14	interesting	interesting	JJ
37681	110	15	,	,	,
37681	110	16	but	but	CC
37681	110	17	it	-PRON-	PRP
37681	110	18	must	must	MD
37681	110	19	be	be	VB
37681	110	20	confessed	confess	VBN
37681	110	21	that	that	IN
37681	110	22	most	most	JJS
37681	110	23	of	of	IN
37681	110	24	their	-PRON-	PRP$
37681	110	25	work	work	NN
37681	110	26	is	be	VBZ
37681	110	27	merely	merely	RB
37681	110	28	the	the	DT
37681	110	29	threshing	threshing	NN
37681	110	30	of	of	IN
37681	110	31	old	old	JJ
37681	110	32	straw	straw	NN
37681	110	33	,	,	,
37681	110	34	like	like	IN
37681	110	35	the	the	DT
37681	110	36	work	work	NN
37681	110	37	of	of	IN
37681	110	38	those	those	DT
37681	110	39	who	who	WP
37681	110	40	follow	follow	VBP
37681	110	41	the	the	DT
37681	110	42	will	will	NNP
37681	110	43	-	-	HYPH
37681	110	44	o'-the	o'-the	NN
37681	110	45	-	-	HYPH
37681	110	46	wisp	wisp	NN
37681	110	47	of	of	IN
37681	110	48	the	the	DT
37681	110	49	circle	circle	NN
37681	110	50	squarers	squarer	NNS
37681	110	51	.	.	.
37681	111	1	The	the	DT
37681	111	2	medieval	medieval	JJ
37681	111	3	astrologers	astrologer	NNS
37681	111	4	wished	wish	VBD
37681	111	5	to	to	TO
37681	111	6	make	make	VB
37681	111	7	geometry	geometry	NN
37681	111	8	more	more	RBR
37681	111	9	practical	practical	JJ
37681	111	10	,	,	,
37681	111	11	and	and	CC
37681	111	12	so	so	RB
37681	111	13	they	-PRON-	PRP
37681	111	14	carried	carry	VBD
37681	111	15	to	to	IN
37681	111	16	a	a	DT
37681	111	17	considerable	considerable	JJ
37681	111	18	length	length	NN
37681	111	19	the	the	DT
37681	111	20	study	study	NN
37681	111	21	of	of	IN
37681	111	22	the	the	DT
37681	111	23	star	star	NN
37681	111	24	polygon	polygon	NN
37681	111	25	,	,	,
37681	111	26	a	a	DT
37681	111	27	figure	figure	NN
37681	111	28	that	that	IN
37681	111	29	they	-PRON-	PRP
37681	111	30	could	could	MD
37681	111	31	use	use	VB
37681	111	32	in	in	IN
37681	111	33	their	-PRON-	PRP$
37681	111	34	profession	profession	NN
37681	111	35	.	.	.
37681	112	1	The	the	DT
37681	112	2	cathedral	cathedral	JJ
37681	112	3	builders	builder	NNS
37681	112	4	,	,	,
37681	112	5	as	as	IN
37681	112	6	their	-PRON-	PRP$
37681	112	7	art	art	NN
37681	112	8	progressed	progress	VBN
37681	112	9	,	,	,
37681	112	10	found	find	VBD
37681	112	11	that	that	IN
37681	112	12	architectural	architectural	JJ
37681	112	13	drawings	drawing	NNS
37681	112	14	were	be	VBD
37681	112	15	more	more	RBR
37681	112	16	exact	exact	JJ
37681	112	17	if	if	IN
37681	112	18	made	make	VBN
37681	112	19	with	with	IN
37681	112	20	a	a	DT
37681	112	21	single	single	JJ
37681	112	22	opening	opening	NN
37681	112	23	of	of	IN
37681	112	24	the	the	DT
37681	112	25	compasses	compass	NNS
37681	112	26	,	,	,
37681	112	27	and	and	CC
37681	112	28	it	-PRON-	PRP
37681	112	29	is	be	VBZ
37681	112	30	probable	probable	JJ
37681	112	31	that	that	IN
37681	112	32	their	-PRON-	PRP$
37681	112	33	influence	influence	NN
37681	112	34	led	lead	VBD
37681	112	35	to	to	IN
37681	112	36	the	the	DT
37681	112	37	development	development	NN
37681	112	38	of	of	IN
37681	112	39	this	this	DT
37681	112	40	phase	phase	NN
37681	112	41	of	of	IN
37681	112	42	geometry	geometry	NN
37681	112	43	in	in	IN
37681	112	44	the	the	DT
37681	112	45	Middle	Middle	NNP
37681	112	46	Ages	Ages	NNP
37681	112	47	as	as	IN
37681	112	48	a	a	DT
37681	112	49	practical	practical	JJ
37681	112	50	application	application	NN
37681	112	51	of	of	IN
37681	112	52	the	the	DT
37681	112	53	science	science	NN
37681	112	54	.	.	.
37681	113	1	Later	later	RB
37681	113	2	,	,	,
37681	113	3	and	and	CC
37681	113	4	about	about	IN
37681	113	5	the	the	DT
37681	113	6	beginning	beginning	NN
37681	113	7	of	of	IN
37681	113	8	the	the	DT
37681	113	9	sixteenth	sixteenth	JJ
37681	113	10	century	century	NN
37681	113	11	,	,	,
37681	113	12	the	the	DT
37681	113	13	revival	revival	NN
37681	113	14	of	of	IN
37681	113	15	art	art	NN
37681	113	16	,	,	,
37681	113	17	and	and	CC
37681	113	18	particularly	particularly	RB
37681	113	19	the	the	DT
37681	113	20	great	great	JJ
37681	113	21	development	development	NN
37681	113	22	of	of	IN
37681	113	23	painting	painting	NN
37681	113	24	,	,	,
37681	113	25	led	lead	VBD
37681	113	26	to	to	IN
37681	113	27	the	the	DT
37681	113	28	practical	practical	JJ
37681	113	29	application	application	NN
37681	113	30	of	of	IN
37681	113	31	geometry	geometry	NN
37681	113	32	to	to	IN
37681	113	33	the	the	DT
37681	113	34	study	study	NN
37681	113	35	of	of	IN
37681	113	36	perspective	perspective	NN
37681	113	37	and	and	CC
37681	113	38	of	of	IN
37681	113	39	those	those	DT
37681	113	40	curves[6	curves[6	FW
37681	113	41	]	]	-RRB-
37681	113	42	that	that	WDT
37681	113	43	occur	occur	VBP
37681	113	44	most	most	RBS
37681	113	45	frequently	frequently	RB
37681	113	46	in	in	IN
37681	113	47	the	the	DT
37681	113	48	graphic	graphic	JJ
37681	113	49	arts	art	NNS
37681	113	50	.	.	.
37681	114	1	The	the	DT
37681	114	2	sixteenth	sixteenth	JJ
37681	114	3	and	and	CC
37681	114	4	seventeenth	seventeenth	JJ
37681	114	5	centuries	century	NNS
37681	114	6	witnessed	witness	VBD
37681	114	7	the	the	DT
37681	114	8	publication	publication	NN
37681	114	9	of	of	IN
37681	114	10	a	a	DT
37681	114	11	large	large	JJ
37681	114	12	number	number	NN
37681	114	13	of	of	IN
37681	114	14	treatises	treatise	NNS
37681	114	15	on	on	IN
37681	114	16	practical	practical	JJ
37681	114	17	geometry	geometry	NN
37681	114	18	,	,	,
37681	114	19	usually	usually	RB
37681	114	20	relating	relate	VBG
37681	114	21	to	to	IN
37681	114	22	the	the	DT
37681	114	23	measuring	measuring	NN
37681	114	24	of	of	IN
37681	114	25	distances	distance	NNS
37681	114	26	and	and	CC
37681	114	27	partly	partly	RB
37681	114	28	answering	answer	VBG
37681	114	29	the	the	DT
37681	114	30	purposes	purpose	NNS
37681	114	31	of	of	IN
37681	114	32	our	-PRON-	PRP$
37681	114	33	present	present	JJ
37681	114	34	trigonometry	trigonometry	NN
37681	114	35	.	.	.
37681	115	1	Such	such	JJ
37681	115	2	were	be	VBD
37681	115	3	the	the	DT
37681	115	4	well	well	RB
37681	115	5	-	-	HYPH
37681	115	6	known	know	VBN
37681	115	7	treatises	treatise	NNS
37681	115	8	of	of	IN
37681	115	9	Belli	Belli	NNP
37681	115	10	(	(	-LRB-
37681	115	11	1569	1569	CD
37681	115	12	)	)	-RRB-
37681	115	13	,	,	,
37681	115	14	Cataneo	Cataneo	NNP
37681	115	15	(	(	-LRB-
37681	115	16	1567	1567	CD
37681	115	17	)	)	-RRB-
37681	115	18	,	,	,
37681	115	19	and	and	CC
37681	115	20	Bartoli	Bartoli	NNP
37681	115	21	(	(	-LRB-
37681	115	22	1589	1589	CD
37681	115	23	)	)	-RRB-
37681	115	24	.	.	.
37681	116	1	[	[	-LRB-
37681	116	2	7	7	LS
37681	116	3	]	]	-RRB-
37681	116	4	The	the	DT
37681	116	5	period	period	NN
37681	116	6	of	of	IN
37681	116	7	two	two	CD
37681	116	8	centuries	century	NNS
37681	116	9	from	from	IN
37681	116	10	about	about	RB
37681	116	11	1600	1600	CD
37681	116	12	to	to	IN
37681	116	13	about	about	IN
37681	116	14	1800	1800	CD
37681	116	15	was	be	VBD
37681	116	16	quite	quite	RB
37681	116	17	as	as	RB
37681	116	18	much	much	JJ
37681	116	19	given	give	VBN
37681	116	20	to	to	IN
37681	116	21	experiments	experiment	NNS
37681	116	22	in	in	IN
37681	116	23	the	the	DT
37681	116	24	creation	creation	NN
37681	116	25	of	of	IN
37681	116	26	a	a	DT
37681	116	27	practical	practical	JJ
37681	116	28	geometry	geometry	NN
37681	116	29	as	as	IN
37681	116	30	is	be	VBZ
37681	116	31	the	the	DT
37681	116	32	present	present	JJ
37681	116	33	time	time	NN
37681	116	34	,	,	,
37681	116	35	and	and	CC
37681	116	36	it	-PRON-	PRP
37681	116	37	was	be	VBD
37681	116	38	no	no	DT
37681	116	39	doubt	doubt	NN
37681	116	40	as	as	RB
37681	116	41	much	much	JJ
37681	116	42	by	by	IN
37681	116	43	way	way	NN
37681	116	44	of	of	IN
37681	116	45	protest	protest	NN
37681	116	46	against	against	IN
37681	116	47	this	this	DT
37681	116	48	false	false	JJ
37681	116	49	idea	idea	NN
37681	116	50	of	of	IN
37681	116	51	the	the	DT
37681	116	52	subject	subject	NN
37681	116	53	as	as	IN
37681	116	54	a	a	DT
37681	116	55	desire	desire	NN
37681	116	56	to	to	TO
37681	116	57	improve	improve	VB
37681	116	58	upon	upon	IN
37681	116	59	Euclid	Euclid	NNP
37681	116	60	that	that	WDT
37681	116	61	led	lead	VBD
37681	116	62	the	the	DT
37681	116	63	great	great	JJ
37681	116	64	French	french	JJ
37681	116	65	mathematician	mathematician	NN
37681	116	66	,	,	,
37681	116	67	Legendre	Legendre	NNP
37681	116	68	,	,	,
37681	116	69	to	to	TO
37681	116	70	publish	publish	VB
37681	116	71	his	-PRON-	PRP$
37681	116	72	geometry	geometry	NN
37681	116	73	in	in	IN
37681	116	74	1794,--a	1794,--a	NN
37681	116	75	work	work	NN
37681	116	76	that	that	WDT
37681	116	77	soon	soon	RB
37681	116	78	replaced	replace	VBD
37681	116	79	Euclid	Euclid	NNP
37681	116	80	in	in	IN
37681	116	81	the	the	DT
37681	116	82	schools	school	NNS
37681	116	83	of	of	IN
37681	116	84	America	America	NNP
37681	116	85	.	.	.
37681	117	1	It	-PRON-	PRP
37681	117	2	thus	thus	RB
37681	117	3	appears	appear	VBZ
37681	117	4	that	that	IN
37681	117	5	the	the	DT
37681	117	6	effort	effort	NN
37681	117	7	to	to	TO
37681	117	8	make	make	VB
37681	117	9	geometry	geometry	NN
37681	117	10	practical	practical	JJ
37681	117	11	is	be	VBZ
37681	117	12	by	by	IN
37681	117	13	no	no	DT
37681	117	14	means	means	NN
37681	117	15	new	new	JJ
37681	117	16	.	.	.
37681	118	1	Euclid	Euclid	NNP
37681	118	2	knew	know	VBD
37681	118	3	of	of	IN
37681	118	4	it	-PRON-	PRP
37681	118	5	,	,	,
37681	118	6	the	the	DT
37681	118	7	Middle	Middle	NNP
37681	118	8	Ages	Ages	NNPS
37681	118	9	contributed	contribute	VBD
37681	118	10	to	to	IN
37681	118	11	it	-PRON-	PRP
37681	118	12	,	,	,
37681	118	13	that	that	DT
37681	118	14	period	period	NN
37681	118	15	vaguely	vaguely	RB
37681	118	16	styled	style	VBD
37681	118	17	the	the	DT
37681	118	18	Renaissance	Renaissance	NNP
37681	118	19	joined	join	VBN
37681	118	20	in	in	IN
37681	118	21	the	the	DT
37681	118	22	movement	movement	NN
37681	118	23	,	,	,
37681	118	24	and	and	CC
37681	118	25	the	the	DT
37681	118	26	first	first	JJ
37681	118	27	three	three	CD
37681	118	28	centuries	century	NNS
37681	118	29	of	of	IN
37681	118	30	printing	printing	NN
37681	118	31	contributed	contribute	VBD
37681	118	32	a	a	DT
37681	118	33	large	large	JJ
37681	118	34	literature	literature	NN
37681	118	35	to	to	IN
37681	118	36	the	the	DT
37681	118	37	subject	subject	NN
37681	118	38	.	.	.
37681	119	1	Out	out	IN
37681	119	2	of	of	IN
37681	119	3	all	all	PDT
37681	119	4	this	this	DT
37681	119	5	effort	effort	NN
37681	119	6	some	some	DT
37681	119	7	genuine	genuine	JJ
37681	119	8	good	good	JJ
37681	119	9	remains	remain	NNS
37681	119	10	,	,	,
37681	119	11	but	but	CC
37681	119	12	relatively	relatively	RB
37681	119	13	not	not	RB
37681	119	14	very	very	RB
37681	119	15	much	much	RB
37681	119	16	.	.	.
37681	120	1	[	[	-LRB-
37681	120	2	8	8	CD
37681	120	3	]	]	-RRB-
37681	120	4	And	and	CC
37681	120	5	so	so	RB
37681	120	6	it	-PRON-	PRP
37681	120	7	will	will	MD
37681	120	8	be	be	VB
37681	120	9	with	with	IN
37681	120	10	the	the	DT
37681	120	11	present	present	JJ
37681	120	12	movement	movement	NN
37681	120	13	;	;	:
37681	120	14	it	-PRON-	PRP
37681	120	15	will	will	MD
37681	120	16	serve	serve	VB
37681	120	17	its	-PRON-	PRP$
37681	120	18	greatest	great	JJS
37681	120	19	purpose	purpose	NN
37681	120	20	in	in	IN
37681	120	21	making	make	VBG
37681	120	22	teachers	teacher	NNS
37681	120	23	think	think	VB
37681	120	24	and	and	CC
37681	120	25	read	read	VBP
37681	120	26	,	,	,
37681	120	27	and	and	CC
37681	120	28	in	in	IN
37681	120	29	adding	add	VBG
37681	120	30	to	to	IN
37681	120	31	their	-PRON-	PRP$
37681	120	32	interest	interest	NN
37681	120	33	and	and	CC
37681	120	34	enthusiasm	enthusiasm	NN
37681	120	35	and	and	CC
37681	120	36	to	to	IN
37681	120	37	the	the	DT
37681	120	38	interest	interest	NN
37681	120	39	of	of	IN
37681	120	40	their	-PRON-	PRP$
37681	120	41	pupils	pupil	NNS
37681	120	42	;	;	:
37681	120	43	but	but	CC
37681	120	44	it	-PRON-	PRP
37681	120	45	will	will	MD
37681	120	46	not	not	RB
37681	120	47	greatly	greatly	RB
37681	120	48	change	change	VB
37681	120	49	geometry	geometry	NN
37681	120	50	,	,	,
37681	120	51	because	because	IN
37681	120	52	no	no	DT
37681	120	53	serious	serious	JJ
37681	120	54	person	person	NN
37681	120	55	ever	ever	RB
37681	120	56	believed	believe	VBD
37681	120	57	that	that	IN
37681	120	58	geometry	geometry	NN
37681	120	59	was	be	VBD
37681	120	60	taught	teach	VBN
37681	120	61	chiefly	chiefly	RB
37681	120	62	for	for	IN
37681	120	63	practical	practical	JJ
37681	120	64	purposes	purpose	NNS
37681	120	65	,	,	,
37681	120	66	or	or	CC
37681	120	67	was	be	VBD
37681	120	68	made	make	VBN
37681	120	69	more	more	RBR
37681	120	70	interesting	interesting	JJ
37681	120	71	or	or	CC
37681	120	72	valuable	valuable	JJ
37681	120	73	through	through	IN
37681	120	74	such	such	PDT
37681	120	75	a	a	DT
37681	120	76	pretense	pretense	NN
37681	120	77	.	.	.
37681	121	1	Changes	change	NNS
37681	121	2	in	in	IN
37681	121	3	sequence	sequence	NN
37681	121	4	,	,	,
37681	121	5	in	in	IN
37681	121	6	definitions	definition	NNS
37681	121	7	,	,	,
37681	121	8	and	and	CC
37681	121	9	in	in	IN
37681	121	10	proofs	proofs	NNP
37681	121	11	will	will	MD
37681	121	12	come	come	VB
37681	121	13	little	little	JJ
37681	121	14	by	by	IN
37681	121	15	little	little	JJ
37681	121	16	;	;	:
37681	121	17	but	but	CC
37681	121	18	that	that	IN
37681	121	19	there	there	EX
37681	121	20	will	will	MD
37681	121	21	be	be	VB
37681	121	22	any	any	DT
37681	121	23	such	such	JJ
37681	121	24	radical	radical	JJ
37681	121	25	change	change	NN
37681	121	26	in	in	IN
37681	121	27	these	these	DT
37681	121	28	matters	matter	NNS
37681	121	29	in	in	IN
37681	121	30	the	the	DT
37681	121	31	immediate	immediate	JJ
37681	121	32	future	future	NN
37681	121	33	,	,	,
37681	121	34	as	as	IN
37681	121	35	some	some	DT
37681	121	36	writers	writer	NNS
37681	121	37	have	have	VBP
37681	121	38	anticipated	anticipate	VBN
37681	121	39	,	,	,
37681	121	40	is	be	VBZ
37681	121	41	not	not	RB
37681	121	42	probable	probable	JJ
37681	121	43	.	.	.
37681	122	1	[	[	-LRB-
37681	122	2	9	9	CD
37681	122	3	]	]	-RRB-
37681	122	4	A	a	DT
37681	122	5	recent	recent	JJ
37681	122	6	writer	writer	NN
37681	122	7	of	of	IN
37681	122	8	much	much	JJ
37681	122	9	acumen[10	acumen[10	NN
37681	122	10	]	]	-RRB-
37681	122	11	has	have	VBZ
37681	122	12	summed	sum	VBN
37681	122	13	up	up	RP
37681	122	14	this	this	DT
37681	122	15	thought	thought	NN
37681	122	16	in	in	IN
37681	122	17	these	these	DT
37681	122	18	words	word	NNS
37681	122	19	:	:	:
37681	122	20	Not	not	RB
37681	122	21	one	one	CD
37681	122	22	tenth	tenth	NN
37681	122	23	of	of	IN
37681	122	24	the	the	DT
37681	122	25	graduates	graduate	NNS
37681	122	26	of	of	IN
37681	122	27	our	-PRON-	PRP$
37681	122	28	high	high	JJ
37681	122	29	schools	school	NNS
37681	122	30	ever	ever	RB
37681	122	31	enter	enter	VBP
37681	122	32	professions	profession	NNS
37681	122	33	in	in	IN
37681	122	34	which	which	WDT
37681	122	35	their	-PRON-	PRP$
37681	122	36	algebra	algebra	NN
37681	122	37	and	and	CC
37681	122	38	geometry	geometry	NN
37681	122	39	are	be	VBP
37681	122	40	applied	apply	VBN
37681	122	41	to	to	IN
37681	122	42	concrete	concrete	JJ
37681	122	43	realities	reality	NNS
37681	122	44	;	;	:
37681	122	45	not	not	RB
37681	122	46	one	one	CD
37681	122	47	day	day	NN
37681	122	48	in	in	IN
37681	122	49	three	three	CD
37681	122	50	hundred	hundred	CD
37681	122	51	sixty	sixty	CD
37681	122	52	-	-	HYPH
37681	122	53	five	five	CD
37681	122	54	is	be	VBZ
37681	122	55	a	a	DT
37681	122	56	high	high	JJ
37681	122	57	school	school	NN
37681	122	58	graduate	graduate	NN
37681	122	59	called	call	VBN
37681	122	60	upon	upon	IN
37681	122	61	to	to	TO
37681	122	62	"	"	``
37681	122	63	apply	apply	VB
37681	122	64	,	,	,
37681	122	65	"	"	''
37681	122	66	as	as	IN
37681	122	67	it	-PRON-	PRP
37681	122	68	is	be	VBZ
37681	122	69	called	call	VBN
37681	122	70	,	,	,
37681	122	71	an	an	DT
37681	122	72	algebraic	algebraic	NN
37681	122	73	or	or	CC
37681	122	74	a	a	DT
37681	122	75	geometrical	geometrical	JJ
37681	122	76	proposition	proposition	NN
37681	122	77	....	....	.
37681	122	78	Why	why	WRB
37681	122	79	,	,	,
37681	122	80	then	then	RB
37681	122	81	,	,	,
37681	122	82	do	do	VBP
37681	122	83	we	-PRON-	PRP
37681	122	84	teach	teach	VB
37681	122	85	these	these	DT
37681	122	86	subjects	subject	NNS
37681	122	87	,	,	,
37681	122	88	if	if	IN
37681	122	89	this	this	DT
37681	122	90	alone	alone	RB
37681	122	91	is	be	VBZ
37681	122	92	the	the	DT
37681	122	93	sense	sense	NN
37681	122	94	of	of	IN
37681	122	95	the	the	DT
37681	122	96	word	word	NN
37681	122	97	"	"	``
37681	122	98	practical	practical	JJ
37681	122	99	"	"	''
37681	122	100	!	!	.
37681	122	101	...	...	.
37681	123	1	To	to	IN
37681	123	2	me	-PRON-	PRP
37681	123	3	the	the	DT
37681	123	4	solution	solution	NN
37681	123	5	of	of	IN
37681	123	6	this	this	DT
37681	123	7	paradox	paradox	NN
37681	123	8	consists	consist	VBZ
37681	123	9	in	in	IN
37681	123	10	boldly	boldly	RB
37681	123	11	confronting	confront	VBG
37681	123	12	the	the	DT
37681	123	13	dilemma	dilemma	NN
37681	123	14	,	,	,
37681	123	15	and	and	CC
37681	123	16	in	in	IN
37681	123	17	saying	say	VBG
37681	123	18	that	that	IN
37681	123	19	our	-PRON-	PRP$
37681	123	20	conception	conception	NN
37681	123	21	of	of	IN
37681	123	22	the	the	DT
37681	123	23	practical	practical	JJ
37681	123	24	utility	utility	NN
37681	123	25	of	of	IN
37681	123	26	those	those	DT
37681	123	27	studies	study	NNS
37681	123	28	must	must	MD
37681	123	29	be	be	VB
37681	123	30	readjusted	readjust	VBN
37681	123	31	,	,	,
37681	123	32	and	and	CC
37681	123	33	that	that	IN
37681	123	34	we	-PRON-	PRP
37681	123	35	have	have	VBP
37681	123	36	frankly	frankly	RB
37681	123	37	to	to	TO
37681	123	38	face	face	VB
37681	123	39	the	the	DT
37681	123	40	truth	truth	NN
37681	123	41	that	that	WDT
37681	123	42	the	the	DT
37681	123	43	"	"	``
37681	123	44	practical	practical	JJ
37681	123	45	"	"	''
37681	123	46	ends	end	VBZ
37681	123	47	we	-PRON-	PRP
37681	123	48	seek	seek	VBP
37681	123	49	are	be	VBP
37681	123	50	in	in	IN
37681	123	51	a	a	DT
37681	123	52	sense	sense	NN
37681	123	53	_	_	NNP
37681	123	54	ideal	ideal	JJ
37681	123	55	_	_	NNP
37681	123	56	practical	practical	JJ
37681	123	57	ends	end	NNS
37681	123	58	,	,	,
37681	123	59	yet	yet	CC
37681	123	60	such	such	JJ
37681	123	61	as	as	IN
37681	123	62	have	have	VBP
37681	123	63	,	,	,
37681	123	64	after	after	RB
37681	123	65	all	all	RB
37681	123	66	,	,	,
37681	123	67	an	an	DT
37681	123	68	eminently	eminently	RB
37681	123	69	utilitarian	utilitarian	JJ
37681	123	70	value	value	NN
37681	123	71	in	in	IN
37681	123	72	the	the	DT
37681	123	73	intellectual	intellectual	JJ
37681	123	74	sphere	sphere	NN
37681	123	75	.	.	.
37681	124	1	He	-PRON-	PRP
37681	124	2	quotes	quote	VBZ
37681	124	3	from	from	IN
37681	124	4	C.	C.	NNP
37681	124	5	S.	S.	NNP
37681	124	6	Jackson	Jackson	NNP
37681	124	7	,	,	,
37681	124	8	a	a	DT
37681	124	9	progressive	progressive	JJ
37681	124	10	contemporary	contemporary	JJ
37681	124	11	teacher	teacher	NN
37681	124	12	of	of	IN
37681	124	13	mechanics	mechanic	NNS
37681	124	14	in	in	IN
37681	124	15	England	England	NNP
37681	124	16	,	,	,
37681	124	17	who	who	WP
37681	124	18	speaks	speak	VBZ
37681	124	19	of	of	IN
37681	124	20	pupils	pupil	NNS
37681	124	21	confusing	confuse	VBG
37681	124	22	millimeters	millimeter	NNS
37681	124	23	and	and	CC
37681	124	24	centimeters	centimeter	NNS
37681	124	25	in	in	IN
37681	124	26	some	some	DT
37681	124	27	simple	simple	JJ
37681	124	28	computation	computation	NN
37681	124	29	,	,	,
37681	124	30	and	and	CC
37681	124	31	who	who	WP
37681	124	32	adds	add	VBZ
37681	124	33	:	:	:
37681	124	34	There	there	EX
37681	124	35	is	be	VBZ
37681	124	36	the	the	DT
37681	124	37	enemy	enemy	NN
37681	124	38	!	!	.
37681	125	1	The	the	DT
37681	125	2	real	real	JJ
37681	125	3	enemy	enemy	NN
37681	125	4	we	-PRON-	PRP
37681	125	5	have	have	VBP
37681	125	6	to	to	TO
37681	125	7	fight	fight	VB
37681	125	8	against	against	IN
37681	125	9	,	,	,
37681	125	10	whatever	whatever	WDT
37681	125	11	we	-PRON-	PRP
37681	125	12	teach	teach	VBP
37681	125	13	,	,	,
37681	125	14	is	be	VBZ
37681	125	15	carelessness	carelessness	NN
37681	125	16	,	,	,
37681	125	17	inaccuracy	inaccuracy	NN
37681	125	18	,	,	,
37681	125	19	forgetfulness	forgetfulness	NN
37681	125	20	,	,	,
37681	125	21	and	and	CC
37681	125	22	slovenliness	slovenliness	NN
37681	125	23	.	.	.
37681	126	1	That	that	DT
37681	126	2	battle	battle	NN
37681	126	3	has	have	VBZ
37681	126	4	been	be	VBN
37681	126	5	fought	fight	VBN
37681	126	6	and	and	CC
37681	126	7	won	win	VBN
37681	126	8	with	with	IN
37681	126	9	diverse	diverse	JJ
37681	126	10	weapons	weapon	NNS
37681	126	11	.	.	.
37681	127	1	It	-PRON-	PRP
37681	127	2	has	have	VBZ
37681	127	3	,	,	,
37681	127	4	for	for	IN
37681	127	5	instance	instance	NN
37681	127	6	,	,	,
37681	127	7	been	be	VBN
37681	127	8	fought	fight	VBN
37681	127	9	with	with	IN
37681	127	10	Latin	Latin	NNP
37681	127	11	grammar	grammar	NN
37681	127	12	before	before	RB
37681	127	13	now	now	RB
37681	127	14	,	,	,
37681	127	15	and	and	CC
37681	127	16	won	win	VBD
37681	127	17	.	.	.
37681	128	1	I	-PRON-	PRP
37681	128	2	say	say	VBP
37681	128	3	that	that	IN
37681	128	4	because	because	IN
37681	128	5	we	-PRON-	PRP
37681	128	6	must	must	MD
37681	128	7	be	be	VB
37681	128	8	very	very	RB
37681	128	9	careful	careful	JJ
37681	128	10	to	to	TO
37681	128	11	guard	guard	VB
37681	128	12	against	against	IN
37681	128	13	the	the	DT
37681	128	14	notion	notion	NN
37681	128	15	that	that	IN
37681	128	16	there	there	EX
37681	128	17	is	be	VBZ
37681	128	18	any	any	DT
37681	128	19	one	one	CD
37681	128	20	panacea	panacea	NN
37681	128	21	for	for	IN
37681	128	22	this	this	DT
37681	128	23	sort	sort	NN
37681	128	24	of	of	IN
37681	128	25	thing	thing	NN
37681	128	26	.	.	.
37681	129	1	It	-PRON-	PRP
37681	129	2	borders	border	VBZ
37681	129	3	on	on	IN
37681	129	4	quackery	quackery	NN
37681	129	5	to	to	TO
37681	129	6	say	say	VB
37681	129	7	that	that	IN
37681	129	8	elementary	elementary	JJ
37681	129	9	physics	physics	NN
37681	129	10	will	will	MD
37681	129	11	cure	cure	VB
37681	129	12	everything	everything	NN
37681	129	13	.	.	.
37681	130	1	And	and	CC
37681	130	2	of	of	IN
37681	130	3	course	course	NN
37681	130	4	the	the	DT
37681	130	5	same	same	JJ
37681	130	6	thing	thing	NN
37681	130	7	may	may	MD
37681	130	8	be	be	VB
37681	130	9	said	say	VBN
37681	130	10	for	for	IN
37681	130	11	mathematics	mathematic	NNS
37681	130	12	.	.	.
37681	131	1	Nevertheless	nevertheless	RB
37681	131	2	it	-PRON-	PRP
37681	131	3	is	be	VBZ
37681	131	4	doubtful	doubtful	JJ
37681	131	5	if	if	IN
37681	131	6	we	-PRON-	PRP
37681	131	7	have	have	VBP
37681	131	8	any	any	DT
37681	131	9	other	other	JJ
37681	131	10	subject	subject	NN
37681	131	11	that	that	WDT
37681	131	12	does	do	VBZ
37681	131	13	so	so	RB
37681	131	14	much	much	RB
37681	131	15	to	to	TO
37681	131	16	bring	bring	VB
37681	131	17	to	to	IN
37681	131	18	the	the	DT
37681	131	19	front	front	NN
37681	131	20	this	this	DT
37681	131	21	danger	danger	NN
37681	131	22	of	of	IN
37681	131	23	carelessness	carelessness	NN
37681	131	24	,	,	,
37681	131	25	of	of	IN
37681	131	26	slovenly	slovenly	JJ
37681	131	27	reasoning	reasoning	NN
37681	131	28	,	,	,
37681	131	29	of	of	IN
37681	131	30	inaccuracy	inaccuracy	NN
37681	131	31	,	,	,
37681	131	32	and	and	CC
37681	131	33	of	of	IN
37681	131	34	forgetfulness	forgetfulness	NN
37681	131	35	as	as	IN
37681	131	36	this	this	DT
37681	131	37	science	science	NN
37681	131	38	of	of	IN
37681	131	39	geometry	geometry	NN
37681	131	40	,	,	,
37681	131	41	which	which	WDT
37681	131	42	has	have	VBZ
37681	131	43	been	be	VBN
37681	131	44	so	so	RB
37681	131	45	polished	polished	JJ
37681	131	46	and	and	CC
37681	131	47	perfected	perfect	VBD
37681	131	48	as	as	IN
37681	131	49	the	the	DT
37681	131	50	centuries	century	NNS
37681	131	51	have	have	VBP
37681	131	52	gone	go	VBN
37681	131	53	on	on	RP
37681	131	54	.	.	.
37681	132	1	There	there	EX
37681	132	2	have	have	VBP
37681	132	3	been	be	VBN
37681	132	4	those	those	DT
37681	132	5	who	who	WP
37681	132	6	did	do	VBD
37681	132	7	not	not	RB
37681	132	8	proclaim	proclaim	VB
37681	132	9	the	the	DT
37681	132	10	utilitarian	utilitarian	JJ
37681	132	11	value	value	NN
37681	132	12	of	of	IN
37681	132	13	geometry	geometry	NN
37681	132	14	,	,	,
37681	132	15	but	but	CC
37681	132	16	who	who	WP
37681	132	17	fell	fall	VBD
37681	132	18	into	into	IN
37681	132	19	as	as	RB
37681	132	20	serious	serious	JJ
37681	132	21	an	an	DT
37681	132	22	error	error	NN
37681	132	23	,	,	,
37681	132	24	namely	namely	RB
37681	132	25	,	,	,
37681	132	26	the	the	DT
37681	132	27	advocating	advocating	NN
37681	132	28	of	of	IN
37681	132	29	geometry	geometry	NN
37681	132	30	as	as	IN
37681	132	31	a	a	DT
37681	132	32	means	means	NN
37681	132	33	of	of	IN
37681	132	34	training	train	VBG
37681	132	35	the	the	DT
37681	132	36	memory	memory	NN
37681	132	37	.	.	.
37681	133	1	In	in	IN
37681	133	2	times	time	NNS
37681	133	3	not	not	RB
37681	133	4	so	so	RB
37681	133	5	very	very	RB
37681	133	6	far	far	RB
37681	133	7	past	past	JJ
37681	133	8	,	,	,
37681	133	9	and	and	CC
37681	133	10	to	to	IN
37681	133	11	some	some	DT
37681	133	12	extent	extent	NN
37681	133	13	to	to	IN
37681	133	14	-	-	HYPH
37681	133	15	day	day	NN
37681	133	16	,	,	,
37681	133	17	the	the	DT
37681	133	18	memorizing	memorizing	NN
37681	133	19	of	of	IN
37681	133	20	proofs	proofs	NNP
37681	133	21	has	have	VBZ
37681	133	22	been	be	VBN
37681	133	23	justified	justify	VBN
37681	133	24	on	on	IN
37681	133	25	this	this	DT
37681	133	26	ground	ground	NN
37681	133	27	.	.	.
37681	134	1	This	this	DT
37681	134	2	error	error	NN
37681	134	3	has	have	VBZ
37681	134	4	,	,	,
37681	134	5	however	however	RB
37681	134	6	,	,	,
37681	134	7	been	be	VBN
37681	134	8	fully	fully	RB
37681	134	9	exposed	expose	VBN
37681	134	10	by	by	IN
37681	134	11	our	-PRON-	PRP$
37681	134	12	modern	modern	JJ
37681	134	13	psychologists	psychologist	NNS
37681	134	14	.	.	.
37681	135	1	They	-PRON-	PRP
37681	135	2	have	have	VBP
37681	135	3	shown	show	VBN
37681	135	4	that	that	IN
37681	135	5	the	the	DT
37681	135	6	person	person	NN
37681	135	7	who	who	WP
37681	135	8	memorizes	memorize	VBZ
37681	135	9	the	the	DT
37681	135	10	propositions	proposition	NNS
37681	135	11	of	of	IN
37681	135	12	Euclid	Euclid	NNP
37681	135	13	by	by	IN
37681	135	14	number	number	NN
37681	135	15	is	be	VBZ
37681	135	16	no	no	DT
37681	135	17	more	more	RBR
37681	135	18	capable	capable	JJ
37681	135	19	of	of	IN
37681	135	20	memorizing	memorize	VBG
37681	135	21	other	other	JJ
37681	135	22	facts	fact	NNS
37681	135	23	than	than	IN
37681	135	24	he	-PRON-	PRP
37681	135	25	was	be	VBD
37681	135	26	before	before	RB
37681	135	27	,	,	,
37681	135	28	and	and	CC
37681	135	29	that	that	IN
37681	135	30	the	the	DT
37681	135	31	learning	learning	NN
37681	135	32	of	of	IN
37681	135	33	proofs	proofs	NNP
37681	135	34	verbatim	verbatim	NNP
37681	135	35	is	be	VBZ
37681	135	36	of	of	IN
37681	135	37	no	no	DT
37681	135	38	assistance	assistance	NN
37681	135	39	whatever	whatever	WDT
37681	135	40	in	in	IN
37681	135	41	retaining	retain	VBG
37681	135	42	matter	matter	NN
37681	135	43	that	that	WDT
37681	135	44	is	be	VBZ
37681	135	45	helpful	helpful	JJ
37681	135	46	in	in	IN
37681	135	47	other	other	JJ
37681	135	48	lines	line	NNS
37681	135	49	of	of	IN
37681	135	50	work	work	NN
37681	135	51	.	.	.
37681	136	1	Geometry	geometry	NN
37681	136	2	,	,	,
37681	136	3	therefore	therefore	RB
37681	136	4	,	,	,
37681	136	5	as	as	IN
37681	136	6	a	a	DT
37681	136	7	training	training	NN
37681	136	8	of	of	IN
37681	136	9	the	the	DT
37681	136	10	memory	memory	NN
37681	136	11	is	be	VBZ
37681	136	12	of	of	IN
37681	136	13	no	no	DT
37681	136	14	more	more	JJR
37681	136	15	value	value	NN
37681	136	16	than	than	IN
37681	136	17	any	any	DT
37681	136	18	other	other	JJ
37681	136	19	subject	subject	NN
37681	136	20	in	in	IN
37681	136	21	the	the	DT
37681	136	22	curriculum	curriculum	NN
37681	136	23	.	.	.
37681	137	1	If	if	IN
37681	137	2	geometry	geometry	NN
37681	137	3	is	be	VBZ
37681	137	4	not	not	RB
37681	137	5	studied	study	VBN
37681	137	6	chiefly	chiefly	RB
37681	137	7	because	because	IN
37681	137	8	it	-PRON-	PRP
37681	137	9	is	be	VBZ
37681	137	10	practical	practical	JJ
37681	137	11	,	,	,
37681	137	12	or	or	CC
37681	137	13	because	because	IN
37681	137	14	it	-PRON-	PRP
37681	137	15	trains	train	VBZ
37681	137	16	the	the	DT
37681	137	17	memory	memory	NN
37681	137	18	,	,	,
37681	137	19	what	what	WDT
37681	137	20	reasons	reason	NNS
37681	137	21	can	can	MD
37681	137	22	be	be	VB
37681	137	23	adduced	adduce	VBN
37681	137	24	for	for	IN
37681	137	25	its	-PRON-	PRP$
37681	137	26	presence	presence	NN
37681	137	27	in	in	IN
37681	137	28	the	the	DT
37681	137	29	courses	course	NNS
37681	137	30	of	of	IN
37681	137	31	study	study	NN
37681	137	32	of	of	IN
37681	137	33	every	every	DT
37681	137	34	civilized	civilized	JJ
37681	137	35	country	country	NN
37681	137	36	?	?	.
37681	138	1	Is	be	VBZ
37681	138	2	it	-PRON-	PRP
37681	138	3	not	not	RB
37681	138	4	,	,	,
37681	138	5	after	after	RB
37681	138	6	all	all	RB
37681	138	7	,	,	,
37681	138	8	a	a	DT
37681	138	9	mere	mere	JJ
37681	138	10	fetish	fetish	NN
37681	138	11	,	,	,
37681	138	12	and	and	CC
37681	138	13	are	be	VBP
37681	138	14	not	not	RB
37681	138	15	those	those	DT
37681	138	16	virulent	virulent	JJ
37681	138	17	writers	writer	NNS
37681	138	18	correct	correct	VB
37681	138	19	who	who	WP
37681	138	20	see	see	VBP
37681	138	21	nothing	nothing	NN
37681	138	22	good	good	JJ
37681	138	23	in	in	IN
37681	138	24	the	the	DT
37681	138	25	subject	subject	NN
37681	138	26	save	save	VB
37681	138	27	only	only	RB
37681	138	28	its	-PRON-	PRP$
37681	138	29	utilities	utility	NNS
37681	138	30	?	?	.
37681	139	1	[	[	-LRB-
37681	139	2	11	11	CD
37681	139	3	]	]	-RRB-
37681	139	4	Of	of	IN
37681	139	5	this	this	DT
37681	139	6	type	type	NN
37681	139	7	one	one	CD
37681	139	8	of	of	IN
37681	139	9	the	the	DT
37681	139	10	most	most	RBS
37681	139	11	entertaining	entertaining	JJ
37681	139	12	is	be	VBZ
37681	139	13	William	William	NNP
37681	139	14	J.	J.	NNP
37681	139	15	Locke,[12	Locke,[12	NNP
37681	139	16	]	]	-RRB-
37681	139	17	whose	whose	WP$
37681	139	18	words	word	NNS
37681	139	19	upon	upon	IN
37681	139	20	the	the	DT
37681	139	21	subject	subject	NN
37681	139	22	are	be	VBP
37681	139	23	well	well	RB
37681	139	24	worth	worth	JJ
37681	139	25	reading	reading	NN
37681	139	26	:	:	:
37681	139	27	...	...	.
37681	140	1	I	-PRON-	PRP
37681	140	2	earned	earn	VBD
37681	140	3	my	-PRON-	PRP$
37681	140	4	living	living	NN
37681	140	5	at	at	IN
37681	140	6	school	school	NN
37681	140	7	slavery	slavery	NN
37681	140	8	,	,	,
37681	140	9	teaching	teach	VBG
37681	140	10	to	to	IN
37681	140	11	children	child	NNS
37681	140	12	the	the	DT
37681	140	13	most	most	RBS
37681	140	14	useless	useless	JJ
37681	140	15	,	,	,
37681	140	16	the	the	DT
37681	140	17	most	most	RBS
37681	140	18	disastrous	disastrous	JJ
37681	140	19	,	,	,
37681	140	20	the	the	DT
37681	140	21	most	most	JJS
37681	140	22	soul	soul	NN
37681	140	23	-	-	HYPH
37681	140	24	cramping	cramp	VBG
37681	140	25	branch	branch	NN
37681	140	26	of	of	IN
37681	140	27	knowledge	knowledge	NN
37681	140	28	wherewith	wherewith	NN
37681	140	29	pedagogues	pedagogue	NNS
37681	140	30	in	in	IN
37681	140	31	their	-PRON-	PRP$
37681	140	32	insensate	insensate	NN
37681	140	33	folly	folly	NN
37681	140	34	have	have	VBP
37681	140	35	crippled	cripple	VBN
37681	140	36	the	the	DT
37681	140	37	minds	mind	NNS
37681	140	38	and	and	CC
37681	140	39	blasted	blast	VBD
37681	140	40	the	the	DT
37681	140	41	lives	life	NNS
37681	140	42	of	of	IN
37681	140	43	thousands	thousand	NNS
37681	140	44	of	of	IN
37681	140	45	their	-PRON-	PRP$
37681	140	46	fellow	fellow	JJ
37681	140	47	creatures	creature	NNS
37681	140	48	--	--	:
37681	140	49	elementary	elementary	JJ
37681	140	50	mathematics	mathematic	NNS
37681	140	51	.	.	.
37681	141	1	There	there	EX
37681	141	2	is	be	VBZ
37681	141	3	no	no	DT
37681	141	4	more	more	JJR
37681	141	5	reason	reason	NN
37681	141	6	for	for	IN
37681	141	7	any	any	DT
37681	141	8	human	human	JJ
37681	141	9	being	being	NN
37681	141	10	on	on	IN
37681	141	11	God	God	NNP
37681	141	12	's	's	POS
37681	141	13	earth	earth	NN
37681	141	14	to	to	TO
37681	141	15	be	be	VB
37681	141	16	acquainted	acquaint	VBN
37681	141	17	with	with	IN
37681	141	18	the	the	DT
37681	141	19	binomial	binomial	JJ
37681	141	20	theorem	theorem	NN
37681	141	21	or	or	CC
37681	141	22	the	the	DT
37681	141	23	solution	solution	NN
37681	141	24	of	of	IN
37681	141	25	triangles	triangle	NNS
37681	141	26	,	,	,
37681	141	27	unless	unless	IN
37681	141	28	he	-PRON-	PRP
37681	141	29	is	be	VBZ
37681	141	30	a	a	DT
37681	141	31	professional	professional	JJ
37681	141	32	scientist,--when	scientist,--when	.
37681	141	33	he	-PRON-	PRP
37681	141	34	can	can	MD
37681	141	35	begin	begin	VB
37681	141	36	to	to	TO
37681	141	37	specialize	specialize	VB
37681	141	38	in	in	IN
37681	141	39	mathematics	mathematic	NNS
37681	141	40	at	at	IN
37681	141	41	the	the	DT
37681	141	42	same	same	JJ
37681	141	43	age	age	NN
37681	141	44	as	as	IN
37681	141	45	the	the	DT
37681	141	46	lawyer	lawyer	NN
37681	141	47	begins	begin	VBZ
37681	141	48	to	to	TO
37681	141	49	specialize	specialize	VB
37681	141	50	in	in	IN
37681	141	51	law	law	NN
37681	141	52	or	or	CC
37681	141	53	the	the	DT
37681	141	54	surgeon	surgeon	NN
37681	141	55	in	in	IN
37681	141	56	anatomy,--than	anatomy,--than	NNP
37681	141	57	for	for	IN
37681	141	58	him	-PRON-	PRP
37681	141	59	to	to	TO
37681	141	60	be	be	VB
37681	141	61	expert	expert	JJ
37681	141	62	in	in	IN
37681	141	63	Choctaw	Choctaw	NNP
37681	141	64	,	,	,
37681	141	65	the	the	DT
37681	141	66	Cabala	Cabala	NNP
37681	141	67	,	,	,
37681	141	68	or	or	CC
37681	141	69	the	the	DT
37681	141	70	Book	Book	NNP
37681	141	71	of	of	IN
37681	141	72	Mormon	Mormon	NNP
37681	141	73	.	.	.
37681	142	1	I	-PRON-	PRP
37681	142	2	look	look	VBP
37681	142	3	back	back	RB
37681	142	4	with	with	IN
37681	142	5	feelings	feeling	NNS
37681	142	6	of	of	IN
37681	142	7	shame	shame	NN
37681	142	8	and	and	CC
37681	142	9	degradation	degradation	NN
37681	142	10	to	to	IN
37681	142	11	the	the	DT
37681	142	12	days	day	NNS
37681	142	13	when	when	WRB
37681	142	14	,	,	,
37681	142	15	for	for	IN
37681	142	16	a	a	DT
37681	142	17	crust	crust	NN
37681	142	18	of	of	IN
37681	142	19	bread	bread	NN
37681	142	20	,	,	,
37681	142	21	I	-PRON-	PRP
37681	142	22	prostituted	prostitute	VBD
37681	142	23	my	-PRON-	PRP$
37681	142	24	intelligence	intelligence	NN
37681	142	25	to	to	IN
37681	142	26	wasting	waste	VBG
37681	142	27	the	the	DT
37681	142	28	precious	precious	JJ
37681	142	29	hours	hour	NNS
37681	142	30	of	of	IN
37681	142	31	impressionable	impressionable	JJ
37681	142	32	childhood	childhood	NN
37681	142	33	,	,	,
37681	142	34	which	which	WDT
37681	142	35	could	could	MD
37681	142	36	have	have	VB
37681	142	37	been	be	VBN
37681	142	38	filled	fill	VBN
37681	142	39	with	with	IN
37681	142	40	so	so	RB
37681	142	41	many	many	JJ
37681	142	42	beautiful	beautiful	JJ
37681	142	43	and	and	CC
37681	142	44	meaningful	meaningful	JJ
37681	142	45	things	thing	NNS
37681	142	46	,	,	,
37681	142	47	over	over	IN
37681	142	48	this	this	DT
37681	142	49	utterly	utterly	RB
37681	142	50	futile	futile	JJ
37681	142	51	and	and	CC
37681	142	52	inhuman	inhuman	JJ
37681	142	53	subject	subject	NN
37681	142	54	.	.	.
37681	143	1	It	-PRON-	PRP
37681	143	2	trains	train	VBZ
37681	143	3	the	the	DT
37681	143	4	mind,--it	mind,--it	NNP
37681	143	5	teaches	teach	VBZ
37681	143	6	boys	boy	NNS
37681	143	7	to	to	TO
37681	143	8	think	think	VB
37681	143	9	,	,	,
37681	143	10	they	-PRON-	PRP
37681	143	11	say	say	VBP
37681	143	12	.	.	.
37681	144	1	It	-PRON-	PRP
37681	144	2	does	do	VBZ
37681	144	3	n't	not	RB
37681	144	4	.	.	.
37681	145	1	In	in	IN
37681	145	2	reality	reality	NN
37681	145	3	it	-PRON-	PRP
37681	145	4	is	be	VBZ
37681	145	5	a	a	DT
37681	145	6	cut	cut	VBN
37681	145	7	-	-	HYPH
37681	145	8	and	and	CC
37681	145	9	-	-	HYPH
37681	145	10	dried	dry	VBN
37681	145	11	subject	subject	JJ
37681	145	12	,	,	,
37681	145	13	easy	easy	JJ
37681	145	14	to	to	TO
37681	145	15	fit	fit	VB
37681	145	16	into	into	IN
37681	145	17	a	a	DT
37681	145	18	school	school	NN
37681	145	19	curriculum	curriculum	NN
37681	145	20	.	.	.
37681	146	1	Its	-PRON-	PRP$
37681	146	2	sacrosanctity	sacrosanctity	NN
37681	146	3	saves	save	VBZ
37681	146	4	educationalists	educationalist	VBZ
37681	146	5	an	an	DT
37681	146	6	enormous	enormous	JJ
37681	146	7	amount	amount	NN
37681	146	8	of	of	IN
37681	146	9	trouble	trouble	NN
37681	146	10	,	,	,
37681	146	11	and	and	CC
37681	146	12	its	-PRON-	PRP$
37681	146	13	chief	chief	JJ
37681	146	14	use	use	NN
37681	146	15	is	be	VBZ
37681	146	16	to	to	TO
37681	146	17	enable	enable	VB
37681	146	18	mindless	mindless	JJ
37681	146	19	young	young	JJ
37681	146	20	men	man	NNS
37681	146	21	from	from	IN
37681	146	22	the	the	DT
37681	146	23	universities	university	NNS
37681	146	24	to	to	TO
37681	146	25	make	make	VB
37681	146	26	a	a	DT
37681	146	27	dishonest	dishonest	JJ
37681	146	28	living	living	NN
37681	146	29	by	by	IN
37681	146	30	teaching	teach	VBG
37681	146	31	it	-PRON-	PRP
37681	146	32	to	to	IN
37681	146	33	others	other	NNS
37681	146	34	,	,	,
37681	146	35	who	who	WP
37681	146	36	in	in	IN
37681	146	37	their	-PRON-	PRP$
37681	146	38	turn	turn	NN
37681	146	39	may	may	MD
37681	146	40	teach	teach	VB
37681	146	41	it	-PRON-	PRP
37681	146	42	to	to	IN
37681	146	43	a	a	DT
37681	146	44	future	future	JJ
37681	146	45	generation	generation	NN
37681	146	46	.	.	.
37681	147	1	To	to	TO
37681	147	2	be	be	VB
37681	147	3	fair	fair	JJ
37681	147	4	we	-PRON-	PRP
37681	147	5	must	must	MD
37681	147	6	face	face	VB
37681	147	7	just	just	RB
37681	147	8	such	such	JJ
37681	147	9	attacks	attack	NNS
37681	147	10	,	,	,
37681	147	11	and	and	CC
37681	147	12	we	-PRON-	PRP
37681	147	13	must	must	MD
37681	147	14	recognize	recognize	VB
37681	147	15	that	that	IN
37681	147	16	they	-PRON-	PRP
37681	147	17	set	set	VBD
37681	147	18	forth	forth	RP
37681	147	19	the	the	DT
37681	147	20	feelings	feeling	NNS
37681	147	21	of	of	IN
37681	147	22	many	many	JJ
37681	147	23	honest	honest	JJ
37681	147	24	people	people	NNS
37681	147	25	.	.	.
37681	148	1	One	one	CD
37681	148	2	is	be	VBZ
37681	148	3	tempted	tempt	VBN
37681	148	4	to	to	TO
37681	148	5	inquire	inquire	VB
37681	148	6	if	if	IN
37681	148	7	Mr.	Mr.	NNP
37681	148	8	Locke	Locke	NNP
37681	148	9	could	could	MD
37681	148	10	have	have	VB
37681	148	11	written	write	VBN
37681	148	12	in	in	IN
37681	148	13	such	such	PDT
37681	148	14	an	an	DT
37681	148	15	incisive	incisive	JJ
37681	148	16	style	style	NN
37681	148	17	if	if	IN
37681	148	18	he	-PRON-	PRP
37681	148	19	had	have	VBD
37681	148	20	not	not	RB
37681	148	21	,	,	,
37681	148	22	as	as	IN
37681	148	23	was	be	VBD
37681	148	24	the	the	DT
37681	148	25	case	case	NN
37681	148	26	,	,	,
37681	148	27	graduated	graduate	VBD
37681	148	28	with	with	IN
37681	148	29	honors	honor	NNS
37681	148	30	in	in	IN
37681	148	31	mathematics	mathematic	NNS
37681	148	32	at	at	IN
37681	148	33	one	one	CD
37681	148	34	of	of	IN
37681	148	35	the	the	DT
37681	148	36	great	great	JJ
37681	148	37	universities	university	NNS
37681	148	38	.	.	.
37681	149	1	But	but	CC
37681	149	2	he	-PRON-	PRP
37681	149	3	might	may	MD
37681	149	4	reply	reply	VB
37681	149	5	that	that	IN
37681	149	6	if	if	IN
37681	149	7	his	-PRON-	PRP$
37681	149	8	mind	mind	NN
37681	149	9	had	have	VBD
37681	149	10	not	not	RB
37681	149	11	been	be	VBN
37681	149	12	warped	warp	VBN
37681	149	13	by	by	IN
37681	149	14	mathematics	mathematic	NNS
37681	149	15	,	,	,
37681	149	16	he	-PRON-	PRP
37681	149	17	would	would	MD
37681	149	18	have	have	VB
37681	149	19	written	write	VBN
37681	149	20	more	more	RBR
37681	149	21	temperately	temperately	RB
37681	149	22	,	,	,
37681	149	23	so	so	RB
37681	149	24	the	the	DT
37681	149	25	honors	honor	NNS
37681	149	26	in	in	IN
37681	149	27	the	the	DT
37681	149	28	argument	argument	NN
37681	149	29	would	would	MD
37681	149	30	be	be	VB
37681	149	31	even	even	RB
37681	149	32	.	.	.
37681	150	1	Much	much	RB
37681	150	2	more	more	JJR
37681	150	3	to	to	IN
37681	150	4	the	the	DT
37681	150	5	point	point	NN
37681	150	6	is	be	VBZ
37681	150	7	the	the	DT
37681	150	8	fact	fact	NN
37681	150	9	that	that	IN
37681	150	10	Mr.	Mr.	NNP
37681	150	11	Locke	Locke	NNP
37681	150	12	taught	teach	VBD
37681	150	13	mathematics	mathematic	NNS
37681	150	14	in	in	IN
37681	150	15	the	the	DT
37681	150	16	schools	school	NNS
37681	150	17	of	of	IN
37681	150	18	England	England	NNP
37681	150	19	,	,	,
37681	150	20	and	and	CC
37681	150	21	that	that	IN
37681	150	22	these	these	DT
37681	150	23	schools	school	NNS
37681	150	24	do	do	VBP
37681	150	25	not	not	RB
37681	150	26	seem	seem	VB
37681	150	27	to	to	IN
37681	150	28	the	the	DT
37681	150	29	rest	rest	NN
37681	150	30	of	of	IN
37681	150	31	the	the	DT
37681	150	32	world	world	NN
37681	150	33	to	to	TO
37681	150	34	furnish	furnish	VB
37681	150	35	a	a	DT
37681	150	36	good	good	JJ
37681	150	37	type	type	NN
37681	150	38	of	of	IN
37681	150	39	the	the	DT
37681	150	40	teaching	teaching	NN
37681	150	41	of	of	IN
37681	150	42	elementary	elementary	JJ
37681	150	43	mathematics	mathematic	NNS
37681	150	44	.	.	.
37681	151	1	No	no	DT
37681	151	2	country	country	NN
37681	151	3	goes	go	VBZ
37681	151	4	to	to	IN
37681	151	5	England	England	NNP
37681	151	6	for	for	IN
37681	151	7	its	-PRON-	PRP$
37681	151	8	model	model	NN
37681	151	9	in	in	IN
37681	151	10	this	this	DT
37681	151	11	particular	particular	JJ
37681	151	12	branch	branch	NN
37681	151	13	of	of	IN
37681	151	14	education	education	NN
37681	151	15	,	,	,
37681	151	16	although	although	IN
37681	151	17	the	the	DT
37681	151	18	work	work	NN
37681	151	19	is	be	VBZ
37681	151	20	rapidly	rapidly	RB
37681	151	21	changing	change	VBG
37681	151	22	there	there	RB
37681	151	23	,	,	,
37681	151	24	and	and	CC
37681	151	25	Mr.	Mr.	NNP
37681	151	26	Locke	Locke	NNP
37681	151	27	pictures	picture	VBZ
37681	151	28	a	a	DT
37681	151	29	local	local	JJ
37681	151	30	condition	condition	NN
37681	151	31	in	in	IN
37681	151	32	teaching	teaching	NN
37681	151	33	rather	rather	RB
37681	151	34	than	than	IN
37681	151	35	a	a	DT
37681	151	36	general	general	JJ
37681	151	37	condition	condition	NN
37681	151	38	in	in	IN
37681	151	39	mathematics	mathematic	NNS
37681	151	40	.	.	.
37681	152	1	Few	few	JJ
37681	152	2	visitors	visitor	NNS
37681	152	3	to	to	IN
37681	152	4	the	the	DT
37681	152	5	schools	school	NNS
37681	152	6	of	of	IN
37681	152	7	England	England	NNP
37681	152	8	would	would	MD
37681	152	9	care	care	VB
37681	152	10	to	to	TO
37681	152	11	teach	teach	VB
37681	152	12	mathematics	mathematic	NNS
37681	152	13	as	as	IN
37681	152	14	they	-PRON-	PRP
37681	152	15	see	see	VBP
37681	152	16	it	-PRON-	PRP
37681	152	17	taught	teach	VBD
37681	152	18	there	there	RB
37681	152	19	,	,	,
37681	152	20	in	in	IN
37681	152	21	spite	spite	NN
37681	152	22	of	of	IN
37681	152	23	their	-PRON-	PRP$
37681	152	24	recognition	recognition	NN
37681	152	25	of	of	IN
37681	152	26	the	the	DT
37681	152	27	thoroughness	thoroughness	NN
37681	152	28	of	of	IN
37681	152	29	the	the	DT
37681	152	30	work	work	NN
37681	152	31	and	and	CC
37681	152	32	the	the	DT
37681	152	33	earnestness	earnestness	NN
37681	152	34	of	of	IN
37681	152	35	many	many	JJ
37681	152	36	of	of	IN
37681	152	37	the	the	DT
37681	152	38	teachers	teacher	NNS
37681	152	39	.	.	.
37681	153	1	It	-PRON-	PRP
37681	153	2	is	be	VBZ
37681	153	3	also	also	RB
37681	153	4	of	of	IN
37681	153	5	interest	interest	NN
37681	153	6	to	to	TO
37681	153	7	note	note	VB
37681	153	8	that	that	IN
37681	153	9	the	the	DT
37681	153	10	greatest	great	JJS
37681	153	11	protests	protest	NNS
37681	153	12	against	against	IN
37681	153	13	formal	formal	JJ
37681	153	14	mathematics	mathematic	NNS
37681	153	15	have	have	VBP
37681	153	16	come	come	VBN
37681	153	17	from	from	IN
37681	153	18	England	England	NNP
37681	153	19	,	,	,
37681	153	20	as	as	IN
37681	153	21	witness	witness	NN
37681	153	22	the	the	DT
37681	153	23	utterances	utterance	NNS
37681	153	24	of	of	IN
37681	153	25	such	such	JJ
37681	153	26	men	man	NNS
37681	153	27	as	as	IN
37681	153	28	Sir	Sir	NNP
37681	153	29	William	William	NNP
37681	153	30	Hamilton	Hamilton	NNP
37681	153	31	and	and	CC
37681	153	32	Professors	Professors	NNPS
37681	153	33	Perry	Perry	NNP
37681	153	34	,	,	,
37681	153	35	Minchin	Minchin	NNP
37681	153	36	,	,	,
37681	153	37	Henrici	Henrici	NNP
37681	153	38	,	,	,
37681	153	39	and	and	CC
37681	153	40	Alfred	Alfred	NNP
37681	153	41	Lodge	Lodge	NNP
37681	153	42	.	.	.
37681	154	1	It	-PRON-	PRP
37681	154	2	may	may	MD
37681	154	3	therefore	therefore	RB
37681	154	4	be	be	VB
37681	154	5	questioned	question	VBN
37681	154	6	whether	whether	IN
37681	154	7	these	these	DT
37681	154	8	scholars	scholar	NNS
37681	154	9	are	be	VBP
37681	154	10	not	not	RB
37681	154	11	unconsciously	unconsciously	RB
37681	154	12	protesting	protest	VBG
37681	154	13	against	against	IN
37681	154	14	the	the	DT
37681	154	15	English	english	JJ
37681	154	16	methods	method	NNS
37681	154	17	and	and	CC
37681	154	18	curriculum	curriculum	NN
37681	154	19	rather	rather	RB
37681	154	20	than	than	IN
37681	154	21	against	against	IN
37681	154	22	the	the	DT
37681	154	23	subject	subject	NN
37681	154	24	itself	-PRON-	PRP
37681	154	25	.	.	.
37681	155	1	When	when	WRB
37681	155	2	Professor	Professor	NNP
37681	155	3	Minchin	Minchin	NNP
37681	155	4	says	say	VBZ
37681	155	5	that	that	IN
37681	155	6	he	-PRON-	PRP
37681	155	7	had	have	VBD
37681	155	8	been	be	VBN
37681	155	9	through	through	IN
37681	155	10	the	the	DT
37681	155	11	six	six	CD
37681	155	12	books	book	NNS
37681	155	13	of	of	IN
37681	155	14	Euclid	Euclid	NNP
37681	155	15	without	without	IN
37681	155	16	really	really	RB
37681	155	17	understanding	understand	VBG
37681	155	18	an	an	DT
37681	155	19	angle	angle	NN
37681	155	20	,	,	,
37681	155	21	it	-PRON-	PRP
37681	155	22	is	be	VBZ
37681	155	23	Euclid	Euclid	NNP
37681	155	24	's	's	POS
37681	155	25	text	text	NN
37681	155	26	and	and	CC
37681	155	27	his	-PRON-	PRP$
37681	155	28	own	own	JJ
37681	155	29	teacher	teacher	NN
37681	155	30	that	that	WDT
37681	155	31	are	be	VBP
37681	155	32	at	at	IN
37681	155	33	fault	fault	NN
37681	155	34	,	,	,
37681	155	35	and	and	CC
37681	155	36	not	not	RB
37681	155	37	geometry	geometry	VB
37681	155	38	.	.	.
37681	156	1	Before	before	IN
37681	156	2	considering	consider	VBG
37681	156	3	directly	directly	RB
37681	156	4	the	the	DT
37681	156	5	question	question	NN
37681	156	6	as	as	IN
37681	156	7	to	to	IN
37681	156	8	why	why	WRB
37681	156	9	geometry	geometry	NN
37681	156	10	should	should	MD
37681	156	11	be	be	VB
37681	156	12	taught	teach	VBN
37681	156	13	,	,	,
37681	156	14	let	let	VB
37681	156	15	us	-PRON-	PRP
37681	156	16	turn	turn	VB
37681	156	17	for	for	IN
37681	156	18	a	a	DT
37681	156	19	moment	moment	NN
37681	156	20	to	to	IN
37681	156	21	the	the	DT
37681	156	22	other	other	JJ
37681	156	23	subjects	subject	NNS
37681	156	24	in	in	IN
37681	156	25	the	the	DT
37681	156	26	secondary	secondary	JJ
37681	156	27	curriculum	curriculum	NN
37681	156	28	.	.	.
37681	157	1	Why	why	WRB
37681	157	2	,	,	,
37681	157	3	for	for	IN
37681	157	4	example	example	NN
37681	157	5	,	,	,
37681	157	6	do	do	VBP
37681	157	7	we	-PRON-	PRP
37681	157	8	study	study	VB
37681	157	9	literature	literature	NN
37681	157	10	?	?	.
37681	158	1	"	"	``
37681	158	2	It	-PRON-	PRP
37681	158	3	does	do	VBZ
37681	158	4	not	not	RB
37681	158	5	lower	lower	VB
37681	158	6	the	the	DT
37681	158	7	price	price	NN
37681	158	8	of	of	IN
37681	158	9	bread	bread	NN
37681	158	10	,	,	,
37681	158	11	"	"	''
37681	158	12	as	as	IN
37681	158	13	Malherbe	Malherbe	NNP
37681	158	14	remarked	remark	VBD
37681	158	15	in	in	IN
37681	158	16	speaking	speaking	NN
37681	158	17	of	of	IN
37681	158	18	the	the	DT
37681	158	19	commentary	commentary	NN
37681	158	20	of	of	IN
37681	158	21	Bachet	Bachet	NNP
37681	158	22	on	on	IN
37681	158	23	the	the	DT
37681	158	24	great	great	JJ
37681	158	25	work	work	NN
37681	158	26	of	of	IN
37681	158	27	Diophantus	Diophantus	NNP
37681	158	28	.	.	.
37681	159	1	Is	be	VBZ
37681	159	2	it	-PRON-	PRP
37681	159	3	for	for	IN
37681	159	4	the	the	DT
37681	159	5	purpose	purpose	NN
37681	159	6	of	of	IN
37681	159	7	making	make	VBG
37681	159	8	authors	author	NNS
37681	159	9	?	?	.
37681	160	1	Not	not	RB
37681	160	2	one	one	CD
37681	160	3	person	person	NN
37681	160	4	out	out	IN
37681	160	5	of	of	IN
37681	160	6	ten	ten	CD
37681	160	7	thousand	thousand	CD
37681	160	8	who	who	WP
37681	160	9	study	study	VBP
37681	160	10	literature	literature	NN
37681	160	11	ever	ever	RB
37681	160	12	writes	write	VBZ
37681	160	13	for	for	IN
37681	160	14	publication	publication	NN
37681	160	15	.	.	.
37681	161	1	And	and	CC
37681	161	2	why	why	WRB
37681	161	3	do	do	VBP
37681	161	4	we	-PRON-	PRP
37681	161	5	allow	allow	VB
37681	161	6	pupils	pupil	NNS
37681	161	7	to	to	TO
37681	161	8	waste	waste	VB
37681	161	9	their	-PRON-	PRP$
37681	161	10	time	time	NN
37681	161	11	in	in	IN
37681	161	12	physical	physical	JJ
37681	161	13	education	education	NN
37681	161	14	?	?	.
37681	162	1	It	-PRON-	PRP
37681	162	2	uses	use	VBZ
37681	162	3	valuable	valuable	JJ
37681	162	4	hours	hour	NNS
37681	162	5	,	,	,
37681	162	6	it	-PRON-	PRP
37681	162	7	wastes	waste	VBZ
37681	162	8	money	money	NN
37681	162	9	,	,	,
37681	162	10	and	and	CC
37681	162	11	it	-PRON-	PRP
37681	162	12	is	be	VBZ
37681	162	13	dangerous	dangerous	JJ
37681	162	14	to	to	IN
37681	162	15	life	life	NN
37681	162	16	and	and	CC
37681	162	17	limb	limb	NN
37681	162	18	.	.	.
37681	163	1	Would	Would	MD
37681	163	2	it	-PRON-	PRP
37681	163	3	not	not	RB
37681	163	4	be	be	VB
37681	163	5	better	well	JJR
37681	163	6	to	to	TO
37681	163	7	set	set	VB
37681	163	8	pupils	pupil	NNS
37681	163	9	at	at	IN
37681	163	10	sawing	saw	VBG
37681	163	11	wood	wood	NN
37681	163	12	?	?	.
37681	164	1	And	and	CC
37681	164	2	why	why	WRB
37681	164	3	do	do	VBP
37681	164	4	we	-PRON-	PRP
37681	164	5	study	study	VB
37681	164	6	music	music	NN
37681	164	7	?	?	.
37681	165	1	To	to	TO
37681	165	2	give	give	VB
37681	165	3	pleasure	pleasure	NN
37681	165	4	by	by	IN
37681	165	5	our	-PRON-	PRP$
37681	165	6	performances	performance	NNS
37681	165	7	?	?	.
37681	166	1	How	how	WRB
37681	166	2	many	many	JJ
37681	166	3	who	who	WP
37681	166	4	attempt	attempt	VBP
37681	166	5	to	to	TO
37681	166	6	play	play	VB
37681	166	7	the	the	DT
37681	166	8	piano	piano	NN
37681	166	9	or	or	CC
37681	166	10	to	to	TO
37681	166	11	sing	sing	VB
37681	166	12	give	give	VB
37681	166	13	much	much	JJ
37681	166	14	pleasure	pleasure	NN
37681	166	15	to	to	IN
37681	166	16	any	any	DT
37681	166	17	but	but	CC
37681	166	18	themselves	-PRON-	PRP
37681	166	19	,	,	,
37681	166	20	and	and	CC
37681	166	21	possibly	possibly	RB
37681	166	22	their	-PRON-	PRP$
37681	166	23	parents	parent	NNS
37681	166	24	?	?	.
37681	167	1	The	the	DT
37681	167	2	study	study	NN
37681	167	3	of	of	IN
37681	167	4	grammar	grammar	NN
37681	167	5	does	do	VBZ
37681	167	6	not	not	RB
37681	167	7	make	make	VB
37681	167	8	an	an	DT
37681	167	9	accurate	accurate	JJ
37681	167	10	writer	writer	NN
37681	167	11	,	,	,
37681	167	12	nor	nor	CC
37681	167	13	the	the	DT
37681	167	14	study	study	NN
37681	167	15	of	of	IN
37681	167	16	rhetoric	rhetoric	NN
37681	167	17	an	an	DT
37681	167	18	orator	orator	NN
37681	167	19	,	,	,
37681	167	20	nor	nor	CC
37681	167	21	the	the	DT
37681	167	22	study	study	NN
37681	167	23	of	of	IN
37681	167	24	meter	meter	NN
37681	167	25	a	a	DT
37681	167	26	poet	poet	NN
37681	167	27	,	,	,
37681	167	28	nor	nor	CC
37681	167	29	the	the	DT
37681	167	30	study	study	NN
37681	167	31	of	of	IN
37681	167	32	pedagogy	pedagogy	NN
37681	167	33	a	a	DT
37681	167	34	teacher	teacher	NN
37681	167	35	.	.	.
37681	168	1	The	the	DT
37681	168	2	study	study	NN
37681	168	3	of	of	IN
37681	168	4	geography	geography	NN
37681	168	5	in	in	IN
37681	168	6	the	the	DT
37681	168	7	school	school	NN
37681	168	8	does	do	VBZ
37681	168	9	not	not	RB
37681	168	10	make	make	VB
37681	168	11	travel	travel	NN
37681	168	12	particularly	particularly	RB
37681	168	13	easier	easy	JJR
37681	168	14	,	,	,
37681	168	15	nor	nor	CC
37681	168	16	does	do	VBZ
37681	168	17	the	the	DT
37681	168	18	study	study	NN
37681	168	19	of	of	IN
37681	168	20	biology	biology	NN
37681	168	21	tend	tend	VBP
37681	168	22	to	to	TO
37681	168	23	populate	populate	VB
37681	168	24	the	the	DT
37681	168	25	earth	earth	NN
37681	168	26	.	.	.
37681	169	1	So	so	RB
37681	169	2	we	-PRON-	PRP
37681	169	3	might	may	MD
37681	169	4	pass	pass	VB
37681	169	5	in	in	RP
37681	169	6	review	review	NN
37681	169	7	the	the	DT
37681	169	8	various	various	JJ
37681	169	9	subjects	subject	NNS
37681	169	10	that	that	WDT
37681	169	11	we	-PRON-	PRP
37681	169	12	study	study	VBP
37681	169	13	and	and	CC
37681	169	14	ought	ought	MD
37681	169	15	to	to	TO
37681	169	16	study	study	VB
37681	169	17	,	,	,
37681	169	18	and	and	CC
37681	169	19	in	in	IN
37681	169	20	no	no	DT
37681	169	21	case	case	NN
37681	169	22	would	would	MD
37681	169	23	we	-PRON-	PRP
37681	169	24	find	find	VB
37681	169	25	utility	utility	NN
37681	169	26	the	the	DT
37681	169	27	moving	move	VBG
37681	169	28	cause	cause	NN
37681	169	29	,	,	,
37681	169	30	and	and	CC
37681	169	31	in	in	IN
37681	169	32	every	every	DT
37681	169	33	case	case	NN
37681	169	34	would	would	MD
37681	169	35	we	-PRON-	PRP
37681	169	36	find	find	VB
37681	169	37	it	-PRON-	PRP
37681	169	38	difficult	difficult	JJ
37681	169	39	to	to	TO
37681	169	40	state	state	VB
37681	169	41	the	the	DT
37681	169	42	one	one	CD
37681	169	43	great	great	JJ
37681	169	44	reason	reason	NN
37681	169	45	for	for	IN
37681	169	46	the	the	DT
37681	169	47	pursuit	pursuit	NN
37681	169	48	of	of	IN
37681	169	49	the	the	DT
37681	169	50	subject	subject	NN
37681	169	51	in	in	IN
37681	169	52	question,--and	question,--and	XX
37681	169	53	so	so	IN
37681	169	54	it	-PRON-	PRP
37681	169	55	is	be	VBZ
37681	169	56	with	with	IN
37681	169	57	geometry	geometry	NN
37681	169	58	.	.	.
37681	170	1	What	what	WDT
37681	170	2	positive	positive	JJ
37681	170	3	reasons	reason	NNS
37681	170	4	can	can	MD
37681	170	5	now	now	RB
37681	170	6	be	be	VB
37681	170	7	adduced	adduce	VBN
37681	170	8	for	for	IN
37681	170	9	the	the	DT
37681	170	10	study	study	NN
37681	170	11	of	of	IN
37681	170	12	a	a	DT
37681	170	13	subject	subject	NN
37681	170	14	that	that	WDT
37681	170	15	occupies	occupy	VBZ
37681	170	16	upwards	upwards	RB
37681	170	17	of	of	IN
37681	170	18	a	a	DT
37681	170	19	year	year	NN
37681	170	20	in	in	IN
37681	170	21	the	the	DT
37681	170	22	school	school	NN
37681	170	23	course	course	NN
37681	170	24	,	,	,
37681	170	25	and	and	CC
37681	170	26	that	that	DT
37681	170	27	is	be	VBZ
37681	170	28	,	,	,
37681	170	29	perhaps	perhaps	RB
37681	170	30	unwisely	unwisely	RB
37681	170	31	,	,	,
37681	170	32	required	require	VBN
37681	170	33	of	of	IN
37681	170	34	all	all	DT
37681	170	35	pupils	pupil	NNS
37681	170	36	?	?	.
37681	171	1	Probably	probably	RB
37681	171	2	the	the	DT
37681	171	3	primary	primary	JJ
37681	171	4	reason	reason	NN
37681	171	5	,	,	,
37681	171	6	if	if	IN
37681	171	7	we	-PRON-	PRP
37681	171	8	do	do	VBP
37681	171	9	not	not	RB
37681	171	10	attempt	attempt	VB
37681	171	11	to	to	TO
37681	171	12	deceive	deceive	VB
37681	171	13	ourselves	-PRON-	PRP
37681	171	14	,	,	,
37681	171	15	is	be	VBZ
37681	171	16	pleasure	pleasure	NN
37681	171	17	.	.	.
37681	172	1	We	-PRON-	PRP
37681	172	2	study	study	VBP
37681	172	3	music	music	NN
37681	172	4	because	because	IN
37681	172	5	music	music	NN
37681	172	6	gives	give	VBZ
37681	172	7	us	-PRON-	PRP
37681	172	8	pleasure	pleasure	NN
37681	172	9	,	,	,
37681	172	10	not	not	RB
37681	172	11	necessarily	necessarily	RB
37681	172	12	our	-PRON-	PRP$
37681	172	13	own	own	JJ
37681	172	14	music	music	NN
37681	172	15	,	,	,
37681	172	16	but	but	CC
37681	172	17	good	good	JJ
37681	172	18	music	music	NN
37681	172	19	,	,	,
37681	172	20	whether	whether	IN
37681	172	21	ours	our	NNS
37681	172	22	,	,	,
37681	172	23	or	or	CC
37681	172	24	,	,	,
37681	172	25	as	as	IN
37681	172	26	is	be	VBZ
37681	172	27	more	more	RBR
37681	172	28	probable	probable	JJ
37681	172	29	,	,	,
37681	172	30	that	that	DT
37681	172	31	of	of	IN
37681	172	32	others	other	NNS
37681	172	33	.	.	.
37681	173	1	We	-PRON-	PRP
37681	173	2	study	study	VBP
37681	173	3	literature	literature	NN
37681	173	4	because	because	IN
37681	173	5	we	-PRON-	PRP
37681	173	6	derive	derive	VBP
37681	173	7	pleasure	pleasure	NN
37681	173	8	from	from	IN
37681	173	9	books	book	NNS
37681	173	10	;	;	:
37681	173	11	the	the	DT
37681	173	12	better	well	JJR
37681	173	13	the	the	DT
37681	173	14	book	book	NN
37681	173	15	the	the	DT
37681	173	16	more	more	RBR
37681	173	17	subtle	subtle	JJ
37681	173	18	and	and	CC
37681	173	19	lasting	last	VBG
37681	173	20	the	the	DT
37681	173	21	pleasure	pleasure	NN
37681	173	22	.	.	.
37681	174	1	We	-PRON-	PRP
37681	174	2	study	study	VBP
37681	174	3	art	art	NN
37681	174	4	because	because	IN
37681	174	5	we	-PRON-	PRP
37681	174	6	receive	receive	VBP
37681	174	7	pleasure	pleasure	NN
37681	174	8	from	from	IN
37681	174	9	the	the	DT
37681	174	10	great	great	JJ
37681	174	11	works	work	NNS
37681	174	12	of	of	IN
37681	174	13	the	the	DT
37681	174	14	masters	master	NNS
37681	174	15	,	,	,
37681	174	16	and	and	CC
37681	174	17	probably	probably	RB
37681	174	18	we	-PRON-	PRP
37681	174	19	appreciate	appreciate	VBP
37681	174	20	them	-PRON-	PRP
37681	174	21	the	the	DT
37681	174	22	more	more	JJR
37681	174	23	because	because	IN
37681	174	24	we	-PRON-	PRP
37681	174	25	have	have	VBP
37681	174	26	dabbled	dabble	VBN
37681	174	27	a	a	DT
37681	174	28	little	little	JJ
37681	174	29	in	in	IN
37681	174	30	pigments	pigment	NNS
37681	174	31	or	or	CC
37681	174	32	in	in	IN
37681	174	33	clay	clay	NN
37681	174	34	.	.	.
37681	175	1	We	-PRON-	PRP
37681	175	2	do	do	VBP
37681	175	3	not	not	RB
37681	175	4	expect	expect	VB
37681	175	5	to	to	TO
37681	175	6	be	be	VB
37681	175	7	composers	composer	NNS
37681	175	8	,	,	,
37681	175	9	or	or	CC
37681	175	10	poets	poet	NNS
37681	175	11	,	,	,
37681	175	12	or	or	CC
37681	175	13	sculptors	sculptor	NNS
37681	175	14	,	,	,
37681	175	15	but	but	CC
37681	175	16	we	-PRON-	PRP
37681	175	17	wish	wish	VBP
37681	175	18	to	to	TO
37681	175	19	appreciate	appreciate	VB
37681	175	20	music	music	NN
37681	175	21	and	and	CC
37681	175	22	letters	letter	NNS
37681	175	23	and	and	CC
37681	175	24	the	the	DT
37681	175	25	fine	fine	JJ
37681	175	26	arts	art	NNS
37681	175	27	,	,	,
37681	175	28	and	and	CC
37681	175	29	to	to	TO
37681	175	30	derive	derive	VB
37681	175	31	pleasure	pleasure	NN
37681	175	32	from	from	IN
37681	175	33	them	-PRON-	PRP
37681	175	34	and	and	CC
37681	175	35	to	to	TO
37681	175	36	be	be	VB
37681	175	37	uplifted	uplift	VBN
37681	175	38	by	by	IN
37681	175	39	them	-PRON-	PRP
37681	175	40	.	.	.
37681	176	1	At	at	IN
37681	176	2	any	any	DT
37681	176	3	rate	rate	NN
37681	176	4	,	,	,
37681	176	5	these	these	DT
37681	176	6	are	be	VBP
37681	176	7	the	the	DT
37681	176	8	nobler	noble	JJR
37681	176	9	reasons	reason	NNS
37681	176	10	for	for	IN
37681	176	11	their	-PRON-	PRP$
37681	176	12	study	study	NN
37681	176	13	.	.	.
37681	177	1	So	so	CC
37681	177	2	it	-PRON-	PRP
37681	177	3	is	be	VBZ
37681	177	4	with	with	IN
37681	177	5	geometry	geometry	NN
37681	177	6	.	.	.
37681	178	1	We	-PRON-	PRP
37681	178	2	study	study	VBP
37681	178	3	it	-PRON-	PRP
37681	178	4	because	because	IN
37681	178	5	we	-PRON-	PRP
37681	178	6	derive	derive	VBP
37681	178	7	pleasure	pleasure	NN
37681	178	8	from	from	IN
37681	178	9	contact	contact	NN
37681	178	10	with	with	IN
37681	178	11	a	a	DT
37681	178	12	great	great	JJ
37681	178	13	and	and	CC
37681	178	14	an	an	DT
37681	178	15	ancient	ancient	JJ
37681	178	16	body	body	NN
37681	178	17	of	of	IN
37681	178	18	learning	learning	NN
37681	178	19	that	that	WDT
37681	178	20	has	have	VBZ
37681	178	21	occupied	occupy	VBN
37681	178	22	the	the	DT
37681	178	23	attention	attention	NN
37681	178	24	of	of	IN
37681	178	25	master	master	NN
37681	178	26	minds	mind	NNS
37681	178	27	during	during	IN
37681	178	28	the	the	DT
37681	178	29	thousands	thousand	NNS
37681	178	30	of	of	IN
37681	178	31	years	year	NNS
37681	178	32	in	in	IN
37681	178	33	which	which	WDT
37681	178	34	it	-PRON-	PRP
37681	178	35	has	have	VBZ
37681	178	36	been	be	VBN
37681	178	37	perfected	perfect	VBN
37681	178	38	,	,	,
37681	178	39	and	and	CC
37681	178	40	we	-PRON-	PRP
37681	178	41	are	be	VBP
37681	178	42	uplifted	uplifted	JJ
37681	178	43	by	by	IN
37681	178	44	it	-PRON-	PRP
37681	178	45	.	.	.
37681	179	1	To	to	TO
37681	179	2	deny	deny	VB
37681	179	3	that	that	IN
37681	179	4	our	-PRON-	PRP$
37681	179	5	pupils	pupil	NNS
37681	179	6	derive	derive	VBP
37681	179	7	this	this	DT
37681	179	8	pleasure	pleasure	NN
37681	179	9	from	from	IN
37681	179	10	the	the	DT
37681	179	11	study	study	NN
37681	179	12	is	be	VBZ
37681	179	13	to	to	TO
37681	179	14	confess	confess	VB
37681	179	15	ourselves	-PRON-	PRP
37681	179	16	poor	poor	JJ
37681	179	17	teachers	teacher	NNS
37681	179	18	,	,	,
37681	179	19	for	for	IN
37681	179	20	most	most	JJS
37681	179	21	pupils	pupil	NNS
37681	179	22	do	do	VBP
37681	179	23	have	have	VB
37681	179	24	positive	positive	JJ
37681	179	25	enjoyment	enjoyment	NN
37681	179	26	in	in	IN
37681	179	27	the	the	DT
37681	179	28	pursuit	pursuit	NN
37681	179	29	of	of	IN
37681	179	30	geometry	geometry	NNP
37681	179	31	,	,	,
37681	179	32	in	in	IN
37681	179	33	spite	spite	NN
37681	179	34	of	of	IN
37681	179	35	the	the	DT
37681	179	36	tradition	tradition	NN
37681	179	37	that	that	WDT
37681	179	38	leads	lead	VBZ
37681	179	39	them	-PRON-	PRP
37681	179	40	to	to	TO
37681	179	41	proclaim	proclaim	VB
37681	179	42	a	a	DT
37681	179	43	general	general	JJ
37681	179	44	dislike	dislike	NN
37681	179	45	for	for	IN
37681	179	46	all	all	DT
37681	179	47	study	study	NN
37681	179	48	.	.	.
37681	180	1	This	this	DT
37681	180	2	enjoyment	enjoyment	NN
37681	180	3	is	be	VBZ
37681	180	4	partly	partly	RB
37681	180	5	that	that	DT
37681	180	6	of	of	IN
37681	180	7	the	the	DT
37681	180	8	game,--the	game,--the	NNP
37681	180	9	playing	playing	NN
37681	180	10	of	of	IN
37681	180	11	a	a	DT
37681	180	12	game	game	NN
37681	180	13	that	that	WDT
37681	180	14	can	can	MD
37681	180	15	always	always	RB
37681	180	16	be	be	VB
37681	180	17	won	win	VBN
37681	180	18	,	,	,
37681	180	19	but	but	CC
37681	180	20	that	that	DT
37681	180	21	can	can	MD
37681	180	22	not	not	RB
37681	180	23	be	be	VB
37681	180	24	won	win	VBN
37681	180	25	too	too	RB
37681	180	26	easily	easily	RB
37681	180	27	.	.	.
37681	181	1	It	-PRON-	PRP
37681	181	2	is	be	VBZ
37681	181	3	partly	partly	RB
37681	181	4	that	that	DT
37681	181	5	of	of	IN
37681	181	6	the	the	DT
37681	181	7	æsthetic	æsthetic	NN
37681	181	8	,	,	,
37681	181	9	the	the	DT
37681	181	10	pleasure	pleasure	NN
37681	181	11	of	of	IN
37681	181	12	symmetry	symmetry	NN
37681	181	13	of	of	IN
37681	181	14	form	form	NN
37681	181	15	,	,	,
37681	181	16	the	the	DT
37681	181	17	delight	delight	NN
37681	181	18	of	of	IN
37681	181	19	fitting	fitting	JJ
37681	181	20	things	thing	NNS
37681	181	21	together	together	RB
37681	181	22	.	.	.
37681	182	1	But	but	CC
37681	182	2	probably	probably	RB
37681	182	3	it	-PRON-	PRP
37681	182	4	lies	lie	VBZ
37681	182	5	chiefly	chiefly	RB
37681	182	6	in	in	IN
37681	182	7	the	the	DT
37681	182	8	mental	mental	JJ
37681	182	9	uplift	uplift	NN
37681	182	10	that	that	WDT
37681	182	11	geometry	geometry	NN
37681	182	12	brings	bring	VBZ
37681	182	13	,	,	,
37681	182	14	the	the	DT
37681	182	15	contact	contact	NN
37681	182	16	with	with	IN
37681	182	17	absolute	absolute	JJ
37681	182	18	truth	truth	NN
37681	182	19	,	,	,
37681	182	20	and	and	CC
37681	182	21	the	the	DT
37681	182	22	approach	approach	NN
37681	182	23	that	that	IN
37681	182	24	one	one	PRP
37681	182	25	makes	make	VBZ
37681	182	26	to	to	IN
37681	182	27	the	the	DT
37681	182	28	Infinite	Infinite	NNP
37681	182	29	.	.	.
37681	183	1	We	-PRON-	PRP
37681	183	2	are	be	VBP
37681	183	3	not	not	RB
37681	183	4	quite	quite	RB
37681	183	5	sure	sure	JJ
37681	183	6	of	of	IN
37681	183	7	any	any	DT
37681	183	8	one	one	CD
37681	183	9	thing	thing	NN
37681	183	10	in	in	IN
37681	183	11	biology	biology	NN
37681	183	12	;	;	:
37681	183	13	our	-PRON-	PRP$
37681	183	14	knowledge	knowledge	NN
37681	183	15	of	of	IN
37681	183	16	geology	geology	NN
37681	183	17	is	be	VBZ
37681	183	18	relatively	relatively	RB
37681	183	19	very	very	RB
37681	183	20	slight	slight	JJ
37681	183	21	,	,	,
37681	183	22	and	and	CC
37681	183	23	the	the	DT
37681	183	24	economic	economic	JJ
37681	183	25	laws	law	NNS
37681	183	26	of	of	IN
37681	183	27	society	society	NN
37681	183	28	are	be	VBP
37681	183	29	uncertain	uncertain	JJ
37681	183	30	to	to	IN
37681	183	31	every	every	DT
37681	183	32	one	one	CD
37681	183	33	except	except	IN
37681	183	34	some	some	DT
37681	183	35	individual	individual	NN
37681	183	36	who	who	WP
37681	183	37	attempts	attempt	VBZ
37681	183	38	to	to	TO
37681	183	39	set	set	VB
37681	183	40	them	-PRON-	PRP
37681	183	41	forth	forth	RB
37681	183	42	;	;	:
37681	183	43	but	but	CC
37681	183	44	before	before	IN
37681	183	45	the	the	DT
37681	183	46	world	world	NN
37681	183	47	was	be	VBD
37681	183	48	fashioned	fashion	VBN
37681	183	49	the	the	DT
37681	183	50	square	square	NN
37681	183	51	on	on	IN
37681	183	52	the	the	DT
37681	183	53	hypotenuse	hypotenuse	NN
37681	183	54	was	be	VBD
37681	183	55	equal	equal	JJ
37681	183	56	to	to	IN
37681	183	57	the	the	DT
37681	183	58	sum	sum	NN
37681	183	59	of	of	IN
37681	183	60	the	the	DT
37681	183	61	squares	square	NNS
37681	183	62	on	on	IN
37681	183	63	the	the	DT
37681	183	64	other	other	JJ
37681	183	65	two	two	CD
37681	183	66	sides	side	NNS
37681	183	67	of	of	IN
37681	183	68	a	a	DT
37681	183	69	right	right	JJ
37681	183	70	triangle	triangle	NN
37681	183	71	,	,	,
37681	183	72	and	and	CC
37681	183	73	it	-PRON-	PRP
37681	183	74	will	will	MD
37681	183	75	be	be	VB
37681	183	76	so	so	RB
37681	183	77	after	after	IN
37681	183	78	this	this	DT
37681	183	79	world	world	NN
37681	183	80	is	be	VBZ
37681	183	81	dead	dead	JJ
37681	183	82	;	;	:
37681	183	83	and	and	CC
37681	183	84	the	the	DT
37681	183	85	inhabitant	inhabitant	NN
37681	183	86	of	of	IN
37681	183	87	Mars	Mars	NNP
37681	183	88	,	,	,
37681	183	89	if	if	IN
37681	183	90	he	-PRON-	PRP
37681	183	91	exists	exist	VBZ
37681	183	92	,	,	,
37681	183	93	probably	probably	RB
37681	183	94	knows	know	VBZ
37681	183	95	its	-PRON-	PRP$
37681	183	96	truth	truth	NN
37681	183	97	as	as	IN
37681	183	98	we	-PRON-	PRP
37681	183	99	know	know	VBP
37681	183	100	it	-PRON-	PRP
37681	183	101	.	.	.
37681	184	1	The	the	DT
37681	184	2	uplift	uplift	NN
37681	184	3	of	of	IN
37681	184	4	this	this	DT
37681	184	5	contact	contact	NN
37681	184	6	with	with	IN
37681	184	7	absolute	absolute	JJ
37681	184	8	truth	truth	NN
37681	184	9	,	,	,
37681	184	10	with	with	IN
37681	184	11	truth	truth	NN
37681	184	12	eternal	eternal	JJ
37681	184	13	,	,	,
37681	184	14	gives	give	VBZ
37681	184	15	pleasure	pleasure	NN
37681	184	16	to	to	IN
37681	184	17	humanity	humanity	NN
37681	184	18	to	to	IN
37681	184	19	a	a	DT
37681	184	20	greater	great	JJR
37681	184	21	or	or	CC
37681	184	22	less	less	JJR
37681	184	23	degree	degree	NN
37681	184	24	,	,	,
37681	184	25	depending	depend	VBG
37681	184	26	upon	upon	IN
37681	184	27	the	the	DT
37681	184	28	mental	mental	JJ
37681	184	29	equipment	equipment	NN
37681	184	30	of	of	IN
37681	184	31	the	the	DT
37681	184	32	particular	particular	JJ
37681	184	33	individual	individual	NN
37681	184	34	;	;	:
37681	184	35	but	but	CC
37681	184	36	it	-PRON-	PRP
37681	184	37	probably	probably	RB
37681	184	38	gives	give	VBZ
37681	184	39	an	an	DT
37681	184	40	appreciable	appreciable	JJ
37681	184	41	amount	amount	NN
37681	184	42	of	of	IN
37681	184	43	pleasure	pleasure	NN
37681	184	44	to	to	IN
37681	184	45	every	every	DT
37681	184	46	student	student	NN
37681	184	47	of	of	IN
37681	184	48	geometry	geometry	NN
37681	184	49	who	who	WP
37681	184	50	has	have	VBZ
37681	184	51	a	a	DT
37681	184	52	teacher	teacher	NN
37681	184	53	worthy	worthy	JJ
37681	184	54	of	of	IN
37681	184	55	the	the	DT
37681	184	56	name	name	NN
37681	184	57	.	.	.
37681	185	1	First	first	RB
37681	185	2	,	,	,
37681	185	3	then	then	RB
37681	185	4	,	,	,
37681	185	5	and	and	CC
37681	185	6	foremost	foremost	RB
37681	185	7	as	as	IN
37681	185	8	a	a	DT
37681	185	9	reason	reason	NN
37681	185	10	for	for	IN
37681	185	11	studying	study	VBG
37681	185	12	geometry	geometry	NN
37681	185	13	has	have	VBZ
37681	185	14	always	always	RB
37681	185	15	stood	stand	VBN
37681	185	16	,	,	,
37681	185	17	and	and	CC
37681	185	18	will	will	MD
37681	185	19	always	always	RB
37681	185	20	stand	stand	VB
37681	185	21	,	,	,
37681	185	22	the	the	DT
37681	185	23	pleasure	pleasure	NN
37681	185	24	and	and	CC
37681	185	25	the	the	DT
37681	185	26	mental	mental	JJ
37681	185	27	uplift	uplift	NN
37681	185	28	that	that	WDT
37681	185	29	comes	come	VBZ
37681	185	30	from	from	IN
37681	185	31	contact	contact	NN
37681	185	32	with	with	IN
37681	185	33	such	such	PDT
37681	185	34	a	a	DT
37681	185	35	great	great	JJ
37681	185	36	body	body	NN
37681	185	37	of	of	IN
37681	185	38	human	human	JJ
37681	185	39	learning	learning	NN
37681	185	40	,	,	,
37681	185	41	and	and	CC
37681	185	42	particularly	particularly	RB
37681	185	43	with	with	IN
37681	185	44	the	the	DT
37681	185	45	exact	exact	JJ
37681	185	46	truth	truth	NN
37681	185	47	that	that	WDT
37681	185	48	it	-PRON-	PRP
37681	185	49	contains	contain	VBZ
37681	185	50	.	.	.
37681	186	1	The	the	DT
37681	186	2	teacher	teacher	NN
37681	186	3	who	who	WP
37681	186	4	is	be	VBZ
37681	186	5	imbued	imbue	VBN
37681	186	6	with	with	IN
37681	186	7	this	this	DT
37681	186	8	feeling	feeling	NN
37681	186	9	is	be	VBZ
37681	186	10	on	on	IN
37681	186	11	the	the	DT
37681	186	12	road	road	NN
37681	186	13	to	to	IN
37681	186	14	success	success	NN
37681	186	15	,	,	,
37681	186	16	whatever	whatever	WDT
37681	186	17	method	method	NN
37681	186	18	of	of	IN
37681	186	19	presentation	presentation	NN
37681	186	20	he	-PRON-	PRP
37681	186	21	may	may	MD
37681	186	22	use	use	VB
37681	186	23	;	;	:
37681	186	24	the	the	DT
37681	186	25	one	one	NN
37681	186	26	who	who	WP
37681	186	27	is	be	VBZ
37681	186	28	not	not	RB
37681	186	29	imbued	imbue	VBN
37681	186	30	with	with	IN
37681	186	31	it	-PRON-	PRP
37681	186	32	is	be	VBZ
37681	186	33	on	on	IN
37681	186	34	the	the	DT
37681	186	35	road	road	NN
37681	186	36	to	to	IN
37681	186	37	failure	failure	NN
37681	186	38	,	,	,
37681	186	39	however	however	RB
37681	186	40	logical	logical	JJ
37681	186	41	his	-PRON-	PRP$
37681	186	42	presentation	presentation	NN
37681	186	43	or	or	CC
37681	186	44	however	however	RB
37681	186	45	large	large	JJ
37681	186	46	his	-PRON-	PRP$
37681	186	47	supply	supply	NN
37681	186	48	of	of	IN
37681	186	49	practical	practical	JJ
37681	186	50	applications	application	NNS
37681	186	51	.	.	.
37681	187	1	Subordinate	subordinate	JJ
37681	187	2	to	to	IN
37681	187	3	these	these	DT
37681	187	4	reasons	reason	NNS
37681	187	5	for	for	IN
37681	187	6	studying	study	VBG
37681	187	7	geometry	geometry	NN
37681	187	8	are	be	VBP
37681	187	9	many	many	JJ
37681	187	10	others	other	NNS
37681	187	11	,	,	,
37681	187	12	exactly	exactly	RB
37681	187	13	as	as	IN
37681	187	14	with	with	IN
37681	187	15	all	all	DT
37681	187	16	other	other	JJ
37681	187	17	subjects	subject	NNS
37681	187	18	of	of	IN
37681	187	19	the	the	DT
37681	187	20	curriculum	curriculum	NN
37681	187	21	.	.	.
37681	188	1	Geometry	geometry	NN
37681	188	2	,	,	,
37681	188	3	for	for	IN
37681	188	4	example	example	NN
37681	188	5	,	,	,
37681	188	6	offers	offer	VBZ
37681	188	7	the	the	DT
37681	188	8	best	well	RBS
37681	188	9	developed	developed	JJ
37681	188	10	application	application	NN
37681	188	11	of	of	IN
37681	188	12	logic	logic	NN
37681	188	13	that	that	WDT
37681	188	14	we	-PRON-	PRP
37681	188	15	have	have	VBP
37681	188	16	,	,	,
37681	188	17	or	or	CC
37681	188	18	are	be	VBP
37681	188	19	likely	likely	JJ
37681	188	20	to	to	TO
37681	188	21	have	have	VB
37681	188	22	,	,	,
37681	188	23	in	in	IN
37681	188	24	the	the	DT
37681	188	25	school	school	NN
37681	188	26	course	course	NN
37681	188	27	.	.	.
37681	189	1	This	this	DT
37681	189	2	does	do	VBZ
37681	189	3	not	not	RB
37681	189	4	mean	mean	VB
37681	189	5	that	that	IN
37681	189	6	it	-PRON-	PRP
37681	189	7	always	always	RB
37681	189	8	exemplifies	exemplify	VBZ
37681	189	9	perfect	perfect	JJ
37681	189	10	logic	logic	NN
37681	189	11	,	,	,
37681	189	12	for	for	IN
37681	189	13	it	-PRON-	PRP
37681	189	14	does	do	VBZ
37681	189	15	not	not	RB
37681	189	16	;	;	:
37681	189	17	but	but	CC
37681	189	18	to	to	IN
37681	189	19	the	the	DT
37681	189	20	pupil	pupil	NN
37681	189	21	who	who	WP
37681	189	22	is	be	VBZ
37681	189	23	not	not	RB
37681	189	24	ready	ready	JJ
37681	189	25	for	for	IN
37681	189	26	logic	logic	NN
37681	189	27	,	,	,
37681	189	28	per	per	FW
37681	189	29	se	se	FW
37681	189	30	,	,	,
37681	189	31	it	-PRON-	PRP
37681	189	32	offers	offer	VBZ
37681	189	33	an	an	DT
37681	189	34	example	example	NN
37681	189	35	of	of	IN
37681	189	36	close	close	JJ
37681	189	37	reasoning	reasoning	NN
37681	189	38	such	such	JJ
37681	189	39	as	as	IN
37681	189	40	his	-PRON-	PRP$
37681	189	41	other	other	JJ
37681	189	42	subjects	subject	NNS
37681	189	43	do	do	VBP
37681	189	44	not	not	RB
37681	189	45	offer	offer	VB
37681	189	46	.	.	.
37681	190	1	We	-PRON-	PRP
37681	190	2	may	may	MD
37681	190	3	say	say	VB
37681	190	4	,	,	,
37681	190	5	and	and	CC
37681	190	6	possibly	possibly	RB
37681	190	7	with	with	IN
37681	190	8	truth	truth	NN
37681	190	9	,	,	,
37681	190	10	that	that	IN
37681	190	11	one	one	NN
37681	190	12	who	who	WP
37681	190	13	studies	study	VBZ
37681	190	14	geometry	geometry	NN
37681	190	15	will	will	MD
37681	190	16	not	not	RB
37681	190	17	reason	reason	VB
37681	190	18	more	more	RBR
37681	190	19	clearly	clearly	RB
37681	190	20	on	on	IN
37681	190	21	a	a	DT
37681	190	22	financial	financial	JJ
37681	190	23	proposition	proposition	NN
37681	190	24	than	than	IN
37681	190	25	one	one	NN
37681	190	26	who	who	WP
37681	190	27	does	do	VBZ
37681	190	28	not	not	RB
37681	190	29	;	;	:
37681	190	30	but	but	CC
37681	190	31	in	in	IN
37681	190	32	spite	spite	NN
37681	190	33	of	of	IN
37681	190	34	the	the	DT
37681	190	35	results	result	NNS
37681	190	36	of	of	IN
37681	190	37	the	the	DT
37681	190	38	very	very	RB
37681	190	39	meager	meager	JJ
37681	190	40	experiments	experiment	NNS
37681	190	41	of	of	IN
37681	190	42	the	the	DT
37681	190	43	psychologists	psychologist	NNS
37681	190	44	,	,	,
37681	190	45	it	-PRON-	PRP
37681	190	46	is	be	VBZ
37681	190	47	probable	probable	JJ
37681	190	48	that	that	IN
37681	190	49	the	the	DT
37681	190	50	man	man	NN
37681	190	51	who	who	WP
37681	190	52	has	have	VBZ
37681	190	53	had	have	VBN
37681	190	54	some	some	DT
37681	190	55	drill	drill	NN
37681	190	56	in	in	IN
37681	190	57	syllogisms	syllogism	NNS
37681	190	58	,	,	,
37681	190	59	and	and	CC
37681	190	60	who	who	WP
37681	190	61	has	have	VBZ
37681	190	62	learned	learn	VBN
37681	190	63	to	to	TO
37681	190	64	select	select	VB
37681	190	65	the	the	DT
37681	190	66	essentials	essential	NNS
37681	190	67	and	and	CC
37681	190	68	to	to	TO
37681	190	69	neglect	neglect	VB
37681	190	70	the	the	DT
37681	190	71	nonessentials	nonessential	NNS
37681	190	72	in	in	IN
37681	190	73	reaching	reach	VBG
37681	190	74	his	-PRON-	PRP$
37681	190	75	conclusions	conclusion	NNS
37681	190	76	,	,	,
37681	190	77	has	have	VBZ
37681	190	78	acquired	acquire	VBN
37681	190	79	habits	habit	NNS
37681	190	80	in	in	IN
37681	190	81	reasoning	reasoning	NN
37681	190	82	that	that	WDT
37681	190	83	will	will	MD
37681	190	84	help	help	VB
37681	190	85	him	-PRON-	PRP
37681	190	86	in	in	IN
37681	190	87	every	every	DT
37681	190	88	line	line	NN
37681	190	89	of	of	IN
37681	190	90	work	work	NN
37681	190	91	.	.	.
37681	191	1	As	as	IN
37681	191	2	part	part	NN
37681	191	3	of	of	IN
37681	191	4	this	this	DT
37681	191	5	equipment	equipment	NN
37681	191	6	there	there	EX
37681	191	7	is	be	VBZ
37681	191	8	also	also	RB
37681	191	9	a	a	DT
37681	191	10	terseness	terseness	NN
37681	191	11	of	of	IN
37681	191	12	statement	statement	NN
37681	191	13	and	and	CC
37681	191	14	a	a	DT
37681	191	15	clearness	clearness	NN
37681	191	16	in	in	IN
37681	191	17	arrangement	arrangement	NN
37681	191	18	of	of	IN
37681	191	19	points	point	NNS
37681	191	20	in	in	IN
37681	191	21	an	an	DT
37681	191	22	argument	argument	NN
37681	191	23	that	that	WDT
37681	191	24	has	have	VBZ
37681	191	25	been	be	VBN
37681	191	26	the	the	DT
37681	191	27	subject	subject	NN
37681	191	28	of	of	IN
37681	191	29	comment	comment	NN
37681	191	30	by	by	IN
37681	191	31	many	many	JJ
37681	191	32	writers	writer	NNS
37681	191	33	.	.	.
37681	192	1	Upon	upon	IN
37681	192	2	this	this	DT
37681	192	3	same	same	JJ
37681	192	4	topic	topic	NN
37681	192	5	an	an	DT
37681	192	6	English	english	JJ
37681	192	7	writer	writer	NN
37681	192	8	,	,	,
37681	192	9	in	in	IN
37681	192	10	one	one	CD
37681	192	11	of	of	IN
37681	192	12	the	the	DT
37681	192	13	sanest	sane	JJS
37681	192	14	of	of	IN
37681	192	15	recent	recent	JJ
37681	192	16	monographs	monographs	NN
37681	192	17	upon	upon	IN
37681	192	18	the	the	DT
37681	192	19	subject,[13	subject,[13	CD
37681	192	20	]	]	-RRB-
37681	192	21	has	have	VBZ
37681	192	22	expressed	express	VBN
37681	192	23	his	-PRON-	PRP$
37681	192	24	views	view	NNS
37681	192	25	in	in	IN
37681	192	26	the	the	DT
37681	192	27	following	follow	VBG
37681	192	28	words	word	NNS
37681	192	29	:	:	:
37681	192	30	The	the	DT
37681	192	31	statement	statement	NN
37681	192	32	that	that	WDT
37681	192	33	a	a	DT
37681	192	34	given	give	VBN
37681	192	35	individual	individual	NN
37681	192	36	has	have	VBZ
37681	192	37	received	receive	VBN
37681	192	38	a	a	DT
37681	192	39	sound	sound	JJ
37681	192	40	geometrical	geometrical	JJ
37681	192	41	training	training	NN
37681	192	42	implies	imply	VBZ
37681	192	43	that	that	IN
37681	192	44	he	-PRON-	PRP
37681	192	45	has	have	VBZ
37681	192	46	segregated	segregate	VBN
37681	192	47	from	from	IN
37681	192	48	the	the	DT
37681	192	49	whole	whole	NN
37681	192	50	of	of	IN
37681	192	51	his	-PRON-	PRP$
37681	192	52	sense	sense	NN
37681	192	53	impressions	impression	VBZ
37681	192	54	a	a	DT
37681	192	55	certain	certain	JJ
37681	192	56	set	set	NN
37681	192	57	of	of	IN
37681	192	58	these	these	DT
37681	192	59	impressions	impression	NNS
37681	192	60	,	,	,
37681	192	61	that	that	IN
37681	192	62	he	-PRON-	PRP
37681	192	63	has	have	VBZ
37681	192	64	then	then	RB
37681	192	65	eliminated	eliminate	VBN
37681	192	66	from	from	IN
37681	192	67	their	-PRON-	PRP$
37681	192	68	consideration	consideration	NN
37681	192	69	all	all	DT
37681	192	70	irrelevant	irrelevant	JJ
37681	192	71	impressions	impression	NNS
37681	192	72	(	(	-LRB-
37681	192	73	in	in	IN
37681	192	74	other	other	JJ
37681	192	75	words	word	NNS
37681	192	76	,	,	,
37681	192	77	acquired	acquire	VBD
37681	192	78	a	a	DT
37681	192	79	subjective	subjective	JJ
37681	192	80	command	command	NN
37681	192	81	of	of	IN
37681	192	82	these	these	DT
37681	192	83	impressions	impression	NNS
37681	192	84	)	)	-RRB-
37681	192	85	,	,	,
37681	192	86	that	that	IN
37681	192	87	he	-PRON-	PRP
37681	192	88	has	have	VBZ
37681	192	89	developed	develop	VBN
37681	192	90	on	on	IN
37681	192	91	the	the	DT
37681	192	92	basis	basis	NN
37681	192	93	of	of	IN
37681	192	94	these	these	DT
37681	192	95	impressions	impression	NNS
37681	192	96	an	an	DT
37681	192	97	ordered	ordered	JJ
37681	192	98	and	and	CC
37681	192	99	continuous	continuous	JJ
37681	192	100	system	system	NN
37681	192	101	of	of	IN
37681	192	102	logical	logical	JJ
37681	192	103	deduction	deduction	NN
37681	192	104	,	,	,
37681	192	105	and	and	CC
37681	192	106	finally	finally	RB
37681	192	107	that	that	IN
37681	192	108	he	-PRON-	PRP
37681	192	109	is	be	VBZ
37681	192	110	capable	capable	JJ
37681	192	111	of	of	IN
37681	192	112	expressing	express	VBG
37681	192	113	the	the	DT
37681	192	114	nature	nature	NN
37681	192	115	of	of	IN
37681	192	116	these	these	DT
37681	192	117	impressions	impression	NNS
37681	192	118	and	and	CC
37681	192	119	his	-PRON-	PRP$
37681	192	120	deductions	deduction	NNS
37681	192	121	therefrom	therefrom	NN
37681	192	122	in	in	IN
37681	192	123	terms	term	NNS
37681	192	124	simple	simple	JJ
37681	192	125	and	and	CC
37681	192	126	free	free	JJ
37681	192	127	from	from	IN
37681	192	128	ambiguity	ambiguity	NN
37681	192	129	.	.	.
37681	193	1	Now	now	RB
37681	193	2	the	the	DT
37681	193	3	slightest	slight	JJS
37681	193	4	consideration	consideration	NN
37681	193	5	will	will	MD
37681	193	6	convince	convince	VB
37681	193	7	any	any	DT
37681	193	8	one	one	NN
37681	193	9	not	not	RB
37681	193	10	already	already	RB
37681	193	11	conversant	conversant	JJ
37681	193	12	with	with	IN
37681	193	13	the	the	DT
37681	193	14	idea	idea	NN
37681	193	15	,	,	,
37681	193	16	that	that	IN
37681	193	17	the	the	DT
37681	193	18	same	same	JJ
37681	193	19	sequence	sequence	NN
37681	193	20	of	of	IN
37681	193	21	mental	mental	JJ
37681	193	22	processes	process	NNS
37681	193	23	underlies	underlie	VBZ
37681	193	24	the	the	DT
37681	193	25	whole	whole	JJ
37681	193	26	career	career	NN
37681	193	27	of	of	IN
37681	193	28	any	any	DT
37681	193	29	individual	individual	NN
37681	193	30	in	in	IN
37681	193	31	any	any	DT
37681	193	32	walk	walk	NN
37681	193	33	of	of	IN
37681	193	34	life	life	NN
37681	193	35	if	if	IN
37681	193	36	only	only	RB
37681	193	37	he	-PRON-	PRP
37681	193	38	is	be	VBZ
37681	193	39	not	not	RB
37681	193	40	concerned	concerned	JJ
37681	193	41	entirely	entirely	RB
37681	193	42	with	with	IN
37681	193	43	manual	manual	JJ
37681	193	44	labor	labor	NN
37681	193	45	;	;	:
37681	193	46	consequently	consequently	RB
37681	193	47	a	a	DT
37681	193	48	full	full	JJ
37681	193	49	training	training	NN
37681	193	50	in	in	IN
37681	193	51	the	the	DT
37681	193	52	performance	performance	NN
37681	193	53	of	of	IN
37681	193	54	such	such	JJ
37681	193	55	sequences	sequence	NNS
37681	193	56	must	must	MD
37681	193	57	be	be	VB
37681	193	58	regarded	regard	VBN
37681	193	59	as	as	IN
37681	193	60	forming	form	VBG
37681	193	61	an	an	DT
37681	193	62	essential	essential	JJ
37681	193	63	part	part	NN
37681	193	64	of	of	IN
37681	193	65	any	any	DT
37681	193	66	education	education	NN
37681	193	67	worthy	worthy	JJ
37681	193	68	of	of	IN
37681	193	69	the	the	DT
37681	193	70	name	name	NN
37681	193	71	.	.	.
37681	194	1	Moreover	moreover	RB
37681	194	2	,	,	,
37681	194	3	the	the	DT
37681	194	4	full	full	JJ
37681	194	5	appreciation	appreciation	NN
37681	194	6	of	of	IN
37681	194	7	such	such	JJ
37681	194	8	processes	process	NNS
37681	194	9	has	have	VBZ
37681	194	10	a	a	DT
37681	194	11	higher	high	JJR
37681	194	12	value	value	NN
37681	194	13	than	than	IN
37681	194	14	is	be	VBZ
37681	194	15	contained	contain	VBN
37681	194	16	in	in	IN
37681	194	17	the	the	DT
37681	194	18	mental	mental	JJ
37681	194	19	training	training	NN
37681	194	20	involved	involve	VBN
37681	194	21	,	,	,
37681	194	22	great	great	JJ
37681	194	23	though	though	IN
37681	194	24	this	this	DT
37681	194	25	be	be	NN
37681	194	26	,	,	,
37681	194	27	for	for	IN
37681	194	28	it	-PRON-	PRP
37681	194	29	induces	induce	VBZ
37681	194	30	an	an	DT
37681	194	31	appreciation	appreciation	NN
37681	194	32	of	of	IN
37681	194	33	intellectual	intellectual	JJ
37681	194	34	unity	unity	NN
37681	194	35	and	and	CC
37681	194	36	beauty	beauty	NN
37681	194	37	which	which	WDT
37681	194	38	plays	play	VBZ
37681	194	39	for	for	IN
37681	194	40	the	the	DT
37681	194	41	mind	mind	NN
37681	194	42	that	that	IN
37681	194	43	part	part	NN
37681	194	44	which	which	WDT
37681	194	45	the	the	DT
37681	194	46	appreciation	appreciation	NN
37681	194	47	of	of	IN
37681	194	48	schemes	scheme	NNS
37681	194	49	of	of	IN
37681	194	50	shape	shape	NN
37681	194	51	and	and	CC
37681	194	52	color	color	NN
37681	194	53	plays	play	NNS
37681	194	54	for	for	IN
37681	194	55	the	the	DT
37681	194	56	artistic	artistic	JJ
37681	194	57	faculties	faculty	NNS
37681	194	58	;	;	:
37681	194	59	or	or	CC
37681	194	60	,	,	,
37681	194	61	again	again	RB
37681	194	62	,	,	,
37681	194	63	that	that	DT
37681	194	64	part	part	NN
37681	194	65	which	which	WDT
37681	194	66	the	the	DT
37681	194	67	appreciation	appreciation	NN
37681	194	68	of	of	IN
37681	194	69	a	a	DT
37681	194	70	body	body	NN
37681	194	71	of	of	IN
37681	194	72	religious	religious	JJ
37681	194	73	doctrine	doctrine	NN
37681	194	74	plays	play	NNS
37681	194	75	for	for	IN
37681	194	76	the	the	DT
37681	194	77	ethical	ethical	JJ
37681	194	78	aspirations	aspiration	NNS
37681	194	79	.	.	.
37681	195	1	Now	now	RB
37681	195	2	geometry	geometry	NN
37681	195	3	is	be	VBZ
37681	195	4	not	not	RB
37681	195	5	the	the	DT
37681	195	6	sole	sole	JJ
37681	195	7	possible	possible	JJ
37681	195	8	basis	basis	NN
37681	195	9	for	for	IN
37681	195	10	inculcating	inculcate	VBG
37681	195	11	this	this	DT
37681	195	12	appreciation	appreciation	NN
37681	195	13	.	.	.
37681	196	1	Logic	logic	NN
37681	196	2	is	be	VBZ
37681	196	3	an	an	DT
37681	196	4	alternative	alternative	NN
37681	196	5	for	for	IN
37681	196	6	adults	adult	NNS
37681	196	7	,	,	,
37681	196	8	provided	provide	VBN
37681	196	9	that	that	IN
37681	196	10	the	the	DT
37681	196	11	individual	individual	NN
37681	196	12	is	be	VBZ
37681	196	13	possessed	possess	VBN
37681	196	14	of	of	IN
37681	196	15	sufficient	sufficient	JJ
37681	196	16	wide	wide	NN
37681	196	17	,	,	,
37681	196	18	though	though	IN
37681	196	19	rough	rough	JJ
37681	196	20	,	,	,
37681	196	21	experience	experience	NN
37681	196	22	on	on	IN
37681	196	23	which	which	WDT
37681	196	24	to	to	TO
37681	196	25	base	base	VB
37681	196	26	his	-PRON-	PRP$
37681	196	27	reasoning	reasoning	NN
37681	196	28	.	.	.
37681	197	1	Geometry	geometry	NN
37681	197	2	is	be	VBZ
37681	197	3	,	,	,
37681	197	4	however	however	RB
37681	197	5	,	,	,
37681	197	6	highly	highly	RB
37681	197	7	desirable	desirable	JJ
37681	197	8	in	in	IN
37681	197	9	that	that	IN
37681	197	10	the	the	DT
37681	197	11	objective	objective	JJ
37681	197	12	bases	basis	NNS
37681	197	13	are	be	VBP
37681	197	14	so	so	RB
37681	197	15	simple	simple	JJ
37681	197	16	and	and	CC
37681	197	17	precise	precise	JJ
37681	197	18	that	that	IN
37681	197	19	they	-PRON-	PRP
37681	197	20	can	can	MD
37681	197	21	be	be	VB
37681	197	22	grasped	grasp	VBN
37681	197	23	at	at	IN
37681	197	24	an	an	DT
37681	197	25	early	early	JJ
37681	197	26	age	age	NN
37681	197	27	,	,	,
37681	197	28	that	that	IN
37681	197	29	the	the	DT
37681	197	30	amount	amount	NN
37681	197	31	of	of	IN
37681	197	32	training	training	NN
37681	197	33	for	for	IN
37681	197	34	the	the	DT
37681	197	35	imagination	imagination	NN
37681	197	36	is	be	VBZ
37681	197	37	very	very	RB
37681	197	38	large	large	JJ
37681	197	39	,	,	,
37681	197	40	that	that	IN
37681	197	41	the	the	DT
37681	197	42	deductive	deductive	JJ
37681	197	43	processes	process	NNS
37681	197	44	are	be	VBP
37681	197	45	not	not	RB
37681	197	46	beyond	beyond	IN
37681	197	47	the	the	DT
37681	197	48	scope	scope	NN
37681	197	49	of	of	IN
37681	197	50	ordinary	ordinary	JJ
37681	197	51	boys	boy	NNS
37681	197	52	,	,	,
37681	197	53	and	and	CC
37681	197	54	finally	finally	RB
37681	197	55	that	that	IN
37681	197	56	it	-PRON-	PRP
37681	197	57	affords	afford	VBZ
37681	197	58	a	a	DT
37681	197	59	better	well	JJR
37681	197	60	basis	basis	NN
37681	197	61	for	for	IN
37681	197	62	exercise	exercise	NN
37681	197	63	in	in	IN
37681	197	64	the	the	DT
37681	197	65	art	art	NN
37681	197	66	of	of	IN
37681	197	67	simple	simple	JJ
37681	197	68	and	and	CC
37681	197	69	exact	exact	JJ
37681	197	70	expression	expression	NN
37681	197	71	than	than	IN
37681	197	72	any	any	DT
37681	197	73	other	other	JJ
37681	197	74	possible	possible	JJ
37681	197	75	subject	subject	NN
37681	197	76	of	of	IN
37681	197	77	a	a	DT
37681	197	78	school	school	NN
37681	197	79	course	course	NN
37681	197	80	.	.	.
37681	198	1	Are	be	VBP
37681	198	2	these	these	DT
37681	198	3	results	result	NNS
37681	198	4	really	really	RB
37681	198	5	secured	secure	VBN
37681	198	6	by	by	IN
37681	198	7	teachers	teacher	NNS
37681	198	8	,	,	,
37681	198	9	however	however	RB
37681	198	10	,	,	,
37681	198	11	or	or	CC
37681	198	12	are	be	VBP
37681	198	13	they	-PRON-	PRP
37681	198	14	merely	merely	RB
37681	198	15	imagined	imagine	VBN
37681	198	16	by	by	IN
37681	198	17	the	the	DT
37681	198	18	pedagogue	pedagogue	NN
37681	198	19	as	as	IN
37681	198	20	a	a	DT
37681	198	21	justification	justification	NN
37681	198	22	for	for	IN
37681	198	23	his	-PRON-	PRP$
37681	198	24	existence	existence	NN
37681	198	25	?	?	.
37681	199	1	Do	do	VBP
37681	199	2	teachers	teacher	NNS
37681	199	3	have	have	VB
37681	199	4	any	any	DT
37681	199	5	such	such	JJ
37681	199	6	appreciation	appreciation	NN
37681	199	7	of	of	IN
37681	199	8	geometry	geometry	NN
37681	199	9	as	as	IN
37681	199	10	has	have	VBZ
37681	199	11	been	be	VBN
37681	199	12	suggested	suggest	VBN
37681	199	13	,	,	,
37681	199	14	and	and	CC
37681	199	15	even	even	RB
37681	199	16	if	if	IN
37681	199	17	they	-PRON-	PRP
37681	199	18	have	have	VBP
37681	199	19	it	-PRON-	PRP
37681	199	20	,	,	,
37681	199	21	do	do	VBP
37681	199	22	they	-PRON-	PRP
37681	199	23	impart	impart	VB
37681	199	24	it	-PRON-	PRP
37681	199	25	to	to	IN
37681	199	26	their	-PRON-	PRP$
37681	199	27	pupils	pupil	NNS
37681	199	28	?	?	.
37681	200	1	In	in	IN
37681	200	2	reply	reply	NN
37681	200	3	it	-PRON-	PRP
37681	200	4	may	may	MD
37681	200	5	be	be	VB
37681	200	6	said	say	VBN
37681	200	7	,	,	,
37681	200	8	probably	probably	RB
37681	200	9	with	with	IN
37681	200	10	perfect	perfect	JJ
37681	200	11	safety	safety	NN
37681	200	12	,	,	,
37681	200	13	that	that	IN
37681	200	14	teachers	teacher	NNS
37681	200	15	of	of	IN
37681	200	16	geometry	geometry	NN
37681	200	17	appreciate	appreciate	VBP
37681	200	18	their	-PRON-	PRP$
37681	200	19	subject	subject	NN
37681	200	20	and	and	CC
37681	200	21	lead	lead	VBP
37681	200	22	their	-PRON-	PRP$
37681	200	23	pupils	pupil	NNS
37681	200	24	to	to	TO
37681	200	25	appreciate	appreciate	VB
37681	200	26	it	-PRON-	PRP
37681	200	27	to	to	IN
37681	200	28	quite	quite	RB
37681	200	29	as	as	RB
37681	200	30	great	great	JJ
37681	200	31	a	a	DT
37681	200	32	degree	degree	NN
37681	200	33	as	as	IN
37681	200	34	obtains	obtain	NNS
37681	200	35	in	in	IN
37681	200	36	any	any	DT
37681	200	37	other	other	JJ
37681	200	38	branch	branch	NN
37681	200	39	of	of	IN
37681	200	40	education	education	NN
37681	200	41	.	.	.
37681	201	1	What	what	WP
37681	201	2	teacher	teacher	NN
37681	201	3	appreciates	appreciate	VBZ
37681	201	4	fully	fully	RB
37681	201	5	the	the	DT
37681	201	6	beauties	beauty	NNS
37681	201	7	of	of	IN
37681	201	8	"	"	``
37681	201	9	In	in	IN
37681	201	10	Memoriam	Memoriam	NNP
37681	201	11	,	,	,
37681	201	12	"	"	''
37681	201	13	or	or	CC
37681	201	14	of	of	IN
37681	201	15	"	"	``
37681	201	16	Hamlet	Hamlet	NNP
37681	201	17	,	,	,
37681	201	18	"	"	''
37681	201	19	or	or	CC
37681	201	20	of	of	IN
37681	201	21	"	"	``
37681	201	22	Paradise	Paradise	NNP
37681	201	23	Lost	lose	VBN
37681	201	24	,	,	,
37681	201	25	"	"	''
37681	201	26	and	and	CC
37681	201	27	what	what	WP
37681	201	28	one	one	NN
37681	201	29	inspires	inspire	VBZ
37681	201	30	his	-PRON-	PRP$
37681	201	31	pupils	pupil	NNS
37681	201	32	with	with	IN
37681	201	33	all	all	PDT
37681	201	34	the	the	DT
37681	201	35	nobility	nobility	NN
37681	201	36	of	of	IN
37681	201	37	these	these	DT
37681	201	38	world	world	NN
37681	201	39	classics	classic	NNS
37681	201	40	?	?	.
37681	202	1	What	what	WP
37681	202	2	teacher	teacher	NN
37681	202	3	sees	see	VBZ
37681	202	4	in	in	IN
37681	202	5	biology	biology	NN
37681	202	6	all	all	PDT
37681	202	7	the	the	DT
37681	202	8	grandeur	grandeur	NN
37681	202	9	of	of	IN
37681	202	10	the	the	DT
37681	202	11	evolution	evolution	NN
37681	202	12	of	of	IN
37681	202	13	the	the	DT
37681	202	14	race	race	NN
37681	202	15	,	,	,
37681	202	16	or	or	CC
37681	202	17	imparts	impart	VBZ
37681	202	18	to	to	IN
37681	202	19	his	-PRON-	PRP$
37681	202	20	pupils	pupil	NNS
37681	202	21	the	the	DT
37681	202	22	noble	noble	JJ
37681	202	23	lessons	lesson	NNS
37681	202	24	of	of	IN
37681	202	25	life	life	NN
37681	202	26	that	that	WDT
37681	202	27	the	the	DT
37681	202	28	study	study	NN
37681	202	29	of	of	IN
37681	202	30	this	this	DT
37681	202	31	subject	subject	NN
37681	202	32	should	should	MD
37681	202	33	suggest	suggest	VB
37681	202	34	?	?	.
37681	203	1	What	what	WP
37681	203	2	teacher	teacher	NN
37681	203	3	of	of	IN
37681	203	4	Latin	Latin	NNP
37681	203	5	brings	bring	VBZ
37681	203	6	his	-PRON-	PRP$
37681	203	7	pupils	pupil	NNS
37681	203	8	to	to	TO
37681	203	9	read	read	VB
37681	203	10	the	the	DT
37681	203	11	ancient	ancient	JJ
37681	203	12	letters	letter	NNS
37681	203	13	with	with	IN
37681	203	14	full	full	JJ
37681	203	15	appreciation	appreciation	NN
37681	203	16	of	of	IN
37681	203	17	the	the	DT
37681	203	18	dignity	dignity	NN
37681	203	19	of	of	IN
37681	203	20	style	style	NN
37681	203	21	and	and	CC
37681	203	22	the	the	DT
37681	203	23	nobility	nobility	NN
37681	203	24	of	of	IN
37681	203	25	thought	thought	NN
37681	203	26	that	that	IN
37681	203	27	they	-PRON-	PRP
37681	203	28	contain	contain	VBP
37681	203	29	?	?	.
37681	204	1	And	and	CC
37681	204	2	what	what	WP
37681	204	3	teacher	teacher	NN
37681	204	4	of	of	IN
37681	204	5	French	French	NNP
37681	204	6	succeeds	succeed	VBZ
37681	204	7	in	in	IN
37681	204	8	bringing	bring	VBG
37681	204	9	a	a	DT
37681	204	10	pupil	pupil	NN
37681	204	11	to	to	TO
37681	204	12	carry	carry	VB
37681	204	13	on	on	RP
37681	204	14	a	a	DT
37681	204	15	conversation	conversation	NN
37681	204	16	,	,	,
37681	204	17	to	to	TO
37681	204	18	read	read	VB
37681	204	19	a	a	DT
37681	204	20	French	french	JJ
37681	204	21	magazine	magazine	NN
37681	204	22	,	,	,
37681	204	23	to	to	TO
37681	204	24	see	see	VB
37681	204	25	the	the	DT
37681	204	26	history	history	NN
37681	204	27	imbedded	imbed	VBN
37681	204	28	in	in	IN
37681	204	29	the	the	DT
37681	204	30	words	word	NNS
37681	204	31	that	that	WDT
37681	204	32	are	be	VBP
37681	204	33	used	use	VBN
37681	204	34	,	,	,
37681	204	35	to	to	TO
37681	204	36	realize	realize	VB
37681	204	37	the	the	DT
37681	204	38	charm	charm	NN
37681	204	39	and	and	CC
37681	204	40	power	power	NN
37681	204	41	of	of	IN
37681	204	42	the	the	DT
37681	204	43	language	language	NN
37681	204	44	,	,	,
37681	204	45	or	or	CC
37681	204	46	to	to	TO
37681	204	47	appreciate	appreciate	VB
37681	204	48	to	to	IN
37681	204	49	the	the	DT
37681	204	50	full	full	JJ
37681	204	51	a	a	DT
37681	204	52	single	single	JJ
37681	204	53	classic	classic	NN
37681	204	54	?	?	.
37681	205	1	In	in	IN
37681	205	2	other	other	JJ
37681	205	3	words	word	NNS
37681	205	4	,	,	,
37681	205	5	none	none	NN
37681	205	6	of	of	IN
37681	205	7	us	-PRON-	PRP
37681	205	8	fully	fully	RB
37681	205	9	appreciates	appreciate	VBZ
37681	205	10	his	-PRON-	PRP$
37681	205	11	subject	subject	NN
37681	205	12	,	,	,
37681	205	13	and	and	CC
37681	205	14	none	none	NN
37681	205	15	of	of	IN
37681	205	16	us	-PRON-	PRP
37681	205	17	can	can	MD
37681	205	18	hope	hope	VB
37681	205	19	to	to	TO
37681	205	20	bring	bring	VB
37681	205	21	his	-PRON-	PRP$
37681	205	22	pupils	pupil	NNS
37681	205	23	to	to	IN
37681	205	24	the	the	DT
37681	205	25	ideal	ideal	JJ
37681	205	26	attitude	attitude	NN
37681	205	27	toward	toward	IN
37681	205	28	any	any	DT
37681	205	29	part	part	NN
37681	205	30	of	of	IN
37681	205	31	it	-PRON-	PRP
37681	205	32	.	.	.
37681	206	1	But	but	CC
37681	206	2	it	-PRON-	PRP
37681	206	3	is	be	VBZ
37681	206	4	probable	probable	JJ
37681	206	5	that	that	IN
37681	206	6	the	the	DT
37681	206	7	teacher	teacher	NN
37681	206	8	of	of	IN
37681	206	9	geometry	geometry	NN
37681	206	10	succeeds	succeed	VBZ
37681	206	11	relatively	relatively	RB
37681	206	12	better	well	JJR
37681	206	13	than	than	IN
37681	206	14	the	the	DT
37681	206	15	teacher	teacher	NN
37681	206	16	of	of	IN
37681	206	17	other	other	JJ
37681	206	18	subjects	subject	NNS
37681	206	19	,	,	,
37681	206	20	because	because	IN
37681	206	21	the	the	DT
37681	206	22	science	science	NN
37681	206	23	has	have	VBZ
37681	206	24	reached	reach	VBN
37681	206	25	a	a	DT
37681	206	26	relatively	relatively	RB
37681	206	27	higher	high	JJR
37681	206	28	state	state	NN
37681	206	29	of	of	IN
37681	206	30	perfection	perfection	NN
37681	206	31	.	.	.
37681	207	1	The	the	DT
37681	207	2	body	body	NN
37681	207	3	of	of	IN
37681	207	4	truth	truth	NN
37681	207	5	in	in	IN
37681	207	6	geometry	geometry	NN
37681	207	7	has	have	VBZ
37681	207	8	been	be	VBN
37681	207	9	more	more	RBR
37681	207	10	clearly	clearly	RB
37681	207	11	marked	mark	VBN
37681	207	12	out	out	RP
37681	207	13	,	,	,
37681	207	14	it	-PRON-	PRP
37681	207	15	has	have	VBZ
37681	207	16	been	be	VBN
37681	207	17	more	more	RBR
37681	207	18	successfully	successfully	RB
37681	207	19	fitted	fit	VBN
37681	207	20	together	together	RB
37681	207	21	,	,	,
37681	207	22	its	-PRON-	PRP$
37681	207	23	lesson	lesson	NN
37681	207	24	is	be	VBZ
37681	207	25	more	more	RBR
37681	207	26	patent	patent	NN
37681	207	27	,	,	,
37681	207	28	and	and	CC
37681	207	29	the	the	DT
37681	207	30	experience	experience	NN
37681	207	31	of	of	IN
37681	207	32	centuries	century	NNS
37681	207	33	has	have	VBZ
37681	207	34	brought	bring	VBN
37681	207	35	it	-PRON-	PRP
37681	207	36	into	into	IN
37681	207	37	a	a	DT
37681	207	38	shape	shape	NN
37681	207	39	that	that	WDT
37681	207	40	is	be	VBZ
37681	207	41	more	more	RBR
37681	207	42	usable	usable	JJ
37681	207	43	in	in	IN
37681	207	44	the	the	DT
37681	207	45	school	school	NN
37681	207	46	.	.	.
37681	208	1	While	while	IN
37681	208	2	,	,	,
37681	208	3	therefore	therefore	RB
37681	208	4	,	,	,
37681	208	5	we	-PRON-	PRP
37681	208	6	have	have	VBP
37681	208	7	all	all	DT
37681	208	8	kinds	kind	NNS
37681	208	9	of	of	IN
37681	208	10	teaching	teaching	NN
37681	208	11	in	in	IN
37681	208	12	all	all	DT
37681	208	13	kinds	kind	NNS
37681	208	14	of	of	IN
37681	208	15	subjects	subject	NNS
37681	208	16	,	,	,
37681	208	17	the	the	DT
37681	208	18	very	very	JJ
37681	208	19	nature	nature	NN
37681	208	20	of	of	IN
37681	208	21	the	the	DT
37681	208	22	case	case	NN
37681	208	23	leads	lead	VBZ
37681	208	24	to	to	IN
37681	208	25	the	the	DT
37681	208	26	belief	belief	NN
37681	208	27	that	that	IN
37681	208	28	the	the	DT
37681	208	29	class	class	NN
37681	208	30	in	in	IN
37681	208	31	geometry	geometry	NN
37681	208	32	receives	receive	VBZ
37681	208	33	quite	quite	RB
37681	208	34	as	as	RB
37681	208	35	much	much	RB
37681	208	36	from	from	IN
37681	208	37	the	the	DT
37681	208	38	teacher	teacher	NN
37681	208	39	and	and	CC
37681	208	40	the	the	DT
37681	208	41	subject	subject	NN
37681	208	42	as	as	IN
37681	208	43	the	the	DT
37681	208	44	class	class	NN
37681	208	45	in	in	IN
37681	208	46	any	any	DT
37681	208	47	other	other	JJ
37681	208	48	branch	branch	NN
37681	208	49	in	in	IN
37681	208	50	the	the	DT
37681	208	51	school	school	NN
37681	208	52	curriculum	curriculum	NN
37681	208	53	.	.	.
37681	209	1	But	but	CC
37681	209	2	is	be	VBZ
37681	209	3	this	this	DT
37681	209	4	not	not	RB
37681	209	5	mere	mere	JJ
37681	209	6	conjecture	conjecture	NN
37681	209	7	?	?	.
37681	210	1	What	what	WP
37681	210	2	are	be	VBP
37681	210	3	the	the	DT
37681	210	4	results	result	NNS
37681	210	5	of	of	IN
37681	210	6	scientific	scientific	JJ
37681	210	7	investigation	investigation	NN
37681	210	8	of	of	IN
37681	210	9	the	the	DT
37681	210	10	teaching	teaching	NN
37681	210	11	of	of	IN
37681	210	12	geometry	geometry	NN
37681	210	13	?	?	.
37681	211	1	Unfortunately	unfortunately	RB
37681	211	2	there	there	EX
37681	211	3	is	be	VBZ
37681	211	4	little	little	JJ
37681	211	5	hope	hope	NN
37681	211	6	from	from	IN
37681	211	7	the	the	DT
37681	211	8	results	result	NNS
37681	211	9	of	of	IN
37681	211	10	such	such	PDT
37681	211	11	an	an	DT
37681	211	12	inquiry	inquiry	NN
37681	211	13	,	,	,
37681	211	14	either	either	CC
37681	211	15	here	here	RB
37681	211	16	or	or	CC
37681	211	17	in	in	IN
37681	211	18	other	other	JJ
37681	211	19	fields	field	NNS
37681	211	20	.	.	.
37681	212	1	We	-PRON-	PRP
37681	212	2	can	can	MD
37681	212	3	not	not	RB
37681	212	4	first	first	RB
37681	212	5	weigh	weigh	VB
37681	212	6	a	a	DT
37681	212	7	pupil	pupil	NN
37681	212	8	in	in	IN
37681	212	9	an	an	DT
37681	212	10	intellectual	intellectual	JJ
37681	212	11	or	or	CC
37681	212	12	moral	moral	JJ
37681	212	13	balance	balance	NN
37681	212	14	,	,	,
37681	212	15	then	then	RB
37681	212	16	feed	feed	VB
37681	212	17	him	-PRON-	PRP
37681	212	18	geometry	geometry	NN
37681	212	19	,	,	,
37681	212	20	and	and	CC
37681	212	21	then	then	RB
37681	212	22	weigh	weigh	VB
37681	212	23	him	-PRON-	PRP
37681	212	24	again	again	RB
37681	212	25	,	,	,
37681	212	26	and	and	CC
37681	212	27	then	then	RB
37681	212	28	set	set	VB
37681	212	29	back	back	RP
37681	212	30	his	-PRON-	PRP$
37681	212	31	clock	clock	NN
37681	212	32	of	of	IN
37681	212	33	time	time	NN
37681	212	34	and	and	CC
37681	212	35	begin	begin	VB
37681	212	36	all	all	RB
37681	212	37	over	over	RB
37681	212	38	again	again	RB
37681	212	39	with	with	IN
37681	212	40	the	the	DT
37681	212	41	same	same	JJ
37681	212	42	individual	individual	NN
37681	212	43	.	.	.
37681	213	1	There	there	EX
37681	213	2	is	be	VBZ
37681	213	3	no	no	DT
37681	213	4	"	"	``
37681	213	5	before	before	IN
37681	213	6	taking	take	VBG
37681	213	7	"	"	''
37681	213	8	and	and	CC
37681	213	9	"	"	``
37681	213	10	after	after	IN
37681	213	11	taking	take	VBG
37681	213	12	"	"	''
37681	213	13	of	of	IN
37681	213	14	a	a	DT
37681	213	15	subject	subject	NN
37681	213	16	that	that	WDT
37681	213	17	extends	extend	VBZ
37681	213	18	over	over	IN
37681	213	19	a	a	DT
37681	213	20	year	year	NN
37681	213	21	or	or	CC
37681	213	22	two	two	CD
37681	213	23	of	of	IN
37681	213	24	a	a	DT
37681	213	25	pupil	pupil	NN
37681	213	26	's	's	POS
37681	213	27	life	life	NN
37681	213	28	.	.	.
37681	214	1	We	-PRON-	PRP
37681	214	2	can	can	MD
37681	214	3	weigh	weigh	VB
37681	214	4	utilities	utility	NNS
37681	214	5	roughly	roughly	RB
37681	214	6	,	,	,
37681	214	7	we	-PRON-	PRP
37681	214	8	can	can	MD
37681	214	9	estimate	estimate	VB
37681	214	10	the	the	DT
37681	214	11	pleasure	pleasure	NN
37681	214	12	of	of	IN
37681	214	13	a	a	DT
37681	214	14	subject	subject	NN
37681	214	15	relatively	relatively	RB
37681	214	16	,	,	,
37681	214	17	but	but	CC
37681	214	18	we	-PRON-	PRP
37681	214	19	can	can	MD
37681	214	20	not	not	RB
37681	214	21	say	say	VB
37681	214	22	that	that	IN
37681	214	23	geometry	geometry	NN
37681	214	24	is	be	VBZ
37681	214	25	worth	worth	JJ
37681	214	26	so	so	RB
37681	214	27	many	many	JJ
37681	214	28	dollars	dollar	NNS
37681	214	29	,	,	,
37681	214	30	and	and	CC
37681	214	31	history	history	NN
37681	214	32	so	so	RB
37681	214	33	many	many	JJ
37681	214	34	,	,	,
37681	214	35	and	and	CC
37681	214	36	so	so	RB
37681	214	37	on	on	RB
37681	214	38	through	through	IN
37681	214	39	the	the	DT
37681	214	40	curriculum	curriculum	NN
37681	214	41	.	.	.
37681	215	1	The	the	DT
37681	215	2	best	good	JJS
37681	215	3	we	-PRON-	PRP
37681	215	4	can	can	MD
37681	215	5	do	do	VB
37681	215	6	is	be	VBZ
37681	215	7	to	to	TO
37681	215	8	ask	ask	VB
37681	215	9	ourselves	-PRON-	PRP
37681	215	10	what	what	WP
37681	215	11	the	the	DT
37681	215	12	various	various	JJ
37681	215	13	subjects	subject	NNS
37681	215	14	,	,	,
37681	215	15	with	with	IN
37681	215	16	teachers	teacher	NNS
37681	215	17	of	of	IN
37681	215	18	fairly	fairly	RB
37681	215	19	equal	equal	JJ
37681	215	20	merit	merit	NN
37681	215	21	,	,	,
37681	215	22	have	have	VBP
37681	215	23	done	do	VBN
37681	215	24	for	for	IN
37681	215	25	us	-PRON-	PRP
37681	215	26	,	,	,
37681	215	27	and	and	CC
37681	215	28	to	to	TO
37681	215	29	inquire	inquire	VB
37681	215	30	what	what	WP
37681	215	31	has	have	VBZ
37681	215	32	been	be	VBN
37681	215	33	the	the	DT
37681	215	34	experience	experience	NN
37681	215	35	of	of	IN
37681	215	36	other	other	JJ
37681	215	37	persons	person	NNS
37681	215	38	.	.	.
37681	216	1	Such	such	PDT
37681	216	2	an	an	DT
37681	216	3	investigation	investigation	NN
37681	216	4	results	result	VBZ
37681	216	5	in	in	IN
37681	216	6	showing	show	VBG
37681	216	7	that	that	IN
37681	216	8	,	,	,
37681	216	9	with	with	IN
37681	216	10	few	few	JJ
37681	216	11	exceptions	exception	NNS
37681	216	12	,	,	,
37681	216	13	people	people	NNS
37681	216	14	who	who	WP
37681	216	15	have	have	VBP
37681	216	16	studied	study	VBN
37681	216	17	geometry	geometry	NN
37681	216	18	received	receive	VBD
37681	216	19	as	as	RB
37681	216	20	much	much	JJ
37681	216	21	of	of	IN
37681	216	22	pleasure	pleasure	NN
37681	216	23	,	,	,
37681	216	24	of	of	IN
37681	216	25	inspiration	inspiration	NN
37681	216	26	,	,	,
37681	216	27	of	of	IN
37681	216	28	satisfaction	satisfaction	NN
37681	216	29	,	,	,
37681	216	30	of	of	IN
37681	216	31	what	what	WP
37681	216	32	they	-PRON-	PRP
37681	216	33	call	call	VBP
37681	216	34	training	training	NN
37681	216	35	from	from	IN
37681	216	36	geometry	geometry	NN
37681	216	37	as	as	IN
37681	216	38	from	from	IN
37681	216	39	any	any	DT
37681	216	40	other	other	JJ
37681	216	41	subject	subject	NN
37681	216	42	of	of	IN
37681	216	43	study,--given	study,--given	NNP
37681	216	44	teachers	teacher	NNS
37681	216	45	of	of	IN
37681	216	46	equal	equal	JJ
37681	216	47	merit,--and	merit,--and	NNP
37681	216	48	that	that	IN
37681	216	49	they	-PRON-	PRP
37681	216	50	would	would	MD
37681	216	51	not	not	RB
37681	216	52	willingly	willingly	RB
37681	216	53	give	give	VB
37681	216	54	up	up	RP
37681	216	55	the	the	DT
37681	216	56	something	something	NN
37681	216	57	which	which	WDT
37681	216	58	geometry	geometry	NN
37681	216	59	brought	bring	VBD
37681	216	60	to	to	IN
37681	216	61	them	-PRON-	PRP
37681	216	62	.	.	.
37681	217	1	If	if	IN
37681	217	2	this	this	DT
37681	217	3	were	be	VBD
37681	217	4	not	not	RB
37681	217	5	the	the	DT
37681	217	6	feeling	feeling	NN
37681	217	7	,	,	,
37681	217	8	and	and	CC
37681	217	9	if	if	IN
37681	217	10	humanity	humanity	NN
37681	217	11	believed	believe	VBD
37681	217	12	that	that	IN
37681	217	13	geometry	geometry	NN
37681	217	14	is	be	VBZ
37681	217	15	what	what	WP
37681	217	16	Mr.	Mr.	NNP
37681	217	17	Locke	Locke	NNP
37681	217	18	's	's	POS
37681	217	19	words	word	NNS
37681	217	20	would	would	MD
37681	217	21	seem	seem	VB
37681	217	22	to	to	TO
37681	217	23	indicate	indicate	VB
37681	217	24	,	,	,
37681	217	25	it	-PRON-	PRP
37681	217	26	would	would	MD
37681	217	27	long	long	RB
37681	217	28	ago	ago	RB
37681	217	29	have	have	VBP
37681	217	30	banished	banish	VBN
37681	217	31	it	-PRON-	PRP
37681	217	32	from	from	IN
37681	217	33	the	the	DT
37681	217	34	schools	school	NNS
37681	217	35	,	,	,
37681	217	36	since	since	IN
37681	217	37	upon	upon	IN
37681	217	38	this	this	DT
37681	217	39	ground	ground	NN
37681	217	40	rather	rather	RB
37681	217	41	than	than	IN
37681	217	42	upon	upon	IN
37681	217	43	the	the	DT
37681	217	44	ground	ground	NN
37681	217	45	of	of	IN
37681	217	46	utility	utility	NN
37681	217	47	the	the	DT
37681	217	48	subject	subject	NN
37681	217	49	has	have	VBZ
37681	217	50	always	always	RB
37681	217	51	stood	stand	VBN
37681	217	52	.	.	.
37681	218	1	These	these	DT
37681	218	2	seem	seem	VBP
37681	218	3	to	to	TO
37681	218	4	be	be	VB
37681	218	5	the	the	DT
37681	218	6	great	great	JJ
37681	218	7	reasons	reason	NNS
37681	218	8	for	for	IN
37681	218	9	the	the	DT
37681	218	10	study	study	NN
37681	218	11	of	of	IN
37681	218	12	geometry	geometry	NN
37681	218	13	,	,	,
37681	218	14	and	and	CC
37681	218	15	to	to	TO
37681	218	16	search	search	VB
37681	218	17	for	for	IN
37681	218	18	others	other	NNS
37681	218	19	would	would	MD
37681	218	20	tend	tend	VB
37681	218	21	to	to	TO
37681	218	22	weaken	weaken	VB
37681	218	23	the	the	DT
37681	218	24	argument	argument	NN
37681	218	25	.	.	.
37681	219	1	At	at	IN
37681	219	2	first	first	JJ
37681	219	3	sight	sight	NN
37681	219	4	they	-PRON-	PRP
37681	219	5	may	may	MD
37681	219	6	not	not	RB
37681	219	7	seem	seem	VB
37681	219	8	to	to	TO
37681	219	9	justify	justify	VB
37681	219	10	the	the	DT
37681	219	11	expenditure	expenditure	NN
37681	219	12	of	of	IN
37681	219	13	time	time	NN
37681	219	14	that	that	WDT
37681	219	15	geometry	geometry	NN
37681	219	16	demands	demand	VBZ
37681	219	17	,	,	,
37681	219	18	and	and	CC
37681	219	19	they	-PRON-	PRP
37681	219	20	may	may	MD
37681	219	21	seem	seem	VB
37681	219	22	unduly	unduly	RB
37681	219	23	to	to	TO
37681	219	24	neglect	neglect	VB
37681	219	25	the	the	DT
37681	219	26	argument	argument	NN
37681	219	27	that	that	IN
37681	219	28	geometry	geometry	NN
37681	219	29	is	be	VBZ
37681	219	30	a	a	DT
37681	219	31	stepping	stepping	JJ
37681	219	32	-	-	HYPH
37681	219	33	stone	stone	NN
37681	219	34	to	to	IN
37681	219	35	higher	high	JJR
37681	219	36	mathematics	mathematic	NNS
37681	219	37	.	.	.
37681	220	1	Each	each	DT
37681	220	2	of	of	IN
37681	220	3	these	these	DT
37681	220	4	points	point	NNS
37681	220	5	,	,	,
37681	220	6	however	however	RB
37681	220	7	,	,	,
37681	220	8	has	have	VBZ
37681	220	9	been	be	VBN
37681	220	10	neglected	neglect	VBN
37681	220	11	purposely	purposely	RB
37681	220	12	.	.	.
37681	221	1	A	a	DT
37681	221	2	pupil	pupil	NN
37681	221	3	has	have	VBZ
37681	221	4	a	a	DT
37681	221	5	number	number	NN
37681	221	6	of	of	IN
37681	221	7	school	school	NN
37681	221	8	years	year	NNS
37681	221	9	at	at	IN
37681	221	10	his	-PRON-	PRP$
37681	221	11	disposal	disposal	NN
37681	221	12	;	;	:
37681	221	13	to	to	IN
37681	221	14	what	what	WP
37681	221	15	shall	shall	MD
37681	221	16	they	-PRON-	PRP
37681	221	17	be	be	VB
37681	221	18	devoted	devote	VBN
37681	221	19	?	?	.
37681	222	1	To	to	TO
37681	222	2	literature	literature	VB
37681	222	3	?	?	.
37681	223	1	What	what	WDT
37681	223	2	claim	claim	NN
37681	223	3	has	have	VBZ
37681	223	4	letters	letter	NNS
37681	223	5	that	that	WDT
37681	223	6	is	be	VBZ
37681	223	7	such	such	JJ
37681	223	8	as	as	IN
37681	223	9	to	to	TO
37681	223	10	justify	justify	VB
37681	223	11	the	the	DT
37681	223	12	exclusion	exclusion	NN
37681	223	13	of	of	IN
37681	223	14	geometry	geometry	NN
37681	223	15	?	?	.
37681	224	1	To	to	IN
37681	224	2	music	music	NN
37681	224	3	,	,	,
37681	224	4	or	or	CC
37681	224	5	natural	natural	JJ
37681	224	6	science	science	NN
37681	224	7	,	,	,
37681	224	8	or	or	CC
37681	224	9	language	language	NN
37681	224	10	?	?	.
37681	225	1	These	these	DT
37681	225	2	are	be	VBP
37681	225	3	all	all	DT
37681	225	4	valuable	valuable	JJ
37681	225	5	,	,	,
37681	225	6	and	and	CC
37681	225	7	all	all	DT
37681	225	8	should	should	MD
37681	225	9	be	be	VB
37681	225	10	studied	study	VBN
37681	225	11	by	by	IN
37681	225	12	one	one	CD
37681	225	13	seeking	seek	VBG
37681	225	14	a	a	DT
37681	225	15	liberal	liberal	JJ
37681	225	16	education	education	NN
37681	225	17	;	;	:
37681	225	18	but	but	CC
37681	225	19	for	for	IN
37681	225	20	the	the	DT
37681	225	21	same	same	JJ
37681	225	22	reason	reason	NN
37681	225	23	geometry	geometry	NN
37681	225	24	should	should	MD
37681	225	25	have	have	VB
37681	225	26	its	-PRON-	PRP$
37681	225	27	place	place	NN
37681	225	28	.	.	.
37681	226	1	What	what	WDT
37681	226	2	subject	subject	NN
37681	226	3	,	,	,
37681	226	4	in	in	IN
37681	226	5	fine	fine	NN
37681	226	6	,	,	,
37681	226	7	can	can	MD
37681	226	8	supply	supply	VB
37681	226	9	exactly	exactly	RB
37681	226	10	what	what	WP
37681	226	11	geometry	geometry	NN
37681	226	12	does	do	VBZ
37681	226	13	?	?	.
37681	227	1	And	and	CC
37681	227	2	if	if	IN
37681	227	3	none	none	NN
37681	227	4	,	,	,
37681	227	5	then	then	RB
37681	227	6	how	how	WRB
37681	227	7	can	can	MD
37681	227	8	the	the	DT
37681	227	9	pupil	pupil	NN
37681	227	10	's	's	POS
37681	227	11	time	time	NN
37681	227	12	be	be	VB
37681	227	13	better	well	RBR
37681	227	14	expended	expend	VBN
37681	227	15	than	than	IN
37681	227	16	in	in	IN
37681	227	17	the	the	DT
37681	227	18	study	study	NN
37681	227	19	of	of	IN
37681	227	20	this	this	DT
37681	227	21	science	science	NN
37681	227	22	?	?	.
37681	228	1	[	[	-LRB-
37681	228	2	14	14	CD
37681	228	3	]	]	-RRB-
37681	228	4	As	as	IN
37681	228	5	to	to	IN
37681	228	6	the	the	DT
37681	228	7	second	second	JJ
37681	228	8	point	point	NN
37681	228	9	,	,	,
37681	228	10	that	that	IN
37681	228	11	a	a	DT
37681	228	12	claim	claim	NN
37681	228	13	should	should	MD
37681	228	14	be	be	VB
37681	228	15	set	set	VBN
37681	228	16	forth	forth	RP
37681	228	17	that	that	IN
37681	228	18	geometry	geometry	NN
37681	228	19	is	be	VBZ
37681	228	20	a	a	DT
37681	228	21	_	_	NNP
37681	228	22	sine	sine	NN
37681	228	23	qua	qua	NN
37681	228	24	non	non	AFX
37681	228	25	_	_	NNP
37681	228	26	to	to	IN
37681	228	27	higher	high	JJR
37681	228	28	mathematics	mathematic	NNS
37681	228	29	,	,	,
37681	228	30	this	this	DT
37681	228	31	belief	belief	NN
37681	228	32	is	be	VBZ
37681	228	33	considerably	considerably	RB
37681	228	34	exaggerated	exaggerated	JJ
37681	228	35	because	because	IN
37681	228	36	there	there	EX
37681	228	37	are	be	VBP
37681	228	38	relatively	relatively	RB
37681	228	39	few	few	JJ
37681	228	40	who	who	WP
37681	228	41	proceed	proceed	VBP
37681	228	42	from	from	IN
37681	228	43	geometry	geometry	NN
37681	228	44	to	to	IN
37681	228	45	a	a	DT
37681	228	46	higher	high	JJR
37681	228	47	branch	branch	NN
37681	228	48	of	of	IN
37681	228	49	mathematics	mathematic	NNS
37681	228	50	.	.	.
37681	229	1	This	this	DT
37681	229	2	argument	argument	NN
37681	229	3	would	would	MD
37681	229	4	justify	justify	VB
37681	229	5	its	-PRON-	PRP$
37681	229	6	status	status	NN
37681	229	7	as	as	IN
37681	229	8	an	an	DT
37681	229	9	elective	elective	NN
37681	229	10	rather	rather	RB
37681	229	11	than	than	IN
37681	229	12	as	as	IN
37681	229	13	a	a	DT
37681	229	14	required	require	VBN
37681	229	15	subject	subject	NN
37681	229	16	.	.	.
37681	230	1	Let	let	VB
37681	230	2	us	-PRON-	PRP
37681	230	3	then	then	RB
37681	230	4	stand	stand	VB
37681	230	5	upon	upon	IN
37681	230	6	the	the	DT
37681	230	7	ground	ground	NN
37681	230	8	already	already	RB
37681	230	9	marked	mark	VBN
37681	230	10	out	out	RP
37681	230	11	,	,	,
37681	230	12	holding	hold	VBG
37681	230	13	that	that	IN
37681	230	14	the	the	DT
37681	230	15	pleasure	pleasure	NN
37681	230	16	,	,	,
37681	230	17	the	the	DT
37681	230	18	culture	culture	NN
37681	230	19	,	,	,
37681	230	20	the	the	DT
37681	230	21	mental	mental	JJ
37681	230	22	poise	poise	NN
37681	230	23	,	,	,
37681	230	24	the	the	DT
37681	230	25	habits	habit	NNS
37681	230	26	of	of	IN
37681	230	27	exact	exact	JJ
37681	230	28	reasoning	reasoning	NN
37681	230	29	that	that	IN
37681	230	30	geometry	geometry	NN
37681	230	31	brings	bring	VBZ
37681	230	32	,	,	,
37681	230	33	and	and	CC
37681	230	34	the	the	DT
37681	230	35	general	general	JJ
37681	230	36	experience	experience	NN
37681	230	37	of	of	IN
37681	230	38	mankind	mankind	NN
37681	230	39	upon	upon	IN
37681	230	40	the	the	DT
37681	230	41	subject	subject	NN
37681	230	42	are	be	VBP
37681	230	43	sufficient	sufficient	JJ
37681	230	44	to	to	TO
37681	230	45	justify	justify	VB
37681	230	46	us	-PRON-	PRP
37681	230	47	in	in	IN
37681	230	48	demanding	demand	VBG
37681	230	49	for	for	IN
37681	230	50	it	-PRON-	PRP
37681	230	51	a	a	DT
37681	230	52	reasonable	reasonable	JJ
37681	230	53	amount	amount	NN
37681	230	54	of	of	IN
37681	230	55	time	time	NN
37681	230	56	in	in	IN
37681	230	57	the	the	DT
37681	230	58	framing	framing	NN
37681	230	59	of	of	IN
37681	230	60	a	a	DT
37681	230	61	curriculum	curriculum	NN
37681	230	62	.	.	.
37681	231	1	Let	let	VB
37681	231	2	us	-PRON-	PRP
37681	231	3	be	be	VB
37681	231	4	fair	fair	JJ
37681	231	5	in	in	IN
37681	231	6	our	-PRON-	PRP$
37681	231	7	appreciation	appreciation	NN
37681	231	8	of	of	IN
37681	231	9	all	all	DT
37681	231	10	other	other	JJ
37681	231	11	branches	branch	NNS
37681	231	12	,	,	,
37681	231	13	but	but	CC
37681	231	14	let	let	VB
37681	231	15	us	-PRON-	PRP
37681	231	16	urge	urge	VB
37681	231	17	that	that	IN
37681	231	18	every	every	DT
37681	231	19	student	student	NN
37681	231	20	may	may	MD
37681	231	21	have	have	VB
37681	231	22	an	an	DT
37681	231	23	opportunity	opportunity	NN
37681	231	24	to	to	TO
37681	231	25	know	know	VB
37681	231	26	of	of	IN
37681	231	27	real	real	JJ
37681	231	28	geometry	geometry	NN
37681	231	29	,	,	,
37681	231	30	say	say	VBP
37681	231	31	for	for	IN
37681	231	32	a	a	DT
37681	231	33	single	single	JJ
37681	231	34	year	year	NN
37681	231	35	,	,	,
37681	231	36	thereafter	thereafter	RB
37681	231	37	pursuing	pursue	VBG
37681	231	38	it	-PRON-	PRP
37681	231	39	or	or	CC
37681	231	40	not	not	RB
37681	231	41	,	,	,
37681	231	42	according	accord	VBG
37681	231	43	as	as	IN
37681	231	44	we	-PRON-	PRP
37681	231	45	succeed	succeed	VBP
37681	231	46	in	in	IN
37681	231	47	making	make	VBG
37681	231	48	its	-PRON-	PRP$
37681	231	49	value	value	NN
37681	231	50	apparent	apparent	JJ
37681	231	51	,	,	,
37681	231	52	or	or	CC
37681	231	53	fail	fail	VB
37681	231	54	in	in	IN
37681	231	55	our	-PRON-	PRP$
37681	231	56	attempt	attempt	NN
37681	231	57	to	to	TO
37681	231	58	present	present	VB
37681	231	59	worthily	worthily	RB
37681	231	60	an	an	DT
37681	231	61	ancient	ancient	JJ
37681	231	62	and	and	CC
37681	231	63	noble	noble	JJ
37681	231	64	science	science	NN
37681	231	65	to	to	IN
37681	231	66	the	the	DT
37681	231	67	mind	mind	NN
37681	231	68	confided	confide	VBN
37681	231	69	to	to	IN
37681	231	70	our	-PRON-	PRP$
37681	231	71	instruction	instruction	NN
37681	231	72	.	.	.
37681	232	1	The	the	DT
37681	232	2	shortsightedness	shortsightedness	NN
37681	232	3	of	of	IN
37681	232	4	a	a	DT
37681	232	5	narrow	narrow	JJ
37681	232	6	education	education	NN
37681	232	7	,	,	,
37681	232	8	of	of	IN
37681	232	9	an	an	DT
37681	232	10	education	education	NN
37681	232	11	that	that	WDT
37681	232	12	teaches	teach	VBZ
37681	232	13	only	only	RB
37681	232	14	machines	machine	NNS
37681	232	15	to	to	IN
37681	232	16	a	a	DT
37681	232	17	prospective	prospective	JJ
37681	232	18	mechanic	mechanic	NN
37681	232	19	,	,	,
37681	232	20	and	and	CC
37681	232	21	agriculture	agriculture	NN
37681	232	22	to	to	IN
37681	232	23	a	a	DT
37681	232	24	prospective	prospective	JJ
37681	232	25	farmer	farmer	NN
37681	232	26	,	,	,
37681	232	27	and	and	CC
37681	232	28	cooking	cooking	NN
37681	232	29	and	and	CC
37681	232	30	dressmaking	dressmaking	NN
37681	232	31	to	to	IN
37681	232	32	the	the	DT
37681	232	33	girl	girl	NN
37681	232	34	,	,	,
37681	232	35	and	and	CC
37681	232	36	that	that	DT
37681	232	37	would	would	MD
37681	232	38	exclude	exclude	VB
37681	232	39	all	all	DT
37681	232	40	mathematics	mathematic	NNS
37681	232	41	that	that	WDT
37681	232	42	is	be	VBZ
37681	232	43	not	not	RB
37681	232	44	utilitarian	utilitarian	JJ
37681	232	45	in	in	IN
37681	232	46	the	the	DT
37681	232	47	narrow	narrow	JJ
37681	232	48	sense	sense	NN
37681	232	49	,	,	,
37681	232	50	can	can	MD
37681	232	51	not	not	RB
37681	232	52	endure	endure	VB
37681	232	53	.	.	.
37681	233	1	The	the	DT
37681	233	2	community	community	NN
37681	233	3	has	have	VBZ
37681	233	4	found	find	VBN
37681	233	5	out	out	RP
37681	233	6	that	that	IN
37681	233	7	such	such	JJ
37681	233	8	schemes	scheme	NNS
37681	233	9	may	may	MD
37681	233	10	be	be	VB
37681	233	11	well	well	RB
37681	233	12	fitted	fit	VBN
37681	233	13	to	to	TO
37681	233	14	give	give	VB
37681	233	15	the	the	DT
37681	233	16	children	child	NNS
37681	233	17	a	a	DT
37681	233	18	good	good	JJ
37681	233	19	time	time	NN
37681	233	20	in	in	IN
37681	233	21	school	school	NN
37681	233	22	,	,	,
37681	233	23	but	but	CC
37681	233	24	lead	lead	VB
37681	233	25	them	-PRON-	PRP
37681	233	26	to	to	IN
37681	233	27	a	a	DT
37681	233	28	bad	bad	JJ
37681	233	29	time	time	NN
37681	233	30	afterward	afterward	RB
37681	233	31	.	.	.
37681	234	1	Life	life	NN
37681	234	2	is	be	VBZ
37681	234	3	hard	hard	JJ
37681	234	4	work	work	NN
37681	234	5	,	,	,
37681	234	6	and	and	CC
37681	234	7	if	if	IN
37681	234	8	they	-PRON-	PRP
37681	234	9	have	have	VBP
37681	234	10	never	never	RB
37681	234	11	learned	learn	VBN
37681	234	12	in	in	IN
37681	234	13	school	school	NN
37681	234	14	to	to	TO
37681	234	15	give	give	VB
37681	234	16	their	-PRON-	PRP$
37681	234	17	concentrated	concentrated	JJ
37681	234	18	attention	attention	NN
37681	234	19	to	to	IN
37681	234	20	that	that	DT
37681	234	21	which	which	WDT
37681	234	22	does	do	VBZ
37681	234	23	not	not	RB
37681	234	24	appeal	appeal	VB
37681	234	25	to	to	IN
37681	234	26	them	-PRON-	PRP
37681	234	27	and	and	CC
37681	234	28	which	which	WDT
37681	234	29	does	do	VBZ
37681	234	30	not	not	RB
37681	234	31	interest	interest	VB
37681	234	32	them	-PRON-	PRP
37681	234	33	immediately	immediately	RB
37681	234	34	,	,	,
37681	234	35	they	-PRON-	PRP
37681	234	36	have	have	VBP
37681	234	37	missed	miss	VBN
37681	234	38	the	the	DT
37681	234	39	most	most	RBS
37681	234	40	valuable	valuable	JJ
37681	234	41	lesson	lesson	NN
37681	234	42	of	of	IN
37681	234	43	their	-PRON-	PRP$
37681	234	44	school	school	NN
37681	234	45	years	year	NNS
37681	234	46	.	.	.
37681	235	1	The	the	DT
37681	235	2	little	little	JJ
37681	235	3	practical	practical	JJ
37681	235	4	information	information	NN
37681	235	5	they	-PRON-	PRP
37681	235	6	could	could	MD
37681	235	7	have	have	VB
37681	235	8	learned	learn	VBN
37681	235	9	at	at	IN
37681	235	10	any	any	DT
37681	235	11	time	time	NN
37681	235	12	;	;	:
37681	235	13	the	the	DT
37681	235	14	energy	energy	NN
37681	235	15	of	of	IN
37681	235	16	attention	attention	NN
37681	235	17	and	and	CC
37681	235	18	concentration	concentration	NN
37681	235	19	can	can	MD
37681	235	20	no	no	RB
37681	235	21	longer	longer	RB
37681	235	22	be	be	VB
37681	235	23	learned	learn	VBN
37681	235	24	if	if	IN
37681	235	25	the	the	DT
37681	235	26	early	early	JJ
37681	235	27	years	year	NNS
37681	235	28	are	be	VBP
37681	235	29	wasted	waste	VBN
37681	235	30	.	.	.
37681	236	1	However	however	WRB
37681	236	2	narrow	narrow	JJ
37681	236	3	and	and	CC
37681	236	4	commercial	commercial	JJ
37681	236	5	the	the	DT
37681	236	6	standpoint	standpoint	NN
37681	236	7	which	which	WDT
37681	236	8	is	be	VBZ
37681	236	9	chosen	choose	VBN
37681	236	10	may	may	MD
37681	236	11	be	be	VB
37681	236	12	,	,	,
37681	236	13	it	-PRON-	PRP
37681	236	14	can	can	MD
37681	236	15	always	always	RB
37681	236	16	be	be	VB
37681	236	17	found	find	VBN
37681	236	18	that	that	IN
37681	236	19	it	-PRON-	PRP
37681	236	20	is	be	VBZ
37681	236	21	the	the	DT
37681	236	22	general	general	JJ
37681	236	23	education	education	NN
37681	236	24	which	which	WDT
37681	236	25	pays	pay	VBZ
37681	236	26	best	well	RBS
37681	236	27	,	,	,
37681	236	28	and	and	CC
37681	236	29	the	the	DT
37681	236	30	more	more	JJR
37681	236	31	the	the	DT
37681	236	32	period	period	NN
37681	236	33	of	of	IN
37681	236	34	cultural	cultural	JJ
37681	236	35	work	work	NN
37681	236	36	can	can	MD
37681	236	37	be	be	VB
37681	236	38	expanded	expand	VBN
37681	236	39	the	the	DT
37681	236	40	more	more	RBR
37681	236	41	efficient	efficient	JJ
37681	236	42	will	will	MD
37681	236	43	be	be	VB
37681	236	44	the	the	DT
37681	236	45	services	service	NNS
37681	236	46	of	of	IN
37681	236	47	the	the	DT
37681	236	48	school	school	NN
37681	236	49	for	for	IN
37681	236	50	the	the	DT
37681	236	51	practical	practical	JJ
37681	236	52	services	service	NNS
37681	236	53	of	of	IN
37681	236	54	the	the	DT
37681	236	55	nation	nation	NN
37681	236	56	.	.	.
37681	237	1	[	[	-LRB-
37681	237	2	15	15	CD
37681	237	3	]	]	-RRB-
37681	237	4	Of	of	RB
37681	237	5	course	course	RB
37681	237	6	no	no	DT
37681	237	7	one	one	PRP
37681	237	8	should	should	MD
37681	237	9	construe	construe	VB
37681	237	10	these	these	DT
37681	237	11	remarks	remark	NNS
37681	237	12	as	as	IN
37681	237	13	opposing	oppose	VBG
37681	237	14	in	in	IN
37681	237	15	the	the	DT
37681	237	16	slightest	slight	JJS
37681	237	17	degree	degree	NN
37681	237	18	the	the	DT
37681	237	19	laudable	laudable	JJ
37681	237	20	efforts	effort	NNS
37681	237	21	that	that	WDT
37681	237	22	are	be	VBP
37681	237	23	constantly	constantly	RB
37681	237	24	being	be	VBG
37681	237	25	put	put	VBN
37681	237	26	forth	forth	RB
37681	237	27	to	to	TO
37681	237	28	make	make	VB
37681	237	29	geometry	geometry	NN
37681	237	30	more	more	RBR
37681	237	31	interesting	interesting	JJ
37681	237	32	and	and	CC
37681	237	33	to	to	TO
37681	237	34	vitalize	vitalize	VB
37681	237	35	it	-PRON-	PRP
37681	237	36	by	by	IN
37681	237	37	establishing	establish	VBG
37681	237	38	as	as	IN
37681	237	39	strong	strong	JJ
37681	237	40	motives	motive	NNS
37681	237	41	as	as	IN
37681	237	42	possible	possible	JJ
37681	237	43	for	for	IN
37681	237	44	its	-PRON-	PRP$
37681	237	45	study	study	NN
37681	237	46	.	.	.
37681	238	1	Let	let	VB
37681	238	2	the	the	DT
37681	238	3	home	home	NN
37681	238	4	,	,	,
37681	238	5	the	the	DT
37681	238	6	workshop	workshop	NN
37681	238	7	,	,	,
37681	238	8	physics	physics	NN
37681	238	9	,	,	,
37681	238	10	art	art	NN
37681	238	11	,	,	,
37681	238	12	play,--all	play,--all	LS
37681	238	13	contribute	contribute	VB
37681	238	14	their	-PRON-	PRP$
37681	238	15	quota	quota	NN
37681	238	16	of	of	IN
37681	238	17	motive	motive	NN
37681	238	18	to	to	TO
37681	238	19	geometry	geometry	VB
37681	238	20	as	as	IN
37681	238	21	to	to	IN
37681	238	22	all	all	DT
37681	238	23	mathematics	mathematic	NNS
37681	238	24	and	and	CC
37681	238	25	all	all	DT
37681	238	26	other	other	JJ
37681	238	27	branches	branch	NNS
37681	238	28	.	.	.
37681	239	1	But	but	CC
37681	239	2	let	let	VB
37681	239	3	us	-PRON-	PRP
37681	239	4	never	never	RB
37681	239	5	forget	forget	VB
37681	239	6	that	that	IN
37681	239	7	geometry	geometry	NN
37681	239	8	has	have	VBZ
37681	239	9	a	a	DT
37681	239	10	_	_	NNP
37681	239	11	raison	raison	NNP
37681	239	12	d'être	d'être	NNP
37681	239	13	_	_	NNP
37681	239	14	beyond	beyond	IN
37681	239	15	all	all	PDT
37681	239	16	this	this	DT
37681	239	17	,	,	,
37681	239	18	and	and	CC
37681	239	19	that	that	IN
37681	239	20	these	these	DT
37681	239	21	applications	application	NNS
37681	239	22	are	be	VBP
37681	239	23	sought	seek	VBN
37681	239	24	primarily	primarily	RB
37681	239	25	for	for	IN
37681	239	26	the	the	DT
37681	239	27	sake	sake	NN
37681	239	28	of	of	IN
37681	239	29	geometry	geometry	NN
37681	239	30	,	,	,
37681	239	31	and	and	CC
37681	239	32	that	that	IN
37681	239	33	geometry	geometry	NN
37681	239	34	is	be	VBZ
37681	239	35	not	not	RB
37681	239	36	taught	teach	VBN
37681	239	37	primarily	primarily	RB
37681	239	38	for	for	IN
37681	239	39	the	the	DT
37681	239	40	sake	sake	NN
37681	239	41	of	of	IN
37681	239	42	these	these	DT
37681	239	43	applications	application	NNS
37681	239	44	.	.	.
37681	240	1	When	when	WRB
37681	240	2	we	-PRON-	PRP
37681	240	3	consider	consider	VBP
37681	240	4	how	how	WRB
37681	240	5	often	often	RB
37681	240	6	geometry	geometry	NN
37681	240	7	is	be	VBZ
37681	240	8	attacked	attack	VBN
37681	240	9	by	by	IN
37681	240	10	those	those	DT
37681	240	11	who	who	WP
37681	240	12	profess	profess	VBP
37681	240	13	to	to	TO
37681	240	14	be	be	VB
37681	240	15	its	-PRON-	PRP$
37681	240	16	friends	friend	NNS
37681	240	17	,	,	,
37681	240	18	and	and	CC
37681	240	19	how	how	WRB
37681	240	20	teachers	teacher	NNS
37681	240	21	who	who	WP
37681	240	22	have	have	VBP
37681	240	23	been	be	VBN
37681	240	24	trained	train	VBN
37681	240	25	in	in	IN
37681	240	26	mathematics	mathematic	NNS
37681	240	27	occasionally	occasionally	RB
37681	240	28	seem	seem	VBP
37681	240	29	to	to	TO
37681	240	30	make	make	VB
37681	240	31	of	of	IN
37681	240	32	the	the	DT
37681	240	33	subject	subject	NN
37681	240	34	little	little	JJ
37681	240	35	besides	besides	IN
37681	240	36	a	a	DT
37681	240	37	mongrel	mongrel	NN
37681	240	38	course	course	NN
37681	240	39	in	in	IN
37681	240	40	drawing	drawing	NN
37681	240	41	and	and	CC
37681	240	42	measuring	measure	VBG
37681	240	43	,	,	,
37681	240	44	all	all	PDT
37681	240	45	the	the	DT
37681	240	46	time	time	NN
37681	240	47	insisting	insist	VBG
37681	240	48	that	that	IN
37681	240	49	they	-PRON-	PRP
37681	240	50	are	be	VBP
37681	240	51	progressive	progressive	JJ
37681	240	52	while	while	IN
37681	240	53	the	the	DT
37681	240	54	champions	champion	NNS
37681	240	55	of	of	IN
37681	240	56	real	real	JJ
37681	240	57	geometry	geometry	NN
37681	240	58	are	be	VBP
37681	240	59	reactionary	reactionary	JJ
37681	240	60	,	,	,
37681	240	61	it	-PRON-	PRP
37681	240	62	is	be	VBZ
37681	240	63	well	well	JJ
37681	240	64	to	to	TO
37681	240	65	read	read	VB
37681	240	66	some	some	DT
37681	240	67	of	of	IN
37681	240	68	the	the	DT
37681	240	69	opinions	opinion	NNS
37681	240	70	of	of	IN
37681	240	71	the	the	DT
37681	240	72	masters	master	NNS
37681	240	73	.	.	.
37681	241	1	The	the	DT
37681	241	2	following	follow	VBG
37681	241	3	quotations	quotation	NNS
37681	241	4	may	may	MD
37681	241	5	be	be	VB
37681	241	6	given	give	VBN
37681	241	7	occasionally	occasionally	RB
37681	241	8	in	in	IN
37681	241	9	geometry	geometry	NN
37681	241	10	classes	class	NNS
37681	241	11	as	as	IN
37681	241	12	showing	show	VBG
37681	241	13	the	the	DT
37681	241	14	esteem	esteem	NN
37681	241	15	in	in	IN
37681	241	16	which	which	WDT
37681	241	17	the	the	DT
37681	241	18	subject	subject	NN
37681	241	19	has	have	VBZ
37681	241	20	been	be	VBN
37681	241	21	held	hold	VBN
37681	241	22	in	in	IN
37681	241	23	various	various	JJ
37681	241	24	ages	age	NNS
37681	241	25	,	,	,
37681	241	26	and	and	CC
37681	241	27	at	at	IN
37681	241	28	any	any	DT
37681	241	29	rate	rate	NN
37681	241	30	they	-PRON-	PRP
37681	241	31	should	should	MD
37681	241	32	serve	serve	VB
37681	241	33	to	to	TO
37681	241	34	inspire	inspire	VB
37681	241	35	the	the	DT
37681	241	36	teacher	teacher	NN
37681	241	37	to	to	IN
37681	241	38	greater	great	JJR
37681	241	39	love	love	NN
37681	241	40	for	for	IN
37681	241	41	his	-PRON-	PRP$
37681	241	42	subject	subject	NN
37681	241	43	.	.	.
37681	242	1	The	the	DT
37681	242	2	enemies	enemy	NNS
37681	242	3	of	of	IN
37681	242	4	geometry	geometry	NN
37681	242	5	,	,	,
37681	242	6	those	those	DT
37681	242	7	who	who	WP
37681	242	8	know	know	VBP
37681	242	9	it	-PRON-	PRP
37681	242	10	only	only	RB
37681	242	11	imperfectly	imperfectly	RB
37681	242	12	,	,	,
37681	242	13	look	look	VB
37681	242	14	upon	upon	IN
37681	242	15	the	the	DT
37681	242	16	theoretical	theoretical	JJ
37681	242	17	problems	problem	NNS
37681	242	18	,	,	,
37681	242	19	which	which	WDT
37681	242	20	constitute	constitute	VBP
37681	242	21	the	the	DT
37681	242	22	most	most	RBS
37681	242	23	difficult	difficult	JJ
37681	242	24	part	part	NN
37681	242	25	of	of	IN
37681	242	26	the	the	DT
37681	242	27	subject	subject	NN
37681	242	28	,	,	,
37681	242	29	as	as	IN
37681	242	30	mental	mental	JJ
37681	242	31	games	game	NNS
37681	242	32	which	which	WDT
37681	242	33	consume	consume	VBP
37681	242	34	time	time	NN
37681	242	35	and	and	CC
37681	242	36	energy	energy	NN
37681	242	37	that	that	WDT
37681	242	38	might	may	MD
37681	242	39	better	better	RB
37681	242	40	be	be	VB
37681	242	41	employed	employ	VBN
37681	242	42	in	in	IN
37681	242	43	other	other	JJ
37681	242	44	ways	way	NNS
37681	242	45	.	.	.
37681	243	1	Such	such	PDT
37681	243	2	a	a	DT
37681	243	3	belief	belief	NN
37681	243	4	is	be	VBZ
37681	243	5	false	false	JJ
37681	243	6	,	,	,
37681	243	7	and	and	CC
37681	243	8	it	-PRON-	PRP
37681	243	9	would	would	MD
37681	243	10	block	block	VB
37681	243	11	the	the	DT
37681	243	12	progress	progress	NN
37681	243	13	of	of	IN
37681	243	14	science	science	NN
37681	243	15	if	if	IN
37681	243	16	it	-PRON-	PRP
37681	243	17	were	be	VBD
37681	243	18	credible	credible	JJ
37681	243	19	.	.	.
37681	244	1	But	but	CC
37681	244	2	aside	aside	RB
37681	244	3	from	from	IN
37681	244	4	the	the	DT
37681	244	5	fact	fact	NN
37681	244	6	that	that	IN
37681	244	7	the	the	DT
37681	244	8	speculative	speculative	JJ
37681	244	9	problems	problem	NNS
37681	244	10	,	,	,
37681	244	11	which	which	WDT
37681	244	12	at	at	IN
37681	244	13	first	first	JJ
37681	244	14	sight	sight	NN
37681	244	15	seem	seem	VB
37681	244	16	barren	barren	JJ
37681	244	17	,	,	,
37681	244	18	can	can	MD
37681	244	19	often	often	RB
37681	244	20	be	be	VB
37681	244	21	applied	apply	VBN
37681	244	22	to	to	IN
37681	244	23	useful	useful	JJ
37681	244	24	purposes	purpose	NNS
37681	244	25	,	,	,
37681	244	26	they	-PRON-	PRP
37681	244	27	always	always	RB
37681	244	28	stand	stand	VBP
37681	244	29	as	as	IN
37681	244	30	among	among	IN
37681	244	31	the	the	DT
37681	244	32	best	good	JJS
37681	244	33	means	mean	NNS
37681	244	34	to	to	TO
37681	244	35	develop	develop	VB
37681	244	36	and	and	CC
37681	244	37	to	to	TO
37681	244	38	express	express	VB
37681	244	39	all	all	PDT
37681	244	40	the	the	DT
37681	244	41	forces	force	NNS
37681	244	42	of	of	IN
37681	244	43	the	the	DT
37681	244	44	human	human	NN
37681	244	45	intelligence.--ABBÉ	intelligence.--abbé	XX
37681	244	46	BOSSUT	BOSSUT	NNP
37681	244	47	.	.	.
37681	245	1	The	the	DT
37681	245	2	sailor	sailor	NN
37681	245	3	whom	whom	WP
37681	245	4	an	an	DT
37681	245	5	exact	exact	JJ
37681	245	6	observation	observation	NN
37681	245	7	of	of	IN
37681	245	8	longitude	longitude	NN
37681	245	9	saves	save	VBZ
37681	245	10	from	from	IN
37681	245	11	shipwreck	shipwreck	NNP
37681	245	12	owes	owe	VBZ
37681	245	13	his	-PRON-	PRP$
37681	245	14	life	life	NN
37681	245	15	to	to	IN
37681	245	16	a	a	DT
37681	245	17	theory	theory	NN
37681	245	18	developed	develop	VBN
37681	245	19	two	two	CD
37681	245	20	thousand	thousand	CD
37681	245	21	years	year	NNS
37681	245	22	ago	ago	RB
37681	245	23	by	by	IN
37681	245	24	men	man	NNS
37681	245	25	who	who	WP
37681	245	26	had	have	VBD
37681	245	27	in	in	IN
37681	245	28	mind	mind	NN
37681	245	29	merely	merely	RB
37681	245	30	the	the	DT
37681	245	31	speculations	speculation	NNS
37681	245	32	of	of	IN
37681	245	33	abstract	abstract	NNP
37681	245	34	geometry.--CONDORCET	geometry.--condorcet	NN
37681	245	35	.	.	.
37681	246	1	If	if	IN
37681	246	2	mathematical	mathematical	JJ
37681	246	3	heights	height	NNS
37681	246	4	are	be	VBP
37681	246	5	hard	hard	JJ
37681	246	6	to	to	TO
37681	246	7	climb	climb	VB
37681	246	8	,	,	,
37681	246	9	the	the	DT
37681	246	10	fundamental	fundamental	JJ
37681	246	11	principles	principle	NNS
37681	246	12	lie	lie	VBP
37681	246	13	at	at	IN
37681	246	14	every	every	DT
37681	246	15	threshold	threshold	NN
37681	246	16	,	,	,
37681	246	17	and	and	CC
37681	246	18	this	this	DT
37681	246	19	fact	fact	NN
37681	246	20	allows	allow	VBZ
37681	246	21	them	-PRON-	PRP
37681	246	22	to	to	TO
37681	246	23	be	be	VB
37681	246	24	comprehended	comprehend	VBN
37681	246	25	by	by	IN
37681	246	26	that	that	DT
37681	246	27	common	common	JJ
37681	246	28	sense	sense	NN
37681	246	29	which	which	WDT
37681	246	30	Descartes	Descartes	NNP
37681	246	31	declared	declare	VBD
37681	246	32	was	be	VBD
37681	246	33	"	"	``
37681	246	34	apportioned	apportion	VBN
37681	246	35	equally	equally	RB
37681	246	36	among	among	IN
37681	246	37	all	all	DT
37681	246	38	men	man	NNS
37681	246	39	.	.	.
37681	246	40	"--COLLET	"--collet	UH
37681	246	41	.	.	.
37681	247	1	It	-PRON-	PRP
37681	247	2	may	may	MD
37681	247	3	seem	seem	VB
37681	247	4	strange	strange	JJ
37681	247	5	that	that	IN
37681	247	6	geometry	geometry	NN
37681	247	7	is	be	VBZ
37681	247	8	unable	unable	JJ
37681	247	9	to	to	TO
37681	247	10	define	define	VB
37681	247	11	the	the	DT
37681	247	12	terms	term	NNS
37681	247	13	which	which	WDT
37681	247	14	it	-PRON-	PRP
37681	247	15	uses	use	VBZ
37681	247	16	most	most	RBS
37681	247	17	frequently	frequently	RB
37681	247	18	,	,	,
37681	247	19	since	since	IN
37681	247	20	it	-PRON-	PRP
37681	247	21	defines	define	VBZ
37681	247	22	neither	neither	DT
37681	247	23	movement	movement	NN
37681	247	24	,	,	,
37681	247	25	nor	nor	CC
37681	247	26	number	number	NN
37681	247	27	,	,	,
37681	247	28	nor	nor	CC
37681	247	29	space,---the	space,---the	XX
37681	247	30	three	three	CD
37681	247	31	things	thing	NNS
37681	247	32	with	with	IN
37681	247	33	which	which	WDT
37681	247	34	it	-PRON-	PRP
37681	247	35	is	be	VBZ
37681	247	36	chiefly	chiefly	RB
37681	247	37	concerned	concerned	JJ
37681	247	38	.	.	.
37681	248	1	But	but	CC
37681	248	2	we	-PRON-	PRP
37681	248	3	shall	shall	MD
37681	248	4	not	not	RB
37681	248	5	be	be	VB
37681	248	6	surprised	surprised	JJ
37681	248	7	if	if	IN
37681	248	8	we	-PRON-	PRP
37681	248	9	stop	stop	VBP
37681	248	10	to	to	TO
37681	248	11	consider	consider	VB
37681	248	12	that	that	IN
37681	248	13	this	this	DT
37681	248	14	admirable	admirable	JJ
37681	248	15	science	science	NN
37681	248	16	concerns	concern	NNS
37681	248	17	only	only	RB
37681	248	18	the	the	DT
37681	248	19	most	most	RBS
37681	248	20	simple	simple	JJ
37681	248	21	things	thing	NNS
37681	248	22	,	,	,
37681	248	23	and	and	CC
37681	248	24	the	the	DT
37681	248	25	very	very	JJ
37681	248	26	quality	quality	NN
37681	248	27	that	that	WDT
37681	248	28	renders	render	VBZ
37681	248	29	these	these	DT
37681	248	30	things	thing	NNS
37681	248	31	worthy	worthy	JJ
37681	248	32	of	of	IN
37681	248	33	study	study	NN
37681	248	34	renders	render	VBZ
37681	248	35	them	-PRON-	PRP
37681	248	36	incapable	incapable	JJ
37681	248	37	of	of	IN
37681	248	38	being	be	VBG
37681	248	39	defined	define	VBN
37681	248	40	.	.	.
37681	249	1	Thus	thus	RB
37681	249	2	the	the	DT
37681	249	3	very	very	JJ
37681	249	4	lack	lack	NN
37681	249	5	of	of	IN
37681	249	6	definition	definition	NN
37681	249	7	is	be	VBZ
37681	249	8	rather	rather	RB
37681	249	9	an	an	DT
37681	249	10	evidence	evidence	NN
37681	249	11	of	of	IN
37681	249	12	perfection	perfection	NN
37681	249	13	than	than	IN
37681	249	14	a	a	DT
37681	249	15	defect	defect	NN
37681	249	16	,	,	,
37681	249	17	since	since	IN
37681	249	18	it	-PRON-	PRP
37681	249	19	comes	come	VBZ
37681	249	20	not	not	RB
37681	249	21	from	from	IN
37681	249	22	the	the	DT
37681	249	23	obscurity	obscurity	NN
37681	249	24	of	of	IN
37681	249	25	the	the	DT
37681	249	26	terms	term	NNS
37681	249	27	,	,	,
37681	249	28	but	but	CC
37681	249	29	from	from	IN
37681	249	30	the	the	DT
37681	249	31	fact	fact	NN
37681	249	32	that	that	IN
37681	249	33	they	-PRON-	PRP
37681	249	34	are	be	VBP
37681	249	35	so	so	RB
37681	249	36	very	very	RB
37681	249	37	well	well	RB
37681	249	38	known.--PASCAL	known.--PASCAL	.
37681	249	39	.	.	.
37681	250	1	God	God	NNP
37681	250	2	eternally	eternally	RB
37681	250	3	geometrizes.--PLATO	geometrizes.--plato	VBP
37681	250	4	.	.	.
37681	251	1	God	God	NNP
37681	251	2	is	be	VBZ
37681	251	3	a	a	DT
37681	251	4	circle	circle	NN
37681	251	5	of	of	IN
37681	251	6	which	which	WDT
37681	251	7	the	the	DT
37681	251	8	center	center	NN
37681	251	9	is	be	VBZ
37681	251	10	everywhere	everywhere	RB
37681	251	11	and	and	CC
37681	251	12	the	the	DT
37681	251	13	circumference	circumference	NN
37681	251	14	nowhere.--RABELAIS	nowhere.--rabelais	NN
37681	251	15	.	.	.
37681	252	1	Without	without	IN
37681	252	2	mathematics	mathematic	NNS
37681	252	3	no	no	DT
37681	252	4	one	one	NN
37681	252	5	can	can	MD
37681	252	6	fathom	fathom	VB
37681	252	7	the	the	DT
37681	252	8	depths	depth	NNS
37681	252	9	of	of	IN
37681	252	10	philosophy	philosophy	NN
37681	252	11	.	.	.
37681	253	1	Without	without	IN
37681	253	2	philosophy	philosophy	NN
37681	253	3	no	no	DT
37681	253	4	one	one	NN
37681	253	5	can	can	MD
37681	253	6	fathom	fathom	VB
37681	253	7	the	the	DT
37681	253	8	depths	depth	NNS
37681	253	9	of	of	IN
37681	253	10	mathematics	mathematic	NNS
37681	253	11	.	.	.
37681	254	1	Without	without	IN
37681	254	2	the	the	DT
37681	254	3	two	two	CD
37681	254	4	no	no	DT
37681	254	5	one	one	NN
37681	254	6	can	can	MD
37681	254	7	fathom	fathom	VB
37681	254	8	the	the	DT
37681	254	9	depths	depth	NNS
37681	254	10	of	of	IN
37681	254	11	anything.--BORDAS	anything.--bordas	JJ
37681	254	12	-	-	HYPH
37681	254	13	DEMOULIN	DEMOULIN	NNP
37681	254	14	.	.	.
37681	255	1	We	-PRON-	PRP
37681	255	2	may	may	MD
37681	255	3	look	look	VB
37681	255	4	upon	upon	IN
37681	255	5	geometry	geometry	NN
37681	255	6	as	as	IN
37681	255	7	a	a	DT
37681	255	8	practical	practical	JJ
37681	255	9	logic	logic	NN
37681	255	10	,	,	,
37681	255	11	for	for	IN
37681	255	12	the	the	DT
37681	255	13	truths	truth	NNS
37681	255	14	which	which	WDT
37681	255	15	it	-PRON-	PRP
37681	255	16	studies	study	VBZ
37681	255	17	,	,	,
37681	255	18	being	be	VBG
37681	255	19	the	the	DT
37681	255	20	most	most	RBS
37681	255	21	simple	simple	JJ
37681	255	22	and	and	CC
37681	255	23	most	most	RBS
37681	255	24	clearly	clearly	RB
37681	255	25	understood	understand	VBN
37681	255	26	of	of	IN
37681	255	27	all	all	DT
37681	255	28	truths	truth	NNS
37681	255	29	,	,	,
37681	255	30	are	be	VBP
37681	255	31	on	on	IN
37681	255	32	this	this	DT
37681	255	33	account	account	NN
37681	255	34	the	the	DT
37681	255	35	most	most	RBS
37681	255	36	susceptible	susceptible	JJ
37681	255	37	of	of	IN
37681	255	38	ready	ready	JJ
37681	255	39	application	application	NN
37681	255	40	in	in	IN
37681	255	41	reasoning.--D'ALEMBERT	reasoning.--D'ALEMBERT	NNP
37681	255	42	.	.	.
37681	256	1	The	the	DT
37681	256	2	advance	advance	NN
37681	256	3	and	and	CC
37681	256	4	the	the	DT
37681	256	5	perfecting	perfecting	NN
37681	256	6	of	of	IN
37681	256	7	mathematics	mathematic	NNS
37681	256	8	are	be	VBP
37681	256	9	closely	closely	RB
37681	256	10	joined	joined	JJ
37681	256	11	to	to	IN
37681	256	12	the	the	DT
37681	256	13	prosperity	prosperity	NN
37681	256	14	of	of	IN
37681	256	15	the	the	DT
37681	256	16	nation.--NAPOLEON	nation.--napoleon	NN
37681	256	17	.	.	.
37681	257	1	Hold	hold	VB
37681	257	2	nothing	nothing	NN
37681	257	3	as	as	IN
37681	257	4	certain	certain	JJ
37681	257	5	save	save	NN
37681	257	6	what	what	WP
37681	257	7	can	can	MD
37681	257	8	be	be	VB
37681	257	9	demonstrated.--NEWTON	demonstrated.--newton	CD
37681	257	10	.	.	.
37681	258	1	To	to	TO
37681	258	2	measure	measure	VB
37681	258	3	is	be	VBZ
37681	258	4	to	to	IN
37681	258	5	know.--KEPLER	know.--kepler	ADD
37681	258	6	.	.	.
37681	259	1	The	the	DT
37681	259	2	method	method	NN
37681	259	3	of	of	IN
37681	259	4	making	make	VBG
37681	259	5	no	no	DT
37681	259	6	mistake	mistake	NN
37681	259	7	is	be	VBZ
37681	259	8	sought	seek	VBN
37681	259	9	by	by	IN
37681	259	10	every	every	DT
37681	259	11	one	one	CD
37681	259	12	.	.	.
37681	260	1	The	the	DT
37681	260	2	logicians	logicians	NNPS
37681	260	3	profess	profess	VBP
37681	260	4	to	to	TO
37681	260	5	show	show	VB
37681	260	6	the	the	DT
37681	260	7	way	way	NN
37681	260	8	,	,	,
37681	260	9	but	but	CC
37681	260	10	the	the	DT
37681	260	11	geometers	geometer	NNS
37681	260	12	alone	alone	RB
37681	260	13	ever	ever	RB
37681	260	14	reach	reach	VBP
37681	260	15	it	-PRON-	PRP
37681	260	16	,	,	,
37681	260	17	and	and	CC
37681	260	18	aside	aside	RB
37681	260	19	from	from	IN
37681	260	20	their	-PRON-	PRP$
37681	260	21	science	science	NN
37681	260	22	there	there	EX
37681	260	23	is	be	VBZ
37681	260	24	no	no	DT
37681	260	25	genuine	genuine	JJ
37681	260	26	demonstration.--PASCAL	demonstration.--PASCAL	.
37681	260	27	.	.	.
37681	261	1	The	the	DT
37681	261	2	taste	taste	NN
37681	261	3	for	for	IN
37681	261	4	exactness	exactness	NN
37681	261	5	,	,	,
37681	261	6	the	the	DT
37681	261	7	impossibility	impossibility	NN
37681	261	8	of	of	IN
37681	261	9	contenting	content	VBG
37681	261	10	one	one	PRP
37681	261	11	's	's	POS
37681	261	12	self	self	NN
37681	261	13	with	with	IN
37681	261	14	vague	vague	JJ
37681	261	15	notions	notion	NNS
37681	261	16	or	or	CC
37681	261	17	of	of	IN
37681	261	18	leaning	lean	VBG
37681	261	19	upon	upon	IN
37681	261	20	mere	mere	JJ
37681	261	21	hypotheses	hypothesis	NNS
37681	261	22	,	,	,
37681	261	23	the	the	DT
37681	261	24	necessity	necessity	NN
37681	261	25	for	for	IN
37681	261	26	perceiving	perceive	VBG
37681	261	27	clearly	clearly	RB
37681	261	28	the	the	DT
37681	261	29	connection	connection	NN
37681	261	30	between	between	IN
37681	261	31	certain	certain	JJ
37681	261	32	propositions	proposition	NNS
37681	261	33	and	and	CC
37681	261	34	the	the	DT
37681	261	35	object	object	NN
37681	261	36	in	in	IN
37681	261	37	view,--these	view,--these	NNP
37681	261	38	are	be	VBP
37681	261	39	the	the	DT
37681	261	40	most	most	RBS
37681	261	41	precious	precious	JJ
37681	261	42	fruits	fruit	NNS
37681	261	43	of	of	IN
37681	261	44	the	the	DT
37681	261	45	study	study	NN
37681	261	46	of	of	IN
37681	261	47	mathematics.--LACROIX	mathematics.--LACROIX	NNP
37681	261	48	.	.	.
37681	262	1	=	=	NFP
37681	262	2	Bibliography.=	Bibliography.=	NNP
37681	262	3	Smith	Smith	NNP
37681	262	4	,	,	,
37681	262	5	The	the	DT
37681	262	6	Teaching	Teaching	NNP
37681	262	7	of	of	IN
37681	262	8	Elementary	Elementary	NNP
37681	262	9	Mathematics	Mathematics	NNPS
37681	262	10	,	,	,
37681	262	11	p.	p.	NN
37681	262	12	234	234	CD
37681	262	13	,	,	,
37681	262	14	New	New	NNP
37681	262	15	York	York	NNP
37681	262	16	,	,	,
37681	262	17	1900	1900	CD
37681	262	18	;	;	:
37681	262	19	Henrici	Henrici	NNP
37681	262	20	,	,	,
37681	262	21	Presidential	Presidential	NNP
37681	262	22	Address	Address	NNP
37681	262	23	before	before	IN
37681	262	24	the	the	DT
37681	262	25	British	British	NNP
37681	262	26	Association	Association	NNP
37681	262	27	,	,	,
37681	262	28	_	_	NNP
37681	262	29	Nature	Nature	NNP
37681	262	30	_	_	NNP
37681	262	31	,	,	,
37681	262	32	Vol	Vol	NNP
37681	262	33	.	.	.
37681	263	1	XXVIII	XXVIII	NNP
37681	263	2	,	,	,
37681	263	3	p.	p.	NN
37681	263	4	497	497	CD
37681	263	5	;	;	:
37681	263	6	Hill	Hill	NNP
37681	263	7	,	,	,
37681	263	8	Educational	Educational	NNP
37681	263	9	Value	Value	NNP
37681	263	10	of	of	IN
37681	263	11	Mathematics	Mathematics	NNPS
37681	263	12	,	,	,
37681	263	13	_	_	NNP
37681	263	14	Educational	Educational	NNP
37681	263	15	Review	Review	NNP
37681	263	16	_	_	NNP
37681	263	17	,	,	,
37681	263	18	Vol	Vol	NNP
37681	263	19	.	.	.
37681	264	1	IX	ix	NN
37681	264	2	,	,	,
37681	264	3	p.	p.	NN
37681	264	4	349	349	CD
37681	264	5	;	;	:
37681	264	6	Young	Young	NNP
37681	264	7	,	,	,
37681	264	8	The	the	DT
37681	264	9	Teaching	Teaching	NNP
37681	264	10	of	of	IN
37681	264	11	Mathematics	Mathematics	NNP
37681	264	12	,	,	,
37681	264	13	p.	p.	NN
37681	264	14	9	9	CD
37681	264	15	,	,	,
37681	264	16	New	New	NNP
37681	264	17	York	York	NNP
37681	264	18	,	,	,
37681	264	19	1907	1907	CD
37681	264	20	.	.	.
37681	265	1	The	the	DT
37681	265	2	closing	closing	NN
37681	265	3	quotations	quotation	NNS
37681	265	4	are	be	VBP
37681	265	5	from	from	IN
37681	265	6	Rebière	Rebière	NNP
37681	265	7	,	,	,
37681	265	8	Mathématiques	Mathématiques	NNP
37681	265	9	et	et	NNP
37681	265	10	Mathématiciens	Mathématiciens	NNP
37681	265	11	,	,	,
37681	265	12	Paris	Paris	NNP
37681	265	13	,	,	,
37681	265	14	1893	1893	CD
37681	265	15	.	.	.
37681	266	1	FOOTNOTES	footnote	NNS
37681	266	2	:	:	:
37681	266	3	[	[	-LRB-
37681	266	4	4	4	CD
37681	266	5	]	]	-RRB-
37681	266	6	In	in	IN
37681	266	7	an	an	DT
37681	266	8	address	address	NN
37681	266	9	in	in	IN
37681	266	10	London	London	NNP
37681	266	11	,	,	,
37681	266	12	June	June	NNP
37681	266	13	15	15	CD
37681	266	14	,	,	,
37681	266	15	1909	1909	CD
37681	266	16	,	,	,
37681	266	17	at	at	IN
37681	266	18	a	a	DT
37681	266	19	dinner	dinner	NN
37681	266	20	to	to	IN
37681	266	21	Sir	Sir	NNP
37681	266	22	Ernest	Ernest	NNP
37681	266	23	Shackelton	Shackelton	NNP
37681	266	24	.	.	.
37681	267	1	[	[	-LRB-
37681	267	2	5	5	CD
37681	267	3	]	]	-RRB-
37681	267	4	Governor	Governor	NNP
37681	267	5	Hughes	Hughes	NNP
37681	267	6	,	,	,
37681	267	7	now	now	RB
37681	267	8	Justice	Justice	NNP
37681	267	9	Hughes	Hughes	NNP
37681	267	10	,	,	,
37681	267	11	of	of	IN
37681	267	12	New	New	NNP
37681	267	13	York	York	NNP
37681	267	14	,	,	,
37681	267	15	at	at	IN
37681	267	16	the	the	DT
37681	267	17	Peary	Peary	NNP
37681	267	18	testimonial	testimonial	NN
37681	267	19	on	on	IN
37681	267	20	February	February	NNP
37681	267	21	8	8	CD
37681	267	22	,	,	,
37681	267	23	1910	1910	CD
37681	267	24	,	,	,
37681	267	25	at	at	IN
37681	267	26	New	New	NNP
37681	267	27	York	York	NNP
37681	267	28	City	City	NNP
37681	267	29	.	.	.
37681	268	1	[	[	-LRB-
37681	268	2	6	6	CD
37681	268	3	]	]	-RRB-
37681	268	4	The	the	DT
37681	268	5	first	first	JJ
37681	268	6	work	work	NN
37681	268	7	upon	upon	IN
37681	268	8	this	this	DT
37681	268	9	subject	subject	NN
37681	268	10	,	,	,
37681	268	11	and	and	CC
37681	268	12	indeed	indeed	RB
37681	268	13	the	the	DT
37681	268	14	first	first	JJ
37681	268	15	printed	print	VBN
37681	268	16	treatise	treatise	NN
37681	268	17	on	on	IN
37681	268	18	curves	curve	NNS
37681	268	19	in	in	IN
37681	268	20	general	general	JJ
37681	268	21	,	,	,
37681	268	22	was	be	VBD
37681	268	23	written	write	VBN
37681	268	24	by	by	IN
37681	268	25	the	the	DT
37681	268	26	famous	famous	JJ
37681	268	27	artist	artist	NN
37681	268	28	of	of	IN
37681	268	29	Nürnberg	Nürnberg	NNP
37681	268	30	,	,	,
37681	268	31	Albrecht	Albrecht	NNP
37681	268	32	Dürer	Dürer	NNP
37681	268	33	.	.	.
37681	269	1	[	[	-LRB-
37681	269	2	7	7	LS
37681	269	3	]	]	-RRB-
37681	269	4	Several	several	JJ
37681	269	5	of	of	IN
37681	269	6	these	these	DT
37681	269	7	writers	writer	NNS
37681	269	8	are	be	VBP
37681	269	9	mentioned	mention	VBN
37681	269	10	in	in	IN
37681	269	11	Chapter	Chapter	NNP
37681	269	12	IV	IV	NNP
37681	269	13	.	.	.
37681	270	1	[	[	-LRB-
37681	270	2	8	8	CD
37681	270	3	]	]	-RRB-
37681	270	4	If	if	IN
37681	270	5	any	any	DT
37681	270	6	reader	reader	NN
37681	270	7	chances	chance	VBZ
37681	270	8	upon	upon	IN
37681	270	9	George	George	NNP
37681	270	10	Birkbeck	Birkbeck	NNP
37681	270	11	's	's	POS
37681	270	12	English	english	JJ
37681	270	13	translation	translation	NN
37681	270	14	of	of	IN
37681	270	15	Charles	Charles	NNP
37681	270	16	Dupin	Dupin	NNP
37681	270	17	's	's	POS
37681	270	18	"	"	``
37681	270	19	Mathematics	Mathematics	NNP
37681	270	20	Practically	practically	RB
37681	270	21	Applied	apply	VBN
37681	270	22	,	,	,
37681	270	23	"	"	''
37681	270	24	Halifax	Halifax	NNP
37681	270	25	,	,	,
37681	270	26	1854	1854	CD
37681	270	27	,	,	,
37681	270	28	he	-PRON-	PRP
37681	270	29	will	will	MD
37681	270	30	find	find	VB
37681	270	31	that	that	IN
37681	270	32	Dupin	Dupin	NNP
37681	270	33	gave	give	VBD
37681	270	34	more	more	JJR
37681	270	35	good	good	JJ
37681	270	36	applications	application	NNS
37681	270	37	of	of	IN
37681	270	38	geometry	geometry	NN
37681	270	39	than	than	IN
37681	270	40	all	all	DT
37681	270	41	of	of	IN
37681	270	42	our	-PRON-	PRP$
37681	270	43	American	american	JJ
37681	270	44	advocates	advocate	NNS
37681	270	45	of	of	IN
37681	270	46	practical	practical	JJ
37681	270	47	geometry	geometry	NN
37681	270	48	combined	combine	VBN
37681	270	49	.	.	.
37681	271	1	[	[	-LRB-
37681	271	2	9	9	CD
37681	271	3	]	]	-RRB-
37681	271	4	See	see	VB
37681	271	5	,	,	,
37681	271	6	for	for	IN
37681	271	7	example	example	NN
37681	271	8	,	,	,
37681	271	9	Henrici	Henrici	NNP
37681	271	10	's	's	POS
37681	271	11	"	"	``
37681	271	12	Congruent	congruent	JJ
37681	271	13	Figures	figure	NNS
37681	271	14	,	,	,
37681	271	15	"	"	''
37681	271	16	London	London	NNP
37681	271	17	,	,	,
37681	271	18	1879	1879	CD
37681	271	19	,	,	,
37681	271	20	and	and	CC
37681	271	21	the	the	DT
37681	271	22	review	review	NN
37681	271	23	of	of	IN
37681	271	24	Borel	Borel	NNP
37681	271	25	's	's	POS
37681	271	26	"	"	``
37681	271	27	Elements	Elements	NNPS
37681	271	28	of	of	IN
37681	271	29	Mathematics	Mathematics	NNP
37681	271	30	,	,	,
37681	271	31	"	"	''
37681	271	32	by	by	IN
37681	271	33	Professor	Professor	NNP
37681	271	34	Sisam	Sisam	NNP
37681	271	35	in	in	IN
37681	271	36	the	the	DT
37681	271	37	_	_	NNP
37681	271	38	Bulletin	Bulletin	NNP
37681	271	39	of	of	IN
37681	271	40	the	the	DT
37681	271	41	American	American	NNP
37681	271	42	Mathematical	Mathematical	NNP
37681	271	43	Society	Society	NNP
37681	271	44	_	_	NNP
37681	271	45	,	,	,
37681	271	46	July	July	NNP
37681	271	47	,	,	,
37681	271	48	1910	1910	CD
37681	271	49	,	,	,
37681	271	50	a	a	DT
37681	271	51	matter	matter	NN
37681	271	52	discussed	discuss	VBN
37681	271	53	later	later	RB
37681	271	54	in	in	IN
37681	271	55	this	this	DT
37681	271	56	work	work	NN
37681	271	57	.	.	.
37681	272	1	[	[	-LRB-
37681	272	2	10	10	CD
37681	272	3	]	]	-RRB-
37681	272	4	T.	T.	NNP
37681	272	5	J.	J.	NNP
37681	272	6	McCormack	McCormack	NNP
37681	272	7	,	,	,
37681	272	8	"	"	``
37681	272	9	Why	why	WRB
37681	272	10	do	do	VBP
37681	272	11	we	-PRON-	PRP
37681	272	12	study	study	VB
37681	272	13	Mathematics	Mathematics	NNP
37681	272	14	:	:	:
37681	272	15	a	a	DT
37681	272	16	Philosophical	Philosophical	NNP
37681	272	17	and	and	CC
37681	272	18	Historical	Historical	NNP
37681	272	19	Retrospect	Retrospect	NNP
37681	272	20	,	,	,
37681	272	21	"	"	''
37681	272	22	p.	p.	NN
37681	272	23	9	9	CD
37681	272	24	,	,	,
37681	272	25	Cedar	Cedar	NNP
37681	272	26	Rapids	Rapids	NNP
37681	272	27	,	,	,
37681	272	28	Iowa	Iowa	NNP
37681	272	29	,	,	,
37681	272	30	1910	1910	CD
37681	272	31	.	.	.
37681	273	1	[	[	-LRB-
37681	273	2	11	11	CD
37681	273	3	]	]	-RRB-
37681	273	4	Of	of	IN
37681	273	5	the	the	DT
37681	273	6	fair	fair	JJ
37681	273	7	and	and	CC
37681	273	8	candid	candid	JJ
37681	273	9	arguments	argument	NNS
37681	273	10	against	against	IN
37681	273	11	the	the	DT
37681	273	12	culture	culture	NN
37681	273	13	value	value	NN
37681	273	14	of	of	IN
37681	273	15	mathematics	mathematic	NNS
37681	273	16	,	,	,
37681	273	17	one	one	CD
37681	273	18	of	of	IN
37681	273	19	the	the	DT
37681	273	20	best	good	JJS
37681	273	21	of	of	IN
37681	273	22	the	the	DT
37681	273	23	recent	recent	JJ
37681	273	24	ones	one	NNS
37681	273	25	is	be	VBZ
37681	273	26	that	that	IN
37681	273	27	by	by	IN
37681	273	28	G.	G.	NNP
37681	273	29	F.	F.	NNP
37681	273	30	Swain	Swain	NNP
37681	273	31	,	,	,
37681	273	32	in	in	IN
37681	273	33	the	the	DT
37681	273	34	_	_	NNP
37681	273	35	Atti	Atti	NNP
37681	273	36	del	del	NNP
37681	273	37	IV	IV	NNP
37681	273	38	Congresso	Congresso	NNP
37681	273	39	Internazionale	Internazionale	NNP
37681	273	40	dei	dei	NNP
37681	273	41	Matematici	Matematici	NNP
37681	273	42	_	_	NNP
37681	273	43	,	,	,
37681	273	44	Rome	Rome	NNP
37681	273	45	,	,	,
37681	273	46	1909	1909	CD
37681	273	47	,	,	,
37681	273	48	Vol	Vol	NNP
37681	273	49	.	.	.
37681	274	1	III	III	NNP
37681	274	2	,	,	,
37681	274	3	p.	p.	NN
37681	274	4	361	361	CD
37681	274	5	.	.	.
37681	275	1	The	the	DT
37681	275	2	literature	literature	NN
37681	275	3	of	of	IN
37681	275	4	this	this	DT
37681	275	5	school	school	NN
37681	275	6	is	be	VBZ
37681	275	7	quite	quite	RB
37681	275	8	extensive	extensive	JJ
37681	275	9	,	,	,
37681	275	10	but	but	CC
37681	275	11	Perry	Perry	NNP
37681	275	12	's	's	POS
37681	275	13	"	"	``
37681	275	14	England	England	NNP
37681	275	15	's	's	POS
37681	275	16	Neglect	Neglect	NNP
37681	275	17	of	of	IN
37681	275	18	Science	Science	NNP
37681	275	19	,	,	,
37681	275	20	"	"	''
37681	275	21	London	London	NNP
37681	275	22	,	,	,
37681	275	23	1900	1900	CD
37681	275	24	,	,	,
37681	275	25	and	and	CC
37681	275	26	"	"	``
37681	275	27	Discussion	discussion	NN
37681	275	28	on	on	IN
37681	275	29	the	the	DT
37681	275	30	Teaching	Teaching	NNP
37681	275	31	of	of	IN
37681	275	32	Mathematics	Mathematics	NNP
37681	275	33	,	,	,
37681	275	34	"	"	''
37681	275	35	London	London	NNP
37681	275	36	,	,	,
37681	275	37	1901	1901	CD
37681	275	38	,	,	,
37681	275	39	are	be	VBP
37681	275	40	typical	typical	JJ
37681	275	41	.	.	.
37681	276	1	[	[	-LRB-
37681	276	2	12	12	CD
37681	276	3	]	]	-RRB-
37681	276	4	In	in	IN
37681	276	5	his	-PRON-	PRP$
37681	276	6	novel	novel	NN
37681	276	7	,	,	,
37681	276	8	"	"	``
37681	276	9	The	the	DT
37681	276	10	Morals	Morals	NNPS
37681	276	11	of	of	IN
37681	276	12	Marcus	Marcus	NNP
37681	276	13	Ordeyne	Ordeyne	NNP
37681	276	14	.	.	.
37681	276	15	"	"	''
37681	277	1	[	[	-LRB-
37681	277	2	13	13	CD
37681	277	3	]	]	-RRB-
37681	277	4	G.	G.	NNP
37681	277	5	W.	W.	NNP
37681	277	6	L.	L.	NNP
37681	277	7	Carson	Carson	NNP
37681	277	8	,	,	,
37681	277	9	"	"	``
37681	277	10	The	the	DT
37681	277	11	Functions	Functions	NNPS
37681	277	12	of	of	IN
37681	277	13	Geometry	Geometry	NNP
37681	277	14	as	as	IN
37681	277	15	a	a	DT
37681	277	16	Subject	Subject	NNP
37681	277	17	of	of	IN
37681	277	18	Education	Education	NNP
37681	277	19	,	,	,
37681	277	20	"	"	''
37681	277	21	p.	p.	NN
37681	277	22	3	3	CD
37681	277	23	,	,	,
37681	277	24	Tonbridge	Tonbridge	NNP
37681	277	25	,	,	,
37681	277	26	1910	1910	CD
37681	277	27	.	.	.
37681	278	1	[	[	-LRB-
37681	278	2	14	14	CD
37681	278	3	]	]	-RRB-
37681	278	4	It	-PRON-	PRP
37681	278	5	may	may	MD
37681	278	6	well	well	RB
37681	278	7	be	be	VB
37681	278	8	,	,	,
37681	278	9	however	however	RB
37681	278	10	,	,	,
37681	278	11	that	that	IN
37681	278	12	the	the	DT
37681	278	13	growing	grow	VBG
37681	278	14	curriculum	curriculum	NN
37681	278	15	may	may	MD
37681	278	16	justify	justify	VB
37681	278	17	some	some	DT
37681	278	18	reduction	reduction	NN
37681	278	19	in	in	IN
37681	278	20	the	the	DT
37681	278	21	time	time	NN
37681	278	22	formerly	formerly	RB
37681	278	23	assigned	assign	VBN
37681	278	24	to	to	IN
37681	278	25	geometry	geometry	VB
37681	278	26	,	,	,
37681	278	27	and	and	CC
37681	278	28	any	any	DT
37681	278	29	reasonable	reasonable	JJ
37681	278	30	proposition	proposition	NN
37681	278	31	of	of	IN
37681	278	32	this	this	DT
37681	278	33	nature	nature	NN
37681	278	34	should	should	MD
37681	278	35	be	be	VB
37681	278	36	fairly	fairly	RB
37681	278	37	met	meet	VBN
37681	278	38	by	by	IN
37681	278	39	teachers	teacher	NNS
37681	278	40	of	of	IN
37681	278	41	mathematics	mathematic	NNS
37681	278	42	.	.	.
37681	279	1	[	[	-LRB-
37681	279	2	15	15	CD
37681	279	3	]	]	-RRB-
37681	279	4	Professor	Professor	NNP
37681	279	5	Münsterberg	Münsterberg	NNP
37681	279	6	,	,	,
37681	279	7	in	in	IN
37681	279	8	the	the	DT
37681	279	9	_	_	NNP
37681	279	10	Metropolitan	Metropolitan	NNP
37681	279	11	Magazine	Magazine	NNP
37681	279	12	_	_	NNP
37681	279	13	for	for	IN
37681	279	14	July	July	NNP
37681	279	15	,	,	,
37681	279	16	1910	1910	CD
37681	279	17	.	.	.
37681	280	1	CHAPTER	CHAPTER	NNP
37681	280	2	III	III	NNP
37681	280	3	A	a	DT
37681	280	4	BRIEF	brief	NN
37681	280	5	HISTORY	history	NN
37681	280	6	OF	of	IN
37681	280	7	GEOMETRY	GEOMETRY	NNP
37681	280	8	The	the	DT
37681	280	9	geometry	geometry	NN
37681	280	10	of	of	IN
37681	280	11	very	very	RB
37681	280	12	ancient	ancient	JJ
37681	280	13	peoples	people	NNS
37681	280	14	was	be	VBD
37681	280	15	largely	largely	RB
37681	280	16	the	the	DT
37681	280	17	mensuration	mensuration	NN
37681	280	18	of	of	IN
37681	280	19	simple	simple	JJ
37681	280	20	areas	area	NNS
37681	280	21	and	and	CC
37681	280	22	solids	solid	NNS
37681	280	23	,	,	,
37681	280	24	such	such	JJ
37681	280	25	as	as	IN
37681	280	26	is	be	VBZ
37681	280	27	taught	teach	VBN
37681	280	28	to	to	IN
37681	280	29	children	child	NNS
37681	280	30	in	in	IN
37681	280	31	elementary	elementary	NN
37681	280	32	arithmetic	arithmetic	JJ
37681	280	33	to	to	IN
37681	280	34	-	-	HYPH
37681	280	35	day	day	NN
37681	280	36	.	.	.
37681	281	1	They	-PRON-	PRP
37681	281	2	early	early	RB
37681	281	3	learned	learn	VBD
37681	281	4	how	how	WRB
37681	281	5	to	to	TO
37681	281	6	find	find	VB
37681	281	7	the	the	DT
37681	281	8	area	area	NN
37681	281	9	of	of	IN
37681	281	10	a	a	DT
37681	281	11	rectangle	rectangle	NN
37681	281	12	,	,	,
37681	281	13	and	and	CC
37681	281	14	in	in	IN
37681	281	15	the	the	DT
37681	281	16	oldest	old	JJS
37681	281	17	mathematical	mathematical	JJ
37681	281	18	records	record	NNS
37681	281	19	that	that	WDT
37681	281	20	have	have	VBP
37681	281	21	come	come	VBN
37681	281	22	down	down	RP
37681	281	23	to	to	IN
37681	281	24	us	-PRON-	PRP
37681	281	25	there	there	EX
37681	281	26	is	be	VBZ
37681	281	27	some	some	DT
37681	281	28	discussion	discussion	NN
37681	281	29	of	of	IN
37681	281	30	the	the	DT
37681	281	31	area	area	NN
37681	281	32	of	of	IN
37681	281	33	triangles	triangle	NNS
37681	281	34	and	and	CC
37681	281	35	the	the	DT
37681	281	36	volume	volume	NN
37681	281	37	of	of	IN
37681	281	38	solids	solid	NNS
37681	281	39	.	.	.
37681	282	1	The	the	DT
37681	282	2	earliest	early	JJS
37681	282	3	documents	document	NNS
37681	282	4	that	that	WDT
37681	282	5	we	-PRON-	PRP
37681	282	6	have	have	VBP
37681	282	7	relating	relate	VBG
37681	282	8	to	to	TO
37681	282	9	geometry	geometry	NN
37681	282	10	come	come	VB
37681	282	11	to	to	IN
37681	282	12	us	-PRON-	PRP
37681	282	13	from	from	IN
37681	282	14	Babylon	Babylon	NNP
37681	282	15	and	and	CC
37681	282	16	Egypt	Egypt	NNP
37681	282	17	.	.	.
37681	283	1	Those	those	DT
37681	283	2	from	from	IN
37681	283	3	Babylon	Babylon	NNP
37681	283	4	are	be	VBP
37681	283	5	written	write	VBN
37681	283	6	on	on	IN
37681	283	7	small	small	JJ
37681	283	8	clay	clay	NN
37681	283	9	tablets	tablet	NNS
37681	283	10	,	,	,
37681	283	11	some	some	DT
37681	283	12	of	of	IN
37681	283	13	them	-PRON-	PRP
37681	283	14	about	about	IN
37681	283	15	the	the	DT
37681	283	16	size	size	NN
37681	283	17	of	of	IN
37681	283	18	the	the	DT
37681	283	19	hand	hand	NN
37681	283	20	,	,	,
37681	283	21	these	these	DT
37681	283	22	tablets	tablet	NNS
37681	283	23	afterwards	afterwards	RB
37681	283	24	having	have	VBG
37681	283	25	been	be	VBN
37681	283	26	baked	bake	VBN
37681	283	27	in	in	IN
37681	283	28	the	the	DT
37681	283	29	sun	sun	NN
37681	283	30	.	.	.
37681	284	1	They	-PRON-	PRP
37681	284	2	show	show	VBP
37681	284	3	that	that	IN
37681	284	4	the	the	DT
37681	284	5	Babylonians	Babylonians	NNPS
37681	284	6	of	of	IN
37681	284	7	that	that	DT
37681	284	8	period	period	NN
37681	284	9	knew	know	VBD
37681	284	10	something	something	NN
37681	284	11	of	of	IN
37681	284	12	land	land	NN
37681	284	13	measures	measure	NNS
37681	284	14	,	,	,
37681	284	15	and	and	CC
37681	284	16	perhaps	perhaps	RB
37681	284	17	had	have	VBD
37681	284	18	advanced	advance	VBN
37681	284	19	far	far	RB
37681	284	20	enough	enough	RB
37681	284	21	to	to	TO
37681	284	22	compute	compute	VB
37681	284	23	the	the	DT
37681	284	24	area	area	NN
37681	284	25	of	of	IN
37681	284	26	a	a	DT
37681	284	27	trapezoid	trapezoid	NN
37681	284	28	.	.	.
37681	285	1	For	for	IN
37681	285	2	the	the	DT
37681	285	3	mensuration	mensuration	NN
37681	285	4	of	of	IN
37681	285	5	the	the	DT
37681	285	6	circle	circle	NN
37681	285	7	they	-PRON-	PRP
37681	285	8	later	later	RB
37681	285	9	used	use	VBD
37681	285	10	,	,	,
37681	285	11	as	as	IN
37681	285	12	did	do	VBD
37681	285	13	the	the	DT
37681	285	14	early	early	JJ
37681	285	15	Hebrews	Hebrews	NNPS
37681	285	16	,	,	,
37681	285	17	the	the	DT
37681	285	18	value	value	NN
37681	285	19	[	[	-LRB-
37681	285	20	pi	pi	NN
37681	285	21	]	]	-RRB-
37681	285	22	=	=	SYM
37681	285	23	3	3	CD
37681	285	24	.	.	.
37681	286	1	A	a	DT
37681	286	2	tablet	tablet	NN
37681	286	3	in	in	IN
37681	286	4	the	the	DT
37681	286	5	British	British	NNP
37681	286	6	Museum	Museum	NNP
37681	286	7	shows	show	VBZ
37681	286	8	that	that	IN
37681	286	9	they	-PRON-	PRP
37681	286	10	also	also	RB
37681	286	11	used	use	VBD
37681	286	12	such	such	JJ
37681	286	13	geometric	geometric	JJ
37681	286	14	forms	form	NNS
37681	286	15	as	as	IN
37681	286	16	triangles	triangle	NNS
37681	286	17	and	and	CC
37681	286	18	circular	circular	JJ
37681	286	19	segments	segment	NNS
37681	286	20	in	in	IN
37681	286	21	astrology	astrology	NN
37681	286	22	or	or	CC
37681	286	23	as	as	IN
37681	286	24	talismans	talisman	NNS
37681	286	25	.	.	.
37681	287	1	The	the	DT
37681	287	2	Egyptians	Egyptians	NNPS
37681	287	3	must	must	MD
37681	287	4	have	have	VB
37681	287	5	had	have	VBN
37681	287	6	a	a	DT
37681	287	7	fair	fair	JJ
37681	287	8	knowledge	knowledge	NN
37681	287	9	of	of	IN
37681	287	10	practical	practical	JJ
37681	287	11	geometry	geometry	NN
37681	287	12	long	long	RB
37681	287	13	before	before	IN
37681	287	14	the	the	DT
37681	287	15	date	date	NN
37681	287	16	of	of	IN
37681	287	17	any	any	DT
37681	287	18	mathematical	mathematical	JJ
37681	287	19	treatise	treatise	NN
37681	287	20	that	that	WDT
37681	287	21	has	have	VBZ
37681	287	22	come	come	VBN
37681	287	23	down	down	RP
37681	287	24	to	to	IN
37681	287	25	us	-PRON-	PRP
37681	287	26	,	,	,
37681	287	27	for	for	IN
37681	287	28	the	the	DT
37681	287	29	building	building	NN
37681	287	30	of	of	IN
37681	287	31	the	the	DT
37681	287	32	pyramids	pyramid	NNS
37681	287	33	,	,	,
37681	287	34	between	between	IN
37681	287	35	3000	3000	CD
37681	287	36	and	and	CC
37681	287	37	2400	2400	CD
37681	287	38	B.C.	B.C.	NNP
37681	287	39	,	,	,
37681	287	40	required	require	VBD
37681	287	41	the	the	DT
37681	287	42	application	application	NN
37681	287	43	of	of	IN
37681	287	44	several	several	JJ
37681	287	45	geometric	geometric	JJ
37681	287	46	principles	principle	NNS
37681	287	47	.	.	.
37681	288	1	Some	some	DT
37681	288	2	knowledge	knowledge	NN
37681	288	3	of	of	IN
37681	288	4	surveying	surveying	NN
37681	288	5	must	must	MD
37681	288	6	also	also	RB
37681	288	7	have	have	VB
37681	288	8	been	be	VBN
37681	288	9	necessary	necessary	JJ
37681	288	10	to	to	TO
37681	288	11	carry	carry	VB
37681	288	12	out	out	RP
37681	288	13	the	the	DT
37681	288	14	extensive	extensive	JJ
37681	288	15	plans	plan	NNS
37681	288	16	for	for	IN
37681	288	17	irrigation	irrigation	NN
37681	288	18	that	that	WDT
37681	288	19	were	be	VBD
37681	288	20	executed	execute	VBN
37681	288	21	under	under	IN
37681	288	22	Amenemhat	Amenemhat	NNP
37681	288	23	III	III	NNP
37681	288	24	,	,	,
37681	288	25	about	about	RB
37681	288	26	2200	2200	CD
37681	288	27	B.C.	B.C.	NNP
37681	289	1	The	the	DT
37681	289	2	first	first	JJ
37681	289	3	definite	definite	JJ
37681	289	4	knowledge	knowledge	NN
37681	289	5	that	that	WDT
37681	289	6	we	-PRON-	PRP
37681	289	7	have	have	VBP
37681	289	8	of	of	IN
37681	289	9	Egyptian	egyptian	JJ
37681	289	10	mathematics	mathematic	NNS
37681	289	11	comes	come	VBZ
37681	289	12	to	to	IN
37681	289	13	us	-PRON-	PRP
37681	289	14	from	from	IN
37681	289	15	a	a	DT
37681	289	16	manuscript	manuscript	NN
37681	289	17	copied	copy	VBN
37681	289	18	on	on	IN
37681	289	19	papyrus	papyrus	NNP
37681	289	20	,	,	,
37681	289	21	a	a	DT
37681	289	22	kind	kind	NN
37681	289	23	of	of	IN
37681	289	24	paper	paper	NN
37681	289	25	used	use	VBN
37681	289	26	about	about	IN
37681	289	27	the	the	DT
37681	289	28	Mediterranean	Mediterranean	NNP
37681	289	29	in	in	IN
37681	289	30	early	early	JJ
37681	289	31	times	time	NNS
37681	289	32	.	.	.
37681	290	1	This	this	DT
37681	290	2	copy	copy	NN
37681	290	3	was	be	VBD
37681	290	4	made	make	VBN
37681	290	5	by	by	IN
37681	290	6	one	one	CD
37681	290	7	Aah	Aah	NNP
37681	290	8	-	-	HYPH
37681	290	9	mesu	mesu	NN
37681	290	10	(	(	-LRB-
37681	290	11	The	the	DT
37681	290	12	Moon	Moon	NNP
37681	290	13	-	-	HYPH
37681	290	14	born	bear	VBN
37681	290	15	)	)	-RRB-
37681	290	16	,	,	,
37681	290	17	commonly	commonly	RB
37681	290	18	called	call	VBN
37681	290	19	Ahmes	Ahmes	NNP
37681	290	20	,	,	,
37681	290	21	who	who	WP
37681	290	22	probably	probably	RB
37681	290	23	flourished	flourish	VBD
37681	290	24	about	about	RB
37681	290	25	1700	1700	CD
37681	290	26	B.C.	B.C.	NNP
37681	291	1	The	the	DT
37681	291	2	original	original	NN
37681	291	3	from	from	IN
37681	291	4	which	which	WDT
37681	291	5	he	-PRON-	PRP
37681	291	6	copied	copy	VBD
37681	291	7	,	,	,
37681	291	8	written	write	VBN
37681	291	9	about	about	RB
37681	291	10	2300	2300	CD
37681	291	11	B.C.	B.C.	NNP
37681	291	12	,	,	,
37681	291	13	has	have	VBZ
37681	291	14	been	be	VBN
37681	291	15	lost	lose	VBN
37681	291	16	,	,	,
37681	291	17	but	but	CC
37681	291	18	the	the	DT
37681	291	19	papyrus	papyrus	NN
37681	291	20	of	of	IN
37681	291	21	Ahmes	Ahmes	NNP
37681	291	22	,	,	,
37681	291	23	written	write	VBN
37681	291	24	nearly	nearly	RB
37681	291	25	four	four	CD
37681	291	26	thousand	thousand	CD
37681	291	27	years	year	NNS
37681	291	28	ago	ago	RB
37681	291	29	,	,	,
37681	291	30	is	be	VBZ
37681	291	31	still	still	RB
37681	291	32	preserved	preserve	VBN
37681	291	33	,	,	,
37681	291	34	and	and	CC
37681	291	35	is	be	VBZ
37681	291	36	now	now	RB
37681	291	37	in	in	IN
37681	291	38	the	the	DT
37681	291	39	British	British	NNP
37681	291	40	Museum	Museum	NNP
37681	291	41	.	.	.
37681	292	1	In	in	IN
37681	292	2	this	this	DT
37681	292	3	manuscript	manuscript	NN
37681	292	4	,	,	,
37681	292	5	which	which	WDT
37681	292	6	is	be	VBZ
37681	292	7	devoted	devote	VBN
37681	292	8	chiefly	chiefly	RB
37681	292	9	to	to	IN
37681	292	10	fractions	fraction	NNS
37681	292	11	and	and	CC
37681	292	12	to	to	IN
37681	292	13	a	a	DT
37681	292	14	crude	crude	JJ
37681	292	15	algebra	algebra	NN
37681	292	16	,	,	,
37681	292	17	is	be	VBZ
37681	292	18	found	find	VBN
37681	292	19	some	some	DT
37681	292	20	work	work	NN
37681	292	21	on	on	IN
37681	292	22	mensuration	mensuration	NN
37681	292	23	.	.	.
37681	293	1	Among	among	IN
37681	293	2	the	the	DT
37681	293	3	curious	curious	JJ
37681	293	4	rules	rule	NNS
37681	293	5	are	be	VBP
37681	293	6	the	the	DT
37681	293	7	incorrect	incorrect	JJ
37681	293	8	ones	one	NNS
37681	293	9	that	that	WDT
37681	293	10	the	the	DT
37681	293	11	area	area	NN
37681	293	12	of	of	IN
37681	293	13	an	an	DT
37681	293	14	isosceles	isoscele	NNS
37681	293	15	triangle	triangle	NN
37681	293	16	equals	equal	VBZ
37681	293	17	half	half	PDT
37681	293	18	the	the	DT
37681	293	19	product	product	NN
37681	293	20	of	of	IN
37681	293	21	the	the	DT
37681	293	22	base	base	NN
37681	293	23	and	and	CC
37681	293	24	one	one	CD
37681	293	25	of	of	IN
37681	293	26	the	the	DT
37681	293	27	equal	equal	JJ
37681	293	28	sides	side	NNS
37681	293	29	;	;	:
37681	293	30	and	and	CC
37681	293	31	that	that	IN
37681	293	32	the	the	DT
37681	293	33	area	area	NN
37681	293	34	of	of	IN
37681	293	35	a	a	DT
37681	293	36	trapezoid	trapezoid	NN
37681	293	37	having	have	VBG
37681	293	38	bases	basis	NNS
37681	293	39	_	_	NNP
37681	293	40	b	b	NNP
37681	293	41	_	_	NNP
37681	293	42	,	,	,
37681	293	43	_	_	NNP
37681	293	44	b	b	NNP
37681	293	45	'	'	``
37681	293	46	_	_	NNP
37681	293	47	,	,	,
37681	293	48	and	and	CC
37681	293	49	the	the	DT
37681	293	50	nonparallel	nonparallel	NNP
37681	293	51	sides	side	VBZ
37681	293	52	each	each	DT
37681	293	53	equal	equal	JJ
37681	293	54	to	to	IN
37681	293	55	_	_	NNP
37681	293	56	a	a	DT
37681	293	57	_	_	NNP
37681	293	58	,	,	,
37681	293	59	is	be	VBZ
37681	293	60	1/2_a_(_b	1/2_a_(_b	CD
37681	293	61	_	_	NNP
37681	293	62	+	+	SYM
37681	293	63	_	_	NNP
37681	293	64	b	b	NNP
37681	293	65	'	'	''
37681	293	66	_	_	NNP
37681	293	67	)	)	-RRB-
37681	293	68	.	.	.
37681	294	1	One	one	CD
37681	294	2	noteworthy	noteworthy	JJ
37681	294	3	advance	advance	NN
37681	294	4	appears	appear	VBZ
37681	294	5	,	,	,
37681	294	6	however	however	RB
37681	294	7	.	.	.
37681	295	1	Ahmes	Ahmes	NNP
37681	295	2	gives	give	VBZ
37681	295	3	a	a	DT
37681	295	4	rule	rule	NN
37681	295	5	for	for	IN
37681	295	6	finding	find	VBG
37681	295	7	the	the	DT
37681	295	8	area	area	NN
37681	295	9	of	of	IN
37681	295	10	a	a	DT
37681	295	11	circle	circle	NN
37681	295	12	,	,	,
37681	295	13	substantially	substantially	RB
37681	295	14	as	as	IN
37681	295	15	follows	follow	VBZ
37681	295	16	:	:	:
37681	295	17	Multiply	multiply	VB
37681	295	18	the	the	DT
37681	295	19	square	square	NN
37681	295	20	on	on	IN
37681	295	21	the	the	DT
37681	295	22	radius	radius	NN
37681	295	23	by	by	IN
37681	295	24	(	(	-LRB-
37681	295	25	16/9)^2	16/9)^2	CD
37681	295	26	,	,	,
37681	295	27	which	which	WDT
37681	295	28	is	be	VBZ
37681	295	29	equivalent	equivalent	JJ
37681	295	30	to	to	IN
37681	295	31	taking	take	VBG
37681	295	32	for	for	IN
37681	295	33	[	[	-LRB-
37681	295	34	pi	pi	NN
37681	295	35	]	]	-RRB-
37681	295	36	the	the	DT
37681	295	37	value	value	NN
37681	295	38	3.1605	3.1605	CD
37681	295	39	.	.	.
37681	296	1	This	this	DT
37681	296	2	papyrus	papyrus	NN
37681	296	3	also	also	RB
37681	296	4	contains	contain	VBZ
37681	296	5	some	some	DT
37681	296	6	treatment	treatment	NN
37681	296	7	of	of	IN
37681	296	8	the	the	DT
37681	296	9	mensuration	mensuration	NN
37681	296	10	of	of	IN
37681	296	11	solids	solid	NNS
37681	296	12	,	,	,
37681	296	13	particularly	particularly	RB
37681	296	14	with	with	IN
37681	296	15	reference	reference	NN
37681	296	16	to	to	IN
37681	296	17	the	the	DT
37681	296	18	capacity	capacity	NN
37681	296	19	of	of	IN
37681	296	20	granaries	granary	NNS
37681	296	21	.	.	.
37681	297	1	There	there	EX
37681	297	2	is	be	VBZ
37681	297	3	also	also	RB
37681	297	4	some	some	DT
37681	297	5	slight	slight	JJ
37681	297	6	mention	mention	NN
37681	297	7	of	of	IN
37681	297	8	similar	similar	JJ
37681	297	9	figures	figure	NNS
37681	297	10	,	,	,
37681	297	11	and	and	CC
37681	297	12	an	an	DT
37681	297	13	extensive	extensive	JJ
37681	297	14	treatment	treatment	NN
37681	297	15	of	of	IN
37681	297	16	unit	unit	NN
37681	297	17	fractions,--fractions	fractions,--fraction	NNS
37681	297	18	that	that	WDT
37681	297	19	were	be	VBD
37681	297	20	quite	quite	RB
37681	297	21	universal	universal	JJ
37681	297	22	among	among	IN
37681	297	23	the	the	DT
37681	297	24	ancients	ancient	NNS
37681	297	25	.	.	.
37681	298	1	In	in	IN
37681	298	2	the	the	DT
37681	298	3	line	line	NN
37681	298	4	of	of	IN
37681	298	5	algebra	algebra	NN
37681	298	6	it	-PRON-	PRP
37681	298	7	contains	contain	VBZ
37681	298	8	a	a	DT
37681	298	9	brief	brief	JJ
37681	298	10	treatment	treatment	NN
37681	298	11	of	of	IN
37681	298	12	the	the	DT
37681	298	13	equation	equation	NN
37681	298	14	of	of	IN
37681	298	15	the	the	DT
37681	298	16	first	first	JJ
37681	298	17	degree	degree	NN
37681	298	18	with	with	IN
37681	298	19	one	one	CD
37681	298	20	unknown	unknown	NN
37681	298	21	,	,	,
37681	298	22	and	and	CC
37681	298	23	of	of	IN
37681	298	24	progressions	progression	NNS
37681	298	25	.	.	.
37681	299	1	[	[	-LRB-
37681	299	2	16	16	CD
37681	299	3	]	]	-RRB-
37681	299	4	Herodotus	Herodotus	NNP
37681	299	5	tells	tell	VBZ
37681	299	6	us	-PRON-	PRP
37681	299	7	that	that	DT
37681	299	8	Sesostris	Sesostris	NNP
37681	299	9	,	,	,
37681	299	10	king	king	NN
37681	299	11	of	of	IN
37681	299	12	Egypt,[17	Egypt,[17	NNP
37681	299	13	]	]	-RRB-
37681	299	14	divided	divide	VBD
37681	299	15	the	the	DT
37681	299	16	land	land	NN
37681	299	17	among	among	IN
37681	299	18	his	-PRON-	PRP$
37681	299	19	people	people	NNS
37681	299	20	and	and	CC
37681	299	21	marked	mark	VBD
37681	299	22	out	out	RP
37681	299	23	the	the	DT
37681	299	24	boundaries	boundary	NNS
37681	299	25	after	after	IN
37681	299	26	the	the	DT
37681	299	27	overflow	overflow	NN
37681	299	28	of	of	IN
37681	299	29	the	the	DT
37681	299	30	Nile	Nile	NNP
37681	299	31	,	,	,
37681	299	32	so	so	IN
37681	299	33	that	that	IN
37681	299	34	surveying	surveying	NN
37681	299	35	must	must	MD
37681	299	36	have	have	VB
37681	299	37	been	be	VBN
37681	299	38	well	well	RB
37681	299	39	known	know	VBN
37681	299	40	in	in	IN
37681	299	41	his	-PRON-	PRP$
37681	299	42	day	day	NN
37681	299	43	.	.	.
37681	300	1	Indeed	indeed	RB
37681	300	2	,	,	,
37681	300	3	the	the	DT
37681	300	4	_	_	NNP
37681	300	5	harpedonaptæ	harpedonaptæ	NN
37681	300	6	_	_	NNP
37681	300	7	,	,	,
37681	300	8	or	or	CC
37681	300	9	rope	rope	NN
37681	300	10	stretchers	stretcher	NNS
37681	300	11	,	,	,
37681	300	12	acquired	acquire	VBD
37681	300	13	their	-PRON-	PRP$
37681	300	14	name	name	NN
37681	300	15	because	because	IN
37681	300	16	they	-PRON-	PRP
37681	300	17	stretched	stretch	VBD
37681	300	18	cords	cord	NNS
37681	300	19	,	,	,
37681	300	20	in	in	IN
37681	300	21	which	which	WDT
37681	300	22	were	be	VBD
37681	300	23	knots	knot	NNS
37681	300	24	,	,	,
37681	300	25	so	so	IN
37681	300	26	as	as	IN
37681	300	27	to	to	TO
37681	300	28	make	make	VB
37681	300	29	the	the	DT
37681	300	30	right	right	JJ
37681	300	31	triangle	triangle	NN
37681	300	32	3	3	CD
37681	300	33	,	,	,
37681	300	34	4	4	CD
37681	300	35	,	,	,
37681	300	36	5	5	CD
37681	300	37	,	,	,
37681	300	38	when	when	WRB
37681	300	39	they	-PRON-	PRP
37681	300	40	wished	wish	VBD
37681	300	41	to	to	TO
37681	300	42	erect	erect	VB
37681	300	43	a	a	DT
37681	300	44	perpendicular	perpendicular	NN
37681	300	45	.	.	.
37681	301	1	This	this	DT
37681	301	2	is	be	VBZ
37681	301	3	a	a	DT
37681	301	4	plan	plan	NN
37681	301	5	occasionally	occasionally	RB
37681	301	6	used	use	VBN
37681	301	7	by	by	IN
37681	301	8	surveyors	surveyor	NNS
37681	301	9	to	to	IN
37681	301	10	-	-	HYPH
37681	301	11	day	day	NN
37681	301	12	,	,	,
37681	301	13	and	and	CC
37681	301	14	it	-PRON-	PRP
37681	301	15	shows	show	VBZ
37681	301	16	that	that	IN
37681	301	17	the	the	DT
37681	301	18	practical	practical	JJ
37681	301	19	application	application	NN
37681	301	20	of	of	IN
37681	301	21	the	the	DT
37681	301	22	Pythagorean	Pythagorean	NNP
37681	301	23	Theorem	Theorem	NNP
37681	301	24	was	be	VBD
37681	301	25	known	know	VBN
37681	301	26	long	long	RB
37681	301	27	before	before	IN
37681	301	28	Pythagoras	Pythagoras	NNP
37681	301	29	gave	give	VBD
37681	301	30	what	what	WP
37681	301	31	seems	seem	VBZ
37681	301	32	to	to	TO
37681	301	33	have	have	VB
37681	301	34	been	be	VBN
37681	301	35	the	the	DT
37681	301	36	first	first	JJ
37681	301	37	general	general	JJ
37681	301	38	proof	proof	NN
37681	301	39	of	of	IN
37681	301	40	the	the	DT
37681	301	41	proposition	proposition	NN
37681	301	42	.	.	.
37681	302	1	From	from	IN
37681	302	2	Egypt	Egypt	NNP
37681	302	3	,	,	,
37681	302	4	and	and	CC
37681	302	5	possibly	possibly	RB
37681	302	6	from	from	IN
37681	302	7	Babylon	Babylon	NNP
37681	302	8	,	,	,
37681	302	9	geometry	geometry	NN
37681	302	10	passed	pass	VBD
37681	302	11	to	to	IN
37681	302	12	the	the	DT
37681	302	13	shores	shore	NNS
37681	302	14	of	of	IN
37681	302	15	Asia	Asia	NNP
37681	302	16	Minor	Minor	NNP
37681	302	17	and	and	CC
37681	302	18	Greece	Greece	NNP
37681	302	19	.	.	.
37681	303	1	The	the	DT
37681	303	2	scientific	scientific	JJ
37681	303	3	study	study	NN
37681	303	4	of	of	IN
37681	303	5	the	the	DT
37681	303	6	subject	subject	NN
37681	303	7	begins	begin	VBZ
37681	303	8	with	with	IN
37681	303	9	Thales	Thales	NNPS
37681	303	10	,	,	,
37681	303	11	one	one	CD
37681	303	12	of	of	IN
37681	303	13	the	the	DT
37681	303	14	Seven	Seven	NNP
37681	303	15	Wise	Wise	NNP
37681	303	16	Men	Men	NNPS
37681	303	17	of	of	IN
37681	303	18	the	the	DT
37681	303	19	Grecian	grecian	JJ
37681	303	20	civilization	civilization	NN
37681	303	21	.	.	.
37681	304	1	Born	bear	VBN
37681	304	2	at	at	IN
37681	304	3	Miletus	Miletus	NNP
37681	304	4	,	,	,
37681	304	5	not	not	RB
37681	304	6	far	far	RB
37681	304	7	from	from	IN
37681	304	8	Smyrna	Smyrna	NNP
37681	304	9	and	and	CC
37681	304	10	Ephesus	Ephesus	NNP
37681	304	11	,	,	,
37681	304	12	about	about	RB
37681	304	13	640	640	CD
37681	304	14	B.C.	B.C.	NNP
37681	304	15	,	,	,
37681	304	16	he	-PRON-	PRP
37681	304	17	died	die	VBD
37681	304	18	at	at	IN
37681	304	19	Athens	Athens	NNP
37681	304	20	in	in	IN
37681	304	21	548	548	CD
37681	304	22	B.C.	B.C.	NNP
37681	305	1	He	-PRON-	PRP
37681	305	2	spent	spend	VBD
37681	305	3	his	-PRON-	PRP$
37681	305	4	early	early	JJ
37681	305	5	manhood	manhood	NN
37681	305	6	as	as	IN
37681	305	7	a	a	DT
37681	305	8	merchant	merchant	NN
37681	305	9	,	,	,
37681	305	10	accumulating	accumulate	VBG
37681	305	11	the	the	DT
37681	305	12	wealth	wealth	NN
37681	305	13	that	that	WDT
37681	305	14	enabled	enable	VBD
37681	305	15	him	-PRON-	PRP
37681	305	16	to	to	TO
37681	305	17	spend	spend	VB
37681	305	18	his	-PRON-	PRP$
37681	305	19	later	later	JJ
37681	305	20	years	year	NNS
37681	305	21	in	in	IN
37681	305	22	study	study	NN
37681	305	23	.	.	.
37681	306	1	He	-PRON-	PRP
37681	306	2	visited	visit	VBD
37681	306	3	Egypt	Egypt	NNP
37681	306	4	,	,	,
37681	306	5	and	and	CC
37681	306	6	is	be	VBZ
37681	306	7	said	say	VBN
37681	306	8	to	to	TO
37681	306	9	have	have	VB
37681	306	10	learned	learn	VBN
37681	306	11	such	such	JJ
37681	306	12	elements	element	NNS
37681	306	13	of	of	IN
37681	306	14	geometry	geometry	NN
37681	306	15	as	as	IN
37681	306	16	were	be	VBD
37681	306	17	known	know	VBN
37681	306	18	there	there	RB
37681	306	19	.	.	.
37681	307	1	He	-PRON-	PRP
37681	307	2	founded	found	VBD
37681	307	3	a	a	DT
37681	307	4	school	school	NN
37681	307	5	of	of	IN
37681	307	6	mathematics	mathematic	NNS
37681	307	7	and	and	CC
37681	307	8	philosophy	philosophy	NN
37681	307	9	at	at	IN
37681	307	10	Miletus	Miletus	NNP
37681	307	11	,	,	,
37681	307	12	known	know	VBN
37681	307	13	from	from	IN
37681	307	14	the	the	DT
37681	307	15	country	country	NN
37681	307	16	as	as	IN
37681	307	17	the	the	DT
37681	307	18	Ionic	Ionic	NNP
37681	307	19	School	School	NNP
37681	307	20	.	.	.
37681	308	1	How	how	WRB
37681	308	2	elementary	elementary	JJ
37681	308	3	the	the	DT
37681	308	4	knowledge	knowledge	NN
37681	308	5	of	of	IN
37681	308	6	geometry	geometry	NN
37681	308	7	then	then	RB
37681	308	8	was	be	VBD
37681	308	9	may	may	MD
37681	308	10	be	be	VB
37681	308	11	understood	understand	VBN
37681	308	12	from	from	IN
37681	308	13	the	the	DT
37681	308	14	fact	fact	NN
37681	308	15	that	that	IN
37681	308	16	tradition	tradition	NN
37681	308	17	attributes	attribute	VBZ
37681	308	18	only	only	RB
37681	308	19	about	about	IN
37681	308	20	four	four	CD
37681	308	21	propositions	proposition	NNS
37681	308	22	to	to	IN
37681	308	23	Thales,--(1	thales,--(1	LS
37681	308	24	)	)	-RRB-
37681	308	25	that	that	IN
37681	308	26	vertical	vertical	JJ
37681	308	27	angles	angle	NNS
37681	308	28	are	be	VBP
37681	308	29	equal	equal	JJ
37681	308	30	,	,	,
37681	308	31	(	(	-LRB-
37681	308	32	2	2	LS
37681	308	33	)	)	-RRB-
37681	308	34	that	that	WDT
37681	308	35	equal	equal	JJ
37681	308	36	angles	angle	NNS
37681	308	37	lie	lie	VBP
37681	308	38	opposite	opposite	IN
37681	308	39	the	the	DT
37681	308	40	equal	equal	JJ
37681	308	41	sides	side	NNS
37681	308	42	of	of	IN
37681	308	43	an	an	DT
37681	308	44	isosceles	isoscele	NNS
37681	308	45	triangle	triangle	NN
37681	308	46	,	,	,
37681	308	47	(	(	-LRB-
37681	308	48	3	3	LS
37681	308	49	)	)	-RRB-
37681	308	50	that	that	IN
37681	308	51	a	a	DT
37681	308	52	triangle	triangle	NN
37681	308	53	is	be	VBZ
37681	308	54	determined	determine	VBN
37681	308	55	by	by	IN
37681	308	56	two	two	CD
37681	308	57	angles	angle	NNS
37681	308	58	and	and	CC
37681	308	59	the	the	DT
37681	308	60	included	include	VBN
37681	308	61	side	side	NN
37681	308	62	,	,	,
37681	308	63	(	(	-LRB-
37681	308	64	4	4	LS
37681	308	65	)	)	-RRB-
37681	308	66	that	that	IN
37681	308	67	a	a	DT
37681	308	68	diameter	diameter	NN
37681	308	69	bisects	bisect	VBZ
37681	308	70	the	the	DT
37681	308	71	circle	circle	NN
37681	308	72	,	,	,
37681	308	73	and	and	CC
37681	308	74	possibly	possibly	RB
37681	308	75	the	the	DT
37681	308	76	propositions	proposition	NNS
37681	308	77	about	about	IN
37681	308	78	the	the	DT
37681	308	79	angle	angle	NN
37681	308	80	-	-	HYPH
37681	308	81	sum	sum	NN
37681	308	82	of	of	IN
37681	308	83	a	a	DT
37681	308	84	triangle	triangle	NN
37681	308	85	for	for	IN
37681	308	86	special	special	JJ
37681	308	87	cases	case	NNS
37681	308	88	,	,	,
37681	308	89	and	and	CC
37681	308	90	the	the	DT
37681	308	91	angle	angle	NN
37681	308	92	inscribed	inscribe	VBN
37681	308	93	in	in	IN
37681	308	94	a	a	DT
37681	308	95	semicircle	semicircle	NN
37681	308	96	.	.	.
37681	309	1	[	[	-LRB-
37681	309	2	18	18	CD
37681	309	3	]	]	-RRB-
37681	309	4	The	the	DT
37681	309	5	greatest	great	JJS
37681	309	6	pupil	pupil	NN
37681	309	7	of	of	IN
37681	309	8	Thales	Thales	NNPS
37681	309	9	,	,	,
37681	309	10	and	and	CC
37681	309	11	one	one	CD
37681	309	12	of	of	IN
37681	309	13	the	the	DT
37681	309	14	most	most	RBS
37681	309	15	remarkable	remarkable	JJ
37681	309	16	men	man	NNS
37681	309	17	of	of	IN
37681	309	18	antiquity	antiquity	NN
37681	309	19	,	,	,
37681	309	20	was	be	VBD
37681	309	21	Pythagoras	Pythagoras	NNP
37681	309	22	.	.	.
37681	310	1	Born	bear	VBN
37681	310	2	probably	probably	RB
37681	310	3	on	on	IN
37681	310	4	the	the	DT
37681	310	5	island	island	NN
37681	310	6	of	of	IN
37681	310	7	Samos	Samos	NNP
37681	310	8	,	,	,
37681	310	9	just	just	RB
37681	310	10	off	off	IN
37681	310	11	the	the	DT
37681	310	12	coast	coast	NN
37681	310	13	of	of	IN
37681	310	14	Asia	Asia	NNP
37681	310	15	Minor	Minor	NNP
37681	310	16	,	,	,
37681	310	17	about	about	IN
37681	310	18	the	the	DT
37681	310	19	year	year	NN
37681	310	20	580	580	CD
37681	310	21	B.C.	B.C.	NNP
37681	310	22	,	,	,
37681	310	23	Pythagoras	Pythagoras	NNP
37681	310	24	set	set	VBD
37681	310	25	forth	forth	RP
37681	310	26	as	as	IN
37681	310	27	a	a	DT
37681	310	28	young	young	JJ
37681	310	29	man	man	NN
37681	310	30	to	to	TO
37681	310	31	travel	travel	VB
37681	310	32	.	.	.
37681	311	1	He	-PRON-	PRP
37681	311	2	went	go	VBD
37681	311	3	to	to	IN
37681	311	4	Miletus	Miletus	NNP
37681	311	5	and	and	CC
37681	311	6	studied	study	VBD
37681	311	7	under	under	IN
37681	311	8	Thales	Thales	NNPS
37681	311	9	,	,	,
37681	311	10	probably	probably	RB
37681	311	11	spent	spend	VBD
37681	311	12	several	several	JJ
37681	311	13	years	year	NNS
37681	311	14	in	in	IN
37681	311	15	Egypt	Egypt	NNP
37681	311	16	,	,	,
37681	311	17	very	very	RB
37681	311	18	likely	likely	RB
37681	311	19	went	go	VBD
37681	311	20	to	to	IN
37681	311	21	Babylon	Babylon	NNP
37681	311	22	,	,	,
37681	311	23	and	and	CC
37681	311	24	possibly	possibly	RB
37681	311	25	went	go	VBD
37681	311	26	even	even	RB
37681	311	27	to	to	IN
37681	311	28	India	India	NNP
37681	311	29	,	,	,
37681	311	30	since	since	IN
37681	311	31	tradition	tradition	NN
37681	311	32	asserts	assert	VBZ
37681	311	33	this	this	DT
37681	311	34	and	and	CC
37681	311	35	the	the	DT
37681	311	36	nature	nature	NN
37681	311	37	of	of	IN
37681	311	38	his	-PRON-	PRP$
37681	311	39	work	work	NN
37681	311	40	in	in	IN
37681	311	41	mathematics	mathematic	NNS
37681	311	42	suggests	suggest	VBZ
37681	311	43	it	-PRON-	PRP
37681	311	44	.	.	.
37681	312	1	In	in	IN
37681	312	2	later	later	JJ
37681	312	3	life	life	NN
37681	312	4	he	-PRON-	PRP
37681	312	5	went	go	VBD
37681	312	6	to	to	IN
37681	312	7	a	a	DT
37681	312	8	Greek	greek	JJ
37681	312	9	colony	colony	NN
37681	312	10	in	in	IN
37681	312	11	southern	southern	JJ
37681	312	12	Italy	Italy	NNP
37681	312	13	,	,	,
37681	312	14	and	and	CC
37681	312	15	at	at	IN
37681	312	16	Crotona	Crotona	NNP
37681	312	17	,	,	,
37681	312	18	in	in	IN
37681	312	19	the	the	DT
37681	312	20	southeastern	southeastern	JJ
37681	312	21	part	part	NN
37681	312	22	of	of	IN
37681	312	23	the	the	DT
37681	312	24	peninsula	peninsula	NN
37681	312	25	,	,	,
37681	312	26	he	-PRON-	PRP
37681	312	27	founded	found	VBD
37681	312	28	a	a	DT
37681	312	29	school	school	NN
37681	312	30	and	and	CC
37681	312	31	established	establish	VBD
37681	312	32	a	a	DT
37681	312	33	secret	secret	JJ
37681	312	34	society	society	NN
37681	312	35	to	to	TO
37681	312	36	propagate	propagate	VB
37681	312	37	his	-PRON-	PRP$
37681	312	38	doctrines	doctrine	NNS
37681	312	39	.	.	.
37681	313	1	In	in	IN
37681	313	2	geometry	geometry	NN
37681	313	3	he	-PRON-	PRP
37681	313	4	is	be	VBZ
37681	313	5	said	say	VBN
37681	313	6	to	to	TO
37681	313	7	have	have	VB
37681	313	8	been	be	VBN
37681	313	9	the	the	DT
37681	313	10	first	first	JJ
37681	313	11	to	to	TO
37681	313	12	demonstrate	demonstrate	VB
37681	313	13	the	the	DT
37681	313	14	proposition	proposition	NN
37681	313	15	that	that	IN
37681	313	16	the	the	DT
37681	313	17	square	square	NN
37681	313	18	on	on	IN
37681	313	19	the	the	DT
37681	313	20	hypotenuse	hypotenuse	NN
37681	313	21	is	be	VBZ
37681	313	22	equal	equal	JJ
37681	313	23	to	to	IN
37681	313	24	the	the	DT
37681	313	25	sum	sum	NN
37681	313	26	of	of	IN
37681	313	27	the	the	DT
37681	313	28	squares	square	NNS
37681	313	29	upon	upon	IN
37681	313	30	the	the	DT
37681	313	31	other	other	JJ
37681	313	32	two	two	CD
37681	313	33	sides	side	NNS
37681	313	34	of	of	IN
37681	313	35	a	a	DT
37681	313	36	right	right	JJ
37681	313	37	triangle	triangle	NN
37681	313	38	.	.	.
37681	314	1	The	the	DT
37681	314	2	proposition	proposition	NN
37681	314	3	was	be	VBD
37681	314	4	known	know	VBN
37681	314	5	in	in	IN
37681	314	6	India	India	NNP
37681	314	7	and	and	CC
37681	314	8	Egypt	Egypt	NNP
37681	314	9	before	before	IN
37681	314	10	his	-PRON-	PRP$
37681	314	11	time	time	NN
37681	314	12	,	,	,
37681	314	13	at	at	IN
37681	314	14	any	any	DT
37681	314	15	rate	rate	NN
37681	314	16	for	for	IN
37681	314	17	special	special	JJ
37681	314	18	cases	case	NNS
37681	314	19	,	,	,
37681	314	20	but	but	CC
37681	314	21	he	-PRON-	PRP
37681	314	22	seems	seem	VBZ
37681	314	23	to	to	TO
37681	314	24	have	have	VB
37681	314	25	been	be	VBN
37681	314	26	the	the	DT
37681	314	27	first	first	JJ
37681	314	28	to	to	TO
37681	314	29	prove	prove	VB
37681	314	30	it	-PRON-	PRP
37681	314	31	.	.	.
37681	315	1	To	to	IN
37681	315	2	him	-PRON-	PRP
37681	315	3	or	or	CC
37681	315	4	to	to	IN
37681	315	5	his	-PRON-	PRP$
37681	315	6	school	school	NN
37681	315	7	seems	seem	VBZ
37681	315	8	also	also	RB
37681	315	9	to	to	TO
37681	315	10	have	have	VB
37681	315	11	been	be	VBN
37681	315	12	due	due	JJ
37681	315	13	the	the	DT
37681	315	14	construction	construction	NN
37681	315	15	of	of	IN
37681	315	16	the	the	DT
37681	315	17	regular	regular	JJ
37681	315	18	pentagon	pentagon	NNP
37681	315	19	and	and	CC
37681	315	20	of	of	IN
37681	315	21	the	the	DT
37681	315	22	five	five	CD
37681	315	23	regular	regular	JJ
37681	315	24	polyhedrons	polyhedron	NNS
37681	315	25	.	.	.
37681	316	1	The	the	DT
37681	316	2	construction	construction	NN
37681	316	3	of	of	IN
37681	316	4	the	the	DT
37681	316	5	regular	regular	JJ
37681	316	6	pentagon	pentagon	NNP
37681	316	7	requires	require	VBZ
37681	316	8	the	the	DT
37681	316	9	dividing	dividing	NN
37681	316	10	of	of	IN
37681	316	11	a	a	DT
37681	316	12	line	line	NN
37681	316	13	into	into	IN
37681	316	14	extreme	extreme	JJ
37681	316	15	and	and	CC
37681	316	16	mean	mean	JJ
37681	316	17	ratio	ratio	NN
37681	316	18	,	,	,
37681	316	19	and	and	CC
37681	316	20	this	this	DT
37681	316	21	problem	problem	NN
37681	316	22	is	be	VBZ
37681	316	23	commonly	commonly	RB
37681	316	24	assigned	assign	VBN
37681	316	25	to	to	IN
37681	316	26	the	the	DT
37681	316	27	Pythagoreans	Pythagoreans	NNPS
37681	316	28	,	,	,
37681	316	29	although	although	IN
37681	316	30	it	-PRON-	PRP
37681	316	31	played	play	VBD
37681	316	32	an	an	DT
37681	316	33	important	important	JJ
37681	316	34	part	part	NN
37681	316	35	in	in	IN
37681	316	36	Plato	Plato	NNP
37681	316	37	's	's	POS
37681	316	38	school	school	NN
37681	316	39	.	.	.
37681	317	1	Pythagoras	Pythagoras	NNP
37681	317	2	is	be	VBZ
37681	317	3	also	also	RB
37681	317	4	said	say	VBN
37681	317	5	to	to	TO
37681	317	6	have	have	VB
37681	317	7	known	know	VBN
37681	317	8	that	that	IN
37681	317	9	six	six	CD
37681	317	10	equilateral	equilateral	JJ
37681	317	11	triangles	triangle	NNS
37681	317	12	,	,	,
37681	317	13	three	three	CD
37681	317	14	regular	regular	JJ
37681	317	15	hexagons	hexagon	NNS
37681	317	16	,	,	,
37681	317	17	or	or	CC
37681	317	18	four	four	CD
37681	317	19	squares	square	NNS
37681	317	20	,	,	,
37681	317	21	can	can	MD
37681	317	22	be	be	VB
37681	317	23	placed	place	VBN
37681	317	24	about	about	IN
37681	317	25	a	a	DT
37681	317	26	point	point	NN
37681	317	27	so	so	IN
37681	317	28	as	as	IN
37681	317	29	just	just	RB
37681	317	30	to	to	TO
37681	317	31	fill	fill	VB
37681	317	32	the	the	DT
37681	317	33	360	360	CD
37681	317	34	°	°	NNS
37681	317	35	,	,	,
37681	317	36	but	but	CC
37681	317	37	that	that	IN
37681	317	38	no	no	DT
37681	317	39	other	other	JJ
37681	317	40	regular	regular	JJ
37681	317	41	polygons	polygon	NNS
37681	317	42	can	can	MD
37681	317	43	be	be	VB
37681	317	44	so	so	RB
37681	317	45	placed	place	VBN
37681	317	46	.	.	.
37681	318	1	To	to	IN
37681	318	2	his	-PRON-	PRP$
37681	318	3	school	school	NN
37681	318	4	is	be	VBZ
37681	318	5	also	also	RB
37681	318	6	due	due	JJ
37681	318	7	the	the	DT
37681	318	8	proof	proof	NN
37681	318	9	for	for	IN
37681	318	10	the	the	DT
37681	318	11	general	general	JJ
37681	318	12	case	case	NN
37681	318	13	that	that	IN
37681	318	14	the	the	DT
37681	318	15	sum	sum	NN
37681	318	16	of	of	IN
37681	318	17	the	the	DT
37681	318	18	angles	angle	NNS
37681	318	19	of	of	IN
37681	318	20	a	a	DT
37681	318	21	triangle	triangle	NN
37681	318	22	equals	equal	VBZ
37681	318	23	two	two	CD
37681	318	24	right	right	JJ
37681	318	25	angles	angle	NNS
37681	318	26	,	,	,
37681	318	27	the	the	DT
37681	318	28	first	first	JJ
37681	318	29	knowledge	knowledge	NN
37681	318	30	of	of	IN
37681	318	31	the	the	DT
37681	318	32	size	size	NN
37681	318	33	of	of	IN
37681	318	34	each	each	DT
37681	318	35	angle	angle	NN
37681	318	36	of	of	IN
37681	318	37	a	a	DT
37681	318	38	regular	regular	JJ
37681	318	39	polygon	polygon	NN
37681	318	40	,	,	,
37681	318	41	and	and	CC
37681	318	42	the	the	DT
37681	318	43	construction	construction	NN
37681	318	44	of	of	IN
37681	318	45	at	at	RB
37681	318	46	least	least	RBS
37681	318	47	one	one	CD
37681	318	48	star	star	NN
37681	318	49	-	-	HYPH
37681	318	50	polygon	polygon	NN
37681	318	51	,	,	,
37681	318	52	the	the	DT
37681	318	53	star	star	NNP
37681	318	54	-	-	HYPH
37681	318	55	pentagon	pentagon	NNP
37681	318	56	,	,	,
37681	318	57	which	which	WDT
37681	318	58	became	become	VBD
37681	318	59	the	the	DT
37681	318	60	badge	badge	NN
37681	318	61	of	of	IN
37681	318	62	his	-PRON-	PRP$
37681	318	63	fraternity	fraternity	NN
37681	318	64	.	.	.
37681	319	1	The	the	DT
37681	319	2	brotherhood	brotherhood	NN
37681	319	3	founded	found	VBN
37681	319	4	by	by	IN
37681	319	5	Pythagoras	Pythagoras	NNP
37681	319	6	proved	prove	VBD
37681	319	7	so	so	RB
37681	319	8	offensive	offensive	JJ
37681	319	9	to	to	IN
37681	319	10	the	the	DT
37681	319	11	government	government	NN
37681	319	12	that	that	IN
37681	319	13	it	-PRON-	PRP
37681	319	14	was	be	VBD
37681	319	15	dispersed	disperse	VBN
37681	319	16	before	before	IN
37681	319	17	the	the	DT
37681	319	18	death	death	NN
37681	319	19	of	of	IN
37681	319	20	the	the	DT
37681	319	21	master	master	NN
37681	319	22	.	.	.
37681	320	1	Pythagoras	Pythagoras	NNP
37681	320	2	fled	flee	VBD
37681	320	3	to	to	IN
37681	320	4	Megapontum	Megapontum	NNP
37681	320	5	,	,	,
37681	320	6	a	a	DT
37681	320	7	seaport	seaport	NN
37681	320	8	lying	lie	VBG
37681	320	9	to	to	IN
37681	320	10	the	the	DT
37681	320	11	north	north	NN
37681	320	12	of	of	IN
37681	320	13	Crotona	Crotona	NNP
37681	320	14	,	,	,
37681	320	15	and	and	CC
37681	320	16	there	there	RB
37681	320	17	he	-PRON-	PRP
37681	320	18	died	die	VBD
37681	320	19	about	about	RB
37681	320	20	501	501	CD
37681	320	21	B.C.	B.C.	NNS
37681	321	1	[	[	-LRB-
37681	321	2	19	19	CD
37681	321	3	]	]	-RRB-
37681	321	4	[	[	-LRB-
37681	321	5	Illustration	illustration	NN
37681	321	6	:	:	:
37681	321	7	FANCIFUL	fanciful	VB
37681	321	8	PORTRAIT	PORTRAIT	NNS
37681	321	9	OF	of	IN
37681	321	10	PYTHAGORAS	PYTHAGORAS	NNP
37681	321	11	Calandri	Calandri	NNP
37681	321	12	's	's	POS
37681	321	13	Arithmetic	Arithmetic	NNP
37681	321	14	,	,	,
37681	321	15	1491	1491	CD
37681	321	16	]	]	-RRB-
37681	321	17	For	for	IN
37681	321	18	two	two	CD
37681	321	19	centuries	century	NNS
37681	321	20	after	after	IN
37681	321	21	Pythagoras	Pythagoras	NNPS
37681	321	22	geometry	geometry	NN
37681	321	23	passed	pass	VBD
37681	321	24	through	through	IN
37681	321	25	a	a	DT
37681	321	26	period	period	NN
37681	321	27	of	of	IN
37681	321	28	discovery	discovery	NN
37681	321	29	of	of	IN
37681	321	30	propositions	proposition	NNS
37681	321	31	.	.	.
37681	322	1	The	the	DT
37681	322	2	state	state	NN
37681	322	3	of	of	IN
37681	322	4	the	the	DT
37681	322	5	science	science	NN
37681	322	6	may	may	MD
37681	322	7	be	be	VB
37681	322	8	seen	see	VBN
37681	322	9	from	from	IN
37681	322	10	the	the	DT
37681	322	11	fact	fact	NN
37681	322	12	that	that	IN
37681	322	13	Oenopides	Oenopides	NNP
37681	322	14	of	of	IN
37681	322	15	Chios	Chios	NNPS
37681	322	16	,	,	,
37681	322	17	who	who	WP
37681	322	18	flourished	flourish	VBD
37681	322	19	about	about	RB
37681	322	20	465	465	CD
37681	322	21	B.C.	B.C.	NNS
37681	322	22	,	,	,
37681	322	23	and	and	CC
37681	322	24	who	who	WP
37681	322	25	had	have	VBD
37681	322	26	studied	study	VBN
37681	322	27	in	in	IN
37681	322	28	Egypt	Egypt	NNP
37681	322	29	,	,	,
37681	322	30	was	be	VBD
37681	322	31	celebrated	celebrate	VBN
37681	322	32	because	because	IN
37681	322	33	he	-PRON-	PRP
37681	322	34	showed	show	VBD
37681	322	35	how	how	WRB
37681	322	36	to	to	TO
37681	322	37	let	let	VB
37681	322	38	fall	fall	VB
37681	322	39	a	a	DT
37681	322	40	perpendicular	perpendicular	NN
37681	322	41	to	to	IN
37681	322	42	a	a	DT
37681	322	43	line	line	NN
37681	322	44	,	,	,
37681	322	45	and	and	CC
37681	322	46	how	how	WRB
37681	322	47	to	to	TO
37681	322	48	make	make	VB
37681	322	49	an	an	DT
37681	322	50	angle	angle	NN
37681	322	51	equal	equal	JJ
37681	322	52	to	to	IN
37681	322	53	a	a	DT
37681	322	54	given	give	VBN
37681	322	55	angle	angle	NN
37681	322	56	.	.	.
37681	323	1	A	a	DT
37681	323	2	few	few	JJ
37681	323	3	years	year	NNS
37681	323	4	later	later	RB
37681	323	5	,	,	,
37681	323	6	about	about	RB
37681	323	7	440	440	CD
37681	323	8	B.C.	B.C.	NNS
37681	323	9	,	,	,
37681	323	10	Hippocrates	Hippocrates	NNPS
37681	323	11	of	of	IN
37681	323	12	Chios	Chios	NNPS
37681	323	13	wrote	write	VBD
37681	323	14	the	the	DT
37681	323	15	first	first	JJ
37681	323	16	Greek	greek	JJ
37681	323	17	textbook	textbook	NN
37681	323	18	on	on	IN
37681	323	19	mathematics	mathematic	NNS
37681	323	20	.	.	.
37681	324	1	He	-PRON-	PRP
37681	324	2	knew	know	VBD
37681	324	3	that	that	IN
37681	324	4	the	the	DT
37681	324	5	areas	area	NNS
37681	324	6	of	of	IN
37681	324	7	circles	circle	NNS
37681	324	8	are	be	VBP
37681	324	9	proportional	proportional	JJ
37681	324	10	to	to	IN
37681	324	11	the	the	DT
37681	324	12	squares	square	NNS
37681	324	13	on	on	IN
37681	324	14	their	-PRON-	PRP$
37681	324	15	radii	radii	NN
37681	324	16	,	,	,
37681	324	17	but	but	CC
37681	324	18	was	be	VBD
37681	324	19	ignorant	ignorant	JJ
37681	324	20	of	of	IN
37681	324	21	the	the	DT
37681	324	22	fact	fact	NN
37681	324	23	that	that	IN
37681	324	24	equal	equal	JJ
37681	324	25	central	central	JJ
37681	324	26	angles	angle	NNS
37681	324	27	or	or	CC
37681	324	28	equal	equal	JJ
37681	324	29	inscribed	inscribe	VBN
37681	324	30	angles	angle	NNS
37681	324	31	intercept	intercept	VB
37681	324	32	equal	equal	JJ
37681	324	33	arcs	arc	NNS
37681	324	34	.	.	.
37681	325	1	Antiphon	Antiphon	NNP
37681	325	2	and	and	CC
37681	325	3	Bryson	Bryson	NNP
37681	325	4	,	,	,
37681	325	5	two	two	CD
37681	325	6	Greek	greek	JJ
37681	325	7	scholars	scholar	NNS
37681	325	8	,	,	,
37681	325	9	flourished	flourish	VBD
37681	325	10	about	about	RB
37681	325	11	430	430	CD
37681	325	12	B.C.	B.C.	NNS
37681	326	1	The	the	DT
37681	326	2	former	former	JJ
37681	326	3	attempted	attempt	VBD
37681	326	4	to	to	TO
37681	326	5	find	find	VB
37681	326	6	the	the	DT
37681	326	7	area	area	NN
37681	326	8	of	of	IN
37681	326	9	a	a	DT
37681	326	10	circle	circle	NN
37681	326	11	by	by	IN
37681	326	12	doubling	double	VBG
37681	326	13	the	the	DT
37681	326	14	number	number	NN
37681	326	15	of	of	IN
37681	326	16	sides	side	NNS
37681	326	17	of	of	IN
37681	326	18	a	a	DT
37681	326	19	regular	regular	JJ
37681	326	20	inscribed	inscribe	VBN
37681	326	21	polygon	polygon	NN
37681	326	22	,	,	,
37681	326	23	and	and	CC
37681	326	24	the	the	DT
37681	326	25	latter	latter	JJ
37681	326	26	by	by	IN
37681	326	27	doing	do	VBG
37681	326	28	the	the	DT
37681	326	29	same	same	JJ
37681	326	30	for	for	IN
37681	326	31	both	both	CC
37681	326	32	inscribed	inscribe	VBN
37681	326	33	and	and	CC
37681	326	34	circumscribed	circumscribed	JJ
37681	326	35	polygons	polygon	NNS
37681	326	36	.	.	.
37681	327	1	They	-PRON-	PRP
37681	327	2	thus	thus	RB
37681	327	3	approximately	approximately	RB
37681	327	4	exhausted	exhaust	VBD
37681	327	5	the	the	DT
37681	327	6	area	area	NN
37681	327	7	between	between	IN
37681	327	8	the	the	DT
37681	327	9	polygon	polygon	NN
37681	327	10	and	and	CC
37681	327	11	the	the	DT
37681	327	12	circle	circle	NN
37681	327	13	,	,	,
37681	327	14	and	and	CC
37681	327	15	hence	hence	RB
37681	327	16	this	this	DT
37681	327	17	method	method	NN
37681	327	18	is	be	VBZ
37681	327	19	known	know	VBN
37681	327	20	as	as	IN
37681	327	21	the	the	DT
37681	327	22	method	method	NN
37681	327	23	of	of	IN
37681	327	24	exhaustions	exhaustion	NNS
37681	327	25	.	.	.
37681	328	1	About	about	RB
37681	328	2	420	420	CD
37681	328	3	B.C.	B.C.	NNS
37681	329	1	Hippias	Hippias	NNP
37681	329	2	of	of	IN
37681	329	3	Elis	Elis	NNP
37681	329	4	invented	invent	VBD
37681	329	5	a	a	DT
37681	329	6	certain	certain	JJ
37681	329	7	curve	curve	NN
37681	329	8	called	call	VBN
37681	329	9	the	the	DT
37681	329	10	quadratrix	quadratrix	NN
37681	329	11	,	,	,
37681	329	12	by	by	IN
37681	329	13	means	mean	NNS
37681	329	14	of	of	IN
37681	329	15	which	which	WDT
37681	329	16	he	-PRON-	PRP
37681	329	17	could	could	MD
37681	329	18	square	square	VB
37681	329	19	the	the	DT
37681	329	20	circle	circle	NN
37681	329	21	and	and	CC
37681	329	22	trisect	trisect	VB
37681	329	23	any	any	DT
37681	329	24	angle	angle	NN
37681	329	25	.	.	.
37681	330	1	This	this	DT
37681	330	2	curve	curve	NN
37681	330	3	can	can	MD
37681	330	4	not	not	RB
37681	330	5	be	be	VB
37681	330	6	constructed	construct	VBN
37681	330	7	by	by	IN
37681	330	8	the	the	DT
37681	330	9	unmarked	unmarked	JJ
37681	330	10	straightedge	straightedge	NN
37681	330	11	and	and	CC
37681	330	12	the	the	DT
37681	330	13	compasses	compass	NNS
37681	330	14	,	,	,
37681	330	15	and	and	CC
37681	330	16	when	when	WRB
37681	330	17	we	-PRON-	PRP
37681	330	18	say	say	VBP
37681	330	19	that	that	IN
37681	330	20	it	-PRON-	PRP
37681	330	21	is	be	VBZ
37681	330	22	impossible	impossible	JJ
37681	330	23	to	to	TO
37681	330	24	square	square	VB
37681	330	25	the	the	DT
37681	330	26	circle	circle	NN
37681	330	27	or	or	CC
37681	330	28	to	to	TO
37681	330	29	trisect	trisect	VB
37681	330	30	any	any	DT
37681	330	31	angle	angle	NN
37681	330	32	,	,	,
37681	330	33	we	-PRON-	PRP
37681	330	34	mean	mean	VBP
37681	330	35	that	that	IN
37681	330	36	it	-PRON-	PRP
37681	330	37	is	be	VBZ
37681	330	38	impossible	impossible	JJ
37681	330	39	by	by	IN
37681	330	40	the	the	DT
37681	330	41	help	help	NN
37681	330	42	of	of	IN
37681	330	43	these	these	DT
37681	330	44	two	two	CD
37681	330	45	instruments	instrument	NNS
37681	330	46	alone	alone	JJ
37681	330	47	.	.	.
37681	331	1	During	during	IN
37681	331	2	this	this	DT
37681	331	3	period	period	NN
37681	331	4	the	the	DT
37681	331	5	great	great	JJ
37681	331	6	philosophic	philosophic	JJ
37681	331	7	school	school	NN
37681	331	8	of	of	IN
37681	331	9	Plato	Plato	NNP
37681	331	10	(	(	-LRB-
37681	331	11	429	429	CD
37681	331	12	-	-	SYM
37681	331	13	348	348	CD
37681	331	14	B.C.	B.C.	NNP
37681	331	15	)	)	-RRB-
37681	332	1	flourished	flourish	VBD
37681	332	2	at	at	IN
37681	332	3	Athens	Athens	NNP
37681	332	4	,	,	,
37681	332	5	and	and	CC
37681	332	6	to	to	IN
37681	332	7	this	this	DT
37681	332	8	school	school	NN
37681	332	9	is	be	VBZ
37681	332	10	due	due	JJ
37681	332	11	the	the	DT
37681	332	12	first	first	JJ
37681	332	13	systematic	systematic	JJ
37681	332	14	attempt	attempt	NN
37681	332	15	to	to	TO
37681	332	16	create	create	VB
37681	332	17	exact	exact	JJ
37681	332	18	definitions	definition	NNS
37681	332	19	,	,	,
37681	332	20	axioms	axiom	NNS
37681	332	21	,	,	,
37681	332	22	and	and	CC
37681	332	23	postulates	postulate	NNS
37681	332	24	,	,	,
37681	332	25	and	and	CC
37681	332	26	to	to	TO
37681	332	27	distinguish	distinguish	VB
37681	332	28	between	between	IN
37681	332	29	elementary	elementary	JJ
37681	332	30	and	and	CC
37681	332	31	higher	high	JJR
37681	332	32	geometry	geometry	NN
37681	332	33	.	.	.
37681	333	1	It	-PRON-	PRP
37681	333	2	was	be	VBD
37681	333	3	at	at	IN
37681	333	4	this	this	DT
37681	333	5	time	time	NN
37681	333	6	that	that	WDT
37681	333	7	elementary	elementary	JJ
37681	333	8	geometry	geometry	NN
37681	333	9	became	become	VBD
37681	333	10	limited	limited	JJ
37681	333	11	to	to	IN
37681	333	12	the	the	DT
37681	333	13	use	use	NN
37681	333	14	of	of	IN
37681	333	15	the	the	DT
37681	333	16	compasses	compass	NNS
37681	333	17	and	and	CC
37681	333	18	the	the	DT
37681	333	19	unmarked	unmarked	JJ
37681	333	20	straightedge	straightedge	NN
37681	333	21	,	,	,
37681	333	22	which	which	WDT
37681	333	23	took	take	VBD
37681	333	24	from	from	IN
37681	333	25	this	this	DT
37681	333	26	domain	domain	NN
37681	333	27	the	the	DT
37681	333	28	possibility	possibility	NN
37681	333	29	of	of	IN
37681	333	30	constructing	construct	VBG
37681	333	31	a	a	DT
37681	333	32	square	square	JJ
37681	333	33	equivalent	equivalent	NN
37681	333	34	to	to	IN
37681	333	35	a	a	DT
37681	333	36	given	give	VBN
37681	333	37	circle	circle	NN
37681	333	38	(	(	-LRB-
37681	333	39	"	"	``
37681	333	40	squaring	square	VBG
37681	333	41	the	the	DT
37681	333	42	circle	circle	NN
37681	333	43	"	"	''
37681	333	44	)	)	-RRB-
37681	333	45	,	,	,
37681	333	46	of	of	IN
37681	333	47	trisecting	trisect	VBG
37681	333	48	any	any	DT
37681	333	49	given	give	VBN
37681	333	50	angle	angle	NN
37681	333	51	,	,	,
37681	333	52	and	and	CC
37681	333	53	of	of	IN
37681	333	54	constructing	construct	VBG
37681	333	55	a	a	DT
37681	333	56	cube	cube	NN
37681	333	57	that	that	WDT
37681	333	58	should	should	MD
37681	333	59	have	have	VB
37681	333	60	twice	twice	PDT
37681	333	61	the	the	DT
37681	333	62	volume	volume	NN
37681	333	63	of	of	IN
37681	333	64	a	a	DT
37681	333	65	given	give	VBN
37681	333	66	cube	cube	NN
37681	333	67	(	(	-LRB-
37681	333	68	"	"	``
37681	333	69	duplicating	duplicate	VBG
37681	333	70	the	the	DT
37681	333	71	cube	cube	NN
37681	333	72	"	"	''
37681	333	73	)	)	-RRB-
37681	333	74	,	,	,
37681	333	75	these	these	DT
37681	333	76	being	be	VBG
37681	333	77	the	the	DT
37681	333	78	three	three	CD
37681	333	79	famous	famous	JJ
37681	333	80	problems	problem	NNS
37681	333	81	of	of	IN
37681	333	82	antiquity	antiquity	NN
37681	333	83	.	.	.
37681	334	1	Plato	Plato	NNP
37681	334	2	and	and	CC
37681	334	3	his	-PRON-	PRP$
37681	334	4	school	school	NN
37681	334	5	interested	interest	VBD
37681	334	6	themselves	-PRON-	PRP
37681	334	7	with	with	IN
37681	334	8	the	the	DT
37681	334	9	so	so	RB
37681	334	10	-	-	HYPH
37681	334	11	called	call	VBN
37681	334	12	Pythagorean	pythagorean	JJ
37681	334	13	numbers	number	NNS
37681	334	14	,	,	,
37681	334	15	that	that	RB
37681	334	16	is	is	RB
37681	334	17	,	,	,
37681	334	18	with	with	IN
37681	334	19	numbers	number	NNS
37681	334	20	that	that	WDT
37681	334	21	would	would	MD
37681	334	22	represent	represent	VB
37681	334	23	the	the	DT
37681	334	24	three	three	CD
37681	334	25	sides	side	NNS
37681	334	26	of	of	IN
37681	334	27	a	a	DT
37681	334	28	right	right	JJ
37681	334	29	triangle	triangle	NN
37681	334	30	and	and	CC
37681	334	31	hence	hence	RB
37681	334	32	fulfill	fulfill	VB
37681	334	33	the	the	DT
37681	334	34	condition	condition	NN
37681	334	35	that	that	IN
37681	334	36	_	_	NNP
37681	334	37	a_^2	a_^2	NNP
37681	334	38	+	+	SYM
37681	334	39	_	_	NNP
37681	334	40	b_^2	b_^2	NNP
37681	334	41	=	=	SYM
37681	334	42	_	_	NNP
37681	334	43	c_^2	c_^2	NNP
37681	334	44	.	.	.
37681	335	1	Pythagoras	Pythagoras	NNP
37681	335	2	had	have	VBD
37681	335	3	already	already	RB
37681	335	4	given	give	VBN
37681	335	5	a	a	DT
37681	335	6	rule	rule	NN
37681	335	7	that	that	WDT
37681	335	8	would	would	MD
37681	335	9	be	be	VB
37681	335	10	expressed	express	VBN
37681	335	11	in	in	IN
37681	335	12	modern	modern	JJ
37681	335	13	form	form	NN
37681	335	14	,	,	,
37681	335	15	as	as	IN
37681	335	16	1/4(_m_^2	1/4(_m_^2	CD
37681	335	17	+	+	SYM
37681	335	18	1)^2	1)^2	NNP
37681	335	19	=	=	SYM
37681	335	20	_	_	NNP
37681	335	21	m_^2	m_^2	NNP
37681	335	22	+	+	SYM
37681	335	23	1/4(_m_^2	1/4(_m_^2	NNP
37681	335	24	-	-	HYPH
37681	335	25	1)^2	1)^2	NN
37681	335	26	.	.	.
37681	336	1	The	the	DT
37681	336	2	school	school	NN
37681	336	3	of	of	IN
37681	336	4	Plato	Plato	NNP
37681	336	5	found	find	VBD
37681	336	6	that	that	IN
37681	336	7	[	[	-LRB-
37681	336	8	(	(	-LRB-
37681	336	9	1/2_m_)^2	1/2_m_)^2	CD
37681	336	10	+	+	SYM
37681	336	11	1]^2	1]^2	CD
37681	336	12	=	=	SYM
37681	336	13	_	_	NNP
37681	336	14	m_^2	m_^2	NNP
37681	336	15	+	+	NFP
37681	336	16	[	[	-LRB-
37681	336	17	(	(	-LRB-
37681	336	18	1/2_m_)^2	1/2_m_)^2	CD
37681	336	19	-	-	SYM
37681	336	20	1]^2	1]^2	CD
37681	336	21	.	.	.
37681	337	1	By	by	IN
37681	337	2	giving	give	VBG
37681	337	3	various	various	JJ
37681	337	4	values	value	NNS
37681	337	5	to	to	IN
37681	337	6	_	_	NNP
37681	337	7	m	m	NNP
37681	337	8	_	_	NNP
37681	337	9	,	,	,
37681	337	10	different	different	JJ
37681	337	11	Pythagorean	pythagorean	JJ
37681	337	12	numbers	number	NNS
37681	337	13	may	may	MD
37681	337	14	be	be	VB
37681	337	15	found	find	VBN
37681	337	16	.	.	.
37681	338	1	Plato	Plato	NNP
37681	338	2	's	's	POS
37681	338	3	nephew	nephew	NN
37681	338	4	,	,	,
37681	338	5	Speusippus	Speusippus	NNP
37681	338	6	(	(	-LRB-
37681	338	7	about	about	RB
37681	338	8	350	350	CD
37681	338	9	B.C.	B.C.	NNS
37681	339	1	)	)	-RRB-
37681	339	2	,	,	,
37681	339	3	wrote	write	VBD
37681	339	4	upon	upon	IN
37681	339	5	this	this	DT
37681	339	6	subject	subject	NN
37681	339	7	.	.	.
37681	340	1	Such	such	JJ
37681	340	2	numbers	number	NNS
37681	340	3	were	be	VBD
37681	340	4	known	know	VBN
37681	340	5	,	,	,
37681	340	6	however	however	RB
37681	340	7	,	,	,
37681	340	8	both	both	DT
37681	340	9	in	in	IN
37681	340	10	India	India	NNP
37681	340	11	and	and	CC
37681	340	12	in	in	IN
37681	340	13	Egypt	Egypt	NNP
37681	340	14	,	,	,
37681	340	15	long	long	RB
37681	340	16	before	before	IN
37681	340	17	this	this	DT
37681	340	18	time	time	NN
37681	340	19	.	.	.
37681	341	1	One	one	CD
37681	341	2	of	of	IN
37681	341	3	Plato	Plato	NNP
37681	341	4	's	's	POS
37681	341	5	pupils	pupil	NNS
37681	341	6	was	be	VBD
37681	341	7	Philippus	Philippus	NNP
37681	341	8	of	of	IN
37681	341	9	Mende	Mende	NNP
37681	341	10	,	,	,
37681	341	11	in	in	IN
37681	341	12	Egypt	Egypt	NNP
37681	341	13	,	,	,
37681	341	14	who	who	WP
37681	341	15	flourished	flourish	VBD
37681	341	16	about	about	RB
37681	341	17	380	380	CD
37681	341	18	B.C.	B.C.	NNS
37681	342	1	It	-PRON-	PRP
37681	342	2	is	be	VBZ
37681	342	3	said	say	VBN
37681	342	4	that	that	IN
37681	342	5	he	-PRON-	PRP
37681	342	6	discovered	discover	VBD
37681	342	7	the	the	DT
37681	342	8	proposition	proposition	NN
37681	342	9	relating	relate	VBG
37681	342	10	to	to	IN
37681	342	11	the	the	DT
37681	342	12	exterior	exterior	JJ
37681	342	13	angle	angle	NN
37681	342	14	of	of	IN
37681	342	15	a	a	DT
37681	342	16	triangle	triangle	NN
37681	342	17	.	.	.
37681	343	1	His	-PRON-	PRP$
37681	343	2	interest	interest	NN
37681	343	3	,	,	,
37681	343	4	however	however	RB
37681	343	5	,	,	,
37681	343	6	was	be	VBD
37681	343	7	chiefly	chiefly	RB
37681	343	8	in	in	IN
37681	343	9	astronomy	astronomy	NN
37681	343	10	.	.	.
37681	344	1	Another	another	DT
37681	344	2	of	of	IN
37681	344	3	Plato	Plato	NNP
37681	344	4	's	's	POS
37681	344	5	pupils	pupil	NNS
37681	344	6	was	be	VBD
37681	344	7	Eudoxus	eudoxus	NN
37681	344	8	of	of	IN
37681	344	9	Cnidus	Cnidus	NNP
37681	344	10	(	(	-LRB-
37681	344	11	408	408	CD
37681	344	12	-	-	SYM
37681	344	13	355	355	CD
37681	344	14	B.C.	B.C.	NNP
37681	344	15	)	)	-RRB-
37681	344	16	.	.	.
37681	345	1	He	-PRON-	PRP
37681	345	2	elaborated	elaborate	VBD
37681	345	3	the	the	DT
37681	345	4	theory	theory	NN
37681	345	5	of	of	IN
37681	345	6	proportion	proportion	NN
37681	345	7	,	,	,
37681	345	8	placing	place	VBG
37681	345	9	it	-PRON-	PRP
37681	345	10	upon	upon	IN
37681	345	11	a	a	DT
37681	345	12	thoroughly	thoroughly	RB
37681	345	13	scientific	scientific	JJ
37681	345	14	foundation	foundation	NN
37681	345	15	.	.	.
37681	346	1	It	-PRON-	PRP
37681	346	2	is	be	VBZ
37681	346	3	probable	probable	JJ
37681	346	4	that	that	IN
37681	346	5	Book	Book	NNP
37681	346	6	V	V	NNP
37681	346	7	of	of	IN
37681	346	8	Euclid	Euclid	NNP
37681	346	9	,	,	,
37681	346	10	which	which	WDT
37681	346	11	is	be	VBZ
37681	346	12	devoted	devote	VBN
37681	346	13	to	to	IN
37681	346	14	proportion	proportion	NN
37681	346	15	,	,	,
37681	346	16	is	be	VBZ
37681	346	17	essentially	essentially	RB
37681	346	18	the	the	DT
37681	346	19	work	work	NN
37681	346	20	of	of	IN
37681	346	21	Eudoxus	Eudoxus	NNP
37681	346	22	.	.	.
37681	347	1	By	by	IN
37681	347	2	means	mean	NNS
37681	347	3	of	of	IN
37681	347	4	the	the	DT
37681	347	5	method	method	NN
37681	347	6	of	of	IN
37681	347	7	exhaustions	exhaustion	NNS
37681	347	8	of	of	IN
37681	347	9	Antiphon	Antiphon	NNP
37681	347	10	and	and	CC
37681	347	11	Bryson	Bryson	NNP
37681	347	12	he	-PRON-	PRP
37681	347	13	proved	prove	VBD
37681	347	14	that	that	IN
37681	347	15	the	the	DT
37681	347	16	pyramid	pyramid	NN
37681	347	17	is	be	VBZ
37681	347	18	one	one	CD
37681	347	19	third	third	NN
37681	347	20	of	of	IN
37681	347	21	a	a	DT
37681	347	22	prism	prism	NN
37681	347	23	,	,	,
37681	347	24	and	and	CC
37681	347	25	the	the	DT
37681	347	26	cone	cone	NN
37681	347	27	is	be	VBZ
37681	347	28	one	one	CD
37681	347	29	third	third	NN
37681	347	30	of	of	IN
37681	347	31	a	a	DT
37681	347	32	cylinder	cylinder	NN
37681	347	33	,	,	,
37681	347	34	each	each	DT
37681	347	35	of	of	IN
37681	347	36	the	the	DT
37681	347	37	same	same	JJ
37681	347	38	base	base	NN
37681	347	39	and	and	CC
37681	347	40	the	the	DT
37681	347	41	same	same	JJ
37681	347	42	altitude	altitude	NN
37681	347	43	.	.	.
37681	348	1	He	-PRON-	PRP
37681	348	2	wrote	write	VBD
37681	348	3	the	the	DT
37681	348	4	first	first	JJ
37681	348	5	textbook	textbook	NN
37681	348	6	known	know	VBN
37681	348	7	on	on	IN
37681	348	8	solid	solid	JJ
37681	348	9	geometry	geometry	NN
37681	348	10	.	.	.
37681	349	1	The	the	DT
37681	349	2	subject	subject	NN
37681	349	3	of	of	IN
37681	349	4	conic	conic	JJ
37681	349	5	sections	section	NNS
37681	349	6	starts	start	VBZ
37681	349	7	with	with	IN
37681	349	8	another	another	DT
37681	349	9	pupil	pupil	NN
37681	349	10	of	of	IN
37681	349	11	Plato	Plato	NNP
37681	349	12	's	's	POS
37681	349	13	,	,	,
37681	349	14	Menæchmus	Menæchmus	NNP
37681	349	15	,	,	,
37681	349	16	who	who	WP
37681	349	17	lived	live	VBD
37681	349	18	about	about	RB
37681	349	19	350	350	CD
37681	349	20	B.C.	B.C.	NNS
37681	350	1	He	-PRON-	PRP
37681	350	2	cut	cut	VBD
37681	350	3	the	the	DT
37681	350	4	three	three	CD
37681	350	5	forms	form	NNS
37681	350	6	of	of	IN
37681	350	7	conics	conic	NNS
37681	350	8	(	(	-LRB-
37681	350	9	the	the	DT
37681	350	10	ellipse	ellipse	NN
37681	350	11	,	,	,
37681	350	12	parabola	parabola	NNP
37681	350	13	,	,	,
37681	350	14	and	and	CC
37681	350	15	hyperbola	hyperbola	NNP
37681	350	16	)	)	-RRB-
37681	350	17	out	out	IN
37681	350	18	of	of	IN
37681	350	19	three	three	CD
37681	350	20	different	different	JJ
37681	350	21	forms	form	NNS
37681	350	22	of	of	IN
37681	350	23	cone,--the	cone,--the	DT
37681	350	24	acute	acute	RB
37681	350	25	-	-	HYPH
37681	350	26	angled	angled	JJ
37681	350	27	,	,	,
37681	350	28	right	right	RB
37681	350	29	-	-	HYPH
37681	350	30	angled	angle	VBN
37681	350	31	,	,	,
37681	350	32	and	and	CC
37681	350	33	obtuse	obtuse	NNP
37681	350	34	-	-	HYPH
37681	350	35	angled,--not	angled,--not	NN
37681	350	36	noticing	notice	VBG
37681	350	37	that	that	IN
37681	350	38	he	-PRON-	PRP
37681	350	39	could	could	MD
37681	350	40	have	have	VB
37681	350	41	obtained	obtain	VBN
37681	350	42	all	all	DT
37681	350	43	three	three	CD
37681	350	44	from	from	IN
37681	350	45	any	any	DT
37681	350	46	form	form	NN
37681	350	47	of	of	IN
37681	350	48	right	right	JJ
37681	350	49	circular	circular	JJ
37681	350	50	cone	cone	NN
37681	350	51	.	.	.
37681	351	1	It	-PRON-	PRP
37681	351	2	is	be	VBZ
37681	351	3	interesting	interesting	JJ
37681	351	4	to	to	TO
37681	351	5	see	see	VB
37681	351	6	the	the	DT
37681	351	7	far	far	RB
37681	351	8	-	-	HYPH
37681	351	9	reaching	reach	VBG
37681	351	10	influence	influence	NN
37681	351	11	of	of	IN
37681	351	12	Plato	Plato	NNP
37681	351	13	.	.	.
37681	352	1	While	while	IN
37681	352	2	primarily	primarily	RB
37681	352	3	interested	interested	JJ
37681	352	4	in	in	IN
37681	352	5	philosophy	philosophy	NN
37681	352	6	,	,	,
37681	352	7	he	-PRON-	PRP
37681	352	8	laid	lay	VBD
37681	352	9	the	the	DT
37681	352	10	first	first	JJ
37681	352	11	scientific	scientific	JJ
37681	352	12	foundations	foundation	NNS
37681	352	13	for	for	IN
37681	352	14	a	a	DT
37681	352	15	system	system	NN
37681	352	16	of	of	IN
37681	352	17	mathematics	mathematic	NNS
37681	352	18	,	,	,
37681	352	19	and	and	CC
37681	352	20	his	-PRON-	PRP$
37681	352	21	pupils	pupil	NNS
37681	352	22	were	be	VBD
37681	352	23	the	the	DT
37681	352	24	leaders	leader	NNS
37681	352	25	in	in	IN
37681	352	26	this	this	DT
37681	352	27	science	science	NN
37681	352	28	in	in	IN
37681	352	29	the	the	DT
37681	352	30	generation	generation	NN
37681	352	31	following	follow	VBG
37681	352	32	his	-PRON-	PRP$
37681	352	33	greatest	great	JJS
37681	352	34	activity	activity	NN
37681	352	35	.	.	.
37681	353	1	The	the	DT
37681	353	2	great	great	JJ
37681	353	3	successor	successor	NN
37681	353	4	of	of	IN
37681	353	5	Plato	Plato	NNP
37681	353	6	at	at	IN
37681	353	7	Athens	Athens	NNP
37681	353	8	was	be	VBD
37681	353	9	Aristotle	Aristotle	NNP
37681	353	10	,	,	,
37681	353	11	the	the	DT
37681	353	12	teacher	teacher	NN
37681	353	13	of	of	IN
37681	353	14	Alexander	Alexander	NNP
37681	353	15	the	the	DT
37681	353	16	Great	great	JJ
37681	353	17	.	.	.
37681	354	1	He	-PRON-	PRP
37681	354	2	also	also	RB
37681	354	3	was	be	VBD
37681	354	4	more	more	RBR
37681	354	5	interested	interested	JJ
37681	354	6	in	in	IN
37681	354	7	philosophy	philosophy	NN
37681	354	8	than	than	IN
37681	354	9	in	in	IN
37681	354	10	mathematics	mathematic	NNS
37681	354	11	,	,	,
37681	354	12	but	but	CC
37681	354	13	in	in	IN
37681	354	14	natural	natural	JJ
37681	354	15	rather	rather	RB
37681	354	16	than	than	IN
37681	354	17	mental	mental	JJ
37681	354	18	philosophy	philosophy	NN
37681	354	19	.	.	.
37681	355	1	With	with	IN
37681	355	2	him	-PRON-	PRP
37681	355	3	comes	come	VBZ
37681	355	4	the	the	DT
37681	355	5	first	first	JJ
37681	355	6	application	application	NN
37681	355	7	of	of	IN
37681	355	8	mathematics	mathematic	NNS
37681	355	9	to	to	IN
37681	355	10	physics	physic	NNS
37681	355	11	in	in	IN
37681	355	12	the	the	DT
37681	355	13	hands	hand	NNS
37681	355	14	of	of	IN
37681	355	15	a	a	DT
37681	355	16	great	great	JJ
37681	355	17	man	man	NN
37681	355	18	,	,	,
37681	355	19	and	and	CC
37681	355	20	with	with	IN
37681	355	21	noteworthy	noteworthy	JJ
37681	355	22	results	result	NNS
37681	355	23	.	.	.
37681	356	1	He	-PRON-	PRP
37681	356	2	seems	seem	VBZ
37681	356	3	to	to	TO
37681	356	4	have	have	VB
37681	356	5	been	be	VBN
37681	356	6	the	the	DT
37681	356	7	first	first	JJ
37681	356	8	to	to	TO
37681	356	9	represent	represent	VB
37681	356	10	an	an	DT
37681	356	11	unknown	unknown	JJ
37681	356	12	quantity	quantity	NN
37681	356	13	by	by	IN
37681	356	14	letters	letter	NNS
37681	356	15	.	.	.
37681	357	1	He	-PRON-	PRP
37681	357	2	set	set	VBD
37681	357	3	forth	forth	RP
37681	357	4	the	the	DT
37681	357	5	theory	theory	NN
37681	357	6	of	of	IN
37681	357	7	the	the	DT
37681	357	8	parallelogram	parallelogram	NN
37681	357	9	of	of	IN
37681	357	10	forces	force	NNS
37681	357	11	,	,	,
37681	357	12	using	use	VBG
37681	357	13	only	only	RB
37681	357	14	rectangular	rectangular	JJ
37681	357	15	components	component	NNS
37681	357	16	,	,	,
37681	357	17	however	however	RB
37681	357	18	.	.	.
37681	358	1	To	to	IN
37681	358	2	one	one	CD
37681	358	3	of	of	IN
37681	358	4	his	-PRON-	PRP$
37681	358	5	pupils	pupil	NNS
37681	358	6	,	,	,
37681	358	7	Eudemus	Eudemus	NNP
37681	358	8	of	of	IN
37681	358	9	Rhodes	Rhodes	NNP
37681	358	10	,	,	,
37681	358	11	we	-PRON-	PRP
37681	358	12	are	be	VBP
37681	358	13	indebted	indebted	JJ
37681	358	14	for	for	IN
37681	358	15	a	a	DT
37681	358	16	history	history	NN
37681	358	17	of	of	IN
37681	358	18	ancient	ancient	JJ
37681	358	19	geometry	geometry	NN
37681	358	20	,	,	,
37681	358	21	some	some	DT
37681	358	22	fragments	fragment	NNS
37681	358	23	of	of	IN
37681	358	24	which	which	WDT
37681	358	25	have	have	VBP
37681	358	26	come	come	VBN
37681	358	27	down	down	RP
37681	358	28	to	to	IN
37681	358	29	us	-PRON-	PRP
37681	358	30	.	.	.
37681	359	1	The	the	DT
37681	359	2	first	first	JJ
37681	359	3	great	great	JJ
37681	359	4	textbook	textbook	NN
37681	359	5	on	on	IN
37681	359	6	geometry	geometry	NN
37681	359	7	,	,	,
37681	359	8	and	and	CC
37681	359	9	the	the	DT
37681	359	10	greatest	great	JJS
37681	359	11	one	one	NN
37681	359	12	that	that	WDT
37681	359	13	has	have	VBZ
37681	359	14	ever	ever	RB
37681	359	15	appeared	appear	VBN
37681	359	16	,	,	,
37681	359	17	was	be	VBD
37681	359	18	written	write	VBN
37681	359	19	by	by	IN
37681	359	20	Euclid	Euclid	NNP
37681	359	21	,	,	,
37681	359	22	who	who	WP
37681	359	23	taught	teach	VBD
37681	359	24	mathematics	mathematic	NNS
37681	359	25	in	in	IN
37681	359	26	the	the	DT
37681	359	27	great	great	JJ
37681	359	28	university	university	NN
37681	359	29	at	at	IN
37681	359	30	Alexandria	Alexandria	NNP
37681	359	31	,	,	,
37681	359	32	Egypt	Egypt	NNP
37681	359	33	,	,	,
37681	359	34	about	about	RB
37681	359	35	300	300	CD
37681	359	36	B.C.	B.C.	NNP
37681	360	1	Alexandria	Alexandria	NNP
37681	360	2	was	be	VBD
37681	360	3	then	then	RB
37681	360	4	practically	practically	RB
37681	360	5	a	a	DT
37681	360	6	Greek	greek	JJ
37681	360	7	city	city	NN
37681	360	8	,	,	,
37681	360	9	having	have	VBG
37681	360	10	been	be	VBN
37681	360	11	named	name	VBN
37681	360	12	in	in	IN
37681	360	13	honor	honor	NN
37681	360	14	of	of	IN
37681	360	15	Alexander	Alexander	NNP
37681	360	16	the	the	DT
37681	360	17	Great	great	JJ
37681	360	18	,	,	,
37681	360	19	and	and	CC
37681	360	20	being	be	VBG
37681	360	21	ruled	rule	VBN
37681	360	22	by	by	IN
37681	360	23	the	the	DT
37681	360	24	Greeks	Greeks	NNPS
37681	360	25	.	.	.
37681	361	1	In	in	IN
37681	361	2	his	-PRON-	PRP$
37681	361	3	work	work	NN
37681	361	4	Euclid	Euclid	NNP
37681	361	5	placed	place	VBD
37681	361	6	all	all	DT
37681	361	7	of	of	IN
37681	361	8	the	the	DT
37681	361	9	leading	lead	VBG
37681	361	10	propositions	proposition	NNS
37681	361	11	of	of	IN
37681	361	12	plane	plane	NN
37681	361	13	geometry	geometry	NN
37681	361	14	then	then	RB
37681	361	15	known	know	VBN
37681	361	16	,	,	,
37681	361	17	and	and	CC
37681	361	18	arranged	arrange	VBD
37681	361	19	them	-PRON-	PRP
37681	361	20	in	in	IN
37681	361	21	a	a	DT
37681	361	22	logical	logical	JJ
37681	361	23	order	order	NN
37681	361	24	.	.	.
37681	362	1	Most	Most	JJS
37681	362	2	geometries	geometry	NNS
37681	362	3	of	of	IN
37681	362	4	any	any	DT
37681	362	5	importance	importance	NN
37681	362	6	written	write	VBN
37681	362	7	since	since	IN
37681	362	8	his	-PRON-	PRP$
37681	362	9	time	time	NN
37681	362	10	have	have	VBP
37681	362	11	been	be	VBN
37681	362	12	based	base	VBN
37681	362	13	upon	upon	IN
37681	362	14	Euclid	Euclid	NNP
37681	362	15	,	,	,
37681	362	16	improving	improve	VBG
37681	362	17	the	the	DT
37681	362	18	sequence	sequence	NN
37681	362	19	,	,	,
37681	362	20	symbols	symbol	NNS
37681	362	21	,	,	,
37681	362	22	and	and	CC
37681	362	23	wording	wording	NN
37681	362	24	as	as	IN
37681	362	25	occasion	occasion	NN
37681	362	26	demanded	demand	VBD
37681	362	27	.	.	.
37681	363	1	He	-PRON-	PRP
37681	363	2	also	also	RB
37681	363	3	wrote	write	VBD
37681	363	4	upon	upon	IN
37681	363	5	other	other	JJ
37681	363	6	branches	branch	NNS
37681	363	7	of	of	IN
37681	363	8	mathematics	mathematic	NNS
37681	363	9	besides	besides	IN
37681	363	10	elementary	elementary	JJ
37681	363	11	geometry	geometry	NN
37681	363	12	,	,	,
37681	363	13	including	include	VBG
37681	363	14	a	a	DT
37681	363	15	work	work	NN
37681	363	16	on	on	IN
37681	363	17	optics	optic	NNS
37681	363	18	.	.	.
37681	364	1	He	-PRON-	PRP
37681	364	2	was	be	VBD
37681	364	3	not	not	RB
37681	364	4	a	a	DT
37681	364	5	great	great	JJ
37681	364	6	creator	creator	NN
37681	364	7	of	of	IN
37681	364	8	mathematics	mathematic	NNS
37681	364	9	,	,	,
37681	364	10	but	but	CC
37681	364	11	was	be	VBD
37681	364	12	rather	rather	RB
37681	364	13	a	a	DT
37681	364	14	compiler	compiler	NN
37681	364	15	of	of	IN
37681	364	16	the	the	DT
37681	364	17	work	work	NN
37681	364	18	of	of	IN
37681	364	19	others	other	NNS
37681	364	20	,	,	,
37681	364	21	an	an	DT
37681	364	22	office	office	NN
37681	364	23	quite	quite	RB
37681	364	24	as	as	RB
37681	364	25	difficult	difficult	JJ
37681	364	26	to	to	TO
37681	364	27	fill	fill	VB
37681	364	28	and	and	CC
37681	364	29	quite	quite	RB
37681	364	30	as	as	RB
37681	364	31	honorable	honorable	JJ
37681	364	32	.	.	.
37681	365	1	Euclid	Euclid	NNP
37681	365	2	did	do	VBD
37681	365	3	not	not	RB
37681	365	4	give	give	VB
37681	365	5	much	much	JJ
37681	365	6	solid	solid	JJ
37681	365	7	geometry	geometry	NN
37681	365	8	because	because	IN
37681	365	9	not	not	RB
37681	365	10	much	much	JJ
37681	365	11	was	be	VBD
37681	365	12	known	know	VBN
37681	365	13	then	then	RB
37681	365	14	.	.	.
37681	366	1	It	-PRON-	PRP
37681	366	2	was	be	VBD
37681	366	3	to	to	IN
37681	366	4	Archimedes	Archimedes	NNP
37681	366	5	(	(	-LRB-
37681	366	6	287	287	CD
37681	366	7	-	-	SYM
37681	366	8	212	212	CD
37681	366	9	B.C.	B.C.	NNP
37681	367	1	)	)	-RRB-
37681	367	2	,	,	,
37681	367	3	a	a	DT
37681	367	4	famous	famous	JJ
37681	367	5	mathematician	mathematician	NN
37681	367	6	of	of	IN
37681	367	7	Syracuse	Syracuse	NNP
37681	367	8	,	,	,
37681	367	9	on	on	IN
37681	367	10	the	the	DT
37681	367	11	island	island	NN
37681	367	12	of	of	IN
37681	367	13	Sicily	Sicily	NNP
37681	367	14	,	,	,
37681	367	15	that	that	IN
37681	367	16	some	some	DT
37681	367	17	of	of	IN
37681	367	18	the	the	DT
37681	367	19	most	most	RBS
37681	367	20	important	important	JJ
37681	367	21	propositions	proposition	NNS
37681	367	22	of	of	IN
37681	367	23	solid	solid	JJ
37681	367	24	geometry	geometry	NN
37681	367	25	are	be	VBP
37681	367	26	due	due	JJ
37681	367	27	,	,	,
37681	367	28	particularly	particularly	RB
37681	367	29	those	those	DT
37681	367	30	relating	relate	VBG
37681	367	31	to	to	IN
37681	367	32	the	the	DT
37681	367	33	sphere	sphere	NN
37681	367	34	and	and	CC
37681	367	35	cylinder	cylinder	NN
37681	367	36	.	.	.
37681	368	1	He	-PRON-	PRP
37681	368	2	also	also	RB
37681	368	3	showed	show	VBD
37681	368	4	how	how	WRB
37681	368	5	to	to	TO
37681	368	6	find	find	VB
37681	368	7	the	the	DT
37681	368	8	approximate	approximate	JJ
37681	368	9	value	value	NN
37681	368	10	of	of	IN
37681	368	11	[	[	-LRB-
37681	368	12	pi	pi	NN
37681	368	13	]	]	-RRB-
37681	368	14	by	by	IN
37681	368	15	a	a	DT
37681	368	16	method	method	NN
37681	368	17	similar	similar	JJ
37681	368	18	to	to	IN
37681	368	19	the	the	DT
37681	368	20	one	one	NN
37681	368	21	we	-PRON-	PRP
37681	368	22	teach	teach	VBP
37681	368	23	to	to	IN
37681	368	24	-	-	HYPH
37681	368	25	day	day	NN
37681	368	26	,	,	,
37681	368	27	proving	prove	VBG
37681	368	28	that	that	IN
37681	368	29	the	the	DT
37681	368	30	real	real	JJ
37681	368	31	value	value	NN
37681	368	32	lay	lie	VBD
37681	368	33	between	between	IN
37681	368	34	3	3	CD
37681	368	35	1/7	1/7	CD
37681	368	36	and	and	CC
37681	368	37	3	3	CD
37681	368	38	10/71	10/71	CD
37681	368	39	.	.	.
37681	369	1	The	the	DT
37681	369	2	story	story	NN
37681	369	3	goes	go	VBZ
37681	369	4	that	that	IN
37681	369	5	the	the	DT
37681	369	6	sphere	sphere	NN
37681	369	7	and	and	CC
37681	369	8	cylinder	cylinder	NN
37681	369	9	were	be	VBD
37681	369	10	engraved	engrave	VBN
37681	369	11	upon	upon	IN
37681	369	12	his	-PRON-	PRP$
37681	369	13	tomb	tomb	NN
37681	369	14	,	,	,
37681	369	15	and	and	CC
37681	369	16	Cicero	Cicero	NNP
37681	369	17	,	,	,
37681	369	18	visiting	visit	VBG
37681	369	19	Syracuse	Syracuse	NNP
37681	369	20	many	many	JJ
37681	369	21	years	year	NNS
37681	369	22	after	after	IN
37681	369	23	his	-PRON-	PRP$
37681	369	24	death	death	NN
37681	369	25	,	,	,
37681	369	26	found	find	VBD
37681	369	27	the	the	DT
37681	369	28	tomb	tomb	NN
37681	369	29	by	by	IN
37681	369	30	looking	look	VBG
37681	369	31	for	for	IN
37681	369	32	these	these	DT
37681	369	33	symbols	symbol	NNS
37681	369	34	.	.	.
37681	370	1	Archimedes	Archimedes	NNP
37681	370	2	was	be	VBD
37681	370	3	the	the	DT
37681	370	4	greatest	great	JJS
37681	370	5	mathematical	mathematical	JJ
37681	370	6	physicist	physicist	NN
37681	370	7	of	of	IN
37681	370	8	ancient	ancient	JJ
37681	370	9	times	time	NNS
37681	370	10	.	.	.
37681	371	1	The	the	DT
37681	371	2	Greeks	Greeks	NNPS
37681	371	3	contributed	contribute	VBD
37681	371	4	little	little	JJ
37681	371	5	more	more	JJR
37681	371	6	to	to	IN
37681	371	7	elementary	elementary	JJ
37681	371	8	geometry	geometry	NN
37681	371	9	,	,	,
37681	371	10	although	although	IN
37681	371	11	Apollonius	Apollonius	NNP
37681	371	12	of	of	IN
37681	371	13	Perga	Perga	NNP
37681	371	14	,	,	,
37681	371	15	who	who	WP
37681	371	16	taught	teach	VBD
37681	371	17	at	at	IN
37681	371	18	Alexandria	Alexandria	NNP
37681	371	19	between	between	IN
37681	371	20	250	250	CD
37681	371	21	and	and	CC
37681	371	22	200	200	CD
37681	371	23	B.C.	B.C.	NNP
37681	371	24	,	,	,
37681	371	25	wrote	write	VBD
37681	371	26	extensively	extensively	RB
37681	371	27	on	on	IN
37681	371	28	conic	conic	JJ
37681	371	29	sections	section	NNS
37681	371	30	,	,	,
37681	371	31	and	and	CC
37681	371	32	Hypsicles	Hypsicles	NNPS
37681	371	33	of	of	IN
37681	371	34	Alexandria	Alexandria	NNP
37681	371	35	,	,	,
37681	371	36	about	about	RB
37681	371	37	190	190	CD
37681	371	38	B.C.	B.C.	NNP
37681	371	39	,	,	,
37681	371	40	wrote	write	VBD
37681	371	41	on	on	IN
37681	371	42	regular	regular	JJ
37681	371	43	polyhedrons	polyhedron	NNS
37681	371	44	.	.	.
37681	372	1	Hypsicles	Hypsicles	NNP
37681	372	2	was	be	VBD
37681	372	3	the	the	DT
37681	372	4	first	first	JJ
37681	372	5	Greek	greek	JJ
37681	372	6	writer	writer	NN
37681	372	7	who	who	WP
37681	372	8	is	be	VBZ
37681	372	9	known	know	VBN
37681	372	10	to	to	TO
37681	372	11	have	have	VB
37681	372	12	used	use	VBN
37681	372	13	sexagesimal	sexagesimal	JJ
37681	372	14	fractions,--the	fractions,--the	NNP
37681	372	15	degrees	degree	NNS
37681	372	16	,	,	,
37681	372	17	minutes	minute	NNS
37681	372	18	,	,	,
37681	372	19	and	and	CC
37681	372	20	seconds	second	NNS
37681	372	21	of	of	IN
37681	372	22	our	-PRON-	PRP$
37681	372	23	angle	angle	NN
37681	372	24	measure	measure	NN
37681	372	25	.	.	.
37681	373	1	Zenodorus	Zenodorus	NNP
37681	373	2	(	(	-LRB-
37681	373	3	180	180	CD
37681	373	4	B.C.	B.C.	NNP
37681	373	5	)	)	-RRB-
37681	374	1	wrote	write	VBD
37681	374	2	on	on	IN
37681	374	3	isoperimetric	isoperimetric	JJ
37681	374	4	figures	figure	NNS
37681	374	5	,	,	,
37681	374	6	and	and	CC
37681	374	7	his	-PRON-	PRP$
37681	374	8	contemporary	contemporary	NN
37681	374	9	,	,	,
37681	374	10	Nicomedes	Nicomedes	NNP
37681	374	11	of	of	IN
37681	374	12	Gerasa	Gerasa	NNP
37681	374	13	,	,	,
37681	374	14	invented	invent	VBD
37681	374	15	a	a	DT
37681	374	16	curve	curve	NN
37681	374	17	known	know	VBN
37681	374	18	as	as	IN
37681	374	19	the	the	DT
37681	374	20	conchoid	conchoid	NN
37681	374	21	,	,	,
37681	374	22	by	by	IN
37681	374	23	means	mean	NNS
37681	374	24	of	of	IN
37681	374	25	which	which	WDT
37681	374	26	he	-PRON-	PRP
37681	374	27	could	could	MD
37681	374	28	trisect	trisect	VB
37681	374	29	any	any	DT
37681	374	30	angle	angle	NN
37681	374	31	.	.	.
37681	375	1	Another	another	DT
37681	375	2	contemporary	contemporary	NN
37681	375	3	,	,	,
37681	375	4	Diocles	Diocles	NNP
37681	375	5	,	,	,
37681	375	6	invented	invent	VBD
37681	375	7	the	the	DT
37681	375	8	cissoid	cissoid	NN
37681	375	9	,	,	,
37681	375	10	or	or	CC
37681	375	11	ivy	ivy	NN
37681	375	12	-	-	HYPH
37681	375	13	shaped	shape	VBN
37681	375	14	curve	curve	NN
37681	375	15	,	,	,
37681	375	16	by	by	IN
37681	375	17	means	mean	NNS
37681	375	18	of	of	IN
37681	375	19	which	which	WDT
37681	375	20	he	-PRON-	PRP
37681	375	21	solved	solve	VBD
37681	375	22	the	the	DT
37681	375	23	famous	famous	JJ
37681	375	24	problem	problem	NN
37681	375	25	of	of	IN
37681	375	26	duplicating	duplicate	VBG
37681	375	27	the	the	DT
37681	375	28	cube	cube	NN
37681	375	29	,	,	,
37681	375	30	that	that	RB
37681	375	31	is	is	RB
37681	375	32	,	,	,
37681	375	33	constructing	construct	VBG
37681	375	34	a	a	DT
37681	375	35	cube	cube	NN
37681	375	36	that	that	WDT
37681	375	37	should	should	MD
37681	375	38	have	have	VB
37681	375	39	twice	twice	PDT
37681	375	40	the	the	DT
37681	375	41	volume	volume	NN
37681	375	42	of	of	IN
37681	375	43	a	a	DT
37681	375	44	given	give	VBN
37681	375	45	cube	cube	NN
37681	375	46	.	.	.
37681	376	1	The	the	DT
37681	376	2	greatest	great	JJS
37681	376	3	of	of	IN
37681	376	4	the	the	DT
37681	376	5	Greek	greek	JJ
37681	376	6	astronomers	astronomer	NNS
37681	376	7	,	,	,
37681	376	8	Hipparchus	Hipparchus	NNP
37681	376	9	(	(	-LRB-
37681	376	10	180	180	CD
37681	376	11	-	-	SYM
37681	376	12	125	125	CD
37681	376	13	B.C.	B.C.	NNP
37681	377	1	)	)	-RRB-
37681	377	2	,	,	,
37681	377	3	lived	live	VBD
37681	377	4	about	about	IN
37681	377	5	this	this	DT
37681	377	6	period	period	NN
37681	377	7	,	,	,
37681	377	8	and	and	CC
37681	377	9	with	with	IN
37681	377	10	him	-PRON-	PRP
37681	377	11	begins	begin	VBZ
37681	377	12	spherical	spherical	JJ
37681	377	13	trigonometry	trigonometry	NN
37681	377	14	as	as	IN
37681	377	15	a	a	DT
37681	377	16	definite	definite	JJ
37681	377	17	science	science	NN
37681	377	18	.	.	.
37681	378	1	A	a	DT
37681	378	2	kind	kind	NN
37681	378	3	of	of	IN
37681	378	4	plane	plane	NN
37681	378	5	trigonometry	trigonometry	NN
37681	378	6	had	have	VBD
37681	378	7	been	be	VBN
37681	378	8	known	know	VBN
37681	378	9	to	to	IN
37681	378	10	the	the	DT
37681	378	11	ancient	ancient	JJ
37681	378	12	Egyptians	Egyptians	NNPS
37681	378	13	.	.	.
37681	379	1	The	the	DT
37681	379	2	Greeks	Greeks	NNPS
37681	379	3	usually	usually	RB
37681	379	4	employed	employ	VBD
37681	379	5	the	the	DT
37681	379	6	chord	chord	NN
37681	379	7	of	of	IN
37681	379	8	an	an	DT
37681	379	9	angle	angle	NN
37681	379	10	instead	instead	RB
37681	379	11	of	of	IN
37681	379	12	the	the	DT
37681	379	13	half	half	NN
37681	379	14	chord	chord	NN
37681	379	15	(	(	-LRB-
37681	379	16	sine	sine	NNP
37681	379	17	)	)	-RRB-
37681	379	18	,	,	,
37681	379	19	the	the	DT
37681	379	20	latter	latter	JJ
37681	379	21	having	have	VBG
37681	379	22	been	be	VBN
37681	379	23	preferred	prefer	VBN
37681	379	24	by	by	IN
37681	379	25	the	the	DT
37681	379	26	later	later	JJ
37681	379	27	Arab	arab	JJ
37681	379	28	writers	writer	NNS
37681	379	29	.	.	.
37681	380	1	The	the	DT
37681	380	2	most	most	RBS
37681	380	3	celebrated	celebrated	JJ
37681	380	4	of	of	IN
37681	380	5	the	the	DT
37681	380	6	later	later	JJ
37681	380	7	Greek	greek	JJ
37681	380	8	physicists	physicist	NNS
37681	380	9	was	be	VBD
37681	380	10	Heron	Heron	NNP
37681	380	11	of	of	IN
37681	380	12	Alexandria	Alexandria	NNP
37681	380	13	,	,	,
37681	380	14	formerly	formerly	RB
37681	380	15	supposed	suppose	VBN
37681	380	16	to	to	TO
37681	380	17	have	have	VB
37681	380	18	lived	live	VBN
37681	380	19	about	about	RB
37681	380	20	100	100	CD
37681	380	21	B.C.	B.C.	NNS
37681	380	22	,	,	,
37681	380	23	but	but	CC
37681	380	24	now	now	RB
37681	380	25	assigned	assign	VBN
37681	380	26	to	to	IN
37681	380	27	the	the	DT
37681	380	28	first	first	JJ
37681	380	29	century	century	NN
37681	380	30	A.D.	a.d.	NN
37681	380	31	His	-PRON-	PRP$
37681	380	32	contribution	contribution	NN
37681	380	33	to	to	IN
37681	380	34	geometry	geometry	NN
37681	380	35	was	be	VBD
37681	380	36	the	the	DT
37681	380	37	formula	formula	NN
37681	380	38	for	for	IN
37681	380	39	the	the	DT
37681	380	40	area	area	NN
37681	380	41	of	of	IN
37681	380	42	a	a	DT
37681	380	43	triangle	triangle	NN
37681	380	44	in	in	IN
37681	380	45	terms	term	NNS
37681	380	46	of	of	IN
37681	380	47	its	-PRON-	PRP$
37681	380	48	sides	side	NNS
37681	380	49	a	a	NNP
37681	380	50	,	,	,
37681	380	51	b	b	NN
37681	380	52	,	,	,
37681	380	53	and	and	CC
37681	380	54	c	c	NNP
37681	380	55	,	,	,
37681	380	56	with	with	IN
37681	380	57	s	s	NN
37681	380	58	standing	stand	VBG
37681	380	59	for	for	IN
37681	380	60	the	the	DT
37681	380	61	semiperimeter	semiperimeter	JJ
37681	380	62	1/2(_a	1/2(_a	CD
37681	380	63	_	_	NNP
37681	380	64	+	+	NNP
37681	380	65	_	_	NNP
37681	380	66	b	b	NNP
37681	380	67	_	_	NNP
37681	380	68	+	+	NNP
37681	380	69	_	_	NNP
37681	380	70	c	c	NNP
37681	380	71	_	_	NNP
37681	380	72	)	)	-RRB-
37681	380	73	.	.	.
37681	381	1	The	the	DT
37681	381	2	formula	formula	NN
37681	381	3	is	be	VBZ
37681	381	4	[	[	-LRB-
37681	381	5	sqrt](_s_(_s_-_a_)(_s_-_b_)(_s_-_c	sqrt](_s_(_s_-_a_)(_s_-_b_)(_s_-_c	NNP
37681	381	6	_	_	NNP
37681	381	7	)	)	-RRB-
37681	381	8	)	)	-RRB-
37681	381	9	.	.	.
37681	382	1	Probably	probably	RB
37681	382	2	nearly	nearly	RB
37681	382	3	contemporary	contemporary	JJ
37681	382	4	with	with	IN
37681	382	5	Heron	Heron	NNP
37681	382	6	was	be	VBD
37681	382	7	Menelaus	Menelaus	NNP
37681	382	8	of	of	IN
37681	382	9	Alexandria	Alexandria	NNP
37681	382	10	,	,	,
37681	382	11	who	who	WP
37681	382	12	wrote	write	VBD
37681	382	13	a	a	DT
37681	382	14	spherical	spherical	JJ
37681	382	15	trigonometry	trigonometry	NN
37681	382	16	.	.	.
37681	383	1	He	-PRON-	PRP
37681	383	2	gave	give	VBD
37681	383	3	an	an	DT
37681	383	4	interesting	interesting	JJ
37681	383	5	proposition	proposition	NN
37681	383	6	relating	relate	VBG
37681	383	7	to	to	IN
37681	383	8	plane	plane	NN
37681	383	9	and	and	CC
37681	383	10	spherical	spherical	JJ
37681	383	11	triangles	triangle	NNS
37681	383	12	,	,	,
37681	383	13	their	-PRON-	PRP$
37681	383	14	sides	side	NNS
37681	383	15	being	be	VBG
37681	383	16	cut	cut	VBN
37681	383	17	by	by	IN
37681	383	18	a	a	DT
37681	383	19	transversal	transversal	NN
37681	383	20	.	.	.
37681	384	1	For	for	IN
37681	384	2	the	the	DT
37681	384	3	plane	plane	NN
37681	384	4	triangle	triangle	NN
37681	384	5	_	_	NNP
37681	384	6	ABC	ABC	NNP
37681	384	7	_	_	NNP
37681	384	8	,	,	,
37681	384	9	the	the	DT
37681	384	10	sides	side	NNS
37681	384	11	_	_	NNP
37681	384	12	a	a	DT
37681	384	13	_	_	NNP
37681	384	14	,	,	,
37681	384	15	_	_	NNP
37681	384	16	b	b	NNP
37681	384	17	_	_	NNP
37681	384	18	,	,	,
37681	384	19	and	and	CC
37681	384	20	_	_	NNP
37681	384	21	c	c	NNP
37681	384	22	_	_	NNP
37681	384	23	being	be	VBG
37681	384	24	cut	cut	VBN
37681	384	25	respectively	respectively	RB
37681	384	26	in	in	IN
37681	384	27	_	_	NNP
37681	384	28	X	X	NNP
37681	384	29	_	_	NNP
37681	384	30	,	,	,
37681	384	31	_	_	NNP
37681	384	32	Y	Y	NNP
37681	384	33	_	_	NNP
37681	384	34	,	,	,
37681	384	35	and	and	CC
37681	384	36	_	_	NNP
37681	384	37	Z	Z	NNP
37681	384	38	_	_	NNP
37681	384	39	,	,	,
37681	384	40	the	the	DT
37681	384	41	theorem	theorem	NN
37681	384	42	asserts	assert	VBZ
37681	384	43	substantially	substantially	RB
37681	384	44	that	that	IN
37681	384	45	(	(	-LRB-
37681	384	46	_	_	NNP
37681	384	47	AZ_/_BZ	AZ_/_BZ	NNP
37681	384	48	_	_	NNP
37681	384	49	)	)	-RRB-
37681	384	50	·	·	NFP
37681	384	51	(	(	-LRB-
37681	384	52	_	_	NNP
37681	384	53	BX_/_CX	BX_/_CX	NNP
37681	384	54	_	_	NNP
37681	384	55	)	)	-RRB-
37681	384	56	·	·	NFP
37681	384	57	(	(	-LRB-
37681	384	58	_	_	NNP
37681	384	59	CY_/_AY	CY_/_AY	NNP
37681	384	60	_	_	NNP
37681	384	61	)	)	-RRB-
37681	384	62	=	=	SYM
37681	384	63	1	1	CD
37681	384	64	.	.	.
37681	385	1	The	the	DT
37681	385	2	most	most	RBS
37681	385	3	popular	popular	JJ
37681	385	4	writer	writer	NN
37681	385	5	on	on	IN
37681	385	6	astronomy	astronomy	NN
37681	385	7	among	among	IN
37681	385	8	the	the	DT
37681	385	9	Greeks	Greeks	NNPS
37681	385	10	was	be	VBD
37681	385	11	Ptolemy	Ptolemy	NNP
37681	385	12	(	(	-LRB-
37681	385	13	Claudius	Claudius	NNP
37681	385	14	Ptolemaeus	Ptolemaeus	NNP
37681	385	15	,	,	,
37681	385	16	87	87	CD
37681	385	17	-	-	SYM
37681	385	18	165	165	CD
37681	385	19	A.D.	A.D.	NNP
37681	385	20	)	)	-RRB-
37681	385	21	,	,	,
37681	385	22	who	who	WP
37681	385	23	lived	live	VBD
37681	385	24	at	at	IN
37681	385	25	Alexandria	Alexandria	NNP
37681	385	26	.	.	.
37681	386	1	He	-PRON-	PRP
37681	386	2	wrote	write	VBD
37681	386	3	a	a	DT
37681	386	4	work	work	NN
37681	386	5	entitled	entitle	VBN
37681	386	6	"	"	``
37681	386	7	Megale	Megale	NNP
37681	386	8	Syntaxis	Syntaxis	NNP
37681	386	9	"	"	''
37681	386	10	(	(	-LRB-
37681	386	11	The	the	DT
37681	386	12	Great	Great	NNP
37681	386	13	Collection	Collection	NNP
37681	386	14	)	)	-RRB-
37681	386	15	,	,	,
37681	386	16	which	which	WDT
37681	386	17	his	-PRON-	PRP$
37681	386	18	followers	follower	NNS
37681	386	19	designated	designate	VBD
37681	386	20	as	as	IN
37681	386	21	_	_	NNP
37681	386	22	Megistos	Megistos	NNP
37681	386	23	_	_	NNP
37681	386	24	(	(	-LRB-
37681	386	25	greatest	great	JJS
37681	386	26	)	)	-RRB-
37681	386	27	,	,	,
37681	386	28	on	on	IN
37681	386	29	which	which	WDT
37681	386	30	account	account	NN
37681	386	31	the	the	DT
37681	386	32	Arab	arab	JJ
37681	386	33	translators	translator	NNS
37681	386	34	gave	give	VBD
37681	386	35	it	-PRON-	PRP
37681	386	36	the	the	DT
37681	386	37	name	name	NN
37681	386	38	"	"	``
37681	386	39	Almagest	Almagest	NNP
37681	386	40	"	"	''
37681	386	41	(	(	-LRB-
37681	386	42	_	_	NNP
37681	386	43	al	al	NNP
37681	386	44	_	_	NNP
37681	386	45	meaning	mean	VBG
37681	386	46	"	"	``
37681	386	47	the	the	DT
37681	386	48	"	"	''
37681	386	49	)	)	-RRB-
37681	386	50	.	.	.
37681	387	1	He	-PRON-	PRP
37681	387	2	advanced	advance	VBD
37681	387	3	the	the	DT
37681	387	4	science	science	NN
37681	387	5	of	of	IN
37681	387	6	trigonometry	trigonometry	NN
37681	387	7	,	,	,
37681	387	8	but	but	CC
37681	387	9	did	do	VBD
37681	387	10	not	not	RB
37681	387	11	contribute	contribute	VB
37681	387	12	to	to	IN
37681	387	13	geometry	geometry	NN
37681	387	14	.	.	.
37681	388	1	At	at	IN
37681	388	2	the	the	DT
37681	388	3	close	close	NN
37681	388	4	of	of	IN
37681	388	5	the	the	DT
37681	388	6	third	third	JJ
37681	388	7	century	century	NN
37681	388	8	Pappus	Pappus	NNP
37681	388	9	of	of	IN
37681	388	10	Alexandria	Alexandria	NNP
37681	388	11	(	(	-LRB-
37681	388	12	295	295	CD
37681	388	13	A.D.	A.D.	NNP
37681	388	14	)	)	-RRB-
37681	388	15	wrote	write	VBD
37681	388	16	on	on	IN
37681	388	17	geometry	geometry	NN
37681	388	18	,	,	,
37681	388	19	and	and	CC
37681	388	20	one	one	CD
37681	388	21	of	of	IN
37681	388	22	his	-PRON-	PRP$
37681	388	23	theorems	theorem	NNS
37681	388	24	,	,	,
37681	388	25	a	a	DT
37681	388	26	generalized	generalize	VBN
37681	388	27	form	form	NN
37681	388	28	of	of	IN
37681	388	29	the	the	DT
37681	388	30	Pythagorean	pythagorean	JJ
37681	388	31	proposition	proposition	NN
37681	388	32	,	,	,
37681	388	33	is	be	VBZ
37681	388	34	mentioned	mention	VBN
37681	388	35	in	in	IN
37681	388	36	Chapter	Chapter	NNP
37681	388	37	XVI	XVI	NNP
37681	388	38	of	of	IN
37681	388	39	this	this	DT
37681	388	40	work	work	NN
37681	388	41	.	.	.
37681	389	1	Only	only	RB
37681	389	2	two	two	CD
37681	389	3	other	other	JJ
37681	389	4	Greek	greek	JJ
37681	389	5	writers	writer	NNS
37681	389	6	on	on	IN
37681	389	7	geometry	geometry	NN
37681	389	8	need	need	VBP
37681	389	9	be	be	VB
37681	389	10	mentioned	mention	VBN
37681	389	11	.	.	.
37681	390	1	Theon	Theon	NNP
37681	390	2	of	of	IN
37681	390	3	Alexandria	Alexandria	NNP
37681	390	4	(	(	-LRB-
37681	390	5	370	370	CD
37681	390	6	A.D.	A.D.	NNP
37681	390	7	)	)	-RRB-
37681	390	8	,	,	,
37681	390	9	the	the	DT
37681	390	10	father	father	NN
37681	390	11	of	of	IN
37681	390	12	the	the	DT
37681	390	13	Hypatia	Hypatia	NNP
37681	390	14	who	who	WP
37681	390	15	is	be	VBZ
37681	390	16	the	the	DT
37681	390	17	heroine	heroine	NN
37681	390	18	of	of	IN
37681	390	19	Charles	Charles	NNP
37681	390	20	Kingsley	Kingsley	NNP
37681	390	21	's	's	POS
37681	390	22	well	well	RB
37681	390	23	-	-	HYPH
37681	390	24	known	know	VBN
37681	390	25	novel	novel	NN
37681	390	26	,	,	,
37681	390	27	wrote	write	VBD
37681	390	28	a	a	DT
37681	390	29	commentary	commentary	NN
37681	390	30	on	on	IN
37681	390	31	Euclid	Euclid	NNP
37681	390	32	to	to	TO
37681	390	33	which	which	WDT
37681	390	34	we	-PRON-	PRP
37681	390	35	are	be	VBP
37681	390	36	indebted	indebted	JJ
37681	390	37	for	for	IN
37681	390	38	some	some	DT
37681	390	39	historical	historical	JJ
37681	390	40	information	information	NN
37681	390	41	.	.	.
37681	391	1	Proclus	Proclus	NNP
37681	391	2	(	(	-LRB-
37681	391	3	410	410	CD
37681	391	4	-	-	SYM
37681	391	5	485	485	CD
37681	391	6	A.D.	A.D.	NNP
37681	391	7	)	)	-RRB-
37681	391	8	also	also	RB
37681	391	9	wrote	write	VBD
37681	391	10	a	a	DT
37681	391	11	commentary	commentary	NN
37681	391	12	on	on	IN
37681	391	13	Euclid	Euclid	NNP
37681	391	14	,	,	,
37681	391	15	and	and	CC
37681	391	16	much	much	JJ
37681	391	17	of	of	IN
37681	391	18	our	-PRON-	PRP$
37681	391	19	information	information	NN
37681	391	20	concerning	concern	VBG
37681	391	21	the	the	DT
37681	391	22	first	first	JJ
37681	391	23	Book	Book	NNP
37681	391	24	of	of	IN
37681	391	25	Euclid	Euclid	NNP
37681	391	26	is	be	VBZ
37681	391	27	due	due	JJ
37681	391	28	to	to	IN
37681	391	29	him	-PRON-	PRP
37681	391	30	.	.	.
37681	392	1	The	the	DT
37681	392	2	East	East	NNP
37681	392	3	did	do	VBD
37681	392	4	little	little	JJ
37681	392	5	for	for	IN
37681	392	6	geometry	geometry	NN
37681	392	7	,	,	,
37681	392	8	although	although	IN
37681	392	9	contributing	contribute	VBG
37681	392	10	considerably	considerably	RB
37681	392	11	to	to	IN
37681	392	12	algebra	algebra	NN
37681	392	13	.	.	.
37681	393	1	The	the	DT
37681	393	2	first	first	JJ
37681	393	3	great	great	JJ
37681	393	4	Hindu	Hindu	NNP
37681	393	5	writer	writer	NN
37681	393	6	was	be	VBD
37681	393	7	Aryabhatta	Aryabhatta	NNP
37681	393	8	,	,	,
37681	393	9	who	who	WP
37681	393	10	was	be	VBD
37681	393	11	born	bear	VBN
37681	393	12	in	in	IN
37681	393	13	476	476	CD
37681	393	14	A.D.	A.D.	NNP
37681	394	1	He	-PRON-	PRP
37681	394	2	gave	give	VBD
37681	394	3	the	the	DT
37681	394	4	very	very	RB
37681	394	5	close	close	JJ
37681	394	6	approximation	approximation	NN
37681	394	7	for	for	IN
37681	394	8	[	[	-LRB-
37681	394	9	pi	pi	NN
37681	394	10	]	]	-RRB-
37681	394	11	,	,	,
37681	394	12	expressed	express	VBN
37681	394	13	in	in	IN
37681	394	14	modern	modern	JJ
37681	394	15	notation	notation	NN
37681	394	16	as	as	IN
37681	394	17	3.1416	3.1416	CD
37681	394	18	.	.	.
37681	395	1	He	-PRON-	PRP
37681	395	2	also	also	RB
37681	395	3	gave	give	VBD
37681	395	4	rules	rule	NNS
37681	395	5	for	for	IN
37681	395	6	finding	find	VBG
37681	395	7	the	the	DT
37681	395	8	volume	volume	NN
37681	395	9	of	of	IN
37681	395	10	the	the	DT
37681	395	11	pyramid	pyramid	NN
37681	395	12	and	and	CC
37681	395	13	sphere	sphere	NN
37681	395	14	,	,	,
37681	395	15	but	but	CC
37681	395	16	they	-PRON-	PRP
37681	395	17	were	be	VBD
37681	395	18	incorrect	incorrect	JJ
37681	395	19	,	,	,
37681	395	20	showing	show	VBG
37681	395	21	that	that	IN
37681	395	22	the	the	DT
37681	395	23	Greek	greek	JJ
37681	395	24	mathematics	mathematic	NNS
37681	395	25	had	have	VBD
37681	395	26	not	not	RB
37681	395	27	yet	yet	RB
37681	395	28	reached	reach	VBN
37681	395	29	the	the	DT
37681	395	30	Ganges	Ganges	NNPS
37681	395	31	.	.	.
37681	396	1	Another	another	DT
37681	396	2	Hindu	Hindu	NNP
37681	396	3	writer	writer	NN
37681	396	4	,	,	,
37681	396	5	Brahmagupta	Brahmagupta	NNP
37681	396	6	(	(	-LRB-
37681	396	7	born	bear	VBN
37681	396	8	in	in	IN
37681	396	9	598	598	CD
37681	396	10	A.D.	A.D.	NNP
37681	396	11	)	)	-RRB-
37681	396	12	,	,	,
37681	396	13	wrote	write	VBD
37681	396	14	an	an	DT
37681	396	15	encyclopedia	encyclopedia	NN
37681	396	16	of	of	IN
37681	396	17	mathematics	mathematic	NNS
37681	396	18	.	.	.
37681	397	1	He	-PRON-	PRP
37681	397	2	gave	give	VBD
37681	397	3	a	a	DT
37681	397	4	rule	rule	NN
37681	397	5	for	for	IN
37681	397	6	finding	find	VBG
37681	397	7	Pythagorean	pythagorean	JJ
37681	397	8	numbers	number	NNS
37681	397	9	,	,	,
37681	397	10	expressed	express	VBN
37681	397	11	in	in	IN
37681	397	12	modern	modern	JJ
37681	397	13	symbols	symbol	NNS
37681	397	14	as	as	IN
37681	397	15	follows	follow	VBZ
37681	397	16	:	:	:
37681	397	17	1/4((_p_^2/_q	1/4((_p_^2/_q	CD
37681	397	18	_	_	NNP
37681	397	19	)	)	-RRB-
37681	397	20	+	+	CC
37681	397	21	_	_	NNP
37681	397	22	q_)^2	q_)^2	NNP
37681	397	23	=	=	SYM
37681	397	24	1/4((_p_^2/_q	1/4((_p_^2/_q	CD
37681	397	25	_	_	NNP
37681	397	26	)	)	-RRB-
37681	397	27	-	-	:
37681	397	28	_	_	NNP
37681	397	29	q_)^2	q_)^2	NN
37681	397	30	+	+	CC
37681	397	31	_	_	NNP
37681	397	32	p_^2	p_^2	NNP
37681	397	33	.	.	.
37681	398	1	He	-PRON-	PRP
37681	398	2	also	also	RB
37681	398	3	generalized	generalize	VBD
37681	398	4	Heron	Heron	NNP
37681	398	5	's	's	POS
37681	398	6	formula	formula	NN
37681	398	7	by	by	IN
37681	398	8	asserting	assert	VBG
37681	398	9	that	that	IN
37681	398	10	the	the	DT
37681	398	11	area	area	NN
37681	398	12	of	of	IN
37681	398	13	an	an	DT
37681	398	14	inscribed	inscribe	VBN
37681	398	15	quadrilateral	quadrilateral	NN
37681	398	16	of	of	IN
37681	398	17	sides	side	NNS
37681	398	18	_	_	NNP
37681	398	19	a	a	DT
37681	398	20	_	_	NNP
37681	398	21	,	,	,
37681	398	22	_	_	NNP
37681	398	23	b	b	NNP
37681	398	24	_	_	NNP
37681	398	25	,	,	,
37681	398	26	_	_	NNP
37681	398	27	c	c	NNP
37681	398	28	_	_	NNP
37681	398	29	,	,	,
37681	398	30	_	_	NNP
37681	398	31	d	d	NNP
37681	398	32	_	_	NNP
37681	398	33	,	,	,
37681	398	34	and	and	CC
37681	398	35	semiperimeter	semiperimeter	NNP
37681	398	36	_	_	NNP
37681	398	37	s	s	NNP
37681	398	38	_	_	NNP
37681	398	39	,	,	,
37681	398	40	is	be	VBZ
37681	398	41	[	[	-LRB-
37681	398	42	sqrt]((_s	sqrt]((_s	NNP
37681	398	43	_	_	NNP
37681	398	44	-	-	HYPH
37681	398	45	_	_	NNP
37681	398	46	a_)(_s	a_)(_s	NN
37681	398	47	_	_	NNP
37681	398	48	-	-	HYPH
37681	398	49	_	_	NNP
37681	398	50	b_)(_s	b_)(_s	NN
37681	398	51	_	_	NNP
37681	398	52	-	-	HYPH
37681	398	53	_	_	NNP
37681	398	54	c_)(_s	c_)(_s	NN
37681	398	55	_	_	NNP
37681	398	56	-	-	HYPH
37681	398	57	_	_	NNP
37681	398	58	d	d	NNP
37681	398	59	_	_	NNP
37681	398	60	)	)	-RRB-
37681	398	61	)	)	-RRB-
37681	398	62	.	.	.
37681	399	1	The	the	DT
37681	399	2	Arabs	Arabs	NNPS
37681	399	3	,	,	,
37681	399	4	about	about	RB
37681	399	5	the	the	DT
37681	399	6	time	time	NN
37681	399	7	of	of	IN
37681	399	8	the	the	DT
37681	399	9	"	"	``
37681	399	10	Arabian	Arabian	NNP
37681	399	11	Nights	Nights	NNPS
37681	399	12	Tales	Tales	NNP
37681	399	13	"	"	''
37681	399	14	(	(	-LRB-
37681	399	15	800	800	CD
37681	399	16	A.D.	A.D.	NNP
37681	399	17	)	)	-RRB-
37681	399	18	,	,	,
37681	399	19	did	do	VBD
37681	399	20	much	much	JJ
37681	399	21	for	for	IN
37681	399	22	mathematics	mathematic	NNS
37681	399	23	,	,	,
37681	399	24	translating	translate	VBG
37681	399	25	the	the	DT
37681	399	26	Greek	greek	JJ
37681	399	27	authors	author	NNS
37681	399	28	into	into	IN
37681	399	29	their	-PRON-	PRP$
37681	399	30	language	language	NN
37681	399	31	and	and	CC
37681	399	32	also	also	RB
37681	399	33	bringing	bring	VBG
37681	399	34	learning	learn	VBG
37681	399	35	from	from	IN
37681	399	36	India	India	NNP
37681	399	37	.	.	.
37681	400	1	Indeed	indeed	RB
37681	400	2	,	,	,
37681	400	3	it	-PRON-	PRP
37681	400	4	is	be	VBZ
37681	400	5	to	to	IN
37681	400	6	them	-PRON-	PRP
37681	400	7	that	that	IN
37681	400	8	modern	modern	JJ
37681	400	9	Europe	Europe	NNP
37681	400	10	owed	owe	VBD
37681	400	11	its	-PRON-	PRP$
37681	400	12	first	first	JJ
37681	400	13	knowledge	knowledge	NN
37681	400	14	of	of	IN
37681	400	15	Euclid	Euclid	NNP
37681	400	16	.	.	.
37681	401	1	They	-PRON-	PRP
37681	401	2	contributed	contribute	VBD
37681	401	3	nothing	nothing	NN
37681	401	4	of	of	IN
37681	401	5	importance	importance	NN
37681	401	6	to	to	IN
37681	401	7	elementary	elementary	JJ
37681	401	8	geometry	geometry	NN
37681	401	9	,	,	,
37681	401	10	however	however	RB
37681	401	11	.	.	.
37681	402	1	The	the	DT
37681	402	2	greatest	great	JJS
37681	402	3	of	of	IN
37681	402	4	the	the	DT
37681	402	5	Arab	arab	JJ
37681	402	6	writers	writer	NNS
37681	402	7	was	be	VBD
37681	402	8	Mohammed	Mohammed	NNP
37681	402	9	ibn	ibn	NNP
37681	402	10	Musa	Musa	NNP
37681	402	11	al	al	NNP
37681	402	12	-	-	HYPH
37681	402	13	Khowarazmi	Khowarazmi	NNP
37681	402	14	(	(	-LRB-
37681	402	15	820	820	CD
37681	402	16	A.D.	A.D.	NNP
37681	402	17	)	)	-RRB-
37681	402	18	.	.	.
37681	403	1	He	-PRON-	PRP
37681	403	2	lived	live	VBD
37681	403	3	at	at	IN
37681	403	4	Bagdad	Bagdad	NNP
37681	403	5	and	and	CC
37681	403	6	Damascus	Damascus	NNP
37681	403	7	.	.	.
37681	404	1	Although	although	IN
37681	404	2	chiefly	chiefly	RB
37681	404	3	interested	interested	JJ
37681	404	4	in	in	IN
37681	404	5	astronomy	astronomy	NN
37681	404	6	,	,	,
37681	404	7	he	-PRON-	PRP
37681	404	8	wrote	write	VBD
37681	404	9	the	the	DT
37681	404	10	first	first	JJ
37681	404	11	book	book	NN
37681	404	12	bearing	bear	VBG
37681	404	13	the	the	DT
37681	404	14	name	name	NN
37681	404	15	"	"	``
37681	404	16	algebra	algebra	NN
37681	404	17	"	"	''
37681	404	18	(	(	-LRB-
37681	404	19	"	"	``
37681	404	20	Al	Al	NNP
37681	404	21	-	-	HYPH
37681	404	22	jabr	jabr	NNP
37681	404	23	wa'l	wa'l	NNP
37681	404	24	-	-	HYPH
37681	404	25	muq[=a]balah	muq[=a]balah	NNP
37681	404	26	,	,	,
37681	404	27	"	"	``
37681	404	28	Restoration	Restoration	NNP
37681	404	29	and	and	CC
37681	404	30	Equation	Equation	NNP
37681	404	31	)	)	-RRB-
37681	404	32	,	,	,
37681	404	33	composed	compose	VBD
37681	404	34	an	an	DT
37681	404	35	arithmetic	arithmetic	JJ
37681	404	36	using	use	VBG
37681	404	37	the	the	DT
37681	404	38	Hindu	Hindu	NNP
37681	404	39	numerals,[20	numerals,[20	NNP
37681	404	40	]	]	-RRB-
37681	404	41	and	and	CC
37681	404	42	paid	pay	VBD
37681	404	43	much	much	JJ
37681	404	44	attention	attention	NN
37681	404	45	to	to	IN
37681	404	46	geometry	geometry	NN
37681	404	47	and	and	CC
37681	404	48	trigonometry	trigonometry	VB
37681	404	49	.	.	.
37681	405	1	Euclid	Euclid	NNP
37681	405	2	was	be	VBD
37681	405	3	translated	translate	VBN
37681	405	4	from	from	IN
37681	405	5	the	the	DT
37681	405	6	Arabic	Arabic	NNP
37681	405	7	into	into	IN
37681	405	8	Latin	Latin	NNPS
37681	405	9	in	in	IN
37681	405	10	the	the	DT
37681	405	11	twelfth	twelfth	JJ
37681	405	12	century	century	NN
37681	405	13	,	,	,
37681	405	14	Greek	greek	JJ
37681	405	15	manuscripts	manuscript	NNS
37681	405	16	not	not	RB
37681	405	17	being	be	VBG
37681	405	18	then	then	RB
37681	405	19	at	at	IN
37681	405	20	hand	hand	NN
37681	405	21	,	,	,
37681	405	22	or	or	CC
37681	405	23	being	be	VBG
37681	405	24	neglected	neglect	VBN
37681	405	25	because	because	IN
37681	405	26	of	of	IN
37681	405	27	ignorance	ignorance	NN
37681	405	28	of	of	IN
37681	405	29	the	the	DT
37681	405	30	language	language	NN
37681	405	31	.	.	.
37681	406	1	The	the	DT
37681	406	2	leading	lead	VBG
37681	406	3	translators	translator	NNS
37681	406	4	were	be	VBD
37681	406	5	Athelhard	Athelhard	NNP
37681	406	6	of	of	IN
37681	406	7	Bath	Bath	NNP
37681	406	8	(	(	-LRB-
37681	406	9	1120	1120	CD
37681	406	10	)	)	-RRB-
37681	406	11	,	,	,
37681	406	12	an	an	DT
37681	406	13	English	english	JJ
37681	406	14	monk	monk	NN
37681	406	15	;	;	:
37681	406	16	Gherard	Gherard	NNP
37681	406	17	of	of	IN
37681	406	18	Cremona	Cremona	NNP
37681	406	19	(	(	-LRB-
37681	406	20	1160	1160	CD
37681	406	21	)	)	-RRB-
37681	406	22	,	,	,
37681	406	23	an	an	DT
37681	406	24	Italian	italian	JJ
37681	406	25	monk	monk	NN
37681	406	26	;	;	:
37681	406	27	and	and	CC
37681	406	28	Johannes	Johannes	NNP
37681	406	29	Campanus	Campanus	NNP
37681	406	30	(	(	-LRB-
37681	406	31	1250	1250	CD
37681	406	32	)	)	-RRB-
37681	406	33	,	,	,
37681	406	34	chaplain	chaplain	VB
37681	406	35	to	to	IN
37681	406	36	Pope	Pope	NNP
37681	406	37	Urban	Urban	NNP
37681	406	38	IV	IV	NNP
37681	406	39	.	.	.
37681	407	1	The	the	DT
37681	407	2	greatest	great	JJS
37681	407	3	European	european	JJ
37681	407	4	mathematician	mathematician	NN
37681	407	5	of	of	IN
37681	407	6	the	the	DT
37681	407	7	Middle	Middle	NNP
37681	407	8	Ages	Ages	NNPS
37681	407	9	was	be	VBD
37681	407	10	Leonardo	Leonardo	NNP
37681	407	11	of	of	IN
37681	407	12	Pisa[21	Pisa[21	NNP
37681	407	13	]	]	-RRB-
37681	407	14	(	(	-LRB-
37681	407	15	_	_	NNP
37681	407	16	ca	ca	NNP
37681	407	17	.	.	.
37681	407	18	_	_	NNP
37681	407	19	1170	1170	CD
37681	407	20	-	-	SYM
37681	407	21	1250	1250	CD
37681	407	22	)	)	-RRB-
37681	407	23	.	.	.
37681	408	1	He	-PRON-	PRP
37681	408	2	was	be	VBD
37681	408	3	very	very	RB
37681	408	4	influential	influential	JJ
37681	408	5	in	in	IN
37681	408	6	making	make	VBG
37681	408	7	the	the	DT
37681	408	8	Hindu	hindu	JJ
37681	408	9	-	-	HYPH
37681	408	10	Arabic	arabic	JJ
37681	408	11	numerals	numeral	NNS
37681	408	12	known	know	VBN
37681	408	13	in	in	IN
37681	408	14	Europe	Europe	NNP
37681	408	15	,	,	,
37681	408	16	wrote	write	VBD
37681	408	17	extensively	extensively	RB
37681	408	18	on	on	IN
37681	408	19	algebra	algebra	NN
37681	408	20	,	,	,
37681	408	21	and	and	CC
37681	408	22	was	be	VBD
37681	408	23	the	the	DT
37681	408	24	author	author	NN
37681	408	25	of	of	IN
37681	408	26	one	one	CD
37681	408	27	book	book	NN
37681	408	28	on	on	IN
37681	408	29	geometry	geometry	NN
37681	408	30	.	.	.
37681	409	1	He	-PRON-	PRP
37681	409	2	contributed	contribute	VBD
37681	409	3	nothing	nothing	NN
37681	409	4	to	to	IN
37681	409	5	the	the	DT
37681	409	6	elementary	elementary	JJ
37681	409	7	theory	theory	NN
37681	409	8	,	,	,
37681	409	9	however	however	RB
37681	409	10	.	.	.
37681	410	1	The	the	DT
37681	410	2	first	first	JJ
37681	410	3	edition	edition	NN
37681	410	4	of	of	IN
37681	410	5	Euclid	Euclid	NNP
37681	410	6	was	be	VBD
37681	410	7	printed	print	VBN
37681	410	8	in	in	IN
37681	410	9	Latin	Latin	NNP
37681	410	10	in	in	IN
37681	410	11	1482	1482	CD
37681	410	12	,	,	,
37681	410	13	the	the	DT
37681	410	14	first	first	JJ
37681	410	15	one	one	CD
37681	410	16	in	in	IN
37681	410	17	English	English	NNP
37681	410	18	appearing	appear	VBG
37681	410	19	in	in	IN
37681	410	20	1570	1570	CD
37681	410	21	.	.	.
37681	411	1	Our	-PRON-	PRP$
37681	411	2	symbols	symbol	NNS
37681	411	3	are	be	VBP
37681	411	4	modern	modern	JJ
37681	411	5	,	,	,
37681	411	6	+	+	NFP
37681	411	7	and	and	CC
37681	411	8	-	-	HYPH
37681	411	9	first	first	RB
37681	411	10	appearing	appear	VBG
37681	411	11	in	in	IN
37681	411	12	a	a	DT
37681	411	13	German	german	JJ
37681	411	14	work	work	NN
37681	411	15	in	in	IN
37681	411	16	1489	1489	CD
37681	411	17	;	;	:
37681	411	18	=	=	NFP
37681	411	19	in	in	IN
37681	411	20	Recorde	Recorde	NNP
37681	411	21	's	's	POS
37681	411	22	"	"	``
37681	411	23	Whetstone	Whetstone	NNP
37681	411	24	of	of	IN
37681	411	25	Witte	Witte	NNP
37681	411	26	"	"	''
37681	411	27	in	in	IN
37681	411	28	1557	1557	CD
37681	411	29	;	;	:
37681	411	30	>	>	XX
37681	411	31	and	and	CC
37681	411	32	<	<	XX
37681	411	33	in	in	IN
37681	411	34	the	the	DT
37681	411	35	works	work	NNS
37681	411	36	of	of	IN
37681	411	37	Harriot	Harriot	NNP
37681	411	38	(	(	-LRB-
37681	411	39	1560	1560	CD
37681	411	40	-	-	SYM
37681	411	41	1621	1621	CD
37681	411	42	)	)	-RRB-
37681	411	43	;	;	:
37681	411	44	and	and	CC
37681	411	45	×	×	NNS
37681	411	46	in	in	IN
37681	411	47	a	a	DT
37681	411	48	publication	publication	NN
37681	411	49	by	by	IN
37681	411	50	Oughtred	Oughtred	NNP
37681	411	51	(	(	-LRB-
37681	411	52	1574	1574	CD
37681	411	53	-	-	SYM
37681	411	54	1660	1660	CD
37681	411	55	)	)	-RRB-
37681	411	56	.	.	.
37681	412	1	The	the	DT
37681	412	2	most	most	RBS
37681	412	3	noteworthy	noteworthy	JJ
37681	412	4	advance	advance	NN
37681	412	5	in	in	IN
37681	412	6	geometry	geometry	NN
37681	412	7	in	in	IN
37681	412	8	modern	modern	JJ
37681	412	9	times	time	NNS
37681	412	10	was	be	VBD
37681	412	11	made	make	VBN
37681	412	12	by	by	IN
37681	412	13	the	the	DT
37681	412	14	great	great	JJ
37681	412	15	French	french	JJ
37681	412	16	philosopher	philosopher	NN
37681	412	17	Descartes	Descartes	NNPS
37681	412	18	,	,	,
37681	412	19	who	who	WP
37681	412	20	published	publish	VBD
37681	412	21	a	a	DT
37681	412	22	small	small	JJ
37681	412	23	work	work	NN
37681	412	24	entitled	entitle	VBN
37681	412	25	"	"	``
37681	412	26	La	La	NNP
37681	412	27	Géométrie	Géométrie	NNP
37681	412	28	"	"	''
37681	412	29	in	in	IN
37681	412	30	1637	1637	CD
37681	412	31	.	.	.
37681	413	1	From	from	IN
37681	413	2	this	this	DT
37681	413	3	springs	spring	NNS
37681	413	4	the	the	DT
37681	413	5	modern	modern	JJ
37681	413	6	analytic	analytic	JJ
37681	413	7	geometry	geometry	NN
37681	413	8	,	,	,
37681	413	9	a	a	DT
37681	413	10	subject	subject	NN
37681	413	11	that	that	WDT
37681	413	12	has	have	VBZ
37681	413	13	revolutionized	revolutionize	VBN
37681	413	14	the	the	DT
37681	413	15	methods	method	NNS
37681	413	16	of	of	IN
37681	413	17	all	all	DT
37681	413	18	mathematics	mathematic	NNS
37681	413	19	.	.	.
37681	414	1	Most	Most	JJS
37681	414	2	of	of	IN
37681	414	3	the	the	DT
37681	414	4	subsequent	subsequent	JJ
37681	414	5	discoveries	discovery	NNS
37681	414	6	in	in	IN
37681	414	7	mathematics	mathematic	NNS
37681	414	8	have	have	VBP
37681	414	9	been	be	VBN
37681	414	10	in	in	IN
37681	414	11	higher	high	JJR
37681	414	12	branches	branch	NNS
37681	414	13	.	.	.
37681	415	1	To	to	IN
37681	415	2	the	the	DT
37681	415	3	great	great	JJ
37681	415	4	Swiss	swiss	JJ
37681	415	5	mathematician	mathematician	NN
37681	415	6	Euler	euler	NN
37681	415	7	(	(	-LRB-
37681	415	8	1707	1707	CD
37681	415	9	-	-	SYM
37681	415	10	1783	1783	CD
37681	415	11	)	)	-RRB-
37681	415	12	is	be	VBZ
37681	415	13	due	due	JJ
37681	415	14	,	,	,
37681	415	15	however	however	RB
37681	415	16	,	,	,
37681	415	17	one	one	CD
37681	415	18	proposition	proposition	NN
37681	415	19	that	that	WDT
37681	415	20	has	have	VBZ
37681	415	21	found	find	VBN
37681	415	22	its	-PRON-	PRP$
37681	415	23	way	way	NN
37681	415	24	into	into	IN
37681	415	25	elementary	elementary	JJ
37681	415	26	geometry	geometry	NN
37681	415	27	,	,	,
37681	415	28	the	the	DT
37681	415	29	one	one	NN
37681	415	30	showing	show	VBG
37681	415	31	the	the	DT
37681	415	32	relation	relation	NN
37681	415	33	between	between	IN
37681	415	34	the	the	DT
37681	415	35	number	number	NN
37681	415	36	of	of	IN
37681	415	37	edges	edge	NNS
37681	415	38	,	,	,
37681	415	39	vertices	vertex	NNS
37681	415	40	,	,	,
37681	415	41	and	and	CC
37681	415	42	faces	face	NNS
37681	415	43	of	of	IN
37681	415	44	a	a	DT
37681	415	45	polyhedron	polyhedron	NN
37681	415	46	.	.	.
37681	416	1	There	there	EX
37681	416	2	has	have	VBZ
37681	416	3	of	of	IN
37681	416	4	late	late	JJ
37681	416	5	arisen	arise	VBN
37681	416	6	a	a	DT
37681	416	7	modern	modern	JJ
37681	416	8	elementary	elementary	JJ
37681	416	9	geometry	geometry	NN
37681	416	10	devoted	devote	VBN
37681	416	11	chiefly	chiefly	RB
37681	416	12	to	to	IN
37681	416	13	special	special	JJ
37681	416	14	points	point	NNS
37681	416	15	and	and	CC
37681	416	16	lines	line	NNS
37681	416	17	relating	relate	VBG
37681	416	18	to	to	IN
37681	416	19	the	the	DT
37681	416	20	triangle	triangle	NN
37681	416	21	and	and	CC
37681	416	22	the	the	DT
37681	416	23	circle	circle	NN
37681	416	24	,	,	,
37681	416	25	and	and	CC
37681	416	26	many	many	JJ
37681	416	27	interesting	interesting	JJ
37681	416	28	propositions	proposition	NNS
37681	416	29	have	have	VBP
37681	416	30	been	be	VBN
37681	416	31	discovered	discover	VBN
37681	416	32	.	.	.
37681	417	1	The	the	DT
37681	417	2	subject	subject	NN
37681	417	3	is	be	VBZ
37681	417	4	so	so	RB
37681	417	5	extensive	extensive	JJ
37681	417	6	that	that	IN
37681	417	7	it	-PRON-	PRP
37681	417	8	can	can	MD
37681	417	9	not	not	RB
37681	417	10	find	find	VB
37681	417	11	any	any	DT
37681	417	12	place	place	NN
37681	417	13	in	in	IN
37681	417	14	our	-PRON-	PRP$
37681	417	15	crowded	crowded	JJ
37681	417	16	curriculum	curriculum	NN
37681	417	17	,	,	,
37681	417	18	and	and	CC
37681	417	19	must	must	MD
37681	417	20	necessarily	necessarily	RB
37681	417	21	be	be	VB
37681	417	22	left	leave	VBN
37681	417	23	to	to	IN
37681	417	24	the	the	DT
37681	417	25	specialist	specialist	NN
37681	417	26	.	.	.
37681	418	1	[	[	-LRB-
37681	418	2	22	22	CD
37681	418	3	]	]	-RRB-
37681	418	4	Some	some	DT
37681	418	5	idea	idea	NN
37681	418	6	of	of	IN
37681	418	7	the	the	DT
37681	418	8	nature	nature	NN
37681	418	9	of	of	IN
37681	418	10	the	the	DT
37681	418	11	work	work	NN
37681	418	12	may	may	MD
37681	418	13	be	be	VB
37681	418	14	obtained	obtain	VBN
37681	418	15	from	from	IN
37681	418	16	a	a	DT
37681	418	17	mention	mention	NN
37681	418	18	of	of	IN
37681	418	19	a	a	DT
37681	418	20	few	few	JJ
37681	418	21	propositions	proposition	NNS
37681	418	22	:	:	:
37681	418	23	The	the	DT
37681	418	24	medians	median	NNS
37681	418	25	of	of	IN
37681	418	26	a	a	DT
37681	418	27	triangle	triangle	NN
37681	418	28	are	be	VBP
37681	418	29	concurrent	concurrent	JJ
37681	418	30	in	in	IN
37681	418	31	the	the	DT
37681	418	32	centroid	centroid	NN
37681	418	33	,	,	,
37681	418	34	or	or	CC
37681	418	35	center	center	NN
37681	418	36	of	of	IN
37681	418	37	gravity	gravity	NN
37681	418	38	of	of	IN
37681	418	39	the	the	DT
37681	418	40	triangle	triangle	NN
37681	418	41	.	.	.
37681	419	1	The	the	DT
37681	419	2	bisectors	bisector	NNS
37681	419	3	of	of	IN
37681	419	4	the	the	DT
37681	419	5	various	various	JJ
37681	419	6	interior	interior	NN
37681	419	7	and	and	CC
37681	419	8	exterior	exterior	JJ
37681	419	9	angles	angle	NNS
37681	419	10	of	of	IN
37681	419	11	a	a	DT
37681	419	12	triangle	triangle	NN
37681	419	13	are	be	VBP
37681	419	14	concurrent	concurrent	JJ
37681	419	15	by	by	IN
37681	419	16	threes	three	NNS
37681	419	17	in	in	IN
37681	419	18	the	the	DT
37681	419	19	incenter	incenter	NN
37681	419	20	or	or	CC
37681	419	21	in	in	IN
37681	419	22	one	one	CD
37681	419	23	of	of	IN
37681	419	24	the	the	DT
37681	419	25	three	three	CD
37681	419	26	excenters	excenter	NNS
37681	419	27	of	of	IN
37681	419	28	the	the	DT
37681	419	29	triangle	triangle	NN
37681	419	30	.	.	.
37681	420	1	The	the	DT
37681	420	2	common	common	JJ
37681	420	3	chord	chord	NN
37681	420	4	of	of	IN
37681	420	5	two	two	CD
37681	420	6	intersecting	intersect	VBG
37681	420	7	circles	circle	NNS
37681	420	8	is	be	VBZ
37681	420	9	a	a	DT
37681	420	10	special	special	JJ
37681	420	11	case	case	NN
37681	420	12	of	of	IN
37681	420	13	their	-PRON-	PRP$
37681	420	14	radical	radical	JJ
37681	420	15	axis	axi	NNS
37681	420	16	,	,	,
37681	420	17	and	and	CC
37681	420	18	tangents	tangent	VBZ
37681	420	19	to	to	IN
37681	420	20	the	the	DT
37681	420	21	circles	circle	NNS
37681	420	22	from	from	IN
37681	420	23	any	any	DT
37681	420	24	point	point	NN
37681	420	25	on	on	IN
37681	420	26	the	the	DT
37681	420	27	radical	radical	JJ
37681	420	28	axis	axi	NNS
37681	420	29	are	be	VBP
37681	420	30	equal	equal	JJ
37681	420	31	.	.	.
37681	421	1	If	if	IN
37681	421	2	_	_	NNP
37681	421	3	O	O	NNP
37681	421	4	_	_	NNP
37681	421	5	is	be	VBZ
37681	421	6	the	the	DT
37681	421	7	orthocenter	orthocenter	NN
37681	421	8	of	of	IN
37681	421	9	the	the	DT
37681	421	10	triangle	triangle	NN
37681	421	11	_	_	NNP
37681	421	12	ABC	ABC	NNP
37681	421	13	_	_	NNP
37681	421	14	,	,	,
37681	421	15	and	and	CC
37681	421	16	_	_	NNP
37681	421	17	X	X	NNP
37681	421	18	_	_	NNP
37681	421	19	,	,	,
37681	421	20	_	_	NNP
37681	421	21	Y	Y	NNP
37681	421	22	_	_	NNP
37681	421	23	,	,	,
37681	421	24	_	_	NNP
37681	421	25	Z	Z	NNP
37681	421	26	_	_	NNP
37681	421	27	are	be	VBP
37681	421	28	the	the	DT
37681	421	29	feet	foot	NNS
37681	421	30	of	of	IN
37681	421	31	the	the	DT
37681	421	32	perpendiculars	perpendicular	NNS
37681	421	33	from	from	IN
37681	421	34	_	_	NNP
37681	421	35	A	A	NNP
37681	421	36	_	_	NNP
37681	421	37	,	,	,
37681	421	38	_	_	NNP
37681	421	39	B	B	NNP
37681	421	40	_	_	NNP
37681	421	41	,	,	,
37681	421	42	_	_	NNP
37681	421	43	C	C	NNP
37681	421	44	_	_	NNP
37681	421	45	respectively	respectively	RB
37681	421	46	,	,	,
37681	421	47	and	and	CC
37681	421	48	_	_	NNP
37681	421	49	P	P	NNP
37681	421	50	_	_	NNP
37681	421	51	,	,	,
37681	421	52	_	_	NNP
37681	421	53	Q	Q	NNP
37681	421	54	_	_	NNP
37681	421	55	,	,	,
37681	421	56	_	_	NNP
37681	421	57	R	R	NNP
37681	421	58	_	_	NNP
37681	421	59	are	be	VBP
37681	421	60	the	the	DT
37681	421	61	mid	mid	NN
37681	421	62	-	-	NN
37681	421	63	points	point	NNS
37681	421	64	of	of	IN
37681	421	65	_	_	NNP
37681	421	66	a	a	DT
37681	421	67	_	_	NNP
37681	421	68	,	,	,
37681	421	69	_	_	NNP
37681	421	70	b	b	NNP
37681	421	71	_	_	NNP
37681	421	72	,	,	,
37681	421	73	_	_	NNP
37681	421	74	c	c	NNP
37681	421	75	_	_	NNP
37681	421	76	respectively	respectively	RB
37681	421	77	,	,	,
37681	421	78	and	and	CC
37681	421	79	_	_	NNP
37681	421	80	L	L	NNP
37681	421	81	_	_	NNP
37681	421	82	,	,	,
37681	421	83	_	_	NNP
37681	421	84	M	M	NNP
37681	421	85	_	_	NNP
37681	421	86	,	,	,
37681	421	87	_	_	NNP
37681	421	88	N	N	NNP
37681	421	89	_	_	NNP
37681	421	90	are	be	VBP
37681	421	91	the	the	DT
37681	421	92	mid	mid	NN
37681	421	93	-	-	NN
37681	421	94	points	point	NNS
37681	421	95	of	of	IN
37681	421	96	_	_	NNP
37681	421	97	OA	OA	NNP
37681	421	98	_	_	NNP
37681	421	99	,	,	,
37681	421	100	_	_	NNP
37681	421	101	OB	OB	NNP
37681	421	102	_	_	NNP
37681	421	103	,	,	,
37681	421	104	_	_	NNP
37681	421	105	OC	OC	NNP
37681	421	106	_	_	NNP
37681	421	107	respectively	respectively	RB
37681	421	108	;	;	:
37681	421	109	then	then	RB
37681	421	110	the	the	DT
37681	421	111	points	point	NNS
37681	421	112	_	_	NNP
37681	421	113	L	L	NNP
37681	421	114	_	_	NNP
37681	421	115	,	,	,
37681	421	116	_	_	NNP
37681	421	117	M	M	NNP
37681	421	118	_	_	NNP
37681	421	119	,	,	,
37681	421	120	_	_	NNP
37681	421	121	N	N	NNP
37681	421	122	_	_	NNP
37681	421	123	;	;	:
37681	421	124	_	_	NNP
37681	421	125	P	P	NNP
37681	421	126	_	_	NNP
37681	421	127	,	,	,
37681	421	128	_	_	NNP
37681	421	129	Q	Q	NNP
37681	421	130	_	_	NNP
37681	421	131	,	,	,
37681	421	132	_	_	NNP
37681	421	133	R	R	NNP
37681	421	134	_	_	NNP
37681	421	135	;	;	:
37681	421	136	_	_	NNP
37681	421	137	X	X	NNP
37681	421	138	_	_	NNP
37681	421	139	,	,	,
37681	421	140	_	_	NNP
37681	421	141	Y	Y	NNP
37681	421	142	_	_	NNP
37681	421	143	,	,	,
37681	421	144	_	_	NNP
37681	421	145	Z	Z	NNP
37681	421	146	_	_	NNP
37681	421	147	all	all	DT
37681	421	148	lie	lie	NN
37681	421	149	on	on	IN
37681	421	150	a	a	DT
37681	421	151	circle	circle	NN
37681	421	152	,	,	,
37681	421	153	the	the	DT
37681	421	154	"	"	``
37681	421	155	nine	nine	CD
37681	421	156	points	point	NNS
37681	421	157	circle	circle	NN
37681	421	158	.	.	.
37681	421	159	"	"	''
37681	422	1	In	in	IN
37681	422	2	the	the	DT
37681	422	3	teaching	teaching	NN
37681	422	4	of	of	IN
37681	422	5	geometry	geometry	NN
37681	422	6	it	-PRON-	PRP
37681	422	7	adds	add	VBZ
37681	422	8	a	a	DT
37681	422	9	human	human	JJ
37681	422	10	interest	interest	NN
37681	422	11	to	to	IN
37681	422	12	the	the	DT
37681	422	13	subject	subject	NN
37681	422	14	to	to	TO
37681	422	15	mention	mention	VB
37681	422	16	occasionally	occasionally	RB
37681	422	17	some	some	DT
37681	422	18	of	of	IN
37681	422	19	the	the	DT
37681	422	20	historical	historical	JJ
37681	422	21	facts	fact	NNS
37681	422	22	connected	connect	VBN
37681	422	23	with	with	IN
37681	422	24	it	-PRON-	PRP
37681	422	25	.	.	.
37681	423	1	For	for	IN
37681	423	2	this	this	DT
37681	423	3	reason	reason	NN
37681	423	4	this	this	DT
37681	423	5	brief	brief	JJ
37681	423	6	sketch	sketch	NN
37681	423	7	will	will	MD
37681	423	8	be	be	VB
37681	423	9	supplemented	supplement	VBN
37681	423	10	by	by	IN
37681	423	11	many	many	JJ
37681	423	12	notes	note	NNS
37681	423	13	upon	upon	IN
37681	423	14	the	the	DT
37681	423	15	various	various	JJ
37681	423	16	important	important	JJ
37681	423	17	propositions	proposition	NNS
37681	423	18	as	as	IN
37681	423	19	they	-PRON-	PRP
37681	423	20	occur	occur	VBP
37681	423	21	in	in	IN
37681	423	22	the	the	DT
37681	423	23	several	several	JJ
37681	423	24	books	book	NNS
37681	423	25	described	describe	VBN
37681	423	26	in	in	IN
37681	423	27	the	the	DT
37681	423	28	later	later	JJ
37681	423	29	chapters	chapter	NNS
37681	423	30	of	of	IN
37681	423	31	this	this	DT
37681	423	32	work	work	NN
37681	423	33	.	.	.
37681	424	1	FOOTNOTES	footnote	NNS
37681	424	2	:	:	:
37681	424	3	[	[	-LRB-
37681	424	4	16	16	CD
37681	424	5	]	]	-RRB-
37681	424	6	It	-PRON-	PRP
37681	424	7	was	be	VBD
37681	424	8	published	publish	VBN
37681	424	9	in	in	IN
37681	424	10	German	german	JJ
37681	424	11	translation	translation	NN
37681	424	12	by	by	IN
37681	424	13	A.	a.	NN
37681	424	14	Eisenlohr	Eisenlohr	NNP
37681	424	15	,	,	,
37681	424	16	"	"	``
37681	424	17	Ein	Ein	NNP
37681	424	18	mathematisches	mathematische	NNS
37681	424	19	Handbuch	Handbuch	NNP
37681	424	20	der	der	NN
37681	424	21	alten	alten	VB
37681	424	22	Aegypter	Aegypter	NNP
37681	424	23	,	,	,
37681	424	24	"	"	''
37681	424	25	Leipzig	Leipzig	NNP
37681	424	26	,	,	,
37681	424	27	1877	1877	CD
37681	424	28	,	,	,
37681	424	29	and	and	CC
37681	424	30	in	in	IN
37681	424	31	facsimile	facsimile	NN
37681	424	32	by	by	IN
37681	424	33	the	the	DT
37681	424	34	British	British	NNP
37681	424	35	Museum	Museum	NNP
37681	424	36	,	,	,
37681	424	37	under	under	IN
37681	424	38	the	the	DT
37681	424	39	title	title	NN
37681	424	40	,	,	,
37681	424	41	"	"	``
37681	424	42	The	the	DT
37681	424	43	Rhind	Rhind	NNP
37681	424	44	Papyrus	Papyrus	NNP
37681	424	45	,	,	,
37681	424	46	"	"	''
37681	424	47	in	in	IN
37681	424	48	1898	1898	CD
37681	424	49	.	.	.
37681	425	1	[	[	-LRB-
37681	425	2	17	17	CD
37681	425	3	]	]	-RRB-
37681	425	4	Generally	generally	RB
37681	425	5	known	know	VBN
37681	425	6	as	as	IN
37681	425	7	Rameses	Rameses	NNP
37681	425	8	II	ii	CD
37681	425	9	.	.	.
37681	426	1	He	-PRON-	PRP
37681	426	2	reigned	reign	VBD
37681	426	3	in	in	IN
37681	426	4	Egypt	Egypt	NNP
37681	426	5	about	about	IN
37681	426	6	1350	1350	CD
37681	426	7	B.C.	B.C.	NNP
37681	427	1	[	[	-LRB-
37681	427	2	18	18	CD
37681	427	3	]	]	-RRB-
37681	427	4	Two	two	CD
37681	427	5	excellent	excellent	JJ
37681	427	6	works	work	NNS
37681	427	7	on	on	IN
37681	427	8	Thales	Thales	NNPS
37681	427	9	and	and	CC
37681	427	10	his	-PRON-	PRP$
37681	427	11	successors	successor	NNS
37681	427	12	,	,	,
37681	427	13	and	and	CC
37681	427	14	indeed	indeed	RB
37681	427	15	the	the	DT
37681	427	16	best	good	JJS
37681	427	17	in	in	IN
37681	427	18	English	English	NNP
37681	427	19	,	,	,
37681	427	20	are	be	VBP
37681	427	21	the	the	DT
37681	427	22	following	follow	VBG
37681	427	23	:	:	:
37681	427	24	G.	G.	NNP
37681	427	25	J.	J.	NNP
37681	427	26	Allman	Allman	NNP
37681	427	27	,	,	,
37681	427	28	"	"	``
37681	427	29	Greek	Greek	NNP
37681	427	30	Geometry	Geometry	NNP
37681	427	31	from	from	IN
37681	427	32	Thales	thale	NNS
37681	427	33	to	to	IN
37681	427	34	Euclid	Euclid	NNP
37681	427	35	,	,	,
37681	427	36	"	"	''
37681	427	37	Dublin	Dublin	NNP
37681	427	38	,	,	,
37681	427	39	1889	1889	CD
37681	427	40	;	;	:
37681	427	41	J.	J.	NNP
37681	427	42	Gow	Gow	NNP
37681	427	43	,	,	,
37681	427	44	"	"	``
37681	427	45	A	a	DT
37681	427	46	History	history	NN
37681	427	47	of	of	IN
37681	427	48	Greek	Greek	NNP
37681	427	49	Mathematics	Mathematics	NNP
37681	427	50	,	,	,
37681	427	51	"	"	''
37681	427	52	Cambridge	Cambridge	NNP
37681	427	53	,	,	,
37681	427	54	1884	1884	CD
37681	427	55	.	.	.
37681	428	1	On	on	IN
37681	428	2	all	all	DT
37681	428	3	mathematical	mathematical	JJ
37681	428	4	subjects	subject	NNS
37681	428	5	the	the	DT
37681	428	6	best	good	JJS
37681	428	7	general	general	JJ
37681	428	8	history	history	NN
37681	428	9	is	be	VBZ
37681	428	10	that	that	DT
37681	428	11	of	of	IN
37681	428	12	M.	M.	NNP
37681	428	13	Cantor	Cantor	NNP
37681	428	14	,	,	,
37681	428	15	"	"	``
37681	428	16	Geschichte	Geschichte	NNP
37681	428	17	der	der	VBP
37681	428	18	Mathematik	Mathematik	NNP
37681	428	19	,	,	,
37681	428	20	"	"	``
37681	428	21	4	4	CD
37681	428	22	vols	vol	NNS
37681	428	23	,	,	,
37681	428	24	Leipzig	Leipzig	NNP
37681	428	25	,	,	,
37681	428	26	1880	1880	CD
37681	428	27	-	-	SYM
37681	428	28	1908	1908	CD
37681	428	29	.	.	.
37681	429	1	[	[	-LRB-
37681	429	2	19	19	CD
37681	429	3	]	]	-RRB-
37681	429	4	Another	another	DT
37681	429	5	good	good	JJ
37681	429	6	work	work	NN
37681	429	7	on	on	IN
37681	429	8	Greek	greek	JJ
37681	429	9	geometry	geometry	NN
37681	429	10	,	,	,
37681	429	11	with	with	IN
37681	429	12	considerable	considerable	JJ
37681	429	13	material	material	NN
37681	429	14	on	on	IN
37681	429	15	Pythagoras	Pythagoras	NNP
37681	429	16	,	,	,
37681	429	17	is	be	VBZ
37681	429	18	by	by	IN
37681	429	19	C.	C.	NNP
37681	429	20	A.	A.	NNP
37681	429	21	Bretschneider	Bretschneider	NNP
37681	429	22	,	,	,
37681	429	23	"	"	``
37681	429	24	Die	Die	NNP
37681	429	25	Geometrie	Geometrie	NNP
37681	429	26	und	und	NN
37681	429	27	die	die	VBP
37681	429	28	Geometer	Geometer	NNP
37681	429	29	vor	vor	NNP
37681	429	30	Eukleides	Eukleides	NNP
37681	429	31	,	,	,
37681	429	32	"	"	``
37681	429	33	Leipzig	Leipzig	NNP
37681	429	34	,	,	,
37681	429	35	1870	1870	CD
37681	429	36	.	.	.
37681	430	1	[	[	-LRB-
37681	430	2	20	20	CD
37681	430	3	]	]	-RRB-
37681	430	4	Smith	Smith	NNP
37681	430	5	and	and	CC
37681	430	6	Karpinski	Karpinski	NNP
37681	430	7	,	,	,
37681	430	8	"	"	``
37681	430	9	The	the	DT
37681	430	10	Hindu	Hindu	NNP
37681	430	11	-	-	HYPH
37681	430	12	Arabic	Arabic	NNP
37681	430	13	Numerals	Numerals	NNPS
37681	430	14	,	,	,
37681	430	15	"	"	''
37681	430	16	Boston	Boston	NNP
37681	430	17	,	,	,
37681	430	18	1911	1911	CD
37681	430	19	.	.	.
37681	431	1	[	[	-LRB-
37681	431	2	21	21	CD
37681	431	3	]	]	-RRB-
37681	431	4	For	for	IN
37681	431	5	a	a	DT
37681	431	6	sketch	sketch	NN
37681	431	7	of	of	IN
37681	431	8	his	-PRON-	PRP$
37681	431	9	life	life	NN
37681	431	10	see	see	VBP
37681	431	11	Smith	Smith	NNP
37681	431	12	and	and	CC
37681	431	13	Karpinski	Karpinski	NNP
37681	431	14	,	,	,
37681	431	15	loc	loc	NNP
37681	431	16	.	.	.
37681	432	1	cit	cit	NNP
37681	432	2	.	.	.
37681	433	1	[	[	-LRB-
37681	433	2	22	22	CD
37681	433	3	]	]	-RRB-
37681	433	4	Those	those	DT
37681	433	5	who	who	WP
37681	433	6	care	care	VBP
37681	433	7	for	for	IN
37681	433	8	a	a	DT
37681	433	9	brief	brief	JJ
37681	433	10	description	description	NN
37681	433	11	of	of	IN
37681	433	12	this	this	DT
37681	433	13	phase	phase	NN
37681	433	14	of	of	IN
37681	433	15	the	the	DT
37681	433	16	subject	subject	NN
37681	433	17	may	may	MD
37681	433	18	consult	consult	VB
37681	433	19	J.	J.	NNP
37681	433	20	Casey	Casey	NNP
37681	433	21	,	,	,
37681	433	22	"	"	``
37681	433	23	A	a	DT
37681	433	24	Sequel	Sequel	NNP
37681	433	25	to	to	IN
37681	433	26	Euclid	Euclid	NNP
37681	433	27	,	,	,
37681	433	28	"	"	''
37681	433	29	Dublin	Dublin	NNP
37681	433	30	,	,	,
37681	433	31	fifth	fifth	JJ
37681	433	32	edition	edition	NN
37681	433	33	,	,	,
37681	433	34	1888	1888	CD
37681	433	35	;	;	:
37681	433	36	W.	W.	NNP
37681	433	37	J.	J.	NNP
37681	433	38	M'Clelland	M'Clelland	NNP
37681	433	39	,	,	,
37681	433	40	"	"	``
37681	433	41	A	a	DT
37681	433	42	Treatise	Treatise	NNP
37681	433	43	on	on	IN
37681	433	44	the	the	DT
37681	433	45	Geometry	Geometry	NNP
37681	433	46	of	of	IN
37681	433	47	the	the	DT
37681	433	48	Circle	Circle	NNP
37681	433	49	,	,	,
37681	433	50	"	"	``
37681	433	51	New	New	NNP
37681	433	52	York	York	NNP
37681	433	53	,	,	,
37681	433	54	1891	1891	CD
37681	433	55	;	;	:
37681	433	56	M.	M.	NNP
37681	433	57	Simon	Simon	NNP
37681	433	58	,	,	,
37681	433	59	"	"	``
37681	433	60	Über	Über	NNP
37681	433	61	die	die	NN
37681	433	62	Entwicklung	Entwicklung	NNP
37681	433	63	der	der	VB
37681	433	64	Elementar	Elementar	NNP
37681	433	65	-	-	HYPH
37681	433	66	Geometrie	Geometrie	NNP
37681	433	67	i	-PRON-	PRP
37681	433	68	m	be	VBP
37681	433	69	XIX	XIX	NNP
37681	433	70	.	.	.
37681	434	1	Jahrhundert	Jahrhundert	NNP
37681	434	2	,	,	,
37681	434	3	"	"	``
37681	434	4	Leipzig	Leipzig	NNP
37681	434	5	,	,	,
37681	434	6	1906	1906	CD
37681	434	7	.	.	.
37681	435	1	CHAPTER	CHAPTER	NNP
37681	435	2	IV	IV	NNP
37681	435	3	DEVELOPMENT	DEVELOPMENT	NNP
37681	435	4	OF	of	IN
37681	435	5	THE	the	DT
37681	435	6	TEACHING	teaching	NN
37681	435	7	OF	of	IN
37681	435	8	GEOMETRY	GEOMETRY	NNP
37681	435	9	We	-PRON-	PRP
37681	435	10	know	know	VBP
37681	435	11	little	little	JJ
37681	435	12	of	of	IN
37681	435	13	the	the	DT
37681	435	14	teaching	teaching	NN
37681	435	15	of	of	IN
37681	435	16	geometry	geometry	NN
37681	435	17	in	in	IN
37681	435	18	very	very	RB
37681	435	19	ancient	ancient	JJ
37681	435	20	times	time	NNS
37681	435	21	,	,	,
37681	435	22	but	but	CC
37681	435	23	we	-PRON-	PRP
37681	435	24	can	can	MD
37681	435	25	infer	infer	VB
37681	435	26	its	-PRON-	PRP$
37681	435	27	nature	nature	NN
37681	435	28	from	from	IN
37681	435	29	the	the	DT
37681	435	30	teaching	teaching	NN
37681	435	31	that	that	WDT
37681	435	32	is	be	VBZ
37681	435	33	still	still	RB
37681	435	34	seen	see	VBN
37681	435	35	in	in	IN
37681	435	36	the	the	DT
37681	435	37	native	native	JJ
37681	435	38	schools	school	NNS
37681	435	39	of	of	IN
37681	435	40	the	the	DT
37681	435	41	East	East	NNP
37681	435	42	.	.	.
37681	436	1	Here	here	RB
37681	436	2	a	a	DT
37681	436	3	man	man	NN
37681	436	4	,	,	,
37681	436	5	learned	learn	VBN
37681	436	6	in	in	IN
37681	436	7	any	any	DT
37681	436	8	science	science	NN
37681	436	9	,	,	,
37681	436	10	will	will	MD
37681	436	11	have	have	VB
37681	436	12	a	a	DT
37681	436	13	group	group	NN
37681	436	14	of	of	IN
37681	436	15	voluntary	voluntary	JJ
37681	436	16	students	student	NNS
37681	436	17	sitting	sit	VBG
37681	436	18	about	about	IN
37681	436	19	him	-PRON-	PRP
37681	436	20	,	,	,
37681	436	21	and	and	CC
37681	436	22	to	to	IN
37681	436	23	them	-PRON-	PRP
37681	436	24	he	-PRON-	PRP
37681	436	25	will	will	MD
37681	436	26	expound	expound	VB
37681	436	27	the	the	DT
37681	436	28	truth	truth	NN
37681	436	29	.	.	.
37681	437	1	Such	such	JJ
37681	437	2	schools	school	NNS
37681	437	3	may	may	MD
37681	437	4	still	still	RB
37681	437	5	be	be	VB
37681	437	6	seen	see	VBN
37681	437	7	in	in	IN
37681	437	8	India	India	NNP
37681	437	9	,	,	,
37681	437	10	Persia	Persia	NNP
37681	437	11	,	,	,
37681	437	12	and	and	CC
37681	437	13	China	China	NNP
37681	437	14	,	,	,
37681	437	15	the	the	DT
37681	437	16	master	master	NN
37681	437	17	sitting	sit	VBG
37681	437	18	on	on	IN
37681	437	19	a	a	DT
37681	437	20	mat	mat	NN
37681	437	21	placed	place	VBN
37681	437	22	on	on	IN
37681	437	23	the	the	DT
37681	437	24	ground	ground	NN
37681	437	25	or	or	CC
37681	437	26	on	on	IN
37681	437	27	the	the	DT
37681	437	28	floor	floor	NN
37681	437	29	of	of	IN
37681	437	30	a	a	DT
37681	437	31	veranda	veranda	NN
37681	437	32	,	,	,
37681	437	33	and	and	CC
37681	437	34	the	the	DT
37681	437	35	pupils	pupil	NNS
37681	437	36	reading	read	VBG
37681	437	37	aloud	aloud	RB
37681	437	38	or	or	CC
37681	437	39	listening	listen	VBG
37681	437	40	to	to	IN
37681	437	41	his	-PRON-	PRP$
37681	437	42	words	word	NNS
37681	437	43	of	of	IN
37681	437	44	exposition	exposition	NN
37681	437	45	.	.	.
37681	438	1	In	in	IN
37681	438	2	Egypt	Egypt	NNP
37681	438	3	geometry	geometry	NN
37681	438	4	seems	seem	VBZ
37681	438	5	to	to	TO
37681	438	6	have	have	VB
37681	438	7	been	be	VBN
37681	438	8	in	in	IN
37681	438	9	early	early	JJ
37681	438	10	times	time	NNS
37681	438	11	mere	mere	JJ
37681	438	12	mensuration	mensuration	NN
37681	438	13	,	,	,
37681	438	14	confined	confine	VBN
37681	438	15	largely	largely	RB
37681	438	16	to	to	IN
37681	438	17	the	the	DT
37681	438	18	priestly	priestly	RB
37681	438	19	caste	caste	JJ
37681	438	20	.	.	.
37681	439	1	It	-PRON-	PRP
37681	439	2	was	be	VBD
37681	439	3	taught	teach	VBN
37681	439	4	to	to	IN
37681	439	5	novices	novice	NNS
37681	439	6	who	who	WP
37681	439	7	gave	give	VBD
37681	439	8	promise	promise	NN
37681	439	9	of	of	IN
37681	439	10	success	success	NN
37681	439	11	in	in	IN
37681	439	12	this	this	DT
37681	439	13	subject	subject	NN
37681	439	14	,	,	,
37681	439	15	and	and	CC
37681	439	16	not	not	RB
37681	439	17	to	to	IN
37681	439	18	others	other	NNS
37681	439	19	,	,	,
37681	439	20	the	the	DT
37681	439	21	idea	idea	NN
37681	439	22	of	of	IN
37681	439	23	general	general	JJ
37681	439	24	culture	culture	NN
37681	439	25	,	,	,
37681	439	26	of	of	IN
37681	439	27	training	training	NN
37681	439	28	in	in	IN
37681	439	29	logic	logic	NN
37681	439	30	,	,	,
37681	439	31	of	of	IN
37681	439	32	the	the	DT
37681	439	33	cultivation	cultivation	NN
37681	439	34	of	of	IN
37681	439	35	exact	exact	JJ
37681	439	36	expression	expression	NN
37681	439	37	,	,	,
37681	439	38	and	and	CC
37681	439	39	of	of	IN
37681	439	40	coming	come	VBG
37681	439	41	in	in	IN
37681	439	42	contact	contact	NN
37681	439	43	with	with	IN
37681	439	44	truth	truth	NN
37681	439	45	being	be	VBG
37681	439	46	wholly	wholly	RB
37681	439	47	wanting	want	VBG
37681	439	48	.	.	.
37681	440	1	In	in	IN
37681	440	2	Greece	Greece	NNP
37681	440	3	it	-PRON-	PRP
37681	440	4	was	be	VBD
37681	440	5	taught	teach	VBN
37681	440	6	in	in	IN
37681	440	7	the	the	DT
37681	440	8	schools	school	NNS
37681	440	9	of	of	IN
37681	440	10	philosophy	philosophy	NN
37681	440	11	,	,	,
37681	440	12	often	often	RB
37681	440	13	as	as	IN
37681	440	14	a	a	DT
37681	440	15	general	general	JJ
37681	440	16	preparation	preparation	NN
37681	440	17	for	for	IN
37681	440	18	philosophic	philosophic	JJ
37681	440	19	study	study	NN
37681	440	20	.	.	.
37681	441	1	Thus	thus	RB
37681	441	2	Thales	thale	NNS
37681	441	3	introduced	introduce	VBD
37681	441	4	it	-PRON-	PRP
37681	441	5	into	into	IN
37681	441	6	his	-PRON-	PRP$
37681	441	7	Ionic	ionic	JJ
37681	441	8	school	school	NN
37681	441	9	,	,	,
37681	441	10	Pythagoras	Pythagoras	NNP
37681	441	11	made	make	VBD
37681	441	12	it	-PRON-	PRP
37681	441	13	very	very	RB
37681	441	14	prominent	prominent	JJ
37681	441	15	in	in	IN
37681	441	16	his	-PRON-	PRP$
37681	441	17	great	great	JJ
37681	441	18	school	school	NN
37681	441	19	at	at	IN
37681	441	20	Crotona	Crotona	NNP
37681	441	21	in	in	IN
37681	441	22	southern	southern	JJ
37681	441	23	Italy	Italy	NNP
37681	441	24	(	(	-LRB-
37681	441	25	Magna	Magna	NNPS
37681	441	26	Græcia	Græcia	NNP
37681	441	27	)	)	-RRB-
37681	441	28	,	,	,
37681	441	29	and	and	CC
37681	441	30	Plato	Plato	NNP
37681	441	31	placed	place	VBD
37681	441	32	above	above	IN
37681	441	33	the	the	DT
37681	441	34	door	door	NN
37681	441	35	of	of	IN
37681	441	36	his	-PRON-	PRP$
37681	441	37	_	_	NNP
37681	441	38	Academia	Academia	NNP
37681	441	39	_	_	NNP
37681	441	40	the	the	DT
37681	441	41	words	word	NNS
37681	441	42	,	,	,
37681	441	43	"	"	``
37681	441	44	Let	let	VB
37681	441	45	no	no	DT
37681	441	46	one	one	CD
37681	441	47	ignorant	ignorant	NN
37681	441	48	of	of	IN
37681	441	49	geometry	geometry	NN
37681	441	50	enter	enter	VBP
37681	441	51	here,"--a	here,"--a	NNP
37681	441	52	kind	kind	RB
37681	441	53	of	of	RB
37681	441	54	entrance	entrance	NN
37681	441	55	examination	examination	NN
37681	441	56	for	for	IN
37681	441	57	his	-PRON-	PRP$
37681	441	58	school	school	NN
37681	441	59	of	of	IN
37681	441	60	philosophy	philosophy	NN
37681	441	61	.	.	.
37681	442	1	In	in	IN
37681	442	2	these	these	DT
37681	442	3	gatherings	gathering	NNS
37681	442	4	of	of	IN
37681	442	5	students	student	NNS
37681	442	6	it	-PRON-	PRP
37681	442	7	is	be	VBZ
37681	442	8	probable	probable	JJ
37681	442	9	that	that	IN
37681	442	10	geometry	geometry	NN
37681	442	11	was	be	VBD
37681	442	12	taught	teach	VBN
37681	442	13	in	in	IN
37681	442	14	much	much	RB
37681	442	15	the	the	DT
37681	442	16	way	way	NN
37681	442	17	already	already	RB
37681	442	18	mentioned	mention	VBN
37681	442	19	for	for	IN
37681	442	20	the	the	DT
37681	442	21	schools	school	NNS
37681	442	22	of	of	IN
37681	442	23	the	the	DT
37681	442	24	East	East	NNP
37681	442	25	,	,	,
37681	442	26	a	a	DT
37681	442	27	small	small	JJ
37681	442	28	group	group	NN
37681	442	29	of	of	IN
37681	442	30	students	student	NNS
37681	442	31	being	be	VBG
37681	442	32	instructed	instruct	VBN
37681	442	33	by	by	IN
37681	442	34	a	a	DT
37681	442	35	master	master	NN
37681	442	36	.	.	.
37681	443	1	Printing	printing	NN
37681	443	2	was	be	VBD
37681	443	3	unknown	unknown	JJ
37681	443	4	,	,	,
37681	443	5	papyrus	papyrus	NNP
37681	443	6	was	be	VBD
37681	443	7	dear	dear	JJ
37681	443	8	,	,	,
37681	443	9	parchment	parchment	NN
37681	443	10	was	be	VBD
37681	443	11	only	only	RB
37681	443	12	in	in	IN
37681	443	13	process	process	NN
37681	443	14	of	of	IN
37681	443	15	invention	invention	NN
37681	443	16	.	.	.
37681	444	1	Paper	paper	NN
37681	444	2	such	such	JJ
37681	444	3	as	as	IN
37681	444	4	we	-PRON-	PRP
37681	444	5	know	know	VBP
37681	444	6	had	have	VBD
37681	444	7	not	not	RB
37681	444	8	yet	yet	RB
37681	444	9	appeared	appear	VBN
37681	444	10	,	,	,
37681	444	11	so	so	IN
37681	444	12	that	that	IN
37681	444	13	instruction	instruction	NN
37681	444	14	was	be	VBD
37681	444	15	largely	largely	RB
37681	444	16	oral	oral	JJ
37681	444	17	,	,	,
37681	444	18	and	and	CC
37681	444	19	geometric	geometric	JJ
37681	444	20	figures	figure	NNS
37681	444	21	were	be	VBD
37681	444	22	drawn	draw	VBN
37681	444	23	by	by	IN
37681	444	24	a	a	DT
37681	444	25	pointed	pointed	JJ
37681	444	26	stick	stick	NN
37681	444	27	on	on	IN
37681	444	28	a	a	DT
37681	444	29	board	board	NN
37681	444	30	covered	cover	VBN
37681	444	31	with	with	IN
37681	444	32	fine	fine	JJ
37681	444	33	sand	sand	NN
37681	444	34	,	,	,
37681	444	35	or	or	CC
37681	444	36	on	on	IN
37681	444	37	a	a	DT
37681	444	38	tablet	tablet	NN
37681	444	39	of	of	IN
37681	444	40	wax	wax	NN
37681	444	41	.	.	.
37681	445	1	But	but	CC
37681	445	2	with	with	IN
37681	445	3	these	these	DT
37681	445	4	crude	crude	JJ
37681	445	5	materials	material	NNS
37681	445	6	there	there	EX
37681	445	7	went	go	VBD
37681	445	8	an	an	DT
37681	445	9	abundance	abundance	NN
37681	445	10	of	of	IN
37681	445	11	time	time	NN
37681	445	12	,	,	,
37681	445	13	so	so	IN
37681	445	14	that	that	IN
37681	445	15	a	a	DT
37681	445	16	number	number	NN
37681	445	17	of	of	IN
37681	445	18	great	great	JJ
37681	445	19	results	result	NNS
37681	445	20	were	be	VBD
37681	445	21	accomplished	accomplish	VBN
37681	445	22	in	in	IN
37681	445	23	spite	spite	NN
37681	445	24	of	of	IN
37681	445	25	the	the	DT
37681	445	26	difficulties	difficulty	NNS
37681	445	27	attending	attend	VBG
37681	445	28	the	the	DT
37681	445	29	study	study	NN
37681	445	30	of	of	IN
37681	445	31	the	the	DT
37681	445	32	subject	subject	NN
37681	445	33	.	.	.
37681	446	1	It	-PRON-	PRP
37681	446	2	is	be	VBZ
37681	446	3	said	say	VBN
37681	446	4	that	that	IN
37681	446	5	Hippocrates	hippocrate	NNS
37681	446	6	of	of	IN
37681	446	7	Chios	Chios	NNP
37681	446	8	(	(	-LRB-
37681	446	9	_	_	NNP
37681	446	10	ca	ca	NNP
37681	446	11	.	.	.
37681	446	12	_	_	NNP
37681	446	13	440	440	CD
37681	446	14	B.C.	B.C.	NNP
37681	446	15	)	)	-RRB-
37681	447	1	wrote	write	VBD
37681	447	2	the	the	DT
37681	447	3	first	first	JJ
37681	447	4	elementary	elementary	JJ
37681	447	5	textbook	textbook	NN
37681	447	6	on	on	IN
37681	447	7	mathematics	mathematic	NNS
37681	447	8	and	and	CC
37681	447	9	invented	invent	VBD
37681	447	10	the	the	DT
37681	447	11	method	method	NN
37681	447	12	of	of	IN
37681	447	13	geometric	geometric	JJ
37681	447	14	reduction	reduction	NN
37681	447	15	,	,	,
37681	447	16	the	the	DT
37681	447	17	replacing	replacing	NN
37681	447	18	of	of	IN
37681	447	19	a	a	DT
37681	447	20	proposition	proposition	NN
37681	447	21	to	to	TO
37681	447	22	be	be	VB
37681	447	23	proved	prove	VBN
37681	447	24	by	by	IN
37681	447	25	another	another	DT
37681	447	26	which	which	WDT
37681	447	27	,	,	,
37681	447	28	when	when	WRB
37681	447	29	proved	prove	VBN
37681	447	30	,	,	,
37681	447	31	allows	allow	VBZ
37681	447	32	the	the	DT
37681	447	33	first	first	JJ
37681	447	34	one	one	CD
37681	447	35	to	to	TO
37681	447	36	be	be	VB
37681	447	37	demonstrated	demonstrate	VBN
37681	447	38	.	.	.
37681	448	1	A	a	DT
37681	448	2	little	little	JJ
37681	448	3	later	later	JJ
37681	448	4	Eudoxus	eudoxus	NN
37681	448	5	of	of	IN
37681	448	6	Cnidus	Cnidus	NNP
37681	448	7	(	(	-LRB-
37681	448	8	_	_	NNP
37681	448	9	ca	ca	NNP
37681	448	10	.	.	.
37681	448	11	_	_	NNP
37681	448	12	375	375	CD
37681	448	13	B.C.	B.C.	NNP
37681	449	1	)	)	-RRB-
37681	449	2	,	,	,
37681	449	3	a	a	DT
37681	449	4	pupil	pupil	NN
37681	449	5	of	of	IN
37681	449	6	Plato	Plato	NNP
37681	449	7	's	's	POS
37681	449	8	,	,	,
37681	449	9	used	use	VBD
37681	449	10	the	the	DT
37681	449	11	_	_	NNP
37681	449	12	reductio	reductio	NN
37681	449	13	ad	ad	NN
37681	449	14	absurdum	absurdum	NN
37681	449	15	_	_	NNP
37681	449	16	,	,	,
37681	449	17	and	and	CC
37681	449	18	Plato	Plato	NNP
37681	449	19	is	be	VBZ
37681	449	20	said	say	VBN
37681	449	21	to	to	TO
37681	449	22	have	have	VB
37681	449	23	invented	invent	VBN
37681	449	24	the	the	DT
37681	449	25	method	method	NN
37681	449	26	of	of	IN
37681	449	27	proof	proof	NN
37681	449	28	by	by	IN
37681	449	29	analysis	analysis	NN
37681	449	30	,	,	,
37681	449	31	an	an	DT
37681	449	32	elaboration	elaboration	NN
37681	449	33	of	of	IN
37681	449	34	the	the	DT
37681	449	35	plan	plan	NN
37681	449	36	used	use	VBN
37681	449	37	by	by	IN
37681	449	38	Hippocrates	hippocrate	NNS
37681	449	39	.	.	.
37681	450	1	Thus	thus	RB
37681	450	2	these	these	DT
37681	450	3	early	early	JJ
37681	450	4	philosophers	philosopher	NNS
37681	450	5	taught	teach	VBD
37681	450	6	their	-PRON-	PRP$
37681	450	7	pupils	pupil	NNS
37681	450	8	not	not	RB
37681	450	9	facts	fact	NNS
37681	450	10	alone	alone	RB
37681	450	11	,	,	,
37681	450	12	but	but	CC
37681	450	13	methods	method	NNS
37681	450	14	of	of	IN
37681	450	15	proof	proof	NN
37681	450	16	,	,	,
37681	450	17	giving	give	VBG
37681	450	18	them	-PRON-	PRP
37681	450	19	power	power	NN
37681	450	20	as	as	RB
37681	450	21	well	well	RB
37681	450	22	as	as	IN
37681	450	23	knowledge	knowledge	NN
37681	450	24	.	.	.
37681	451	1	Furthermore	furthermore	RB
37681	451	2	,	,	,
37681	451	3	they	-PRON-	PRP
37681	451	4	taught	teach	VBD
37681	451	5	them	-PRON-	PRP
37681	451	6	how	how	WRB
37681	451	7	to	to	TO
37681	451	8	discuss	discuss	VB
37681	451	9	their	-PRON-	PRP$
37681	451	10	problems	problem	NNS
37681	451	11	,	,	,
37681	451	12	investigating	investigate	VBG
37681	451	13	the	the	DT
37681	451	14	conditions	condition	NNS
37681	451	15	under	under	IN
37681	451	16	which	which	WDT
37681	451	17	they	-PRON-	PRP
37681	451	18	are	be	VBP
37681	451	19	capable	capable	JJ
37681	451	20	of	of	IN
37681	451	21	solution	solution	NN
37681	451	22	.	.	.
37681	452	1	This	this	DT
37681	452	2	feature	feature	NN
37681	452	3	of	of	IN
37681	452	4	the	the	DT
37681	452	5	work	work	NN
37681	452	6	they	-PRON-	PRP
37681	452	7	called	call	VBD
37681	452	8	the	the	DT
37681	452	9	_	_	NNP
37681	452	10	diorismus	diorismus	NNP
37681	452	11	_	_	NNP
37681	452	12	,	,	,
37681	452	13	and	and	CC
37681	452	14	it	-PRON-	PRP
37681	452	15	seems	seem	VBZ
37681	452	16	to	to	TO
37681	452	17	have	have	VB
37681	452	18	started	start	VBN
37681	452	19	with	with	IN
37681	452	20	Leon	Leon	NNP
37681	452	21	,	,	,
37681	452	22	a	a	DT
37681	452	23	follower	follower	NN
37681	452	24	of	of	IN
37681	452	25	Plato	Plato	NNP
37681	452	26	.	.	.
37681	453	1	Between	between	IN
37681	453	2	the	the	DT
37681	453	3	time	time	NN
37681	453	4	of	of	IN
37681	453	5	Plato	Plato	NNP
37681	453	6	(	(	-LRB-
37681	453	7	_	_	NNP
37681	453	8	ca	ca	NNP
37681	453	9	.	.	.
37681	453	10	_	_	NNP
37681	453	11	400	400	CD
37681	453	12	B.C.	B.C.	NNP
37681	453	13	)	)	-RRB-
37681	454	1	and	and	CC
37681	454	2	Euclid	Euclid	NNP
37681	454	3	(	(	-LRB-
37681	454	4	_	_	NNP
37681	454	5	ca	ca	NNP
37681	454	6	.	.	.
37681	454	7	_	_	NNP
37681	454	8	300	300	CD
37681	454	9	B.C.	B.C.	NNP
37681	454	10	)	)	-RRB-
37681	455	1	several	several	JJ
37681	455	2	attempts	attempt	NNS
37681	455	3	were	be	VBD
37681	455	4	made	make	VBN
37681	455	5	to	to	TO
37681	455	6	arrange	arrange	VB
37681	455	7	the	the	DT
37681	455	8	accumulated	accumulate	VBN
37681	455	9	material	material	NN
37681	455	10	of	of	IN
37681	455	11	elementary	elementary	JJ
37681	455	12	geometry	geometry	NN
37681	455	13	in	in	IN
37681	455	14	a	a	DT
37681	455	15	textbook	textbook	NN
37681	455	16	.	.	.
37681	456	1	Plato	Plato	NNP
37681	456	2	had	have	VBD
37681	456	3	laid	lay	VBN
37681	456	4	the	the	DT
37681	456	5	foundations	foundation	NNS
37681	456	6	for	for	IN
37681	456	7	the	the	DT
37681	456	8	science	science	NN
37681	456	9	,	,	,
37681	456	10	in	in	IN
37681	456	11	the	the	DT
37681	456	12	form	form	NN
37681	456	13	of	of	IN
37681	456	14	axioms	axiom	NNS
37681	456	15	,	,	,
37681	456	16	postulates	postulate	NNS
37681	456	17	,	,	,
37681	456	18	and	and	CC
37681	456	19	definitions	definition	NNS
37681	456	20	,	,	,
37681	456	21	and	and	CC
37681	456	22	he	-PRON-	PRP
37681	456	23	had	have	VBD
37681	456	24	limited	limit	VBN
37681	456	25	the	the	DT
37681	456	26	instruments	instrument	NNS
37681	456	27	to	to	IN
37681	456	28	the	the	DT
37681	456	29	straightedge	straightedge	NN
37681	456	30	and	and	CC
37681	456	31	the	the	DT
37681	456	32	compasses	compass	NNS
37681	456	33	.	.	.
37681	457	1	Aristotle	Aristotle	NNP
37681	457	2	(	(	-LRB-
37681	457	3	_	_	NNP
37681	457	4	ca	ca	NNP
37681	457	5	.	.	.
37681	457	6	_	_	NNP
37681	457	7	350	350	CD
37681	457	8	B.C.	B.C.	NNP
37681	457	9	)	)	-RRB-
37681	458	1	had	have	VBD
37681	458	2	paid	pay	VBN
37681	458	3	special	special	JJ
37681	458	4	attention	attention	NN
37681	458	5	to	to	IN
37681	458	6	the	the	DT
37681	458	7	history	history	NN
37681	458	8	of	of	IN
37681	458	9	the	the	DT
37681	458	10	subject	subject	NN
37681	458	11	,	,	,
37681	458	12	thus	thus	RB
37681	458	13	finding	find	VBG
37681	458	14	out	out	RP
37681	458	15	what	what	WP
37681	458	16	had	have	VBD
37681	458	17	already	already	RB
37681	458	18	been	be	VBN
37681	458	19	accomplished	accomplish	VBN
37681	458	20	,	,	,
37681	458	21	and	and	CC
37681	458	22	had	have	VBD
37681	458	23	also	also	RB
37681	458	24	made	make	VBN
37681	458	25	much	much	JJ
37681	458	26	of	of	IN
37681	458	27	the	the	DT
37681	458	28	applications	application	NNS
37681	458	29	of	of	IN
37681	458	30	geometry	geometry	NN
37681	458	31	.	.	.
37681	459	1	The	the	DT
37681	459	2	world	world	NN
37681	459	3	was	be	VBD
37681	459	4	therefore	therefore	RB
37681	459	5	ready	ready	JJ
37681	459	6	for	for	IN
37681	459	7	a	a	DT
37681	459	8	good	good	JJ
37681	459	9	teacher	teacher	NN
37681	459	10	who	who	WP
37681	459	11	should	should	MD
37681	459	12	gather	gather	VB
37681	459	13	the	the	DT
37681	459	14	material	material	NN
37681	459	15	and	and	CC
37681	459	16	arrange	arrange	VB
37681	459	17	it	-PRON-	PRP
37681	459	18	scientifically	scientifically	RB
37681	459	19	.	.	.
37681	460	1	After	after	IN
37681	460	2	several	several	JJ
37681	460	3	attempts	attempt	NNS
37681	460	4	to	to	TO
37681	460	5	find	find	VB
37681	460	6	the	the	DT
37681	460	7	man	man	NN
37681	460	8	for	for	IN
37681	460	9	such	such	PDT
37681	460	10	a	a	DT
37681	460	11	task	task	NN
37681	460	12	,	,	,
37681	460	13	he	-PRON-	PRP
37681	460	14	was	be	VBD
37681	460	15	discovered	discover	VBN
37681	460	16	in	in	IN
37681	460	17	Euclid	Euclid	NNP
37681	460	18	,	,	,
37681	460	19	and	and	CC
37681	460	20	to	to	IN
37681	460	21	his	-PRON-	PRP$
37681	460	22	work	work	NN
37681	460	23	the	the	DT
37681	460	24	next	next	JJ
37681	460	25	chapter	chapter	NN
37681	460	26	is	be	VBZ
37681	460	27	devoted	devoted	JJ
37681	460	28	.	.	.
37681	461	1	After	after	IN
37681	461	2	Euclid	Euclid	NNP
37681	461	3	,	,	,
37681	461	4	Archimedes	Archimedes	NNP
37681	461	5	(	(	-LRB-
37681	461	6	_	_	NNP
37681	461	7	ca	ca	NNP
37681	461	8	.	.	.
37681	461	9	_	_	NNP
37681	461	10	250	250	CD
37681	461	11	B.C.	B.C.	NNP
37681	461	12	)	)	-RRB-
37681	462	1	made	make	VBD
37681	462	2	his	-PRON-	PRP$
37681	462	3	great	great	JJ
37681	462	4	contributions	contribution	NNS
37681	462	5	.	.	.
37681	463	1	He	-PRON-	PRP
37681	463	2	was	be	VBD
37681	463	3	not	not	RB
37681	463	4	a	a	DT
37681	463	5	teacher	teacher	NN
37681	463	6	like	like	IN
37681	463	7	his	-PRON-	PRP$
37681	463	8	illustrious	illustrious	JJ
37681	463	9	predecessor	predecessor	NN
37681	463	10	,	,	,
37681	463	11	but	but	CC
37681	463	12	he	-PRON-	PRP
37681	463	13	was	be	VBD
37681	463	14	a	a	DT
37681	463	15	great	great	JJ
37681	463	16	discoverer	discoverer	NN
37681	463	17	.	.	.
37681	464	1	He	-PRON-	PRP
37681	464	2	has	have	VBZ
37681	464	3	left	leave	VBN
37681	464	4	us	-PRON-	PRP
37681	464	5	,	,	,
37681	464	6	however	however	RB
37681	464	7	,	,	,
37681	464	8	a	a	DT
37681	464	9	statement	statement	NN
37681	464	10	of	of	IN
37681	464	11	his	-PRON-	PRP$
37681	464	12	methods	method	NNS
37681	464	13	of	of	IN
37681	464	14	investigation	investigation	NN
37681	464	15	which	which	WDT
37681	464	16	is	be	VBZ
37681	464	17	helpful	helpful	JJ
37681	464	18	to	to	IN
37681	464	19	those	those	DT
37681	464	20	who	who	WP
37681	464	21	teach	teach	VBP
37681	464	22	.	.	.
37681	465	1	These	these	DT
37681	465	2	methods	method	NNS
37681	465	3	were	be	VBD
37681	465	4	largely	largely	RB
37681	465	5	experimental	experimental	JJ
37681	465	6	,	,	,
37681	465	7	even	even	RB
37681	465	8	extending	extend	VBG
37681	465	9	to	to	IN
37681	465	10	the	the	DT
37681	465	11	weighing	weighing	NN
37681	465	12	of	of	IN
37681	465	13	geometric	geometric	JJ
37681	465	14	forms	form	NNS
37681	465	15	to	to	TO
37681	465	16	discover	discover	VB
37681	465	17	certain	certain	JJ
37681	465	18	relations	relation	NNS
37681	465	19	,	,	,
37681	465	20	the	the	DT
37681	465	21	proof	proof	NN
37681	465	22	being	be	VBG
37681	465	23	given	give	VBN
37681	465	24	later	later	RB
37681	465	25	.	.	.
37681	466	1	Here	here	RB
37681	466	2	was	be	VBD
37681	466	3	born	bear	VBN
37681	466	4	,	,	,
37681	466	5	perhaps	perhaps	RB
37681	466	6	,	,	,
37681	466	7	what	what	WP
37681	466	8	has	have	VBZ
37681	466	9	been	be	VBN
37681	466	10	called	call	VBN
37681	466	11	the	the	DT
37681	466	12	laboratory	laboratory	NN
37681	466	13	method	method	NN
37681	466	14	of	of	IN
37681	466	15	the	the	DT
37681	466	16	present	present	NN
37681	466	17	.	.	.
37681	467	1	Of	of	IN
37681	467	2	the	the	DT
37681	467	3	other	other	JJ
37681	467	4	Greek	greek	JJ
37681	467	5	teachers	teacher	NNS
37681	467	6	we	-PRON-	PRP
37681	467	7	have	have	VBP
37681	467	8	but	but	CC
37681	467	9	little	little	JJ
37681	467	10	information	information	NN
37681	467	11	as	as	IN
37681	467	12	to	to	IN
37681	467	13	methods	method	NNS
37681	467	14	of	of	IN
37681	467	15	imparting	impart	VBG
37681	467	16	instruction	instruction	NN
37681	467	17	.	.	.
37681	468	1	It	-PRON-	PRP
37681	468	2	is	be	VBZ
37681	468	3	not	not	RB
37681	468	4	until	until	IN
37681	468	5	the	the	DT
37681	468	6	Middle	Middle	NNP
37681	468	7	Ages	Ages	NNPS
37681	468	8	that	that	IN
37681	468	9	there	there	EX
37681	468	10	is	be	VBZ
37681	468	11	much	much	RB
37681	468	12	known	know	VBN
37681	468	13	in	in	IN
37681	468	14	this	this	DT
37681	468	15	line	line	NN
37681	468	16	.	.	.
37681	469	1	Whatever	whatever	WDT
37681	469	2	of	of	IN
37681	469	3	geometry	geometry	NN
37681	469	4	was	be	VBD
37681	469	5	taught	teach	VBN
37681	469	6	seems	seem	VBZ
37681	469	7	to	to	TO
37681	469	8	have	have	VB
37681	469	9	been	be	VBN
37681	469	10	imparted	impart	VBN
37681	469	11	by	by	IN
37681	469	12	word	word	NN
37681	469	13	of	of	IN
37681	469	14	mouth	mouth	NN
37681	469	15	in	in	IN
37681	469	16	the	the	DT
37681	469	17	way	way	NN
37681	469	18	of	of	IN
37681	469	19	expounding	expound	VBG
37681	469	20	Euclid	Euclid	NNP
37681	469	21	,	,	,
37681	469	22	and	and	CC
37681	469	23	this	this	DT
37681	469	24	was	be	VBD
37681	469	25	done	do	VBN
37681	469	26	in	in	IN
37681	469	27	the	the	DT
37681	469	28	ancient	ancient	JJ
37681	469	29	fashion	fashion	NN
37681	469	30	.	.	.
37681	470	1	The	the	DT
37681	470	2	early	early	JJ
37681	470	3	Church	church	NN
37681	470	4	leaders	leader	NNS
37681	470	5	usually	usually	RB
37681	470	6	paid	pay	VBD
37681	470	7	no	no	DT
37681	470	8	attention	attention	NN
37681	470	9	to	to	IN
37681	470	10	geometry	geometry	NN
37681	470	11	,	,	,
37681	470	12	but	but	CC
37681	470	13	as	as	IN
37681	470	14	time	time	NN
37681	470	15	progressed	progress	VBD
37681	470	16	the	the	DT
37681	470	17	_	_	NNP
37681	470	18	quadrivium	quadrivium	NN
37681	470	19	_	_	NNP
37681	470	20	,	,	,
37681	470	21	or	or	CC
37681	470	22	four	four	CD
37681	470	23	sciences	science	NNS
37681	470	24	of	of	IN
37681	470	25	arithmetic	arithmetic	JJ
37681	470	26	,	,	,
37681	470	27	music	music	NN
37681	470	28	,	,	,
37681	470	29	geometry	geometry	NN
37681	470	30	,	,	,
37681	470	31	and	and	CC
37681	470	32	astronomy	astronomy	NN
37681	470	33	,	,	,
37681	470	34	came	come	VBD
37681	470	35	to	to	IN
37681	470	36	rank	rank	VB
37681	470	37	with	with	IN
37681	470	38	the	the	DT
37681	470	39	_	_	NNP
37681	470	40	trivium	trivium	NN
37681	470	41	_	_	NNP
37681	470	42	(	(	-LRB-
37681	470	43	grammar	grammar	NN
37681	470	44	,	,	,
37681	470	45	rhetoric	rhetoric	NN
37681	470	46	,	,	,
37681	470	47	dialectics	dialectic	NNS
37681	470	48	)	)	-RRB-
37681	470	49	,	,	,
37681	470	50	the	the	DT
37681	470	51	two	two	CD
37681	470	52	making	make	VBG
37681	470	53	up	up	RP
37681	470	54	the	the	DT
37681	470	55	"	"	``
37681	470	56	seven	seven	CD
37681	470	57	liberal	liberal	JJ
37681	470	58	arts	art	NNS
37681	470	59	.	.	.
37681	470	60	"	"	''
37681	471	1	All	all	DT
37681	471	2	that	that	WDT
37681	471	3	there	there	EX
37681	471	4	was	be	VBD
37681	471	5	of	of	IN
37681	471	6	geometry	geometry	NN
37681	471	7	in	in	IN
37681	471	8	the	the	DT
37681	471	9	first	first	JJ
37681	471	10	thousand	thousand	CD
37681	471	11	years	year	NNS
37681	471	12	of	of	IN
37681	471	13	Christianity	Christianity	NNP
37681	471	14	,	,	,
37681	471	15	however	however	RB
37681	471	16	,	,	,
37681	471	17	at	at	IN
37681	471	18	least	least	JJS
37681	471	19	in	in	IN
37681	471	20	the	the	DT
37681	471	21	great	great	JJ
37681	471	22	majority	majority	NN
37681	471	23	of	of	IN
37681	471	24	Church	Church	NNP
37681	471	25	schools	school	NNS
37681	471	26	,	,	,
37681	471	27	was	be	VBD
37681	471	28	summed	sum	VBN
37681	471	29	up	up	RP
37681	471	30	in	in	IN
37681	471	31	a	a	DT
37681	471	32	few	few	JJ
37681	471	33	definitions	definition	NNS
37681	471	34	and	and	CC
37681	471	35	rules	rule	NNS
37681	471	36	of	of	IN
37681	471	37	mensuration	mensuration	NN
37681	471	38	.	.	.
37681	472	1	Gerbert	Gerbert	NNP
37681	472	2	,	,	,
37681	472	3	who	who	WP
37681	472	4	became	become	VBD
37681	472	5	Pope	Pope	NNP
37681	472	6	Sylvester	Sylvester	NNP
37681	472	7	II	II	NNP
37681	472	8	in	in	IN
37681	472	9	999	999	CD
37681	472	10	A.D.	A.D.	NNP
37681	472	11	,	,	,
37681	472	12	gave	give	VBD
37681	472	13	a	a	DT
37681	472	14	new	new	JJ
37681	472	15	impetus	impetus	NN
37681	472	16	to	to	TO
37681	472	17	geometry	geometry	VB
37681	472	18	by	by	IN
37681	472	19	discovering	discover	VBG
37681	472	20	a	a	DT
37681	472	21	manuscript	manuscript	NN
37681	472	22	of	of	IN
37681	472	23	the	the	DT
37681	472	24	old	old	JJ
37681	472	25	Roman	roman	JJ
37681	472	26	surveyors	surveyor	NNS
37681	472	27	and	and	CC
37681	472	28	a	a	DT
37681	472	29	copy	copy	NN
37681	472	30	of	of	IN
37681	472	31	the	the	DT
37681	472	32	geometry	geometry	NN
37681	472	33	of	of	IN
37681	472	34	Boethius	Boethius	NNP
37681	472	35	,	,	,
37681	472	36	who	who	WP
37681	472	37	paraphrased	paraphrase	VBD
37681	472	38	Euclid	Euclid	NNP
37681	472	39	about	about	IN
37681	472	40	500	500	CD
37681	472	41	A.D.	A.D.	NNP
37681	473	1	He	-PRON-	PRP
37681	473	2	thereupon	thereupon	RB
37681	473	3	wrote	write	VBD
37681	473	4	a	a	DT
37681	473	5	brief	brief	JJ
37681	473	6	geometry	geometry	NN
37681	473	7	,	,	,
37681	473	8	and	and	CC
37681	473	9	his	-PRON-	PRP$
37681	473	10	elevation	elevation	NN
37681	473	11	to	to	IN
37681	473	12	the	the	DT
37681	473	13	papal	papal	JJ
37681	473	14	chair	chair	NN
37681	473	15	tended	tend	VBD
37681	473	16	to	to	TO
37681	473	17	bring	bring	VB
37681	473	18	the	the	DT
37681	473	19	study	study	NN
37681	473	20	of	of	IN
37681	473	21	mathematics	mathematic	NNS
37681	473	22	again	again	RB
37681	473	23	into	into	IN
37681	473	24	prominence	prominence	NN
37681	473	25	.	.	.
37681	474	1	Geometry	geometry	NN
37681	474	2	now	now	RB
37681	474	3	began	begin	VBD
37681	474	4	to	to	TO
37681	474	5	have	have	VB
37681	474	6	some	some	DT
37681	474	7	place	place	NN
37681	474	8	in	in	IN
37681	474	9	the	the	DT
37681	474	10	Church	Church	NNP
37681	474	11	schools	school	NNS
37681	474	12	,	,	,
37681	474	13	naturally	naturally	RB
37681	474	14	the	the	DT
37681	474	15	only	only	JJ
37681	474	16	schools	school	NNS
37681	474	17	of	of	IN
37681	474	18	high	high	JJ
37681	474	19	rank	rank	NN
37681	474	20	in	in	IN
37681	474	21	the	the	DT
37681	474	22	Middle	Middle	NNP
37681	474	23	Ages	Ages	NNPS
37681	474	24	.	.	.
37681	475	1	The	the	DT
37681	475	2	study	study	NN
37681	475	3	of	of	IN
37681	475	4	the	the	DT
37681	475	5	subject	subject	NN
37681	475	6	,	,	,
37681	475	7	however	however	RB
37681	475	8	,	,	,
37681	475	9	seems	seem	VBZ
37681	475	10	to	to	TO
37681	475	11	have	have	VB
37681	475	12	been	be	VBN
37681	475	13	merely	merely	RB
37681	475	14	a	a	DT
37681	475	15	matter	matter	NN
37681	475	16	of	of	IN
37681	475	17	memorizing	memorize	VBG
37681	475	18	.	.	.
37681	476	1	Geometry	Geometry	NNP
37681	476	2	received	receive	VBD
37681	476	3	another	another	DT
37681	476	4	impetus	impetus	NN
37681	476	5	in	in	IN
37681	476	6	the	the	DT
37681	476	7	book	book	NN
37681	476	8	written	write	VBN
37681	476	9	by	by	IN
37681	476	10	Leonardo	Leonardo	NNP
37681	476	11	of	of	IN
37681	476	12	Pisa	Pisa	NNP
37681	476	13	in	in	IN
37681	476	14	1220	1220	CD
37681	476	15	,	,	,
37681	476	16	the	the	DT
37681	476	17	"	"	``
37681	476	18	Practica	Practica	NNP
37681	476	19	Geometriae	Geometriae	NNP
37681	476	20	.	.	.
37681	476	21	"	"	''
37681	477	1	Euclid	Euclid	NNP
37681	477	2	was	be	VBD
37681	477	3	also	also	RB
37681	477	4	translated	translate	VBN
37681	477	5	into	into	IN
37681	477	6	Latin	Latin	NNP
37681	477	7	about	about	IN
37681	477	8	this	this	DT
37681	477	9	time	time	NN
37681	477	10	(	(	-LRB-
37681	477	11	strangely	strangely	RB
37681	477	12	enough	enough	RB
37681	477	13	,	,	,
37681	477	14	as	as	RB
37681	477	15	already	already	RB
37681	477	16	stated	state	VBN
37681	477	17	,	,	,
37681	477	18	from	from	IN
37681	477	19	the	the	DT
37681	477	20	Arabic	Arabic	NNP
37681	477	21	instead	instead	RB
37681	477	22	of	of	IN
37681	477	23	the	the	DT
37681	477	24	Greek	Greek	NNP
37681	477	25	)	)	-RRB-
37681	477	26	,	,	,
37681	477	27	and	and	CC
37681	477	28	thus	thus	RB
37681	477	29	the	the	DT
37681	477	30	treasury	treasury	NNP
37681	477	31	of	of	IN
37681	477	32	elementary	elementary	NNP
37681	477	33	geometry	geometry	NNP
37681	477	34	was	be	VBD
37681	477	35	opened	open	VBN
37681	477	36	to	to	IN
37681	477	37	scholars	scholar	NNS
37681	477	38	in	in	IN
37681	477	39	Europe	Europe	NNP
37681	477	40	.	.	.
37681	478	1	From	from	IN
37681	478	2	now	now	RB
37681	478	3	on	on	RB
37681	478	4	,	,	,
37681	478	5	until	until	IN
37681	478	6	the	the	DT
37681	478	7	invention	invention	NN
37681	478	8	of	of	IN
37681	478	9	printing	printing	NN
37681	478	10	(	(	-LRB-
37681	478	11	_	_	NNP
37681	478	12	ca	ca	NNP
37681	478	13	.	.	.
37681	478	14	_	_	NNP
37681	478	15	1450	1450	CD
37681	478	16	)	)	-RRB-
37681	478	17	,	,	,
37681	478	18	numerous	numerous	JJ
37681	478	19	writers	writer	NNS
37681	478	20	on	on	IN
37681	478	21	geometry	geometry	NN
37681	478	22	appear	appear	VBP
37681	478	23	,	,	,
37681	478	24	but	but	CC
37681	478	25	,	,	,
37681	478	26	so	so	RB
37681	478	27	far	far	RB
37681	478	28	as	as	IN
37681	478	29	we	-PRON-	PRP
37681	478	30	know	know	VBP
37681	478	31	,	,	,
37681	478	32	the	the	DT
37681	478	33	method	method	NN
37681	478	34	of	of	IN
37681	478	35	instruction	instruction	NN
37681	478	36	remained	remain	VBD
37681	478	37	much	much	RB
37681	478	38	as	as	IN
37681	478	39	it	-PRON-	PRP
37681	478	40	had	have	VBD
37681	478	41	always	always	RB
37681	478	42	been	be	VBN
37681	478	43	.	.	.
37681	479	1	The	the	DT
37681	479	2	universities	university	NNS
37681	479	3	began	begin	VBD
37681	479	4	to	to	TO
37681	479	5	appear	appear	VB
37681	479	6	about	about	IN
37681	479	7	the	the	DT
37681	479	8	thirteenth	thirteenth	JJ
37681	479	9	century	century	NN
37681	479	10	,	,	,
37681	479	11	and	and	CC
37681	479	12	Sacrobosco	Sacrobosco	NNP
37681	479	13	,	,	,
37681	479	14	a	a	DT
37681	479	15	well	well	RB
37681	479	16	-	-	HYPH
37681	479	17	known	know	VBN
37681	479	18	medieval	medieval	JJ
37681	479	19	mathematician	mathematician	NN
37681	479	20	,	,	,
37681	479	21	taught	teach	VBD
37681	479	22	mathematics	mathematic	NNS
37681	479	23	about	about	IN
37681	479	24	1250	1250	CD
37681	479	25	in	in	IN
37681	479	26	the	the	DT
37681	479	27	University	University	NNP
37681	479	28	of	of	IN
37681	479	29	Paris	Paris	NNP
37681	479	30	.	.	.
37681	480	1	In	in	IN
37681	480	2	1336	1336	CD
37681	480	3	this	this	DT
37681	480	4	university	university	NN
37681	480	5	decreed	decreed	NN
37681	480	6	that	that	IN
37681	480	7	mathematics	mathematic	NNS
37681	480	8	should	should	MD
37681	480	9	be	be	VB
37681	480	10	required	require	VBN
37681	480	11	for	for	IN
37681	480	12	a	a	DT
37681	480	13	degree	degree	NN
37681	480	14	.	.	.
37681	481	1	In	in	IN
37681	481	2	the	the	DT
37681	481	3	thirteenth	thirteenth	JJ
37681	481	4	century	century	NN
37681	481	5	Oxford	Oxford	NNP
37681	481	6	required	require	VBD
37681	481	7	six	six	CD
37681	481	8	books	book	NNS
37681	481	9	of	of	IN
37681	481	10	Euclid	Euclid	NNP
37681	481	11	for	for	IN
37681	481	12	one	one	CD
37681	481	13	who	who	WP
37681	481	14	was	be	VBD
37681	481	15	to	to	TO
37681	481	16	teach	teach	VB
37681	481	17	,	,	,
37681	481	18	but	but	CC
37681	481	19	this	this	DT
37681	481	20	amount	amount	NN
37681	481	21	of	of	IN
37681	481	22	work	work	NN
37681	481	23	seems	seem	VBZ
37681	481	24	to	to	TO
37681	481	25	have	have	VB
37681	481	26	been	be	VBN
37681	481	27	merely	merely	RB
37681	481	28	nominal	nominal	JJ
37681	481	29	,	,	,
37681	481	30	for	for	IN
37681	481	31	in	in	IN
37681	481	32	1450	1450	CD
37681	481	33	only	only	RB
37681	481	34	two	two	CD
37681	481	35	books	book	NNS
37681	481	36	were	be	VBD
37681	481	37	actually	actually	RB
37681	481	38	read	read	VBN
37681	481	39	.	.	.
37681	482	1	The	the	DT
37681	482	2	universities	university	NNS
37681	482	3	of	of	IN
37681	482	4	Prague	Prague	NNP
37681	482	5	(	(	-LRB-
37681	482	6	founded	found	VBN
37681	482	7	in	in	IN
37681	482	8	1350	1350	CD
37681	482	9	)	)	-RRB-
37681	482	10	and	and	CC
37681	482	11	Vienna	Vienna	NNP
37681	482	12	(	(	-LRB-
37681	482	13	statutes	statute	NNS
37681	482	14	of	of	IN
37681	482	15	1389	1389	CD
37681	482	16	)	)	-RRB-
37681	482	17	required	require	VBD
37681	482	18	most	most	JJS
37681	482	19	of	of	IN
37681	482	20	plane	plane	NN
37681	482	21	geometry	geometry	NN
37681	482	22	for	for	IN
37681	482	23	the	the	DT
37681	482	24	teacher	teacher	NN
37681	482	25	's	's	POS
37681	482	26	license	license	NN
37681	482	27	,	,	,
37681	482	28	although	although	IN
37681	482	29	Vienna	Vienna	NNP
37681	482	30	demanded	demand	VBD
37681	482	31	but	but	CC
37681	482	32	one	one	CD
37681	482	33	book	book	NN
37681	482	34	for	for	IN
37681	482	35	the	the	DT
37681	482	36	bachelor	bachelor	NN
37681	482	37	's	's	POS
37681	482	38	degree	degree	NN
37681	482	39	.	.	.
37681	483	1	So	so	CC
37681	483	2	,	,	,
37681	483	3	in	in	IN
37681	483	4	general	general	JJ
37681	483	5	,	,	,
37681	483	6	the	the	DT
37681	483	7	universities	university	NNS
37681	483	8	of	of	IN
37681	483	9	the	the	DT
37681	483	10	thirteenth	thirteenth	JJ
37681	483	11	,	,	,
37681	483	12	fourteenth	fourteenth	JJ
37681	483	13	,	,	,
37681	483	14	and	and	CC
37681	483	15	fifteenth	fifteenth	JJ
37681	483	16	centuries	century	NNS
37681	483	17	required	require	VBD
37681	483	18	less	less	JJR
37681	483	19	for	for	IN
37681	483	20	the	the	DT
37681	483	21	degree	degree	NN
37681	483	22	of	of	IN
37681	483	23	master	master	NN
37681	483	24	of	of	IN
37681	483	25	arts	art	NNS
37681	483	26	than	than	IN
37681	483	27	we	-PRON-	PRP
37681	483	28	now	now	RB
37681	483	29	require	require	VBP
37681	483	30	from	from	IN
37681	483	31	a	a	DT
37681	483	32	pupil	pupil	NN
37681	483	33	in	in	IN
37681	483	34	our	-PRON-	PRP$
37681	483	35	American	american	JJ
37681	483	36	high	high	JJ
37681	483	37	schools	school	NNS
37681	483	38	.	.	.
37681	484	1	On	on	IN
37681	484	2	the	the	DT
37681	484	3	other	other	JJ
37681	484	4	hand	hand	NN
37681	484	5	,	,	,
37681	484	6	the	the	DT
37681	484	7	university	university	NN
37681	484	8	students	student	NNS
37681	484	9	were	be	VBD
37681	484	10	younger	young	JJR
37681	484	11	than	than	IN
37681	484	12	now	now	RB
37681	484	13	,	,	,
37681	484	14	and	and	CC
37681	484	15	were	be	VBD
37681	484	16	really	really	RB
37681	484	17	doing	do	VBG
37681	484	18	only	only	RB
37681	484	19	high	high	JJ
37681	484	20	school	school	NN
37681	484	21	work	work	NN
37681	484	22	.	.	.
37681	485	1	The	the	DT
37681	485	2	invention	invention	NN
37681	485	3	of	of	IN
37681	485	4	printing	printing	NN
37681	485	5	made	make	VBD
37681	485	6	possible	possible	JJ
37681	485	7	the	the	DT
37681	485	8	study	study	NN
37681	485	9	of	of	IN
37681	485	10	geometry	geometry	NN
37681	485	11	in	in	IN
37681	485	12	a	a	DT
37681	485	13	new	new	JJ
37681	485	14	fashion	fashion	NN
37681	485	15	.	.	.
37681	486	1	It	-PRON-	PRP
37681	486	2	now	now	RB
37681	486	3	became	become	VBD
37681	486	4	possible	possible	JJ
37681	486	5	for	for	IN
37681	486	6	any	any	DT
37681	486	7	one	one	NN
37681	486	8	to	to	TO
37681	486	9	study	study	VB
37681	486	10	from	from	IN
37681	486	11	a	a	DT
37681	486	12	book	book	NN
37681	486	13	,	,	,
37681	486	14	whereas	whereas	IN
37681	486	15	before	before	IN
37681	486	16	this	this	DT
37681	486	17	time	time	NN
37681	486	18	instruction	instruction	NN
37681	486	19	was	be	VBD
37681	486	20	chiefly	chiefly	RB
37681	486	21	by	by	IN
37681	486	22	word	word	NN
37681	486	23	of	of	IN
37681	486	24	mouth	mouth	NN
37681	486	25	,	,	,
37681	486	26	consisting	consist	VBG
37681	486	27	of	of	IN
37681	486	28	an	an	DT
37681	486	29	explanation	explanation	NN
37681	486	30	of	of	IN
37681	486	31	Euclid	Euclid	NNP
37681	486	32	.	.	.
37681	487	1	The	the	DT
37681	487	2	first	first	JJ
37681	487	3	Euclid	Euclid	NNP
37681	487	4	was	be	VBD
37681	487	5	printed	print	VBN
37681	487	6	in	in	IN
37681	487	7	1482	1482	CD
37681	487	8	,	,	,
37681	487	9	at	at	IN
37681	487	10	Venice	Venice	NNP
37681	487	11	,	,	,
37681	487	12	and	and	CC
37681	487	13	new	new	JJ
37681	487	14	editions	edition	NNS
37681	487	15	and	and	CC
37681	487	16	variations	variation	NNS
37681	487	17	of	of	IN
37681	487	18	this	this	DT
37681	487	19	text	text	NN
37681	487	20	came	come	VBD
37681	487	21	out	out	RP
37681	487	22	frequently	frequently	RB
37681	487	23	in	in	IN
37681	487	24	the	the	DT
37681	487	25	next	next	JJ
37681	487	26	century	century	NN
37681	487	27	.	.	.
37681	488	1	Practical	practical	JJ
37681	488	2	geometries	geometry	NNS
37681	488	3	became	become	VBD
37681	488	4	very	very	RB
37681	488	5	popular	popular	JJ
37681	488	6	,	,	,
37681	488	7	and	and	CC
37681	488	8	the	the	DT
37681	488	9	reaction	reaction	NN
37681	488	10	against	against	IN
37681	488	11	the	the	DT
37681	488	12	idea	idea	NN
37681	488	13	of	of	IN
37681	488	14	mental	mental	JJ
37681	488	15	discipline	discipline	NN
37681	488	16	threatened	threaten	VBD
37681	488	17	to	to	TO
37681	488	18	abolish	abolish	VB
37681	488	19	the	the	DT
37681	488	20	old	old	JJ
37681	488	21	style	style	NN
37681	488	22	of	of	IN
37681	488	23	text	text	NN
37681	488	24	.	.	.
37681	489	1	It	-PRON-	PRP
37681	489	2	was	be	VBD
37681	489	3	argued	argue	VBN
37681	489	4	that	that	IN
37681	489	5	geometry	geometry	NN
37681	489	6	was	be	VBD
37681	489	7	uninteresting	uninteresting	JJ
37681	489	8	,	,	,
37681	489	9	that	that	IN
37681	489	10	it	-PRON-	PRP
37681	489	11	was	be	VBD
37681	489	12	not	not	RB
37681	489	13	sufficient	sufficient	JJ
37681	489	14	in	in	IN
37681	489	15	itself	-PRON-	PRP
37681	489	16	,	,	,
37681	489	17	that	that	IN
37681	489	18	boys	boy	NNS
37681	489	19	needed	need	VBD
37681	489	20	to	to	TO
37681	489	21	see	see	VB
37681	489	22	the	the	DT
37681	489	23	practical	practical	JJ
37681	489	24	uses	use	NNS
37681	489	25	of	of	IN
37681	489	26	the	the	DT
37681	489	27	subject	subject	NN
37681	489	28	,	,	,
37681	489	29	that	that	IN
37681	489	30	only	only	RB
37681	489	31	those	those	DT
37681	489	32	propositions	proposition	NNS
37681	489	33	that	that	WDT
37681	489	34	were	be	VBD
37681	489	35	capable	capable	JJ
37681	489	36	of	of	IN
37681	489	37	application	application	NN
37681	489	38	should	should	MD
37681	489	39	be	be	VB
37681	489	40	retained	retain	VBN
37681	489	41	,	,	,
37681	489	42	that	that	IN
37681	489	43	there	there	EX
37681	489	44	must	must	MD
37681	489	45	be	be	VB
37681	489	46	a	a	DT
37681	489	47	fusion	fusion	NN
37681	489	48	between	between	IN
37681	489	49	the	the	DT
37681	489	50	demands	demand	NNS
37681	489	51	of	of	IN
37681	489	52	culture	culture	NN
37681	489	53	and	and	CC
37681	489	54	the	the	DT
37681	489	55	demands	demand	NNS
37681	489	56	of	of	IN
37681	489	57	business	business	NN
37681	489	58	,	,	,
37681	489	59	and	and	CC
37681	489	60	that	that	IN
37681	489	61	every	every	DT
37681	489	62	man	man	NN
37681	489	63	who	who	WP
37681	489	64	stood	stand	VBD
37681	489	65	for	for	IN
37681	489	66	mathematical	mathematical	JJ
37681	489	67	ideals	ideal	NNS
37681	489	68	represented	represent	VBD
37681	489	69	an	an	DT
37681	489	70	obsolete	obsolete	JJ
37681	489	71	type	type	NN
37681	489	72	.	.	.
37681	490	1	Such	such	JJ
37681	490	2	writers	writer	NNS
37681	490	3	as	as	IN
37681	490	4	Finæus	Finæus	NNP
37681	490	5	(	(	-LRB-
37681	490	6	1556	1556	CD
37681	490	7	)	)	-RRB-
37681	490	8	,	,	,
37681	490	9	Bartoli	Bartoli	NNP
37681	490	10	(	(	-LRB-
37681	490	11	1589	1589	CD
37681	490	12	)	)	-RRB-
37681	490	13	,	,	,
37681	490	14	Belli	Belli	NNP
37681	490	15	(	(	-LRB-
37681	490	16	1569	1569	CD
37681	490	17	)	)	-RRB-
37681	490	18	,	,	,
37681	490	19	and	and	CC
37681	490	20	Cataneo	Cataneo	NNP
37681	490	21	(	(	-LRB-
37681	490	22	1567	1567	CD
37681	490	23	)	)	-RRB-
37681	490	24	,	,	,
37681	490	25	in	in	IN
37681	490	26	the	the	DT
37681	490	27	sixteenth	sixteenth	JJ
37681	490	28	century	century	NN
37681	490	29	,	,	,
37681	490	30	and	and	CC
37681	490	31	Capra	Capra	NNP
37681	490	32	(	(	-LRB-
37681	490	33	1678	1678	CD
37681	490	34	)	)	-RRB-
37681	490	35	,	,	,
37681	490	36	Gargiolli	Gargiolli	NNP
37681	490	37	(	(	-LRB-
37681	490	38	1655	1655	CD
37681	490	39	)	)	-RRB-
37681	490	40	,	,	,
37681	490	41	and	and	CC
37681	490	42	many	many	JJ
37681	490	43	others	other	NNS
37681	490	44	in	in	IN
37681	490	45	the	the	DT
37681	490	46	seventeenth	seventeenth	JJ
37681	490	47	century	century	NN
37681	490	48	,	,	,
37681	490	49	either	either	CC
37681	490	50	directly	directly	RB
37681	490	51	or	or	CC
37681	490	52	inferentially	inferentially	RB
37681	490	53	,	,	,
37681	490	54	took	take	VBD
37681	490	55	this	this	DT
37681	490	56	attitude	attitude	NN
37681	490	57	towards	towards	IN
37681	490	58	the	the	DT
37681	490	59	subject,--exactly	subject,--exactly	RB
37681	490	60	the	the	DT
37681	490	61	attitude	attitude	NN
37681	490	62	that	that	WDT
37681	490	63	is	be	VBZ
37681	490	64	being	be	VBG
37681	490	65	taken	take	VBN
37681	490	66	at	at	IN
37681	490	67	the	the	DT
37681	490	68	present	present	JJ
37681	490	69	time	time	NN
37681	490	70	by	by	IN
37681	490	71	a	a	DT
37681	490	72	number	number	NN
37681	490	73	of	of	IN
37681	490	74	teachers	teacher	NNS
37681	490	75	in	in	IN
37681	490	76	the	the	DT
37681	490	77	United	United	NNP
37681	490	78	States	States	NNP
37681	490	79	.	.	.
37681	491	1	As	as	IN
37681	491	2	is	be	VBZ
37681	491	3	always	always	RB
37681	491	4	the	the	DT
37681	491	5	case	case	NN
37681	491	6	,	,	,
37681	491	7	to	to	IN
37681	491	8	such	such	PDT
37681	491	9	an	an	DT
37681	491	10	extreme	extreme	NN
37681	491	11	did	do	VBD
37681	491	12	this	this	DT
37681	491	13	movement	movement	NN
37681	491	14	lead	lead	VB
37681	491	15	that	that	IN
37681	491	16	there	there	EX
37681	491	17	was	be	VBD
37681	491	18	a	a	DT
37681	491	19	reaction	reaction	NN
37681	491	20	that	that	WDT
37681	491	21	brought	bring	VBD
37681	491	22	the	the	DT
37681	491	23	Euclid	euclid	JJ
37681	491	24	type	type	NN
37681	491	25	of	of	IN
37681	491	26	book	book	NN
37681	491	27	again	again	RB
37681	491	28	to	to	IN
37681	491	29	the	the	DT
37681	491	30	front	front	NN
37681	491	31	,	,	,
37681	491	32	and	and	CC
37681	491	33	it	-PRON-	PRP
37681	491	34	has	have	VBZ
37681	491	35	maintained	maintain	VBN
37681	491	36	its	-PRON-	PRP$
37681	491	37	prominence	prominence	NN
37681	491	38	even	even	RB
37681	491	39	to	to	IN
37681	491	40	the	the	DT
37681	491	41	present	present	NN
37681	491	42	.	.	.
37681	492	1	The	the	DT
37681	492	2	study	study	NN
37681	492	3	of	of	IN
37681	492	4	geometry	geometry	NN
37681	492	5	in	in	IN
37681	492	6	the	the	DT
37681	492	7	high	high	JJ
37681	492	8	schools	school	NNS
37681	492	9	is	be	VBZ
37681	492	10	relatively	relatively	RB
37681	492	11	recent	recent	JJ
37681	492	12	.	.	.
37681	493	1	The	the	DT
37681	493	2	Gymnasium	Gymnasium	NNP
37681	493	3	(	(	-LRB-
37681	493	4	classical	classical	JJ
37681	493	5	school	school	NN
37681	493	6	preparatory	preparatory	NN
37681	493	7	to	to	IN
37681	493	8	the	the	DT
37681	493	9	university	university	NN
37681	493	10	)	)	-RRB-
37681	493	11	at	at	IN
37681	493	12	Nürnberg	Nürnberg	NNP
37681	493	13	,	,	,
37681	493	14	founded	found	VBN
37681	493	15	in	in	IN
37681	493	16	1526	1526	CD
37681	493	17	,	,	,
37681	493	18	and	and	CC
37681	493	19	the	the	DT
37681	493	20	Cathedral	cathedral	JJ
37681	493	21	school	school	NN
37681	493	22	at	at	IN
37681	493	23	Württemberg	Württemberg	NNP
37681	493	24	(	(	-LRB-
37681	493	25	as	as	IN
37681	493	26	shown	show	VBN
37681	493	27	by	by	IN
37681	493	28	the	the	DT
37681	493	29	curriculum	curriculum	NN
37681	493	30	of	of	IN
37681	493	31	1556	1556	CD
37681	493	32	)	)	-RRB-
37681	493	33	seem	seem	VBP
37681	493	34	to	to	TO
37681	493	35	have	have	VB
37681	493	36	had	have	VBN
37681	493	37	no	no	DT
37681	493	38	geometry	geometry	NN
37681	493	39	before	before	IN
37681	493	40	1600	1600	CD
37681	493	41	,	,	,
37681	493	42	although	although	IN
37681	493	43	the	the	DT
37681	493	44	Gymnasium	Gymnasium	NNP
37681	493	45	at	at	IN
37681	493	46	Strassburg	Strassburg	NNP
37681	493	47	included	include	VBD
37681	493	48	some	some	DT
37681	493	49	of	of	IN
37681	493	50	this	this	DT
37681	493	51	branch	branch	NN
37681	493	52	of	of	IN
37681	493	53	mathematics	mathematic	NNS
37681	493	54	in	in	IN
37681	493	55	1578	1578	CD
37681	493	56	,	,	,
37681	493	57	and	and	CC
37681	493	58	an	an	DT
37681	493	59	elective	elective	JJ
37681	493	60	course	course	NN
37681	493	61	in	in	IN
37681	493	62	geometry	geometry	NN
37681	493	63	was	be	VBD
37681	493	64	offered	offer	VBN
37681	493	65	at	at	IN
37681	493	66	Zwickau	Zwickau	NNP
37681	493	67	,	,	,
37681	493	68	in	in	IN
37681	493	69	Saxony	Saxony	NNP
37681	493	70	,	,	,
37681	493	71	in	in	IN
37681	493	72	1521	1521	CD
37681	493	73	.	.	.
37681	494	1	In	in	IN
37681	494	2	the	the	DT
37681	494	3	seventeenth	seventeenth	JJ
37681	494	4	century	century	NN
37681	494	5	geometry	geometry	NN
37681	494	6	is	be	VBZ
37681	494	7	found	find	VBN
37681	494	8	in	in	IN
37681	494	9	a	a	DT
37681	494	10	considerable	considerable	JJ
37681	494	11	number	number	NN
37681	494	12	of	of	IN
37681	494	13	secondary	secondary	JJ
37681	494	14	schools	school	NNS
37681	494	15	,	,	,
37681	494	16	as	as	IN
37681	494	17	at	at	IN
37681	494	18	Coburg	Coburg	NNP
37681	494	19	(	(	-LRB-
37681	494	20	1605	1605	CD
37681	494	21	)	)	-RRB-
37681	494	22	,	,	,
37681	494	23	Kurfalz	Kurfalz	NNP
37681	494	24	(	(	-LRB-
37681	494	25	1615	1615	CD
37681	494	26	,	,	,
37681	494	27	elective	elective	JJ
37681	494	28	)	)	-RRB-
37681	494	29	,	,	,
37681	494	30	Erfurt	Erfurt	NNP
37681	494	31	(	(	-LRB-
37681	494	32	1643	1643	CD
37681	494	33	)	)	-RRB-
37681	494	34	,	,	,
37681	494	35	Gotha	Gotha	NNP
37681	494	36	(	(	-LRB-
37681	494	37	1605	1605	CD
37681	494	38	)	)	-RRB-
37681	494	39	,	,	,
37681	494	40	Giessen	Giessen	NNP
37681	494	41	(	(	-LRB-
37681	494	42	1605	1605	CD
37681	494	43	)	)	-RRB-
37681	494	44	,	,	,
37681	494	45	and	and	CC
37681	494	46	numerous	numerous	JJ
37681	494	47	other	other	JJ
37681	494	48	places	place	NNS
37681	494	49	in	in	IN
37681	494	50	Germany	Germany	NNP
37681	494	51	,	,	,
37681	494	52	although	although	IN
37681	494	53	it	-PRON-	PRP
37681	494	54	appeared	appear	VBD
37681	494	55	but	but	CC
37681	494	56	rarely	rarely	RB
37681	494	57	in	in	IN
37681	494	58	the	the	DT
37681	494	59	secondary	secondary	JJ
37681	494	60	schools	school	NNS
37681	494	61	of	of	IN
37681	494	62	France	France	NNP
37681	494	63	before	before	IN
37681	494	64	the	the	DT
37681	494	65	eighteenth	eighteenth	JJ
37681	494	66	century	century	NN
37681	494	67	.	.	.
37681	495	1	In	in	IN
37681	495	2	Germany	Germany	NNP
37681	495	3	the	the	DT
37681	495	4	Realschulen	Realschulen	NNP
37681	495	5	--	--	:
37681	495	6	schools	school	NNS
37681	495	7	with	with	IN
37681	495	8	more	more	JJR
37681	495	9	science	science	NN
37681	495	10	and	and	CC
37681	495	11	less	less	JJR
37681	495	12	classics	classic	NNS
37681	495	13	than	than	IN
37681	495	14	are	be	VBP
37681	495	15	found	find	VBN
37681	495	16	in	in	IN
37681	495	17	the	the	DT
37681	495	18	Gymnasium	Gymnasium	NNP
37681	495	19	--	--	:
37681	495	20	came	come	VBD
37681	495	21	into	into	IN
37681	495	22	being	being	NN
37681	495	23	in	in	IN
37681	495	24	the	the	DT
37681	495	25	eighteenth	eighteenth	JJ
37681	495	26	century	century	NN
37681	495	27	,	,	,
37681	495	28	and	and	CC
37681	495	29	considerable	considerable	JJ
37681	495	30	effort	effort	NN
37681	495	31	was	be	VBD
37681	495	32	made	make	VBN
37681	495	33	to	to	TO
37681	495	34	construct	construct	VB
37681	495	35	a	a	DT
37681	495	36	course	course	NN
37681	495	37	in	in	IN
37681	495	38	geometry	geometry	NN
37681	495	39	that	that	WDT
37681	495	40	should	should	MD
37681	495	41	be	be	VB
37681	495	42	more	more	RBR
37681	495	43	practical	practical	JJ
37681	495	44	than	than	IN
37681	495	45	that	that	DT
37681	495	46	of	of	IN
37681	495	47	the	the	DT
37681	495	48	modified	modify	VBN
37681	495	49	Euclid	Euclid	NNP
37681	495	50	.	.	.
37681	496	1	At	at	IN
37681	496	2	the	the	DT
37681	496	3	opening	opening	NN
37681	496	4	of	of	IN
37681	496	5	the	the	DT
37681	496	6	nineteenth	nineteenth	JJ
37681	496	7	century	century	NN
37681	496	8	the	the	DT
37681	496	9	Prussian	prussian	JJ
37681	496	10	schools	school	NNS
37681	496	11	were	be	VBD
37681	496	12	reorganized	reorganize	VBN
37681	496	13	,	,	,
37681	496	14	and	and	CC
37681	496	15	from	from	IN
37681	496	16	that	that	DT
37681	496	17	time	time	NN
37681	496	18	on	on	IN
37681	496	19	geometry	geometry	NN
37681	496	20	has	have	VBZ
37681	496	21	had	have	VBN
37681	496	22	a	a	DT
37681	496	23	firm	firm	JJ
37681	496	24	position	position	NN
37681	496	25	in	in	IN
37681	496	26	the	the	DT
37681	496	27	secondary	secondary	JJ
37681	496	28	schools	school	NNS
37681	496	29	of	of	IN
37681	496	30	all	all	DT
37681	496	31	Germany	Germany	NNP
37681	496	32	.	.	.
37681	497	1	In	in	IN
37681	497	2	the	the	DT
37681	497	3	eighteenth	eighteenth	JJ
37681	497	4	century	century	NN
37681	497	5	some	some	DT
37681	497	6	excellent	excellent	JJ
37681	497	7	textbooks	textbook	NNS
37681	497	8	on	on	IN
37681	497	9	geometry	geometry	NN
37681	497	10	appeared	appear	VBD
37681	497	11	in	in	IN
37681	497	12	France	France	NNP
37681	497	13	,	,	,
37681	497	14	among	among	IN
37681	497	15	the	the	DT
37681	497	16	best	good	JJS
37681	497	17	being	being	NN
37681	497	18	that	that	DT
37681	497	19	of	of	IN
37681	497	20	Legendre	Legendre	NNP
37681	497	21	(	(	-LRB-
37681	497	22	1794	1794	CD
37681	497	23	)	)	-RRB-
37681	497	24	,	,	,
37681	497	25	which	which	WDT
37681	497	26	influenced	influence	VBD
37681	497	27	in	in	IN
37681	497	28	such	such	PDT
37681	497	29	a	a	DT
37681	497	30	marked	mark	VBN
37681	497	31	degree	degree	NN
37681	497	32	the	the	DT
37681	497	33	geometries	geometry	NNS
37681	497	34	of	of	IN
37681	497	35	America	America	NNP
37681	497	36	.	.	.
37681	498	1	Soon	soon	RB
37681	498	2	after	after	IN
37681	498	3	the	the	DT
37681	498	4	opening	opening	NN
37681	498	5	of	of	IN
37681	498	6	the	the	DT
37681	498	7	nineteenth	nineteenth	JJ
37681	498	8	century	century	NN
37681	498	9	the	the	DT
37681	498	10	_	_	NNP
37681	498	11	lycées	lycées	NN
37681	498	12	_	_	NNP
37681	498	13	of	of	IN
37681	498	14	France	France	NNP
37681	498	15	became	become	VBD
37681	498	16	strong	strong	JJ
37681	498	17	institutions	institution	NNS
37681	498	18	,	,	,
37681	498	19	and	and	CC
37681	498	20	geometry	geometry	NN
37681	498	21	,	,	,
37681	498	22	chiefly	chiefly	RB
37681	498	23	based	base	VBN
37681	498	24	on	on	IN
37681	498	25	Legendre	Legendre	NNP
37681	498	26	,	,	,
37681	498	27	was	be	VBD
37681	498	28	well	well	RB
37681	498	29	taught	teach	VBN
37681	498	30	in	in	IN
37681	498	31	the	the	DT
37681	498	32	mathematical	mathematical	JJ
37681	498	33	divisions	division	NNS
37681	498	34	.	.	.
37681	499	1	A	a	DT
37681	499	2	worthy	worthy	JJ
37681	499	3	rival	rival	NN
37681	499	4	of	of	IN
37681	499	5	Legendre	Legendre	NNP
37681	499	6	's	's	POS
37681	499	7	geometry	geometry	NN
37681	499	8	was	be	VBD
37681	499	9	the	the	DT
37681	499	10	work	work	NN
37681	499	11	of	of	IN
37681	499	12	Lacroix	Lacroix	NNP
37681	499	13	,	,	,
37681	499	14	who	who	WP
37681	499	15	called	call	VBD
37681	499	16	attention	attention	NN
37681	499	17	continually	continually	RB
37681	499	18	to	to	IN
37681	499	19	the	the	DT
37681	499	20	analogy	analogy	NN
37681	499	21	between	between	IN
37681	499	22	the	the	DT
37681	499	23	theorems	theorem	NNS
37681	499	24	of	of	IN
37681	499	25	plane	plane	NN
37681	499	26	and	and	CC
37681	499	27	solid	solid	JJ
37681	499	28	geometry	geometry	NN
37681	499	29	,	,	,
37681	499	30	and	and	CC
37681	499	31	even	even	RB
37681	499	32	went	go	VBD
37681	499	33	so	so	RB
37681	499	34	far	far	RB
37681	499	35	as	as	IN
37681	499	36	to	to	TO
37681	499	37	suggest	suggest	VB
37681	499	38	treating	treat	VBG
37681	499	39	the	the	DT
37681	499	40	related	related	JJ
37681	499	41	propositions	proposition	NNS
37681	499	42	together	together	RB
37681	499	43	in	in	IN
37681	499	44	certain	certain	JJ
37681	499	45	cases	case	NNS
37681	499	46	.	.	.
37681	500	1	In	in	IN
37681	500	2	England	England	NNP
37681	500	3	the	the	DT
37681	500	4	preparatory	preparatory	JJ
37681	500	5	schools	school	NNS
37681	500	6	,	,	,
37681	500	7	such	such	JJ
37681	500	8	as	as	IN
37681	500	9	Rugby	Rugby	NNP
37681	500	10	,	,	,
37681	500	11	Harrow	Harrow	NNP
37681	500	12	,	,	,
37681	500	13	and	and	CC
37681	500	14	Eton	Eton	NNP
37681	500	15	,	,	,
37681	500	16	did	do	VBD
37681	500	17	not	not	RB
37681	500	18	commonly	commonly	RB
37681	500	19	teach	teach	VB
37681	500	20	geometry	geometry	NN
37681	500	21	until	until	IN
37681	500	22	quite	quite	RB
37681	500	23	recently	recently	RB
37681	500	24	,	,	,
37681	500	25	leaving	leave	VBG
37681	500	26	this	this	DT
37681	500	27	work	work	NN
37681	500	28	for	for	IN
37681	500	29	the	the	DT
37681	500	30	universities	university	NNS
37681	500	31	.	.	.
37681	501	1	In	in	IN
37681	501	2	Christ	Christ	NNP
37681	501	3	's	's	POS
37681	501	4	Hospital	Hospital	NNP
37681	501	5	,	,	,
37681	501	6	London	London	NNP
37681	501	7	,	,	,
37681	501	8	however	however	RB
37681	501	9	,	,	,
37681	501	10	geometry	geometry	NNP
37681	501	11	was	be	VBD
37681	501	12	taught	teach	VBN
37681	501	13	as	as	RB
37681	501	14	early	early	RB
37681	501	15	as	as	IN
37681	501	16	1681	1681	CD
37681	501	17	,	,	,
37681	501	18	from	from	IN
37681	501	19	a	a	DT
37681	501	20	work	work	NN
37681	501	21	written	write	VBN
37681	501	22	by	by	IN
37681	501	23	several	several	JJ
37681	501	24	teachers	teacher	NNS
37681	501	25	of	of	IN
37681	501	26	prominence	prominence	NN
37681	501	27	.	.	.
37681	502	1	The	the	DT
37681	502	2	highest	high	JJS
37681	502	3	class	class	NN
37681	502	4	at	at	IN
37681	502	5	Harrow	Harrow	NNP
37681	502	6	studied	study	VBD
37681	502	7	"	"	``
37681	502	8	Euclid	Euclid	NNP
37681	502	9	and	and	CC
37681	502	10	vulgar	vulgar	JJ
37681	502	11	fractions	fraction	NNS
37681	502	12	"	"	''
37681	502	13	one	one	CD
37681	502	14	period	period	NN
37681	502	15	a	a	DT
37681	502	16	week	week	NN
37681	502	17	in	in	IN
37681	502	18	1829	1829	CD
37681	502	19	,	,	,
37681	502	20	but	but	CC
37681	502	21	geometry	geometry	NN
37681	502	22	was	be	VBD
37681	502	23	not	not	RB
37681	502	24	seriously	seriously	RB
37681	502	25	studied	study	VBN
37681	502	26	before	before	IN
37681	502	27	1837	1837	CD
37681	502	28	.	.	.
37681	503	1	In	in	IN
37681	503	2	the	the	DT
37681	503	3	Edinburgh	Edinburgh	NNP
37681	503	4	Academy	Academy	NNP
37681	503	5	as	as	RB
37681	503	6	early	early	RB
37681	503	7	as	as	IN
37681	503	8	1885	1885	CD
37681	503	9	,	,	,
37681	503	10	and	and	CC
37681	503	11	in	in	IN
37681	503	12	Rugby	Rugby	NNP
37681	503	13	by	by	IN
37681	503	14	1839	1839	CD
37681	503	15	,	,	,
37681	503	16	plane	plane	NN
37681	503	17	geometry	geometry	NN
37681	503	18	was	be	VBD
37681	503	19	completed	complete	VBN
37681	503	20	.	.	.
37681	504	1	Not	not	RB
37681	504	2	until	until	IN
37681	504	3	1844	1844	CD
37681	504	4	did	do	VBD
37681	504	5	Harvard	Harvard	NNP
37681	504	6	require	require	VB
37681	504	7	any	any	DT
37681	504	8	plane	plane	NN
37681	504	9	geometry	geometry	NN
37681	504	10	for	for	IN
37681	504	11	entrance	entrance	NN
37681	504	12	.	.	.
37681	505	1	In	in	IN
37681	505	2	1855	1855	CD
37681	505	3	Yale	Yale	NNP
37681	505	4	required	require	VBD
37681	505	5	only	only	RB
37681	505	6	two	two	CD
37681	505	7	books	book	NNS
37681	505	8	of	of	IN
37681	505	9	Euclid	Euclid	NNP
37681	505	10	.	.	.
37681	506	1	It	-PRON-	PRP
37681	506	2	was	be	VBD
37681	506	3	therefore	therefore	RB
37681	506	4	from	from	IN
37681	506	5	1850	1850	CD
37681	506	6	to	to	IN
37681	506	7	1875	1875	CD
37681	506	8	that	that	DT
37681	506	9	plane	plane	NN
37681	506	10	geometry	geometry	NN
37681	506	11	took	take	VBD
37681	506	12	a	a	DT
37681	506	13	definite	definite	JJ
37681	506	14	place	place	NN
37681	506	15	in	in	IN
37681	506	16	the	the	DT
37681	506	17	American	american	JJ
37681	506	18	high	high	JJ
37681	506	19	school	school	NN
37681	506	20	.	.	.
37681	507	1	Solid	solid	JJ
37681	507	2	geometry	geometry	NN
37681	507	3	has	have	VBZ
37681	507	4	not	not	RB
37681	507	5	been	be	VBN
37681	507	6	generally	generally	RB
37681	507	7	required	require	VBN
37681	507	8	for	for	IN
37681	507	9	entrance	entrance	NN
37681	507	10	to	to	IN
37681	507	11	any	any	DT
37681	507	12	eastern	eastern	JJ
37681	507	13	college	college	NN
37681	507	14	,	,	,
37681	507	15	although	although	IN
37681	507	16	in	in	IN
37681	507	17	the	the	DT
37681	507	18	West	West	NNP
37681	507	19	this	this	DT
37681	507	20	is	be	VBZ
37681	507	21	not	not	RB
37681	507	22	the	the	DT
37681	507	23	case	case	NN
37681	507	24	.	.	.
37681	508	1	The	the	DT
37681	508	2	East	East	NNP
37681	508	3	teaches	teach	VBZ
37681	508	4	plane	plane	NN
37681	508	5	geometry	geometry	NN
37681	508	6	more	more	RBR
37681	508	7	thoroughly	thoroughly	RB
37681	508	8	,	,	,
37681	508	9	but	but	CC
37681	508	10	allows	allow	VBZ
37681	508	11	a	a	DT
37681	508	12	pupil	pupil	NN
37681	508	13	to	to	TO
37681	508	14	enter	enter	VB
37681	508	15	college	college	NN
37681	508	16	or	or	CC
37681	508	17	to	to	TO
37681	508	18	go	go	VB
37681	508	19	into	into	IN
37681	508	20	business	business	NN
37681	508	21	with	with	IN
37681	508	22	no	no	DT
37681	508	23	solid	solid	JJ
37681	508	24	geometry	geometry	NN
37681	508	25	.	.	.
37681	509	1	Given	give	VBN
37681	509	2	a	a	DT
37681	509	3	year	year	NN
37681	509	4	to	to	IN
37681	509	5	the	the	DT
37681	509	6	subject	subject	NN
37681	509	7	,	,	,
37681	509	8	it	-PRON-	PRP
37681	509	9	is	be	VBZ
37681	509	10	possible	possible	JJ
37681	509	11	to	to	TO
37681	509	12	do	do	VB
37681	509	13	little	little	JJ
37681	509	14	more	more	JJR
37681	509	15	than	than	IN
37681	509	16	cover	cover	VB
37681	509	17	plane	plane	NN
37681	509	18	geometry	geometry	NN
37681	509	19	;	;	:
37681	509	20	with	with	IN
37681	509	21	a	a	DT
37681	509	22	year	year	NN
37681	509	23	and	and	CC
37681	509	24	a	a	DT
37681	509	25	half	half	NN
37681	509	26	the	the	DT
37681	509	27	solid	solid	JJ
37681	509	28	geometry	geometry	NN
37681	509	29	ought	ought	MD
37681	509	30	easily	easily	RB
37681	509	31	to	to	TO
37681	509	32	be	be	VB
37681	509	33	covered	cover	VBN
37681	509	34	also	also	RB
37681	509	35	.	.	.
37681	510	1	=	=	NFP
37681	510	2	Bibliography.=	Bibliography.=	NNP
37681	510	3	Stamper	Stamper	NNP
37681	510	4	,	,	,
37681	510	5	A	a	DT
37681	510	6	History	history	NN
37681	510	7	of	of	IN
37681	510	8	the	the	DT
37681	510	9	Teaching	Teaching	NNP
37681	510	10	of	of	IN
37681	510	11	Elementary	Elementary	NNP
37681	510	12	Geometry	Geometry	NNP
37681	510	13	,	,	,
37681	510	14	New	New	NNP
37681	510	15	York	York	NNP
37681	510	16	,	,	,
37681	510	17	1909	1909	CD
37681	510	18	,	,	,
37681	510	19	with	with	IN
37681	510	20	a	a	DT
37681	510	21	very	very	RB
37681	510	22	full	full	JJ
37681	510	23	bibliography	bibliography	NN
37681	510	24	of	of	IN
37681	510	25	the	the	DT
37681	510	26	subject	subject	NN
37681	510	27	;	;	:
37681	510	28	Cajori	Cajori	NNP
37681	510	29	,	,	,
37681	510	30	The	the	DT
37681	510	31	Teaching	Teaching	NNP
37681	510	32	of	of	IN
37681	510	33	Mathematics	Mathematics	NNPS
37681	510	34	in	in	IN
37681	510	35	the	the	DT
37681	510	36	United	United	NNP
37681	510	37	States	States	NNP
37681	510	38	,	,	,
37681	510	39	Washington	Washington	NNP
37681	510	40	,	,	,
37681	510	41	1890	1890	CD
37681	510	42	;	;	:
37681	510	43	Cantor	Cantor	NNP
37681	510	44	,	,	,
37681	510	45	Geschichte	Geschichte	NNP
37681	510	46	der	der	VBD
37681	510	47	Mathematik	Mathematik	NNP
37681	510	48	,	,	,
37681	510	49	Vol	Vol	NNP
37681	510	50	.	.	.
37681	511	1	IV	IV	NNP
37681	511	2	,	,	,
37681	511	3	p.	p.	NN
37681	511	4	321	321	CD
37681	511	5	,	,	,
37681	511	6	Leipzig	Leipzig	NNP
37681	511	7	,	,	,
37681	511	8	1908	1908	CD
37681	511	9	;	;	:
37681	511	10	Schotten	Schotten	NNP
37681	511	11	,	,	,
37681	511	12	Inhalt	Inhalt	NNP
37681	511	13	und	und	NN
37681	511	14	Methode	Methode	NNP
37681	511	15	des	des	FW
37681	511	16	planimetrischen	planimetrischen	NN
37681	511	17	Unterrichts	Unterrichts	NNPS
37681	511	18	,	,	,
37681	511	19	Leipzig	Leipzig	NNP
37681	511	20	,	,	,
37681	511	21	1890	1890	CD
37681	511	22	.	.	.
37681	512	1	CHAPTER	chapter	NN
37681	512	2	V	v	NN
37681	512	3	EUCLID	EUCLID	NNP
37681	512	4	It	-PRON-	PRP
37681	512	5	is	be	VBZ
37681	512	6	fitting	fitting	JJ
37681	512	7	that	that	IN
37681	512	8	a	a	DT
37681	512	9	chapter	chapter	NN
37681	512	10	in	in	IN
37681	512	11	a	a	DT
37681	512	12	book	book	NN
37681	512	13	upon	upon	IN
37681	512	14	the	the	DT
37681	512	15	teaching	teaching	NN
37681	512	16	of	of	IN
37681	512	17	this	this	DT
37681	512	18	subject	subject	NN
37681	512	19	should	should	MD
37681	512	20	be	be	VB
37681	512	21	devoted	devoted	JJ
37681	512	22	to	to	IN
37681	512	23	the	the	DT
37681	512	24	life	life	NN
37681	512	25	and	and	CC
37681	512	26	labors	labor	NNS
37681	512	27	of	of	IN
37681	512	28	the	the	DT
37681	512	29	greatest	great	JJS
37681	512	30	of	of	IN
37681	512	31	all	all	DT
37681	512	32	textbook	textbook	NN
37681	512	33	writers	writer	NNS
37681	512	34	,	,	,
37681	512	35	Euclid,--a	Euclid,--a	NNP
37681	512	36	man	man	NNP
37681	512	37	whose	whose	WP$
37681	512	38	name	name	NN
37681	512	39	has	have	VBZ
37681	512	40	been	be	VBN
37681	512	41	,	,	,
37681	512	42	for	for	IN
37681	512	43	more	more	JJR
37681	512	44	than	than	IN
37681	512	45	two	two	CD
37681	512	46	thousand	thousand	CD
37681	512	47	years	year	NNS
37681	512	48	,	,	,
37681	512	49	a	a	DT
37681	512	50	synonym	synonym	NN
37681	512	51	for	for	IN
37681	512	52	elementary	elementary	JJ
37681	512	53	plane	plane	NN
37681	512	54	geometry	geometry	NN
37681	512	55	wherever	wherever	WRB
37681	512	56	the	the	DT
37681	512	57	subject	subject	NN
37681	512	58	has	have	VBZ
37681	512	59	been	be	VBN
37681	512	60	studied	study	VBN
37681	512	61	.	.	.
37681	513	1	And	and	CC
37681	513	2	yet	yet	RB
37681	513	3	when	when	WRB
37681	513	4	an	an	DT
37681	513	5	effort	effort	NN
37681	513	6	is	be	VBZ
37681	513	7	made	make	VBN
37681	513	8	to	to	TO
37681	513	9	pick	pick	VB
37681	513	10	up	up	RP
37681	513	11	the	the	DT
37681	513	12	scattered	scatter	VBN
37681	513	13	fragments	fragment	NNS
37681	513	14	of	of	IN
37681	513	15	his	-PRON-	PRP$
37681	513	16	biography	biography	NN
37681	513	17	,	,	,
37681	513	18	we	-PRON-	PRP
37681	513	19	are	be	VBP
37681	513	20	surprised	surprised	JJ
37681	513	21	to	to	TO
37681	513	22	find	find	VB
37681	513	23	how	how	WRB
37681	513	24	little	little	JJ
37681	513	25	is	be	VBZ
37681	513	26	known	know	VBN
37681	513	27	of	of	IN
37681	513	28	one	one	CD
37681	513	29	whose	whose	WP$
37681	513	30	fame	fame	NN
37681	513	31	is	be	VBZ
37681	513	32	so	so	RB
37681	513	33	universal	universal	JJ
37681	513	34	.	.	.
37681	514	1	Although	although	IN
37681	514	2	more	more	JJR
37681	514	3	editions	edition	NNS
37681	514	4	of	of	IN
37681	514	5	his	-PRON-	PRP$
37681	514	6	work	work	NN
37681	514	7	have	have	VBP
37681	514	8	been	be	VBN
37681	514	9	printed	print	VBN
37681	514	10	than	than	IN
37681	514	11	of	of	IN
37681	514	12	any	any	DT
37681	514	13	other	other	JJ
37681	514	14	book	book	NN
37681	514	15	save	save	VB
37681	514	16	the	the	DT
37681	514	17	Bible,[23	Bible,[23	NNP
37681	514	18	]	]	-RRB-
37681	514	19	we	-PRON-	PRP
37681	514	20	do	do	VBP
37681	514	21	not	not	RB
37681	514	22	know	know	VB
37681	514	23	when	when	WRB
37681	514	24	he	-PRON-	PRP
37681	514	25	was	be	VBD
37681	514	26	born	bear	VBN
37681	514	27	,	,	,
37681	514	28	or	or	CC
37681	514	29	in	in	IN
37681	514	30	what	what	WP
37681	514	31	city	city	NN
37681	514	32	,	,	,
37681	514	33	or	or	CC
37681	514	34	even	even	RB
37681	514	35	in	in	IN
37681	514	36	what	what	WP
37681	514	37	country	country	NN
37681	514	38	,	,	,
37681	514	39	nor	nor	CC
37681	514	40	do	do	VBP
37681	514	41	we	-PRON-	PRP
37681	514	42	know	know	VB
37681	514	43	his	-PRON-	PRP$
37681	514	44	race	race	NN
37681	514	45	,	,	,
37681	514	46	his	-PRON-	PRP$
37681	514	47	parentage	parentage	NN
37681	514	48	,	,	,
37681	514	49	or	or	CC
37681	514	50	the	the	DT
37681	514	51	time	time	NN
37681	514	52	of	of	IN
37681	514	53	his	-PRON-	PRP$
37681	514	54	death	death	NN
37681	514	55	.	.	.
37681	515	1	We	-PRON-	PRP
37681	515	2	should	should	MD
37681	515	3	not	not	RB
37681	515	4	feel	feel	VB
37681	515	5	that	that	IN
37681	515	6	we	-PRON-	PRP
37681	515	7	knew	know	VBD
37681	515	8	much	much	JJ
37681	515	9	of	of	IN
37681	515	10	the	the	DT
37681	515	11	life	life	NN
37681	515	12	of	of	IN
37681	515	13	a	a	DT
37681	515	14	man	man	NN
37681	515	15	who	who	WP
37681	515	16	lived	live	VBD
37681	515	17	when	when	WRB
37681	515	18	the	the	DT
37681	515	19	Magna	Magna	NNPS
37681	515	20	Charta	Charta	NNP
37681	515	21	was	be	VBD
37681	515	22	wrested	wrest	VBN
37681	515	23	from	from	IN
37681	515	24	King	King	NNP
37681	515	25	John	John	NNP
37681	515	26	,	,	,
37681	515	27	if	if	IN
37681	515	28	our	-PRON-	PRP$
37681	515	29	first	first	JJ
37681	515	30	and	and	CC
37681	515	31	only	only	JJ
37681	515	32	source	source	NN
37681	515	33	of	of	IN
37681	515	34	information	information	NN
37681	515	35	was	be	VBD
37681	515	36	a	a	DT
37681	515	37	paragraph	paragraph	NN
37681	515	38	in	in	IN
37681	515	39	the	the	DT
37681	515	40	works	work	NNS
37681	515	41	of	of	IN
37681	515	42	some	some	DT
37681	515	43	historian	historian	NN
37681	515	44	of	of	IN
37681	515	45	to	to	IN
37681	515	46	-	-	HYPH
37681	515	47	day	day	NN
37681	515	48	;	;	:
37681	515	49	and	and	CC
37681	515	50	yet	yet	RB
37681	515	51	this	this	DT
37681	515	52	is	be	VBZ
37681	515	53	about	about	IN
37681	515	54	the	the	DT
37681	515	55	situation	situation	NN
37681	515	56	in	in	IN
37681	515	57	respect	respect	NN
37681	515	58	to	to	IN
37681	515	59	Euclid	Euclid	NNP
37681	515	60	.	.	.
37681	516	1	Proclus	Proclus	NNP
37681	516	2	of	of	IN
37681	516	3	Alexandria	Alexandria	NNP
37681	516	4	,	,	,
37681	516	5	philosopher	philosopher	NN
37681	516	6	,	,	,
37681	516	7	teacher	teacher	NN
37681	516	8	,	,	,
37681	516	9	and	and	CC
37681	516	10	mathematician	mathematician	NNP
37681	516	11	,	,	,
37681	516	12	lived	live	VBD
37681	516	13	from	from	IN
37681	516	14	410	410	CD
37681	516	15	to	to	TO
37681	516	16	485	485	CD
37681	516	17	A.D.	a.d.	NN
37681	516	18	,	,	,
37681	516	19	and	and	CC
37681	516	20	wrote	write	VBD
37681	516	21	a	a	DT
37681	516	22	commentary	commentary	NN
37681	516	23	on	on	IN
37681	516	24	the	the	DT
37681	516	25	works	work	NNS
37681	516	26	of	of	IN
37681	516	27	Euclid	Euclid	NNP
37681	516	28	.	.	.
37681	517	1	In	in	IN
37681	517	2	his	-PRON-	PRP$
37681	517	3	writings	writing	NNS
37681	517	4	,	,	,
37681	517	5	which	which	WDT
37681	517	6	seem	seem	VBP
37681	517	7	to	to	TO
37681	517	8	set	set	VB
37681	517	9	forth	forth	RP
37681	517	10	in	in	IN
37681	517	11	amplified	amplified	JJ
37681	517	12	form	form	NN
37681	517	13	his	-PRON-	PRP$
37681	517	14	lectures	lecture	NNS
37681	517	15	to	to	IN
37681	517	16	the	the	DT
37681	517	17	students	student	NNS
37681	517	18	in	in	IN
37681	517	19	the	the	DT
37681	517	20	Neoplatonist	Neoplatonist	NNP
37681	517	21	School	School	NNP
37681	517	22	of	of	IN
37681	517	23	Alexandria	Alexandria	NNP
37681	517	24	,	,	,
37681	517	25	Proclus	Proclus	NNP
37681	517	26	makes	make	VBZ
37681	517	27	this	this	DT
37681	517	28	statement	statement	NN
37681	517	29	,	,	,
37681	517	30	and	and	CC
37681	517	31	of	of	IN
37681	517	32	Euclid	Euclid	NNP
37681	517	33	's	's	POS
37681	517	34	life	life	NN
37681	517	35	we	-PRON-	PRP
37681	517	36	have	have	VBP
37681	517	37	little	little	JJ
37681	517	38	else	else	RB
37681	517	39	:	:	:
37681	517	40	Not	not	RB
37681	517	41	much	much	RB
37681	517	42	younger	young	JJR
37681	517	43	than	than	IN
37681	517	44	these[24	these[24	NN
37681	517	45	]	]	-RRB-
37681	517	46	is	be	VBZ
37681	517	47	Euclid	Euclid	NNP
37681	517	48	,	,	,
37681	517	49	who	who	WP
37681	517	50	put	put	VBD
37681	517	51	together	together	RP
37681	517	52	the	the	DT
37681	517	53	"	"	``
37681	517	54	Elements	element	NNS
37681	517	55	,	,	,
37681	517	56	"	"	''
37681	517	57	collecting	collect	VBG
37681	517	58	many	many	JJ
37681	517	59	of	of	IN
37681	517	60	the	the	DT
37681	517	61	theorems	theorem	NNS
37681	517	62	of	of	IN
37681	517	63	Eudoxus	Eudoxus	NNP
37681	517	64	,	,	,
37681	517	65	perfecting	perfect	VBG
37681	517	66	many	many	JJ
37681	517	67	of	of	IN
37681	517	68	those	those	DT
37681	517	69	of	of	IN
37681	517	70	Theætetus	Theætetus	NNP
37681	517	71	,	,	,
37681	517	72	and	and	CC
37681	517	73	also	also	RB
37681	517	74	demonstrating	demonstrate	VBG
37681	517	75	with	with	IN
37681	517	76	perfect	perfect	JJ
37681	517	77	certainty	certainty	NN
37681	517	78	what	what	WP
37681	517	79	his	-PRON-	PRP$
37681	517	80	predecessors	predecessor	NNS
37681	517	81	had	have	VBD
37681	517	82	but	but	CC
37681	517	83	insufficiently	insufficiently	RB
37681	517	84	proved	prove	VBN
37681	517	85	.	.	.
37681	518	1	He	-PRON-	PRP
37681	518	2	flourished	flourish	VBD
37681	518	3	in	in	IN
37681	518	4	the	the	DT
37681	518	5	time	time	NN
37681	518	6	of	of	IN
37681	518	7	the	the	DT
37681	518	8	first	first	JJ
37681	518	9	Ptolemy	Ptolemy	NNP
37681	518	10	,	,	,
37681	518	11	for	for	IN
37681	518	12	Archimedes	Archimedes	NNP
37681	518	13	,	,	,
37681	518	14	who	who	WP
37681	518	15	closely	closely	RB
37681	518	16	followed	follow	VBD
37681	518	17	this	this	DT
37681	518	18	ruler,[25	ruler,[25	NN
37681	518	19	]	]	-RRB-
37681	518	20	speaks	speak	VBZ
37681	518	21	of	of	IN
37681	518	22	Euclid	Euclid	NNP
37681	518	23	.	.	.
37681	519	1	Furthermore	furthermore	RB
37681	519	2	it	-PRON-	PRP
37681	519	3	is	be	VBZ
37681	519	4	related	relate	VBN
37681	519	5	that	that	IN
37681	519	6	Ptolemy	Ptolemy	NNP
37681	519	7	one	one	CD
37681	519	8	time	time	NN
37681	519	9	demanded	demand	VBD
37681	519	10	of	of	IN
37681	519	11	him	-PRON-	PRP
37681	519	12	if	if	IN
37681	519	13	there	there	EX
37681	519	14	was	be	VBD
37681	519	15	in	in	IN
37681	519	16	geometry	geometry	NN
37681	519	17	no	no	DT
37681	519	18	shorter	short	JJR
37681	519	19	way	way	NN
37681	519	20	than	than	IN
37681	519	21	that	that	DT
37681	519	22	of	of	IN
37681	519	23	the	the	DT
37681	519	24	"	"	``
37681	519	25	Elements	Elements	NNPS
37681	519	26	,	,	,
37681	519	27	"	"	''
37681	519	28	to	to	TO
37681	519	29	whom	whom	WP
37681	519	30	he	-PRON-	PRP
37681	519	31	replied	reply	VBD
37681	519	32	that	that	IN
37681	519	33	there	there	EX
37681	519	34	was	be	VBD
37681	519	35	no	no	DT
37681	519	36	royal	royal	JJ
37681	519	37	road	road	NN
37681	519	38	to	to	IN
37681	519	39	geometry	geometry	NN
37681	519	40	.	.	.
37681	520	1	[	[	-LRB-
37681	520	2	26	26	CD
37681	520	3	]	]	-RRB-
37681	520	4	He	-PRON-	PRP
37681	520	5	was	be	VBD
37681	520	6	therefore	therefore	RB
37681	520	7	younger	young	JJR
37681	520	8	than	than	IN
37681	520	9	the	the	DT
37681	520	10	pupils	pupil	NNS
37681	520	11	of	of	IN
37681	520	12	Plato	Plato	NNP
37681	520	13	,	,	,
37681	520	14	but	but	CC
37681	520	15	older	old	JJR
37681	520	16	than	than	IN
37681	520	17	Eratosthenes	Eratosthenes	NNPS
37681	520	18	and	and	CC
37681	520	19	Archimedes	archimede	NNS
37681	520	20	;	;	:
37681	520	21	for	for	IN
37681	520	22	the	the	DT
37681	520	23	latter	latter	JJ
37681	520	24	were	be	VBD
37681	520	25	contemporary	contemporary	JJ
37681	520	26	with	with	IN
37681	520	27	one	one	CD
37681	520	28	another	another	DT
37681	520	29	,	,	,
37681	520	30	as	as	IN
37681	520	31	Eratosthenes	Eratosthenes	NNP
37681	520	32	somewhere	somewhere	RB
37681	520	33	says	say	VBZ
37681	520	34	.	.	.
37681	521	1	[	[	-LRB-
37681	521	2	27	27	CD
37681	521	3	]	]	-RRB-
37681	521	4	Thus	thus	RB
37681	521	5	we	-PRON-	PRP
37681	521	6	have	have	VBP
37681	521	7	in	in	IN
37681	521	8	a	a	DT
37681	521	9	few	few	JJ
37681	521	10	lines	line	NNS
37681	521	11	,	,	,
37681	521	12	from	from	IN
37681	521	13	one	one	CD
37681	521	14	who	who	WP
37681	521	15	lived	live	VBD
37681	521	16	perhaps	perhaps	RB
37681	521	17	seven	seven	CD
37681	521	18	or	or	CC
37681	521	19	eight	eight	CD
37681	521	20	hundred	hundred	CD
37681	521	21	years	year	NNS
37681	521	22	after	after	IN
37681	521	23	Euclid	Euclid	NNP
37681	521	24	,	,	,
37681	521	25	nearly	nearly	RB
37681	521	26	all	all	DT
37681	521	27	that	that	WDT
37681	521	28	is	be	VBZ
37681	521	29	known	know	VBN
37681	521	30	of	of	IN
37681	521	31	the	the	DT
37681	521	32	most	most	RBS
37681	521	33	famous	famous	JJ
37681	521	34	teacher	teacher	NN
37681	521	35	of	of	IN
37681	521	36	geometry	geometry	NN
37681	521	37	that	that	WDT
37681	521	38	ever	ever	RB
37681	521	39	lived	live	VBD
37681	521	40	.	.	.
37681	522	1	Nevertheless	nevertheless	RB
37681	522	2	,	,	,
37681	522	3	even	even	RB
37681	522	4	this	this	DT
37681	522	5	little	little	JJ
37681	522	6	tells	tell	VBZ
37681	522	7	us	-PRON-	PRP
37681	522	8	about	about	IN
37681	522	9	when	when	WRB
37681	522	10	he	-PRON-	PRP
37681	522	11	flourished	flourish	VBD
37681	522	12	,	,	,
37681	522	13	for	for	IN
37681	522	14	Hermotimus	Hermotimus	NNP
37681	522	15	and	and	CC
37681	522	16	Philippus	Philippus	NNP
37681	522	17	were	be	VBD
37681	522	18	pupils	pupil	NNS
37681	522	19	of	of	IN
37681	522	20	Plato	Plato	NNP
37681	522	21	,	,	,
37681	522	22	who	who	WP
37681	522	23	died	die	VBD
37681	522	24	in	in	IN
37681	522	25	347	347	CD
37681	522	26	B.C.	B.C.	NNP
37681	522	27	,	,	,
37681	522	28	whereas	whereas	IN
37681	522	29	Archimedes	Archimedes	NNP
37681	522	30	was	be	VBD
37681	522	31	born	bear	VBN
37681	522	32	about	about	RB
37681	522	33	287	287	CD
37681	522	34	B.C.	B.C.	NNS
37681	523	1	and	and	CC
37681	523	2	was	be	VBD
37681	523	3	writing	write	VBG
37681	523	4	about	about	RB
37681	523	5	250	250	CD
37681	523	6	B.C.	B.C.	NNS
37681	524	1	Furthermore	furthermore	RB
37681	524	2	,	,	,
37681	524	3	since	since	IN
37681	524	4	Ptolemy	Ptolemy	NNP
37681	524	5	I	-PRON-	PRP
37681	524	6	reigned	reign	VBD
37681	524	7	from	from	IN
37681	524	8	306	306	CD
37681	524	9	to	to	IN
37681	524	10	283	283	CD
37681	524	11	B.C.	B.C.	NNP
37681	524	12	,	,	,
37681	524	13	Euclid	Euclid	NNP
37681	524	14	must	must	MD
37681	524	15	have	have	VB
37681	524	16	been	be	VBN
37681	524	17	teaching	teach	VBG
37681	524	18	about	about	RB
37681	524	19	300	300	CD
37681	524	20	B.C.	B.C.	NNP
37681	524	21	,	,	,
37681	524	22	and	and	CC
37681	524	23	this	this	DT
37681	524	24	is	be	VBZ
37681	524	25	the	the	DT
37681	524	26	date	date	NN
37681	524	27	that	that	WDT
37681	524	28	is	be	VBZ
37681	524	29	generally	generally	RB
37681	524	30	assigned	assign	VBN
37681	524	31	to	to	IN
37681	524	32	him	-PRON-	PRP
37681	524	33	.	.	.
37681	525	1	Euclid	Euclid	NNP
37681	525	2	probably	probably	RB
37681	525	3	studied	study	VBD
37681	525	4	at	at	IN
37681	525	5	Athens	Athens	NNP
37681	525	6	,	,	,
37681	525	7	for	for	IN
37681	525	8	until	until	IN
37681	525	9	he	-PRON-	PRP
37681	525	10	himself	-PRON-	PRP
37681	525	11	assisted	assist	VBD
37681	525	12	in	in	IN
37681	525	13	transferring	transfer	VBG
37681	525	14	the	the	DT
37681	525	15	center	center	NN
37681	525	16	of	of	IN
37681	525	17	mathematical	mathematical	JJ
37681	525	18	culture	culture	NN
37681	525	19	to	to	IN
37681	525	20	Alexandria	Alexandria	NNP
37681	525	21	,	,	,
37681	525	22	it	-PRON-	PRP
37681	525	23	had	have	VBD
37681	525	24	long	long	RB
37681	525	25	been	be	VBN
37681	525	26	in	in	IN
37681	525	27	the	the	DT
37681	525	28	Grecian	grecian	JJ
37681	525	29	capital	capital	NN
37681	525	30	,	,	,
37681	525	31	indeed	indeed	RB
37681	525	32	since	since	IN
37681	525	33	the	the	DT
37681	525	34	time	time	NN
37681	525	35	of	of	IN
37681	525	36	Pythagoras	Pythagoras	NNP
37681	525	37	.	.	.
37681	526	1	Moreover	moreover	RB
37681	526	2	,	,	,
37681	526	3	numerous	numerous	JJ
37681	526	4	attempts	attempt	NNS
37681	526	5	had	have	VBD
37681	526	6	been	be	VBN
37681	526	7	made	make	VBN
37681	526	8	at	at	IN
37681	526	9	Athens	Athens	NNP
37681	526	10	to	to	TO
37681	526	11	do	do	VB
37681	526	12	exactly	exactly	RB
37681	526	13	what	what	WP
37681	526	14	Euclid	Euclid	NNP
37681	526	15	succeeded	succeed	VBD
37681	526	16	in	in	IN
37681	526	17	doing,--to	doing,--to	FW
37681	526	18	construct	construct	VB
37681	526	19	a	a	DT
37681	526	20	logical	logical	JJ
37681	526	21	sequence	sequence	NN
37681	526	22	of	of	IN
37681	526	23	propositions	proposition	NNS
37681	526	24	;	;	:
37681	526	25	in	in	IN
37681	526	26	other	other	JJ
37681	526	27	words	word	NNS
37681	526	28	,	,	,
37681	526	29	to	to	TO
37681	526	30	write	write	VB
37681	526	31	a	a	DT
37681	526	32	textbook	textbook	NN
37681	526	33	on	on	IN
37681	526	34	plane	plane	NN
37681	526	35	geometry	geometry	NN
37681	526	36	.	.	.
37681	527	1	It	-PRON-	PRP
37681	527	2	was	be	VBD
37681	527	3	at	at	IN
37681	527	4	Athens	Athens	NNP
37681	527	5	,	,	,
37681	527	6	therefore	therefore	RB
37681	527	7	,	,	,
37681	527	8	that	that	IN
37681	527	9	he	-PRON-	PRP
37681	527	10	could	could	MD
37681	527	11	best	well	RBS
37681	527	12	have	have	VB
37681	527	13	received	receive	VBN
37681	527	14	the	the	DT
37681	527	15	inspiration	inspiration	NN
37681	527	16	to	to	TO
37681	527	17	compose	compose	VB
37681	527	18	his	-PRON-	PRP$
37681	527	19	"	"	``
37681	527	20	Elements	Elements	NNPS
37681	527	21	.	.	.
37681	528	1	"	"	``
37681	528	2	[	[	-LRB-
37681	528	3	28	28	CD
37681	528	4	]	]	-RRB-
37681	528	5	After	after	IN
37681	528	6	finishing	finish	VBG
37681	528	7	his	-PRON-	PRP$
37681	528	8	education	education	NN
37681	528	9	at	at	IN
37681	528	10	Athens	Athens	NNP
37681	528	11	it	-PRON-	PRP
37681	528	12	is	be	VBZ
37681	528	13	quite	quite	RB
37681	528	14	probable	probable	JJ
37681	528	15	that	that	IN
37681	528	16	he	-PRON-	PRP
37681	528	17	,	,	,
37681	528	18	like	like	IN
37681	528	19	other	other	JJ
37681	528	20	savants	savant	NNS
37681	528	21	of	of	IN
37681	528	22	the	the	DT
37681	528	23	period	period	NN
37681	528	24	,	,	,
37681	528	25	was	be	VBD
37681	528	26	called	call	VBN
37681	528	27	to	to	IN
37681	528	28	Alexandria	Alexandria	NNP
37681	528	29	by	by	IN
37681	528	30	Ptolemy	Ptolemy	NNP
37681	528	31	Soter	Soter	NNP
37681	528	32	,	,	,
37681	528	33	the	the	DT
37681	528	34	king	king	NN
37681	528	35	,	,	,
37681	528	36	to	to	TO
37681	528	37	assist	assist	VB
37681	528	38	in	in	IN
37681	528	39	establishing	establish	VBG
37681	528	40	the	the	DT
37681	528	41	great	great	JJ
37681	528	42	school	school	NN
37681	528	43	which	which	WDT
37681	528	44	made	make	VBD
37681	528	45	that	that	DT
37681	528	46	city	city	NN
37681	528	47	the	the	DT
37681	528	48	center	center	NN
37681	528	49	of	of	IN
37681	528	50	the	the	DT
37681	528	51	world	world	NN
37681	528	52	's	's	POS
37681	528	53	learning	learn	VBG
37681	528	54	for	for	IN
37681	528	55	several	several	JJ
37681	528	56	centuries	century	NNS
37681	528	57	.	.	.
37681	529	1	In	in	IN
37681	529	2	this	this	DT
37681	529	3	school	school	NN
37681	529	4	he	-PRON-	PRP
37681	529	5	taught	teach	VBD
37681	529	6	,	,	,
37681	529	7	and	and	CC
37681	529	8	here	here	RB
37681	529	9	he	-PRON-	PRP
37681	529	10	wrote	write	VBD
37681	529	11	the	the	DT
37681	529	12	"	"	``
37681	529	13	Elements	Elements	NNPS
37681	529	14	"	"	''
37681	529	15	and	and	CC
37681	529	16	numerous	numerous	JJ
37681	529	17	other	other	JJ
37681	529	18	works	work	NNS
37681	529	19	,	,	,
37681	529	20	perhaps	perhaps	RB
37681	529	21	ten	ten	CD
37681	529	22	in	in	IN
37681	529	23	all	all	DT
37681	529	24	.	.	.
37681	530	1	Although	although	IN
37681	530	2	the	the	DT
37681	530	3	Greek	greek	JJ
37681	530	4	writers	writer	NNS
37681	530	5	who	who	WP
37681	530	6	may	may	MD
37681	530	7	have	have	VB
37681	530	8	known	know	VBN
37681	530	9	something	something	NN
37681	530	10	of	of	IN
37681	530	11	the	the	DT
37681	530	12	life	life	NN
37681	530	13	of	of	IN
37681	530	14	Euclid	Euclid	NNP
37681	530	15	have	have	VBP
37681	530	16	little	little	JJ
37681	530	17	to	to	TO
37681	530	18	say	say	VB
37681	530	19	of	of	IN
37681	530	20	him	-PRON-	PRP
37681	530	21	,	,	,
37681	530	22	the	the	DT
37681	530	23	Arab	arab	JJ
37681	530	24	writers	writer	NNS
37681	530	25	,	,	,
37681	530	26	who	who	WP
37681	530	27	could	could	MD
37681	530	28	have	have	VB
37681	530	29	known	know	VBN
37681	530	30	nothing	nothing	NN
37681	530	31	save	save	IN
37681	530	32	from	from	IN
37681	530	33	Greek	greek	JJ
37681	530	34	sources	source	NNS
37681	530	35	,	,	,
37681	530	36	have	have	VBP
37681	530	37	allowed	allow	VBN
37681	530	38	their	-PRON-	PRP$
37681	530	39	imaginations	imagination	NNS
37681	530	40	the	the	DT
37681	530	41	usual	usual	JJ
37681	530	42	latitude	latitude	NN
37681	530	43	in	in	IN
37681	530	44	speaking	speak	VBG
37681	530	45	of	of	IN
37681	530	46	him	-PRON-	PRP
37681	530	47	and	and	CC
37681	530	48	of	of	IN
37681	530	49	his	-PRON-	PRP$
37681	530	50	labors	labor	NNS
37681	530	51	.	.	.
37681	531	1	Thus	thus	RB
37681	531	2	Al	Al	NNP
37681	531	3	-	-	HYPH
37681	531	4	Qif[t.][=i	Qif[t.][=i	NNP
37681	531	5	]	]	-RRB-
37681	531	6	,	,	,
37681	531	7	who	who	WP
37681	531	8	wrote	write	VBD
37681	531	9	in	in	IN
37681	531	10	the	the	DT
37681	531	11	thirteenth	thirteenth	JJ
37681	531	12	century	century	NN
37681	531	13	,	,	,
37681	531	14	has	have	VBZ
37681	531	15	this	this	DT
37681	531	16	to	to	TO
37681	531	17	say	say	VB
37681	531	18	in	in	IN
37681	531	19	his	-PRON-	PRP$
37681	531	20	biographical	biographical	JJ
37681	531	21	treatise	treatise	NN
37681	531	22	"	"	''
37681	531	23	Ta'r[=i]kh	Ta'r[=i]kh	NNP
37681	531	24	al-[H.]ukam[=a	al-[h.]ukam[=a	NN
37681	531	25	]	]	-RRB-
37681	531	26	"	"	''
37681	531	27	:	:	:
37681	531	28	Euclid	euclid	JJ
37681	531	29	,	,	,
37681	531	30	son	son	NN
37681	531	31	of	of	IN
37681	531	32	Naucrates	Naucrates	NNP
37681	531	33	,	,	,
37681	531	34	grandson	grandson	NN
37681	531	35	of	of	IN
37681	531	36	Zenarchus	Zenarchus	NNP
37681	531	37	,	,	,
37681	531	38	called	call	VBD
37681	531	39	the	the	DT
37681	531	40	author	author	NN
37681	531	41	of	of	IN
37681	531	42	geometry	geometry	NN
37681	531	43	,	,	,
37681	531	44	a	a	DT
37681	531	45	Greek	Greek	NNP
37681	531	46	by	by	IN
37681	531	47	nationality	nationality	NN
37681	531	48	,	,	,
37681	531	49	domiciled	domicile	VBN
37681	531	50	at	at	IN
37681	531	51	Damascus	Damascus	NNP
37681	531	52	,	,	,
37681	531	53	born	bear	VBN
37681	531	54	at	at	IN
37681	531	55	Tyre	Tyre	NNP
37681	531	56	,	,	,
37681	531	57	most	most	RBS
37681	531	58	learned	learn	VBN
37681	531	59	in	in	IN
37681	531	60	the	the	DT
37681	531	61	science	science	NN
37681	531	62	of	of	IN
37681	531	63	geometry	geometry	NN
37681	531	64	,	,	,
37681	531	65	published	publish	VBD
37681	531	66	a	a	DT
37681	531	67	most	most	RBS
37681	531	68	excellent	excellent	JJ
37681	531	69	and	and	CC
37681	531	70	most	most	RBS
37681	531	71	useful	useful	JJ
37681	531	72	work	work	NN
37681	531	73	entitled	entitle	VBN
37681	531	74	"	"	``
37681	531	75	The	the	DT
37681	531	76	Foundation	Foundation	NNP
37681	531	77	or	or	CC
37681	531	78	Elements	Elements	NNPS
37681	531	79	of	of	IN
37681	531	80	Geometry	Geometry	NNP
37681	531	81	,	,	,
37681	531	82	"	"	''
37681	531	83	a	a	DT
37681	531	84	subject	subject	NN
37681	531	85	in	in	IN
37681	531	86	which	which	WDT
37681	531	87	no	no	DT
37681	531	88	more	more	RBR
37681	531	89	general	general	JJ
37681	531	90	treatise	treatise	NN
37681	531	91	existed	exist	VBD
37681	531	92	before	before	RB
37681	531	93	among	among	IN
37681	531	94	the	the	DT
37681	531	95	Greeks	Greeks	NNPS
37681	531	96	;	;	:
37681	531	97	nay	nay	NN
37681	531	98	,	,	,
37681	531	99	there	there	EX
37681	531	100	was	be	VBD
37681	531	101	no	no	DT
37681	531	102	one	one	NN
37681	531	103	even	even	RB
37681	531	104	of	of	IN
37681	531	105	later	later	JJ
37681	531	106	date	date	NN
37681	531	107	who	who	WP
37681	531	108	did	do	VBD
37681	531	109	not	not	RB
37681	531	110	walk	walk	VB
37681	531	111	in	in	IN
37681	531	112	his	-PRON-	PRP$
37681	531	113	footsteps	footstep	NNS
37681	531	114	and	and	CC
37681	531	115	frankly	frankly	RB
37681	531	116	profess	profess	IN
37681	531	117	his	-PRON-	PRP$
37681	531	118	doctrine	doctrine	NN
37681	531	119	.	.	.
37681	532	1	This	this	DT
37681	532	2	is	be	VBZ
37681	532	3	rather	rather	RB
37681	532	4	a	a	DT
37681	532	5	specimen	speciman	NNS
37681	532	6	of	of	IN
37681	532	7	the	the	DT
37681	532	8	Arab	arab	JJ
37681	532	9	tendency	tendency	NN
37681	532	10	to	to	TO
37681	532	11	manufacture	manufacture	VB
37681	532	12	history	history	NN
37681	532	13	than	than	IN
37681	532	14	a	a	DT
37681	532	15	serious	serious	JJ
37681	532	16	contribution	contribution	NN
37681	532	17	to	to	IN
37681	532	18	the	the	DT
37681	532	19	biography	biography	NN
37681	532	20	of	of	IN
37681	532	21	Euclid	Euclid	NNP
37681	532	22	,	,	,
37681	532	23	of	of	IN
37681	532	24	whose	whose	WP$
37681	532	25	personal	personal	JJ
37681	532	26	history	history	NN
37681	532	27	we	-PRON-	PRP
37681	532	28	have	have	VBP
37681	532	29	only	only	RB
37681	532	30	the	the	DT
37681	532	31	information	information	NN
37681	532	32	given	give	VBN
37681	532	33	by	by	IN
37681	532	34	Proclus	Proclus	NNP
37681	532	35	.	.	.
37681	533	1	[	[	-LRB-
37681	533	2	Illustration	illustration	NN
37681	533	3	:	:	:
37681	533	4	EUCLID	EUCLID	NNP
37681	533	5	From	from	IN
37681	533	6	an	an	DT
37681	533	7	old	old	JJ
37681	533	8	print	print	NN
37681	533	9	]	]	-RRB-
37681	533	10	Euclid	Euclid	NNP
37681	533	11	's	's	POS
37681	533	12	works	work	NNS
37681	533	13	at	at	IN
37681	533	14	once	once	RB
37681	533	15	took	take	VBD
37681	533	16	high	high	JJ
37681	533	17	rank	rank	NN
37681	533	18	,	,	,
37681	533	19	and	and	CC
37681	533	20	they	-PRON-	PRP
37681	533	21	are	be	VBP
37681	533	22	mentioned	mention	VBN
37681	533	23	by	by	IN
37681	533	24	various	various	JJ
37681	533	25	classical	classical	JJ
37681	533	26	authors	author	NNS
37681	533	27	.	.	.
37681	534	1	Cicero	Cicero	NNP
37681	534	2	knew	know	VBD
37681	534	3	of	of	IN
37681	534	4	them	-PRON-	PRP
37681	534	5	,	,	,
37681	534	6	and	and	CC
37681	534	7	Capella	Capella	NNP
37681	534	8	(	(	-LRB-
37681	534	9	_	_	NNP
37681	534	10	ca	ca	NNP
37681	534	11	.	.	.
37681	534	12	_	_	NNP
37681	534	13	470	470	CD
37681	534	14	A.D.	A.D.	NNP
37681	534	15	)	)	-RRB-
37681	534	16	,	,	,
37681	534	17	Cassiodorius	Cassiodorius	NNP
37681	534	18	(	(	-LRB-
37681	534	19	_	_	NNP
37681	534	20	ca	ca	NNP
37681	534	21	.	.	.
37681	534	22	_	_	NNP
37681	534	23	515	515	CD
37681	534	24	A.D.	A.D.	NNP
37681	534	25	)	)	-RRB-
37681	534	26	,	,	,
37681	534	27	and	and	CC
37681	534	28	Boethius	Boethius	NNP
37681	534	29	(	(	-LRB-
37681	534	30	_	_	NNP
37681	534	31	ca	ca	NNP
37681	534	32	.	.	.
37681	534	33	_	_	NNP
37681	534	34	480	480	CD
37681	534	35	-	-	SYM
37681	534	36	524	524	CD
37681	534	37	A.D.	A.D.	NNP
37681	534	38	)	)	-RRB-
37681	534	39	were	be	VBD
37681	534	40	all	all	DT
37681	534	41	more	more	RBR
37681	534	42	or	or	CC
37681	534	43	less	less	RBR
37681	534	44	familiar	familiar	JJ
37681	534	45	with	with	IN
37681	534	46	the	the	DT
37681	534	47	"	"	``
37681	534	48	Elements	Elements	NNPS
37681	534	49	.	.	.
37681	534	50	"	"	''
37681	535	1	With	with	IN
37681	535	2	the	the	DT
37681	535	3	advance	advance	NN
37681	535	4	of	of	IN
37681	535	5	the	the	DT
37681	535	6	Dark	Dark	NNP
37681	535	7	Ages	Ages	NNPS
37681	535	8	,	,	,
37681	535	9	however	however	RB
37681	535	10	,	,	,
37681	535	11	learning	learning	NN
37681	535	12	was	be	VBD
37681	535	13	held	hold	VBN
37681	535	14	in	in	IN
37681	535	15	less	less	JJR
37681	535	16	and	and	CC
37681	535	17	less	less	RBR
37681	535	18	esteem	esteem	VB
37681	535	19	,	,	,
37681	535	20	so	so	IN
37681	535	21	that	that	IN
37681	535	22	Euclid	Euclid	NNP
37681	535	23	was	be	VBD
37681	535	24	finally	finally	RB
37681	535	25	forgotten	forget	VBN
37681	535	26	,	,	,
37681	535	27	and	and	CC
37681	535	28	manuscripts	manuscript	NNS
37681	535	29	of	of	IN
37681	535	30	his	-PRON-	PRP$
37681	535	31	works	work	NNS
37681	535	32	were	be	VBD
37681	535	33	either	either	CC
37681	535	34	destroyed	destroy	VBN
37681	535	35	or	or	CC
37681	535	36	buried	bury	VBN
37681	535	37	in	in	IN
37681	535	38	some	some	DT
37681	535	39	remote	remote	JJ
37681	535	40	cloister	cloister	NN
37681	535	41	.	.	.
37681	536	1	The	the	DT
37681	536	2	Arabs	Arabs	NNPS
37681	536	3	,	,	,
37681	536	4	however	however	RB
37681	536	5	,	,	,
37681	536	6	whose	whose	WP$
37681	536	7	civilization	civilization	NN
37681	536	8	assumed	assume	VBD
37681	536	9	prominence	prominence	NN
37681	536	10	from	from	IN
37681	536	11	about	about	IN
37681	536	12	750	750	CD
37681	536	13	A.D.	A.D.	NNP
37681	536	14	to	to	IN
37681	536	15	about	about	IN
37681	536	16	1500	1500	CD
37681	536	17	,	,	,
37681	536	18	translated	translate	VBD
37681	536	19	the	the	DT
37681	536	20	most	most	RBS
37681	536	21	important	important	JJ
37681	536	22	treatises	treatise	NNS
37681	536	23	of	of	IN
37681	536	24	the	the	DT
37681	536	25	Greeks	Greeks	NNPS
37681	536	26	,	,	,
37681	536	27	and	and	CC
37681	536	28	Euclid	Euclid	NNP
37681	536	29	's	's	POS
37681	536	30	"	"	``
37681	536	31	Elements	Elements	NNPS
37681	536	32	"	"	''
37681	536	33	among	among	IN
37681	536	34	the	the	DT
37681	536	35	rest	rest	NN
37681	536	36	.	.	.
37681	537	1	One	one	CD
37681	537	2	of	of	IN
37681	537	3	these	these	DT
37681	537	4	Arabic	arabic	JJ
37681	537	5	editions	edition	NNS
37681	537	6	an	an	DT
37681	537	7	English	english	JJ
37681	537	8	monk	monk	NN
37681	537	9	of	of	IN
37681	537	10	the	the	DT
37681	537	11	twelfth	twelfth	JJ
37681	537	12	century	century	NN
37681	537	13	,	,	,
37681	537	14	one	one	CD
37681	537	15	Athelhard	Athelhard	NNP
37681	537	16	(	(	-LRB-
37681	537	17	Æthelhard	Æthelhard	NNP
37681	537	18	)	)	-RRB-
37681	537	19	of	of	IN
37681	537	20	Bath	Bath	NNP
37681	537	21	,	,	,
37681	537	22	found	find	VBD
37681	537	23	and	and	CC
37681	537	24	translated	translate	VBN
37681	537	25	into	into	IN
37681	537	26	Latin	Latin	NNP
37681	537	27	(	(	-LRB-
37681	537	28	_	_	NNP
37681	537	29	ca	ca	NNP
37681	537	30	.	.	.
37681	537	31	_	_	NNP
37681	537	32	1120	1120	CD
37681	537	33	A.D.	A.D.	NNP
37681	537	34	)	)	-RRB-
37681	537	35	.	.	.
37681	538	1	A	a	DT
37681	538	2	little	little	JJ
37681	538	3	later	later	JJ
37681	538	4	Gherard	Gherard	NNP
37681	538	5	of	of	IN
37681	538	6	Cremona	Cremona	NNP
37681	538	7	(	(	-LRB-
37681	538	8	1114	1114	CD
37681	538	9	-	-	SYM
37681	538	10	1187	1187	CD
37681	538	11	)	)	-RRB-
37681	538	12	made	make	VBD
37681	538	13	a	a	DT
37681	538	14	new	new	JJ
37681	538	15	translation	translation	NN
37681	538	16	from	from	IN
37681	538	17	the	the	DT
37681	538	18	Arabic	Arabic	NNP
37681	538	19	,	,	,
37681	538	20	differing	differ	VBG
37681	538	21	in	in	IN
37681	538	22	essential	essential	JJ
37681	538	23	features	feature	NNS
37681	538	24	from	from	IN
37681	538	25	that	that	DT
37681	538	26	of	of	IN
37681	538	27	Athelhard	Athelhard	NNP
37681	538	28	,	,	,
37681	538	29	and	and	CC
37681	538	30	about	about	RB
37681	538	31	1260	1260	CD
37681	538	32	Johannes	Johannes	NNP
37681	538	33	Campanus	Campanus	NNP
37681	538	34	made	make	VBD
37681	538	35	still	still	RB
37681	538	36	a	a	DT
37681	538	37	third	third	JJ
37681	538	38	translation	translation	NN
37681	538	39	,	,	,
37681	538	40	also	also	RB
37681	538	41	from	from	IN
37681	538	42	Arabic	Arabic	NNP
37681	538	43	into	into	IN
37681	538	44	Latin	Latin	NNP
37681	538	45	.	.	.
37681	539	1	[	[	-LRB-
37681	539	2	29	29	CD
37681	539	3	]	]	-RRB-
37681	539	4	There	there	EX
37681	539	5	is	be	VBZ
37681	539	6	reason	reason	NN
37681	539	7	to	to	TO
37681	539	8	believe	believe	VB
37681	539	9	that	that	IN
37681	539	10	Athelhard	Athelhard	NNP
37681	539	11	,	,	,
37681	539	12	Campanus	Campanus	NNP
37681	539	13	,	,	,
37681	539	14	and	and	CC
37681	539	15	Gherard	Gherard	NNP
37681	539	16	may	may	MD
37681	539	17	all	all	RB
37681	539	18	have	have	VB
37681	539	19	had	have	VBN
37681	539	20	access	access	NN
37681	539	21	to	to	IN
37681	539	22	an	an	DT
37681	539	23	earlier	early	JJR
37681	539	24	Latin	latin	JJ
37681	539	25	translation	translation	NN
37681	539	26	,	,	,
37681	539	27	since	since	IN
37681	539	28	all	all	DT
37681	539	29	are	be	VBP
37681	539	30	quite	quite	RB
37681	539	31	alike	alike	RB
37681	539	32	in	in	IN
37681	539	33	some	some	DT
37681	539	34	particulars	particular	NNS
37681	539	35	while	while	IN
37681	539	36	diverging	diverge	VBG
37681	539	37	noticeably	noticeably	RB
37681	539	38	in	in	IN
37681	539	39	others	other	NNS
37681	539	40	.	.	.
37681	540	1	Indeed	indeed	RB
37681	540	2	,	,	,
37681	540	3	there	there	EX
37681	540	4	is	be	VBZ
37681	540	5	an	an	DT
37681	540	6	old	old	JJ
37681	540	7	English	english	JJ
37681	540	8	verse	verse	NN
37681	540	9	that	that	WDT
37681	540	10	relates	relate	VBZ
37681	540	11	:	:	:
37681	540	12	The	the	DT
37681	540	13	clerk	clerk	NN
37681	540	14	Euclide	Euclide	NNP
37681	540	15	on	on	IN
37681	540	16	this	this	DT
37681	540	17	wyse	wyse	NN
37681	540	18	hit	hit	VBN
37681	540	19	fonde	fonde	JJ
37681	540	20	Thys	Thys	NNP
37681	540	21	craft	craft	NN
37681	540	22	of	of	IN
37681	540	23	gemetry	gemetry	NN
37681	540	24	yn	yn	NNP
37681	540	25	Egypte	Egypte	NNP
37681	540	26	londe	londe	JJ
37681	540	27	...	...	:
37681	540	28	Thys	thys	NN
37681	540	29	craft	craft	NN
37681	540	30	com	com	NN
37681	540	31	into	into	IN
37681	540	32	England	England	NNP
37681	540	33	,	,	,
37681	540	34	as	as	IN
37681	540	35	y	y	NNP
37681	540	36	yow	yow	UH
37681	540	37	say	say	VBP
37681	540	38	,	,	,
37681	540	39	Yn	Yn	NNP
37681	540	40	tyme	tyme	NNS
37681	540	41	of	of	IN
37681	540	42	good	good	JJ
37681	540	43	Kyng	Kyng	NNP
37681	540	44	Adelstone	Adelstone	NNP
37681	540	45	's	's	POS
37681	540	46	day	day	NN
37681	540	47	.	.	.
37681	541	1	If	if	IN
37681	541	2	this	this	DT
37681	541	3	be	be	VB
37681	541	4	true	true	JJ
37681	541	5	,	,	,
37681	541	6	Euclid	Euclid	NNP
37681	541	7	was	be	VBD
37681	541	8	known	know	VBN
37681	541	9	in	in	IN
37681	541	10	England	England	NNP
37681	541	11	as	as	RB
37681	541	12	early	early	RB
37681	541	13	as	as	IN
37681	541	14	924	924	CD
37681	541	15	-	-	SYM
37681	541	16	940	940	CD
37681	541	17	A.D.	A.D.	NNP
37681	542	1	Without	without	IN
37681	542	2	going	go	VBG
37681	542	3	into	into	IN
37681	542	4	particulars	particular	NNS
37681	542	5	further	far	RBR
37681	542	6	,	,	,
37681	542	7	it	-PRON-	PRP
37681	542	8	suffices	suffice	VBZ
37681	542	9	to	to	TO
37681	542	10	say	say	VB
37681	542	11	that	that	IN
37681	542	12	the	the	DT
37681	542	13	modern	modern	JJ
37681	542	14	knowledge	knowledge	NN
37681	542	15	of	of	IN
37681	542	16	Euclid	Euclid	NNP
37681	542	17	came	come	VBD
37681	542	18	first	first	RB
37681	542	19	through	through	IN
37681	542	20	the	the	DT
37681	542	21	Arabic	Arabic	NNP
37681	542	22	into	into	IN
37681	542	23	the	the	DT
37681	542	24	Latin	Latin	NNP
37681	542	25	,	,	,
37681	542	26	and	and	CC
37681	542	27	the	the	DT
37681	542	28	first	first	JJ
37681	542	29	printed	print	VBN
37681	542	30	edition	edition	NN
37681	542	31	of	of	IN
37681	542	32	the	the	DT
37681	542	33	"	"	``
37681	542	34	Elements	Elements	NNPS
37681	542	35	"	"	''
37681	542	36	(	(	-LRB-
37681	542	37	Venice	Venice	NNP
37681	542	38	,	,	,
37681	542	39	1482	1482	CD
37681	542	40	)	)	-RRB-
37681	542	41	was	be	VBD
37681	542	42	the	the	DT
37681	542	43	Campanus	Campanus	NNP
37681	542	44	translation	translation	NN
37681	542	45	.	.	.
37681	543	1	Greek	greek	JJ
37681	543	2	manuscripts	manuscript	NNS
37681	543	3	now	now	RB
37681	543	4	began	begin	VBD
37681	543	5	to	to	TO
37681	543	6	appear	appear	VB
37681	543	7	,	,	,
37681	543	8	and	and	CC
37681	543	9	at	at	IN
37681	543	10	the	the	DT
37681	543	11	present	present	JJ
37681	543	12	time	time	NN
37681	543	13	several	several	JJ
37681	543	14	are	be	VBP
37681	543	15	known	know	VBN
37681	543	16	.	.	.
37681	544	1	There	there	EX
37681	544	2	is	be	VBZ
37681	544	3	a	a	DT
37681	544	4	manuscript	manuscript	NN
37681	544	5	of	of	IN
37681	544	6	the	the	DT
37681	544	7	ninth	ninth	JJ
37681	544	8	century	century	NN
37681	544	9	in	in	IN
37681	544	10	the	the	DT
37681	544	11	Bodleian	bodleian	JJ
37681	544	12	library	library	NN
37681	544	13	at	at	IN
37681	544	14	Oxford	Oxford	NNP
37681	544	15	,	,	,
37681	544	16	one	one	CD
37681	544	17	of	of	IN
37681	544	18	the	the	DT
37681	544	19	tenth	tenth	JJ
37681	544	20	century	century	NN
37681	544	21	in	in	IN
37681	544	22	the	the	DT
37681	544	23	Vatican	Vatican	NNP
37681	544	24	,	,	,
37681	544	25	another	another	DT
37681	544	26	of	of	IN
37681	544	27	the	the	DT
37681	544	28	tenth	tenth	JJ
37681	544	29	century	century	NN
37681	544	30	in	in	IN
37681	544	31	Florence	Florence	NNP
37681	544	32	,	,	,
37681	544	33	one	one	CD
37681	544	34	of	of	IN
37681	544	35	the	the	DT
37681	544	36	eleventh	eleventh	JJ
37681	544	37	century	century	NN
37681	544	38	at	at	IN
37681	544	39	Bologna	Bologna	NNPS
37681	544	40	,	,	,
37681	544	41	and	and	CC
37681	544	42	two	two	CD
37681	544	43	of	of	IN
37681	544	44	the	the	DT
37681	544	45	twelfth	twelfth	JJ
37681	544	46	century	century	NN
37681	544	47	at	at	IN
37681	544	48	Paris	Paris	NNP
37681	544	49	.	.	.
37681	545	1	There	there	EX
37681	545	2	are	be	VBP
37681	545	3	also	also	RB
37681	545	4	fragments	fragment	NNS
37681	545	5	containing	contain	VBG
37681	545	6	bits	bit	NNS
37681	545	7	of	of	IN
37681	545	8	Euclid	Euclid	NNP
37681	545	9	in	in	IN
37681	545	10	Greek	Greek	NNP
37681	545	11	,	,	,
37681	545	12	and	and	CC
37681	545	13	going	go	VBG
37681	545	14	back	back	RB
37681	545	15	as	as	RB
37681	545	16	far	far	RB
37681	545	17	as	as	IN
37681	545	18	the	the	DT
37681	545	19	second	second	JJ
37681	545	20	and	and	CC
37681	545	21	third	third	JJ
37681	545	22	century	century	NN
37681	545	23	A.D.	A.D.	NNP
37681	546	1	The	the	DT
37681	546	2	first	first	JJ
37681	546	3	modern	modern	JJ
37681	546	4	translation	translation	NN
37681	546	5	from	from	IN
37681	546	6	the	the	DT
37681	546	7	Greek	Greek	NNP
37681	546	8	into	into	IN
37681	546	9	the	the	DT
37681	546	10	Latin	Latin	NNP
37681	546	11	was	be	VBD
37681	546	12	made	make	VBN
37681	546	13	by	by	IN
37681	546	14	Zamberti	Zamberti	NNP
37681	546	15	(	(	-LRB-
37681	546	16	or	or	CC
37681	546	17	Zamberto),[30	Zamberto),[30	NNP
37681	546	18	]	]	-RRB-
37681	546	19	and	and	CC
37681	546	20	was	be	VBD
37681	546	21	printed	print	VBN
37681	546	22	at	at	IN
37681	546	23	Venice	Venice	NNP
37681	546	24	in	in	IN
37681	546	25	1513	1513	CD
37681	546	26	.	.	.
37681	547	1	The	the	DT
37681	547	2	first	first	JJ
37681	547	3	translation	translation	NN
37681	547	4	into	into	IN
37681	547	5	English	English	NNP
37681	547	6	was	be	VBD
37681	547	7	made	make	VBN
37681	547	8	by	by	IN
37681	547	9	Sir	Sir	NNP
37681	547	10	Henry	Henry	NNP
37681	547	11	Billingsley	Billingsley	NNP
37681	547	12	and	and	CC
37681	547	13	was	be	VBD
37681	547	14	printed	print	VBN
37681	547	15	in	in	IN
37681	547	16	1570	1570	CD
37681	547	17	,	,	,
37681	547	18	sixteen	sixteen	CD
37681	547	19	years	year	NNS
37681	547	20	before	before	IN
37681	547	21	he	-PRON-	PRP
37681	547	22	became	become	VBD
37681	547	23	Lord	Lord	NNP
37681	547	24	Mayor	Mayor	NNP
37681	547	25	of	of	IN
37681	547	26	London	London	NNP
37681	547	27	.	.	.
37681	548	1	Proclus	Proclus	NNP
37681	548	2	,	,	,
37681	548	3	in	in	IN
37681	548	4	his	-PRON-	PRP$
37681	548	5	commentary	commentary	NN
37681	548	6	upon	upon	IN
37681	548	7	Euclid	Euclid	NNP
37681	548	8	's	's	POS
37681	548	9	work	work	NN
37681	548	10	,	,	,
37681	548	11	remarks	remark	VBZ
37681	548	12	:	:	:
37681	548	13	In	in	IN
37681	548	14	the	the	DT
37681	548	15	whole	whole	NN
37681	548	16	of	of	IN
37681	548	17	geometry	geometry	NN
37681	548	18	there	there	EX
37681	548	19	are	be	VBP
37681	548	20	certain	certain	JJ
37681	548	21	leading	lead	VBG
37681	548	22	theorems	theorem	NNS
37681	548	23	,	,	,
37681	548	24	bearing	bear	VBG
37681	548	25	to	to	IN
37681	548	26	those	those	DT
37681	548	27	which	which	WDT
37681	548	28	follow	follow	VBP
37681	548	29	the	the	DT
37681	548	30	relation	relation	NN
37681	548	31	of	of	IN
37681	548	32	a	a	DT
37681	548	33	principle	principle	NN
37681	548	34	,	,	,
37681	548	35	all	all	RB
37681	548	36	-	-	HYPH
37681	548	37	pervading	pervading	JJ
37681	548	38	,	,	,
37681	548	39	and	and	CC
37681	548	40	furnishing	furnish	VBG
37681	548	41	proofs	proof	NNS
37681	548	42	of	of	IN
37681	548	43	many	many	JJ
37681	548	44	properties	property	NNS
37681	548	45	.	.	.
37681	549	1	Such	such	JJ
37681	549	2	theorems	theorem	NNS
37681	549	3	are	be	VBP
37681	549	4	called	call	VBN
37681	549	5	by	by	IN
37681	549	6	the	the	DT
37681	549	7	name	name	NN
37681	549	8	of	of	IN
37681	549	9	_	_	NNP
37681	549	10	elements	elements	NNPS
37681	549	11	_	_	NNP
37681	549	12	,	,	,
37681	549	13	and	and	CC
37681	549	14	their	-PRON-	PRP$
37681	549	15	function	function	NN
37681	549	16	may	may	MD
37681	549	17	be	be	VB
37681	549	18	compared	compare	VBN
37681	549	19	to	to	IN
37681	549	20	that	that	DT
37681	549	21	of	of	IN
37681	549	22	the	the	DT
37681	549	23	letters	letter	NNS
37681	549	24	of	of	IN
37681	549	25	the	the	DT
37681	549	26	alphabet	alphabet	NN
37681	549	27	in	in	IN
37681	549	28	relation	relation	NN
37681	549	29	to	to	IN
37681	549	30	language	language	NN
37681	549	31	,	,	,
37681	549	32	letters	letter	NNS
37681	549	33	being	be	VBG
37681	549	34	indeed	indeed	RB
37681	549	35	called	call	VBN
37681	549	36	by	by	IN
37681	549	37	the	the	DT
37681	549	38	same	same	JJ
37681	549	39	name	name	NN
37681	549	40	in	in	IN
37681	549	41	Greek	Greek	NNP
37681	549	42	[	[	-LRB-
37681	549	43	[	[	-LRB-
37681	549	44	Greek	Greek	NNP
37681	549	45	:	:	:
37681	549	46	stoicheia	stoicheia	NNP
37681	549	47	]	]	-RRB-
37681	549	48	,	,	,
37681	549	49	stoicheia	stoicheia	NNP
37681	549	50	]	]	-RRB-
37681	549	51	.	.	.
37681	550	1	[	[	-LRB-
37681	550	2	31	31	CD
37681	550	3	]	]	-RRB-
37681	550	4	This	this	DT
37681	550	5	characterizes	characterize	VBZ
37681	550	6	the	the	DT
37681	550	7	work	work	NN
37681	550	8	of	of	IN
37681	550	9	Euclid	Euclid	NNP
37681	550	10	,	,	,
37681	550	11	a	a	DT
37681	550	12	collection	collection	NN
37681	550	13	of	of	IN
37681	550	14	the	the	DT
37681	550	15	basic	basic	JJ
37681	550	16	propositions	proposition	NNS
37681	550	17	of	of	IN
37681	550	18	geometry	geometry	NN
37681	550	19	,	,	,
37681	550	20	and	and	CC
37681	550	21	chiefly	chiefly	RB
37681	550	22	of	of	IN
37681	550	23	plane	plane	NN
37681	550	24	geometry	geometry	NN
37681	550	25	,	,	,
37681	550	26	arranged	arrange	VBN
37681	550	27	in	in	IN
37681	550	28	logical	logical	JJ
37681	550	29	sequence	sequence	NN
37681	550	30	,	,	,
37681	550	31	the	the	DT
37681	550	32	proof	proof	NN
37681	550	33	of	of	IN
37681	550	34	each	each	DT
37681	550	35	depending	depend	VBG
37681	550	36	upon	upon	IN
37681	550	37	some	some	DT
37681	550	38	preceding	precede	VBG
37681	550	39	proposition	proposition	NN
37681	550	40	,	,	,
37681	550	41	definition	definition	NN
37681	550	42	,	,	,
37681	550	43	or	or	CC
37681	550	44	assumption	assumption	NN
37681	550	45	(	(	-LRB-
37681	550	46	axiom	axiom	JJ
37681	550	47	or	or	CC
37681	550	48	postulate	postulate	NN
37681	550	49	)	)	-RRB-
37681	550	50	.	.	.
37681	551	1	The	the	DT
37681	551	2	number	number	NN
37681	551	3	of	of	IN
37681	551	4	the	the	DT
37681	551	5	propositions	proposition	NNS
37681	551	6	of	of	IN
37681	551	7	plane	plane	NN
37681	551	8	geometry	geometry	NN
37681	551	9	included	include	VBN
37681	551	10	in	in	IN
37681	551	11	the	the	DT
37681	551	12	"	"	``
37681	551	13	Elements	Elements	NNPS
37681	551	14	"	"	''
37681	551	15	is	be	VBZ
37681	551	16	not	not	RB
37681	551	17	entirely	entirely	RB
37681	551	18	certain	certain	JJ
37681	551	19	,	,	,
37681	551	20	owing	owe	VBG
37681	551	21	to	to	IN
37681	551	22	some	some	DT
37681	551	23	disagreement	disagreement	NN
37681	551	24	in	in	IN
37681	551	25	the	the	DT
37681	551	26	manuscripts	manuscript	NNS
37681	551	27	,	,	,
37681	551	28	but	but	CC
37681	551	29	it	-PRON-	PRP
37681	551	30	was	be	VBD
37681	551	31	between	between	IN
37681	551	32	one	one	CD
37681	551	33	hundred	hundred	CD
37681	551	34	sixty	sixty	CD
37681	551	35	and	and	CC
37681	551	36	one	one	CD
37681	551	37	hundred	hundred	CD
37681	551	38	seventy	seventy	CD
37681	551	39	-	-	HYPH
37681	551	40	five	five	CD
37681	551	41	.	.	.
37681	552	1	It	-PRON-	PRP
37681	552	2	is	be	VBZ
37681	552	3	possible	possible	JJ
37681	552	4	to	to	TO
37681	552	5	reduce	reduce	VB
37681	552	6	this	this	DT
37681	552	7	number	number	NN
37681	552	8	by	by	IN
37681	552	9	about	about	RB
37681	552	10	thirty	thirty	CD
37681	552	11	or	or	CC
37681	552	12	forty	forty	CD
37681	552	13	,	,	,
37681	552	14	because	because	IN
37681	552	15	Euclid	Euclid	NNP
37681	552	16	included	include	VBD
37681	552	17	a	a	DT
37681	552	18	certain	certain	JJ
37681	552	19	amount	amount	NN
37681	552	20	of	of	IN
37681	552	21	geometric	geometric	JJ
37681	552	22	algebra	algebra	NN
37681	552	23	;	;	:
37681	552	24	but	but	CC
37681	552	25	beyond	beyond	IN
37681	552	26	this	this	DT
37681	552	27	we	-PRON-	PRP
37681	552	28	can	can	MD
37681	552	29	not	not	RB
37681	552	30	safely	safely	RB
37681	552	31	go	go	VB
37681	552	32	in	in	IN
37681	552	33	the	the	DT
37681	552	34	way	way	NN
37681	552	35	of	of	IN
37681	552	36	elimination	elimination	NN
37681	552	37	,	,	,
37681	552	38	since	since	IN
37681	552	39	from	from	IN
37681	552	40	the	the	DT
37681	552	41	very	very	JJ
37681	552	42	nature	nature	NN
37681	552	43	of	of	IN
37681	552	44	the	the	DT
37681	552	45	"	"	``
37681	552	46	Elements	Elements	NNPS
37681	552	47	"	"	''
37681	552	48	these	these	DT
37681	552	49	propositions	proposition	NNS
37681	552	50	are	be	VBP
37681	552	51	basic	basic	JJ
37681	552	52	.	.	.
37681	553	1	The	the	DT
37681	553	2	efforts	effort	NNS
37681	553	3	at	at	IN
37681	553	4	revising	revise	VBG
37681	553	5	Euclid	Euclid	NNP
37681	553	6	have	have	VBP
37681	553	7	been	be	VBN
37681	553	8	generally	generally	RB
37681	553	9	confined	confine	VBN
37681	553	10	,	,	,
37681	553	11	therefore	therefore	RB
37681	553	12	,	,	,
37681	553	13	to	to	IN
37681	553	14	rearranging	rearrange	VBG
37681	553	15	his	-PRON-	PRP$
37681	553	16	material	material	NN
37681	553	17	,	,	,
37681	553	18	to	to	IN
37681	553	19	rendering	render	VBG
37681	553	20	more	more	JJR
37681	553	21	modern	modern	JJ
37681	553	22	his	-PRON-	PRP$
37681	553	23	phraseology	phraseology	NN
37681	553	24	,	,	,
37681	553	25	and	and	CC
37681	553	26	to	to	IN
37681	553	27	making	make	VBG
37681	553	28	a	a	DT
37681	553	29	book	book	NN
37681	553	30	that	that	WDT
37681	553	31	is	be	VBZ
37681	553	32	more	more	RBR
37681	553	33	usable	usable	JJ
37681	553	34	with	with	IN
37681	553	35	beginners	beginner	NNS
37681	553	36	if	if	IN
37681	553	37	not	not	RB
37681	553	38	more	more	RBR
37681	553	39	logical	logical	JJ
37681	553	40	in	in	IN
37681	553	41	its	-PRON-	PRP$
37681	553	42	presentation	presentation	NN
37681	553	43	of	of	IN
37681	553	44	the	the	DT
37681	553	45	subject	subject	NN
37681	553	46	.	.	.
37681	554	1	While	while	IN
37681	554	2	there	there	EX
37681	554	3	has	have	VBZ
37681	554	4	been	be	VBN
37681	554	5	an	an	DT
37681	554	6	improvement	improvement	NN
37681	554	7	upon	upon	IN
37681	554	8	Euclid	Euclid	NNP
37681	554	9	in	in	IN
37681	554	10	the	the	DT
37681	554	11	art	art	NN
37681	554	12	of	of	IN
37681	554	13	bookmaking	bookmaking	NN
37681	554	14	,	,	,
37681	554	15	and	and	CC
37681	554	16	in	in	IN
37681	554	17	minor	minor	JJ
37681	554	18	matters	matter	NNS
37681	554	19	of	of	IN
37681	554	20	phraseology	phraseology	NN
37681	554	21	and	and	CC
37681	554	22	sequence	sequence	NN
37681	554	23	,	,	,
37681	554	24	the	the	DT
37681	554	25	educational	educational	JJ
37681	554	26	gain	gain	NN
37681	554	27	has	have	VBZ
37681	554	28	not	not	RB
37681	554	29	been	be	VBN
37681	554	30	commensurate	commensurate	JJ
37681	554	31	with	with	IN
37681	554	32	the	the	DT
37681	554	33	effort	effort	NN
37681	554	34	put	put	VBN
37681	554	35	forth	forth	RB
37681	554	36	.	.	.
37681	555	1	With	with	IN
37681	555	2	a	a	DT
37681	555	3	little	little	JJ
37681	555	4	modification	modification	NN
37681	555	5	of	of	IN
37681	555	6	Euclid	Euclid	NNP
37681	555	7	's	's	POS
37681	555	8	semi	semi	JJ
37681	555	9	-	-	JJ
37681	555	10	algebraic	algebraic	JJ
37681	555	11	Book	Book	NNP
37681	555	12	II	II	NNP
37681	555	13	and	and	CC
37681	555	14	of	of	IN
37681	555	15	his	-PRON-	PRP$
37681	555	16	treatment	treatment	NN
37681	555	17	of	of	IN
37681	555	18	proportion	proportion	NN
37681	555	19	,	,	,
37681	555	20	with	with	IN
37681	555	21	some	some	DT
37681	555	22	scattering	scattering	NN
37681	555	23	of	of	IN
37681	555	24	the	the	DT
37681	555	25	definitions	definition	NNS
37681	555	26	and	and	CC
37681	555	27	the	the	DT
37681	555	28	inclusion	inclusion	NN
37681	555	29	of	of	IN
37681	555	30	well	well	RB
37681	555	31	-	-	HYPH
37681	555	32	graded	grade	VBN
37681	555	33	exercises	exercise	NNS
37681	555	34	at	at	IN
37681	555	35	proper	proper	JJ
37681	555	36	places	place	NNS
37681	555	37	,	,	,
37681	555	38	and	and	CC
37681	555	39	with	with	IN
37681	555	40	attention	attention	NN
37681	555	41	to	to	IN
37681	555	42	the	the	DT
37681	555	43	modern	modern	JJ
37681	555	44	science	science	NN
37681	555	45	of	of	IN
37681	555	46	bookmaking	bookmaking	NN
37681	555	47	,	,	,
37681	555	48	the	the	DT
37681	555	49	"	"	``
37681	555	50	Elements	Elements	NNPS
37681	555	51	"	"	''
37681	555	52	would	would	MD
37681	555	53	answer	answer	VB
37681	555	54	quite	quite	RB
37681	555	55	as	as	RB
37681	555	56	well	well	RB
37681	555	57	for	for	IN
37681	555	58	a	a	DT
37681	555	59	textbook	textbook	NN
37681	555	60	to	to	IN
37681	555	61	-	-	HYPH
37681	555	62	day	day	NN
37681	555	63	as	as	IN
37681	555	64	most	most	JJS
37681	555	65	of	of	IN
37681	555	66	our	-PRON-	PRP$
37681	555	67	modern	modern	JJ
37681	555	68	substitutes	substitute	NNS
37681	555	69	,	,	,
37681	555	70	and	and	CC
37681	555	71	much	much	RB
37681	555	72	better	well	JJR
37681	555	73	than	than	IN
37681	555	74	some	some	DT
37681	555	75	of	of	IN
37681	555	76	them	-PRON-	PRP
37681	555	77	.	.	.
37681	556	1	It	-PRON-	PRP
37681	556	2	would	would	MD
37681	556	3	,	,	,
37681	556	4	moreover	moreover	RB
37681	556	5	,	,	,
37681	556	6	have	have	VBP
37681	556	7	the	the	DT
37681	556	8	advantage	advantage	NN
37681	556	9	of	of	IN
37681	556	10	being	be	VBG
37681	556	11	a	a	DT
37681	556	12	classic,--somewhat	classic,--somewhat	NNP
37681	556	13	the	the	DT
37681	556	14	same	same	JJ
37681	556	15	advantage	advantage	NN
37681	556	16	that	that	WDT
37681	556	17	comes	come	VBZ
37681	556	18	from	from	IN
37681	556	19	reading	read	VBG
37681	556	20	Homer	Homer	NNP
37681	556	21	in	in	IN
37681	556	22	the	the	DT
37681	556	23	original	original	JJ
37681	556	24	instead	instead	RB
37681	556	25	of	of	IN
37681	556	26	from	from	IN
37681	556	27	Pope	Pope	NNP
37681	556	28	's	's	POS
37681	556	29	metrical	metrical	JJ
37681	556	30	translation	translation	NN
37681	556	31	.	.	.
37681	557	1	This	this	DT
37681	557	2	is	be	VBZ
37681	557	3	not	not	RB
37681	557	4	a	a	DT
37681	557	5	plea	plea	NN
37681	557	6	for	for	IN
37681	557	7	a	a	DT
37681	557	8	return	return	NN
37681	557	9	to	to	IN
37681	557	10	the	the	DT
37681	557	11	Euclid	Euclid	NNP
37681	557	12	text	text	NN
37681	557	13	,	,	,
37681	557	14	but	but	CC
37681	557	15	for	for	IN
37681	557	16	a	a	DT
37681	557	17	recognition	recognition	NN
37681	557	18	of	of	IN
37681	557	19	the	the	DT
37681	557	20	excellence	excellence	NN
37681	557	21	of	of	IN
37681	557	22	Euclid	Euclid	NNP
37681	557	23	's	's	POS
37681	557	24	work	work	NN
37681	557	25	.	.	.
37681	558	1	The	the	DT
37681	558	2	distinctive	distinctive	JJ
37681	558	3	feature	feature	NN
37681	558	4	of	of	IN
37681	558	5	Euclid	Euclid	NNP
37681	558	6	's	's	POS
37681	558	7	"	"	``
37681	558	8	Elements	element	NNS
37681	558	9	,	,	,
37681	558	10	"	"	''
37681	558	11	compared	compare	VBN
37681	558	12	with	with	IN
37681	558	13	the	the	DT
37681	558	14	modern	modern	JJ
37681	558	15	American	american	JJ
37681	558	16	textbook	textbook	NN
37681	558	17	,	,	,
37681	558	18	is	be	VBZ
37681	558	19	perhaps	perhaps	RB
37681	558	20	this	this	DT
37681	558	21	:	:	:
37681	558	22	Euclid	Euclid	NNP
37681	558	23	begins	begin	VBZ
37681	558	24	a	a	DT
37681	558	25	book	book	NN
37681	558	26	with	with	IN
37681	558	27	what	what	WP
37681	558	28	seems	seem	VBZ
37681	558	29	to	to	IN
37681	558	30	him	-PRON-	PRP
37681	558	31	the	the	DT
37681	558	32	easiest	easy	JJS
37681	558	33	proposition	proposition	NN
37681	558	34	,	,	,
37681	558	35	be	be	VB
37681	558	36	it	-PRON-	PRP
37681	558	37	theorem	theorem	JJ
37681	558	38	or	or	CC
37681	558	39	problem	problem	NN
37681	558	40	;	;	:
37681	558	41	upon	upon	IN
37681	558	42	this	this	DT
37681	558	43	he	-PRON-	PRP
37681	558	44	builds	build	VBZ
37681	558	45	another	another	DT
37681	558	46	;	;	:
37681	558	47	upon	upon	IN
37681	558	48	these	these	DT
37681	558	49	a	a	DT
37681	558	50	third	third	NN
37681	558	51	,	,	,
37681	558	52	and	and	CC
37681	558	53	so	so	RB
37681	558	54	on	on	RB
37681	558	55	,	,	,
37681	558	56	concerning	concern	VBG
37681	558	57	himself	-PRON-	PRP
37681	558	58	but	but	CC
37681	558	59	little	little	JJ
37681	558	60	with	with	IN
37681	558	61	the	the	DT
37681	558	62	classification	classification	NN
37681	558	63	of	of	IN
37681	558	64	propositions	proposition	NNS
37681	558	65	.	.	.
37681	559	1	Furthermore	furthermore	RB
37681	559	2	,	,	,
37681	559	3	he	-PRON-	PRP
37681	559	4	arranges	arrange	VBZ
37681	559	5	his	-PRON-	PRP$
37681	559	6	propositions	proposition	NNS
37681	559	7	so	so	IN
37681	559	8	as	as	IN
37681	559	9	to	to	TO
37681	559	10	construct	construct	VB
37681	559	11	his	-PRON-	PRP$
37681	559	12	figures	figure	NNS
37681	559	13	before	before	IN
37681	559	14	using	use	VBG
37681	559	15	them	-PRON-	PRP
37681	559	16	.	.	.
37681	560	1	We	-PRON-	PRP
37681	560	2	,	,	,
37681	560	3	on	on	IN
37681	560	4	the	the	DT
37681	560	5	other	other	JJ
37681	560	6	hand	hand	NN
37681	560	7	,	,	,
37681	560	8	make	make	VB
37681	560	9	some	some	DT
37681	560	10	little	little	JJ
37681	560	11	attempt	attempt	NN
37681	560	12	to	to	TO
37681	560	13	classify	classify	VB
37681	560	14	our	-PRON-	PRP$
37681	560	15	propositions	proposition	NNS
37681	560	16	within	within	IN
37681	560	17	each	each	DT
37681	560	18	book	book	NN
37681	560	19	,	,	,
37681	560	20	and	and	CC
37681	560	21	we	-PRON-	PRP
37681	560	22	make	make	VBP
37681	560	23	no	no	DT
37681	560	24	attempt	attempt	NN
37681	560	25	to	to	TO
37681	560	26	construct	construct	VB
37681	560	27	our	-PRON-	PRP$
37681	560	28	figures	figure	NNS
37681	560	29	before	before	IN
37681	560	30	using	use	VBG
37681	560	31	them	-PRON-	PRP
37681	560	32	,	,	,
37681	560	33	or	or	CC
37681	560	34	at	at	IN
37681	560	35	least	least	JJS
37681	560	36	to	to	TO
37681	560	37	prove	prove	VB
37681	560	38	that	that	IN
37681	560	39	the	the	DT
37681	560	40	constructions	construction	NNS
37681	560	41	are	be	VBP
37681	560	42	correct	correct	JJ
37681	560	43	.	.	.
37681	561	1	Indeed	indeed	RB
37681	561	2	,	,	,
37681	561	3	we	-PRON-	PRP
37681	561	4	go	go	VBP
37681	561	5	so	so	RB
37681	561	6	far	far	RB
37681	561	7	as	as	IN
37681	561	8	to	to	TO
37681	561	9	study	study	VB
37681	561	10	the	the	DT
37681	561	11	properties	property	NNS
37681	561	12	of	of	IN
37681	561	13	figures	figure	NNS
37681	561	14	that	that	WDT
37681	561	15	we	-PRON-	PRP
37681	561	16	can	can	MD
37681	561	17	not	not	RB
37681	561	18	construct	construct	VB
37681	561	19	,	,	,
37681	561	20	as	as	IN
37681	561	21	when	when	WRB
37681	561	22	we	-PRON-	PRP
37681	561	23	ask	ask	VBP
37681	561	24	for	for	IN
37681	561	25	the	the	DT
37681	561	26	size	size	NN
37681	561	27	of	of	IN
37681	561	28	the	the	DT
37681	561	29	angle	angle	NN
37681	561	30	of	of	IN
37681	561	31	a	a	DT
37681	561	32	regular	regular	JJ
37681	561	33	heptagon	heptagon	NN
37681	561	34	.	.	.
37681	562	1	Thus	thus	RB
37681	562	2	Euclid	Euclid	NNP
37681	562	3	begins	begin	VBZ
37681	562	4	Book	Book	NNP
37681	562	5	I	-PRON-	PRP
37681	562	6	by	by	IN
37681	562	7	a	a	DT
37681	562	8	problem	problem	NN
37681	562	9	,	,	,
37681	562	10	to	to	TO
37681	562	11	construct	construct	VB
37681	562	12	an	an	DT
37681	562	13	equilateral	equilateral	JJ
37681	562	14	triangle	triangle	NN
37681	562	15	on	on	IN
37681	562	16	a	a	DT
37681	562	17	given	give	VBN
37681	562	18	line	line	NN
37681	562	19	.	.	.
37681	563	1	His	-PRON-	PRP$
37681	563	2	object	object	NN
37681	563	3	is	be	VBZ
37681	563	4	to	to	TO
37681	563	5	follow	follow	VB
37681	563	6	this	this	DT
37681	563	7	by	by	IN
37681	563	8	problems	problem	NNS
37681	563	9	on	on	IN
37681	563	10	drawing	draw	VBG
37681	563	11	a	a	DT
37681	563	12	straight	straight	JJ
37681	563	13	line	line	NN
37681	563	14	equal	equal	JJ
37681	563	15	to	to	IN
37681	563	16	a	a	DT
37681	563	17	given	give	VBN
37681	563	18	straight	straight	JJ
37681	563	19	line	line	NN
37681	563	20	,	,	,
37681	563	21	and	and	CC
37681	563	22	cutting	cut	VBG
37681	563	23	off	off	RP
37681	563	24	from	from	IN
37681	563	25	the	the	DT
37681	563	26	greater	great	JJR
37681	563	27	of	of	IN
37681	563	28	two	two	CD
37681	563	29	straight	straight	JJ
37681	563	30	lines	line	NNS
37681	563	31	a	a	DT
37681	563	32	line	line	NN
37681	563	33	equal	equal	JJ
37681	563	34	to	to	IN
37681	563	35	the	the	DT
37681	563	36	less	less	JJR
37681	563	37	.	.	.
37681	564	1	He	-PRON-	PRP
37681	564	2	now	now	RB
37681	564	3	introduces	introduce	VBZ
37681	564	4	a	a	DT
37681	564	5	theorem	theorem	NN
37681	564	6	,	,	,
37681	564	7	which	which	WDT
37681	564	8	might	may	MD
37681	564	9	equally	equally	RB
37681	564	10	well	well	RB
37681	564	11	have	have	VB
37681	564	12	been	be	VBN
37681	564	13	his	-PRON-	PRP$
37681	564	14	first	first	JJ
37681	564	15	proposition	proposition	NN
37681	564	16	,	,	,
37681	564	17	namely	namely	RB
37681	564	18	,	,	,
37681	564	19	the	the	DT
37681	564	20	case	case	NN
37681	564	21	of	of	IN
37681	564	22	the	the	DT
37681	564	23	congruence	congruence	NN
37681	564	24	of	of	IN
37681	564	25	two	two	CD
37681	564	26	triangles	triangle	NNS
37681	564	27	,	,	,
37681	564	28	having	have	VBG
37681	564	29	given	give	VBN
37681	564	30	two	two	CD
37681	564	31	sides	side	NNS
37681	564	32	and	and	CC
37681	564	33	the	the	DT
37681	564	34	included	include	VBN
37681	564	35	angle	angle	NN
37681	564	36	.	.	.
37681	565	1	By	by	IN
37681	565	2	means	mean	NNS
37681	565	3	of	of	IN
37681	565	4	his	-PRON-	PRP$
37681	565	5	third	third	JJ
37681	565	6	and	and	CC
37681	565	7	fourth	fourth	JJ
37681	565	8	propositions	proposition	NNS
37681	565	9	he	-PRON-	PRP
37681	565	10	is	be	VBZ
37681	565	11	now	now	RB
37681	565	12	able	able	JJ
37681	565	13	to	to	TO
37681	565	14	prove	prove	VB
37681	565	15	the	the	DT
37681	565	16	_	_	NNP
37681	565	17	pons	pons	NNP
37681	565	18	asinorum	asinorum	NNP
37681	565	19	_	_	NNP
37681	565	20	,	,	,
37681	565	21	that	that	IN
37681	565	22	the	the	DT
37681	565	23	angles	angle	NNS
37681	565	24	at	at	IN
37681	565	25	the	the	DT
37681	565	26	base	base	NN
37681	565	27	of	of	IN
37681	565	28	an	an	DT
37681	565	29	isosceles	isoscele	NNS
37681	565	30	triangle	triangle	NN
37681	565	31	are	be	VBP
37681	565	32	equal	equal	JJ
37681	565	33	.	.	.
37681	566	1	We	-PRON-	PRP
37681	566	2	,	,	,
37681	566	3	on	on	IN
37681	566	4	the	the	DT
37681	566	5	other	other	JJ
37681	566	6	hand	hand	NN
37681	566	7	,	,	,
37681	566	8	seek	seek	VB
37681	566	9	to	to	TO
37681	566	10	group	group	VB
37681	566	11	our	-PRON-	PRP$
37681	566	12	propositions	proposition	NNS
37681	566	13	where	where	WRB
37681	566	14	this	this	DT
37681	566	15	can	can	MD
37681	566	16	conveniently	conveniently	RB
37681	566	17	be	be	VB
37681	566	18	done	do	VBN
37681	566	19	,	,	,
37681	566	20	putting	put	VBG
37681	566	21	the	the	DT
37681	566	22	congruent	congruent	JJ
37681	566	23	propositions	proposition	NNS
37681	566	24	together	together	RB
37681	566	25	,	,	,
37681	566	26	those	those	DT
37681	566	27	about	about	IN
37681	566	28	inequalities	inequality	NNS
37681	566	29	by	by	IN
37681	566	30	themselves	-PRON-	PRP
37681	566	31	,	,	,
37681	566	32	and	and	CC
37681	566	33	the	the	DT
37681	566	34	propositions	proposition	NNS
37681	566	35	about	about	IN
37681	566	36	parallels	parallel	NNS
37681	566	37	in	in	IN
37681	566	38	one	one	CD
37681	566	39	set	set	NN
37681	566	40	.	.	.
37681	567	1	The	the	DT
37681	567	2	results	result	NNS
37681	567	3	of	of	IN
37681	567	4	the	the	DT
37681	567	5	two	two	CD
37681	567	6	arrangements	arrangement	NNS
37681	567	7	are	be	VBP
37681	567	8	not	not	RB
37681	567	9	radically	radically	RB
37681	567	10	different	different	JJ
37681	567	11	,	,	,
37681	567	12	and	and	CC
37681	567	13	the	the	DT
37681	567	14	effect	effect	NN
37681	567	15	of	of	IN
37681	567	16	either	either	CC
37681	567	17	upon	upon	IN
37681	567	18	the	the	DT
37681	567	19	pupil	pupil	NN
37681	567	20	's	's	POS
37681	567	21	mind	mind	NN
37681	567	22	does	do	VBZ
37681	567	23	not	not	RB
37681	567	24	seem	seem	VB
37681	567	25	particularly	particularly	RB
37681	567	26	better	well	JJR
37681	567	27	than	than	IN
37681	567	28	that	that	DT
37681	567	29	of	of	IN
37681	567	30	the	the	DT
37681	567	31	other	other	JJ
37681	567	32	.	.	.
37681	568	1	Teachers	teacher	NNS
37681	568	2	who	who	WP
37681	568	3	have	have	VBP
37681	568	4	used	use	VBN
37681	568	5	both	both	DT
37681	568	6	plans	plan	NNS
37681	568	7	quite	quite	RB
37681	568	8	commonly	commonly	RB
37681	568	9	feel	feel	VBP
37681	568	10	that	that	IN
37681	568	11	,	,	,
37681	568	12	apart	apart	RB
37681	568	13	from	from	IN
37681	568	14	Books	Books	NNP
37681	568	15	II	II	NNP
37681	568	16	and	and	CC
37681	568	17	V	v	NN
37681	568	18	,	,	,
37681	568	19	Euclid	Euclid	NNP
37681	568	20	is	be	VBZ
37681	568	21	nearly	nearly	RB
37681	568	22	as	as	RB
37681	568	23	easily	easily	RB
37681	568	24	understood	understand	VBN
37681	568	25	as	as	IN
37681	568	26	our	-PRON-	PRP$
37681	568	27	modern	modern	JJ
37681	568	28	texts	text	NNS
37681	568	29	,	,	,
37681	568	30	if	if	IN
37681	568	31	presented	present	VBN
37681	568	32	in	in	IN
37681	568	33	as	as	RB
37681	568	34	satisfactory	satisfactory	JJ
37681	568	35	dress	dress	NN
37681	568	36	.	.	.
37681	569	1	The	the	DT
37681	569	2	topics	topic	NNS
37681	569	3	treated	treat	VBN
37681	569	4	and	and	CC
37681	569	5	the	the	DT
37681	569	6	number	number	NN
37681	569	7	of	of	IN
37681	569	8	propositions	proposition	NNS
37681	569	9	in	in	IN
37681	569	10	the	the	DT
37681	569	11	plane	plane	NN
37681	569	12	geometry	geometry	NN
37681	569	13	of	of	IN
37681	569	14	the	the	DT
37681	569	15	"	"	``
37681	569	16	Elements	Elements	NNPS
37681	569	17	"	"	''
37681	569	18	are	be	VBP
37681	569	19	as	as	IN
37681	569	20	follows	follow	VBZ
37681	569	21	:	:	:
37681	569	22	Book	Book	NNP
37681	569	23	I.	I.	NNP
37681	569	24	Rectilinear	Rectilinear	NNP
37681	569	25	figures	figure	VBZ
37681	569	26	48	48	CD
37681	569	27	Book	Book	NNP
37681	569	28	II	II	NNP
37681	569	29	.	.	.
37681	570	1	Geometric	geometric	JJ
37681	570	2	algebra	algebra	NN
37681	570	3	14	14	CD
37681	570	4	Book	book	NN
37681	570	5	III	III	NNP
37681	570	6	.	.	.
37681	571	1	Circles	Circles	NNP
37681	571	2	37	37	CD
37681	571	3	Book	Book	NNP
37681	571	4	IV	IV	NNP
37681	571	5	.	.	.
37681	572	1	Problems	problem	NNS
37681	572	2	about	about	IN
37681	572	3	circles	circle	NNS
37681	572	4	16	16	CD
37681	572	5	Book	Book	NNP
37681	572	6	V.	V.	NNP
37681	572	7	Proportion	Proportion	NNP
37681	572	8	25	25	CD
37681	572	9	Book	Book	NNP
37681	572	10	VI	VI	NNP
37681	572	11	.	.	.
37681	573	1	Applications	application	NNS
37681	573	2	of	of	IN
37681	573	3	proportion	proportion	NN
37681	573	4	33	33	CD
37681	573	5	----	----	NFP
37681	573	6	173	173	CD
37681	573	7	Of	of	IN
37681	573	8	these	these	DT
37681	573	9	we	-PRON-	PRP
37681	573	10	now	now	RB
37681	573	11	omit	omit	VBP
37681	573	12	Euclid	Euclid	NNP
37681	573	13	's	's	POS
37681	573	14	Book	Book	NNP
37681	573	15	II	II	NNP
37681	573	16	,	,	,
37681	573	17	because	because	IN
37681	573	18	we	-PRON-	PRP
37681	573	19	have	have	VBP
37681	573	20	an	an	DT
37681	573	21	algebraic	algebraic	JJ
37681	573	22	symbolism	symbolism	NN
37681	573	23	that	that	WDT
37681	573	24	was	be	VBD
37681	573	25	unknown	unknown	JJ
37681	573	26	in	in	IN
37681	573	27	his	-PRON-	PRP$
37681	573	28	time	time	NN
37681	573	29	,	,	,
37681	573	30	although	although	IN
37681	573	31	he	-PRON-	PRP
37681	573	32	would	would	MD
37681	573	33	not	not	RB
37681	573	34	have	have	VB
37681	573	35	used	use	VBN
37681	573	36	it	-PRON-	PRP
37681	573	37	in	in	IN
37681	573	38	geometry	geometry	NN
37681	573	39	even	even	RB
37681	573	40	had	have	VBD
37681	573	41	it	-PRON-	PRP
37681	573	42	been	be	VBN
37681	573	43	known	know	VBN
37681	573	44	.	.	.
37681	574	1	Thus	thus	RB
37681	574	2	his	-PRON-	PRP$
37681	574	3	first	first	JJ
37681	574	4	proposition	proposition	NN
37681	574	5	in	in	IN
37681	574	6	Book	Book	NNP
37681	574	7	II	II	NNP
37681	574	8	is	be	VBZ
37681	574	9	as	as	IN
37681	574	10	follows	follow	VBZ
37681	574	11	:	:	:
37681	574	12	If	if	IN
37681	574	13	there	there	EX
37681	574	14	be	be	VB
37681	574	15	two	two	CD
37681	574	16	straight	straight	JJ
37681	574	17	lines	line	NNS
37681	574	18	,	,	,
37681	574	19	and	and	CC
37681	574	20	one	one	CD
37681	574	21	of	of	IN
37681	574	22	them	-PRON-	PRP
37681	574	23	be	be	VB
37681	574	24	cut	cut	VBN
37681	574	25	into	into	IN
37681	574	26	any	any	DT
37681	574	27	number	number	NN
37681	574	28	of	of	IN
37681	574	29	segments	segment	NNS
37681	574	30	whatever	whatever	WDT
37681	574	31	,	,	,
37681	574	32	the	the	DT
37681	574	33	rectangle	rectangle	NN
37681	574	34	contained	contain	VBN
37681	574	35	by	by	IN
37681	574	36	the	the	DT
37681	574	37	two	two	CD
37681	574	38	straight	straight	JJ
37681	574	39	lines	line	NNS
37681	574	40	is	be	VBZ
37681	574	41	equal	equal	JJ
37681	574	42	to	to	IN
37681	574	43	the	the	DT
37681	574	44	rectangles	rectangle	NNS
37681	574	45	contained	contain	VBN
37681	574	46	by	by	IN
37681	574	47	the	the	DT
37681	574	48	uncut	uncut	JJ
37681	574	49	straight	straight	JJ
37681	574	50	line	line	NN
37681	574	51	and	and	CC
37681	574	52	each	each	DT
37681	574	53	of	of	IN
37681	574	54	the	the	DT
37681	574	55	segments	segment	NNS
37681	574	56	.	.	.
37681	575	1	This	this	DT
37681	575	2	amounts	amount	VBZ
37681	575	3	to	to	IN
37681	575	4	saying	say	VBG
37681	575	5	that	that	IN
37681	575	6	if	if	IN
37681	575	7	_	_	NNP
37681	575	8	x	x	NNP
37681	575	9	_	_	NNP
37681	575	10	=	=	SYM
37681	575	11	_	_	NNP
37681	575	12	p	p	NNP
37681	575	13	_	_	NNP
37681	575	14	+	+	CC
37681	575	15	_	_	NNP
37681	575	16	q	q	NNP
37681	575	17	_	_	NNP
37681	575	18	+	+	NNP
37681	575	19	_	_	NNP
37681	575	20	r	r	NNP
37681	575	21	_	_	NNP
37681	575	22	+	+	NNP
37681	575	23	·	·	NFP
37681	575	24	·	·	NFP
37681	575	25	·	·	NFP
37681	575	26	,	,	,
37681	575	27	then	then	RB
37681	575	28	_	_	NNP
37681	575	29	ax	ax	NN
37681	575	30	_	_	NNP
37681	575	31	=	=	SYM
37681	575	32	_	_	NNP
37681	575	33	ap	ap	NNP
37681	575	34	_	_	NNP
37681	575	35	+	+	NNP
37681	575	36	_	_	NNP
37681	575	37	aq	aq	NNP
37681	575	38	_	_	NNP
37681	575	39	+	+	NNP
37681	575	40	_	_	NNP
37681	575	41	ar	ar	NNP
37681	575	42	_	_	NNP
37681	575	43	+	+	SYM
37681	575	44	·	·	NFP
37681	575	45	·	·	NFP
37681	575	46	·	·	NFP
37681	575	47	.	.	.
37681	576	1	We	-PRON-	PRP
37681	576	2	also	also	RB
37681	576	3	materially	materially	RB
37681	576	4	simplify	simplify	VBP
37681	576	5	Euclid	Euclid	NNP
37681	576	6	's	's	POS
37681	576	7	Book	Book	NNP
37681	576	8	V.	V.	NNP
37681	576	9	He	He	NNP
37681	576	10	,	,	,
37681	576	11	for	for	IN
37681	576	12	example	example	NN
37681	576	13	,	,	,
37681	576	14	proves	prove	VBZ
37681	576	15	that	that	IN
37681	576	16	"	"	``
37681	576	17	If	if	IN
37681	576	18	four	four	CD
37681	576	19	magnitudes	magnitude	NNS
37681	576	20	be	be	VB
37681	576	21	proportional	proportional	JJ
37681	576	22	,	,	,
37681	576	23	they	-PRON-	PRP
37681	576	24	will	will	MD
37681	576	25	also	also	RB
37681	576	26	be	be	VB
37681	576	27	proportional	proportional	JJ
37681	576	28	alternately	alternately	RB
37681	576	29	.	.	.
37681	576	30	"	"	''
37681	577	1	This	this	DT
37681	577	2	he	-PRON-	PRP
37681	577	3	proves	prove	VBZ
37681	577	4	generally	generally	RB
37681	577	5	for	for	IN
37681	577	6	any	any	DT
37681	577	7	kind	kind	NN
37681	577	8	of	of	IN
37681	577	9	magnitude	magnitude	NN
37681	577	10	,	,	,
37681	577	11	while	while	IN
37681	577	12	we	-PRON-	PRP
37681	577	13	merely	merely	RB
37681	577	14	prove	prove	VBP
37681	577	15	it	-PRON-	PRP
37681	577	16	for	for	IN
37681	577	17	numbers	number	NNS
37681	577	18	having	have	VBG
37681	577	19	a	a	DT
37681	577	20	common	common	JJ
37681	577	21	measure	measure	NN
37681	577	22	.	.	.
37681	578	1	We	-PRON-	PRP
37681	578	2	say	say	VBP
37681	578	3	that	that	IN
37681	578	4	we	-PRON-	PRP
37681	578	5	may	may	MD
37681	578	6	substitute	substitute	VB
37681	578	7	for	for	IN
37681	578	8	the	the	DT
37681	578	9	older	old	JJR
37681	578	10	form	form	NN
37681	578	11	of	of	IN
37681	578	12	proportion	proportion	NN
37681	578	13	,	,	,
37681	578	14	namely	namely	RB
37681	578	15	,	,	,
37681	578	16	_	_	NNP
37681	578	17	a	a	DT
37681	578	18	_	_	NNP
37681	578	19	:	:	:
37681	578	20	_	_	NNP
37681	578	21	b	b	NNP
37681	578	22	_	_	NNP
37681	578	23	=	=	SYM
37681	578	24	_	_	NNP
37681	578	25	c	c	NNP
37681	578	26	_	_	NNP
37681	578	27	:	:	:
37681	578	28	_	_	NNP
37681	578	29	d	d	NNP
37681	578	30	_	_	NNP
37681	578	31	,	,	,
37681	578	32	the	the	DT
37681	578	33	fractional	fractional	JJ
37681	578	34	form	form	NN
37681	578	35	_	_	NNP
37681	578	36	a_/_b	a_/_b	NNP
37681	578	37	_	_	NNP
37681	578	38	=	=	SYM
37681	578	39	_	_	NNP
37681	578	40	c_/_d	c_/_d	NNP
37681	578	41	_	_	NNP
37681	578	42	.	.	.
37681	579	1	From	from	IN
37681	579	2	this	this	DT
37681	579	3	we	-PRON-	PRP
37681	579	4	have	have	VBP
37681	579	5	_	_	NNP
37681	579	6	ad	ad	NN
37681	579	7	_	_	NNP
37681	579	8	=	=	SYM
37681	579	9	_	_	NNP
37681	579	10	bc	bc	NNP
37681	579	11	_	_	NNP
37681	579	12	.	.	.
37681	580	1	Whence	Whence	NNP
37681	580	2	_	_	NNP
37681	580	3	a_/_c	a_/_c	NNP
37681	580	4	_	_	NNP
37681	580	5	=	=	SYM
37681	580	6	_	_	NNP
37681	580	7	b_/_d	b_/_d	NNP
37681	580	8	_	_	NNP
37681	580	9	.	.	.
37681	581	1	In	in	IN
37681	581	2	this	this	DT
37681	581	3	work	work	NN
37681	581	4	we	-PRON-	PRP
37681	581	5	assume	assume	VBP
37681	581	6	that	that	IN
37681	581	7	we	-PRON-	PRP
37681	581	8	may	may	MD
37681	581	9	multiply	multiply	VB
37681	581	10	equals	equal	NNS
37681	581	11	by	by	IN
37681	581	12	_	_	NNP
37681	581	13	b	b	NNP
37681	581	14	_	_	NNP
37681	581	15	and	and	CC
37681	581	16	_	_	NNP
37681	581	17	d	d	NNP
37681	581	18	_	_	NNP
37681	581	19	.	.	.
37681	582	1	But	but	CC
37681	582	2	suppose	suppose	VB
37681	582	3	_	_	NNP
37681	582	4	b	b	NNP
37681	582	5	_	_	NNP
37681	582	6	and	and	CC
37681	582	7	_	_	NNP
37681	582	8	d	d	NNP
37681	582	9	_	_	NNP
37681	582	10	are	be	VBP
37681	582	11	cubes	cube	NNS
37681	582	12	,	,	,
37681	582	13	of	of	IN
37681	582	14	which	which	WDT
37681	582	15	,	,	,
37681	582	16	indeed	indeed	RB
37681	582	17	,	,	,
37681	582	18	we	-PRON-	PRP
37681	582	19	do	do	VBP
37681	582	20	not	not	RB
37681	582	21	even	even	RB
37681	582	22	know	know	VB
37681	582	23	the	the	DT
37681	582	24	approximate	approximate	JJ
37681	582	25	numerical	numerical	JJ
37681	582	26	measure	measure	NN
37681	582	27	;	;	:
37681	582	28	what	what	WP
37681	582	29	shall	shall	MD
37681	582	30	we	-PRON-	PRP
37681	582	31	do	do	VB
37681	582	32	?	?	.
37681	583	1	To	to	IN
37681	583	2	Euclid	Euclid	NNP
37681	583	3	the	the	DT
37681	583	4	multiplication	multiplication	NN
37681	583	5	by	by	IN
37681	583	6	a	a	DT
37681	583	7	cube	cube	NN
37681	583	8	or	or	CC
37681	583	9	a	a	DT
37681	583	10	polygon	polygon	NN
37681	583	11	or	or	CC
37681	583	12	a	a	DT
37681	583	13	sphere	sphere	NN
37681	583	14	would	would	MD
37681	583	15	have	have	VB
37681	583	16	been	be	VBN
37681	583	17	entirely	entirely	RB
37681	583	18	meaningless	meaningless	JJ
37681	583	19	,	,	,
37681	583	20	as	as	IN
37681	583	21	it	-PRON-	PRP
37681	583	22	always	always	RB
37681	583	23	is	be	VBZ
37681	583	24	from	from	IN
37681	583	25	the	the	DT
37681	583	26	standpoint	standpoint	NN
37681	583	27	of	of	IN
37681	583	28	pure	pure	JJ
37681	583	29	geometry	geometry	NN
37681	583	30	.	.	.
37681	584	1	Hence	hence	RB
37681	584	2	it	-PRON-	PRP
37681	584	3	is	be	VBZ
37681	584	4	that	that	IN
37681	584	5	our	-PRON-	PRP$
37681	584	6	treatment	treatment	NN
37681	584	7	of	of	IN
37681	584	8	proportion	proportion	NN
37681	584	9	has	have	VBZ
37681	584	10	no	no	DT
37681	584	11	serious	serious	JJ
37681	584	12	standing	standing	NN
37681	584	13	in	in	IN
37681	584	14	geometry	geometry	NN
37681	584	15	as	as	IN
37681	584	16	compared	compare	VBN
37681	584	17	with	with	IN
37681	584	18	Euclid	Euclid	NNP
37681	584	19	's	's	POS
37681	584	20	,	,	,
37681	584	21	and	and	CC
37681	584	22	our	-PRON-	PRP$
37681	584	23	only	only	JJ
37681	584	24	justification	justification	NN
37681	584	25	for	for	IN
37681	584	26	it	-PRON-	PRP
37681	584	27	lies	lie	VBZ
37681	584	28	in	in	IN
37681	584	29	the	the	DT
37681	584	30	fact	fact	NN
37681	584	31	that	that	IN
37681	584	32	it	-PRON-	PRP
37681	584	33	is	be	VBZ
37681	584	34	easier	easy	JJR
37681	584	35	.	.	.
37681	585	1	Euclid	Euclid	NNP
37681	585	2	's	's	POS
37681	585	3	treatment	treatment	NN
37681	585	4	is	be	VBZ
37681	585	5	much	much	RB
37681	585	6	more	more	RBR
37681	585	7	rigorous	rigorous	JJ
37681	585	8	than	than	IN
37681	585	9	ours	our	NNS
37681	585	10	,	,	,
37681	585	11	but	but	CC
37681	585	12	it	-PRON-	PRP
37681	585	13	is	be	VBZ
37681	585	14	adapted	adapt	VBN
37681	585	15	to	to	IN
37681	585	16	the	the	DT
37681	585	17	comprehension	comprehension	NN
37681	585	18	of	of	IN
37681	585	19	only	only	JJ
37681	585	20	advanced	advanced	JJ
37681	585	21	students	student	NNS
37681	585	22	,	,	,
37681	585	23	while	while	IN
37681	585	24	ours	ours	JJ
37681	585	25	is	be	VBZ
37681	585	26	merely	merely	RB
37681	585	27	a	a	DT
37681	585	28	confession	confession	NN
37681	585	29	,	,	,
37681	585	30	and	and	CC
37681	585	31	it	-PRON-	PRP
37681	585	32	should	should	MD
37681	585	33	be	be	VB
37681	585	34	a	a	DT
37681	585	35	frank	frank	JJ
37681	585	36	confession	confession	NN
37681	585	37	,	,	,
37681	585	38	of	of	IN
37681	585	39	the	the	DT
37681	585	40	weakness	weakness	NN
37681	585	41	of	of	IN
37681	585	42	our	-PRON-	PRP$
37681	585	43	pupils	pupil	NNS
37681	585	44	,	,	,
37681	585	45	and	and	CC
37681	585	46	possibly	possibly	RB
37681	585	47	,	,	,
37681	585	48	at	at	IN
37681	585	49	times	time	NNS
37681	585	50	,	,	,
37681	585	51	of	of	IN
37681	585	52	ourselves	-PRON-	PRP
37681	585	53	.	.	.
37681	586	1	If	if	IN
37681	586	2	we	-PRON-	PRP
37681	586	3	should	should	MD
37681	586	4	take	take	VB
37681	586	5	Euclid	Euclid	NNP
37681	586	6	's	's	POS
37681	586	7	Books	Books	NNP
37681	586	8	II	II	NNP
37681	586	9	and	and	CC
37681	586	10	V	V	NNP
37681	586	11	for	for	IN
37681	586	12	granted	grant	VBN
37681	586	13	,	,	,
37681	586	14	or	or	CC
37681	586	15	as	as	IN
37681	586	16	sufficiently	sufficiently	RB
37681	586	17	evident	evident	JJ
37681	586	18	from	from	IN
37681	586	19	our	-PRON-	PRP$
37681	586	20	study	study	NN
37681	586	21	of	of	IN
37681	586	22	algebra	algebra	NN
37681	586	23	,	,	,
37681	586	24	we	-PRON-	PRP
37681	586	25	should	should	MD
37681	586	26	have	have	VB
37681	586	27	remaining	remain	VBG
37681	586	28	only	only	RB
37681	586	29	one	one	CD
37681	586	30	hundred	hundred	CD
37681	586	31	thirty	thirty	CD
37681	586	32	-	-	HYPH
37681	586	33	four	four	CD
37681	586	34	propositions	proposition	NNS
37681	586	35	,	,	,
37681	586	36	most	most	JJS
37681	586	37	of	of	IN
37681	586	38	which	which	WDT
37681	586	39	may	may	MD
37681	586	40	be	be	VB
37681	586	41	designated	designate	VBN
37681	586	42	as	as	IN
37681	586	43	basal	basal	NN
37681	586	44	propositions	proposition	NNS
37681	586	45	of	of	IN
37681	586	46	plane	plane	NN
37681	586	47	geometry	geometry	NN
37681	586	48	.	.	.
37681	587	1	Revise	Revise	NNP
37681	587	2	Euclid	Euclid	NNP
37681	587	3	as	as	IN
37681	587	4	we	-PRON-	PRP
37681	587	5	will	will	MD
37681	587	6	,	,	,
37681	587	7	we	-PRON-	PRP
37681	587	8	shall	shall	MD
37681	587	9	not	not	RB
37681	587	10	be	be	VB
37681	587	11	able	able	JJ
37681	587	12	to	to	TO
37681	587	13	eliminate	eliminate	VB
37681	587	14	any	any	DT
37681	587	15	large	large	JJ
37681	587	16	number	number	NN
37681	587	17	of	of	IN
37681	587	18	his	-PRON-	PRP$
37681	587	19	fundamental	fundamental	JJ
37681	587	20	truths	truth	NNS
37681	587	21	,	,	,
37681	587	22	while	while	IN
37681	587	23	we	-PRON-	PRP
37681	587	24	might	may	MD
37681	587	25	do	do	VB
37681	587	26	much	much	RB
37681	587	27	worse	bad	JJR
37681	587	28	than	than	IN
37681	587	29	to	to	TO
37681	587	30	adopt	adopt	VB
37681	587	31	these	these	DT
37681	587	32	one	one	CD
37681	587	33	hundred	hundred	CD
37681	587	34	thirty	thirty	CD
37681	587	35	-	-	HYPH
37681	587	36	four	four	CD
37681	587	37	propositions	proposition	NNS
37681	587	38	_	_	NNP
37681	587	39	in	in	IN
37681	587	40	toto	toto	NN
37681	587	41	_	_	NNP
37681	587	42	as	as	IN
37681	587	43	the	the	DT
37681	587	44	bases	basis	NNS
37681	587	45	,	,	,
37681	587	46	and	and	CC
37681	587	47	indeed	indeed	RB
37681	587	48	as	as	IN
37681	587	49	the	the	DT
37681	587	50	definition	definition	NN
37681	587	51	,	,	,
37681	587	52	of	of	IN
37681	587	53	elementary	elementary	JJ
37681	587	54	plane	plane	NN
37681	587	55	geometry	geometry	NN
37681	587	56	.	.	.
37681	588	1	=	=	NFP
37681	588	2	Bibliography.=	Bibliography.=	NNP
37681	588	3	Heath	Heath	NNP
37681	588	4	,	,	,
37681	588	5	The	the	DT
37681	588	6	Thirteen	Thirteen	NNP
37681	588	7	Books	Books	NNPS
37681	588	8	of	of	IN
37681	588	9	Euclid	Euclid	NNP
37681	588	10	's	's	POS
37681	588	11	Elements	Elements	NNPS
37681	588	12	,	,	,
37681	588	13	3	3	CD
37681	588	14	vols	vol	NNS
37681	588	15	.	.	.
37681	588	16	,	,	,
37681	588	17	Cambridge	Cambridge	NNP
37681	588	18	,	,	,
37681	588	19	1908	1908	CD
37681	588	20	;	;	:
37681	588	21	Frankland	Frankland	NNP
37681	588	22	,	,	,
37681	588	23	The	the	DT
37681	588	24	First	First	NNP
37681	588	25	Book	Book	NNP
37681	588	26	of	of	IN
37681	588	27	Euclid	Euclid	NNP
37681	588	28	,	,	,
37681	588	29	Cambridge	Cambridge	NNP
37681	588	30	,	,	,
37681	588	31	1906	1906	CD
37681	588	32	;	;	:
37681	588	33	Smith	Smith	NNP
37681	588	34	,	,	,
37681	588	35	Dictionary	Dictionary	NNP
37681	588	36	of	of	IN
37681	588	37	Greek	Greek	NNP
37681	588	38	and	and	CC
37681	588	39	Roman	Roman	NNP
37681	588	40	Biography	Biography	NNP
37681	588	41	,	,	,
37681	588	42	article	article	NN
37681	588	43	Eukleides	eukleide	NNS
37681	588	44	;	;	:
37681	588	45	Simon	Simon	NNP
37681	588	46	,	,	,
37681	588	47	Euclid	Euclid	NNP
37681	588	48	und	und	NN
37681	588	49	die	die	VBP
37681	588	50	sechs	sechs	NN
37681	588	51	planimetrischen	planimetrischen	NN
37681	588	52	Bücher	Bücher	NNP
37681	588	53	,	,	,
37681	588	54	Leipzig	Leipzig	NNP
37681	588	55	,	,	,
37681	588	56	1901	1901	CD
37681	588	57	;	;	:
37681	588	58	Gow	Gow	NNP
37681	588	59	,	,	,
37681	588	60	History	history	NN
37681	588	61	of	of	IN
37681	588	62	Greek	Greek	NNP
37681	588	63	Mathematics	Mathematics	NNP
37681	588	64	,	,	,
37681	588	65	Cambridge	Cambridge	NNP
37681	588	66	,	,	,
37681	588	67	1884	1884	CD
37681	588	68	,	,	,
37681	588	69	and	and	CC
37681	588	70	any	any	DT
37681	588	71	of	of	IN
37681	588	72	the	the	DT
37681	588	73	standard	standard	JJ
37681	588	74	histories	history	NNS
37681	588	75	of	of	IN
37681	588	76	mathematics	mathematic	NNS
37681	588	77	.	.	.
37681	589	1	Both	both	DT
37681	589	2	Heath	Heath	NNP
37681	589	3	and	and	CC
37681	589	4	Simon	Simon	NNP
37681	589	5	give	give	VBP
37681	589	6	extensive	extensive	JJ
37681	589	7	bibliographies	bibliography	NNS
37681	589	8	.	.	.
37681	590	1	The	the	DT
37681	590	2	latest	late	JJS
37681	590	3	standard	standard	JJ
37681	590	4	Greek	Greek	NNP
37681	590	5	and	and	CC
37681	590	6	Latin	Latin	NNP
37681	590	7	texts	text	NNS
37681	590	8	are	be	VBP
37681	590	9	Heiberg	Heiberg	NNP
37681	590	10	's	's	POS
37681	590	11	,	,	,
37681	590	12	published	publish	VBN
37681	590	13	by	by	IN
37681	590	14	Teubner	Teubner	NNP
37681	590	15	of	of	IN
37681	590	16	Leipzig	Leipzig	NNP
37681	590	17	.	.	.
37681	591	1	FOOTNOTES	footnote	NNS
37681	591	2	:	:	:
37681	591	3	[	[	-LRB-
37681	591	4	23	23	CD
37681	591	5	]	]	-RRB-
37681	591	6	Riccardi	Riccardi	NNPS
37681	591	7	,	,	,
37681	591	8	Saggio	Saggio	NNP
37681	591	9	di	di	NNP
37681	591	10	una	una	NNP
37681	591	11	bibliografia	bibliografia	JJ
37681	591	12	Euclidea	Euclidea	NNP
37681	591	13	,	,	,
37681	591	14	Part	Part	NNP
37681	591	15	I	I	NNP
37681	591	16	,	,	,
37681	591	17	p.	p.	NN
37681	591	18	3	3	CD
37681	591	19	,	,	,
37681	591	20	Bologna	Bologna	NNPS
37681	591	21	,	,	,
37681	591	22	1887	1887	CD
37681	591	23	.	.	.
37681	592	1	Riccardi	Riccardi	NNS
37681	592	2	lists	list	VBZ
37681	592	3	well	well	RB
37681	592	4	towards	towards	IN
37681	592	5	two	two	CD
37681	592	6	thousand	thousand	CD
37681	592	7	editions	edition	NNS
37681	592	8	.	.	.
37681	593	1	[	[	-LRB-
37681	593	2	24	24	CD
37681	593	3	]	]	-RRB-
37681	593	4	Hermotimus	Hermotimus	NNP
37681	593	5	of	of	IN
37681	593	6	Colophon	Colophon	NNP
37681	593	7	and	and	CC
37681	593	8	Philippus	Philippus	NNP
37681	593	9	of	of	IN
37681	593	10	Mende	Mende	NNP
37681	593	11	.	.	.
37681	594	1	[	[	-LRB-
37681	594	2	25	25	CD
37681	594	3	]	]	-RRB-
37681	594	4	Literally	literally	RB
37681	594	5	,	,	,
37681	594	6	"	"	``
37681	594	7	Who	who	WP
37681	594	8	closely	closely	RB
37681	594	9	followed	follow	VBD
37681	594	10	the	the	DT
37681	594	11	first	first	JJ
37681	594	12	,	,	,
37681	594	13	"	"	''
37681	594	14	i.e.	i.e.	FW
37681	595	1	the	the	DT
37681	595	2	first	first	JJ
37681	595	3	Ptolemy	Ptolemy	NNP
37681	595	4	.	.	.
37681	596	1	[	[	-LRB-
37681	596	2	26	26	CD
37681	596	3	]	]	-RRB-
37681	596	4	Menæchmus	Menæchmus	NNP
37681	596	5	is	be	VBZ
37681	596	6	said	say	VBN
37681	596	7	to	to	TO
37681	596	8	have	have	VB
37681	596	9	replied	reply	VBN
37681	596	10	to	to	IN
37681	596	11	a	a	DT
37681	596	12	similar	similar	JJ
37681	596	13	question	question	NN
37681	596	14	of	of	IN
37681	596	15	Alexander	Alexander	NNP
37681	596	16	the	the	DT
37681	596	17	Great	Great	NNP
37681	596	18	:	:	:
37681	596	19	"	"	``
37681	596	20	O	o	UH
37681	596	21	King	King	NNP
37681	596	22	,	,	,
37681	596	23	through	through	IN
37681	596	24	the	the	DT
37681	596	25	country	country	NN
37681	596	26	there	there	EX
37681	596	27	are	be	VBP
37681	596	28	royal	royal	JJ
37681	596	29	roads	road	NNS
37681	596	30	and	and	CC
37681	596	31	roads	road	NNS
37681	596	32	for	for	IN
37681	596	33	common	common	JJ
37681	596	34	citizens	citizen	NNS
37681	596	35	,	,	,
37681	596	36	but	but	CC
37681	596	37	in	in	IN
37681	596	38	geometry	geometry	NN
37681	596	39	there	there	EX
37681	596	40	is	be	VBZ
37681	596	41	one	one	CD
37681	596	42	road	road	NN
37681	596	43	for	for	IN
37681	596	44	all	all	DT
37681	596	45	.	.	.
37681	596	46	"	"	''
37681	597	1	[	[	-LRB-
37681	597	2	27	27	CD
37681	597	3	]	]	-RRB-
37681	597	4	This	this	DT
37681	597	5	is	be	VBZ
37681	597	6	also	also	RB
37681	597	7	shown	show	VBN
37681	597	8	in	in	IN
37681	597	9	a	a	DT
37681	597	10	letter	letter	NN
37681	597	11	from	from	IN
37681	597	12	Archimedes	Archimedes	NNP
37681	597	13	to	to	IN
37681	597	14	Eratosthenes	Eratosthenes	NNP
37681	597	15	,	,	,
37681	597	16	recently	recently	RB
37681	597	17	discovered	discover	VBN
37681	597	18	by	by	IN
37681	597	19	Heiberg	Heiberg	NNP
37681	597	20	.	.	.
37681	598	1	[	[	-LRB-
37681	598	2	28	28	CD
37681	598	3	]	]	-RRB-
37681	598	4	On	on	IN
37681	598	5	this	this	DT
37681	598	6	phase	phase	NN
37681	598	7	of	of	IN
37681	598	8	the	the	DT
37681	598	9	subject	subject	NN
37681	598	10	,	,	,
37681	598	11	and	and	CC
37681	598	12	indeed	indeed	RB
37681	598	13	upon	upon	IN
37681	598	14	Euclid	Euclid	NNP
37681	598	15	and	and	CC
37681	598	16	his	-PRON-	PRP$
37681	598	17	propositions	proposition	NNS
37681	598	18	and	and	CC
37681	598	19	works	work	NNS
37681	598	20	in	in	IN
37681	598	21	general	general	JJ
37681	598	22	,	,	,
37681	598	23	consult	consult	NNP
37681	598	24	T.	T.	NNP
37681	598	25	L.	L.	NNP
37681	598	26	Heath	Heath	NNP
37681	598	27	,	,	,
37681	598	28	"	"	``
37681	598	29	The	the	DT
37681	598	30	Thirteen	Thirteen	NNP
37681	598	31	Books	Books	NNPS
37681	598	32	of	of	IN
37681	598	33	Euclid	Euclid	NNP
37681	598	34	's	's	POS
37681	598	35	Elements	Elements	NNPS
37681	598	36	,	,	,
37681	598	37	"	"	''
37681	598	38	3	3	CD
37681	598	39	vols	vol	NNS
37681	598	40	.	.	.
37681	598	41	,	,	,
37681	598	42	Cambridge	Cambridge	NNP
37681	598	43	,	,	,
37681	598	44	1908	1908	CD
37681	598	45	,	,	,
37681	598	46	a	a	DT
37681	598	47	masterly	masterly	JJ
37681	598	48	treatise	treatise	NN
37681	598	49	of	of	IN
37681	598	50	which	which	WDT
37681	598	51	frequent	frequent	JJ
37681	598	52	use	use	NN
37681	598	53	has	have	VBZ
37681	598	54	been	be	VBN
37681	598	55	made	make	VBN
37681	598	56	in	in	IN
37681	598	57	preparing	prepare	VBG
37681	598	58	this	this	DT
37681	598	59	work	work	NN
37681	598	60	.	.	.
37681	599	1	[	[	-LRB-
37681	599	2	29	29	CD
37681	599	3	]	]	-RRB-
37681	599	4	A	a	DT
37681	599	5	contemporary	contemporary	JJ
37681	599	6	copy	copy	NN
37681	599	7	of	of	IN
37681	599	8	this	this	DT
37681	599	9	translation	translation	NN
37681	599	10	is	be	VBZ
37681	599	11	now	now	RB
37681	599	12	in	in	IN
37681	599	13	the	the	DT
37681	599	14	library	library	NN
37681	599	15	of	of	IN
37681	599	16	George	George	NNP
37681	599	17	A.	A.	NNP
37681	599	18	Plimpton	Plimpton	NNP
37681	599	19	,	,	,
37681	599	20	Esq	Esq	NNP
37681	599	21	.	.	NNP
37681	599	22	,	,	,
37681	599	23	of	of	IN
37681	599	24	New	New	NNP
37681	599	25	York	York	NNP
37681	599	26	.	.	.
37681	600	1	See	see	VB
37681	600	2	the	the	DT
37681	600	3	author	author	NN
37681	600	4	's	's	POS
37681	600	5	"	"	``
37681	600	6	Rara	Rara	NNP
37681	600	7	Arithmetica	Arithmetica	NNP
37681	600	8	,	,	,
37681	600	9	"	"	''
37681	600	10	p.	p.	NN
37681	600	11	433	433	CD
37681	600	12	,	,	,
37681	600	13	Boston	Boston	NNP
37681	600	14	,	,	,
37681	600	15	1909	1909	CD
37681	600	16	.	.	.
37681	601	1	[	[	-LRB-
37681	601	2	30	30	CD
37681	601	3	]	]	-RRB-
37681	601	4	A	a	DT
37681	601	5	beautiful	beautiful	JJ
37681	601	6	vellum	vellum	NN
37681	601	7	manuscript	manuscript	NN
37681	601	8	of	of	IN
37681	601	9	this	this	DT
37681	601	10	translation	translation	NN
37681	601	11	is	be	VBZ
37681	601	12	in	in	IN
37681	601	13	the	the	DT
37681	601	14	library	library	NN
37681	601	15	of	of	IN
37681	601	16	George	George	NNP
37681	601	17	A.	A.	NNP
37681	601	18	Plimpton	Plimpton	NNP
37681	601	19	,	,	,
37681	601	20	Esq	Esq	NNP
37681	601	21	.	.	NNP
37681	601	22	,	,	,
37681	601	23	of	of	IN
37681	601	24	New	New	NNP
37681	601	25	York	York	NNP
37681	601	26	.	.	.
37681	602	1	See	see	VB
37681	602	2	the	the	DT
37681	602	3	author	author	NN
37681	602	4	's	's	POS
37681	602	5	"	"	``
37681	602	6	Rara	Rara	NNP
37681	602	7	Arithmetica	Arithmetica	NNP
37681	602	8	,	,	,
37681	602	9	"	"	''
37681	602	10	p.	p.	NN
37681	602	11	481	481	CD
37681	602	12	,	,	,
37681	602	13	Boston	Boston	NNP
37681	602	14	,	,	,
37681	602	15	1909	1909	CD
37681	602	16	.	.	.
37681	603	1	[	[	-LRB-
37681	603	2	31	31	CD
37681	603	3	]	]	-RRB-
37681	603	4	Heath	Heath	NNP
37681	603	5	,	,	,
37681	603	6	loc	loc	NNP
37681	603	7	.	.	.
37681	604	1	cit	cit	NNP
37681	604	2	.	.	.
37681	604	3	,	,	,
37681	604	4	Vol	Vol	NNP
37681	604	5	.	.	.
37681	605	1	I	-PRON-	PRP
37681	605	2	,	,	,
37681	605	3	p.	p.	NN
37681	605	4	114	114	CD
37681	605	5	.	.	.
37681	606	1	CHAPTER	chapter	NN
37681	606	2	VI	VI	NNP
37681	606	3	EFFORTS	EFFORTS	NNP
37681	606	4	AT	at	IN
37681	606	5	IMPROVING	improve	VBG
37681	606	6	EUCLID	euclid	NN
37681	606	7	From	from	IN
37681	606	8	time	time	NN
37681	606	9	to	to	IN
37681	606	10	time	time	NN
37681	606	11	an	an	DT
37681	606	12	effort	effort	NN
37681	606	13	is	be	VBZ
37681	606	14	made	make	VBN
37681	606	15	by	by	IN
37681	606	16	some	some	DT
37681	606	17	teacher	teacher	NN
37681	606	18	,	,	,
37681	606	19	or	or	CC
37681	606	20	association	association	NNP
37681	606	21	of	of	IN
37681	606	22	teachers	teacher	NNS
37681	606	23	,	,	,
37681	606	24	animated	animate	VBN
37681	606	25	by	by	IN
37681	606	26	a	a	DT
37681	606	27	serious	serious	JJ
37681	606	28	desire	desire	NN
37681	606	29	to	to	TO
37681	606	30	improve	improve	VB
37681	606	31	the	the	DT
37681	606	32	instruction	instruction	NN
37681	606	33	in	in	IN
37681	606	34	geometry	geometry	NN
37681	606	35	,	,	,
37681	606	36	to	to	TO
37681	606	37	prepare	prepare	VB
37681	606	38	a	a	DT
37681	606	39	new	new	JJ
37681	606	40	syllabus	syllabus	NN
37681	606	41	that	that	WDT
37681	606	42	shall	shall	MD
37681	606	43	mark	mark	VB
37681	606	44	out	out	RP
37681	606	45	some	some	DT
37681	606	46	"	"	``
37681	606	47	royal	royal	JJ
37681	606	48	road	road	NN
37681	606	49	,	,	,
37681	606	50	"	"	''
37681	606	51	and	and	CC
37681	606	52	it	-PRON-	PRP
37681	606	53	therefore	therefore	RB
37681	606	54	becomes	become	VBZ
37681	606	55	those	those	DT
37681	606	56	who	who	WP
37681	606	57	are	be	VBP
37681	606	58	interested	interested	JJ
37681	606	59	in	in	IN
37681	606	60	teaching	teach	VBG
37681	606	61	to	to	TO
37681	606	62	consider	consider	VB
37681	606	63	with	with	IN
37681	606	64	care	care	NN
37681	606	65	the	the	DT
37681	606	66	results	result	NNS
37681	606	67	of	of	IN
37681	606	68	similar	similar	JJ
37681	606	69	efforts	effort	NNS
37681	606	70	in	in	IN
37681	606	71	recent	recent	JJ
37681	606	72	years	year	NNS
37681	606	73	.	.	.
37681	607	1	There	there	EX
37681	607	2	are	be	VBP
37681	607	3	many	many	JJ
37681	607	4	questions	question	NNS
37681	607	5	which	which	WDT
37681	607	6	such	such	PDT
37681	607	7	an	an	DT
37681	607	8	attempt	attempt	NN
37681	607	9	suggests	suggest	VBZ
37681	607	10	:	:	:
37681	607	11	What	what	WP
37681	607	12	is	be	VBZ
37681	607	13	the	the	DT
37681	607	14	real	real	JJ
37681	607	15	purpose	purpose	NN
37681	607	16	of	of	IN
37681	607	17	the	the	DT
37681	607	18	movement	movement	NN
37681	607	19	?	?	.
37681	608	1	What	what	WP
37681	608	2	will	will	MD
37681	608	3	the	the	DT
37681	608	4	teaching	teaching	NN
37681	608	5	world	world	NN
37681	608	6	say	say	VB
37681	608	7	of	of	IN
37681	608	8	the	the	DT
37681	608	9	result	result	NN
37681	608	10	?	?	.
37681	609	1	Shall	Shall	MD
37681	609	2	a	a	DT
37681	609	3	reckless	reckless	JJ
37681	609	4	,	,	,
37681	609	5	ill	ill	RB
37681	609	6	-	-	HYPH
37681	609	7	considered	consider	VBN
37681	609	8	radicalism	radicalism	NN
37681	609	9	dominate	dominate	VBP
37681	609	10	the	the	DT
37681	609	11	effort	effort	NN
37681	609	12	,	,	,
37681	609	13	bringing	bring	VBG
37681	609	14	in	in	RP
37681	609	15	a	a	DT
37681	609	16	distasteful	distasteful	JJ
37681	609	17	terminology	terminology	NN
37681	609	18	and	and	CC
37681	609	19	symbolism	symbolism	NN
37681	609	20	merely	merely	RB
37681	609	21	for	for	IN
37681	609	22	its	-PRON-	PRP$
37681	609	23	novelty	novelty	NN
37681	609	24	,	,	,
37681	609	25	insisting	insist	VBG
37681	609	26	upon	upon	IN
37681	609	27	an	an	DT
37681	609	28	ultralogical	ultralogical	JJ
37681	609	29	treatment	treatment	NN
37681	609	30	that	that	WDT
37681	609	31	is	be	VBZ
37681	609	32	beyond	beyond	IN
37681	609	33	the	the	DT
37681	609	34	powers	power	NNS
37681	609	35	of	of	IN
37681	609	36	the	the	DT
37681	609	37	learner	learner	NN
37681	609	38	,	,	,
37681	609	39	rearranging	rearrange	VBG
37681	609	40	the	the	DT
37681	609	41	subject	subject	JJ
37681	609	42	matter	matter	NN
37681	609	43	to	to	TO
37681	609	44	fit	fit	VB
37681	609	45	some	some	DT
37681	609	46	narrow	narrow	JJ
37681	609	47	notion	notion	NN
37681	609	48	of	of	IN
37681	609	49	the	the	DT
37681	609	50	projectors	projector	NNS
37681	609	51	,	,	,
37681	609	52	seeking	seek	VBG
37681	609	53	to	to	TO
37681	609	54	emasculate	emasculate	VB
37681	609	55	mathematics	mathematic	NNS
37681	609	56	by	by	IN
37681	609	57	looking	look	VBG
37681	609	58	only	only	RB
37681	609	59	to	to	IN
37681	609	60	the	the	DT
37681	609	61	applications	application	NNS
37681	609	62	,	,	,
37681	609	63	riding	ride	VBG
37681	609	64	some	some	DT
37681	609	65	little	little	JJ
37681	609	66	hobby	hobby	NN
37681	609	67	in	in	IN
37681	609	68	the	the	DT
37681	609	69	way	way	NN
37681	609	70	of	of	IN
37681	609	71	some	some	DT
37681	609	72	particular	particular	JJ
37681	609	73	class	class	NN
37681	609	74	of	of	IN
37681	609	75	exercises	exercise	NNS
37681	609	76	,	,	,
37681	609	77	and	and	CC
37681	609	78	cutting	cut	VBG
37681	609	79	the	the	DT
37681	609	80	number	number	NN
37681	609	81	of	of	IN
37681	609	82	propositions	proposition	NNS
37681	609	83	to	to	IN
37681	609	84	a	a	DT
37681	609	85	minimum	minimum	NN
37681	609	86	that	that	WDT
37681	609	87	will	will	MD
37681	609	88	satisfy	satisfy	VB
37681	609	89	the	the	DT
37681	609	90	mere	mere	JJ
37681	609	91	demands	demand	NNS
37681	609	92	of	of	IN
37681	609	93	the	the	DT
37681	609	94	artisan	artisan	NNP
37681	609	95	?	?	.
37681	610	1	Such	such	JJ
37681	610	2	are	be	VBP
37681	610	3	some	some	DT
37681	610	4	of	of	IN
37681	610	5	the	the	DT
37681	610	6	questions	question	NNS
37681	610	7	that	that	WDT
37681	610	8	naturally	naturally	RB
37681	610	9	arise	arise	VBP
37681	610	10	in	in	IN
37681	610	11	the	the	DT
37681	610	12	mind	mind	NN
37681	610	13	of	of	IN
37681	610	14	every	every	DT
37681	610	15	one	one	NN
37681	610	16	who	who	WP
37681	610	17	wishes	wish	VBZ
37681	610	18	well	well	RB
37681	610	19	for	for	IN
37681	610	20	the	the	DT
37681	610	21	ancient	ancient	JJ
37681	610	22	science	science	NN
37681	610	23	of	of	IN
37681	610	24	geometry	geometry	NN
37681	610	25	.	.	.
37681	611	1	It	-PRON-	PRP
37681	611	2	is	be	VBZ
37681	611	3	not	not	RB
37681	611	4	proposed	propose	VBN
37681	611	5	in	in	IN
37681	611	6	this	this	DT
37681	611	7	chapter	chapter	NN
37681	611	8	to	to	TO
37681	611	9	attempt	attempt	VB
37681	611	10	to	to	TO
37681	611	11	answer	answer	VB
37681	611	12	these	these	DT
37681	611	13	questions	question	NNS
37681	611	14	,	,	,
37681	611	15	but	but	CC
37681	611	16	rather	rather	RB
37681	611	17	to	to	TO
37681	611	18	assist	assist	VB
37681	611	19	in	in	IN
37681	611	20	understanding	understand	VBG
37681	611	21	the	the	DT
37681	611	22	problem	problem	NN
37681	611	23	by	by	IN
37681	611	24	considering	consider	VBG
37681	611	25	the	the	DT
37681	611	26	results	result	NNS
37681	611	27	of	of	IN
37681	611	28	similar	similar	JJ
37681	611	29	attempts	attempt	NNS
37681	611	30	.	.	.
37681	612	1	If	if	IN
37681	612	2	it	-PRON-	PRP
37681	612	3	shall	shall	MD
37681	612	4	be	be	VB
37681	612	5	found	find	VBN
37681	612	6	that	that	IN
37681	612	7	syllabi	syllabi	NNP
37681	612	8	have	have	VBP
37681	612	9	been	be	VBN
37681	612	10	prepared	prepare	VBN
37681	612	11	under	under	IN
37681	612	12	circumstances	circumstance	NNS
37681	612	13	quite	quite	RB
37681	612	14	as	as	RB
37681	612	15	favorable	favorable	JJ
37681	612	16	as	as	IN
37681	612	17	those	those	DT
37681	612	18	that	that	WDT
37681	612	19	obtain	obtain	VBP
37681	612	20	at	at	IN
37681	612	21	present	present	JJ
37681	612	22	,	,	,
37681	612	23	and	and	CC
37681	612	24	if	if	IN
37681	612	25	these	these	DT
37681	612	26	syllabi	syllabi	NN
37681	612	27	have	have	VBP
37681	612	28	had	have	VBN
37681	612	29	little	little	JJ
37681	612	30	or	or	CC
37681	612	31	no	no	DT
37681	612	32	real	real	JJ
37681	612	33	influence	influence	NN
37681	612	34	,	,	,
37681	612	35	then	then	RB
37681	612	36	it	-PRON-	PRP
37681	612	37	becomes	become	VBZ
37681	612	38	our	-PRON-	PRP$
37681	612	39	duty	duty	NN
37681	612	40	to	to	TO
37681	612	41	see	see	VB
37681	612	42	if	if	IN
37681	612	43	new	new	JJ
37681	612	44	plans	plan	NNS
37681	612	45	may	may	MD
37681	612	46	be	be	VB
37681	612	47	worked	work	VBN
37681	612	48	out	out	RP
37681	612	49	so	so	IN
37681	612	50	as	as	IN
37681	612	51	to	to	TO
37681	612	52	be	be	VB
37681	612	53	more	more	RBR
37681	612	54	successful	successful	JJ
37681	612	55	than	than	IN
37681	612	56	their	-PRON-	PRP$
37681	612	57	predecessors	predecessor	NNS
37681	612	58	.	.	.
37681	613	1	If	if	IN
37681	613	2	the	the	DT
37681	613	3	older	old	JJR
37681	613	4	attempts	attempt	NNS
37681	613	5	have	have	VBP
37681	613	6	led	lead	VBN
37681	613	7	to	to	IN
37681	613	8	some	some	DT
37681	613	9	good	good	JJ
37681	613	10	,	,	,
37681	613	11	it	-PRON-	PRP
37681	613	12	is	be	VBZ
37681	613	13	well	well	JJ
37681	613	14	to	to	TO
37681	613	15	know	know	VB
37681	613	16	what	what	WP
37681	613	17	is	be	VBZ
37681	613	18	the	the	DT
37681	613	19	nature	nature	NN
37681	613	20	of	of	IN
37681	613	21	this	this	DT
37681	613	22	good	good	JJ
37681	613	23	,	,	,
37681	613	24	to	to	IN
37681	613	25	the	the	DT
37681	613	26	end	end	NN
37681	613	27	that	that	IN
37681	613	28	new	new	JJ
37681	613	29	efforts	effort	NNS
37681	613	30	may	may	MD
37681	613	31	also	also	RB
37681	613	32	result	result	VB
37681	613	33	in	in	IN
37681	613	34	something	something	NN
37681	613	35	of	of	IN
37681	613	36	benefit	benefit	NN
37681	613	37	to	to	IN
37681	613	38	the	the	DT
37681	613	39	schools	school	NNS
37681	613	40	.	.	.
37681	614	1	It	-PRON-	PRP
37681	614	2	is	be	VBZ
37681	614	3	proposed	propose	VBN
37681	614	4	in	in	IN
37681	614	5	this	this	DT
37681	614	6	chapter	chapter	NN
37681	614	7	to	to	TO
37681	614	8	call	call	VB
37681	614	9	attention	attention	NN
37681	614	10	to	to	IN
37681	614	11	four	four	CD
37681	614	12	important	important	JJ
37681	614	13	syllabi	syllabi	NN
37681	614	14	,	,	,
37681	614	15	setting	set	VBG
37681	614	16	forth	forth	RP
37681	614	17	briefly	briefly	RB
37681	614	18	their	-PRON-	PRP$
37681	614	19	distinguishing	distinguish	VBG
37681	614	20	features	feature	NNS
37681	614	21	and	and	CC
37681	614	22	drawing	draw	VBG
37681	614	23	some	some	DT
37681	614	24	conclusions	conclusion	NNS
37681	614	25	that	that	WDT
37681	614	26	may	may	MD
37681	614	27	be	be	VB
37681	614	28	helpful	helpful	JJ
37681	614	29	in	in	IN
37681	614	30	other	other	JJ
37681	614	31	efforts	effort	NNS
37681	614	32	of	of	IN
37681	614	33	this	this	DT
37681	614	34	nature	nature	NN
37681	614	35	.	.	.
37681	615	1	In	in	IN
37681	615	2	England	England	NNP
37681	615	3	two	two	CD
37681	615	4	noteworthy	noteworthy	JJ
37681	615	5	attempts	attempt	NNS
37681	615	6	have	have	VBP
37681	615	7	been	be	VBN
37681	615	8	made	make	VBN
37681	615	9	within	within	IN
37681	615	10	a	a	DT
37681	615	11	century	century	NN
37681	615	12	,	,	,
37681	615	13	looking	look	VBG
37681	615	14	to	to	IN
37681	615	15	a	a	DT
37681	615	16	more	more	RBR
37681	615	17	satisfactory	satisfactory	JJ
37681	615	18	sequence	sequence	NN
37681	615	19	and	and	CC
37681	615	20	selection	selection	NN
37681	615	21	of	of	IN
37681	615	22	propositions	proposition	NNS
37681	615	23	than	than	IN
37681	615	24	is	be	VBZ
37681	615	25	found	find	VBN
37681	615	26	in	in	IN
37681	615	27	Euclid	Euclid	NNP
37681	615	28	.	.	.
37681	616	1	Each	each	DT
37681	616	2	began	begin	VBD
37681	616	3	with	with	IN
37681	616	4	a	a	DT
37681	616	5	list	list	NN
37681	616	6	of	of	IN
37681	616	7	propositions	proposition	NNS
37681	616	8	arranged	arrange	VBN
37681	616	9	in	in	IN
37681	616	10	proper	proper	JJ
37681	616	11	sequence	sequence	NN
37681	616	12	,	,	,
37681	616	13	and	and	CC
37681	616	14	each	each	DT
37681	616	15	was	be	VBD
37681	616	16	thereafter	thereafter	RB
37681	616	17	elaborated	elaborate	VBN
37681	616	18	into	into	IN
37681	616	19	a	a	DT
37681	616	20	textbook	textbook	NN
37681	616	21	.	.	.
37681	617	1	Neither	neither	DT
37681	617	2	accomplished	accomplish	VBN
37681	617	3	fully	fully	RB
37681	617	4	the	the	DT
37681	617	5	purpose	purpose	NN
37681	617	6	intended	intend	VBN
37681	617	7	,	,	,
37681	617	8	but	but	CC
37681	617	9	each	each	DT
37681	617	10	was	be	VBD
37681	617	11	instrumental	instrumental	JJ
37681	617	12	in	in	IN
37681	617	13	provoking	provoke	VBG
37681	617	14	healthy	healthy	JJ
37681	617	15	discussion	discussion	NN
37681	617	16	and	and	CC
37681	617	17	in	in	IN
37681	617	18	improving	improve	VBG
37681	617	19	the	the	DT
37681	617	20	texts	text	NNS
37681	617	21	from	from	IN
37681	617	22	which	which	WDT
37681	617	23	geometry	geometry	NN
37681	617	24	is	be	VBZ
37681	617	25	studied	study	VBN
37681	617	26	.	.	.
37681	618	1	The	the	DT
37681	618	2	first	first	JJ
37681	618	3	of	of	IN
37681	618	4	these	these	DT
37681	618	5	attempts	attempt	NNS
37681	618	6	was	be	VBD
37681	618	7	made	make	VBN
37681	618	8	by	by	IN
37681	618	9	Professor	Professor	NNP
37681	618	10	Augustus	Augustus	NNP
37681	618	11	de	de	NNP
37681	618	12	Morgan	Morgan	NNP
37681	618	13	,	,	,
37681	618	14	under	under	IN
37681	618	15	the	the	DT
37681	618	16	auspices	auspex	NNS
37681	618	17	of	of	IN
37681	618	18	the	the	DT
37681	618	19	Society	Society	NNP
37681	618	20	for	for	IN
37681	618	21	the	the	DT
37681	618	22	Diffusion	Diffusion	NNP
37681	618	23	of	of	IN
37681	618	24	Useful	Useful	NNP
37681	618	25	Knowledge	Knowledge	NNP
37681	618	26	,	,	,
37681	618	27	and	and	CC
37681	618	28	it	-PRON-	PRP
37681	618	29	resulted	result	VBD
37681	618	30	in	in	IN
37681	618	31	a	a	DT
37681	618	32	textbook	textbook	NN
37681	618	33	,	,	,
37681	618	34	including	include	VBG
37681	618	35	"	"	``
37681	618	36	plane	plane	NN
37681	618	37	,	,	,
37681	618	38	solid	solid	JJ
37681	618	39	,	,	,
37681	618	40	and	and	CC
37681	618	41	spherical	spherical	JJ
37681	618	42	"	"	``
37681	618	43	geometry	geometry	NN
37681	618	44	,	,	,
37681	618	45	in	in	IN
37681	618	46	six	six	CD
37681	618	47	books	book	NNS
37681	618	48	.	.	.
37681	619	1	According	accord	VBG
37681	619	2	to	to	IN
37681	619	3	De	De	NNP
37681	619	4	Morgan	Morgan	NNP
37681	619	5	's	's	POS
37681	619	6	plan	plan	NN
37681	619	7	,	,	,
37681	619	8	plane	plane	NN
37681	619	9	geometry	geometry	NN
37681	619	10	consisted	consist	VBD
37681	619	11	of	of	IN
37681	619	12	three	three	CD
37681	619	13	books	book	NNS
37681	619	14	,	,	,
37681	619	15	the	the	DT
37681	619	16	number	number	NN
37681	619	17	of	of	IN
37681	619	18	propositions	proposition	NNS
37681	619	19	being	be	VBG
37681	619	20	as	as	IN
37681	619	21	follows	follow	VBZ
37681	619	22	:	:	:
37681	619	23	Book	Book	NNP
37681	619	24	I.	I.	NNP
37681	619	25	Rectilinear	Rectilinear	NNP
37681	619	26	figures	figure	VBZ
37681	619	27	60	60	CD
37681	619	28	Book	Book	NNP
37681	619	29	II	II	NNP
37681	619	30	.	.	.
37681	620	1	Ratio	ratio	NN
37681	620	2	,	,	,
37681	620	3	proportion	proportion	NN
37681	620	4	,	,	,
37681	620	5	applications	application	NNS
37681	620	6	69	69	CD
37681	620	7	Book	Book	NNP
37681	620	8	III	iii	CD
37681	620	9	.	.	.
37681	621	1	The	the	DT
37681	621	2	circle	circle	NN
37681	621	3	65	65	CD
37681	621	4	----	----	NFP
37681	621	5	Total	total	NN
37681	621	6	for	for	IN
37681	621	7	plane	plane	NN
37681	621	8	geometry	geometry	NN
37681	621	9	194	194	CD
37681	621	10	Of	of	IN
37681	621	11	the	the	DT
37681	621	12	194	194	CD
37681	621	13	propositions	proposition	NNS
37681	621	14	De	De	NNP
37681	621	15	Morgan	Morgan	NNP
37681	621	16	selected	select	VBD
37681	621	17	114	114	CD
37681	621	18	with	with	IN
37681	621	19	their	-PRON-	PRP$
37681	621	20	corollaries	corollary	NNS
37681	621	21	as	as	IN
37681	621	22	necessary	necessary	JJ
37681	621	23	for	for	IN
37681	621	24	a	a	DT
37681	621	25	beginner	beginner	NN
37681	621	26	who	who	WP
37681	621	27	is	be	VBZ
37681	621	28	teaching	teach	VBG
37681	621	29	himself	-PRON-	PRP
37681	621	30	.	.	.
37681	622	1	In	in	IN
37681	622	2	solid	solid	JJ
37681	622	3	geometry	geometry	NN
37681	622	4	the	the	DT
37681	622	5	plan	plan	NN
37681	622	6	was	be	VBD
37681	622	7	as	as	IN
37681	622	8	follows	follow	VBZ
37681	622	9	:	:	:
37681	622	10	Book	Book	NNP
37681	622	11	IV	IV	NNP
37681	622	12	.	.	.
37681	623	1	Lines	line	NNS
37681	623	2	in	in	IN
37681	623	3	different	different	JJ
37681	623	4	planes	plane	NNS
37681	623	5	,	,	,
37681	623	6	solids	solid	NNS
37681	623	7	contained	contain	VBN
37681	623	8	by	by	IN
37681	623	9	planes	plane	NNS
37681	623	10	52	52	CD
37681	623	11	Book	Book	NNP
37681	623	12	V.	V.	NNP
37681	623	13	Cylinder	Cylinder	NNP
37681	623	14	,	,	,
37681	623	15	cone	cone	NN
37681	623	16	,	,	,
37681	623	17	sphere	sphere	VBD
37681	623	18	25	25	CD
37681	623	19	Book	Book	NNP
37681	623	20	VI	VI	NNP
37681	623	21	.	.	.
37681	624	1	Figures	figure	NNS
37681	624	2	on	on	IN
37681	624	3	a	a	DT
37681	624	4	sphere	sphere	JJ
37681	624	5	42	42	CD
37681	624	6	----	----	NFP
37681	624	7	Total	total	NN
37681	624	8	for	for	IN
37681	624	9	solid	solid	JJ
37681	624	10	geometry	geometry	NN
37681	624	11	119	119	CD
37681	624	12	Of	of	IN
37681	624	13	these	these	DT
37681	624	14	119	119	CD
37681	624	15	propositions	proposition	NNS
37681	624	16	De	De	NNP
37681	624	17	Morgan	Morgan	NNP
37681	624	18	selected	select	VBD
37681	624	19	76	76	CD
37681	624	20	with	with	IN
37681	624	21	their	-PRON-	PRP$
37681	624	22	corollaries	corollary	NNS
37681	624	23	as	as	IN
37681	624	24	necessary	necessary	JJ
37681	624	25	for	for	IN
37681	624	26	a	a	DT
37681	624	27	beginner	beginner	NN
37681	624	28	,	,	,
37681	624	29	thus	thus	RB
37681	624	30	making	make	VBG
37681	624	31	190	190	CD
37681	624	32	necessary	necessary	JJ
37681	624	33	propositions	proposition	NNS
37681	624	34	out	out	IN
37681	624	35	of	of	IN
37681	624	36	305	305	CD
37681	624	37	desirable	desirable	JJ
37681	624	38	ones	one	NNS
37681	624	39	,	,	,
37681	624	40	besides	besides	IN
37681	624	41	the	the	DT
37681	624	42	corollaries	corollary	NNS
37681	624	43	in	in	IN
37681	624	44	plane	plane	NN
37681	624	45	and	and	CC
37681	624	46	solid	solid	JJ
37681	624	47	geometry	geometry	NN
37681	624	48	.	.	.
37681	625	1	In	in	IN
37681	625	2	other	other	JJ
37681	625	3	words	word	NNS
37681	625	4	,	,	,
37681	625	5	of	of	IN
37681	625	6	the	the	DT
37681	625	7	desirable	desirable	JJ
37681	625	8	propositions	proposition	NNS
37681	625	9	he	-PRON-	PRP
37681	625	10	considered	consider	VBD
37681	625	11	that	that	IN
37681	625	12	about	about	RB
37681	625	13	two	two	CD
37681	625	14	thirds	third	NNS
37681	625	15	are	be	VBP
37681	625	16	absolutely	absolutely	RB
37681	625	17	necessary	necessary	JJ
37681	625	18	.	.	.
37681	626	1	It	-PRON-	PRP
37681	626	2	is	be	VBZ
37681	626	3	interesting	interesting	JJ
37681	626	4	to	to	TO
37681	626	5	note	note	VB
37681	626	6	,	,	,
37681	626	7	however	however	RB
37681	626	8	,	,	,
37681	626	9	that	that	IN
37681	626	10	he	-PRON-	PRP
37681	626	11	summed	sum	VBD
37681	626	12	up	up	RP
37681	626	13	the	the	DT
37681	626	14	results	result	NNS
37681	626	15	of	of	IN
37681	626	16	his	-PRON-	PRP$
37681	626	17	labors	labor	NNS
37681	626	18	by	by	IN
37681	626	19	saying	say	VBG
37681	626	20	:	:	:
37681	626	21	It	-PRON-	PRP
37681	626	22	will	will	MD
37681	626	23	be	be	VB
37681	626	24	found	find	VBN
37681	626	25	that	that	IN
37681	626	26	the	the	DT
37681	626	27	course	course	NN
37681	626	28	just	just	RB
37681	626	29	laid	lay	VBD
37681	626	30	down	down	RP
37681	626	31	,	,	,
37681	626	32	excepting	except	VBG
37681	626	33	the	the	DT
37681	626	34	sixth	sixth	JJ
37681	626	35	book	book	NN
37681	626	36	of	of	IN
37681	626	37	it	-PRON-	PRP
37681	626	38	only	only	RB
37681	626	39	,	,	,
37681	626	40	is	be	VBZ
37681	626	41	not	not	RB
37681	626	42	of	of	IN
37681	626	43	much	much	RB
37681	626	44	greater	great	JJR
37681	626	45	extent	extent	NN
37681	626	46	,	,	,
37681	626	47	nor	nor	CC
37681	626	48	very	very	RB
37681	626	49	different	different	JJ
37681	626	50	in	in	IN
37681	626	51	point	point	NN
37681	626	52	of	of	IN
37681	626	53	matter	matter	NN
37681	626	54	from	from	IN
37681	626	55	that	that	DT
37681	626	56	of	of	IN
37681	626	57	Euclid	Euclid	NNP
37681	626	58	,	,	,
37681	626	59	whose	whose	WP$
37681	626	60	"	"	``
37681	626	61	Elements	element	NNS
37681	626	62	"	"	''
37681	626	63	have	have	VBP
37681	626	64	at	at	RB
37681	626	65	all	all	DT
37681	626	66	times	time	NNS
37681	626	67	been	be	VBN
37681	626	68	justly	justly	RB
37681	626	69	esteemed	esteem	VBD
37681	626	70	a	a	DT
37681	626	71	model	model	NN
37681	626	72	not	not	RB
37681	626	73	only	only	RB
37681	626	74	of	of	IN
37681	626	75	easy	easy	JJ
37681	626	76	and	and	CC
37681	626	77	progressive	progressive	JJ
37681	626	78	instruction	instruction	NN
37681	626	79	in	in	IN
37681	626	80	geometry	geometry	NN
37681	626	81	,	,	,
37681	626	82	but	but	CC
37681	626	83	of	of	IN
37681	626	84	accuracy	accuracy	NN
37681	626	85	and	and	CC
37681	626	86	perspicuity	perspicuity	NN
37681	626	87	in	in	IN
37681	626	88	reasoning	reasoning	NN
37681	626	89	.	.	.
37681	627	1	De	De	NNP
37681	627	2	Morgan	Morgan	NNP
37681	627	3	's	's	POS
37681	627	4	effort	effort	NN
37681	627	5	,	,	,
37681	627	6	essentially	essentially	RB
37681	627	7	that	that	DT
37681	627	8	of	of	IN
37681	627	9	a	a	DT
37681	627	10	syllabus	syllabus	NN
37681	627	11	-	-	HYPH
37681	627	12	maker	maker	NN
37681	627	13	rather	rather	RB
37681	627	14	than	than	IN
37681	627	15	a	a	DT
37681	627	16	textbook	textbook	NN
37681	627	17	writer	writer	NN
37681	627	18	,	,	,
37681	627	19	although	although	IN
37681	627	20	it	-PRON-	PRP
37681	627	21	was	be	VBD
37681	627	22	published	publish	VBN
37681	627	23	under	under	IN
37681	627	24	the	the	DT
37681	627	25	patronage	patronage	NN
37681	627	26	of	of	IN
37681	627	27	a	a	DT
37681	627	28	prominent	prominent	JJ
37681	627	29	society	society	NN
37681	627	30	with	with	IN
37681	627	31	which	which	WDT
37681	627	32	were	be	VBD
37681	627	33	associated	associate	VBN
37681	627	34	the	the	DT
37681	627	35	names	name	NNS
37681	627	36	of	of	IN
37681	627	37	men	man	NNS
37681	627	38	like	like	IN
37681	627	39	Henry	Henry	NNP
37681	627	40	Hallam	Hallam	NNP
37681	627	41	,	,	,
37681	627	42	Rowland	Rowland	NNP
37681	627	43	Hill	Hill	NNP
37681	627	44	,	,	,
37681	627	45	Lord	Lord	NNP
37681	627	46	John	John	NNP
37681	627	47	Russell	Russell	NNP
37681	627	48	,	,	,
37681	627	49	and	and	CC
37681	627	50	George	George	NNP
37681	627	51	Peacock	Peacock	NNP
37681	627	52	,	,	,
37681	627	53	had	have	VBD
37681	627	54	no	no	DT
37681	627	55	apparent	apparent	JJ
37681	627	56	influence	influence	NN
37681	627	57	on	on	IN
37681	627	58	geometry	geometry	NN
37681	627	59	either	either	CC
37681	627	60	in	in	IN
37681	627	61	England	England	NNP
37681	627	62	or	or	CC
37681	627	63	abroad	abroad	RB
37681	627	64	.	.	.
37681	628	1	Nevertheless	nevertheless	RB
37681	628	2	the	the	DT
37681	628	3	syllabus	syllabus	NN
37681	628	4	was	be	VBD
37681	628	5	in	in	IN
37681	628	6	many	many	JJ
37681	628	7	respects	respect	NNS
37681	628	8	excellent	excellent	JJ
37681	628	9	;	;	:
37681	628	10	it	-PRON-	PRP
37681	628	11	rearranged	rearrange	VBD
37681	628	12	the	the	DT
37681	628	13	matter	matter	NN
37681	628	14	,	,	,
37681	628	15	it	-PRON-	PRP
37681	628	16	classified	classify	VBD
37681	628	17	the	the	DT
37681	628	18	propositions	proposition	NNS
37681	628	19	,	,	,
37681	628	20	it	-PRON-	PRP
37681	628	21	improved	improve	VBD
37681	628	22	some	some	DT
37681	628	23	of	of	IN
37681	628	24	the	the	DT
37681	628	25	terminology	terminology	NN
37681	628	26	,	,	,
37681	628	27	and	and	CC
37681	628	28	it	-PRON-	PRP
37681	628	29	reduced	reduce	VBD
37681	628	30	the	the	DT
37681	628	31	number	number	NN
37681	628	32	of	of	IN
37681	628	33	essential	essential	JJ
37681	628	34	propositions	proposition	NNS
37681	628	35	;	;	:
37681	628	36	it	-PRON-	PRP
37681	628	37	had	have	VBD
37681	628	38	the	the	DT
37681	628	39	assistance	assistance	NN
37681	628	40	of	of	IN
37681	628	41	De	De	NNP
37681	628	42	Morgan	Morgan	NNP
37681	628	43	's	's	POS
37681	628	44	enthusiasm	enthusiasm	NN
37681	628	45	and	and	CC
37681	628	46	of	of	IN
37681	628	47	the	the	DT
37681	628	48	society	society	NN
37681	628	49	with	with	IN
37681	628	50	which	which	WDT
37681	628	51	he	-PRON-	PRP
37681	628	52	was	be	VBD
37681	628	53	so	so	RB
37681	628	54	prominently	prominently	RB
37681	628	55	connected	connect	VBN
37681	628	56	,	,	,
37681	628	57	and	and	CC
37681	628	58	it	-PRON-	PRP
37681	628	59	was	be	VBD
37681	628	60	circulated	circulate	VBN
37681	628	61	with	with	IN
37681	628	62	considerable	considerable	JJ
37681	628	63	generosity	generosity	NN
37681	628	64	throughout	throughout	IN
37681	628	65	the	the	DT
37681	628	66	English	English	NNP
37681	628	67	-	-	HYPH
37681	628	68	speaking	speak	VBG
37681	628	69	world	world	NN
37681	628	70	;	;	,
37681	628	71	but	but	CC
37681	628	72	in	in	IN
37681	628	73	spite	spite	NN
37681	628	74	of	of	IN
37681	628	75	all	all	PDT
37681	628	76	this	this	DT
37681	628	77	it	-PRON-	PRP
37681	628	78	is	be	VBZ
37681	628	79	to	to	IN
37681	628	80	-	-	HYPH
37681	628	81	day	day	NN
37681	628	82	practically	practically	RB
37681	628	83	unknown	unknown	JJ
37681	628	84	.	.	.
37681	629	1	A	a	DT
37681	629	2	second	second	JJ
37681	629	3	noteworthy	noteworthy	JJ
37681	629	4	attempt	attempt	NN
37681	629	5	in	in	IN
37681	629	6	England	England	NNP
37681	629	7	was	be	VBD
37681	629	8	made	make	VBN
37681	629	9	about	about	IN
37681	629	10	a	a	DT
37681	629	11	quarter	quarter	NN
37681	629	12	of	of	IN
37681	629	13	a	a	DT
37681	629	14	century	century	NN
37681	629	15	ago	ago	RB
37681	629	16	by	by	IN
37681	629	17	a	a	DT
37681	629	18	society	society	NN
37681	629	19	that	that	WDT
37681	629	20	was	be	VBD
37681	629	21	organized	organize	VBN
37681	629	22	practically	practically	RB
37681	629	23	for	for	IN
37681	629	24	this	this	DT
37681	629	25	very	very	JJ
37681	629	26	purpose	purpose	NN
37681	629	27	,	,	,
37681	629	28	the	the	DT
37681	629	29	Association	Association	NNP
37681	629	30	for	for	IN
37681	629	31	the	the	DT
37681	629	32	Improvement	Improvement	NNP
37681	629	33	of	of	IN
37681	629	34	Geometrical	Geometrical	NNP
37681	629	35	Teaching	Teaching	NNP
37681	629	36	.	.	.
37681	630	1	This	this	DT
37681	630	2	society	society	NN
37681	630	3	was	be	VBD
37681	630	4	composed	compose	VBN
37681	630	5	of	of	IN
37681	630	6	many	many	JJ
37681	630	7	of	of	IN
37681	630	8	the	the	DT
37681	630	9	most	most	RBS
37681	630	10	progressive	progressive	JJ
37681	630	11	teachers	teacher	NNS
37681	630	12	in	in	IN
37681	630	13	England	England	NNP
37681	630	14	,	,	,
37681	630	15	and	and	CC
37681	630	16	it	-PRON-	PRP
37681	630	17	included	include	VBD
37681	630	18	in	in	IN
37681	630	19	its	-PRON-	PRP$
37681	630	20	membership	membership	NN
37681	630	21	men	man	NNS
37681	630	22	of	of	IN
37681	630	23	high	high	JJ
37681	630	24	standing	standing	NN
37681	630	25	in	in	IN
37681	630	26	mathematics	mathematic	NNS
37681	630	27	in	in	IN
37681	630	28	the	the	DT
37681	630	29	universities	university	NNS
37681	630	30	.	.	.
37681	631	1	As	as	IN
37681	631	2	a	a	DT
37681	631	3	result	result	NN
37681	631	4	of	of	IN
37681	631	5	their	-PRON-	PRP$
37681	631	6	labors	labor	NNS
37681	631	7	a	a	DT
37681	631	8	syllabus	syllabus	NN
37681	631	9	was	be	VBD
37681	631	10	prepared	prepare	VBN
37681	631	11	,	,	,
37681	631	12	which	which	WDT
37681	631	13	was	be	VBD
37681	631	14	elaborated	elaborate	VBN
37681	631	15	into	into	IN
37681	631	16	a	a	DT
37681	631	17	textbook	textbook	NN
37681	631	18	,	,	,
37681	631	19	and	and	CC
37681	631	20	in	in	IN
37681	631	21	1889	1889	CD
37681	631	22	a	a	DT
37681	631	23	revised	revised	JJ
37681	631	24	syllabus	syllabus	NN
37681	631	25	was	be	VBD
37681	631	26	issued	issue	VBN
37681	631	27	.	.	.
37681	632	1	As	as	IN
37681	632	2	to	to	IN
37681	632	3	the	the	DT
37681	632	4	arrangement	arrangement	NN
37681	632	5	of	of	IN
37681	632	6	matter	matter	NN
37681	632	7	,	,	,
37681	632	8	the	the	DT
37681	632	9	syllabus	syllabus	JJ
37681	632	10	departs	depart	VBZ
37681	632	11	from	from	IN
37681	632	12	Euclid	Euclid	NNP
37681	632	13	chiefly	chiefly	RB
37681	632	14	by	by	IN
37681	632	15	separating	separate	VBG
37681	632	16	the	the	DT
37681	632	17	problems	problem	NNS
37681	632	18	from	from	IN
37681	632	19	the	the	DT
37681	632	20	theorems	theorem	NNS
37681	632	21	,	,	,
37681	632	22	as	as	IN
37681	632	23	is	be	VBZ
37681	632	24	the	the	DT
37681	632	25	case	case	NN
37681	632	26	in	in	IN
37681	632	27	our	-PRON-	PRP$
37681	632	28	American	american	JJ
37681	632	29	textbooks	textbook	NNS
37681	632	30	,	,	,
37681	632	31	and	and	CC
37681	632	32	in	in	IN
37681	632	33	improving	improve	VBG
37681	632	34	the	the	DT
37681	632	35	phraseology	phraseology	NN
37681	632	36	.	.	.
37681	633	1	The	the	DT
37681	633	2	course	course	NN
37681	633	3	is	be	VBZ
37681	633	4	preceded	precede	VBN
37681	633	5	by	by	IN
37681	633	6	some	some	DT
37681	633	7	simple	simple	JJ
37681	633	8	exercises	exercise	NNS
37681	633	9	in	in	IN
37681	633	10	the	the	DT
37681	633	11	use	use	NN
37681	633	12	of	of	IN
37681	633	13	the	the	DT
37681	633	14	compasses	compass	NNS
37681	633	15	and	and	CC
37681	633	16	ruler	ruler	NN
37681	633	17	,	,	,
37681	633	18	a	a	DT
37681	633	19	valuable	valuable	JJ
37681	633	20	plan	plan	NN
37681	633	21	that	that	WDT
37681	633	22	is	be	VBZ
37681	633	23	followed	follow	VBN
37681	633	24	by	by	IN
37681	633	25	many	many	JJ
37681	633	26	of	of	IN
37681	633	27	the	the	DT
37681	633	28	best	good	JJS
37681	633	29	teachers	teacher	NNS
37681	633	30	everywhere	everywhere	RB
37681	633	31	.	.	.
37681	634	1	Considerable	considerable	JJ
37681	634	2	attention	attention	NN
37681	634	3	is	be	VBZ
37681	634	4	paid	pay	VBN
37681	634	5	to	to	IN
37681	634	6	logical	logical	JJ
37681	634	7	processes	process	NNS
37681	634	8	before	before	IN
37681	634	9	beginning	begin	VBG
37681	634	10	the	the	DT
37681	634	11	work	work	NN
37681	634	12	,	,	,
37681	634	13	such	such	JJ
37681	634	14	terms	term	NNS
37681	634	15	as	as	IN
37681	634	16	"	"	``
37681	634	17	contrapositive	contrapositive	JJ
37681	634	18	"	"	''
37681	634	19	and	and	CC
37681	634	20	"	"	``
37681	634	21	obverse	obverse	JJ
37681	634	22	,	,	,
37681	634	23	"	"	''
37681	634	24	and	and	CC
37681	634	25	such	such	JJ
37681	634	26	rules	rule	NNS
37681	634	27	as	as	IN
37681	634	28	the	the	DT
37681	634	29	"	"	``
37681	634	30	rule	rule	NN
37681	634	31	of	of	IN
37681	634	32	conversion	conversion	NN
37681	634	33	"	"	''
37681	634	34	and	and	CC
37681	634	35	the	the	DT
37681	634	36	"	"	``
37681	634	37	rule	rule	NN
37681	634	38	of	of	IN
37681	634	39	identity	identity	NN
37681	634	40	"	"	''
37681	634	41	being	be	VBG
37681	634	42	introduced	introduce	VBN
37681	634	43	before	before	IN
37681	634	44	any	any	DT
37681	634	45	propositions	proposition	NNS
37681	634	46	are	be	VBP
37681	634	47	considered	consider	VBN
37681	634	48	.	.	.
37681	635	1	The	the	DT
37681	635	2	arrangement	arrangement	NN
37681	635	3	of	of	IN
37681	635	4	the	the	DT
37681	635	5	work	work	NN
37681	635	6	and	and	CC
37681	635	7	the	the	DT
37681	635	8	number	number	NN
37681	635	9	of	of	IN
37681	635	10	propositions	proposition	NNS
37681	635	11	in	in	IN
37681	635	12	plane	plane	NN
37681	635	13	geometry	geometry	NN
37681	635	14	are	be	VBP
37681	635	15	as	as	IN
37681	635	16	follows	follow	VBZ
37681	635	17	:	:	:
37681	635	18	Book	book	NN
37681	635	19	I.	i.	NN
37681	636	1	The	the	DT
37681	636	2	straight	straight	JJ
37681	636	3	line	line	NN
37681	636	4	51	51	CD
37681	636	5	Book	Book	NNP
37681	636	6	II	II	NNP
37681	636	7	.	.	.
37681	637	1	Equality	equality	NN
37681	637	2	of	of	IN
37681	637	3	areas	area	NNS
37681	637	4	19	19	CD
37681	637	5	Book	book	NN
37681	637	6	III	iii	CD
37681	637	7	.	.	.
37681	638	1	The	the	DT
37681	638	2	circle	circle	NN
37681	638	3	42	42	CD
37681	638	4	Book	Book	NNP
37681	638	5	IV	IV	NNP
37681	638	6	.	.	.
37681	639	1	Ratio	ratio	NN
37681	639	2	and	and	CC
37681	639	3	proportion	proportion	NN
37681	639	4	32	32	CD
37681	639	5	Book	Book	NNP
37681	639	6	V.	V.	NNP
37681	639	7	Proportion	Proportion	NNP
37681	639	8	24	24	CD
37681	639	9	----	----	NFP
37681	639	10	Total	total	NN
37681	639	11	for	for	IN
37681	639	12	plane	plane	NN
37681	639	13	geometry	geometry	NN
37681	639	14	168	168	CD
37681	639	15	Here	here	RB
37681	639	16	,	,	,
37681	639	17	then	then	RB
37681	639	18	,	,	,
37681	639	19	is	be	VBZ
37681	639	20	the	the	DT
37681	639	21	result	result	NN
37681	639	22	of	of	IN
37681	639	23	several	several	JJ
37681	639	24	years	year	NNS
37681	639	25	of	of	IN
37681	639	26	labor	labor	NN
37681	639	27	by	by	IN
37681	639	28	a	a	DT
37681	639	29	somewhat	somewhat	RB
37681	639	30	radical	radical	JJ
37681	639	31	organization	organization	NN
37681	639	32	,	,	,
37681	639	33	fostered	foster	VBN
37681	639	34	by	by	IN
37681	639	35	excellent	excellent	JJ
37681	639	36	mathematicians	mathematician	NNS
37681	639	37	,	,	,
37681	639	38	and	and	CC
37681	639	39	carried	carry	VBN
37681	639	40	on	on	RP
37681	639	41	in	in	IN
37681	639	42	a	a	DT
37681	639	43	country	country	NN
37681	639	44	where	where	WRB
37681	639	45	elementary	elementary	JJ
37681	639	46	geometry	geometry	NN
37681	639	47	is	be	VBZ
37681	639	48	held	hold	VBN
37681	639	49	in	in	IN
37681	639	50	highest	high	JJS
37681	639	51	esteem	esteem	NN
37681	639	52	,	,	,
37681	639	53	and	and	CC
37681	639	54	where	where	WRB
37681	639	55	Euclid	Euclid	NNP
37681	639	56	was	be	VBD
37681	639	57	thought	think	VBN
37681	639	58	unsuited	unsuited	JJ
37681	639	59	to	to	IN
37681	639	60	the	the	DT
37681	639	61	needs	need	NNS
37681	639	62	of	of	IN
37681	639	63	the	the	DT
37681	639	64	beginner	beginner	NN
37681	639	65	.	.	.
37681	640	1	The	the	DT
37681	640	2	number	number	NN
37681	640	3	of	of	IN
37681	640	4	propositions	proposition	NNS
37681	640	5	remains	remain	VBZ
37681	640	6	substantially	substantially	RB
37681	640	7	the	the	DT
37681	640	8	same	same	JJ
37681	640	9	as	as	IN
37681	640	10	in	in	IN
37681	640	11	Euclid	Euclid	NNP
37681	640	12	,	,	,
37681	640	13	and	and	CC
37681	640	14	the	the	DT
37681	640	15	introduction	introduction	NN
37681	640	16	of	of	IN
37681	640	17	some	some	DT
37681	640	18	unusable	unusable	JJ
37681	640	19	logic	logic	NN
37681	640	20	tends	tend	VBZ
37681	640	21	to	to	TO
37681	640	22	counterbalance	counterbalance	VB
37681	640	23	the	the	DT
37681	640	24	improvement	improvement	NN
37681	640	25	in	in	IN
37681	640	26	sequence	sequence	NN
37681	640	27	of	of	IN
37681	640	28	the	the	DT
37681	640	29	propositions	proposition	NNS
37681	640	30	.	.	.
37681	641	1	The	the	DT
37681	641	2	report	report	NN
37681	641	3	provoked	provoke	VBD
37681	641	4	thought	think	VBD
37681	641	5	;	;	:
37681	641	6	it	-PRON-	PRP
37681	641	7	shook	shake	VBD
37681	641	8	the	the	DT
37681	641	9	Euclid	Euclid	NNP
37681	641	10	stronghold	stronghold	NN
37681	641	11	;	;	:
37681	641	12	it	-PRON-	PRP
37681	641	13	was	be	VBD
37681	641	14	probably	probably	RB
37681	641	15	instrumental	instrumental	JJ
37681	641	16	in	in	IN
37681	641	17	bringing	bring	VBG
37681	641	18	about	about	RP
37681	641	19	the	the	DT
37681	641	20	present	present	JJ
37681	641	21	upheaval	upheaval	NN
37681	641	22	in	in	IN
37681	641	23	geometry	geometry	NN
37681	641	24	in	in	IN
37681	641	25	England	England	NNP
37681	641	26	,	,	,
37681	641	27	but	but	CC
37681	641	28	as	as	IN
37681	641	29	a	a	DT
37681	641	30	working	work	VBG
37681	641	31	syllabus	syllabus	NN
37681	641	32	it	-PRON-	PRP
37681	641	33	has	have	VBZ
37681	641	34	not	not	RB
37681	641	35	appealed	appeal	VBN
37681	641	36	to	to	IN
37681	641	37	the	the	DT
37681	641	38	world	world	NN
37681	641	39	as	as	IN
37681	641	40	the	the	DT
37681	641	41	great	great	JJ
37681	641	42	improvement	improvement	NN
37681	641	43	upon	upon	IN
37681	641	44	Euclid	Euclid	NNP
37681	641	45	's	's	POS
37681	641	46	"	"	``
37681	641	47	Elements	Elements	NNPS
37681	641	48	"	"	''
37681	641	49	that	that	WDT
37681	641	50	was	be	VBD
37681	641	51	hoped	hope	VBN
37681	641	52	by	by	IN
37681	641	53	many	many	JJ
37681	641	54	of	of	IN
37681	641	55	its	-PRON-	PRP$
37681	641	56	early	early	JJ
37681	641	57	advocates	advocate	NNS
37681	641	58	.	.	.
37681	642	1	The	the	DT
37681	642	2	same	same	JJ
37681	642	3	association	association	NN
37681	642	4	published	publish	VBD
37681	642	5	later	later	RB
37681	642	6	,	,	,
37681	642	7	and	and	CC
37681	642	8	republished	republish	VBD
37681	642	9	in	in	IN
37681	642	10	1905	1905	CD
37681	642	11	,	,	,
37681	642	12	a	a	DT
37681	642	13	"	"	``
37681	642	14	Report	Report	NNP
37681	642	15	on	on	IN
37681	642	16	the	the	DT
37681	642	17	Teaching	Teaching	NNP
37681	642	18	of	of	IN
37681	642	19	Geometry	Geometry	NNP
37681	642	20	,	,	,
37681	642	21	"	"	''
37681	642	22	in	in	IN
37681	642	23	which	which	WDT
37681	642	24	it	-PRON-	PRP
37681	642	25	returned	return	VBD
37681	642	26	to	to	IN
37681	642	27	Euclid	Euclid	NNP
37681	642	28	,	,	,
37681	642	29	modifying	modify	VBG
37681	642	30	the	the	DT
37681	642	31	"	"	``
37681	642	32	Elements	Elements	NNPS
37681	642	33	"	"	''
37681	642	34	by	by	IN
37681	642	35	omitting	omit	VBG
37681	642	36	certain	certain	JJ
37681	642	37	propositions	proposition	NNS
37681	642	38	,	,	,
37681	642	39	changing	change	VBG
37681	642	40	the	the	DT
37681	642	41	order	order	NN
37681	642	42	and	and	CC
37681	642	43	proof	proof	NN
37681	642	44	of	of	IN
37681	642	45	others	other	NNS
37681	642	46	,	,	,
37681	642	47	and	and	CC
37681	642	48	introducing	introduce	VBG
37681	642	49	a	a	DT
37681	642	50	few	few	JJ
37681	642	51	new	new	JJ
37681	642	52	theorems	theorem	NNS
37681	642	53	.	.	.
37681	643	1	It	-PRON-	PRP
37681	643	2	seems	seem	VBZ
37681	643	3	to	to	TO
37681	643	4	reduce	reduce	VB
37681	643	5	the	the	DT
37681	643	6	propositions	proposition	NNS
37681	643	7	to	to	TO
37681	643	8	be	be	VB
37681	643	9	proved	prove	VBN
37681	643	10	in	in	IN
37681	643	11	plane	plane	NN
37681	643	12	geometry	geometry	NN
37681	643	13	to	to	IN
37681	643	14	about	about	IN
37681	643	15	one	one	CD
37681	643	16	hundred	hundred	CD
37681	643	17	fifteen	fifteen	CD
37681	643	18	,	,	,
37681	643	19	and	and	CC
37681	643	20	it	-PRON-	PRP
37681	643	21	recommends	recommend	VBZ
37681	643	22	the	the	DT
37681	643	23	omission	omission	NN
37681	643	24	of	of	IN
37681	643	25	the	the	DT
37681	643	26	incommensurable	incommensurable	JJ
37681	643	27	case	case	NN
37681	643	28	.	.	.
37681	644	1	This	this	DT
37681	644	2	number	number	NN
37681	644	3	is	be	VBZ
37681	644	4	,	,	,
37681	644	5	however	however	RB
37681	644	6	,	,	,
37681	644	7	somewhat	somewhat	RB
37681	644	8	misleading	misleading	JJ
37681	644	9	,	,	,
37681	644	10	for	for	IN
37681	644	11	Euclid	Euclid	NNP
37681	644	12	frequently	frequently	RB
37681	644	13	puts	put	VBZ
37681	644	14	in	in	IN
37681	644	15	one	one	CD
37681	644	16	proposition	proposition	NN
37681	644	17	what	what	WP
37681	644	18	we	-PRON-	PRP
37681	644	19	in	in	IN
37681	644	20	America	America	NNP
37681	644	21	,	,	,
37681	644	22	for	for	IN
37681	644	23	educational	educational	JJ
37681	644	24	reasons	reason	NNS
37681	644	25	,	,	,
37681	644	26	find	find	VBP
37681	644	27	it	-PRON-	PRP
37681	644	28	better	well	JJR
37681	644	29	to	to	TO
37681	644	30	treat	treat	VB
37681	644	31	in	in	IN
37681	644	32	two	two	CD
37681	644	33	,	,	,
37681	644	34	or	or	CC
37681	644	35	even	even	RB
37681	644	36	three	three	CD
37681	644	37	,	,	,
37681	644	38	propositions	proposition	NNS
37681	644	39	.	.	.
37681	645	1	This	this	DT
37681	645	2	report	report	NN
37681	645	3	,	,	,
37681	645	4	therefore	therefore	RB
37681	645	5	,	,	,
37681	645	6	reaches	reach	VBZ
37681	645	7	about	about	IN
37681	645	8	the	the	DT
37681	645	9	same	same	JJ
37681	645	10	conclusion	conclusion	NN
37681	645	11	as	as	IN
37681	645	12	to	to	IN
37681	645	13	the	the	DT
37681	645	14	geometric	geometric	JJ
37681	645	15	facts	fact	NNS
37681	645	16	to	to	TO
37681	645	17	be	be	VB
37681	645	18	mastered	master	VBN
37681	645	19	as	as	IN
37681	645	20	is	be	VBZ
37681	645	21	reached	reach	VBN
37681	645	22	by	by	IN
37681	645	23	our	-PRON-	PRP$
37681	645	24	later	later	JJ
37681	645	25	textbook	textbook	NN
37681	645	26	writers	writer	NNS
37681	645	27	in	in	IN
37681	645	28	America	America	NNP
37681	645	29	.	.	.
37681	646	1	It	-PRON-	PRP
37681	646	2	is	be	VBZ
37681	646	3	not	not	RB
37681	646	4	extreme	extreme	JJ
37681	646	5	,	,	,
37681	646	6	and	and	CC
37681	646	7	it	-PRON-	PRP
37681	646	8	stands	stand	VBZ
37681	646	9	for	for	IN
37681	646	10	good	good	JJ
37681	646	11	mathematics	mathematic	NNS
37681	646	12	.	.	.
37681	647	1	In	in	IN
37681	647	2	the	the	DT
37681	647	3	United	United	NNP
37681	647	4	States	States	NNP
37681	647	5	the	the	DT
37681	647	6	influence	influence	NN
37681	647	7	of	of	IN
37681	647	8	our	-PRON-	PRP$
37681	647	9	early	early	JJ
37681	647	10	wars	war	NNS
37681	647	11	with	with	IN
37681	647	12	England	England	NNP
37681	647	13	,	,	,
37681	647	14	and	and	CC
37681	647	15	the	the	DT
37681	647	16	sympathy	sympathy	NN
37681	647	17	of	of	IN
37681	647	18	France	France	NNP
37681	647	19	at	at	IN
37681	647	20	that	that	DT
37681	647	21	time	time	NN
37681	647	22	,	,	,
37681	647	23	turned	turn	VBD
37681	647	24	the	the	DT
37681	647	25	attention	attention	NN
37681	647	26	of	of	IN
37681	647	27	our	-PRON-	PRP$
37681	647	28	scholars	scholar	NNS
37681	647	29	of	of	IN
37681	647	30	a	a	DT
37681	647	31	century	century	NN
37681	647	32	ago	ago	RB
37681	647	33	from	from	IN
37681	647	34	Cambridge	Cambridge	NNP
37681	647	35	to	to	IN
37681	647	36	Paris	Paris	NNP
37681	647	37	as	as	IN
37681	647	38	a	a	DT
37681	647	39	mathematical	mathematical	JJ
37681	647	40	center	center	NN
37681	647	41	.	.	.
37681	648	1	The	the	DT
37681	648	2	influx	influx	NN
37681	648	3	of	of	IN
37681	648	4	French	french	JJ
37681	648	5	mathematics	mathematic	NNS
37681	648	6	brought	bring	VBD
37681	648	7	with	with	IN
37681	648	8	it	-PRON-	PRP
37681	648	9	such	such	JJ
37681	648	10	works	work	NNS
37681	648	11	as	as	IN
37681	648	12	Legendre	Legendre	NNP
37681	648	13	's	's	POS
37681	648	14	geometry	geometry	NN
37681	648	15	(	(	-LRB-
37681	648	16	1794	1794	CD
37681	648	17	)	)	-RRB-
37681	648	18	and	and	CC
37681	648	19	Bourdon	Bourdon	NNP
37681	648	20	's	's	POS
37681	648	21	algebra	algebra	NN
37681	648	22	,	,	,
37681	648	23	and	and	CC
37681	648	24	made	make	VBD
37681	648	25	known	known	JJ
37681	648	26	the	the	DT
37681	648	27	texts	text	NNS
37681	648	28	of	of	IN
37681	648	29	Lacroix	Lacroix	NNP
37681	648	30	,	,	,
37681	648	31	Bertrand	Bertrand	NNP
37681	648	32	,	,	,
37681	648	33	and	and	CC
37681	648	34	Bezout	bezout	NN
37681	648	35	.	.	.
37681	649	1	Legendre	Legendre	NNP
37681	649	2	's	's	POS
37681	649	3	geometry	geometry	NN
37681	649	4	was	be	VBD
37681	649	5	the	the	DT
37681	649	6	result	result	NN
37681	649	7	of	of	IN
37681	649	8	the	the	DT
37681	649	9	efforts	effort	NNS
37681	649	10	of	of	IN
37681	649	11	a	a	DT
37681	649	12	great	great	JJ
37681	649	13	mathematician	mathematician	NN
37681	649	14	at	at	IN
37681	649	15	syllabus	syllabus	NN
37681	649	16	-	-	HYPH
37681	649	17	making	make	VBG
37681	649	18	,	,	,
37681	649	19	a	a	DT
37681	649	20	natural	natural	JJ
37681	649	21	thing	thing	NN
37681	649	22	in	in	IN
37681	649	23	a	a	DT
37681	649	24	country	country	NN
37681	649	25	that	that	WDT
37681	649	26	had	have	VBD
37681	649	27	early	early	RB
37681	649	28	broken	break	VBN
37681	649	29	away	away	RB
37681	649	30	from	from	IN
37681	649	31	Euclid	Euclid	NNP
37681	649	32	.	.	.
37681	650	1	Legendre	Legendre	NNP
37681	650	2	changed	change	VBD
37681	650	3	the	the	DT
37681	650	4	Greek	greek	JJ
37681	650	5	sequence	sequence	NN
37681	650	6	,	,	,
37681	650	7	sought	seek	VBD
37681	650	8	to	to	TO
37681	650	9	select	select	VB
37681	650	10	only	only	JJ
37681	650	11	propositions	proposition	NNS
37681	650	12	that	that	WDT
37681	650	13	are	be	VBP
37681	650	14	necessary	necessary	JJ
37681	650	15	to	to	IN
37681	650	16	a	a	DT
37681	650	17	good	good	JJ
37681	650	18	understanding	understanding	NN
37681	650	19	of	of	IN
37681	650	20	the	the	DT
37681	650	21	subject	subject	NN
37681	650	22	,	,	,
37681	650	23	and	and	CC
37681	650	24	added	add	VBD
37681	650	25	a	a	DT
37681	650	26	good	good	JJ
37681	650	27	course	course	NN
37681	650	28	in	in	IN
37681	650	29	solid	solid	JJ
37681	650	30	geometry	geometry	NN
37681	650	31	.	.	.
37681	651	1	His	-PRON-	PRP$
37681	651	2	arrangement	arrangement	NN
37681	651	3	,	,	,
37681	651	4	with	with	IN
37681	651	5	the	the	DT
37681	651	6	number	number	NN
37681	651	7	of	of	IN
37681	651	8	propositions	proposition	NNS
37681	651	9	as	as	IN
37681	651	10	given	give	VBN
37681	651	11	in	in	IN
37681	651	12	the	the	DT
37681	651	13	Davies	Davies	NNP
37681	651	14	translation	translation	NN
37681	651	15	,	,	,
37681	651	16	is	be	VBZ
37681	651	17	as	as	IN
37681	651	18	follows	follow	VBZ
37681	651	19	:	:	:
37681	651	20	Book	Book	NNP
37681	651	21	I.	I.	NNP
37681	651	22	Rectilinear	Rectilinear	NNP
37681	651	23	figures	figure	VBZ
37681	651	24	31	31	CD
37681	651	25	Book	Book	NNP
37681	651	26	II	II	NNP
37681	651	27	.	.	.
37681	652	1	Ratio	ratio	NN
37681	652	2	and	and	CC
37681	652	3	proportion	proportion	NN
37681	652	4	14	14	CD
37681	652	5	Book	book	NN
37681	652	6	III	III	NNP
37681	652	7	.	.	.
37681	653	1	The	the	DT
37681	653	2	circle	circle	NN
37681	653	3	48	48	CD
37681	653	4	Book	Book	NNP
37681	653	5	IV	IV	NNP
37681	653	6	.	.	.
37681	654	1	Proportions	proportion	NNS
37681	654	2	of	of	IN
37681	654	3	figures	figure	NNS
37681	654	4	and	and	CC
37681	654	5	areas	area	NNS
37681	654	6	51	51	CD
37681	654	7	Book	Book	NNP
37681	654	8	V.	V.	NNP
37681	654	9	Polygons	Polygons	NNPS
37681	654	10	and	and	CC
37681	654	11	circles	circle	VBZ
37681	654	12	17	17	CD
37681	654	13	----	----	NFP
37681	654	14	Total	total	NN
37681	654	15	for	for	IN
37681	654	16	plane	plane	NN
37681	654	17	geometry	geometry	NN
37681	654	18	161	161	CD
37681	654	19	Legendre	Legendre	NNP
37681	654	20	made	make	VBD
37681	654	21	,	,	,
37681	654	22	therefore	therefore	RB
37681	654	23	,	,	,
37681	654	24	practically	practically	RB
37681	654	25	no	no	DT
37681	654	26	reduction	reduction	NN
37681	654	27	in	in	IN
37681	654	28	the	the	DT
37681	654	29	number	number	NN
37681	654	30	of	of	IN
37681	654	31	Euclid	Euclid	NNP
37681	654	32	's	's	POS
37681	654	33	propositions	proposition	NNS
37681	654	34	,	,	,
37681	654	35	and	and	CC
37681	654	36	his	-PRON-	PRP$
37681	654	37	improvement	improvement	NN
37681	654	38	on	on	IN
37681	654	39	Euclid	Euclid	NNP
37681	654	40	consisted	consist	VBD
37681	654	41	chiefly	chiefly	RB
37681	654	42	in	in	IN
37681	654	43	his	-PRON-	PRP$
37681	654	44	separation	separation	NN
37681	654	45	of	of	IN
37681	654	46	problems	problem	NNS
37681	654	47	and	and	CC
37681	654	48	theorems	theorem	NNS
37681	654	49	,	,	,
37681	654	50	and	and	CC
37681	654	51	in	in	IN
37681	654	52	a	a	DT
37681	654	53	less	less	RBR
37681	654	54	rigorous	rigorous	JJ
37681	654	55	treatment	treatment	NN
37681	654	56	of	of	IN
37681	654	57	proportion	proportion	NN
37681	654	58	which	which	WDT
37681	654	59	boys	boy	NNS
37681	654	60	and	and	CC
37681	654	61	girls	girl	NNS
37681	654	62	could	could	MD
37681	654	63	comprehend	comprehend	VB
37681	654	64	.	.	.
37681	655	1	D'Alembert	D'Alembert	NNP
37681	655	2	had	have	VBD
37681	655	3	demanded	demand	VBN
37681	655	4	that	that	IN
37681	655	5	the	the	DT
37681	655	6	sequence	sequence	NN
37681	655	7	of	of	IN
37681	655	8	propositions	proposition	NNS
37681	655	9	should	should	MD
37681	655	10	be	be	VB
37681	655	11	determined	determine	VBN
37681	655	12	by	by	IN
37681	655	13	the	the	DT
37681	655	14	order	order	NN
37681	655	15	in	in	IN
37681	655	16	which	which	WDT
37681	655	17	they	-PRON-	PRP
37681	655	18	had	have	VBD
37681	655	19	been	be	VBN
37681	655	20	discovered	discover	VBN
37681	655	21	,	,	,
37681	655	22	but	but	CC
37681	655	23	Legendre	Legendre	NNP
37681	655	24	wisely	wisely	RB
37681	655	25	ignored	ignore	VBD
37681	655	26	such	such	PDT
37681	655	27	an	an	DT
37681	655	28	extreme	extreme	NN
37681	655	29	and	and	CC
37681	655	30	gave	give	VBD
37681	655	31	the	the	DT
37681	655	32	world	world	NN
37681	655	33	a	a	DT
37681	655	34	very	very	RB
37681	655	35	usable	usable	JJ
37681	655	36	book	book	NN
37681	655	37	.	.	.
37681	656	1	The	the	DT
37681	656	2	principal	principal	JJ
37681	656	3	effect	effect	NN
37681	656	4	of	of	IN
37681	656	5	Legendre	Legendre	NNP
37681	656	6	's	's	POS
37681	656	7	geometry	geometry	NN
37681	656	8	in	in	IN
37681	656	9	America	America	NNP
37681	656	10	was	be	VBD
37681	656	11	to	to	TO
37681	656	12	make	make	VB
37681	656	13	every	every	DT
37681	656	14	textbook	textbook	NN
37681	656	15	writer	writer	VB
37681	656	16	his	-PRON-	PRP$
37681	656	17	own	own	JJ
37681	656	18	syllabus	syllabus	NN
37681	656	19	-	-	HYPH
37681	656	20	maker	maker	NN
37681	656	21	,	,	,
37681	656	22	and	and	CC
37681	656	23	to	to	TO
37681	656	24	put	put	VB
37681	656	25	solid	solid	JJ
37681	656	26	geometry	geometry	NN
37681	656	27	on	on	IN
37681	656	28	a	a	DT
37681	656	29	more	more	RBR
37681	656	30	satisfactory	satisfactory	JJ
37681	656	31	footing	footing	NN
37681	656	32	.	.	.
37681	657	1	The	the	DT
37681	657	2	minute	minute	NN
37681	657	3	we	-PRON-	PRP
37681	657	4	depart	depart	VBP
37681	657	5	from	from	IN
37681	657	6	a	a	DT
37681	657	7	standard	standard	JJ
37681	657	8	text	text	NN
37681	657	9	like	like	IN
37681	657	10	Euclid	Euclid	NNP
37681	657	11	's	's	POS
37681	657	12	,	,	,
37681	657	13	and	and	CC
37681	657	14	have	have	VBP
37681	657	15	no	no	DT
37681	657	16	recognized	recognize	VBN
37681	657	17	examining	examine	VBG
37681	657	18	body	body	NN
37681	657	19	,	,	,
37681	657	20	every	every	DT
37681	657	21	one	one	NN
37681	657	22	is	be	VBZ
37681	657	23	free	free	JJ
37681	657	24	to	to	TO
37681	657	25	set	set	VB
37681	657	26	up	up	RP
37681	657	27	his	-PRON-	PRP$
37681	657	28	own	own	JJ
37681	657	29	standard	standard	NN
37681	657	30	,	,	,
37681	657	31	always	always	RB
37681	657	32	within	within	IN
37681	657	33	the	the	DT
37681	657	34	somewhat	somewhat	RB
37681	657	35	uncertain	uncertain	JJ
37681	657	36	boundary	boundary	NN
37681	657	37	prescribed	prescribe	VBN
37681	657	38	by	by	IN
37681	657	39	public	public	JJ
37681	657	40	opinion	opinion	NN
37681	657	41	and	and	CC
37681	657	42	by	by	IN
37681	657	43	the	the	DT
37681	657	44	colleges	college	NNS
37681	657	45	.	.	.
37681	658	1	The	the	DT
37681	658	2	efforts	effort	NNS
37681	658	3	of	of	IN
37681	658	4	the	the	DT
37681	658	5	past	past	JJ
37681	658	6	few	few	JJ
37681	658	7	years	year	NNS
37681	658	8	at	at	IN
37681	658	9	syllabus	syllabus	NN
37681	658	10	-	-	HYPH
37681	658	11	making	making	NN
37681	658	12	have	have	VBP
37681	658	13	been	be	VBN
37681	658	14	merely	merely	RB
37681	658	15	attempts	attempt	NNS
37681	658	16	to	to	TO
37681	658	17	define	define	VB
37681	658	18	this	this	DT
37681	658	19	boundary	boundary	NN
37681	658	20	more	more	RBR
37681	658	21	clearly	clearly	RB
37681	658	22	.	.	.
37681	659	1	Of	of	IN
37681	659	2	these	these	DT
37681	659	3	attempts	attempt	NNS
37681	659	4	two	two	CD
37681	659	5	are	be	VBP
37681	659	6	especially	especially	RB
37681	659	7	worthy	worthy	JJ
37681	659	8	of	of	IN
37681	659	9	consideration	consideration	NN
37681	659	10	as	as	IN
37681	659	11	having	have	VBG
37681	659	12	been	be	VBN
37681	659	13	very	very	RB
37681	659	14	carefully	carefully	RB
37681	659	15	planned	plan	VBN
37681	659	16	and	and	CC
37681	659	17	having	have	VBG
37681	659	18	brought	bring	VBN
37681	659	19	forth	forth	RP
37681	659	20	such	such	JJ
37681	659	21	definite	definite	JJ
37681	659	22	results	result	NNS
37681	659	23	as	as	IN
37681	659	24	to	to	TO
37681	659	25	appeal	appeal	VB
37681	659	26	to	to	IN
37681	659	27	a	a	DT
37681	659	28	large	large	JJ
37681	659	29	number	number	NN
37681	659	30	of	of	IN
37681	659	31	teachers	teacher	NNS
37681	659	32	.	.	.
37681	660	1	Other	other	JJ
37681	660	2	syllabi	syllabi	NN
37681	660	3	have	have	VBP
37681	660	4	been	be	VBN
37681	660	5	made	make	VBN
37681	660	6	and	and	CC
37681	660	7	are	be	VBP
37681	660	8	familiar	familiar	JJ
37681	660	9	to	to	IN
37681	660	10	many	many	JJ
37681	660	11	teachers	teacher	NNS
37681	660	12	,	,	,
37681	660	13	but	but	CC
37681	660	14	in	in	IN
37681	660	15	point	point	NN
37681	660	16	of	of	IN
37681	660	17	clearness	clearness	NN
37681	660	18	of	of	IN
37681	660	19	purpose	purpose	NN
37681	660	20	,	,	,
37681	660	21	conciseness	conciseness	NN
37681	660	22	of	of	IN
37681	660	23	expression	expression	NN
37681	660	24	,	,	,
37681	660	25	and	and	CC
37681	660	26	form	form	NN
37681	660	27	of	of	IN
37681	660	28	publication	publication	NN
37681	660	29	they	-PRON-	PRP
37681	660	30	have	have	VBP
37681	660	31	not	not	RB
37681	660	32	been	be	VBN
37681	660	33	such	such	JJ
37681	660	34	as	as	IN
37681	660	35	to	to	TO
37681	660	36	compare	compare	VB
37681	660	37	with	with	IN
37681	660	38	the	the	DT
37681	660	39	two	two	CD
37681	660	40	in	in	IN
37681	660	41	question	question	NN
37681	660	42	.	.	.
37681	661	1	The	the	DT
37681	661	2	first	first	JJ
37681	661	3	of	of	IN
37681	661	4	these	these	DT
37681	661	5	is	be	VBZ
37681	661	6	the	the	DT
37681	661	7	Harvard	Harvard	NNP
37681	661	8	syllabus	syllabus	NN
37681	661	9	,	,	,
37681	661	10	which	which	WDT
37681	661	11	is	be	VBZ
37681	661	12	placed	place	VBN
37681	661	13	in	in	IN
37681	661	14	the	the	DT
37681	661	15	hands	hand	NNS
37681	661	16	of	of	IN
37681	661	17	students	student	NNS
37681	661	18	for	for	IN
37681	661	19	reference	reference	NN
37681	661	20	when	when	WRB
37681	661	21	trying	try	VBG
37681	661	22	the	the	DT
37681	661	23	entrance	entrance	NN
37681	661	24	examinations	examination	NNS
37681	661	25	of	of	IN
37681	661	26	that	that	DT
37681	661	27	university	university	NN
37681	661	28	,	,	,
37681	661	29	a	a	DT
37681	661	30	plan	plan	NN
37681	661	31	not	not	RB
37681	661	32	followed	follow	VBN
37681	661	33	elsewhere	elsewhere	RB
37681	661	34	.	.	.
37681	662	1	It	-PRON-	PRP
37681	662	2	sets	set	VBZ
37681	662	3	forth	forth	RB
37681	662	4	the	the	DT
37681	662	5	basal	basal	NN
37681	662	6	propositions	proposition	NNS
37681	662	7	that	that	WDT
37681	662	8	should	should	MD
37681	662	9	form	form	VB
37681	662	10	the	the	DT
37681	662	11	essential	essential	JJ
37681	662	12	part	part	NN
37681	662	13	of	of	IN
37681	662	14	the	the	DT
37681	662	15	student	student	NN
37681	662	16	's	's	POS
37681	662	17	preparation	preparation	NN
37681	662	18	,	,	,
37681	662	19	and	and	CC
37681	662	20	that	that	WDT
37681	662	21	are	be	VBP
37681	662	22	necessary	necessary	JJ
37681	662	23	and	and	CC
37681	662	24	sufficient	sufficient	JJ
37681	662	25	for	for	IN
37681	662	26	proving	prove	VBG
37681	662	27	any	any	DT
37681	662	28	"	"	``
37681	662	29	original	original	JJ
37681	662	30	proposition	proposition	NN
37681	662	31	"	"	''
37681	662	32	(	(	-LRB-
37681	662	33	to	to	TO
37681	662	34	take	take	VB
37681	662	35	the	the	DT
37681	662	36	common	common	JJ
37681	662	37	expression	expression	NN
37681	662	38	)	)	-RRB-
37681	662	39	that	that	WDT
37681	662	40	may	may	MD
37681	662	41	be	be	VB
37681	662	42	set	set	VBN
37681	662	43	on	on	IN
37681	662	44	the	the	DT
37681	662	45	examination	examination	NN
37681	662	46	.	.	.
37681	663	1	The	the	DT
37681	663	2	propositions	proposition	NNS
37681	663	3	are	be	VBP
37681	663	4	arranged	arrange	VBN
37681	663	5	by	by	IN
37681	663	6	books	book	NNS
37681	663	7	as	as	IN
37681	663	8	follows	follow	VBZ
37681	663	9	:	:	:
37681	663	10	Book	Book	NNP
37681	663	11	I.	I.	NNP
37681	663	12	Angles	Angles	NNP
37681	663	13	,	,	,
37681	663	14	triangles	triangle	NNS
37681	663	15	,	,	,
37681	663	16	parallels	parallel	VBZ
37681	663	17	25	25	CD
37681	663	18	Book	Book	NNP
37681	663	19	II	II	NNP
37681	663	20	.	.	.
37681	664	1	The	the	DT
37681	664	2	circle	circle	NN
37681	664	3	,	,	,
37681	664	4	angle	angle	NN
37681	664	5	measure	measure	NN
37681	664	6	18	18	CD
37681	664	7	Book	Book	NNP
37681	664	8	III	iii	CD
37681	664	9	.	.	.
37681	665	1	Similar	similar	JJ
37681	665	2	polygons	polygon	NNS
37681	665	3	10	10	CD
37681	665	4	Book	Book	NNP
37681	665	5	IV	IV	NNP
37681	665	6	.	.	.
37681	666	1	Area	area	NN
37681	666	2	of	of	IN
37681	666	3	polygons	polygon	NNS
37681	666	4	8	8	CD
37681	666	5	Book	Book	NNP
37681	666	6	V.	V.	NNP
37681	666	7	Polygons	Polygons	NNPS
37681	666	8	and	and	CC
37681	666	9	circle	circle	NN
37681	666	10	measure	measure	NN
37681	666	11	11	11	CD
37681	666	12	Constructions	construction	NNS
37681	666	13	21	21	CD
37681	666	14	Ratio	ratio	NN
37681	666	15	and	and	CC
37681	666	16	proportion	proportion	NN
37681	666	17	6	6	CD
37681	666	18	----	----	NFP
37681	666	19	Total	total	NN
37681	666	20	for	for	IN
37681	666	21	plane	plane	NN
37681	666	22	geometry	geometry	NN
37681	666	23	99	99	CD
37681	666	24	The	the	DT
37681	666	25	total	total	NN
37681	666	26	for	for	IN
37681	666	27	solid	solid	JJ
37681	666	28	geometry	geometry	NN
37681	666	29	is	be	VBZ
37681	666	30	79	79	CD
37681	666	31	propositions	proposition	NNS
37681	666	32	,	,	,
37681	666	33	or	or	CC
37681	666	34	178	178	CD
37681	666	35	for	for	IN
37681	666	36	both	both	DT
37681	666	37	plane	plane	NN
37681	666	38	and	and	CC
37681	666	39	solid	solid	JJ
37681	666	40	geometry	geometry	NN
37681	666	41	.	.	.
37681	667	1	This	this	DT
37681	667	2	is	be	VBZ
37681	667	3	perhaps	perhaps	RB
37681	667	4	the	the	DT
37681	667	5	most	most	RBS
37681	667	6	successful	successful	JJ
37681	667	7	attempt	attempt	NN
37681	667	8	that	that	WDT
37681	667	9	has	have	VBZ
37681	667	10	been	be	VBN
37681	667	11	made	make	VBN
37681	667	12	at	at	IN
37681	667	13	reaching	reach	VBG
37681	667	14	a	a	DT
37681	667	15	minimum	minimum	JJ
37681	667	16	number	number	NN
37681	667	17	of	of	IN
37681	667	18	propositions	proposition	NNS
37681	667	19	.	.	.
37681	668	1	It	-PRON-	PRP
37681	668	2	might	may	MD
37681	668	3	well	well	RB
37681	668	4	be	be	VB
37681	668	5	further	far	RBR
37681	668	6	reduced	reduce	VBN
37681	668	7	,	,	,
37681	668	8	since	since	IN
37681	668	9	it	-PRON-	PRP
37681	668	10	includes	include	VBZ
37681	668	11	the	the	DT
37681	668	12	proposition	proposition	NN
37681	668	13	about	about	RB
37681	668	14	two	two	CD
37681	668	15	adjacent	adjacent	JJ
37681	668	16	angles	angle	NNS
37681	668	17	formed	form	VBN
37681	668	18	by	by	IN
37681	668	19	one	one	CD
37681	668	20	line	line	NN
37681	668	21	meeting	meet	VBG
37681	668	22	another	another	DT
37681	668	23	,	,	,
37681	668	24	and	and	CC
37681	668	25	the	the	DT
37681	668	26	one	one	CD
37681	668	27	about	about	IN
37681	668	28	the	the	DT
37681	668	29	circle	circle	NN
37681	668	30	as	as	IN
37681	668	31	the	the	DT
37681	668	32	limit	limit	NN
37681	668	33	of	of	IN
37681	668	34	the	the	DT
37681	668	35	inscribed	inscribed	JJ
37681	668	36	and	and	CC
37681	668	37	circumscribed	circumscribe	VBN
37681	668	38	regular	regular	JJ
37681	668	39	polygons	polygon	NNS
37681	668	40	.	.	.
37681	669	1	The	the	DT
37681	669	2	first	first	JJ
37681	669	3	of	of	IN
37681	669	4	these	these	DT
37681	669	5	leads	lead	VBZ
37681	669	6	a	a	DT
37681	669	7	beginner	beginner	NN
37681	669	8	to	to	TO
37681	669	9	doubt	doubt	VB
37681	669	10	the	the	DT
37681	669	11	value	value	NN
37681	669	12	of	of	IN
37681	669	13	geometry	geometry	NN
37681	669	14	,	,	,
37681	669	15	and	and	CC
37681	669	16	the	the	DT
37681	669	17	second	second	JJ
37681	669	18	is	be	VBZ
37681	669	19	beyond	beyond	IN
37681	669	20	the	the	DT
37681	669	21	powers	power	NNS
37681	669	22	of	of	IN
37681	669	23	the	the	DT
37681	669	24	majority	majority	NN
37681	669	25	of	of	IN
37681	669	26	students	student	NNS
37681	669	27	.	.	.
37681	670	1	As	as	IN
37681	670	2	compared	compare	VBN
37681	670	3	with	with	IN
37681	670	4	the	the	DT
37681	670	5	syllabus	syllabus	NN
37681	670	6	reported	report	VBN
37681	670	7	by	by	IN
37681	670	8	a	a	DT
37681	670	9	Wisconsin	Wisconsin	NNP
37681	670	10	committee	committee	NN
37681	670	11	in	in	IN
37681	670	12	1904	1904	CD
37681	670	13	,	,	,
37681	670	14	for	for	IN
37681	670	15	example	example	NN
37681	670	16	,	,	,
37681	670	17	here	here	RB
37681	670	18	are	be	VBP
37681	670	19	99	99	CD
37681	670	20	propositions	proposition	NNS
37681	670	21	against	against	IN
37681	670	22	132	132	CD
37681	670	23	.	.	.
37681	671	1	On	on	IN
37681	671	2	the	the	DT
37681	671	3	other	other	JJ
37681	671	4	hand	hand	NN
37681	671	5	,	,	,
37681	671	6	a	a	DT
37681	671	7	committee	committee	NN
37681	671	8	appointed	appoint	VBN
37681	671	9	by	by	IN
37681	671	10	the	the	DT
37681	671	11	Central	Central	NNP
37681	671	12	Association	Association	NNP
37681	671	13	of	of	IN
37681	671	14	Science	Science	NNP
37681	671	15	and	and	CC
37681	671	16	Mathematics	Mathematics	NNP
37681	671	17	Teachers	Teachers	NNPS
37681	671	18	reported	report	VBD
37681	671	19	in	in	IN
37681	671	20	1909	1909	CD
37681	671	21	a	a	DT
37681	671	22	syllabus	syllabus	NN
37681	671	23	with	with	IN
37681	671	24	what	what	WP
37681	671	25	seems	seem	VBZ
37681	671	26	at	at	IN
37681	671	27	first	first	JJ
37681	671	28	sight	sight	NN
37681	671	29	to	to	TO
37681	671	30	be	be	VB
37681	671	31	a	a	DT
37681	671	32	list	list	NN
37681	671	33	of	of	IN
37681	671	34	only	only	RB
37681	671	35	59	59	CD
37681	671	36	propositions	proposition	NNS
37681	671	37	in	in	IN
37681	671	38	plane	plane	NN
37681	671	39	geometry	geometry	NN
37681	671	40	.	.	.
37681	672	1	This	this	DT
37681	672	2	number	number	NN
37681	672	3	is	be	VBZ
37681	672	4	fictitious	fictitious	JJ
37681	672	5	,	,	,
37681	672	6	however	however	RB
37681	672	7	,	,	,
37681	672	8	for	for	IN
37681	672	9	the	the	DT
37681	672	10	reason	reason	NN
37681	672	11	that	that	IN
37681	672	12	numerous	numerous	JJ
37681	672	13	converses	converse	NNS
37681	672	14	are	be	VBP
37681	672	15	indicated	indicate	VBN
37681	672	16	with	with	IN
37681	672	17	the	the	DT
37681	672	18	propositions	proposition	NNS
37681	672	19	,	,	,
37681	672	20	and	and	CC
37681	672	21	are	be	VBP
37681	672	22	not	not	RB
37681	672	23	included	include	VBN
37681	672	24	in	in	IN
37681	672	25	the	the	DT
37681	672	26	count	count	NN
37681	672	27	,	,	,
37681	672	28	and	and	CC
37681	672	29	directions	direction	NNS
37681	672	30	are	be	VBP
37681	672	31	given	give	VBN
37681	672	32	to	to	TO
37681	672	33	include	include	VB
37681	672	34	"	"	``
37681	672	35	related	related	JJ
37681	672	36	theorems	theorem	NNS
37681	672	37	"	"	''
37681	672	38	and	and	CC
37681	672	39	"	"	``
37681	672	40	problems	problem	NNS
37681	672	41	dealing	deal	VBG
37681	672	42	with	with	IN
37681	672	43	the	the	DT
37681	672	44	length	length	NN
37681	672	45	and	and	CC
37681	672	46	area	area	NN
37681	672	47	of	of	IN
37681	672	48	a	a	DT
37681	672	49	circle	circle	NN
37681	672	50	,	,	,
37681	672	51	"	"	''
37681	672	52	so	so	IN
37681	672	53	that	that	IN
37681	672	54	in	in	IN
37681	672	55	some	some	DT
37681	672	56	cases	case	NNS
37681	672	57	one	one	CD
37681	672	58	proposition	proposition	NN
37681	672	59	is	be	VBZ
37681	672	60	evidently	evidently	RB
37681	672	61	intended	intend	VBN
37681	672	62	to	to	TO
37681	672	63	cover	cover	VB
37681	672	64	several	several	JJ
37681	672	65	others	other	NNS
37681	672	66	.	.	.
37681	673	1	This	this	DT
37681	673	2	syllabus	syllabus	NN
37681	673	3	is	be	VBZ
37681	673	4	therefore	therefore	RB
37681	673	5	lacking	lack	VBG
37681	673	6	in	in	IN
37681	673	7	definiteness	definiteness	NN
37681	673	8	,	,	,
37681	673	9	so	so	IN
37681	673	10	that	that	IN
37681	673	11	the	the	DT
37681	673	12	Harvard	Harvard	NNP
37681	673	13	list	list	NN
37681	673	14	stands	stand	VBZ
37681	673	15	out	out	RP
37681	673	16	as	as	IN
37681	673	17	perhaps	perhaps	RB
37681	673	18	the	the	DT
37681	673	19	best	good	JJS
37681	673	20	of	of	IN
37681	673	21	its	-PRON-	PRP$
37681	673	22	type	type	NN
37681	673	23	.	.	.
37681	674	1	The	the	DT
37681	674	2	second	second	JJ
37681	674	3	noteworthy	noteworthy	JJ
37681	674	4	recent	recent	JJ
37681	674	5	attempt	attempt	NN
37681	674	6	in	in	IN
37681	674	7	America	America	NNP
37681	674	8	is	be	VBZ
37681	674	9	that	that	DT
37681	674	10	made	make	VBN
37681	674	11	by	by	IN
37681	674	12	a	a	DT
37681	674	13	committee	committee	NN
37681	674	14	of	of	IN
37681	674	15	the	the	DT
37681	674	16	Association	Association	NNP
37681	674	17	of	of	IN
37681	674	18	Mathematical	Mathematical	NNP
37681	674	19	Teachers	Teachers	NNPS
37681	674	20	in	in	IN
37681	674	21	New	New	NNP
37681	674	22	England	England	NNP
37681	674	23	.	.	.
37681	675	1	This	this	DT
37681	675	2	committee	committee	NN
37681	675	3	was	be	VBD
37681	675	4	organized	organize	VBN
37681	675	5	in	in	IN
37681	675	6	1904	1904	CD
37681	675	7	.	.	.
37681	676	1	It	-PRON-	PRP
37681	676	2	held	hold	VBD
37681	676	3	sixteen	sixteen	CD
37681	676	4	meetings	meeting	NNS
37681	676	5	and	and	CC
37681	676	6	carried	carry	VBN
37681	676	7	on	on	IN
37681	676	8	a	a	DT
37681	676	9	great	great	JJ
37681	676	10	deal	deal	NN
37681	676	11	of	of	IN
37681	676	12	correspondence	correspondence	NN
37681	676	13	.	.	.
37681	677	1	As	as	IN
37681	677	2	a	a	DT
37681	677	3	result	result	NN
37681	677	4	,	,	,
37681	677	5	it	-PRON-	PRP
37681	677	6	prepared	prepare	VBD
37681	677	7	a	a	DT
37681	677	8	syllabus	syllabus	NN
37681	677	9	arranged	arrange	VBN
37681	677	10	by	by	IN
37681	677	11	topics	topic	NNS
37681	677	12	,	,	,
37681	677	13	the	the	DT
37681	677	14	propositions	proposition	NNS
37681	677	15	of	of	IN
37681	677	16	solid	solid	JJ
37681	677	17	geometry	geometry	NN
37681	677	18	being	be	VBG
37681	677	19	grouped	group	VBN
37681	677	20	immediately	immediately	RB
37681	677	21	after	after	IN
37681	677	22	the	the	DT
37681	677	23	corresponding	corresponding	JJ
37681	677	24	ones	one	NNS
37681	677	25	of	of	IN
37681	677	26	plane	plane	NN
37681	677	27	geometry	geometry	NN
37681	677	28	.	.	.
37681	678	1	For	for	IN
37681	678	2	example	example	NN
37681	678	3	,	,	,
37681	678	4	the	the	DT
37681	678	5	nine	nine	CD
37681	678	6	propositions	proposition	NNS
37681	678	7	on	on	IN
37681	678	8	congruence	congruence	NN
37681	678	9	in	in	IN
37681	678	10	a	a	DT
37681	678	11	plane	plane	NN
37681	678	12	are	be	VBP
37681	678	13	followed	follow	VBN
37681	678	14	by	by	IN
37681	678	15	nine	nine	CD
37681	678	16	on	on	IN
37681	678	17	congruence	congruence	NN
37681	678	18	in	in	IN
37681	678	19	space	space	NN
37681	678	20	.	.	.
37681	679	1	As	as	IN
37681	679	2	a	a	DT
37681	679	3	result	result	NN
37681	679	4	,	,	,
37681	679	5	the	the	DT
37681	679	6	following	following	NN
37681	679	7	summarizes	summarize	VBZ
37681	679	8	the	the	DT
37681	679	9	work	work	NN
37681	679	10	in	in	IN
37681	679	11	plane	plane	NN
37681	679	12	geometry	geometry	NN
37681	679	13	:	:	:
37681	679	14	Congruence	congruence	NN
37681	679	15	in	in	IN
37681	679	16	a	a	DT
37681	679	17	plane	plane	NN
37681	679	18	9	9	CD
37681	679	19	Equivalence	equivalence	NN
37681	679	20	3	3	CD
37681	679	21	Parallels	Parallels	NNPS
37681	679	22	and	and	CC
37681	679	23	perpendiculars	perpendicular	NNS
37681	679	24	9	9	CD
37681	679	25	Symmetry	Symmetry	NNP
37681	679	26	20	20	CD
37681	679	27	Angles	angle	NNS
37681	679	28	15	15	CD
37681	679	29	Tangents	tangent	NNS
37681	679	30	4	4	CD
37681	679	31	Similar	similar	JJ
37681	679	32	figures	figure	NNS
37681	679	33	18	18	CD
37681	679	34	Inequalities	inequality	NNS
37681	679	35	8	8	CD
37681	679	36	Lengths	length	NNS
37681	679	37	and	and	CC
37681	679	38	areas	area	NNS
37681	679	39	17	17	CD
37681	679	40	Loci	loci	NN
37681	679	41	2	2	CD
37681	679	42	Concurrent	concurrent	JJ
37681	679	43	lines	line	NNS
37681	679	44	5	5	CD
37681	679	45	----	----	NFP
37681	679	46	Total	total	NN
37681	679	47	for	for	IN
37681	679	48	plane	plane	NN
37681	679	49	geometry	geometry	NN
37681	679	50	110	110	CD
37681	679	51	Not	not	RB
37681	679	52	so	so	RB
37681	679	53	conventional	conventional	JJ
37681	679	54	in	in	IN
37681	679	55	arrangement	arrangement	NN
37681	679	56	as	as	IN
37681	679	57	the	the	DT
37681	679	58	Harvard	Harvard	NNP
37681	679	59	syllabus	syllabus	NN
37681	679	60	,	,	,
37681	679	61	and	and	CC
37681	679	62	with	with	IN
37681	679	63	a	a	DT
37681	679	64	few	few	JJ
37681	679	65	propositions	proposition	NNS
37681	679	66	that	that	WDT
37681	679	67	are	be	VBP
37681	679	68	evidently	evidently	RB
37681	679	69	not	not	RB
37681	679	70	basal	basal	JJ
37681	679	71	to	to	IN
37681	679	72	the	the	DT
37681	679	73	same	same	JJ
37681	679	74	extent	extent	NN
37681	679	75	as	as	IN
37681	679	76	the	the	DT
37681	679	77	rest	rest	NN
37681	679	78	,	,	,
37681	679	79	the	the	DT
37681	679	80	list	list	NN
37681	679	81	is	be	VBZ
37681	679	82	nevertheless	nevertheless	RB
37681	679	83	a	a	DT
37681	679	84	very	very	RB
37681	679	85	satisfactory	satisfactory	JJ
37681	679	86	one	one	CD
37681	679	87	,	,	,
37681	679	88	and	and	CC
37681	679	89	the	the	DT
37681	679	90	parallelism	parallelism	NN
37681	679	91	shown	show	VBN
37681	679	92	between	between	IN
37681	679	93	plane	plane	NN
37681	679	94	and	and	CC
37681	679	95	solid	solid	JJ
37681	679	96	geometry	geometry	NN
37681	679	97	is	be	VBZ
37681	679	98	suggestive	suggestive	JJ
37681	679	99	to	to	IN
37681	679	100	both	both	DT
37681	679	101	student	student	NN
37681	679	102	and	and	CC
37681	679	103	teacher	teacher	NN
37681	679	104	.	.	.
37681	680	1	On	on	IN
37681	680	2	the	the	DT
37681	680	3	whole	whole	NN
37681	680	4	,	,	,
37681	680	5	however	however	RB
37681	680	6	,	,	,
37681	680	7	the	the	DT
37681	680	8	Harvard	Harvard	NNP
37681	680	9	selection	selection	NN
37681	680	10	of	of	IN
37681	680	11	basal	basal	NN
37681	680	12	propositions	proposition	NNS
37681	680	13	is	be	VBZ
37681	680	14	perhaps	perhaps	RB
37681	680	15	as	as	RB
37681	680	16	satisfactory	satisfactory	JJ
37681	680	17	as	as	IN
37681	680	18	any	any	DT
37681	680	19	that	that	WDT
37681	680	20	has	have	VBZ
37681	680	21	been	be	VBN
37681	680	22	made	make	VBN
37681	680	23	,	,	,
37681	680	24	even	even	RB
37681	680	25	though	though	IN
37681	680	26	it	-PRON-	PRP
37681	680	27	appears	appear	VBZ
37681	680	28	to	to	TO
37681	680	29	lack	lack	VB
37681	680	30	a	a	DT
37681	680	31	"	"	``
37681	680	32	factor	factor	NN
37681	680	33	of	of	IN
37681	680	34	safety	safety	NN
37681	680	35	,	,	,
37681	680	36	"	"	''
37681	680	37	and	and	CC
37681	680	38	it	-PRON-	PRP
37681	680	39	is	be	VBZ
37681	680	40	probable	probable	JJ
37681	680	41	that	that	IN
37681	680	42	any	any	DT
37681	680	43	further	further	JJ
37681	680	44	reduction	reduction	NN
37681	680	45	would	would	MD
37681	680	46	be	be	VB
37681	680	47	unwise	unwise	JJ
37681	680	48	.	.	.
37681	681	1	What	what	WP
37681	681	2	,	,	,
37681	681	3	now	now	RB
37681	681	4	,	,	,
37681	681	5	has	have	VBZ
37681	681	6	been	be	VBN
37681	681	7	the	the	DT
37681	681	8	effect	effect	NN
37681	681	9	of	of	IN
37681	681	10	all	all	PDT
37681	681	11	these	these	DT
37681	681	12	efforts	effort	NNS
37681	681	13	?	?	.
37681	682	1	What	what	WP
37681	682	2	teacher	teacher	NN
37681	682	3	or	or	CC
37681	682	4	school	school	NN
37681	682	5	would	would	MD
37681	682	6	be	be	VB
37681	682	7	content	content	JJ
37681	682	8	to	to	TO
37681	682	9	follow	follow	VB
37681	682	10	any	any	DT
37681	682	11	one	one	CD
37681	682	12	of	of	IN
37681	682	13	these	these	DT
37681	682	14	syllabi	syllabi	VBD
37681	682	15	exactly	exactly	RB
37681	682	16	?	?	.
37681	683	1	What	what	WP
37681	683	2	textbook	textbook	NN
37681	683	3	writer	writer	NN
37681	683	4	would	would	MD
37681	683	5	feel	feel	VB
37681	683	6	it	-PRON-	PRP
37681	683	7	safe	safe	JJ
37681	683	8	to	to	TO
37681	683	9	limit	limit	VB
37681	683	10	his	-PRON-	PRP$
37681	683	11	regular	regular	JJ
37681	683	12	propositions	proposition	NNS
37681	683	13	to	to	IN
37681	683	14	those	those	DT
37681	683	15	in	in	IN
37681	683	16	any	any	DT
37681	683	17	one	one	CD
37681	683	18	syllabus	syllabus	NN
37681	683	19	?	?	.
37681	684	1	These	these	DT
37681	684	2	questions	question	NNS
37681	684	3	suggest	suggest	VBP
37681	684	4	their	-PRON-	PRP$
37681	684	5	own	own	JJ
37681	684	6	answers	answer	NNS
37681	684	7	,	,	,
37681	684	8	and	and	CC
37681	684	9	the	the	DT
37681	684	10	effect	effect	NN
37681	684	11	of	of	IN
37681	684	12	all	all	PDT
37681	684	13	this	this	DT
37681	684	14	effort	effort	NN
37681	684	15	seems	seem	VBZ
37681	684	16	at	at	IN
37681	684	17	first	first	JJ
37681	684	18	thought	think	VBN
37681	684	19	to	to	TO
37681	684	20	have	have	VB
37681	684	21	been	be	VBN
37681	684	22	so	so	RB
37681	684	23	slight	slight	JJ
37681	684	24	as	as	IN
37681	684	25	to	to	TO
37681	684	26	be	be	VB
37681	684	27	entirely	entirely	RB
37681	684	28	out	out	IN
37681	684	29	of	of	IN
37681	684	30	proportion	proportion	NN
37681	684	31	to	to	IN
37681	684	32	the	the	DT
37681	684	33	end	end	NN
37681	684	34	in	in	IN
37681	684	35	view	view	NN
37681	684	36	.	.	.
37681	685	1	This	this	DT
37681	685	2	depends	depend	VBZ
37681	685	3	,	,	,
37681	685	4	however	however	RB
37681	685	5	,	,	,
37681	685	6	on	on	IN
37681	685	7	what	what	WP
37681	685	8	this	this	DT
37681	685	9	end	end	NN
37681	685	10	is	be	VBZ
37681	685	11	conceived	conceive	VBN
37681	685	12	to	to	TO
37681	685	13	be	be	VB
37681	685	14	.	.	.
37681	686	1	If	if	IN
37681	686	2	the	the	DT
37681	686	3	purpose	purpose	NN
37681	686	4	has	have	VBZ
37681	686	5	been	be	VBN
37681	686	6	to	to	TO
37681	686	7	cut	cut	VB
37681	686	8	out	out	RP
37681	686	9	a	a	DT
37681	686	10	very	very	RB
37681	686	11	large	large	JJ
37681	686	12	number	number	NN
37681	686	13	of	of	IN
37681	686	14	the	the	DT
37681	686	15	propositions	proposition	NNS
37681	686	16	that	that	WDT
37681	686	17	are	be	VBP
37681	686	18	found	find	VBN
37681	686	19	in	in	IN
37681	686	20	Euclid	Euclid	NNP
37681	686	21	's	's	POS
37681	686	22	plane	plane	NN
37681	686	23	geometry	geometry	NN
37681	686	24	,	,	,
37681	686	25	the	the	DT
37681	686	26	effort	effort	NN
37681	686	27	has	have	VBZ
37681	686	28	not	not	RB
37681	686	29	been	be	VBN
37681	686	30	successful	successful	JJ
37681	686	31	.	.	.
37681	687	1	We	-PRON-	PRP
37681	687	2	may	may	MD
37681	687	3	reduce	reduce	VB
37681	687	4	this	this	DT
37681	687	5	number	number	NN
37681	687	6	to	to	IN
37681	687	7	about	about	RB
37681	687	8	one	one	CD
37681	687	9	hundred	hundred	CD
37681	687	10	thirty	thirty	CD
37681	687	11	,	,	,
37681	687	12	but	but	CC
37681	687	13	in	in	IN
37681	687	14	general	general	JJ
37681	687	15	,	,	,
37681	687	16	whatever	whatever	WDT
37681	687	17	a	a	DT
37681	687	18	syllabus	syllabus	NN
37681	687	19	may	may	MD
37681	687	20	give	give	VB
37681	687	21	as	as	IN
37681	687	22	a	a	DT
37681	687	23	minimum	minimum	NN
37681	687	24	,	,	,
37681	687	25	teachers	teacher	NNS
37681	687	26	will	will	MD
37681	687	27	favor	favor	VB
37681	687	28	a	a	DT
37681	687	29	larger	large	JJR
37681	687	30	number	number	NN
37681	687	31	than	than	IN
37681	687	32	is	be	VBZ
37681	687	33	suggested	suggest	VBN
37681	687	34	by	by	IN
37681	687	35	the	the	DT
37681	687	36	Harvard	Harvard	NNP
37681	687	37	list	list	NN
37681	687	38	,	,	,
37681	687	39	for	for	IN
37681	687	40	the	the	DT
37681	687	41	purpose	purpose	NN
37681	687	42	of	of	IN
37681	687	43	exercise	exercise	NN
37681	687	44	in	in	IN
37681	687	45	the	the	DT
37681	687	46	reading	reading	NN
37681	687	47	of	of	IN
37681	687	48	mathematics	mathematic	NNS
37681	687	49	if	if	IN
37681	687	50	for	for	IN
37681	687	51	no	no	DT
37681	687	52	other	other	JJ
37681	687	53	reason	reason	NN
37681	687	54	.	.	.
37681	688	1	The	the	DT
37681	688	2	French	french	JJ
37681	688	3	geometer	geometer	NN
37681	688	4	,	,	,
37681	688	5	Lacroix	Lacroix	NNP
37681	688	6	,	,	,
37681	688	7	who	who	WP
37681	688	8	wrote	write	VBD
37681	688	9	more	more	JJR
37681	688	10	than	than	IN
37681	688	11	a	a	DT
37681	688	12	century	century	NN
37681	688	13	ago	ago	RB
37681	688	14	,	,	,
37681	688	15	proposed	propose	VBD
37681	688	16	to	to	TO
37681	688	17	limit	limit	VB
37681	688	18	the	the	DT
37681	688	19	propositions	proposition	NNS
37681	688	20	to	to	IN
37681	688	21	those	those	DT
37681	688	22	needed	need	VBN
37681	688	23	to	to	TO
37681	688	24	prove	prove	VB
37681	688	25	other	other	JJ
37681	688	26	important	important	JJ
37681	688	27	ones	one	NNS
37681	688	28	,	,	,
37681	688	29	and	and	CC
37681	688	30	those	those	DT
37681	688	31	needed	need	VBN
37681	688	32	in	in	IN
37681	688	33	practical	practical	JJ
37681	688	34	mathematics	mathematic	NNS
37681	688	35	.	.	.
37681	689	1	If	if	IN
37681	689	2	to	to	IN
37681	689	3	this	this	DT
37681	689	4	we	-PRON-	PRP
37681	689	5	should	should	MD
37681	689	6	add	add	VB
37681	689	7	those	those	DT
37681	689	8	that	that	WDT
37681	689	9	are	be	VBP
37681	689	10	used	use	VBN
37681	689	11	in	in	IN
37681	689	12	treating	treat	VBG
37681	689	13	a	a	DT
37681	689	14	considerable	considerable	JJ
37681	689	15	range	range	NN
37681	689	16	of	of	IN
37681	689	17	exercises	exercise	NNS
37681	689	18	,	,	,
37681	689	19	we	-PRON-	PRP
37681	689	20	should	should	MD
37681	689	21	have	have	VB
37681	689	22	a	a	DT
37681	689	23	list	list	NN
37681	689	24	of	of	IN
37681	689	25	about	about	RB
37681	689	26	one	one	CD
37681	689	27	hundred	hundred	CD
37681	689	28	thirty	thirty	CD
37681	689	29	.	.	.
37681	690	1	But	but	CC
37681	690	2	this	this	DT
37681	690	3	is	be	VBZ
37681	690	4	not	not	RB
37681	690	5	the	the	DT
37681	690	6	real	real	JJ
37681	690	7	purpose	purpose	NN
37681	690	8	of	of	IN
37681	690	9	these	these	DT
37681	690	10	syllabi	syllabi	NN
37681	690	11	,	,	,
37681	690	12	or	or	CC
37681	690	13	at	at	IN
37681	690	14	most	most	JJS
37681	690	15	it	-PRON-	PRP
37681	690	16	seems	seem	VBZ
37681	690	17	like	like	IN
37681	690	18	a	a	DT
37681	690	19	relatively	relatively	RB
37681	690	20	unimportant	unimportant	JJ
37681	690	21	one	one	CD
37681	690	22	.	.	.
37681	691	1	The	the	DT
37681	691	2	purpose	purpose	NN
37681	691	3	that	that	WDT
37681	691	4	has	have	VBZ
37681	691	5	been	be	VBN
37681	691	6	attained	attain	VBN
37681	691	7	is	be	VBZ
37681	691	8	to	to	TO
37681	691	9	stop	stop	VB
37681	691	10	the	the	DT
37681	691	11	indefinite	indefinite	JJ
37681	691	12	increase	increase	NN
37681	691	13	in	in	IN
37681	691	14	the	the	DT
37681	691	15	number	number	NN
37681	691	16	of	of	IN
37681	691	17	propositions	proposition	NNS
37681	691	18	that	that	WDT
37681	691	19	would	would	MD
37681	691	20	follow	follow	VB
37681	691	21	from	from	IN
37681	691	22	the	the	DT
37681	691	23	recent	recent	JJ
37681	691	24	developments	development	NNS
37681	691	25	in	in	IN
37681	691	26	the	the	DT
37681	691	27	geometry	geometry	NN
37681	691	28	of	of	IN
37681	691	29	the	the	DT
37681	691	30	triangle	triangle	NN
37681	691	31	and	and	CC
37681	691	32	circle	circle	NN
37681	691	33	,	,	,
37681	691	34	and	and	CC
37681	691	35	of	of	IN
37681	691	36	similar	similar	JJ
37681	691	37	modern	modern	JJ
37681	691	38	topics	topic	NNS
37681	691	39	,	,	,
37681	691	40	if	if	IN
37681	691	41	some	some	DT
37681	691	42	such	such	JJ
37681	691	43	counter	counter	JJ
37681	691	44	-	-	NN
37681	691	45	movement	movement	NN
37681	691	46	as	as	IN
37681	691	47	this	this	DT
37681	691	48	did	do	VBD
37681	691	49	not	not	RB
37681	691	50	take	take	VB
37681	691	51	place	place	NN
37681	691	52	.	.	.
37681	692	1	If	if	IN
37681	692	2	the	the	DT
37681	692	3	result	result	NN
37681	692	4	is	be	VBZ
37681	692	5	,	,	,
37681	692	6	as	as	IN
37681	692	7	it	-PRON-	PRP
37681	692	8	probably	probably	RB
37681	692	9	will	will	MD
37681	692	10	be	be	VB
37681	692	11	,	,	,
37681	692	12	to	to	TO
37681	692	13	let	let	VB
37681	692	14	the	the	DT
37681	692	15	basal	basal	NN
37681	692	16	propositions	proposition	NNS
37681	692	17	of	of	IN
37681	692	18	Euclid	Euclid	NNP
37681	692	19	remain	remain	VBP
37681	692	20	about	about	IN
37681	692	21	as	as	IN
37681	692	22	they	-PRON-	PRP
37681	692	23	always	always	RB
37681	692	24	have	have	VBP
37681	692	25	been	be	VBN
37681	692	26	,	,	,
37681	692	27	as	as	IN
37681	692	28	the	the	DT
37681	692	29	standards	standard	NNS
37681	692	30	for	for	IN
37681	692	31	beginners	beginner	NNS
37681	692	32	,	,	,
37681	692	33	the	the	DT
37681	692	34	syllabi	syllabi	NN
37681	692	35	will	will	MD
37681	692	36	have	have	VB
37681	692	37	accomplished	accomplish	VBN
37681	692	38	a	a	DT
37681	692	39	worthy	worthy	JJ
37681	692	40	achievement	achievement	NN
37681	692	41	.	.	.
37681	693	1	If	if	IN
37681	693	2	,	,	,
37681	693	3	in	in	IN
37681	693	4	addition	addition	NN
37681	693	5	,	,	,
37681	693	6	they	-PRON-	PRP
37681	693	7	furnish	furnish	VBP
37681	693	8	an	an	DT
37681	693	9	irreducible	irreducible	JJ
37681	693	10	minimum	minimum	NN
37681	693	11	of	of	IN
37681	693	12	propositions	proposition	NNS
37681	693	13	to	to	TO
37681	693	14	which	which	WDT
37681	693	15	a	a	DT
37681	693	16	student	student	NN
37681	693	17	may	may	MD
37681	693	18	have	have	VB
37681	693	19	access	access	NN
37681	693	20	if	if	IN
37681	693	21	he	-PRON-	PRP
37681	693	22	desires	desire	VBZ
37681	693	23	it	-PRON-	PRP
37681	693	24	,	,	,
37681	693	25	on	on	IN
37681	693	26	an	an	DT
37681	693	27	examination	examination	NN
37681	693	28	,	,	,
37681	693	29	as	as	IN
37681	693	30	was	be	VBD
37681	693	31	intended	intend	VBN
37681	693	32	in	in	IN
37681	693	33	the	the	DT
37681	693	34	case	case	NN
37681	693	35	of	of	IN
37681	693	36	the	the	DT
37681	693	37	Harvard	Harvard	NNP
37681	693	38	and	and	CC
37681	693	39	the	the	DT
37681	693	40	New	New	NNP
37681	693	41	England	England	NNP
37681	693	42	Association	Association	NNP
37681	693	43	syllabi	syllabi	NN
37681	693	44	,	,	,
37681	693	45	the	the	DT
37681	693	46	achievement	achievement	NN
37681	693	47	may	may	MD
37681	693	48	possibly	possibly	RB
37681	693	49	be	be	VB
37681	693	50	still	still	RB
37681	693	51	more	more	RBR
37681	693	52	worthy	worthy	JJ
37681	693	53	.	.	.
37681	694	1	In	in	IN
37681	694	2	preparing	prepare	VBG
37681	694	3	a	a	DT
37681	694	4	syllabus	syllabus	NN
37681	694	5	,	,	,
37681	694	6	therefore	therefore	RB
37681	694	7	,	,	,
37681	694	8	no	no	DT
37681	694	9	one	one	NN
37681	694	10	should	should	MD
37681	694	11	hope	hope	VB
37681	694	12	to	to	TO
37681	694	13	bring	bring	VB
37681	694	14	the	the	DT
37681	694	15	teaching	teaching	NN
37681	694	16	world	world	NN
37681	694	17	at	at	IN
37681	694	18	once	once	RB
37681	694	19	to	to	TO
37681	694	20	agree	agree	VB
37681	694	21	to	to	IN
37681	694	22	any	any	DT
37681	694	23	great	great	JJ
37681	694	24	reduction	reduction	NN
37681	694	25	in	in	IN
37681	694	26	the	the	DT
37681	694	27	number	number	NN
37681	694	28	of	of	IN
37681	694	29	basal	basal	NN
37681	694	30	propositions	proposition	NNS
37681	694	31	,	,	,
37681	694	32	nor	nor	CC
37681	694	33	to	to	TO
37681	694	34	agree	agree	VB
37681	694	35	to	to	IN
37681	694	36	any	any	DT
37681	694	37	radical	radical	JJ
37681	694	38	change	change	NN
37681	694	39	of	of	IN
37681	694	40	terminology	terminology	NN
37681	694	41	,	,	,
37681	694	42	symbolism	symbolism	NN
37681	694	43	,	,	,
37681	694	44	or	or	CC
37681	694	45	sequence	sequence	NN
37681	694	46	.	.	.
37681	695	1	Rather	rather	RB
37681	695	2	should	should	MD
37681	695	3	it	-PRON-	PRP
37681	695	4	be	be	VB
37681	695	5	the	the	DT
37681	695	6	purpose	purpose	NN
37681	695	7	to	to	TO
37681	695	8	show	show	VB
37681	695	9	that	that	IN
37681	695	10	we	-PRON-	PRP
37681	695	11	have	have	VBP
37681	695	12	enough	enough	JJ
37681	695	13	topics	topic	NNS
37681	695	14	in	in	IN
37681	695	15	geometry	geometry	NN
37681	695	16	at	at	IN
37681	695	17	present	present	NN
37681	695	18	,	,	,
37681	695	19	and	and	CC
37681	695	20	that	that	IN
37681	695	21	the	the	DT
37681	695	22	number	number	NN
37681	695	23	of	of	IN
37681	695	24	propositions	proposition	NNS
37681	695	25	is	be	VBZ
37681	695	26	really	really	RB
37681	695	27	greater	great	JJR
37681	695	28	than	than	IN
37681	695	29	is	be	VBZ
37681	695	30	absolutely	absolutely	RB
37681	695	31	necessary	necessary	JJ
37681	695	32	,	,	,
37681	695	33	so	so	IN
37681	695	34	that	that	IN
37681	695	35	teachers	teacher	NNS
37681	695	36	shall	shall	MD
37681	695	37	not	not	RB
37681	695	38	be	be	VB
37681	695	39	led	lead	VBN
37681	695	40	to	to	TO
37681	695	41	introduce	introduce	VB
37681	695	42	any	any	DT
37681	695	43	considerable	considerable	JJ
37681	695	44	number	number	NN
37681	695	45	of	of	IN
37681	695	46	propositions	proposition	NNS
37681	695	47	out	out	IN
37681	695	48	of	of	IN
37681	695	49	the	the	DT
37681	695	50	large	large	JJ
37681	695	51	amount	amount	NN
37681	695	52	of	of	IN
37681	695	53	new	new	JJ
37681	695	54	material	material	NN
37681	695	55	that	that	WDT
37681	695	56	has	have	VBZ
37681	695	57	recently	recently	RB
37681	695	58	been	be	VBN
37681	695	59	accumulating	accumulate	VBG
37681	695	60	.	.	.
37681	696	1	Such	such	PDT
37681	696	2	a	a	DT
37681	696	3	syllabus	syllabus	NN
37681	696	4	will	will	MD
37681	696	5	always	always	RB
37681	696	6	accomplish	accomplish	VB
37681	696	7	a	a	DT
37681	696	8	good	good	JJ
37681	696	9	purpose	purpose	NN
37681	696	10	,	,	,
37681	696	11	for	for	IN
37681	696	12	at	at	IN
37681	696	13	least	least	JJS
37681	696	14	it	-PRON-	PRP
37681	696	15	will	will	MD
37681	696	16	provoke	provoke	VB
37681	696	17	thought	think	VBD
37681	696	18	and	and	CC
37681	696	19	arouse	arouse	NN
37681	696	20	interest	interest	NN
37681	696	21	,	,	,
37681	696	22	but	but	CC
37681	696	23	any	any	DT
37681	696	24	other	other	JJ
37681	696	25	kind	kind	NN
37681	696	26	is	be	VBZ
37681	696	27	bound	bind	VBN
37681	696	28	to	to	TO
37681	696	29	be	be	VB
37681	696	30	ephemeral	ephemeral	JJ
37681	696	31	.	.	.
37681	697	1	[	[	-LRB-
37681	697	2	32	32	CD
37681	697	3	]	]	-RRB-
37681	697	4	Besides	besides	IN
37681	697	5	the	the	DT
37681	697	6	evolutionary	evolutionary	JJ
37681	697	7	attempts	attempt	NNS
37681	697	8	at	at	IN
37681	697	9	rearranging	rearrange	VBG
37681	697	10	and	and	CC
37681	697	11	reducing	reduce	VBG
37681	697	12	in	in	IN
37681	697	13	number	number	NN
37681	697	14	the	the	DT
37681	697	15	propositions	proposition	NNS
37681	697	16	of	of	IN
37681	697	17	Euclid	Euclid	NNP
37681	697	18	,	,	,
37681	697	19	there	there	EX
37681	697	20	have	have	VBP
37681	697	21	been	be	VBN
37681	697	22	very	very	RB
37681	697	23	many	many	JJ
37681	697	24	revolutionary	revolutionary	JJ
37681	697	25	efforts	effort	NNS
37681	697	26	to	to	TO
37681	697	27	change	change	VB
37681	697	28	his	-PRON-	PRP$
37681	697	29	treatment	treatment	NN
37681	697	30	of	of	IN
37681	697	31	geometry	geometry	NN
37681	697	32	entirely	entirely	RB
37681	697	33	.	.	.
37681	698	1	The	the	DT
37681	698	2	great	great	JJ
37681	698	3	French	french	JJ
37681	698	4	mathematician	mathematician	NN
37681	698	5	,	,	,
37681	698	6	D'Alembert	D'Alembert	NNP
37681	698	7	,	,	,
37681	698	8	for	for	IN
37681	698	9	example	example	NN
37681	698	10	,	,	,
37681	698	11	in	in	IN
37681	698	12	the	the	DT
37681	698	13	eighteenth	eighteenth	JJ
37681	698	14	century	century	NN
37681	698	15	,	,	,
37681	698	16	wished	wish	VBD
37681	698	17	to	to	TO
37681	698	18	divide	divide	VB
37681	698	19	geometry	geometry	NN
37681	698	20	into	into	IN
37681	698	21	three	three	CD
37681	698	22	branches	branch	NNS
37681	698	23	:	:	:
37681	698	24	(	(	-LRB-
37681	698	25	1	1	LS
37681	698	26	)	)	-RRB-
37681	698	27	that	that	IN
37681	698	28	dealing	deal	VBG
37681	698	29	with	with	IN
37681	698	30	straight	straight	JJ
37681	698	31	lines	line	NNS
37681	698	32	and	and	CC
37681	698	33	circles	circle	NNS
37681	698	34	,	,	,
37681	698	35	apparently	apparently	RB
37681	698	36	not	not	RB
37681	698	37	limited	limit	VBN
37681	698	38	to	to	IN
37681	698	39	a	a	DT
37681	698	40	plane	plane	NN
37681	698	41	;	;	:
37681	698	42	(	(	-LRB-
37681	698	43	2	2	LS
37681	698	44	)	)	-RRB-
37681	698	45	that	that	IN
37681	698	46	dealing	deal	VBG
37681	698	47	with	with	IN
37681	698	48	surfaces	surface	NNS
37681	698	49	;	;	,
37681	698	50	and	and	CC
37681	698	51	(	(	-LRB-
37681	698	52	3	3	LS
37681	698	53	)	)	-RRB-
37681	698	54	that	that	IN
37681	698	55	dealing	deal	VBG
37681	698	56	with	with	IN
37681	698	57	solids	solid	NNS
37681	698	58	.	.	.
37681	699	1	So	so	RB
37681	699	2	Méray	Méray	NNP
37681	699	3	in	in	IN
37681	699	4	France	France	NNP
37681	699	5	and	and	CC
37681	699	6	De	De	NNP
37681	699	7	Paolis[33	Paolis[33	NNP
37681	699	8	]	]	-RRB-
37681	699	9	in	in	IN
37681	699	10	Italy	Italy	NNP
37681	699	11	have	have	VBP
37681	699	12	attempted	attempt	VBN
37681	699	13	to	to	TO
37681	699	14	fuse	fuse	VB
37681	699	15	plane	plane	NN
37681	699	16	and	and	CC
37681	699	17	solid	solid	JJ
37681	699	18	geometry	geometry	NN
37681	699	19	,	,	,
37681	699	20	but	but	CC
37681	699	21	have	have	VBP
37681	699	22	not	not	RB
37681	699	23	produced	produce	VBN
37681	699	24	a	a	DT
37681	699	25	system	system	NN
37681	699	26	that	that	WDT
37681	699	27	has	have	VBZ
37681	699	28	been	be	VBN
37681	699	29	particularly	particularly	RB
37681	699	30	successful	successful	JJ
37681	699	31	.	.	.
37681	700	1	More	more	RBR
37681	700	2	recently	recently	RB
37681	700	3	Bourlet	Bourlet	NNP
37681	700	4	,	,	,
37681	700	5	Grévy	Grévy	NNP
37681	700	6	,	,	,
37681	700	7	Borel	Borel	NNP
37681	700	8	,	,	,
37681	700	9	and	and	CC
37681	700	10	others	other	NNS
37681	700	11	in	in	IN
37681	700	12	France	France	NNP
37681	700	13	have	have	VBP
37681	700	14	produced	produce	VBN
37681	700	15	several	several	JJ
37681	700	16	works	work	NNS
37681	700	17	on	on	IN
37681	700	18	the	the	DT
37681	700	19	elements	element	NNS
37681	700	20	of	of	IN
37681	700	21	mathematics	mathematic	NNS
37681	700	22	that	that	WDT
37681	700	23	may	may	MD
37681	700	24	lead	lead	VB
37681	700	25	to	to	IN
37681	700	26	something	something	NN
37681	700	27	of	of	IN
37681	700	28	value	value	NN
37681	700	29	.	.	.
37681	701	1	They	-PRON-	PRP
37681	701	2	place	place	VBP
37681	701	3	intuition	intuition	NN
37681	701	4	to	to	IN
37681	701	5	the	the	DT
37681	701	6	front	front	NN
37681	701	7	,	,	,
37681	701	8	favor	favor	NN
37681	701	9	as	as	IN
37681	701	10	much	much	JJ
37681	701	11	applied	applied	JJ
37681	701	12	mathematics	mathematic	NNS
37681	701	13	as	as	IN
37681	701	14	is	be	VBZ
37681	701	15	reasonable	reasonable	JJ
37681	701	16	,	,	,
37681	701	17	to	to	IN
37681	701	18	all	all	DT
37681	701	19	of	of	IN
37681	701	20	which	which	WDT
37681	701	21	American	american	JJ
37681	701	22	teachers	teacher	NNS
37681	701	23	would	would	MD
37681	701	24	generally	generally	RB
37681	701	25	agree	agree	VB
37681	701	26	,	,	,
37681	701	27	but	but	CC
37681	701	28	they	-PRON-	PRP
37681	701	29	claim	claim	VBP
37681	701	30	that	that	IN
37681	701	31	the	the	DT
37681	701	32	basis	basis	NN
37681	701	33	of	of	IN
37681	701	34	elementary	elementary	JJ
37681	701	35	geometry	geometry	NN
37681	701	36	in	in	IN
37681	701	37	the	the	DT
37681	701	38	future	future	NN
37681	701	39	must	must	MD
37681	701	40	be	be	VB
37681	701	41	the	the	DT
37681	701	42	"	"	``
37681	701	43	investigation	investigation	NN
37681	701	44	of	of	IN
37681	701	45	the	the	DT
37681	701	46	group	group	NN
37681	701	47	of	of	IN
37681	701	48	motions	motion	NNS
37681	701	49	.	.	.
37681	701	50	"	"	''
37681	702	1	It	-PRON-	PRP
37681	702	2	is	be	VBZ
37681	702	3	,	,	,
37681	702	4	of	of	IN
37681	702	5	course	course	NN
37681	702	6	,	,	,
37681	702	7	possible	possible	JJ
37681	702	8	that	that	IN
37681	702	9	certain	certain	JJ
37681	702	10	of	of	IN
37681	702	11	the	the	DT
37681	702	12	notions	notion	NNS
37681	702	13	of	of	IN
37681	702	14	the	the	DT
37681	702	15	higher	higher	RBR
37681	702	16	mathematical	mathematical	JJ
37681	702	17	thought	thought	NN
37681	702	18	of	of	IN
37681	702	19	the	the	DT
37681	702	20	nineteenth	nineteenth	JJ
37681	702	21	century	century	NN
37681	702	22	may	may	MD
37681	702	23	be	be	VB
37681	702	24	so	so	RB
37681	702	25	simplified	simplify	VBN
37681	702	26	as	as	IN
37681	702	27	to	to	TO
37681	702	28	be	be	VB
37681	702	29	within	within	IN
37681	702	30	the	the	DT
37681	702	31	comprehension	comprehension	NN
37681	702	32	of	of	IN
37681	702	33	the	the	DT
37681	702	34	tyro	tyro	NN
37681	702	35	in	in	IN
37681	702	36	geometry	geometry	NN
37681	702	37	,	,	,
37681	702	38	and	and	CC
37681	702	39	we	-PRON-	PRP
37681	702	40	should	should	MD
37681	702	41	be	be	VB
37681	702	42	ready	ready	JJ
37681	702	43	to	to	TO
37681	702	44	receive	receive	VB
37681	702	45	all	all	DT
37681	702	46	efforts	effort	NNS
37681	702	47	of	of	IN
37681	702	48	this	this	DT
37681	702	49	kind	kind	NN
37681	702	50	with	with	IN
37681	702	51	open	open	JJ
37681	702	52	mind	mind	NN
37681	702	53	.	.	.
37681	703	1	These	these	DT
37681	703	2	writers	writer	NNS
37681	703	3	have	have	VBP
37681	703	4	not	not	RB
37681	703	5	however	however	RB
37681	703	6	produced	produce	VBN
37681	703	7	the	the	DT
37681	703	8	ideal	ideal	JJ
37681	703	9	work	work	NN
37681	703	10	,	,	,
37681	703	11	and	and	CC
37681	703	12	it	-PRON-	PRP
37681	703	13	may	may	MD
37681	703	14	seriously	seriously	RB
37681	703	15	be	be	VB
37681	703	16	questioned	question	VBN
37681	703	17	whether	whether	IN
37681	703	18	a	a	DT
37681	703	19	work	work	NN
37681	703	20	based	base	VBN
37681	703	21	upon	upon	IN
37681	703	22	their	-PRON-	PRP$
37681	703	23	ideas	idea	NNS
37681	703	24	will	will	MD
37681	703	25	prove	prove	VB
37681	703	26	to	to	TO
37681	703	27	be	be	VB
37681	703	28	educationally	educationally	RB
37681	703	29	any	any	DT
37681	703	30	more	more	JJR
37681	703	31	sound	sound	JJ
37681	703	32	and	and	CC
37681	703	33	usable	usable	JJ
37681	703	34	than	than	IN
37681	703	35	the	the	DT
37681	703	36	labors	labor	NNS
37681	703	37	of	of	IN
37681	703	38	such	such	JJ
37681	703	39	excellent	excellent	JJ
37681	703	40	writers	writer	NNS
37681	703	41	as	as	IN
37681	703	42	Henrici	Henrici	NNP
37681	703	43	and	and	CC
37681	703	44	Treutlein	Treutlein	NNP
37681	703	45	,	,	,
37681	703	46	and	and	CC
37681	703	47	H.	H.	NNP
37681	703	48	Müller	Müller	NNP
37681	703	49	,	,	,
37681	703	50	and	and	CC
37681	703	51	Schlegel	Schlegel	NNP
37681	703	52	a	a	DT
37681	703	53	few	few	JJ
37681	703	54	years	year	NNS
37681	703	55	ago	ago	RB
37681	703	56	in	in	IN
37681	703	57	Germany	Germany	NNP
37681	703	58	,	,	,
37681	703	59	and	and	CC
37681	703	60	of	of	IN
37681	703	61	Veronese	Veronese	NNP
37681	703	62	in	in	IN
37681	703	63	Italy	Italy	NNP
37681	703	64	.	.	.
37681	704	1	All	all	DT
37681	704	2	such	such	JJ
37681	704	3	efforts	effort	NNS
37681	704	4	,	,	,
37681	704	5	however	however	RB
37681	704	6	,	,	,
37681	704	7	should	should	MD
37681	704	8	be	be	VB
37681	704	9	welcomed	welcome	VBN
37681	704	10	and	and	CC
37681	704	11	tried	try	VBN
37681	704	12	out	out	RP
37681	704	13	,	,	,
37681	704	14	although	although	IN
37681	704	15	so	so	RB
37681	704	16	far	far	RB
37681	704	17	as	as	IN
37681	704	18	at	at	IN
37681	704	19	present	present	JJ
37681	704	20	appears	appear	VBZ
37681	704	21	there	there	EX
37681	704	22	is	be	VBZ
37681	704	23	nothing	nothing	NN
37681	704	24	in	in	IN
37681	704	25	sight	sight	NN
37681	704	26	to	to	TO
37681	704	27	replace	replace	VB
37681	704	28	a	a	DT
37681	704	29	well	well	RB
37681	704	30	-	-	HYPH
37681	704	31	arranged	arrange	VBN
37681	704	32	,	,	,
37681	704	33	vitalized	vitalized	JJ
37681	704	34	,	,	,
37681	704	35	simplified	simplify	VBN
37681	704	36	textbook	textbook	NN
37681	704	37	based	base	VBN
37681	704	38	upon	upon	IN
37681	704	39	the	the	DT
37681	704	40	labors	labor	NNS
37681	704	41	of	of	IN
37681	704	42	Euclid	Euclid	NNP
37681	704	43	and	and	CC
37681	704	44	Legendre	Legendre	NNP
37681	704	45	.	.	.
37681	705	1	The	the	DT
37681	705	2	most	most	RBS
37681	705	3	broad	broad	JJ
37681	705	4	-	-	HYPH
37681	705	5	minded	minded	JJ
37681	705	6	of	of	IN
37681	705	7	the	the	DT
37681	705	8	great	great	JJ
37681	705	9	mathematicians	mathematician	NNS
37681	705	10	who	who	WP
37681	705	11	have	have	VBP
37681	705	12	recently	recently	RB
37681	705	13	given	give	VBN
37681	705	14	attention	attention	NN
37681	705	15	to	to	IN
37681	705	16	secondary	secondary	JJ
37681	705	17	problems	problem	NNS
37681	705	18	is	be	VBZ
37681	705	19	Professor	Professor	NNP
37681	705	20	Klein	Klein	NNP
37681	705	21	of	of	IN
37681	705	22	Göttingen	Göttingen	NNP
37681	705	23	.	.	.
37681	706	1	He	-PRON-	PRP
37681	706	2	has	have	VBZ
37681	706	3	had	have	VBN
37681	706	4	the	the	DT
37681	706	5	good	good	JJ
37681	706	6	sense	sense	NN
37681	706	7	to	to	TO
37681	706	8	look	look	VB
37681	706	9	at	at	IN
37681	706	10	something	something	NN
37681	706	11	besides	besides	IN
37681	706	12	the	the	DT
37681	706	13	mere	mere	JJ
37681	706	14	question	question	NN
37681	706	15	of	of	IN
37681	706	16	good	good	JJ
37681	706	17	mathematics	mathematic	NNS
37681	706	18	.	.	.
37681	707	1	[	[	-LRB-
37681	707	2	34	34	CD
37681	707	3	]	]	-RRB-
37681	707	4	Thus	thus	RB
37681	707	5	he	-PRON-	PRP
37681	707	6	insists	insist	VBZ
37681	707	7	upon	upon	IN
37681	707	8	the	the	DT
37681	707	9	psychologic	psychologic	JJ
37681	707	10	point	point	NN
37681	707	11	of	of	IN
37681	707	12	view	view	NN
37681	707	13	,	,	,
37681	707	14	to	to	IN
37681	707	15	the	the	DT
37681	707	16	end	end	NN
37681	707	17	that	that	IN
37681	707	18	the	the	DT
37681	707	19	geometry	geometry	NN
37681	707	20	shall	shall	MD
37681	707	21	be	be	VB
37681	707	22	adapted	adapt	VBN
37681	707	23	to	to	IN
37681	707	24	the	the	DT
37681	707	25	mental	mental	JJ
37681	707	26	development	development	NN
37681	707	27	of	of	IN
37681	707	28	the	the	DT
37681	707	29	pupil,--a	pupil,--a	NNP
37681	707	30	thing	thing	NN
37681	707	31	that	that	WDT
37681	707	32	is	be	VBZ
37681	707	33	apparently	apparently	RB
37681	707	34	ignored	ignore	VBN
37681	707	35	by	by	IN
37681	707	36	Méray	Méray	NNP
37681	707	37	(	(	-LRB-
37681	707	38	at	at	IN
37681	707	39	least	least	JJS
37681	707	40	for	for	IN
37681	707	41	the	the	DT
37681	707	42	average	average	JJ
37681	707	43	pupil	pupil	NN
37681	707	44	)	)	-RRB-
37681	707	45	,	,	,
37681	707	46	and	and	CC
37681	707	47	,	,	,
37681	707	48	it	-PRON-	PRP
37681	707	49	is	be	VBZ
37681	707	50	to	to	TO
37681	707	51	be	be	VB
37681	707	52	feared	fear	VBN
37681	707	53	,	,	,
37681	707	54	by	by	IN
37681	707	55	the	the	DT
37681	707	56	other	other	JJ
37681	707	57	recent	recent	JJ
37681	707	58	French	french	JJ
37681	707	59	writers	writer	NNS
37681	707	60	.	.	.
37681	708	1	He	-PRON-	PRP
37681	708	2	then	then	RB
37681	708	3	demands	demand	VBZ
37681	708	4	a	a	DT
37681	708	5	careful	careful	JJ
37681	708	6	selection	selection	NN
37681	708	7	of	of	IN
37681	708	8	the	the	DT
37681	708	9	subject	subject	JJ
37681	708	10	matter	matter	NN
37681	708	11	,	,	,
37681	708	12	which	which	WDT
37681	708	13	in	in	IN
37681	708	14	our	-PRON-	PRP$
37681	708	15	American	american	JJ
37681	708	16	schools	school	NNS
37681	708	17	would	would	MD
37681	708	18	mean	mean	VB
37681	708	19	the	the	DT
37681	708	20	elimination	elimination	NN
37681	708	21	of	of	IN
37681	708	22	propositions	proposition	NNS
37681	708	23	that	that	WDT
37681	708	24	are	be	VBP
37681	708	25	not	not	RB
37681	708	26	basal	basal	JJ
37681	708	27	,	,	,
37681	708	28	that	that	RB
37681	708	29	is	is	RB
37681	708	30	,	,	,
37681	708	31	that	that	WDT
37681	708	32	are	be	VBP
37681	708	33	not	not	RB
37681	708	34	used	use	VBN
37681	708	35	for	for	IN
37681	708	36	most	most	JJS
37681	708	37	of	of	IN
37681	708	38	the	the	DT
37681	708	39	exercises	exercise	NNS
37681	708	40	that	that	WDT
37681	708	41	one	one	PRP
37681	708	42	naturally	naturally	RB
37681	708	43	meets	meet	VBZ
37681	708	44	in	in	IN
37681	708	45	elementary	elementary	JJ
37681	708	46	geometry	geometry	NNP
37681	708	47	and	and	CC
37681	708	48	in	in	IN
37681	708	49	applied	applied	JJ
37681	708	50	work	work	NN
37681	708	51	.	.	.
37681	709	1	He	-PRON-	PRP
37681	709	2	further	further	RB
37681	709	3	insists	insist	VBZ
37681	709	4	upon	upon	IN
37681	709	5	a	a	DT
37681	709	6	reasonable	reasonable	JJ
37681	709	7	correlation	correlation	NN
37681	709	8	with	with	IN
37681	709	9	practical	practical	JJ
37681	709	10	work	work	NN
37681	709	11	to	to	TO
37681	709	12	which	which	WDT
37681	709	13	every	every	DT
37681	709	14	teacher	teacher	NN
37681	709	15	will	will	MD
37681	709	16	agree	agree	VB
37681	709	17	so	so	RB
37681	709	18	long	long	RB
37681	709	19	as	as	IN
37681	709	20	the	the	DT
37681	709	21	work	work	NN
37681	709	22	is	be	VBZ
37681	709	23	really	really	RB
37681	709	24	or	or	CC
37681	709	25	even	even	RB
37681	709	26	potentially	potentially	RB
37681	709	27	practical	practical	JJ
37681	709	28	.	.	.
37681	710	1	And	and	CC
37681	710	2	finally	finally	RB
37681	710	3	he	-PRON-	PRP
37681	710	4	asks	ask	VBZ
37681	710	5	that	that	IN
37681	710	6	we	-PRON-	PRP
37681	710	7	look	look	VBP
37681	710	8	with	with	IN
37681	710	9	favor	favor	NN
37681	710	10	upon	upon	IN
37681	710	11	the	the	DT
37681	710	12	union	union	NN
37681	710	13	of	of	IN
37681	710	14	plane	plane	NN
37681	710	15	and	and	CC
37681	710	16	solid	solid	JJ
37681	710	17	geometry	geometry	NN
37681	710	18	,	,	,
37681	710	19	and	and	CC
37681	710	20	of	of	IN
37681	710	21	algebra	algebra	NN
37681	710	22	and	and	CC
37681	710	23	geometry	geometry	NN
37681	710	24	.	.	.
37681	711	1	He	-PRON-	PRP
37681	711	2	does	do	VBZ
37681	711	3	not	not	RB
37681	711	4	make	make	VB
37681	711	5	any	any	DT
37681	711	6	plea	plea	NN
37681	711	7	for	for	IN
37681	711	8	extreme	extreme	JJ
37681	711	9	fusion	fusion	NN
37681	711	10	,	,	,
37681	711	11	but	but	CC
37681	711	12	presumably	presumably	RB
37681	711	13	he	-PRON-	PRP
37681	711	14	asks	ask	VBZ
37681	711	15	that	that	IN
37681	711	16	to	to	TO
37681	711	17	which	which	WDT
37681	711	18	every	every	DT
37681	711	19	one	one	CD
37681	711	20	of	of	IN
37681	711	21	open	open	JJ
37681	711	22	mind	mind	NN
37681	711	23	would	would	MD
37681	711	24	agree	agree	VB
37681	711	25	,	,	,
37681	711	26	namely	namely	RB
37681	711	27	,	,	,
37681	711	28	that	that	IN
37681	711	29	whenever	whenever	WRB
37681	711	30	the	the	DT
37681	711	31	opportunity	opportunity	NN
37681	711	32	offers	offer	VBZ
37681	711	33	in	in	IN
37681	711	34	teaching	teach	VBG
37681	711	35	plane	plane	NN
37681	711	36	geometry	geometry	NN
37681	711	37	,	,	,
37681	711	38	to	to	TO
37681	711	39	open	open	VB
37681	711	40	the	the	DT
37681	711	41	vision	vision	NN
37681	711	42	to	to	IN
37681	711	43	a	a	DT
37681	711	44	generalization	generalization	NN
37681	711	45	in	in	IN
37681	711	46	space	space	NN
37681	711	47	,	,	,
37681	711	48	or	or	CC
37681	711	49	to	to	IN
37681	711	50	the	the	DT
37681	711	51	measurement	measurement	NN
37681	711	52	of	of	IN
37681	711	53	well	well	RB
37681	711	54	-	-	HYPH
37681	711	55	known	know	VBN
37681	711	56	solids	solid	NNS
37681	711	57	,	,	,
37681	711	58	or	or	CC
37681	711	59	to	to	IN
37681	711	60	the	the	DT
37681	711	61	use	use	NN
37681	711	62	of	of	IN
37681	711	63	the	the	DT
37681	711	64	algebra	algebra	NN
37681	711	65	that	that	IN
37681	711	66	the	the	DT
37681	711	67	pupil	pupil	NN
37681	711	68	has	have	VBZ
37681	711	69	learned	learn	VBN
37681	711	70	,	,	,
37681	711	71	the	the	DT
37681	711	72	opportunity	opportunity	NN
37681	711	73	should	should	MD
37681	711	74	be	be	VB
37681	711	75	seized	seize	VBN
37681	711	76	.	.	.
37681	712	1	FOOTNOTES	footnote	NNS
37681	712	2	:	:	:
37681	712	3	[	[	-LRB-
37681	712	4	32	32	CD
37681	712	5	]	]	-RRB-
37681	712	6	The	the	DT
37681	712	7	author	author	NN
37681	712	8	is	be	VBZ
37681	712	9	a	a	DT
37681	712	10	member	member	NN
37681	712	11	of	of	IN
37681	712	12	a	a	DT
37681	712	13	committee	committee	NN
37681	712	14	that	that	WDT
37681	712	15	has	have	VBZ
37681	712	16	for	for	IN
37681	712	17	more	more	JJR
37681	712	18	than	than	IN
37681	712	19	a	a	DT
37681	712	20	year	year	NN
37681	712	21	been	be	VBN
37681	712	22	considering	consider	VBG
37681	712	23	a	a	DT
37681	712	24	syllabus	syllabus	NN
37681	712	25	in	in	IN
37681	712	26	geometry	geometry	NN
37681	712	27	.	.	.
37681	713	1	This	this	DT
37681	713	2	committee	committee	NN
37681	713	3	will	will	MD
37681	713	4	probably	probably	RB
37681	713	5	report	report	VB
37681	713	6	sometime	sometime	RB
37681	713	7	during	during	IN
37681	713	8	the	the	DT
37681	713	9	year	year	NN
37681	713	10	1911	1911	CD
37681	713	11	.	.	.
37681	714	1	At	at	IN
37681	714	2	the	the	DT
37681	714	3	present	present	JJ
37681	714	4	writing	writing	NN
37681	714	5	it	-PRON-	PRP
37681	714	6	seems	seem	VBZ
37681	714	7	disposed	disposed	JJ
37681	714	8	to	to	TO
37681	714	9	recommend	recommend	VB
37681	714	10	about	about	IN
37681	714	11	the	the	DT
37681	714	12	usual	usual	JJ
37681	714	13	list	list	NN
37681	714	14	of	of	IN
37681	714	15	basal	basal	NN
37681	714	16	propositions	proposition	NNS
37681	714	17	.	.	.
37681	715	1	[	[	-LRB-
37681	715	2	33	33	CD
37681	715	3	]	]	-RRB-
37681	715	4	"	"	``
37681	715	5	Elementi	Elementi	NNP
37681	715	6	di	di	FW
37681	715	7	Geometria	Geometria	NNP
37681	715	8	,	,	,
37681	715	9	"	"	``
37681	715	10	Milan	Milan	NNP
37681	715	11	,	,	,
37681	715	12	1884	1884	CD
37681	715	13	.	.	.
37681	716	1	[	[	-LRB-
37681	716	2	34	34	CD
37681	716	3	]	]	-RRB-
37681	716	4	See	see	VB
37681	716	5	his	-PRON-	PRP$
37681	716	6	"	"	``
37681	716	7	Elementarmathematik	Elementarmathematik	NNP
37681	716	8	vom	vom	NNS
37681	716	9	höheren	höheren	NNP
37681	716	10	Standpunkt	Standpunkt	NNP
37681	716	11	aus	aus	NN
37681	716	12	,	,	,
37681	716	13	"	"	``
37681	716	14	Part	Part	NNP
37681	716	15	II	II	NNP
37681	716	16	,	,	,
37681	716	17	Leipzig	Leipzig	NNP
37681	716	18	,	,	,
37681	716	19	1909	1909	CD
37681	716	20	.	.	.
37681	717	1	CHAPTER	CHAPTER	NNP
37681	717	2	VII	VII	NNP
37681	717	3	THE	the	DT
37681	717	4	TEXTBOOK	textbook	NN
37681	717	5	IN	in	IN
37681	717	6	GEOMETRY	GEOMETRY	NNP
37681	717	7	In	in	IN
37681	717	8	considering	consider	VBG
37681	717	9	the	the	DT
37681	717	10	nature	nature	NN
37681	717	11	of	of	IN
37681	717	12	the	the	DT
37681	717	13	textbook	textbook	NN
37681	717	14	in	in	IN
37681	717	15	geometry	geometry	NN
37681	717	16	we	-PRON-	PRP
37681	717	17	need	need	VBP
37681	717	18	to	to	TO
37681	717	19	bear	bear	VB
37681	717	20	in	in	IN
37681	717	21	mind	mind	NN
37681	717	22	the	the	DT
37681	717	23	fact	fact	NN
37681	717	24	that	that	IN
37681	717	25	the	the	DT
37681	717	26	subject	subject	NN
37681	717	27	is	be	VBZ
37681	717	28	being	be	VBG
37681	717	29	taught	teach	VBN
37681	717	30	to	to	IN
37681	717	31	-	-	HYPH
37681	717	32	day	day	NN
37681	717	33	in	in	IN
37681	717	34	America	America	NNP
37681	717	35	to	to	IN
37681	717	36	a	a	DT
37681	717	37	class	class	NN
37681	717	38	of	of	IN
37681	717	39	pupils	pupil	NNS
37681	717	40	that	that	WDT
37681	717	41	is	be	VBZ
37681	717	42	not	not	RB
37681	717	43	composed	compose	VBN
37681	717	44	like	like	IN
37681	717	45	the	the	DT
37681	717	46	classes	class	NNS
37681	717	47	found	find	VBN
37681	717	48	in	in	IN
37681	717	49	other	other	JJ
37681	717	50	countries	country	NNS
37681	717	51	or	or	CC
37681	717	52	in	in	IN
37681	717	53	earlier	early	JJR
37681	717	54	generations	generation	NNS
37681	717	55	.	.	.
37681	718	1	In	in	IN
37681	718	2	general	general	JJ
37681	718	3	,	,	,
37681	718	4	in	in	IN
37681	718	5	other	other	JJ
37681	718	6	countries	country	NNS
37681	718	7	,	,	,
37681	718	8	geometry	geometry	NN
37681	718	9	is	be	VBZ
37681	718	10	not	not	RB
37681	718	11	taught	teach	VBN
37681	718	12	to	to	IN
37681	718	13	mixed	mixed	JJ
37681	718	14	classes	class	NNS
37681	718	15	of	of	IN
37681	718	16	boys	boy	NNS
37681	718	17	and	and	CC
37681	718	18	girls	girl	NNS
37681	718	19	.	.	.
37681	719	1	Furthermore	furthermore	RB
37681	719	2	,	,	,
37681	719	3	it	-PRON-	PRP
37681	719	4	is	be	VBZ
37681	719	5	generally	generally	RB
37681	719	6	taught	teach	VBN
37681	719	7	to	to	IN
37681	719	8	a	a	DT
37681	719	9	more	more	RBR
37681	719	10	select	select	JJ
37681	719	11	group	group	NN
37681	719	12	of	of	IN
37681	719	13	pupils	pupil	NNS
37681	719	14	than	than	IN
37681	719	15	in	in	IN
37681	719	16	a	a	DT
37681	719	17	country	country	NN
37681	719	18	where	where	WRB
37681	719	19	the	the	DT
37681	719	20	high	high	JJ
37681	719	21	school	school	NN
37681	719	22	and	and	CC
37681	719	23	college	college	NN
37681	719	24	are	be	VBP
37681	719	25	so	so	RB
37681	719	26	popular	popular	JJ
37681	719	27	with	with	IN
37681	719	28	people	people	NNS
37681	719	29	in	in	IN
37681	719	30	all	all	PDT
37681	719	31	the	the	DT
37681	719	32	walks	walk	NNS
37681	719	33	of	of	IN
37681	719	34	life	life	NN
37681	719	35	.	.	.
37681	720	1	In	in	IN
37681	720	2	America	America	NNP
37681	720	3	it	-PRON-	PRP
37681	720	4	is	be	VBZ
37681	720	5	not	not	RB
37681	720	6	alone	alone	RB
37681	720	7	the	the	DT
37681	720	8	boy	boy	NN
37681	720	9	who	who	WP
37681	720	10	is	be	VBZ
37681	720	11	interested	interested	JJ
37681	720	12	in	in	IN
37681	720	13	education	education	NN
37681	720	14	in	in	IN
37681	720	15	general	general	JJ
37681	720	16	,	,	,
37681	720	17	or	or	CC
37681	720	18	in	in	IN
37681	720	19	mathematics	mathematic	NNS
37681	720	20	in	in	IN
37681	720	21	particular	particular	JJ
37681	720	22	,	,	,
37681	720	23	who	who	WP
37681	720	24	studies	study	VBZ
37681	720	25	geometry	geometry	NN
37681	720	26	,	,	,
37681	720	27	and	and	CC
37681	720	28	who	who	WP
37681	720	29	joins	join	VBZ
37681	720	30	with	with	IN
37681	720	31	others	other	NNS
37681	720	32	of	of	IN
37681	720	33	like	like	JJ
37681	720	34	tastes	taste	NNS
37681	720	35	in	in	IN
37681	720	36	this	this	DT
37681	720	37	pursuit	pursuit	NN
37681	720	38	,	,	,
37681	720	39	but	but	CC
37681	720	40	it	-PRON-	PRP
37681	720	41	is	be	VBZ
37681	720	42	often	often	RB
37681	720	43	the	the	DT
37681	720	44	boy	boy	NN
37681	720	45	and	and	CC
37681	720	46	the	the	DT
37681	720	47	girl	girl	NN
37681	720	48	who	who	WP
37681	720	49	are	be	VBP
37681	720	50	not	not	RB
37681	720	51	compelled	compel	VBN
37681	720	52	to	to	TO
37681	720	53	go	go	VB
37681	720	54	out	out	RP
37681	720	55	and	and	CC
37681	720	56	work	work	VB
37681	720	57	,	,	,
37681	720	58	and	and	CC
37681	720	59	who	who	WP
37681	720	60	fill	fill	VBP
37681	720	61	the	the	DT
37681	720	62	years	year	NNS
37681	720	63	of	of	IN
37681	720	64	youth	youth	NN
37681	720	65	with	with	IN
37681	720	66	a	a	DT
37681	720	67	not	not	RB
37681	720	68	over	over	RB
37681	720	69	-	-	HYPH
37681	720	70	strenuous	strenuous	JJ
37681	720	71	school	school	NN
37681	720	72	life	life	NN
37681	720	73	.	.	.
37681	721	1	It	-PRON-	PRP
37681	721	2	is	be	VBZ
37681	721	3	therefore	therefore	RB
37681	721	4	clear	clear	JJ
37681	721	5	that	that	IN
37681	721	6	we	-PRON-	PRP
37681	721	7	can	can	MD
37681	721	8	not	not	RB
37681	721	9	hold	hold	VB
37681	721	10	the	the	DT
37681	721	11	interest	interest	NN
37681	721	12	of	of	IN
37681	721	13	such	such	JJ
37681	721	14	pupils	pupil	NNS
37681	721	15	by	by	IN
37681	721	16	the	the	DT
37681	721	17	study	study	NN
37681	721	18	of	of	IN
37681	721	19	Euclid	Euclid	NNP
37681	721	20	alone	alone	RB
37681	721	21	.	.	.
37681	722	1	Geometry	geometry	NN
37681	722	2	must	must	MD
37681	722	3	,	,	,
37681	722	4	for	for	IN
37681	722	5	them	-PRON-	PRP
37681	722	6	,	,	,
37681	722	7	be	be	VB
37681	722	8	less	less	RBR
37681	722	9	formal	formal	JJ
37681	722	10	than	than	IN
37681	722	11	it	-PRON-	PRP
37681	722	12	was	be	VBD
37681	722	13	half	half	PDT
37681	722	14	a	a	DT
37681	722	15	century	century	NN
37681	722	16	ago	ago	RB
37681	722	17	.	.	.
37681	723	1	We	-PRON-	PRP
37681	723	2	can	can	MD
37681	723	3	not	not	RB
37681	723	4	expect	expect	VB
37681	723	5	to	to	TO
37681	723	6	make	make	VB
37681	723	7	our	-PRON-	PRP$
37681	723	8	classes	class	NNS
37681	723	9	enthusiastic	enthusiastic	VB
37681	723	10	merely	merely	RB
37681	723	11	over	over	IN
37681	723	12	a	a	DT
37681	723	13	logical	logical	JJ
37681	723	14	sequence	sequence	NN
37681	723	15	of	of	IN
37681	723	16	proved	proved	JJ
37681	723	17	propositions	proposition	NNS
37681	723	18	.	.	.
37681	724	1	It	-PRON-	PRP
37681	724	2	becomes	become	VBZ
37681	724	3	necessary	necessary	JJ
37681	724	4	to	to	TO
37681	724	5	make	make	VB
37681	724	6	the	the	DT
37681	724	7	work	work	NN
37681	724	8	more	more	RBR
37681	724	9	concrete	concrete	JJ
37681	724	10	,	,	,
37681	724	11	and	and	CC
37681	724	12	to	to	TO
37681	724	13	give	give	VB
37681	724	14	a	a	DT
37681	724	15	much	much	RB
37681	724	16	larger	large	JJR
37681	724	17	number	number	NN
37681	724	18	of	of	IN
37681	724	19	simple	simple	JJ
37681	724	20	exercises	exercise	NNS
37681	724	21	in	in	IN
37681	724	22	order	order	NN
37681	724	23	to	to	TO
37681	724	24	create	create	VB
37681	724	25	the	the	DT
37681	724	26	interest	interest	NN
37681	724	27	that	that	WDT
37681	724	28	comes	come	VBZ
37681	724	29	from	from	IN
37681	724	30	independent	independent	JJ
37681	724	31	work	work	NN
37681	724	32	,	,	,
37681	724	33	from	from	IN
37681	724	34	a	a	DT
37681	724	35	feeling	feeling	NN
37681	724	36	of	of	IN
37681	724	37	conquest	conquest	NN
37681	724	38	,	,	,
37681	724	39	and	and	CC
37681	724	40	from	from	IN
37681	724	41	a	a	DT
37681	724	42	desire	desire	NN
37681	724	43	to	to	TO
37681	724	44	do	do	VB
37681	724	45	something	something	NN
37681	724	46	original	original	JJ
37681	724	47	.	.	.
37681	725	1	If	if	IN
37681	725	2	we	-PRON-	PRP
37681	725	3	would	would	MD
37681	725	4	"	"	``
37681	725	5	cast	cast	VB
37681	725	6	a	a	DT
37681	725	7	glamor	glamor	NN
37681	725	8	over	over	IN
37681	725	9	the	the	DT
37681	725	10	multiplication	multiplication	NN
37681	725	11	table	table	NN
37681	725	12	,	,	,
37681	725	13	"	"	''
37681	725	14	as	as	IN
37681	725	15	an	an	DT
37681	725	16	admirer	admirer	NN
37681	725	17	of	of	IN
37681	725	18	Macaulay	Macaulay	NNP
37681	725	19	has	have	VBZ
37681	725	20	said	say	VBN
37681	725	21	that	that	IN
37681	725	22	the	the	DT
37681	725	23	latter	latter	JJ
37681	725	24	could	could	MD
37681	725	25	do	do	VB
37681	725	26	,	,	,
37681	725	27	we	-PRON-	PRP
37681	725	28	must	must	MD
37681	725	29	have	have	VB
37681	725	30	the	the	DT
37681	725	31	facilities	facility	NNS
37681	725	32	for	for	IN
37681	725	33	so	so	RB
37681	725	34	doing	do	VBG
37681	725	35	.	.	.
37681	726	1	It	-PRON-	PRP
37681	726	2	therefore	therefore	RB
37681	726	3	becomes	become	VBZ
37681	726	4	necessary	necessary	JJ
37681	726	5	in	in	IN
37681	726	6	weighing	weigh	VBG
37681	726	7	the	the	DT
37681	726	8	merits	merit	NNS
37681	726	9	of	of	IN
37681	726	10	a	a	DT
37681	726	11	textbook	textbook	NN
37681	726	12	to	to	TO
37681	726	13	consider	consider	VB
37681	726	14	:	:	:
37681	726	15	(	(	-LRB-
37681	726	16	1	1	LS
37681	726	17	)	)	-RRB-
37681	726	18	if	if	IN
37681	726	19	the	the	DT
37681	726	20	number	number	NN
37681	726	21	of	of	IN
37681	726	22	proved	proved	JJ
37681	726	23	propositions	proposition	NNS
37681	726	24	is	be	VBZ
37681	726	25	reduced	reduce	VBN
37681	726	26	to	to	IN
37681	726	27	a	a	DT
37681	726	28	safe	safe	JJ
37681	726	29	minimum	minimum	NN
37681	726	30	;	;	:
37681	726	31	(	(	-LRB-
37681	726	32	2	2	LS
37681	726	33	)	)	-RRB-
37681	726	34	if	if	IN
37681	726	35	there	there	EX
37681	726	36	is	be	VBZ
37681	726	37	reasonable	reasonable	JJ
37681	726	38	opportunity	opportunity	NN
37681	726	39	to	to	TO
37681	726	40	apply	apply	VB
37681	726	41	the	the	DT
37681	726	42	theory	theory	NN
37681	726	43	,	,	,
37681	726	44	the	the	DT
37681	726	45	actual	actual	JJ
37681	726	46	applications	application	NNS
37681	726	47	coming	come	VBG
37681	726	48	best	well	RBS
37681	726	49	,	,	,
37681	726	50	however	however	RB
37681	726	51	,	,	,
37681	726	52	from	from	IN
37681	726	53	the	the	DT
37681	726	54	teacher	teacher	NN
37681	726	55	as	as	IN
37681	726	56	an	an	DT
37681	726	57	outside	outside	JJ
37681	726	58	interest	interest	NN
37681	726	59	;	;	:
37681	726	60	(	(	-LRB-
37681	726	61	3	3	LS
37681	726	62	)	)	-RRB-
37681	726	63	if	if	IN
37681	726	64	there	there	EX
37681	726	65	is	be	VBZ
37681	726	66	an	an	DT
37681	726	67	abundance	abundance	NN
37681	726	68	of	of	IN
37681	726	69	material	material	NN
37681	726	70	in	in	IN
37681	726	71	the	the	DT
37681	726	72	way	way	NN
37681	726	73	of	of	IN
37681	726	74	simple	simple	JJ
37681	726	75	exercises	exercise	NNS
37681	726	76	,	,	,
37681	726	77	since	since	IN
37681	726	78	such	such	JJ
37681	726	79	material	material	NN
37681	726	80	is	be	VBZ
37681	726	81	not	not	RB
37681	726	82	so	so	RB
37681	726	83	readily	readily	RB
37681	726	84	given	give	VBN
37681	726	85	by	by	IN
37681	726	86	the	the	DT
37681	726	87	teacher	teacher	NN
37681	726	88	as	as	IN
37681	726	89	the	the	DT
37681	726	90	seemingly	seemingly	RB
37681	726	91	local	local	JJ
37681	726	92	applications	application	NNS
37681	726	93	of	of	IN
37681	726	94	the	the	DT
37681	726	95	propositions	proposition	NNS
37681	726	96	to	to	IN
37681	726	97	outdoor	outdoor	JJ
37681	726	98	measurements	measurement	NNS
37681	726	99	;	;	:
37681	726	100	(	(	-LRB-
37681	726	101	4	4	LS
37681	726	102	)	)	-RRB-
37681	726	103	if	if	IN
37681	726	104	the	the	DT
37681	726	105	book	book	NN
37681	726	106	gives	give	VBZ
37681	726	107	a	a	DT
37681	726	108	reasonable	reasonable	JJ
37681	726	109	amount	amount	NN
37681	726	110	of	of	IN
37681	726	111	introductory	introductory	JJ
37681	726	112	work	work	NN
37681	726	113	in	in	IN
37681	726	114	the	the	DT
37681	726	115	use	use	NN
37681	726	116	of	of	IN
37681	726	117	simple	simple	JJ
37681	726	118	and	and	CC
37681	726	119	inexpensive	inexpensive	JJ
37681	726	120	instruments	instrument	NNS
37681	726	121	,	,	,
37681	726	122	not	not	RB
37681	726	123	at	at	IN
37681	726	124	that	that	DT
37681	726	125	time	time	NN
37681	726	126	emphasizing	emphasize	VBG
37681	726	127	the	the	DT
37681	726	128	formal	formal	JJ
37681	726	129	side	side	NN
37681	726	130	of	of	IN
37681	726	131	the	the	DT
37681	726	132	subject	subject	NN
37681	726	133	;	;	:
37681	726	134	(	(	-LRB-
37681	726	135	5	5	LS
37681	726	136	)	)	-RRB-
37681	726	137	if	if	IN
37681	726	138	there	there	EX
37681	726	139	is	be	VBZ
37681	726	140	afforded	afford	VBN
37681	726	141	some	some	DT
37681	726	142	opportunity	opportunity	NN
37681	726	143	to	to	TO
37681	726	144	see	see	VB
37681	726	145	the	the	DT
37681	726	146	recreative	recreative	JJ
37681	726	147	side	side	NN
37681	726	148	of	of	IN
37681	726	149	the	the	DT
37681	726	150	subject	subject	NN
37681	726	151	,	,	,
37681	726	152	and	and	CC
37681	726	153	to	to	TO
37681	726	154	know	know	VB
37681	726	155	a	a	DT
37681	726	156	little	little	JJ
37681	726	157	of	of	IN
37681	726	158	the	the	DT
37681	726	159	story	story	NN
37681	726	160	of	of	IN
37681	726	161	geometry	geometry	NN
37681	726	162	as	as	IN
37681	726	163	it	-PRON-	PRP
37681	726	164	has	have	VBZ
37681	726	165	developed	develop	VBN
37681	726	166	from	from	IN
37681	726	167	ancient	ancient	JJ
37681	726	168	to	to	IN
37681	726	169	modern	modern	JJ
37681	726	170	times	time	NNS
37681	726	171	.	.	.
37681	727	1	But	but	CC
37681	727	2	this	this	DT
37681	727	3	does	do	VBZ
37681	727	4	not	not	RB
37681	727	5	mean	mean	VB
37681	727	6	that	that	IN
37681	727	7	there	there	EX
37681	727	8	is	be	VBZ
37681	727	9	to	to	TO
37681	727	10	be	be	VB
37681	727	11	a	a	DT
37681	727	12	geometric	geometric	JJ
37681	727	13	cataclysm	cataclysm	NNS
37681	727	14	.	.	.
37681	728	1	It	-PRON-	PRP
37681	728	2	means	mean	VBZ
37681	728	3	that	that	IN
37681	728	4	we	-PRON-	PRP
37681	728	5	must	must	MD
37681	728	6	have	have	VB
37681	728	7	the	the	DT
37681	728	8	same	same	JJ
37681	728	9	safe	safe	JJ
37681	728	10	,	,	,
37681	728	11	conservative	conservative	JJ
37681	728	12	evolution	evolution	NN
37681	728	13	in	in	IN
37681	728	14	geometry	geometry	NN
37681	728	15	that	that	WDT
37681	728	16	we	-PRON-	PRP
37681	728	17	have	have	VBP
37681	728	18	in	in	IN
37681	728	19	other	other	JJ
37681	728	20	subjects	subject	NNS
37681	728	21	.	.	.
37681	729	1	Geometry	geometry	NN
37681	729	2	is	be	VBZ
37681	729	3	not	not	RB
37681	729	4	going	go	VBG
37681	729	5	to	to	TO
37681	729	6	degenerate	degenerate	VB
37681	729	7	into	into	IN
37681	729	8	mere	mere	JJ
37681	729	9	measuring	measuring	NN
37681	729	10	,	,	,
37681	729	11	nor	nor	CC
37681	729	12	is	be	VBZ
37681	729	13	the	the	DT
37681	729	14	ancient	ancient	JJ
37681	729	15	sequence	sequence	NN
37681	729	16	going	go	VBG
37681	729	17	to	to	TO
37681	729	18	become	become	VB
37681	729	19	a	a	DT
37681	729	20	mere	mere	JJ
37681	729	21	hodge	hodge	NN
37681	729	22	-	-	HYPH
37681	729	23	podge	podge	NN
37681	729	24	without	without	IN
37681	729	25	system	system	NN
37681	729	26	and	and	CC
37681	729	27	with	with	IN
37681	729	28	no	no	DT
37681	729	29	incentive	incentive	NN
37681	729	30	to	to	IN
37681	729	31	strenuous	strenuous	JJ
37681	729	32	effort	effort	NN
37681	729	33	.	.	.
37681	730	1	It	-PRON-	PRP
37681	730	2	is	be	VBZ
37681	730	3	now	now	RB
37681	730	4	about	about	RB
37681	730	5	fifteen	fifteen	CD
37681	730	6	hundred	hundred	CD
37681	730	7	years	year	NNS
37681	730	8	since	since	IN
37681	730	9	Proclus	Proclus	NNP
37681	730	10	laid	lay	VBD
37681	730	11	down	down	RP
37681	730	12	what	what	WP
37681	730	13	he	-PRON-	PRP
37681	730	14	considered	consider	VBD
37681	730	15	the	the	DT
37681	730	16	essential	essential	JJ
37681	730	17	features	feature	NNS
37681	730	18	of	of	IN
37681	730	19	a	a	DT
37681	730	20	good	good	JJ
37681	730	21	textbook	textbook	NN
37681	730	22	,	,	,
37681	730	23	and	and	CC
37681	730	24	in	in	IN
37681	730	25	all	all	DT
37681	730	26	of	of	IN
37681	730	27	our	-PRON-	PRP$
37681	730	28	efforts	effort	NNS
37681	730	29	at	at	IN
37681	730	30	reform	reform	NN
37681	730	31	we	-PRON-	PRP
37681	730	32	can	can	MD
37681	730	33	not	not	RB
37681	730	34	improve	improve	VB
37681	730	35	very	very	RB
37681	730	36	much	much	RB
37681	730	37	upon	upon	IN
37681	730	38	his	-PRON-	PRP$
37681	730	39	statement	statement	NN
37681	730	40	.	.	.
37681	731	1	"	"	``
37681	731	2	It	-PRON-	PRP
37681	731	3	is	be	VBZ
37681	731	4	essential	essential	JJ
37681	731	5	,	,	,
37681	731	6	"	"	''
37681	731	7	he	-PRON-	PRP
37681	731	8	says	say	VBZ
37681	731	9	,	,	,
37681	731	10	"	"	``
37681	731	11	that	that	IN
37681	731	12	such	such	PDT
37681	731	13	a	a	DT
37681	731	14	treatise	treatise	NN
37681	731	15	should	should	MD
37681	731	16	be	be	VB
37681	731	17	rid	rid	VBN
37681	731	18	of	of	IN
37681	731	19	everything	everything	NN
37681	731	20	superfluous	superfluous	JJ
37681	731	21	,	,	,
37681	731	22	for	for	IN
37681	731	23	the	the	DT
37681	731	24	superfluous	superfluous	JJ
37681	731	25	is	be	VBZ
37681	731	26	an	an	DT
37681	731	27	obstacle	obstacle	NN
37681	731	28	to	to	IN
37681	731	29	the	the	DT
37681	731	30	acquisition	acquisition	NN
37681	731	31	of	of	IN
37681	731	32	knowledge	knowledge	NN
37681	731	33	;	;	:
37681	731	34	it	-PRON-	PRP
37681	731	35	should	should	MD
37681	731	36	select	select	VB
37681	731	37	everything	everything	NN
37681	731	38	that	that	WDT
37681	731	39	embraces	embrace	VBZ
37681	731	40	the	the	DT
37681	731	41	subject	subject	NN
37681	731	42	and	and	CC
37681	731	43	brings	bring	VBZ
37681	731	44	it	-PRON-	PRP
37681	731	45	to	to	IN
37681	731	46	a	a	DT
37681	731	47	focus	focus	NN
37681	731	48	,	,	,
37681	731	49	for	for	IN
37681	731	50	this	this	DT
37681	731	51	is	be	VBZ
37681	731	52	of	of	IN
37681	731	53	the	the	DT
37681	731	54	highest	high	JJS
37681	731	55	service	service	NN
37681	731	56	to	to	IN
37681	731	57	science	science	NN
37681	731	58	;	;	:
37681	731	59	it	-PRON-	PRP
37681	731	60	must	must	MD
37681	731	61	have	have	VB
37681	731	62	great	great	JJ
37681	731	63	regard	regard	NN
37681	731	64	both	both	DT
37681	731	65	to	to	IN
37681	731	66	clearness	clearness	NN
37681	731	67	and	and	CC
37681	731	68	to	to	IN
37681	731	69	conciseness	conciseness	NN
37681	731	70	,	,	,
37681	731	71	for	for	IN
37681	731	72	their	-PRON-	PRP$
37681	731	73	opposites	opposite	NNS
37681	731	74	trouble	trouble	VBP
37681	731	75	our	-PRON-	PRP$
37681	731	76	understanding	understanding	NN
37681	731	77	;	;	:
37681	731	78	it	-PRON-	PRP
37681	731	79	must	must	MD
37681	731	80	aim	aim	VB
37681	731	81	to	to	TO
37681	731	82	generalize	generalize	VB
37681	731	83	its	-PRON-	PRP$
37681	731	84	theorems	theorem	NNS
37681	731	85	,	,	,
37681	731	86	for	for	IN
37681	731	87	the	the	DT
37681	731	88	division	division	NN
37681	731	89	of	of	IN
37681	731	90	knowledge	knowledge	NN
37681	731	91	into	into	IN
37681	731	92	small	small	JJ
37681	731	93	elements	element	NNS
37681	731	94	renders	render	VBZ
37681	731	95	it	-PRON-	PRP
37681	731	96	difficult	difficult	JJ
37681	731	97	of	of	IN
37681	731	98	comprehension	comprehension	NN
37681	731	99	.	.	.
37681	731	100	"	"	''
37681	732	1	It	-PRON-	PRP
37681	732	2	being	be	VBG
37681	732	3	prefaced	preface	VBN
37681	732	4	that	that	IN
37681	732	5	we	-PRON-	PRP
37681	732	6	must	must	MD
37681	732	7	make	make	VB
37681	732	8	the	the	DT
37681	732	9	book	book	NN
37681	732	10	more	more	JJR
37681	732	11	concrete	concrete	JJ
37681	732	12	in	in	IN
37681	732	13	its	-PRON-	PRP$
37681	732	14	applications	application	NNS
37681	732	15	,	,	,
37681	732	16	either	either	CC
37681	732	17	directly	directly	RB
37681	732	18	or	or	CC
37681	732	19	by	by	IN
37681	732	20	suggesting	suggest	VBG
37681	732	21	seemingly	seemingly	RB
37681	732	22	practical	practical	JJ
37681	732	23	outdoor	outdoor	JJ
37681	732	24	work	work	NN
37681	732	25	;	;	:
37681	732	26	that	that	IN
37681	732	27	we	-PRON-	PRP
37681	732	28	must	must	MD
37681	732	29	increase	increase	VB
37681	732	30	the	the	DT
37681	732	31	number	number	NN
37681	732	32	of	of	IN
37681	732	33	simple	simple	JJ
37681	732	34	exercises	exercise	NNS
37681	732	35	calling	call	VBG
37681	732	36	for	for	IN
37681	732	37	original	original	JJ
37681	732	38	work	work	NN
37681	732	39	;	;	:
37681	732	40	that	that	IN
37681	732	41	we	-PRON-	PRP
37681	732	42	must	must	MD
37681	732	43	reasonably	reasonably	RB
37681	732	44	reduce	reduce	VB
37681	732	45	the	the	DT
37681	732	46	number	number	NN
37681	732	47	of	of	IN
37681	732	48	proved	proved	JJ
37681	732	49	propositions	proposition	NNS
37681	732	50	;	;	:
37681	732	51	and	and	CC
37681	732	52	that	that	IN
37681	732	53	we	-PRON-	PRP
37681	732	54	must	must	MD
37681	732	55	not	not	RB
37681	732	56	allow	allow	VB
37681	732	57	the	the	DT
37681	732	58	good	good	NN
37681	732	59	of	of	IN
37681	732	60	the	the	DT
37681	732	61	ancient	ancient	JJ
37681	732	62	geometry	geometry	NN
37681	732	63	to	to	TO
37681	732	64	depart	depart	VB
37681	732	65	,	,	,
37681	732	66	let	let	VB
37681	732	67	us	-PRON-	PRP
37681	732	68	consider	consider	VB
37681	732	69	in	in	IN
37681	732	70	detail	detail	NN
37681	732	71	some	some	DT
37681	732	72	of	of	IN
37681	732	73	the	the	DT
37681	732	74	features	feature	NNS
37681	732	75	of	of	IN
37681	732	76	a	a	DT
37681	732	77	good	good	JJ
37681	732	78	,	,	,
37681	732	79	practical	practical	JJ
37681	732	80	,	,	,
37681	732	81	common	common	JJ
37681	732	82	-	-	HYPH
37681	732	83	sense	sense	NN
37681	732	84	textbook	textbook	NN
37681	732	85	.	.	.
37681	733	1	The	the	DT
37681	733	2	early	early	JJ
37681	733	3	textbooks	textbook	NNS
37681	733	4	in	in	IN
37681	733	5	geometry	geometry	NN
37681	733	6	contained	contain	VBD
37681	733	7	only	only	RB
37681	733	8	the	the	DT
37681	733	9	propositions	proposition	NNS
37681	733	10	,	,	,
37681	733	11	with	with	IN
37681	733	12	the	the	DT
37681	733	13	proofs	proof	NNS
37681	733	14	in	in	IN
37681	733	15	full	full	JJ
37681	733	16	,	,	,
37681	733	17	preceded	precede	VBN
37681	733	18	by	by	IN
37681	733	19	lists	list	NNS
37681	733	20	of	of	IN
37681	733	21	definitions	definition	NNS
37681	733	22	and	and	CC
37681	733	23	assumptions	assumption	NNS
37681	733	24	(	(	-LRB-
37681	733	25	axioms	axiom	NNS
37681	733	26	and	and	CC
37681	733	27	postulates	postulate	NNS
37681	733	28	)	)	-RRB-
37681	733	29	.	.	.
37681	734	1	There	there	EX
37681	734	2	were	be	VBD
37681	734	3	no	no	DT
37681	734	4	exercises	exercise	NNS
37681	734	5	,	,	,
37681	734	6	and	and	CC
37681	734	7	the	the	DT
37681	734	8	proofs	proof	NNS
37681	734	9	were	be	VBD
37681	734	10	given	give	VBN
37681	734	11	in	in	IN
37681	734	12	essay	essay	NN
37681	734	13	form	form	NN
37681	734	14	.	.	.
37681	735	1	Then	then	RB
37681	735	2	came	come	VBD
37681	735	3	treatises	treatise	NNS
37681	735	4	with	with	IN
37681	735	5	exercises	exercise	NNS
37681	735	6	,	,	,
37681	735	7	these	these	DT
37681	735	8	exercises	exercise	NNS
37681	735	9	being	be	VBG
37681	735	10	grouped	group	VBN
37681	735	11	at	at	IN
37681	735	12	the	the	DT
37681	735	13	end	end	NN
37681	735	14	of	of	IN
37681	735	15	the	the	DT
37681	735	16	work	work	NN
37681	735	17	or	or	CC
37681	735	18	at	at	IN
37681	735	19	the	the	DT
37681	735	20	close	close	NN
37681	735	21	of	of	IN
37681	735	22	the	the	DT
37681	735	23	respective	respective	JJ
37681	735	24	books	book	NNS
37681	735	25	.	.	.
37681	736	1	The	the	DT
37681	736	2	next	next	JJ
37681	736	3	step	step	NN
37681	736	4	was	be	VBD
37681	736	5	to	to	IN
37681	736	6	the	the	DT
37681	736	7	unit	unit	NN
37681	736	8	page	page	NN
37681	736	9	,	,	,
37681	736	10	arranged	arrange	VBN
37681	736	11	in	in	IN
37681	736	12	steps	step	NNS
37681	736	13	to	to	TO
37681	736	14	aid	aid	VB
37681	736	15	the	the	DT
37681	736	16	eye	eye	NN
37681	736	17	,	,	,
37681	736	18	one	one	CD
37681	736	19	proposition	proposition	NN
37681	736	20	to	to	IN
37681	736	21	a	a	DT
37681	736	22	page	page	NN
37681	736	23	whenever	whenever	WRB
37681	736	24	this	this	DT
37681	736	25	was	be	VBD
37681	736	26	possible	possible	JJ
37681	736	27	.	.	.
37681	737	1	Some	some	DT
37681	737	2	effort	effort	NN
37681	737	3	was	be	VBD
37681	737	4	made	make	VBN
37681	737	5	in	in	IN
37681	737	6	this	this	DT
37681	737	7	direction	direction	NN
37681	737	8	in	in	IN
37681	737	9	France	France	NNP
37681	737	10	about	about	RB
37681	737	11	two	two	CD
37681	737	12	hundred	hundred	CD
37681	737	13	years	year	NNS
37681	737	14	ago	ago	RB
37681	737	15	,	,	,
37681	737	16	but	but	CC
37681	737	17	with	with	IN
37681	737	18	no	no	DT
37681	737	19	success	success	NN
37681	737	20	.	.	.
37681	738	1	The	the	DT
37681	738	2	arrangement	arrangement	NN
37681	738	3	has	have	VBZ
37681	738	4	so	so	RB
37681	738	5	much	much	JJ
37681	738	6	to	to	TO
37681	738	7	commend	commend	VB
37681	738	8	it	-PRON-	PRP
37681	738	9	,	,	,
37681	738	10	however	however	RB
37681	738	11	,	,	,
37681	738	12	the	the	DT
37681	738	13	proof	proof	NN
37681	738	14	being	be	VBG
37681	738	15	so	so	RB
37681	738	16	much	much	RB
37681	738	17	more	more	RBR
37681	738	18	easily	easily	RB
37681	738	19	followed	follow	VBN
37681	738	20	by	by	IN
37681	738	21	the	the	DT
37681	738	22	eye	eye	NN
37681	738	23	than	than	IN
37681	738	24	was	be	VBD
37681	738	25	the	the	DT
37681	738	26	case	case	NN
37681	738	27	in	in	IN
37681	738	28	the	the	DT
37681	738	29	old	old	JJ
37681	738	30	-	-	HYPH
37681	738	31	style	style	NN
37681	738	32	works	work	NNS
37681	738	33	,	,	,
37681	738	34	that	that	IN
37681	738	35	it	-PRON-	PRP
37681	738	36	has	have	VBZ
37681	738	37	of	of	IN
37681	738	38	late	late	RB
37681	738	39	been	be	VBN
37681	738	40	revived	revive	VBN
37681	738	41	.	.	.
37681	739	1	In	in	IN
37681	739	2	this	this	DT
37681	739	3	respect	respect	NN
37681	739	4	the	the	DT
37681	739	5	Wentworth	Wentworth	NNP
37681	739	6	geometry	geometry	NN
37681	739	7	was	be	VBD
37681	739	8	a	a	DT
37681	739	9	pioneer	pioneer	NN
37681	739	10	in	in	IN
37681	739	11	America	America	NNP
37681	739	12	,	,	,
37681	739	13	and	and	CC
37681	739	14	so	so	RB
37681	739	15	successful	successful	JJ
37681	739	16	was	be	VBD
37681	739	17	the	the	DT
37681	739	18	effort	effort	NN
37681	739	19	that	that	WDT
37681	739	20	this	this	DT
37681	739	21	type	type	NN
37681	739	22	of	of	IN
37681	739	23	page	page	NN
37681	739	24	has	have	VBZ
37681	739	25	been	be	VBN
37681	739	26	adopted	adopt	VBN
37681	739	27	,	,	,
37681	739	28	as	as	RB
37681	739	29	far	far	RB
37681	739	30	as	as	IN
37681	739	31	the	the	DT
37681	739	32	various	various	JJ
37681	739	33	writers	writer	NNS
37681	739	34	were	be	VBD
37681	739	35	able	able	JJ
37681	739	36	to	to	TO
37681	739	37	adopt	adopt	VB
37681	739	38	it	-PRON-	PRP
37681	739	39	,	,	,
37681	739	40	in	in	IN
37681	739	41	all	all	DT
37681	739	42	successful	successful	JJ
37681	739	43	geometries	geometry	NNS
37681	739	44	that	that	WDT
37681	739	45	have	have	VBP
37681	739	46	appeared	appear	VBN
37681	739	47	of	of	IN
37681	739	48	late	late	JJ
37681	739	49	years	year	NNS
37681	739	50	in	in	IN
37681	739	51	this	this	DT
37681	739	52	country	country	NN
37681	739	53	.	.	.
37681	740	1	As	as	IN
37681	740	2	a	a	DT
37681	740	3	result	result	NN
37681	740	4	,	,	,
37681	740	5	the	the	DT
37681	740	6	American	american	JJ
37681	740	7	textbooks	textbook	NNS
37681	740	8	on	on	IN
37681	740	9	this	this	DT
37681	740	10	subject	subject	NN
37681	740	11	are	be	VBP
37681	740	12	more	more	RBR
37681	740	13	helpful	helpful	JJ
37681	740	14	and	and	CC
37681	740	15	pleasing	pleasing	JJ
37681	740	16	to	to	IN
37681	740	17	the	the	DT
37681	740	18	eye	eye	NN
37681	740	19	than	than	IN
37681	740	20	those	those	DT
37681	740	21	found	find	VBN
37681	740	22	elsewhere	elsewhere	RB
37681	740	23	.	.	.
37681	741	1	The	the	DT
37681	741	2	latest	late	JJS
37681	741	3	improvements	improvement	NNS
37681	741	4	in	in	IN
37681	741	5	textbook	textbook	NN
37681	741	6	-	-	HYPH
37681	741	7	making	making	NN
37681	741	8	have	have	VBP
37681	741	9	removed	remove	VBN
37681	741	10	most	most	JJS
37681	741	11	of	of	IN
37681	741	12	the	the	DT
37681	741	13	blemishes	blemish	NNS
37681	741	14	of	of	IN
37681	741	15	arrangement	arrangement	NN
37681	741	16	that	that	WDT
37681	741	17	remained	remain	VBD
37681	741	18	,	,	,
37681	741	19	scattering	scatter	VBG
37681	741	20	the	the	DT
37681	741	21	exercises	exercise	NNS
37681	741	22	through	through	IN
37681	741	23	the	the	DT
37681	741	24	book	book	NN
37681	741	25	,	,	,
37681	741	26	grading	grade	VBG
37681	741	27	them	-PRON-	PRP
37681	741	28	with	with	IN
37681	741	29	greater	great	JJR
37681	741	30	care	care	NN
37681	741	31	,	,	,
37681	741	32	and	and	CC
37681	741	33	making	make	VBG
37681	741	34	them	-PRON-	PRP
37681	741	35	more	more	RBR
37681	741	36	modern	modern	JJ
37681	741	37	in	in	IN
37681	741	38	character	character	NN
37681	741	39	.	.	.
37681	742	1	But	but	CC
37681	742	2	the	the	DT
37681	742	3	best	good	JJS
37681	742	4	of	of	IN
37681	742	5	the	the	DT
37681	742	6	latest	late	JJS
37681	742	7	works	work	NNS
37681	742	8	do	do	VBP
37681	742	9	more	more	JJR
37681	742	10	than	than	IN
37681	742	11	this	this	DT
37681	742	12	.	.	.
37681	743	1	They	-PRON-	PRP
37681	743	2	reduce	reduce	VBP
37681	743	3	the	the	DT
37681	743	4	number	number	NN
37681	743	5	of	of	IN
37681	743	6	proved	proved	JJ
37681	743	7	theorems	theorem	NNS
37681	743	8	and	and	CC
37681	743	9	increase	increase	VB
37681	743	10	the	the	DT
37681	743	11	number	number	NN
37681	743	12	of	of	IN
37681	743	13	exercises	exercise	NNS
37681	743	14	,	,	,
37681	743	15	and	and	CC
37681	743	16	they	-PRON-	PRP
37681	743	17	simplify	simplify	VBP
37681	743	18	the	the	DT
37681	743	19	proofs	proof	NNS
37681	743	20	whenever	whenever	WRB
37681	743	21	possible	possible	JJ
37681	743	22	and	and	CC
37681	743	23	eliminate	eliminate	VB
37681	743	24	the	the	DT
37681	743	25	most	most	RBS
37681	743	26	difficult	difficult	JJ
37681	743	27	of	of	IN
37681	743	28	the	the	DT
37681	743	29	exercises	exercise	NNS
37681	743	30	of	of	IN
37681	743	31	twenty	twenty	CD
37681	743	32	-	-	HYPH
37681	743	33	five	five	CD
37681	743	34	years	year	NNS
37681	743	35	ago	ago	RB
37681	743	36	.	.	.
37681	744	1	It	-PRON-	PRP
37681	744	2	would	would	MD
37681	744	3	be	be	VB
37681	744	4	possible	possible	JJ
37681	744	5	to	to	TO
37681	744	6	carry	carry	VB
37681	744	7	this	this	DT
37681	744	8	change	change	NN
37681	744	9	too	too	RB
37681	744	10	far	far	RB
37681	744	11	by	by	IN
37681	744	12	putting	put	VBG
37681	744	13	in	in	RP
37681	744	14	only	only	RB
37681	744	15	half	half	NN
37681	744	16	as	as	RB
37681	744	17	many	many	JJ
37681	744	18	,	,	,
37681	744	19	or	or	CC
37681	744	20	a	a	DT
37681	744	21	quarter	quarter	NN
37681	744	22	as	as	RB
37681	744	23	many	many	JJ
37681	744	24	,	,	,
37681	744	25	regular	regular	JJ
37681	744	26	propositions	proposition	NNS
37681	744	27	,	,	,
37681	744	28	but	but	CC
37681	744	29	it	-PRON-	PRP
37681	744	30	should	should	MD
37681	744	31	not	not	RB
37681	744	32	be	be	VB
37681	744	33	the	the	DT
37681	744	34	object	object	NN
37681	744	35	to	to	TO
37681	744	36	see	see	VB
37681	744	37	how	how	WRB
37681	744	38	the	the	DT
37681	744	39	work	work	NN
37681	744	40	can	can	MD
37681	744	41	be	be	VB
37681	744	42	cut	cut	VBN
37681	744	43	down	down	RP
37681	744	44	,	,	,
37681	744	45	but	but	CC
37681	744	46	to	to	TO
37681	744	47	see	see	VB
37681	744	48	how	how	WRB
37681	744	49	it	-PRON-	PRP
37681	744	50	can	can	MD
37681	744	51	be	be	VB
37681	744	52	improved	improve	VBN
37681	744	53	.	.	.
37681	745	1	What	what	WP
37681	745	2	should	should	MD
37681	745	3	be	be	VB
37681	745	4	the	the	DT
37681	745	5	basis	basis	NN
37681	745	6	of	of	IN
37681	745	7	selection	selection	NN
37681	745	8	of	of	IN
37681	745	9	propositions	proposition	NNS
37681	745	10	and	and	CC
37681	745	11	exercises	exercise	NNS
37681	745	12	?	?	.
37681	746	1	Evidently	evidently	RB
37681	746	2	the	the	DT
37681	746	3	selection	selection	NN
37681	746	4	must	must	MD
37681	746	5	include	include	VB
37681	746	6	the	the	DT
37681	746	7	great	great	JJ
37681	746	8	basal	basal	NN
37681	746	9	propositions	proposition	NNS
37681	746	10	that	that	WDT
37681	746	11	are	be	VBP
37681	746	12	needed	need	VBN
37681	746	13	in	in	IN
37681	746	14	mensuration	mensuration	NN
37681	746	15	and	and	CC
37681	746	16	in	in	IN
37681	746	17	later	late	JJR
37681	746	18	mathematics	mathematic	NNS
37681	746	19	,	,	,
37681	746	20	together	together	RB
37681	746	21	with	with	IN
37681	746	22	others	other	NNS
37681	746	23	that	that	WDT
37681	746	24	are	be	VBP
37681	746	25	necessary	necessary	JJ
37681	746	26	to	to	TO
37681	746	27	prove	prove	VB
37681	746	28	them	-PRON-	PRP
37681	746	29	.	.	.
37681	747	1	Euclid	Euclid	NNP
37681	747	2	's	's	POS
37681	747	3	one	one	CD
37681	747	4	hundred	hundred	CD
37681	747	5	seventy	seventy	CD
37681	747	6	-	-	HYPH
37681	747	7	three	three	CD
37681	747	8	propositions	proposition	NNS
37681	747	9	of	of	IN
37681	747	10	plane	plane	NN
37681	747	11	geometry	geometry	NN
37681	747	12	were	be	VBD
37681	747	13	really	really	RB
37681	747	14	upwards	upwards	JJ
37681	747	15	of	of	IN
37681	747	16	one	one	CD
37681	747	17	hundred	hundred	CD
37681	747	18	eighty	eighty	CD
37681	747	19	,	,	,
37681	747	20	because	because	IN
37681	747	21	he	-PRON-	PRP
37681	747	22	several	several	JJ
37681	747	23	times	time	NNS
37681	747	24	combined	combine	VBD
37681	747	25	two	two	CD
37681	747	26	or	or	CC
37681	747	27	more	more	JJR
37681	747	28	in	in	IN
37681	747	29	one	one	CD
37681	747	30	.	.	.
37681	748	1	These	these	DT
37681	748	2	we	-PRON-	PRP
37681	748	3	may	may	MD
37681	748	4	reduce	reduce	VB
37681	748	5	to	to	IN
37681	748	6	about	about	RB
37681	748	7	one	one	CD
37681	748	8	hundred	hundred	CD
37681	748	9	thirty	thirty	CD
37681	748	10	with	with	IN
37681	748	11	perfect	perfect	JJ
37681	748	12	safety	safety	NN
37681	748	13	,	,	,
37681	748	14	or	or	CC
37681	748	15	less	less	JJR
37681	748	16	than	than	IN
37681	748	17	one	one	CD
37681	748	18	a	a	DT
37681	748	19	day	day	NN
37681	748	20	for	for	IN
37681	748	21	a	a	DT
37681	748	22	school	school	NN
37681	748	23	year	year	NN
37681	748	24	,	,	,
37681	748	25	but	but	CC
37681	748	26	to	to	TO
37681	748	27	reduce	reduce	VB
37681	748	28	still	still	RB
37681	748	29	further	far	RBR
37681	748	30	is	be	VBZ
37681	748	31	undesirable	undesirable	JJ
37681	748	32	as	as	RB
37681	748	33	well	well	RB
37681	748	34	as	as	IN
37681	748	35	unnecessary	unnecessary	JJ
37681	748	36	.	.	.
37681	749	1	It	-PRON-	PRP
37681	749	2	would	would	MD
37681	749	3	not	not	RB
37681	749	4	be	be	VB
37681	749	5	difficult	difficult	JJ
37681	749	6	to	to	TO
37681	749	7	dispense	dispense	VB
37681	749	8	with	with	IN
37681	749	9	a	a	DT
37681	749	10	few	few	JJ
37681	749	11	more	more	JJR
37681	749	12	;	;	:
37681	749	13	indeed	indeed	RB
37681	749	14	,	,	,
37681	749	15	we	-PRON-	PRP
37681	749	16	might	may	MD
37681	749	17	dispense	dispense	VB
37681	749	18	with	with	IN
37681	749	19	thirty	thirty	CD
37681	749	20	more	more	JJR
37681	749	21	if	if	IN
37681	749	22	we	-PRON-	PRP
37681	749	23	should	should	MD
37681	749	24	set	set	VB
37681	749	25	about	about	IN
37681	749	26	it	-PRON-	PRP
37681	749	27	,	,	,
37681	749	28	although	although	IN
37681	749	29	we	-PRON-	PRP
37681	749	30	must	must	MD
37681	749	31	never	never	RB
37681	749	32	forget	forget	VB
37681	749	33	that	that	IN
37681	749	34	a	a	DT
37681	749	35	goodly	goodly	JJ
37681	749	36	number	number	NN
37681	749	37	in	in	IN
37681	749	38	addition	addition	NN
37681	749	39	to	to	IN
37681	749	40	those	those	DT
37681	749	41	needed	need	VBN
37681	749	42	for	for	IN
37681	749	43	the	the	DT
37681	749	44	logical	logical	JJ
37681	749	45	sequence	sequence	NN
37681	749	46	are	be	VBP
37681	749	47	necessary	necessary	JJ
37681	749	48	for	for	IN
37681	749	49	the	the	DT
37681	749	50	wide	wide	JJ
37681	749	51	range	range	NN
37681	749	52	of	of	IN
37681	749	53	exercises	exercise	NNS
37681	749	54	that	that	WDT
37681	749	55	are	be	VBP
37681	749	56	offered	offer	VBN
37681	749	57	.	.	.
37681	750	1	But	but	CC
37681	750	2	let	let	VB
37681	750	3	it	-PRON-	PRP
37681	750	4	be	be	VB
37681	750	5	clear	clear	JJ
37681	750	6	that	that	IN
37681	750	7	if	if	IN
37681	750	8	we	-PRON-	PRP
37681	750	9	teach	teach	VBP
37681	750	10	100	100	CD
37681	750	11	instead	instead	RB
37681	750	12	of	of	IN
37681	750	13	130	130	CD
37681	750	14	,	,	,
37681	750	15	our	-PRON-	PRP$
37681	750	16	results	result	NNS
37681	750	17	are	be	VBP
37681	750	18	liable	liable	JJ
37681	750	19	to	to	TO
37681	750	20	be	be	VB
37681	750	21	about	about	RB
37681	750	22	100/130	100/130	JJ
37681	750	23	as	as	RB
37681	750	24	satisfactory	satisfactory	JJ
37681	750	25	.	.	.
37681	751	1	We	-PRON-	PRP
37681	751	2	may	may	MD
37681	751	3	theorize	theorize	VB
37681	751	4	on	on	IN
37681	751	5	pedagogy	pedagogy	NN
37681	751	6	as	as	IN
37681	751	7	we	-PRON-	PRP
37681	751	8	please	please	VBP
37681	751	9	,	,	,
37681	751	10	but	but	CC
37681	751	11	geometry	geometry	NN
37681	751	12	will	will	MD
37681	751	13	pay	pay	VB
37681	751	14	us	-PRON-	PRP
37681	751	15	about	about	IN
37681	751	16	in	in	IN
37681	751	17	proportion	proportion	NN
37681	751	18	to	to	IN
37681	751	19	what	what	WP
37681	751	20	we	-PRON-	PRP
37681	751	21	give	give	VBP
37681	751	22	.	.	.
37681	752	1	And	and	CC
37681	752	2	as	as	IN
37681	752	3	to	to	IN
37681	752	4	the	the	DT
37681	752	5	exercises	exercise	NNS
37681	752	6	,	,	,
37681	752	7	what	what	WP
37681	752	8	is	be	VBZ
37681	752	9	the	the	DT
37681	752	10	basis	basis	NN
37681	752	11	of	of	IN
37681	752	12	selection	selection	NN
37681	752	13	?	?	.
37681	753	1	In	in	IN
37681	753	2	general	general	JJ
37681	753	3	,	,	,
37681	753	4	let	let	VB
37681	753	5	it	-PRON-	PRP
37681	753	6	be	be	VB
37681	753	7	said	say	VBN
37681	753	8	that	that	IN
37681	753	9	any	any	DT
37681	753	10	exercise	exercise	NN
37681	753	11	that	that	WDT
37681	753	12	pretends	pretend	VBZ
37681	753	13	to	to	TO
37681	753	14	be	be	VB
37681	753	15	real	real	JJ
37681	753	16	should	should	MD
37681	753	17	be	be	VB
37681	753	18	so	so	RB
37681	753	19	,	,	,
37681	753	20	and	and	CC
37681	753	21	that	that	IN
37681	753	22	words	word	NNS
37681	753	23	taken	take	VBN
37681	753	24	from	from	IN
37681	753	25	science	science	NN
37681	753	26	or	or	CC
37681	753	27	measurements	measurement	NNS
37681	753	28	do	do	VBP
37681	753	29	not	not	RB
37681	753	30	necessarily	necessarily	RB
37681	753	31	make	make	VB
37681	753	32	the	the	DT
37681	753	33	problem	problem	NN
37681	753	34	genuine	genuine	JJ
37681	753	35	.	.	.
37681	754	1	To	to	TO
37681	754	2	take	take	VB
37681	754	3	a	a	DT
37681	754	4	proposition	proposition	NN
37681	754	5	and	and	CC
37681	754	6	apply	apply	VB
37681	754	7	it	-PRON-	PRP
37681	754	8	in	in	IN
37681	754	9	a	a	DT
37681	754	10	manner	manner	NN
37681	754	11	that	that	IN
37681	754	12	the	the	DT
37681	754	13	world	world	NN
37681	754	14	never	never	RB
37681	754	15	sanctions	sanction	VBZ
37681	754	16	is	be	VBZ
37681	754	17	to	to	TO
37681	754	18	indulge	indulge	VB
37681	754	19	in	in	IN
37681	754	20	deceit	deceit	NN
37681	754	21	.	.	.
37681	755	1	On	on	IN
37681	755	2	the	the	DT
37681	755	3	other	other	JJ
37681	755	4	hand	hand	NN
37681	755	5	,	,	,
37681	755	6	wholly	wholly	RB
37681	755	7	to	to	TO
37681	755	8	neglect	neglect	VB
37681	755	9	the	the	DT
37681	755	10	common	common	JJ
37681	755	11	applications	application	NNS
37681	755	12	of	of	IN
37681	755	13	geometry	geometry	NN
37681	755	14	to	to	IN
37681	755	15	handwork	handwork	NN
37681	755	16	of	of	IN
37681	755	17	various	various	JJ
37681	755	18	kinds	kind	NNS
37681	755	19	is	be	VBZ
37681	755	20	to	to	TO
37681	755	21	miss	miss	VB
37681	755	22	one	one	CD
37681	755	23	of	of	IN
37681	755	24	our	-PRON-	PRP$
37681	755	25	great	great	JJ
37681	755	26	opportunities	opportunity	NNS
37681	755	27	to	to	TO
37681	755	28	make	make	VB
37681	755	29	the	the	DT
37681	755	30	subject	subject	JJ
37681	755	31	vital	vital	NN
37681	755	32	to	to	IN
37681	755	33	the	the	DT
37681	755	34	pupil	pupil	NN
37681	755	35	,	,	,
37681	755	36	to	to	TO
37681	755	37	arouse	arouse	VB
37681	755	38	new	new	JJ
37681	755	39	interest	interest	NN
37681	755	40	,	,	,
37681	755	41	and	and	CC
37681	755	42	to	to	TO
37681	755	43	give	give	VB
37681	755	44	a	a	DT
37681	755	45	meaning	meaning	NN
37681	755	46	to	to	IN
37681	755	47	it	-PRON-	PRP
37681	755	48	that	that	DT
37681	755	49	is	be	VBZ
37681	755	50	otherwise	otherwise	RB
37681	755	51	wanting	want	VBG
37681	755	52	.	.	.
37681	756	1	It	-PRON-	PRP
37681	756	2	should	should	MD
37681	756	3	always	always	RB
37681	756	4	be	be	VB
37681	756	5	remembered	remember	VBN
37681	756	6	that	that	IN
37681	756	7	mental	mental	JJ
37681	756	8	discipline	discipline	NN
37681	756	9	,	,	,
37681	756	10	whatever	whatever	WDT
37681	756	11	the	the	DT
37681	756	12	phrase	phrase	NN
37681	756	13	may	may	MD
37681	756	14	mean	mean	VB
37681	756	15	,	,	,
37681	756	16	can	can	MD
37681	756	17	as	as	RB
37681	756	18	readily	readily	RB
37681	756	19	be	be	VB
37681	756	20	obtained	obtain	VBN
37681	756	21	from	from	IN
37681	756	22	a	a	DT
37681	756	23	genuine	genuine	JJ
37681	756	24	application	application	NN
37681	756	25	of	of	IN
37681	756	26	a	a	DT
37681	756	27	theorem	theorem	NN
37681	756	28	as	as	IN
37681	756	29	from	from	IN
37681	756	30	a	a	DT
37681	756	31	mere	mere	JJ
37681	756	32	geometric	geometric	JJ
37681	756	33	puzzle	puzzle	NN
37681	756	34	.	.	.
37681	757	1	On	on	IN
37681	757	2	the	the	DT
37681	757	3	other	other	JJ
37681	757	4	hand	hand	NN
37681	757	5	,	,	,
37681	757	6	it	-PRON-	PRP
37681	757	7	is	be	VBZ
37681	757	8	evident	evident	JJ
37681	757	9	that	that	IN
37681	757	10	not	not	RB
37681	757	11	more	more	JJR
37681	757	12	than	than	IN
37681	757	13	25	25	CD
37681	757	14	per	per	NN
37681	757	15	cent	cent	NN
37681	757	16	of	of	IN
37681	757	17	propositions	proposition	NNS
37681	757	18	have	have	VBP
37681	757	19	any	any	DT
37681	757	20	genuine	genuine	JJ
37681	757	21	applications	application	NNS
37681	757	22	outside	outside	RB
37681	757	23	of	of	IN
37681	757	24	geometry	geometry	NN
37681	757	25	,	,	,
37681	757	26	and	and	CC
37681	757	27	that	that	IN
37681	757	28	if	if	IN
37681	757	29	we	-PRON-	PRP
37681	757	30	are	be	VBP
37681	757	31	to	to	TO
37681	757	32	attempt	attempt	VB
37681	757	33	any	any	DT
37681	757	34	applications	application	NNS
37681	757	35	at	at	RB
37681	757	36	all	all	RB
37681	757	37	,	,	,
37681	757	38	these	these	DT
37681	757	39	must	must	MD
37681	757	40	be	be	VB
37681	757	41	sought	seek	VBN
37681	757	42	mainly	mainly	RB
37681	757	43	in	in	IN
37681	757	44	the	the	DT
37681	757	45	field	field	NN
37681	757	46	of	of	IN
37681	757	47	pure	pure	JJ
37681	757	48	geometry	geometry	NN
37681	757	49	.	.	.
37681	758	1	In	in	IN
37681	758	2	the	the	DT
37681	758	3	exercises	exercise	NNS
37681	758	4	,	,	,
37681	758	5	therefore	therefore	RB
37681	758	6	,	,	,
37681	758	7	we	-PRON-	PRP
37681	758	8	seek	seek	VBP
37681	758	9	to	to	IN
37681	758	10	-	-	HYPH
37681	758	11	day	day	NN
37681	758	12	a	a	DT
37681	758	13	sane	sane	NN
37681	758	14	and	and	CC
37681	758	15	a	a	DT
37681	758	16	balanced	balanced	JJ
37681	758	17	book	book	NN
37681	758	18	,	,	,
37681	758	19	giving	give	VBG
37681	758	20	equal	equal	JJ
37681	758	21	weight	weight	NN
37681	758	22	to	to	IN
37681	758	23	theory	theory	NN
37681	758	24	and	and	CC
37681	758	25	to	to	TO
37681	758	26	practice	practice	VB
37681	758	27	,	,	,
37681	758	28	to	to	IN
37681	758	29	the	the	DT
37681	758	30	demands	demand	NNS
37681	758	31	of	of	IN
37681	758	32	the	the	DT
37681	758	33	artisan	artisan	NNP
37681	758	34	and	and	CC
37681	758	35	to	to	IN
37681	758	36	those	those	DT
37681	758	37	of	of	IN
37681	758	38	the	the	DT
37681	758	39	mathematician	mathematician	NN
37681	758	40	,	,	,
37681	758	41	to	to	IN
37681	758	42	the	the	DT
37681	758	43	applications	application	NNS
37681	758	44	of	of	IN
37681	758	45	concrete	concrete	JJ
37681	758	46	science	science	NN
37681	758	47	and	and	CC
37681	758	48	to	to	IN
37681	758	49	those	those	DT
37681	758	50	of	of	IN
37681	758	51	pure	pure	JJ
37681	758	52	geometry	geometry	NN
37681	758	53	,	,	,
37681	758	54	thus	thus	RB
37681	758	55	making	make	VBG
37681	758	56	a	a	DT
37681	758	57	fusion	fusion	NN
37681	758	58	of	of	IN
37681	758	59	pure	pure	JJ
37681	758	60	and	and	CC
37681	758	61	applied	applied	JJ
37681	758	62	mathematics	mathematic	NNS
37681	758	63	,	,	,
37681	758	64	with	with	IN
37681	758	65	the	the	DT
37681	758	66	latter	latter	JJ
37681	758	67	as	as	RB
37681	758	68	prominent	prominent	JJ
37681	758	69	as	as	IN
37681	758	70	the	the	DT
37681	758	71	supply	supply	NN
37681	758	72	of	of	IN
37681	758	73	genuine	genuine	JJ
37681	758	74	problems	problem	NNS
37681	758	75	permits	permit	NNS
37681	758	76	.	.	.
37681	759	1	The	the	DT
37681	759	2	old	old	JJ
37681	759	3	is	be	VBZ
37681	759	4	not	not	RB
37681	759	5	all	all	RB
37681	759	6	bad	bad	JJ
37681	759	7	and	and	CC
37681	759	8	the	the	DT
37681	759	9	new	new	JJ
37681	759	10	is	be	VBZ
37681	759	11	not	not	RB
37681	759	12	all	all	RB
37681	759	13	good	good	JJ
37681	759	14	,	,	,
37681	759	15	and	and	CC
37681	759	16	a	a	DT
37681	759	17	textbook	textbook	NN
37681	759	18	is	be	VBZ
37681	759	19	a	a	DT
37681	759	20	success	success	NN
37681	759	21	in	in	IN
37681	759	22	so	so	RB
37681	759	23	far	far	RB
37681	759	24	as	as	IN
37681	759	25	it	-PRON-	PRP
37681	759	26	selects	select	VBZ
37681	759	27	boldly	boldly	RB
37681	759	28	the	the	DT
37681	759	29	good	good	JJ
37681	759	30	that	that	WDT
37681	759	31	is	be	VBZ
37681	759	32	in	in	IN
37681	759	33	the	the	DT
37681	759	34	old	old	JJ
37681	759	35	and	and	CC
37681	759	36	rejects	reject	VBZ
37681	759	37	with	with	IN
37681	759	38	equal	equal	JJ
37681	759	39	boldness	boldness	NN
37681	759	40	the	the	DT
37681	759	41	bad	bad	JJ
37681	759	42	that	that	WDT
37681	759	43	is	be	VBZ
37681	759	44	in	in	IN
37681	759	45	the	the	DT
37681	759	46	new	new	JJ
37681	759	47	.	.	.
37681	760	1	Lest	lest	IN
37681	760	2	the	the	DT
37681	760	3	nature	nature	NN
37681	760	4	of	of	IN
37681	760	5	the	the	DT
37681	760	6	exercises	exercise	NNS
37681	760	7	of	of	IN
37681	760	8	geometry	geometry	NN
37681	760	9	may	may	MD
37681	760	10	be	be	VB
37681	760	11	misunderstood	misunderstood	NN
37681	760	12	,	,	,
37681	760	13	it	-PRON-	PRP
37681	760	14	is	be	VBZ
37681	760	15	well	well	RB
37681	760	16	that	that	IN
37681	760	17	we	-PRON-	PRP
37681	760	18	consider	consider	VBP
37681	760	19	for	for	IN
37681	760	20	a	a	DT
37681	760	21	moment	moment	NN
37681	760	22	what	what	WP
37681	760	23	constitutes	constitute	VBZ
37681	760	24	a	a	DT
37681	760	25	genuine	genuine	JJ
37681	760	26	application	application	NN
37681	760	27	of	of	IN
37681	760	28	the	the	DT
37681	760	29	subject	subject	NN
37681	760	30	.	.	.
37681	761	1	It	-PRON-	PRP
37681	761	2	is	be	VBZ
37681	761	3	the	the	DT
37681	761	4	ephemeral	ephemeral	JJ
37681	761	5	fashion	fashion	NN
37681	761	6	just	just	RB
37681	761	7	at	at	IN
37681	761	8	present	present	JJ
37681	761	9	in	in	IN
37681	761	10	America	America	NNP
37681	761	11	to	to	TO
37681	761	12	call	call	VB
37681	761	13	these	these	DT
37681	761	14	genuine	genuine	JJ
37681	761	15	applications	application	NNS
37681	761	16	by	by	IN
37681	761	17	the	the	DT
37681	761	18	name	name	NN
37681	761	19	of	of	IN
37681	761	20	"	"	``
37681	761	21	real	real	JJ
37681	761	22	problems	problem	NNS
37681	761	23	.	.	.
37681	761	24	"	"	''
37681	762	1	The	the	DT
37681	762	2	name	name	NN
37681	762	3	is	be	VBZ
37681	762	4	an	an	DT
37681	762	5	unfortunate	unfortunate	JJ
37681	762	6	importation	importation	NN
37681	762	7	,	,	,
37681	762	8	but	but	CC
37681	762	9	that	that	DT
37681	762	10	is	be	VBZ
37681	762	11	not	not	RB
37681	762	12	a	a	DT
37681	762	13	matter	matter	NN
37681	762	14	of	of	IN
37681	762	15	serious	serious	JJ
37681	762	16	moment	moment	NN
37681	762	17	.	.	.
37681	763	1	The	the	DT
37681	763	2	important	important	JJ
37681	763	3	thing	thing	NN
37681	763	4	is	be	VBZ
37681	763	5	that	that	IN
37681	763	6	we	-PRON-	PRP
37681	763	7	should	should	MD
37681	763	8	know	know	VB
37681	763	9	what	what	WP
37681	763	10	makes	make	VBZ
37681	763	11	a	a	DT
37681	763	12	problem	problem	NN
37681	763	13	"	"	``
37681	763	14	real	real	JJ
37681	763	15	"	"	''
37681	763	16	to	to	IN
37681	763	17	the	the	DT
37681	763	18	pupil	pupil	NN
37681	763	19	of	of	IN
37681	763	20	geometry	geometry	NN
37681	763	21	,	,	,
37681	763	22	especially	especially	RB
37681	763	23	as	as	IN
37681	763	24	the	the	DT
37681	763	25	whole	whole	JJ
37681	763	26	thing	thing	NN
37681	763	27	is	be	VBZ
37681	763	28	coming	come	VBG
37681	763	29	rapidly	rapidly	RB
37681	763	30	into	into	IN
37681	763	31	disrepute	disrepute	NN
37681	763	32	through	through	IN
37681	763	33	the	the	DT
37681	763	34	mistaken	mistaken	JJ
37681	763	35	zeal	zeal	NN
37681	763	36	of	of	IN
37681	763	37	some	some	DT
37681	763	38	of	of	IN
37681	763	39	its	-PRON-	PRP$
37681	763	40	supporters	supporter	NNS
37681	763	41	.	.	.
37681	764	1	A	a	DT
37681	764	2	real	real	JJ
37681	764	3	problem	problem	NN
37681	764	4	is	be	VBZ
37681	764	5	a	a	DT
37681	764	6	problem	problem	NN
37681	764	7	that	that	IN
37681	764	8	the	the	DT
37681	764	9	average	average	JJ
37681	764	10	citizen	citizen	NN
37681	764	11	may	may	MD
37681	764	12	sometime	sometime	RB
37681	764	13	be	be	VB
37681	764	14	called	call	VBN
37681	764	15	upon	upon	IN
37681	764	16	to	to	TO
37681	764	17	solve	solve	VB
37681	764	18	;	;	:
37681	764	19	that	that	IN
37681	764	20	,	,	,
37681	764	21	if	if	IN
37681	764	22	so	so	RB
37681	764	23	called	call	VBD
37681	764	24	upon	upon	IN
37681	764	25	,	,	,
37681	764	26	he	-PRON-	PRP
37681	764	27	will	will	MD
37681	764	28	solve	solve	VB
37681	764	29	in	in	IN
37681	764	30	the	the	DT
37681	764	31	manner	manner	NN
37681	764	32	indicated	indicate	VBD
37681	764	33	;	;	:
37681	764	34	and	and	CC
37681	764	35	that	that	DT
37681	764	36	is	be	VBZ
37681	764	37	expressed	express	VBN
37681	764	38	in	in	IN
37681	764	39	terms	term	NNS
37681	764	40	that	that	WDT
37681	764	41	are	be	VBP
37681	764	42	familiar	familiar	JJ
37681	764	43	to	to	IN
37681	764	44	the	the	DT
37681	764	45	pupil	pupil	NN
37681	764	46	.	.	.
37681	765	1	This	this	DT
37681	765	2	definition	definition	NN
37681	765	3	,	,	,
37681	765	4	which	which	WDT
37681	765	5	seems	seem	VBZ
37681	765	6	fairly	fairly	RB
37681	765	7	to	to	TO
37681	765	8	state	state	VB
37681	765	9	the	the	DT
37681	765	10	conditions	condition	NNS
37681	765	11	under	under	IN
37681	765	12	which	which	WDT
37681	765	13	a	a	DT
37681	765	14	problem	problem	NN
37681	765	15	can	can	MD
37681	765	16	be	be	VB
37681	765	17	called	call	VBN
37681	765	18	"	"	``
37681	765	19	real	real	JJ
37681	765	20	"	"	''
37681	765	21	in	in	IN
37681	765	22	the	the	DT
37681	765	23	schoolroom	schoolroom	NN
37681	765	24	,	,	,
37681	765	25	involves	involve	VBZ
37681	765	26	three	three	CD
37681	765	27	points	point	NNS
37681	765	28	:	:	:
37681	765	29	(	(	-LRB-
37681	765	30	1	1	LS
37681	765	31	)	)	-RRB-
37681	765	32	people	people	NNS
37681	765	33	must	must	MD
37681	765	34	be	be	VB
37681	765	35	liable	liable	JJ
37681	765	36	to	to	TO
37681	765	37	meet	meet	VB
37681	765	38	such	such	PDT
37681	765	39	a	a	DT
37681	765	40	problem	problem	NN
37681	765	41	;	;	,
37681	765	42	(	(	-LRB-
37681	765	43	2	2	LS
37681	765	44	)	)	-RRB-
37681	765	45	in	in	IN
37681	765	46	that	that	DT
37681	765	47	case	case	NN
37681	765	48	they	-PRON-	PRP
37681	765	49	will	will	MD
37681	765	50	solve	solve	VB
37681	765	51	it	-PRON-	PRP
37681	765	52	in	in	IN
37681	765	53	the	the	DT
37681	765	54	way	way	NN
37681	765	55	suggested	suggest	VBN
37681	765	56	by	by	IN
37681	765	57	the	the	DT
37681	765	58	book	book	NN
37681	765	59	;	;	,
37681	765	60	(	(	-LRB-
37681	765	61	3	3	LS
37681	765	62	)	)	-RRB-
37681	765	63	it	-PRON-	PRP
37681	765	64	must	must	MD
37681	765	65	be	be	VB
37681	765	66	clothed	clothe	VBN
37681	765	67	in	in	IN
37681	765	68	language	language	NN
37681	765	69	familiar	familiar	JJ
37681	765	70	to	to	IN
37681	765	71	the	the	DT
37681	765	72	pupil	pupil	NN
37681	765	73	.	.	.
37681	766	1	For	for	IN
37681	766	2	example	example	NN
37681	766	3	,	,	,
37681	766	4	let	let	VB
37681	766	5	the	the	DT
37681	766	6	problem	problem	NN
37681	766	7	be	be	VB
37681	766	8	to	to	TO
37681	766	9	find	find	VB
37681	766	10	the	the	DT
37681	766	11	dimensions	dimension	NNS
37681	766	12	of	of	IN
37681	766	13	a	a	DT
37681	766	14	rectangular	rectangular	JJ
37681	766	15	field	field	NN
37681	766	16	,	,	,
37681	766	17	the	the	DT
37681	766	18	data	datum	NNS
37681	766	19	being	be	VBG
37681	766	20	the	the	DT
37681	766	21	area	area	NN
37681	766	22	of	of	IN
37681	766	23	the	the	DT
37681	766	24	field	field	NN
37681	766	25	and	and	CC
37681	766	26	the	the	DT
37681	766	27	area	area	NN
37681	766	28	of	of	IN
37681	766	29	a	a	DT
37681	766	30	road	road	NN
37681	766	31	four	four	CD
37681	766	32	rods	rod	NNS
37681	766	33	wide	wide	JJ
37681	766	34	that	that	WDT
37681	766	35	is	be	VBZ
37681	766	36	cut	cut	VBN
37681	766	37	from	from	IN
37681	766	38	three	three	CD
37681	766	39	sides	side	NNS
37681	766	40	of	of	IN
37681	766	41	the	the	DT
37681	766	42	field	field	NN
37681	766	43	.	.	.
37681	767	1	As	as	IN
37681	767	2	a	a	DT
37681	767	3	real	real	JJ
37681	767	4	problem	problem	NN
37681	767	5	this	this	DT
37681	767	6	is	be	VBZ
37681	767	7	ridiculous	ridiculous	JJ
37681	767	8	,	,	,
37681	767	9	since	since	IN
37681	767	10	no	no	DT
37681	767	11	one	one	NN
37681	767	12	would	would	MD
37681	767	13	ever	ever	RB
37681	767	14	meet	meet	VB
37681	767	15	such	such	PDT
37681	767	16	a	a	DT
37681	767	17	case	case	NN
37681	767	18	outside	outside	IN
37681	767	19	the	the	DT
37681	767	20	puzzle	puzzle	NNP
37681	767	21	department	department	NNP
37681	767	22	of	of	IN
37681	767	23	a	a	DT
37681	767	24	schoolroom	schoolroom	NN
37681	767	25	.	.	.
37681	768	1	Again	again	RB
37681	768	2	,	,	,
37681	768	3	if	if	IN
37681	768	4	by	by	IN
37681	768	5	any	any	DT
37681	768	6	stretch	stretch	NN
37681	768	7	of	of	IN
37681	768	8	a	a	DT
37681	768	9	vigorous	vigorous	JJ
37681	768	10	imagination	imagination	NN
37681	768	11	any	any	DT
37681	768	12	human	human	NN
37681	768	13	being	being	NN
37681	768	14	should	should	MD
37681	768	15	care	care	VB
37681	768	16	to	to	TO
37681	768	17	find	find	VB
37681	768	18	the	the	DT
37681	768	19	area	area	NN
37681	768	20	of	of	IN
37681	768	21	a	a	DT
37681	768	22	piece	piece	NN
37681	768	23	of	of	IN
37681	768	24	glass	glass	NN
37681	768	25	,	,	,
37681	768	26	bounded	bound	VBN
37681	768	27	by	by	IN
37681	768	28	the	the	DT
37681	768	29	arcs	arc	NNS
37681	768	30	of	of	IN
37681	768	31	circles	circle	NNS
37681	768	32	,	,	,
37681	768	33	in	in	IN
37681	768	34	a	a	DT
37681	768	35	Gothic	gothic	JJ
37681	768	36	window	window	NN
37681	768	37	in	in	IN
37681	768	38	York	York	NNP
37681	768	39	Minster	Minster	NNP
37681	768	40	,	,	,
37681	768	41	it	-PRON-	PRP
37681	768	42	is	be	VBZ
37681	768	43	fairly	fairly	RB
37681	768	44	certain	certain	JJ
37681	768	45	that	that	IN
37681	768	46	he	-PRON-	PRP
37681	768	47	would	would	MD
37681	768	48	not	not	RB
37681	768	49	go	go	VB
37681	768	50	about	about	IN
37681	768	51	it	-PRON-	PRP
37681	768	52	in	in	IN
37681	768	53	the	the	DT
37681	768	54	way	way	NN
37681	768	55	suggested	suggest	VBN
37681	768	56	in	in	IN
37681	768	57	some	some	DT
37681	768	58	of	of	IN
37681	768	59	the	the	DT
37681	768	60	earnest	earnest	JJ
37681	768	61	attempts	attempt	NNS
37681	768	62	that	that	WDT
37681	768	63	have	have	VBP
37681	768	64	been	be	VBN
37681	768	65	made	make	VBN
37681	768	66	by	by	IN
37681	768	67	several	several	JJ
37681	768	68	successful	successful	JJ
37681	768	69	teachers	teacher	NNS
37681	768	70	to	to	TO
37681	768	71	add	add	VB
37681	768	72	interest	interest	NN
37681	768	73	to	to	TO
37681	768	74	geometry	geometry	VB
37681	768	75	.	.	.
37681	769	1	And	and	CC
37681	769	2	for	for	IN
37681	769	3	the	the	DT
37681	769	4	third	third	JJ
37681	769	5	point	point	NN
37681	769	6	,	,	,
37681	769	7	a	a	DT
37681	769	8	problem	problem	NN
37681	769	9	is	be	VBZ
37681	769	10	not	not	RB
37681	769	11	real	real	JJ
37681	769	12	to	to	IN
37681	769	13	a	a	DT
37681	769	14	pupil	pupil	NN
37681	769	15	simply	simply	RB
37681	769	16	because	because	IN
37681	769	17	it	-PRON-	PRP
37681	769	18	relates	relate	VBZ
37681	769	19	to	to	IN
37681	769	20	moments	moment	NNS
37681	769	21	of	of	IN
37681	769	22	inertia	inertia	NN
37681	769	23	or	or	CC
37681	769	24	the	the	DT
37681	769	25	tensile	tensile	JJ
37681	769	26	strength	strength	NN
37681	769	27	of	of	IN
37681	769	28	a	a	DT
37681	769	29	steel	steel	NN
37681	769	30	bar	bar	NN
37681	769	31	.	.	.
37681	770	1	Indeed	indeed	RB
37681	770	2	,	,	,
37681	770	3	it	-PRON-	PRP
37681	770	4	is	be	VBZ
37681	770	5	unreal	unreal	JJ
37681	770	6	precisely	precisely	RB
37681	770	7	because	because	IN
37681	770	8	it	-PRON-	PRP
37681	770	9	does	do	VBZ
37681	770	10	talk	talk	VB
37681	770	11	of	of	IN
37681	770	12	these	these	DT
37681	770	13	things	thing	NNS
37681	770	14	at	at	IN
37681	770	15	a	a	DT
37681	770	16	time	time	NN
37681	770	17	when	when	WRB
37681	770	18	they	-PRON-	PRP
37681	770	19	are	be	VBP
37681	770	20	unfamiliar	unfamiliar	JJ
37681	770	21	,	,	,
37681	770	22	and	and	CC
37681	770	23	properly	properly	RB
37681	770	24	so	so	RB
37681	770	25	,	,	,
37681	770	26	to	to	IN
37681	770	27	the	the	DT
37681	770	28	pupil	pupil	NN
37681	770	29	.	.	.
37681	771	1	It	-PRON-	PRP
37681	771	2	must	must	MD
37681	771	3	not	not	RB
37681	771	4	be	be	VB
37681	771	5	thought	think	VBN
37681	771	6	that	that	IN
37681	771	7	puzzle	puzzle	NN
37681	771	8	problems	problem	NNS
37681	771	9	,	,	,
37681	771	10	and	and	CC
37681	771	11	unreal	unreal	JJ
37681	771	12	problems	problem	NNS
37681	771	13	generally	generally	RB
37681	771	14	,	,	,
37681	771	15	have	have	VBP
37681	771	16	no	no	DT
37681	771	17	value	value	NN
37681	771	18	.	.	.
37681	772	1	All	all	DT
37681	772	2	that	that	WDT
37681	772	3	is	be	VBZ
37681	772	4	insisted	insist	VBN
37681	772	5	upon	upon	IN
37681	772	6	is	be	VBZ
37681	772	7	that	that	IN
37681	772	8	such	such	JJ
37681	772	9	problems	problem	NNS
37681	772	10	as	as	IN
37681	772	11	the	the	DT
37681	772	12	above	above	RB
37681	772	13	are	be	VBP
37681	772	14	not	not	RB
37681	772	15	"	"	``
37681	772	16	real	real	JJ
37681	772	17	,	,	,
37681	772	18	"	"	''
37681	772	19	and	and	CC
37681	772	20	that	that	IN
37681	772	21	about	about	RB
37681	772	22	90	90	CD
37681	772	23	per	per	NN
37681	772	24	cent	cent	NN
37681	772	25	of	of	IN
37681	772	26	problems	problem	NNS
37681	772	27	that	that	WDT
37681	772	28	go	go	VBP
37681	772	29	by	by	IN
37681	772	30	this	this	DT
37681	772	31	name	name	NN
37681	772	32	are	be	VBP
37681	772	33	equally	equally	RB
37681	772	34	lacking	lacking	JJ
37681	772	35	in	in	IN
37681	772	36	the	the	DT
37681	772	37	elements	element	NNS
37681	772	38	that	that	WDT
37681	772	39	make	make	VBP
37681	772	40	for	for	IN
37681	772	41	reality	reality	NN
37681	772	42	in	in	IN
37681	772	43	this	this	DT
37681	772	44	sense	sense	NN
37681	772	45	of	of	IN
37681	772	46	the	the	DT
37681	772	47	word	word	NN
37681	772	48	.	.	.
37681	773	1	For	for	IN
37681	773	2	the	the	DT
37681	773	3	other	other	JJ
37681	773	4	10	10	CD
37681	773	5	per	per	NN
37681	773	6	cent	cent	NN
37681	773	7	of	of	IN
37681	773	8	such	such	JJ
37681	773	9	problems	problem	NNS
37681	773	10	we	-PRON-	PRP
37681	773	11	should	should	MD
37681	773	12	be	be	VB
37681	773	13	thankful	thankful	JJ
37681	773	14	,	,	,
37681	773	15	and	and	CC
37681	773	16	we	-PRON-	PRP
37681	773	17	should	should	MD
37681	773	18	endeavor	endeavor	VB
37681	773	19	to	to	TO
37681	773	20	add	add	VB
37681	773	21	to	to	IN
37681	773	22	the	the	DT
37681	773	23	number	number	NN
37681	773	24	.	.	.
37681	774	1	As	as	IN
37681	774	2	for	for	IN
37681	774	3	the	the	DT
37681	774	4	great	great	JJ
37681	774	5	mass	mass	NN
37681	774	6	,	,	,
37681	774	7	however	however	RB
37681	774	8	,	,	,
37681	774	9	they	-PRON-	PRP
37681	774	10	are	be	VBP
37681	774	11	no	no	RB
37681	774	12	better	well	JJR
37681	774	13	than	than	IN
37681	774	14	those	those	DT
37681	774	15	that	that	WDT
37681	774	16	have	have	VBP
37681	774	17	stood	stand	VBN
37681	774	18	the	the	DT
37681	774	19	test	test	NN
37681	774	20	of	of	IN
37681	774	21	generations	generation	NNS
37681	774	22	,	,	,
37681	774	23	and	and	CC
37681	774	24	by	by	IN
37681	774	25	their	-PRON-	PRP$
37681	774	26	pretense	pretense	NN
37681	774	27	they	-PRON-	PRP
37681	774	28	are	be	VBP
37681	774	29	distinctly	distinctly	RB
37681	774	30	worse	bad	JJR
37681	774	31	.	.	.
37681	775	1	It	-PRON-	PRP
37681	775	2	is	be	VBZ
37681	775	3	proper	proper	JJ
37681	775	4	,	,	,
37681	775	5	however	however	RB
37681	775	6	,	,	,
37681	775	7	to	to	TO
37681	775	8	consider	consider	VB
37681	775	9	whether	whether	IN
37681	775	10	a	a	DT
37681	775	11	teacher	teacher	NN
37681	775	12	is	be	VBZ
37681	775	13	not	not	RB
37681	775	14	justified	justify	VBN
37681	775	15	in	in	IN
37681	775	16	relating	relate	VBG
37681	775	17	his	-PRON-	PRP$
37681	775	18	work	work	NN
37681	775	19	to	to	IN
37681	775	20	those	those	DT
37681	775	21	geometric	geometric	JJ
37681	775	22	forms	form	NNS
37681	775	23	that	that	WDT
37681	775	24	are	be	VBP
37681	775	25	found	find	VBN
37681	775	26	in	in	IN
37681	775	27	art	art	NN
37681	775	28	,	,	,
37681	775	29	let	let	VB
37681	775	30	us	-PRON-	PRP
37681	775	31	say	say	VB
37681	775	32	in	in	IN
37681	775	33	floor	floor	NN
37681	775	34	patterns	pattern	NNS
37681	775	35	,	,	,
37681	775	36	in	in	IN
37681	775	37	domes	dome	NNS
37681	775	38	of	of	IN
37681	775	39	buildings	building	NNS
37681	775	40	,	,	,
37681	775	41	in	in	IN
37681	775	42	oilcloth	oilcloth	JJ
37681	775	43	designs	design	NNS
37681	775	44	,	,	,
37681	775	45	and	and	CC
37681	775	46	the	the	DT
37681	775	47	like	like	JJ
37681	775	48	,	,	,
37681	775	49	for	for	IN
37681	775	50	the	the	DT
37681	775	51	purpose	purpose	NN
37681	775	52	of	of	IN
37681	775	53	arousing	arouse	VBG
37681	775	54	interest	interest	NN
37681	775	55	,	,	,
37681	775	56	if	if	IN
37681	775	57	for	for	IN
37681	775	58	no	no	DT
37681	775	59	other	other	JJ
37681	775	60	reason	reason	NN
37681	775	61	.	.	.
37681	776	1	The	the	DT
37681	776	2	answer	answer	NN
37681	776	3	is	be	VBZ
37681	776	4	apparent	apparent	JJ
37681	776	5	to	to	IN
37681	776	6	any	any	DT
37681	776	7	teacher	teacher	NN
37681	776	8	:	:	:
37681	776	9	It	-PRON-	PRP
37681	776	10	is	be	VBZ
37681	776	11	certainly	certainly	RB
37681	776	12	justifiable	justifiable	JJ
37681	776	13	to	to	TO
37681	776	14	arouse	arouse	VB
37681	776	15	the	the	DT
37681	776	16	pupil	pupil	NN
37681	776	17	's	's	POS
37681	776	18	interest	interest	NN
37681	776	19	in	in	IN
37681	776	20	his	-PRON-	PRP$
37681	776	21	subject	subject	NN
37681	776	22	,	,	,
37681	776	23	and	and	CC
37681	776	24	to	to	TO
37681	776	25	call	call	VB
37681	776	26	his	-PRON-	PRP$
37681	776	27	attention	attention	NN
37681	776	28	to	to	IN
37681	776	29	the	the	DT
37681	776	30	fact	fact	NN
37681	776	31	that	that	IN
37681	776	32	geometric	geometric	JJ
37681	776	33	design	design	NN
37681	776	34	plays	play	VBZ
37681	776	35	an	an	DT
37681	776	36	important	important	JJ
37681	776	37	part	part	NN
37681	776	38	in	in	IN
37681	776	39	art	art	NN
37681	776	40	;	;	:
37681	776	41	but	but	CC
37681	776	42	we	-PRON-	PRP
37681	776	43	must	must	MD
37681	776	44	see	see	VB
37681	776	45	to	to	IN
37681	776	46	it	-PRON-	PRP
37681	776	47	that	that	IN
37681	776	48	our	-PRON-	PRP$
37681	776	49	efforts	effort	NNS
37681	776	50	accomplish	accomplish	VBP
37681	776	51	this	this	DT
37681	776	52	purpose	purpose	NN
37681	776	53	.	.	.
37681	777	1	To	to	TO
37681	777	2	make	make	VB
37681	777	3	a	a	DT
37681	777	4	course	course	NN
37681	777	5	in	in	IN
37681	777	6	geometry	geometry	NN
37681	777	7	one	one	CD
37681	777	8	on	on	IN
37681	777	9	oilcloth	oilcloth	JJ
37681	777	10	design	design	NN
37681	777	11	would	would	MD
37681	777	12	be	be	VB
37681	777	13	absurd	absurd	JJ
37681	777	14	,	,	,
37681	777	15	and	and	CC
37681	777	16	nothing	nothing	NN
37681	777	17	more	more	RBR
37681	777	18	unprofitable	unprofitable	JJ
37681	777	19	or	or	CC
37681	777	20	depressing	depressing	JJ
37681	777	21	could	could	MD
37681	777	22	be	be	VB
37681	777	23	imagined	imagine	VBN
37681	777	24	in	in	IN
37681	777	25	connection	connection	NN
37681	777	26	with	with	IN
37681	777	27	this	this	DT
37681	777	28	subject	subject	NN
37681	777	29	.	.	.
37681	778	1	Of	of	RB
37681	778	2	course	course	RB
37681	778	3	no	no	DT
37681	778	4	one	one	PRP
37681	778	5	would	would	MD
37681	778	6	advocate	advocate	VB
37681	778	7	such	such	PDT
37681	778	8	an	an	DT
37681	778	9	extreme	extreme	NN
37681	778	10	,	,	,
37681	778	11	but	but	CC
37681	778	12	it	-PRON-	PRP
37681	778	13	sometimes	sometimes	RB
37681	778	14	seems	seem	VBZ
37681	778	15	as	as	IN
37681	778	16	if	if	IN
37681	778	17	we	-PRON-	PRP
37681	778	18	are	be	VBP
37681	778	19	getting	get	VBG
37681	778	20	painfully	painfully	RB
37681	778	21	near	near	IN
37681	778	22	it	-PRON-	PRP
37681	778	23	in	in	IN
37681	778	24	certain	certain	JJ
37681	778	25	schools	school	NNS
37681	778	26	.	.	.
37681	779	1	A	a	DT
37681	779	2	pupil	pupil	NN
37681	779	3	has	have	VBZ
37681	779	4	a	a	DT
37681	779	5	passing	pass	VBG
37681	779	6	interest	interest	NN
37681	779	7	in	in	IN
37681	779	8	geometric	geometric	JJ
37681	779	9	design	design	NN
37681	779	10	.	.	.
37681	780	1	He	-PRON-	PRP
37681	780	2	should	should	MD
37681	780	3	learn	learn	VB
37681	780	4	to	to	TO
37681	780	5	use	use	VB
37681	780	6	the	the	DT
37681	780	7	instruments	instrument	NNS
37681	780	8	of	of	IN
37681	780	9	geometry	geometry	NN
37681	780	10	,	,	,
37681	780	11	and	and	CC
37681	780	12	he	-PRON-	PRP
37681	780	13	learns	learn	VBZ
37681	780	14	this	this	DT
37681	780	15	most	most	RBS
37681	780	16	easily	easily	RB
37681	780	17	by	by	IN
37681	780	18	drawing	draw	VBG
37681	780	19	a	a	DT
37681	780	20	few	few	JJ
37681	780	21	such	such	JJ
37681	780	22	patterns	pattern	NNS
37681	780	23	.	.	.
37681	781	1	But	but	CC
37681	781	2	to	to	TO
37681	781	3	keep	keep	VB
37681	781	4	him	-PRON-	PRP
37681	781	5	week	week	NN
37681	781	6	after	after	IN
37681	781	7	week	week	NN
37681	781	8	on	on	IN
37681	781	9	questions	question	NNS
37681	781	10	relating	relate	VBG
37681	781	11	to	to	IN
37681	781	12	such	such	JJ
37681	781	13	designs	design	NNS
37681	781	14	of	of	IN
37681	781	15	however	however	RB
37681	781	16	great	great	JJ
37681	781	17	variety	variety	NN
37681	781	18	,	,	,
37681	781	19	and	and	CC
37681	781	20	especially	especially	RB
37681	781	21	to	to	TO
37681	781	22	keep	keep	VB
37681	781	23	him	-PRON-	PRP
37681	781	24	upon	upon	IN
37681	781	25	designs	design	NNS
37681	781	26	relating	relate	VBG
37681	781	27	to	to	IN
37681	781	28	only	only	RB
37681	781	29	one	one	CD
37681	781	30	or	or	CC
37681	781	31	two	two	CD
37681	781	32	types	type	NNS
37681	781	33	,	,	,
37681	781	34	is	be	VBZ
37681	781	35	neither	neither	DT
37681	781	36	sound	sound	JJ
37681	781	37	educational	educational	JJ
37681	781	38	policy	policy	NN
37681	781	39	nor	nor	CC
37681	781	40	even	even	RB
37681	781	41	common	common	JJ
37681	781	42	sense	sense	NN
37681	781	43	.	.	.
37681	782	1	That	that	IN
37681	782	2	this	this	DT
37681	782	3	enthusiastic	enthusiastic	JJ
37681	782	4	teacher	teacher	NN
37681	782	5	or	or	CC
37681	782	6	that	that	IN
37681	782	7	one	one	CD
37681	782	8	succeeds	succeed	VBZ
37681	782	9	by	by	IN
37681	782	10	such	such	PDT
37681	782	11	a	a	DT
37681	782	12	plan	plan	NN
37681	782	13	is	be	VBZ
37681	782	14	of	of	IN
37681	782	15	no	no	DT
37681	782	16	significance	significance	NN
37681	782	17	;	;	:
37681	782	18	it	-PRON-	PRP
37681	782	19	is	be	VBZ
37681	782	20	the	the	DT
37681	782	21	enthusiasm	enthusiasm	NN
37681	782	22	that	that	WDT
37681	782	23	succeeds	succeed	VBZ
37681	782	24	,	,	,
37681	782	25	not	not	RB
37681	782	26	the	the	DT
37681	782	27	plan	plan	NN
37681	782	28	.	.	.
37681	783	1	The	the	DT
37681	783	2	experience	experience	NN
37681	783	3	of	of	IN
37681	783	4	the	the	DT
37681	783	5	world	world	NN
37681	783	6	is	be	VBZ
37681	783	7	that	that	IN
37681	783	8	pupils	pupil	NNS
37681	783	9	of	of	IN
37681	783	10	geometry	geometry	NN
37681	783	11	like	like	VBP
37681	783	12	to	to	TO
37681	783	13	use	use	VB
37681	783	14	the	the	DT
37681	783	15	subject	subject	NN
37681	783	16	practically	practically	RB
37681	783	17	,	,	,
37681	783	18	but	but	CC
37681	783	19	that	that	IN
37681	783	20	they	-PRON-	PRP
37681	783	21	are	be	VBP
37681	783	22	more	more	RBR
37681	783	23	interested	interested	JJ
37681	783	24	in	in	IN
37681	783	25	the	the	DT
37681	783	26	pure	pure	JJ
37681	783	27	theory	theory	NN
37681	783	28	than	than	IN
37681	783	29	in	in	IN
37681	783	30	any	any	DT
37681	783	31	fictitious	fictitious	JJ
37681	783	32	applications	application	NNS
37681	783	33	,	,	,
37681	783	34	and	and	CC
37681	783	35	this	this	DT
37681	783	36	is	be	VBZ
37681	783	37	why	why	WRB
37681	783	38	pure	pure	JJ
37681	783	39	geometry	geometry	NN
37681	783	40	has	have	VBZ
37681	783	41	endured	endure	VBN
37681	783	42	,	,	,
37681	783	43	while	while	IN
37681	783	44	the	the	DT
37681	783	45	great	great	JJ
37681	783	46	mass	mass	NN
37681	783	47	of	of	IN
37681	783	48	applied	applied	JJ
37681	783	49	geometry	geometry	NN
37681	783	50	that	that	WDT
37681	783	51	was	be	VBD
37681	783	52	brought	bring	VBN
37681	783	53	forward	forward	RB
37681	783	54	some	some	DT
37681	783	55	three	three	CD
37681	783	56	hundred	hundred	CD
37681	783	57	years	year	NNS
37681	783	58	ago	ago	RB
37681	783	59	has	have	VBZ
37681	783	60	long	long	RB
37681	783	61	since	since	RB
37681	783	62	been	be	VBN
37681	783	63	forgotten	forget	VBN
37681	783	64	.	.	.
37681	784	1	The	the	DT
37681	784	2	question	question	NN
37681	784	3	of	of	IN
37681	784	4	the	the	DT
37681	784	5	real	real	JJ
37681	784	6	applications	application	NNS
37681	784	7	of	of	IN
37681	784	8	the	the	DT
37681	784	9	subject	subject	NN
37681	784	10	is	be	VBZ
37681	784	11	considered	consider	VBN
37681	784	12	in	in	IN
37681	784	13	subsequent	subsequent	JJ
37681	784	14	chapters	chapter	NNS
37681	784	15	.	.	.
37681	785	1	In	in	IN
37681	785	2	Chapter	chapter	NN
37681	785	3	VI	VI	NNP
37681	785	4	we	-PRON-	PRP
37681	785	5	considered	consider	VBD
37681	785	6	the	the	DT
37681	785	7	question	question	NN
37681	785	8	of	of	IN
37681	785	9	the	the	DT
37681	785	10	number	number	NN
37681	785	11	of	of	IN
37681	785	12	regular	regular	JJ
37681	785	13	propositions	proposition	NNS
37681	785	14	to	to	TO
37681	785	15	be	be	VB
37681	785	16	expected	expect	VBN
37681	785	17	in	in	IN
37681	785	18	the	the	DT
37681	785	19	text	text	NN
37681	785	20	,	,	,
37681	785	21	and	and	CC
37681	785	22	we	-PRON-	PRP
37681	785	23	have	have	VBP
37681	785	24	just	just	RB
37681	785	25	considered	consider	VBN
37681	785	26	the	the	DT
37681	785	27	nature	nature	NN
37681	785	28	of	of	IN
37681	785	29	the	the	DT
37681	785	30	exercises	exercise	NNS
37681	785	31	which	which	WDT
37681	785	32	should	should	MD
37681	785	33	follow	follow	VB
37681	785	34	those	those	DT
37681	785	35	propositions	proposition	NNS
37681	785	36	.	.	.
37681	786	1	It	-PRON-	PRP
37681	786	2	is	be	VBZ
37681	786	3	well	well	JJ
37681	786	4	to	to	TO
37681	786	5	turn	turn	VB
37681	786	6	our	-PRON-	PRP$
37681	786	7	attention	attention	NN
37681	786	8	next	next	RB
37681	786	9	to	to	IN
37681	786	10	the	the	DT
37681	786	11	nature	nature	NN
37681	786	12	of	of	IN
37681	786	13	the	the	DT
37681	786	14	proofs	proof	NNS
37681	786	15	of	of	IN
37681	786	16	the	the	DT
37681	786	17	basal	basal	NN
37681	786	18	theorems	theorem	NNS
37681	786	19	.	.	.
37681	787	1	Shall	Shall	MD
37681	787	2	they	-PRON-	PRP
37681	787	3	appear	appear	VB
37681	787	4	in	in	IN
37681	787	5	full	full	JJ
37681	787	6	?	?	.
37681	788	1	Shall	Shall	MD
37681	788	2	they	-PRON-	PRP
37681	788	3	be	be	VB
37681	788	4	merely	merely	RB
37681	788	5	suggested	suggest	VBN
37681	788	6	demonstrations	demonstration	NNS
37681	788	7	?	?	.
37681	789	1	Shall	Shall	MD
37681	789	2	they	-PRON-	PRP
37681	789	3	be	be	VB
37681	789	4	only	only	RB
37681	789	5	a	a	DT
37681	789	6	series	series	NN
37681	789	7	of	of	IN
37681	789	8	questions	question	NNS
37681	789	9	that	that	WDT
37681	789	10	lead	lead	VBP
37681	789	11	to	to	IN
37681	789	12	the	the	DT
37681	789	13	proof	proof	NN
37681	789	14	?	?	.
37681	790	1	Shall	Shall	MD
37681	790	2	the	the	DT
37681	790	3	proofs	proof	NNS
37681	790	4	be	be	VB
37681	790	5	omitted	omit	VBN
37681	790	6	entirely	entirely	RB
37681	790	7	?	?	.
37681	791	1	Or	or	CC
37681	791	2	shall	shall	MD
37681	791	3	there	there	EX
37681	791	4	be	be	VB
37681	791	5	some	some	DT
37681	791	6	combination	combination	NN
37681	791	7	of	of	IN
37681	791	8	these	these	DT
37681	791	9	plans	plan	NNS
37681	791	10	?	?	.
37681	792	1	The	the	DT
37681	792	2	natural	natural	JJ
37681	792	3	temptation	temptation	NN
37681	792	4	in	in	IN
37681	792	5	the	the	DT
37681	792	6	nervous	nervous	JJ
37681	792	7	atmosphere	atmosphere	NN
37681	792	8	of	of	IN
37681	792	9	America	America	NNP
37681	792	10	is	be	VBZ
37681	792	11	to	to	TO
37681	792	12	listen	listen	VB
37681	792	13	to	to	IN
37681	792	14	the	the	DT
37681	792	15	voice	voice	NN
37681	792	16	of	of	IN
37681	792	17	the	the	DT
37681	792	18	mob	mob	NN
37681	792	19	and	and	CC
37681	792	20	to	to	TO
37681	792	21	proceed	proceed	VB
37681	792	22	at	at	IN
37681	792	23	once	once	RB
37681	792	24	to	to	IN
37681	792	25	lynch	lynch	NNP
37681	792	26	Euclid	Euclid	NNP
37681	792	27	and	and	CC
37681	792	28	every	every	DT
37681	792	29	one	one	NN
37681	792	30	who	who	WP
37681	792	31	stands	stand	VBZ
37681	792	32	for	for	IN
37681	792	33	that	that	DT
37681	792	34	for	for	IN
37681	792	35	which	which	WDT
37681	792	36	the	the	DT
37681	792	37	"	"	``
37681	792	38	Elements	Elements	NNPS
37681	792	39	"	"	''
37681	792	40	has	have	VBZ
37681	792	41	stood	stand	VBN
37681	792	42	these	these	DT
37681	792	43	two	two	CD
37681	792	44	thousand	thousand	CD
37681	792	45	years	year	NNS
37681	792	46	.	.	.
37681	793	1	This	this	DT
37681	793	2	is	be	VBZ
37681	793	3	what	what	WP
37681	793	4	some	some	DT
37681	793	5	who	who	WP
37681	793	6	wish	wish	VBP
37681	793	7	to	to	TO
37681	793	8	be	be	VB
37681	793	9	considered	consider	VBN
37681	793	10	as	as	IN
37681	793	11	educators	educator	NNS
37681	793	12	tend	tend	VBP
37681	793	13	to	to	TO
37681	793	14	do	do	VB
37681	793	15	;	;	:
37681	793	16	in	in	IN
37681	793	17	the	the	DT
37681	793	18	language	language	NN
37681	793	19	of	of	IN
37681	793	20	the	the	DT
37681	793	21	mob	mob	NN
37681	793	22	,	,	,
37681	793	23	to	to	TO
37681	793	24	"	"	``
37681	793	25	smash	smash	VB
37681	793	26	things	thing	NNS
37681	793	27	"	"	''
37681	793	28	;	;	:
37681	793	29	to	to	TO
37681	793	30	call	call	VB
37681	793	31	reactionary	reactionary	NN
37681	793	32	that	that	IN
37681	793	33	which	which	WDT
37681	793	34	does	do	VBZ
37681	793	35	not	not	RB
37681	793	36	conform	conform	VB
37681	793	37	to	to	IN
37681	793	38	their	-PRON-	PRP$
37681	793	39	ephemeral	ephemeral	JJ
37681	793	40	views	view	NNS
37681	793	41	.	.	.
37681	794	1	It	-PRON-	PRP
37681	794	2	is	be	VBZ
37681	794	3	so	so	RB
37681	794	4	easy	easy	JJ
37681	794	5	to	to	TO
37681	794	6	be	be	VB
37681	794	7	an	an	DT
37681	794	8	iconoclast	iconoclast	NN
37681	794	9	,	,	,
37681	794	10	to	to	TO
37681	794	11	think	think	VB
37681	794	12	that	that	IN
37681	794	13	_	_	NNP
37681	794	14	cui	cui	NNP
37681	794	15	bono	bono	FW
37681	794	16	_	_	NNP
37681	794	17	is	be	VBZ
37681	794	18	a	a	DT
37681	794	19	conclusive	conclusive	JJ
37681	794	20	argument	argument	NN
37681	794	21	,	,	,
37681	794	22	to	to	TO
37681	794	23	say	say	VB
37681	794	24	so	so	RB
37681	794	25	glibly	glibly	RB
37681	794	26	that	that	IN
37681	794	27	Raphael	Raphael	NNP
37681	794	28	was	be	VBD
37681	794	29	not	not	RB
37681	794	30	a	a	DT
37681	794	31	great	great	JJ
37681	794	32	painter,--to	painter,--to	NN
37681	794	33	do	do	VB
37681	794	34	anything	anything	NN
37681	794	35	but	but	IN
37681	794	36	construct	construct	VB
37681	794	37	.	.	.
37681	795	1	A	a	DT
37681	795	2	few	few	JJ
37681	795	3	years	year	NNS
37681	795	4	ago	ago	RB
37681	795	5	every	every	DT
37681	795	6	one	one	NN
37681	795	7	must	must	MD
37681	795	8	take	take	VB
37681	795	9	up	up	RP
37681	795	10	with	with	IN
37681	795	11	the	the	DT
37681	795	12	heuristic	heuristic	JJ
37681	795	13	method	method	NN
37681	795	14	developed	develop	VBN
37681	795	15	in	in	IN
37681	795	16	Germany	Germany	NNP
37681	795	17	half	half	PDT
37681	795	18	a	a	DT
37681	795	19	century	century	NN
37681	795	20	back	back	RB
37681	795	21	and	and	CC
37681	795	22	containing	contain	VBG
37681	795	23	much	much	RB
37681	795	24	that	that	WDT
37681	795	25	was	be	VBD
37681	795	26	commendable	commendable	JJ
37681	795	27	.	.	.
37681	796	1	A	a	DT
37681	796	2	little	little	JJ
37681	796	3	later	later	JJ
37681	796	4	one	one	NN
37681	796	5	who	who	WP
37681	796	6	did	do	VBD
37681	796	7	not	not	RB
37681	796	8	believe	believe	VB
37681	796	9	that	that	IN
37681	796	10	the	the	DT
37681	796	11	Culture	Culture	NNP
37681	796	12	Epoch	Epoch	NNP
37681	796	13	Theory	Theory	NNP
37681	796	14	was	be	VBD
37681	796	15	vital	vital	JJ
37681	796	16	in	in	IN
37681	796	17	education	education	NN
37681	796	18	was	be	VBD
37681	796	19	looked	look	VBN
37681	796	20	upon	upon	IN
37681	796	21	with	with	IN
37681	796	22	pity	pity	NN
37681	796	23	by	by	IN
37681	796	24	a	a	DT
37681	796	25	considerable	considerable	JJ
37681	796	26	number	number	NN
37681	796	27	of	of	IN
37681	796	28	serious	serious	JJ
37681	796	29	educators	educator	NNS
37681	796	30	.	.	.
37681	797	1	A	a	DT
37681	797	2	little	little	JJ
37681	797	3	later	later	RB
37681	797	4	the	the	DT
37681	797	5	man	man	NN
37681	797	6	who	who	WP
37681	797	7	did	do	VBD
37681	797	8	not	not	RB
37681	797	9	think	think	VB
37681	797	10	that	that	IN
37681	797	11	the	the	DT
37681	797	12	principle	principle	NN
37681	797	13	of	of	IN
37681	797	14	Concentration	Concentration	NNP
37681	797	15	in	in	IN
37681	797	16	education	education	NN
37681	797	17	was	be	VBD
37681	797	18	a	a	DT
37681	797	19	_	_	NNP
37681	797	20	regula	regula	NN
37681	797	21	aurea	aurea	NNP
37681	797	22	_	_	NNP
37681	797	23	was	be	VBD
37681	797	24	thought	think	VBN
37681	797	25	to	to	TO
37681	797	26	be	be	VB
37681	797	27	hopeless	hopeless	JJ
37681	797	28	.	.	.
37681	798	1	A	a	DT
37681	798	2	little	little	JJ
37681	798	3	later	later	RB
37681	798	4	it	-PRON-	PRP
37681	798	5	may	may	MD
37681	798	6	have	have	VB
37681	798	7	been	be	VBN
37681	798	8	that	that	IN
37681	798	9	Correlation	Correlation	NNP
37681	798	10	was	be	VBD
37681	798	11	the	the	DT
37681	798	12	saving	save	VBG
37681	798	13	factor	factor	NN
37681	798	14	,	,	,
37681	798	15	to	to	TO
37681	798	16	be	be	VB
37681	798	17	looked	look	VBN
37681	798	18	upon	upon	IN
37681	798	19	in	in	IN
37681	798	20	geometry	geometry	NN
37681	798	21	teaching	teaching	NN
37681	798	22	as	as	IN
37681	798	23	a	a	DT
37681	798	24	guiding	guide	VBG
37681	798	25	beacon	beacon	NN
37681	798	26	,	,	,
37681	798	27	even	even	RB
37681	798	28	as	as	IN
37681	798	29	the	the	DT
37681	798	30	fusion	fusion	NN
37681	798	31	of	of	IN
37681	798	32	all	all	DT
37681	798	33	mathematics	mathematic	NNS
37681	798	34	is	be	VBZ
37681	798	35	the	the	DT
37681	798	36	temporary	temporary	JJ
37681	798	37	view	view	NN
37681	798	38	of	of	IN
37681	798	39	a	a	DT
37681	798	40	few	few	JJ
37681	798	41	enthusiasts	enthusiast	NNS
37681	798	42	to	to	IN
37681	798	43	-	-	HYPH
37681	798	44	day	day	NN
37681	798	45	.	.	.
37681	799	1	[	[	-LRB-
37681	799	2	35	35	CD
37681	799	3	]	]	-RRB-
37681	799	4	And	and	CC
37681	799	5	just	just	RB
37681	799	6	now	now	RB
37681	799	7	it	-PRON-	PRP
37681	799	8	is	be	VBZ
37681	799	9	vocational	vocational	JJ
37681	799	10	training	training	NN
37681	799	11	that	that	WDT
37681	799	12	is	be	VBZ
37681	799	13	the	the	DT
37681	799	14	catch	catch	NN
37681	799	15	phrase	phrase	NN
37681	799	16	,	,	,
37681	799	17	and	and	CC
37681	799	18	to	to	IN
37681	799	19	many	many	JJ
37681	799	20	this	this	DT
37681	799	21	phrase	phrase	NN
37681	799	22	seems	seem	VBZ
37681	799	23	to	to	TO
37681	799	24	sound	sound	VB
37681	799	25	the	the	DT
37681	799	26	funeral	funeral	JJ
37681	799	27	knell	knell	NN
37681	799	28	of	of	IN
37681	799	29	the	the	DT
37681	799	30	standard	standard	JJ
37681	799	31	textbook	textbook	NNP
37681	799	32	in	in	IN
37681	799	33	geometry	geometry	NN
37681	799	34	.	.	.
37681	800	1	But	but	CC
37681	800	2	does	do	VBZ
37681	800	3	it	-PRON-	PRP
37681	800	4	do	do	VB
37681	800	5	so	so	RB
37681	800	6	?	?	.
37681	801	1	Does	do	VBZ
37681	801	2	this	this	DT
37681	801	3	present	present	JJ
37681	801	4	cry	cry	NN
37681	801	5	of	of	IN
37681	801	6	the	the	DT
37681	801	7	pedagogical	pedagogical	JJ
37681	801	8	circle	circle	NN
37681	801	9	really	really	RB
37681	801	10	mean	mean	VBP
37681	801	11	that	that	IN
37681	801	12	we	-PRON-	PRP
37681	801	13	are	be	VBP
37681	801	14	no	no	RB
37681	801	15	longer	long	JJR
37681	801	16	to	to	TO
37681	801	17	have	have	VB
37681	801	18	geometry	geometry	NN
37681	801	19	for	for	IN
37681	801	20	geometry	geometry	NN
37681	801	21	's	's	POS
37681	801	22	sake	sake	NN
37681	801	23	?	?	.
37681	802	1	Does	do	VBZ
37681	802	2	it	-PRON-	PRP
37681	802	3	mean	mean	VB
37681	802	4	that	that	IN
37681	802	5	a	a	DT
37681	802	6	panacea	panacea	NN
37681	802	7	has	have	VBZ
37681	802	8	been	be	VBN
37681	802	9	found	find	VBN
37681	802	10	for	for	IN
37681	802	11	the	the	DT
37681	802	12	ills	ill	NNS
37681	802	13	of	of	IN
37681	802	14	memorizing	memorize	VBG
37681	802	15	without	without	IN
37681	802	16	understanding	understand	VBG
37681	802	17	a	a	DT
37681	802	18	proof	proof	NN
37681	802	19	in	in	IN
37681	802	20	the	the	DT
37681	802	21	class	class	NN
37681	802	22	of	of	IN
37681	802	23	a	a	DT
37681	802	24	teacher	teacher	NN
37681	802	25	who	who	WP
37681	802	26	is	be	VBZ
37681	802	27	so	so	RB
37681	802	28	inefficient	inefficient	JJ
37681	802	29	as	as	IN
37681	802	30	to	to	TO
37681	802	31	allow	allow	VB
37681	802	32	this	this	DT
37681	802	33	kind	kind	NN
37681	802	34	of	of	IN
37681	802	35	work	work	NN
37681	802	36	to	to	TO
37681	802	37	go	go	VB
37681	802	38	on	on	RP
37681	802	39	?	?	.
37681	803	1	Does	do	VBZ
37681	803	2	it	-PRON-	PRP
37681	803	3	mean	mean	VB
37681	803	4	that	that	IN
37681	803	5	a	a	DT
37681	803	6	teacher	teacher	NN
37681	803	7	who	who	WP
37681	803	8	does	do	VBZ
37681	803	9	not	not	RB
37681	803	10	see	see	VB
37681	803	11	the	the	DT
37681	803	12	human	human	JJ
37681	803	13	side	side	NN
37681	803	14	of	of	IN
37681	803	15	geometry	geometry	NN
37681	803	16	,	,	,
37681	803	17	who	who	WP
37681	803	18	does	do	VBZ
37681	803	19	not	not	RB
37681	803	20	know	know	VB
37681	803	21	the	the	DT
37681	803	22	real	real	JJ
37681	803	23	uses	use	NNS
37681	803	24	of	of	IN
37681	803	25	geometry	geometry	NN
37681	803	26	,	,	,
37681	803	27	and	and	CC
37681	803	28	who	who	WP
37681	803	29	has	have	VBZ
37681	803	30	no	no	DT
37681	803	31	faculty	faculty	NN
37681	803	32	of	of	IN
37681	803	33	making	make	VBG
37681	803	34	pupils	pupil	NNS
37681	803	35	enthusiastic	enthusiastic	JJ
37681	803	36	over	over	IN
37681	803	37	geometry,--that	geometry,--that	NNP
37681	803	38	this	this	DT
37681	803	39	teacher	teacher	NN
37681	803	40	is	be	VBZ
37681	803	41	to	to	TO
37681	803	42	succeed	succeed	VB
37681	803	43	with	with	IN
37681	803	44	some	some	DT
37681	803	45	scrappy	scrappy	JJ
37681	803	46	,	,	,
37681	803	47	weak	weak	JJ
37681	803	48	,	,	,
37681	803	49	pretending	pretend	VBG
37681	803	50	apology	apology	NN
37681	803	51	for	for	IN
37681	803	52	a	a	DT
37681	803	53	real	real	JJ
37681	803	54	work	work	NN
37681	803	55	on	on	IN
37681	803	56	the	the	DT
37681	803	57	subject	subject	NN
37681	803	58	?	?	.
37681	804	1	No	no	DT
37681	804	2	one	one	NN
37681	804	3	believes	believe	VBZ
37681	804	4	in	in	IN
37681	804	5	stupid	stupid	JJ
37681	804	6	teaching	teaching	NN
37681	804	7	,	,	,
37681	804	8	in	in	IN
37681	804	9	memorizing	memorize	VBG
37681	804	10	a	a	DT
37681	804	11	textbook	textbook	NN
37681	804	12	,	,	,
37681	804	13	in	in	IN
37681	804	14	having	have	VBG
37681	804	15	a	a	DT
37681	804	16	book	book	NN
37681	804	17	that	that	WDT
37681	804	18	does	do	VBZ
37681	804	19	all	all	PDT
37681	804	20	the	the	DT
37681	804	21	work	work	NN
37681	804	22	for	for	IN
37681	804	23	a	a	DT
37681	804	24	pupil	pupil	NN
37681	804	25	,	,	,
37681	804	26	or	or	CC
37681	804	27	in	in	IN
37681	804	28	any	any	DT
37681	804	29	of	of	IN
37681	804	30	the	the	DT
37681	804	31	other	other	JJ
37681	804	32	ills	ill	NNS
37681	804	33	of	of	IN
37681	804	34	inefficient	inefficient	JJ
37681	804	35	instruction	instruction	NN
37681	804	36	.	.	.
37681	805	1	On	on	IN
37681	805	2	the	the	DT
37681	805	3	other	other	JJ
37681	805	4	hand	hand	NN
37681	805	5	,	,	,
37681	805	6	no	no	DT
37681	805	7	fair	fair	JJ
37681	805	8	-	-	HYPH
37681	805	9	minded	minded	JJ
37681	805	10	person	person	NN
37681	805	11	can	can	MD
37681	805	12	condemn	condemn	VB
37681	805	13	a	a	DT
37681	805	14	type	type	NN
37681	805	15	of	of	IN
37681	805	16	book	book	NN
37681	805	17	that	that	WDT
37681	805	18	has	have	VBZ
37681	805	19	stood	stand	VBN
37681	805	20	for	for	IN
37681	805	21	generations	generation	NNS
37681	805	22	until	until	IN
37681	805	23	something	something	NN
37681	805	24	besides	besides	IN
37681	805	25	the	the	DT
37681	805	26	mere	mere	JJ
37681	805	27	transient	transient	JJ
37681	805	28	experiments	experiment	NNS
37681	805	29	of	of	IN
37681	805	30	the	the	DT
37681	805	31	moment	moment	NN
37681	805	32	has	have	VBZ
37681	805	33	been	be	VBN
37681	805	34	suggested	suggest	VBN
37681	805	35	to	to	TO
37681	805	36	replace	replace	VB
37681	805	37	it	-PRON-	PRP
37681	805	38	.	.	.
37681	806	1	Let	let	VB
37681	806	2	us	-PRON-	PRP
37681	806	3	,	,	,
37681	806	4	for	for	IN
37681	806	5	example	example	NN
37681	806	6	,	,	,
37681	806	7	consider	consider	VB
37681	806	8	the	the	DT
37681	806	9	question	question	NN
37681	806	10	of	of	IN
37681	806	11	having	have	VBG
37681	806	12	the	the	DT
37681	806	13	basal	basal	NN
37681	806	14	propositions	proposition	NNS
37681	806	15	proved	prove	VBN
37681	806	16	in	in	IN
37681	806	17	full	full	JJ
37681	806	18	,	,	,
37681	806	19	a	a	DT
37681	806	20	feature	feature	NN
37681	806	21	that	that	WDT
37681	806	22	is	be	VBZ
37681	806	23	so	so	RB
37681	806	24	easy	easy	JJ
37681	806	25	to	to	TO
37681	806	26	condemn	condemn	VB
37681	806	27	as	as	IN
37681	806	28	leading	lead	VBG
37681	806	29	to	to	IN
37681	806	30	memorizing	memorize	VBG
37681	806	31	.	.	.
37681	807	1	The	the	DT
37681	807	2	argument	argument	NN
37681	807	3	in	in	IN
37681	807	4	favor	favor	NN
37681	807	5	of	of	IN
37681	807	6	a	a	DT
37681	807	7	book	book	NN
37681	807	8	with	with	IN
37681	807	9	every	every	DT
37681	807	10	basal	basal	NN
37681	807	11	proposition	proposition	NN
37681	807	12	proved	prove	VBD
37681	807	13	in	in	IN
37681	807	14	full	full	JJ
37681	807	15	,	,	,
37681	807	16	or	or	CC
37681	807	17	with	with	IN
37681	807	18	most	most	JJS
37681	807	19	of	of	IN
37681	807	20	them	-PRON-	PRP
37681	807	21	so	so	RB
37681	807	22	proved	prove	VBD
37681	807	23	,	,	,
37681	807	24	the	the	DT
37681	807	25	rest	rest	NN
37681	807	26	having	have	VBG
37681	807	27	only	only	RB
37681	807	28	suggestions	suggestion	NNS
37681	807	29	for	for	IN
37681	807	30	the	the	DT
37681	807	31	proof	proof	NN
37681	807	32	,	,	,
37681	807	33	is	be	VBZ
37681	807	34	that	that	IN
37681	807	35	the	the	DT
37681	807	36	pupil	pupil	NN
37681	807	37	has	have	VBZ
37681	807	38	before	before	IN
37681	807	39	him	-PRON-	PRP
37681	807	40	standard	standard	JJ
37681	807	41	forms	form	NNS
37681	807	42	exhibiting	exhibit	VBG
37681	807	43	the	the	DT
37681	807	44	best	good	JJS
37681	807	45	,	,	,
37681	807	46	most	most	RBS
37681	807	47	succinct	succinct	JJ
37681	807	48	,	,	,
37681	807	49	most	most	RBS
37681	807	50	clearly	clearly	RB
37681	807	51	stated	state	VBN
37681	807	52	demonstrations	demonstration	NNS
37681	807	53	that	that	WDT
37681	807	54	geometry	geometry	NN
37681	807	55	contains	contain	VBZ
37681	807	56	.	.	.
37681	808	1	The	the	DT
37681	808	2	demonstrations	demonstration	NNS
37681	808	3	stand	stand	VBP
37681	808	4	for	for	IN
37681	808	5	the	the	DT
37681	808	6	same	same	JJ
37681	808	7	thing	thing	NN
37681	808	8	that	that	WDT
37681	808	9	the	the	DT
37681	808	10	type	type	NN
37681	808	11	problems	problem	NNS
37681	808	12	stand	stand	VBP
37681	808	13	for	for	IN
37681	808	14	in	in	IN
37681	808	15	algebra	algebra	NN
37681	808	16	,	,	,
37681	808	17	and	and	CC
37681	808	18	are	be	VBP
37681	808	19	generally	generally	RB
37681	808	20	given	give	VBN
37681	808	21	in	in	IN
37681	808	22	full	full	JJ
37681	808	23	in	in	IN
37681	808	24	the	the	DT
37681	808	25	same	same	JJ
37681	808	26	way	way	NN
37681	808	27	.	.	.
37681	809	1	The	the	DT
37681	809	2	argument	argument	NN
37681	809	3	against	against	IN
37681	809	4	the	the	DT
37681	809	5	plan	plan	NN
37681	809	6	is	be	VBZ
37681	809	7	that	that	IN
37681	809	8	it	-PRON-	PRP
37681	809	9	takes	take	VBZ
37681	809	10	away	away	RB
37681	809	11	the	the	DT
37681	809	12	pupil	pupil	NN
37681	809	13	's	's	POS
37681	809	14	originality	originality	NN
37681	809	15	by	by	IN
37681	809	16	doing	do	VBG
37681	809	17	all	all	PDT
37681	809	18	the	the	DT
37681	809	19	work	work	NN
37681	809	20	for	for	IN
37681	809	21	him	-PRON-	PRP
37681	809	22	,	,	,
37681	809	23	allowing	allow	VBG
37681	809	24	him	-PRON-	PRP
37681	809	25	to	to	TO
37681	809	26	merely	merely	RB
37681	809	27	memorize	memorize	VB
37681	809	28	the	the	DT
37681	809	29	work	work	NN
37681	809	30	.	.	.
37681	810	1	Now	now	RB
37681	810	2	if	if	IN
37681	810	3	all	all	DT
37681	810	4	there	there	EX
37681	810	5	is	be	VBZ
37681	810	6	to	to	TO
37681	810	7	geometry	geometry	VB
37681	810	8	were	be	VBD
37681	810	9	in	in	IN
37681	810	10	the	the	DT
37681	810	11	basal	basal	NN
37681	810	12	propositions	proposition	NNS
37681	810	13	,	,	,
37681	810	14	this	this	DT
37681	810	15	argument	argument	NN
37681	810	16	might	may	MD
37681	810	17	hold	hold	VB
37681	810	18	,	,	,
37681	810	19	just	just	RB
37681	810	20	as	as	IN
37681	810	21	it	-PRON-	PRP
37681	810	22	would	would	MD
37681	810	23	hold	hold	VB
37681	810	24	in	in	RP
37681	810	25	algebra	algebra	NN
37681	810	26	in	in	IN
37681	810	27	case	case	NN
37681	810	28	there	there	EX
37681	810	29	were	be	VBD
37681	810	30	only	only	RB
37681	810	31	those	those	DT
37681	810	32	exercises	exercise	NNS
37681	810	33	that	that	WDT
37681	810	34	are	be	VBP
37681	810	35	solved	solve	VBN
37681	810	36	in	in	IN
37681	810	37	full	full	JJ
37681	810	38	.	.	.
37681	811	1	But	but	CC
37681	811	2	just	just	RB
37681	811	3	as	as	IN
37681	811	4	this	this	DT
37681	811	5	is	be	VBZ
37681	811	6	not	not	RB
37681	811	7	the	the	DT
37681	811	8	case	case	NN
37681	811	9	in	in	IN
37681	811	10	algebra	algebra	NN
37681	811	11	,	,	,
37681	811	12	the	the	DT
37681	811	13	solved	solve	VBN
37681	811	14	exercises	exercise	VBZ
37681	811	15	standing	stand	VBG
37681	811	16	as	as	IN
37681	811	17	types	type	NNS
37681	811	18	or	or	CC
37681	811	19	as	as	IN
37681	811	20	bases	basis	NNS
37681	811	21	for	for	IN
37681	811	22	the	the	DT
37681	811	23	pupil	pupil	NN
37681	811	24	's	's	POS
37681	811	25	real	real	JJ
37681	811	26	work	work	NN
37681	811	27	,	,	,
37681	811	28	so	so	CC
37681	811	29	the	the	DT
37681	811	30	demonstrated	demonstrated	JJ
37681	811	31	proposition	proposition	NN
37681	811	32	forms	form	VBZ
37681	811	33	a	a	DT
37681	811	34	relatively	relatively	RB
37681	811	35	small	small	JJ
37681	811	36	part	part	NN
37681	811	37	of	of	IN
37681	811	38	geometry	geometry	NN
37681	811	39	,	,	,
37681	811	40	standing	stand	VBG
37681	811	41	as	as	IN
37681	811	42	a	a	DT
37681	811	43	type	type	NN
37681	811	44	,	,	,
37681	811	45	a	a	DT
37681	811	46	basis	basis	NN
37681	811	47	for	for	IN
37681	811	48	the	the	DT
37681	811	49	more	more	RBR
37681	811	50	important	important	JJ
37681	811	51	part	part	NN
37681	811	52	of	of	IN
37681	811	53	the	the	DT
37681	811	54	work	work	NN
37681	811	55	.	.	.
37681	812	1	Moreover	moreover	RB
37681	812	2	,	,	,
37681	812	3	a	a	DT
37681	812	4	pupil	pupil	NN
37681	812	5	who	who	WP
37681	812	6	uses	use	VBZ
37681	812	7	a	a	DT
37681	812	8	syllabus	syllabus	NN
37681	812	9	is	be	VBZ
37681	812	10	exposed	expose	VBN
37681	812	11	to	to	IN
37681	812	12	a	a	DT
37681	812	13	danger	danger	NN
37681	812	14	that	that	WDT
37681	812	15	should	should	MD
37681	812	16	be	be	VB
37681	812	17	considered	consider	VBN
37681	812	18	,	,	,
37681	812	19	namely	namely	RB
37681	812	20	,	,	,
37681	812	21	that	that	DT
37681	812	22	of	of	IN
37681	812	23	dishonesty	dishonesty	NN
37681	812	24	.	.	.
37681	813	1	Any	any	DT
37681	813	2	textbook	textbook	NN
37681	813	3	in	in	IN
37681	813	4	geometry	geometry	NN
37681	813	5	will	will	MD
37681	813	6	furnish	furnish	VB
37681	813	7	the	the	DT
37681	813	8	proofs	proof	NNS
37681	813	9	of	of	IN
37681	813	10	most	most	JJS
37681	813	11	of	of	IN
37681	813	12	the	the	DT
37681	813	13	propositions	proposition	NNS
37681	813	14	in	in	IN
37681	813	15	a	a	DT
37681	813	16	syllabus	syllabus	NN
37681	813	17	,	,	,
37681	813	18	whatever	whatever	WDT
37681	813	19	changes	change	NNS
37681	813	20	there	there	EX
37681	813	21	may	may	MD
37681	813	22	be	be	VB
37681	813	23	in	in	IN
37681	813	24	the	the	DT
37681	813	25	sequence	sequence	NN
37681	813	26	,	,	,
37681	813	27	and	and	CC
37681	813	28	it	-PRON-	PRP
37681	813	29	is	be	VBZ
37681	813	30	not	not	RB
37681	813	31	a	a	DT
37681	813	32	healthy	healthy	JJ
37681	813	33	condition	condition	NN
37681	813	34	of	of	IN
37681	813	35	mind	mind	NN
37681	813	36	that	that	WDT
37681	813	37	is	be	VBZ
37681	813	38	induced	induce	VBN
37681	813	39	by	by	IN
37681	813	40	getting	get	VBG
37681	813	41	the	the	DT
37681	813	42	proofs	proof	NNS
37681	813	43	surreptitiously	surreptitiously	RB
37681	813	44	.	.	.
37681	814	1	Unless	unless	IN
37681	814	2	a	a	DT
37681	814	3	teacher	teacher	NN
37681	814	4	has	have	VBZ
37681	814	5	more	more	JJR
37681	814	6	time	time	NN
37681	814	7	for	for	IN
37681	814	8	the	the	DT
37681	814	9	course	course	NN
37681	814	10	than	than	IN
37681	814	11	is	be	VBZ
37681	814	12	usually	usually	RB
37681	814	13	allowed	allow	VBN
37681	814	14	,	,	,
37681	814	15	he	-PRON-	PRP
37681	814	16	can	can	MD
37681	814	17	not	not	RB
37681	814	18	develop	develop	VB
37681	814	19	the	the	DT
37681	814	20	new	new	JJ
37681	814	21	work	work	NN
37681	814	22	as	as	RB
37681	814	23	much	much	RB
37681	814	24	as	as	IN
37681	814	25	is	be	VBZ
37681	814	26	necessary	necessary	JJ
37681	814	27	with	with	IN
37681	814	28	only	only	RB
37681	814	29	a	a	DT
37681	814	30	syllabus	syllabus	NN
37681	814	31	,	,	,
37681	814	32	and	and	CC
37681	814	33	the	the	DT
37681	814	34	result	result	NN
37681	814	35	is	be	VBZ
37681	814	36	that	that	IN
37681	814	37	a	a	DT
37681	814	38	pupil	pupil	NN
37681	814	39	gets	get	VBZ
37681	814	40	more	more	JJR
37681	814	41	of	of	IN
37681	814	42	his	-PRON-	PRP$
37681	814	43	work	work	NN
37681	814	44	from	from	IN
37681	814	45	other	other	JJ
37681	814	46	books	book	NNS
37681	814	47	and	and	CC
37681	814	48	has	have	VBZ
37681	814	49	less	less	JJR
37681	814	50	time	time	NN
37681	814	51	for	for	IN
37681	814	52	exercises	exercise	NNS
37681	814	53	.	.	.
37681	815	1	The	the	DT
37681	815	2	question	question	NN
37681	815	3	therefore	therefore	RB
37681	815	4	comes	come	VBZ
37681	815	5	to	to	IN
37681	815	6	this	this	DT
37681	815	7	:	:	:
37681	815	8	Is	be	VBZ
37681	815	9	it	-PRON-	PRP
37681	815	10	better	well	JJR
37681	815	11	to	to	TO
37681	815	12	use	use	VB
37681	815	13	a	a	DT
37681	815	14	book	book	NN
37681	815	15	containing	contain	VBG
37681	815	16	standard	standard	JJ
37681	815	17	forms	form	NNS
37681	815	18	of	of	IN
37681	815	19	proof	proof	NN
37681	815	20	for	for	IN
37681	815	21	the	the	DT
37681	815	22	basal	basal	NN
37681	815	23	propositions	proposition	NNS
37681	815	24	,	,	,
37681	815	25	and	and	CC
37681	815	26	have	have	VBP
37681	815	27	time	time	NN
37681	815	28	for	for	IN
37681	815	29	solving	solve	VBG
37681	815	30	a	a	DT
37681	815	31	large	large	JJ
37681	815	32	number	number	NN
37681	815	33	of	of	IN
37681	815	34	original	original	JJ
37681	815	35	exercises	exercise	NNS
37681	815	36	and	and	CC
37681	815	37	for	for	IN
37681	815	38	seeking	seek	VBG
37681	815	39	the	the	DT
37681	815	40	applications	application	NNS
37681	815	41	of	of	IN
37681	815	42	geometry	geometry	NN
37681	815	43	?	?	.
37681	816	1	Or	or	CC
37681	816	2	is	be	VBZ
37681	816	3	it	-PRON-	PRP
37681	816	4	better	well	JJR
37681	816	5	to	to	TO
37681	816	6	use	use	VB
37681	816	7	a	a	DT
37681	816	8	book	book	NN
37681	816	9	that	that	WDT
37681	816	10	requires	require	VBZ
37681	816	11	more	more	JJR
37681	816	12	time	time	NN
37681	816	13	on	on	IN
37681	816	14	the	the	DT
37681	816	15	basal	basal	NN
37681	816	16	propositions	proposition	NNS
37681	816	17	,	,	,
37681	816	18	with	with	IN
37681	816	19	the	the	DT
37681	816	20	danger	danger	NN
37681	816	21	of	of	IN
37681	816	22	dishonesty	dishonesty	NN
37681	816	23	,	,	,
37681	816	24	and	and	CC
37681	816	25	allows	allow	VBZ
37681	816	26	less	less	JJR
37681	816	27	time	time	NN
37681	816	28	for	for	IN
37681	816	29	solving	solve	VBG
37681	816	30	originals	original	NNS
37681	816	31	?	?	.
37681	817	1	To	to	IN
37681	817	2	these	these	DT
37681	817	3	questions	question	NNS
37681	817	4	the	the	DT
37681	817	5	great	great	JJ
37681	817	6	majority	majority	NN
37681	817	7	of	of	IN
37681	817	8	teachers	teacher	NNS
37681	817	9	answer	answer	VBP
37681	817	10	in	in	IN
37681	817	11	favor	favor	NN
37681	817	12	of	of	IN
37681	817	13	the	the	DT
37681	817	14	textbook	textbook	NN
37681	817	15	with	with	IN
37681	817	16	most	most	JJS
37681	817	17	of	of	IN
37681	817	18	the	the	DT
37681	817	19	basal	basal	NN
37681	817	20	propositions	proposition	NNS
37681	817	21	fully	fully	RB
37681	817	22	demonstrated	demonstrate	VBD
37681	817	23	.	.	.
37681	818	1	In	in	IN
37681	818	2	general	general	JJ
37681	818	3	,	,	,
37681	818	4	therefore	therefore	RB
37681	818	5	,	,	,
37681	818	6	it	-PRON-	PRP
37681	818	7	is	be	VBZ
37681	818	8	a	a	DT
37681	818	9	good	good	JJ
37681	818	10	rule	rule	NN
37681	818	11	to	to	TO
37681	818	12	use	use	VB
37681	818	13	the	the	DT
37681	818	14	proofs	proof	NNS
37681	818	15	of	of	IN
37681	818	16	the	the	DT
37681	818	17	basal	basal	NN
37681	818	18	propositions	proposition	NNS
37681	818	19	as	as	IN
37681	818	20	models	model	NNS
37681	818	21	,	,	,
37681	818	22	and	and	CC
37681	818	23	to	to	TO
37681	818	24	get	get	VB
37681	818	25	the	the	DT
37681	818	26	original	original	JJ
37681	818	27	work	work	NN
37681	818	28	from	from	IN
37681	818	29	the	the	DT
37681	818	30	exercises	exercise	NNS
37681	818	31	.	.	.
37681	819	1	Unless	unless	IN
37681	819	2	we	-PRON-	PRP
37681	819	3	preserve	preserve	VBP
37681	819	4	these	these	DT
37681	819	5	model	model	NN
37681	819	6	proofs	proof	NNS
37681	819	7	,	,	,
37681	819	8	or	or	CC
37681	819	9	unless	unless	IN
37681	819	10	we	-PRON-	PRP
37681	819	11	supply	supply	VBP
37681	819	12	them	-PRON-	PRP
37681	819	13	with	with	IN
37681	819	14	a	a	DT
37681	819	15	syllabus	syllabus	NN
37681	819	16	,	,	,
37681	819	17	the	the	DT
37681	819	18	habit	habit	NN
37681	819	19	of	of	IN
37681	819	20	correct	correct	JJ
37681	819	21	,	,	,
37681	819	22	succinct	succinct	JJ
37681	819	23	self	self	NN
37681	819	24	-	-	HYPH
37681	819	25	expression	expression	NN
37681	819	26	,	,	,
37681	819	27	which	which	WDT
37681	819	28	is	be	VBZ
37681	819	29	one	one	CD
37681	819	30	of	of	IN
37681	819	31	the	the	DT
37681	819	32	chief	chief	JJ
37681	819	33	assets	asset	NNS
37681	819	34	of	of	IN
37681	819	35	geometry	geometry	NN
37681	819	36	,	,	,
37681	819	37	will	will	MD
37681	819	38	tend	tend	VB
37681	819	39	to	to	TO
37681	819	40	become	become	VB
37681	819	41	atrophied	atrophy	VBN
37681	819	42	.	.	.
37681	820	1	So	so	RB
37681	820	2	important	important	JJ
37681	820	3	is	be	VBZ
37681	820	4	this	this	DT
37681	820	5	habit	habit	NN
37681	820	6	that	that	IN
37681	820	7	"	"	``
37681	820	8	no	no	DT
37681	820	9	system	system	NN
37681	820	10	of	of	IN
37681	820	11	education	education	NN
37681	820	12	in	in	IN
37681	820	13	which	which	WDT
37681	820	14	its	-PRON-	PRP$
37681	820	15	performance	performance	NN
37681	820	16	is	be	VBZ
37681	820	17	neglected	neglect	VBN
37681	820	18	can	can	MD
37681	820	19	hope	hope	VB
37681	820	20	or	or	CC
37681	820	21	profess	profess	JJ
37681	820	22	to	to	TO
37681	820	23	evolve	evolve	VB
37681	820	24	men	man	NNS
37681	820	25	and	and	CC
37681	820	26	women	woman	NNS
37681	820	27	who	who	WP
37681	820	28	are	be	VBP
37681	820	29	competent	competent	JJ
37681	820	30	in	in	IN
37681	820	31	the	the	DT
37681	820	32	full	full	JJ
37681	820	33	sense	sense	NN
37681	820	34	of	of	IN
37681	820	35	the	the	DT
37681	820	36	word	word	NN
37681	820	37	.	.	.
37681	821	1	So	so	RB
37681	821	2	long	long	RB
37681	821	3	as	as	IN
37681	821	4	teachers	teacher	NNS
37681	821	5	of	of	IN
37681	821	6	geometry	geometry	NN
37681	821	7	neglect	neglect	VBP
37681	821	8	the	the	DT
37681	821	9	possibilities	possibility	NNS
37681	821	10	of	of	IN
37681	821	11	the	the	DT
37681	821	12	subject	subject	NN
37681	821	13	in	in	IN
37681	821	14	this	this	DT
37681	821	15	respect	respect	NN
37681	821	16	,	,	,
37681	821	17	so	so	RB
37681	821	18	long	long	RB
37681	821	19	will	will	MD
37681	821	20	the	the	DT
37681	821	21	time	time	NN
37681	821	22	devoted	devote	VBN
37681	821	23	to	to	IN
37681	821	24	it	-PRON-	PRP
37681	821	25	be	be	VB
37681	821	26	in	in	IN
37681	821	27	large	large	JJ
37681	821	28	part	part	NN
37681	821	29	wasted	waste	VBN
37681	821	30	,	,	,
37681	821	31	and	and	CC
37681	821	32	so	so	RB
37681	821	33	long	long	RB
37681	821	34	will	will	MD
37681	821	35	their	-PRON-	PRP$
37681	821	36	pupils	pupil	NNS
37681	821	37	continue	continue	VB
37681	821	38	to	to	TO
37681	821	39	imbibe	imbibe	VB
37681	821	40	the	the	DT
37681	821	41	vicious	vicious	JJ
37681	821	42	idea	idea	NN
37681	821	43	that	that	IN
37681	821	44	it	-PRON-	PRP
37681	821	45	is	be	VBZ
37681	821	46	much	much	RB
37681	821	47	more	more	RBR
37681	821	48	important	important	JJ
37681	821	49	to	to	TO
37681	821	50	be	be	VB
37681	821	51	able	able	JJ
37681	821	52	to	to	TO
37681	821	53	do	do	VB
37681	821	54	a	a	DT
37681	821	55	thing	thing	NN
37681	821	56	than	than	IN
37681	821	57	to	to	TO
37681	821	58	say	say	VB
37681	821	59	how	how	WRB
37681	821	60	it	-PRON-	PRP
37681	821	61	can	can	MD
37681	821	62	be	be	VB
37681	821	63	done	do	VBN
37681	821	64	.	.	.
37681	822	1	"	"	``
37681	822	2	[	[	-LRB-
37681	822	3	36	36	CD
37681	822	4	]	]	-RRB-
37681	822	5	It	-PRON-	PRP
37681	822	6	is	be	VBZ
37681	822	7	here	here	RB
37681	822	8	that	that	IN
37681	822	9	the	the	DT
37681	822	10	chief	chief	JJ
37681	822	11	danger	danger	NN
37681	822	12	of	of	IN
37681	822	13	syllabus	syllabus	NN
37681	822	14	-	-	HYPH
37681	822	15	teaching	teach	VBG
37681	822	16	lies	lie	NNS
37681	822	17	,	,	,
37681	822	18	and	and	CC
37681	822	19	it	-PRON-	PRP
37681	822	20	is	be	VBZ
37681	822	21	because	because	IN
37681	822	22	of	of	IN
37681	822	23	this	this	DT
37681	822	24	patent	patent	NN
37681	822	25	fact	fact	NN
37681	822	26	that	that	IN
37681	822	27	a	a	DT
37681	822	28	syllabus	syllabus	NN
37681	822	29	without	without	IN
37681	822	30	a	a	DT
37681	822	31	carefully	carefully	RB
37681	822	32	selected	select	VBN
37681	822	33	set	set	NN
37681	822	34	of	of	IN
37681	822	35	model	model	NN
37681	822	36	proofs	proof	NNS
37681	822	37	,	,	,
37681	822	38	or	or	CC
37681	822	39	without	without	IN
37681	822	40	the	the	DT
37681	822	41	unnecessary	unnecessary	JJ
37681	822	42	expenditure	expenditure	NN
37681	822	43	of	of	IN
37681	822	44	time	time	NN
37681	822	45	by	by	IN
37681	822	46	the	the	DT
37681	822	47	class	class	NN
37681	822	48	,	,	,
37681	822	49	is	be	VBZ
37681	822	50	a	a	DT
37681	822	51	dangerous	dangerous	JJ
37681	822	52	kind	kind	NN
37681	822	53	of	of	IN
37681	822	54	textbook	textbook	NN
37681	822	55	.	.	.
37681	823	1	What	what	WP
37681	823	2	shall	shall	MD
37681	823	3	then	then	RB
37681	823	4	be	be	VB
37681	823	5	said	say	VBN
37681	823	6	of	of	IN
37681	823	7	those	those	DT
37681	823	8	books	book	NNS
37681	823	9	that	that	WDT
37681	823	10	merely	merely	RB
37681	823	11	suggest	suggest	VBP
37681	823	12	the	the	DT
37681	823	13	proofs	proof	NNS
37681	823	14	,	,	,
37681	823	15	or	or	CC
37681	823	16	that	that	WDT
37681	823	17	give	give	VBP
37681	823	18	a	a	DT
37681	823	19	series	series	NN
37681	823	20	of	of	IN
37681	823	21	questions	question	NNS
37681	823	22	that	that	WDT
37681	823	23	lead	lead	VBP
37681	823	24	to	to	IN
37681	823	25	the	the	DT
37681	823	26	demonstrations	demonstration	NNS
37681	823	27	?	?	.
37681	824	1	There	there	EX
37681	824	2	is	be	VBZ
37681	824	3	a	a	DT
37681	824	4	certain	certain	JJ
37681	824	5	plausibility	plausibility	NN
37681	824	6	about	about	IN
37681	824	7	such	such	PDT
37681	824	8	a	a	DT
37681	824	9	plan	plan	NN
37681	824	10	at	at	IN
37681	824	11	first	first	JJ
37681	824	12	sight	sight	NN
37681	824	13	.	.	.
37681	825	1	But	but	CC
37681	825	2	it	-PRON-	PRP
37681	825	3	is	be	VBZ
37681	825	4	easily	easily	RB
37681	825	5	seen	see	VBN
37681	825	6	to	to	TO
37681	825	7	have	have	VB
37681	825	8	only	only	RB
37681	825	9	a	a	DT
37681	825	10	fictitious	fictitious	JJ
37681	825	11	claim	claim	NN
37681	825	12	to	to	IN
37681	825	13	educational	educational	JJ
37681	825	14	value	value	NN
37681	825	15	.	.	.
37681	826	1	In	in	IN
37681	826	2	the	the	DT
37681	826	3	first	first	JJ
37681	826	4	place	place	NN
37681	826	5	,	,	,
37681	826	6	it	-PRON-	PRP
37681	826	7	is	be	VBZ
37681	826	8	merely	merely	RB
37681	826	9	an	an	DT
37681	826	10	attempt	attempt	NN
37681	826	11	on	on	IN
37681	826	12	the	the	DT
37681	826	13	part	part	NN
37681	826	14	of	of	IN
37681	826	15	the	the	DT
37681	826	16	book	book	NN
37681	826	17	to	to	TO
37681	826	18	take	take	VB
37681	826	19	the	the	DT
37681	826	20	place	place	NN
37681	826	21	of	of	IN
37681	826	22	the	the	DT
37681	826	23	teacher	teacher	NN
37681	826	24	and	and	CC
37681	826	25	to	to	TO
37681	826	26	"	"	``
37681	826	27	develop	develop	VB
37681	826	28	"	"	''
37681	826	29	every	every	DT
37681	826	30	lesson	lesson	NN
37681	826	31	by	by	IN
37681	826	32	the	the	DT
37681	826	33	heuristic	heuristic	JJ
37681	826	34	method	method	NN
37681	826	35	.	.	.
37681	827	1	The	the	DT
37681	827	2	questions	question	NNS
37681	827	3	are	be	VBP
37681	827	4	so	so	RB
37681	827	5	framed	framed	JJ
37681	827	6	as	as	IN
37681	827	7	to	to	TO
37681	827	8	admit	admit	VB
37681	827	9	,	,	,
37681	827	10	in	in	IN
37681	827	11	most	most	JJS
37681	827	12	cases	case	NNS
37681	827	13	,	,	,
37681	827	14	of	of	IN
37681	827	15	only	only	RB
37681	827	16	a	a	DT
37681	827	17	single	single	JJ
37681	827	18	answer	answer	NN
37681	827	19	,	,	,
37681	827	20	so	so	IN
37681	827	21	that	that	IN
37681	827	22	this	this	DT
37681	827	23	answer	answer	NN
37681	827	24	might	may	MD
37681	827	25	just	just	RB
37681	827	26	as	as	RB
37681	827	27	well	well	RB
37681	827	28	be	be	VB
37681	827	29	given	give	VBN
37681	827	30	instead	instead	RB
37681	827	31	of	of	IN
37681	827	32	the	the	DT
37681	827	33	question	question	NN
37681	827	34	.	.	.
37681	828	1	The	the	DT
37681	828	2	pupil	pupil	NN
37681	828	3	has	have	VBZ
37681	828	4	therefore	therefore	RB
37681	828	5	a	a	DT
37681	828	6	proof	proof	NN
37681	828	7	requiring	require	VBG
37681	828	8	no	no	DT
37681	828	9	more	more	JJR
37681	828	10	effort	effort	NN
37681	828	11	than	than	IN
37681	828	12	is	be	VBZ
37681	828	13	the	the	DT
37681	828	14	case	case	NN
37681	828	15	in	in	IN
37681	828	16	the	the	DT
37681	828	17	standard	standard	JJ
37681	828	18	form	form	NN
37681	828	19	of	of	IN
37681	828	20	textbook	textbook	NN
37681	828	21	,	,	,
37681	828	22	but	but	CC
37681	828	23	not	not	RB
37681	828	24	given	give	VBN
37681	828	25	in	in	IN
37681	828	26	the	the	DT
37681	828	27	clear	clear	JJ
37681	828	28	language	language	NN
37681	828	29	of	of	IN
37681	828	30	a	a	DT
37681	828	31	careful	careful	JJ
37681	828	32	writer	writer	NN
37681	828	33	.	.	.
37681	829	1	Furthermore	furthermore	RB
37681	829	2	,	,	,
37681	829	3	the	the	DT
37681	829	4	pupil	pupil	NN
37681	829	5	is	be	VBZ
37681	829	6	losing	lose	VBG
37681	829	7	here	here	RB
37681	829	8	,	,	,
37681	829	9	as	as	IN
37681	829	10	when	when	WRB
37681	829	11	he	-PRON-	PRP
37681	829	12	uses	use	VBZ
37681	829	13	only	only	RB
37681	829	14	a	a	DT
37681	829	15	syllabus	syllabus	NN
37681	829	16	,	,	,
37681	829	17	one	one	CD
37681	829	18	of	of	IN
37681	829	19	the	the	DT
37681	829	20	very	very	JJ
37681	829	21	things	thing	NNS
37681	829	22	that	that	WDT
37681	829	23	he	-PRON-	PRP
37681	829	24	should	should	MD
37681	829	25	be	be	VB
37681	829	26	acquiring	acquire	VBG
37681	829	27	,	,	,
37681	829	28	namely	namely	RB
37681	829	29	,	,	,
37681	829	30	the	the	DT
37681	829	31	habit	habit	NN
37681	829	32	of	of	IN
37681	829	33	reading	read	VBG
37681	829	34	mathematics	mathematic	NNS
37681	829	35	.	.	.
37681	830	1	If	if	IN
37681	830	2	he	-PRON-	PRP
37681	830	3	met	meet	VBD
37681	830	4	only	only	RB
37681	830	5	syllabi	syllabi	NNP
37681	830	6	without	without	IN
37681	830	7	proofs	proofs	NNP
37681	830	8	,	,	,
37681	830	9	or	or	CC
37681	830	10	"	"	``
37681	830	11	suggestive	suggestive	JJ
37681	830	12	"	"	''
37681	830	13	geometries	geometry	NNS
37681	830	14	,	,	,
37681	830	15	or	or	CC
37681	830	16	books	book	NNS
37681	830	17	that	that	WDT
37681	830	18	endeavored	endeavor	VBD
37681	830	19	to	to	TO
37681	830	20	question	question	VB
37681	830	21	every	every	DT
37681	830	22	proof	proof	NN
37681	830	23	out	out	IN
37681	830	24	of	of	IN
37681	830	25	him	-PRON-	PRP
37681	830	26	,	,	,
37681	830	27	he	-PRON-	PRP
37681	830	28	would	would	MD
37681	830	29	be	be	VB
37681	830	30	in	in	IN
37681	830	31	a	a	DT
37681	830	32	sorry	sorry	JJ
37681	830	33	plight	plight	NN
37681	830	34	when	when	WRB
37681	830	35	he	-PRON-	PRP
37681	830	36	tried	try	VBD
37681	830	37	to	to	TO
37681	830	38	read	read	VB
37681	830	39	higher	high	JJR
37681	830	40	mathematics	mathematic	NNS
37681	830	41	,	,	,
37681	830	42	or	or	CC
37681	830	43	even	even	RB
37681	830	44	other	other	JJ
37681	830	45	elementary	elementary	JJ
37681	830	46	treatises	treatise	NNS
37681	830	47	.	.	.
37681	831	1	It	-PRON-	PRP
37681	831	2	is	be	VBZ
37681	831	3	for	for	IN
37681	831	4	reasons	reason	NNS
37681	831	5	such	such	JJ
37681	831	6	as	as	IN
37681	831	7	these	these	DT
37681	831	8	that	that	WDT
37681	831	9	the	the	DT
37681	831	10	heuristic	heuristic	JJ
37681	831	11	textbook	textbook	NN
37681	831	12	has	have	VBZ
37681	831	13	never	never	RB
37681	831	14	succeeded	succeed	VBN
37681	831	15	for	for	IN
37681	831	16	any	any	DT
37681	831	17	great	great	JJ
37681	831	18	length	length	NN
37681	831	19	of	of	IN
37681	831	20	time	time	NN
37681	831	21	or	or	CC
37681	831	22	in	in	IN
37681	831	23	any	any	DT
37681	831	24	wide	wide	JJ
37681	831	25	territory	territory	NN
37681	831	26	.	.	.
37681	832	1	And	and	CC
37681	832	2	finally	finally	RB
37681	832	3	,	,	,
37681	832	4	upon	upon	IN
37681	832	5	this	this	DT
37681	832	6	point	point	NN
37681	832	7	,	,	,
37681	832	8	shall	shall	MD
37681	832	9	the	the	DT
37681	832	10	demonstrations	demonstration	NNS
37681	832	11	be	be	VB
37681	832	12	omitted	omit	VBN
37681	832	13	entirely	entirely	RB
37681	832	14	,	,	,
37681	832	15	leaving	leave	VBG
37681	832	16	only	only	RB
37681	832	17	the	the	DT
37681	832	18	list	list	NN
37681	832	19	of	of	IN
37681	832	20	propositions,--in	propositions,--in	JJ
37681	832	21	other	other	JJ
37681	832	22	words	word	NNS
37681	832	23	,	,	,
37681	832	24	a	a	DT
37681	832	25	pure	pure	JJ
37681	832	26	syllabus	syllabus	NN
37681	832	27	?	?	.
37681	833	1	This	this	DT
37681	833	2	has	have	VBZ
37681	833	3	been	be	VBN
37681	833	4	sufficiently	sufficiently	RB
37681	833	5	answered	answer	VBN
37681	833	6	above	above	RB
37681	833	7	.	.	.
37681	834	1	But	but	CC
37681	834	2	there	there	EX
37681	834	3	is	be	VBZ
37681	834	4	a	a	DT
37681	834	5	modification	modification	NN
37681	834	6	of	of	IN
37681	834	7	the	the	DT
37681	834	8	pure	pure	JJ
37681	834	9	syllabus	syllabus	NN
37681	834	10	that	that	WDT
37681	834	11	has	have	VBZ
37681	834	12	much	much	JJ
37681	834	13	to	to	TO
37681	834	14	commend	commend	VB
37681	834	15	itself	-PRON-	PRP
37681	834	16	to	to	IN
37681	834	17	teachers	teacher	NNS
37681	834	18	of	of	IN
37681	834	19	exceptional	exceptional	JJ
37681	834	20	strength	strength	NN
37681	834	21	and	and	CC
37681	834	22	with	with	IN
37681	834	23	more	more	JJR
37681	834	24	confidence	confidence	NN
37681	834	25	in	in	IN
37681	834	26	themselves	-PRON-	PRP
37681	834	27	than	than	IN
37681	834	28	is	be	VBZ
37681	834	29	usually	usually	RB
37681	834	30	found	find	VBN
37681	834	31	.	.	.
37681	835	1	This	this	DT
37681	835	2	is	be	VBZ
37681	835	3	an	an	DT
37681	835	4	arrangement	arrangement	NN
37681	835	5	that	that	WDT
37681	835	6	begins	begin	VBZ
37681	835	7	like	like	IN
37681	835	8	the	the	DT
37681	835	9	ordinary	ordinary	JJ
37681	835	10	textbook	textbook	NN
37681	835	11	and	and	CC
37681	835	12	,	,	,
37681	835	13	after	after	IN
37681	835	14	the	the	DT
37681	835	15	pupil	pupil	NN
37681	835	16	has	have	VBZ
37681	835	17	acquired	acquire	VBN
37681	835	18	the	the	DT
37681	835	19	form	form	NN
37681	835	20	of	of	IN
37681	835	21	proof	proof	NN
37681	835	22	,	,	,
37681	835	23	gradually	gradually	RB
37681	835	24	merges	merge	VBZ
37681	835	25	into	into	IN
37681	835	26	a	a	DT
37681	835	27	syllabus	syllabus	NN
37681	835	28	,	,	,
37681	835	29	so	so	IN
37681	835	30	that	that	IN
37681	835	31	there	there	EX
37681	835	32	is	be	VBZ
37681	835	33	no	no	DT
37681	835	34	temptation	temptation	NN
37681	835	35	to	to	TO
37681	835	36	go	go	VB
37681	835	37	surreptitiously	surreptitiously	RB
37681	835	38	to	to	IN
37681	835	39	other	other	JJ
37681	835	40	books	book	NNS
37681	835	41	for	for	IN
37681	835	42	help	help	NN
37681	835	43	.	.	.
37681	836	1	Such	such	PDT
37681	836	2	a	a	DT
37681	836	3	book	book	NN
37681	836	4	,	,	,
37681	836	5	if	if	IN
37681	836	6	worked	work	VBD
37681	836	7	out	out	RP
37681	836	8	with	with	IN
37681	836	9	skill	skill	NN
37681	836	10	,	,	,
37681	836	11	would	would	MD
37681	836	12	appeal	appeal	VB
37681	836	13	to	to	IN
37681	836	14	an	an	DT
37681	836	15	enthusiastic	enthusiastic	JJ
37681	836	16	teacher	teacher	NN
37681	836	17	,	,	,
37681	836	18	and	and	CC
37681	836	19	would	would	MD
37681	836	20	accomplish	accomplish	VB
37681	836	21	the	the	DT
37681	836	22	results	result	NNS
37681	836	23	claimed	claim	VBD
37681	836	24	for	for	IN
37681	836	25	the	the	DT
37681	836	26	cruder	cruder	NN
37681	836	27	forms	form	NNS
37681	836	28	of	of	IN
37681	836	29	manual	manual	NNP
37681	836	30	already	already	RB
37681	836	31	described	describe	VBN
37681	836	32	.	.	.
37681	837	1	It	-PRON-	PRP
37681	837	2	would	would	MD
37681	837	3	not	not	RB
37681	837	4	be	be	VB
37681	837	5	in	in	IN
37681	837	6	general	general	JJ
37681	837	7	as	as	IN
37681	837	8	safe	safe	JJ
37681	837	9	a	a	DT
37681	837	10	book	book	NN
37681	837	11	as	as	IN
37681	837	12	the	the	DT
37681	837	13	standard	standard	JJ
37681	837	14	form	form	NN
37681	837	15	,	,	,
37681	837	16	but	but	CC
37681	837	17	with	with	IN
37681	837	18	the	the	DT
37681	837	19	right	right	JJ
37681	837	20	teacher	teacher	NN
37681	837	21	it	-PRON-	PRP
37681	837	22	would	would	MD
37681	837	23	bring	bring	VB
37681	837	24	good	good	JJ
37681	837	25	results	result	NNS
37681	837	26	.	.	.
37681	838	1	In	in	IN
37681	838	2	conclusion	conclusion	NN
37681	838	3	,	,	,
37681	838	4	there	there	EX
37681	838	5	are	be	VBP
37681	838	6	two	two	CD
37681	838	7	types	type	NNS
37681	838	8	of	of	IN
37681	838	9	textbook	textbook	NN
37681	838	10	that	that	WDT
37681	838	11	have	have	VBP
37681	838	12	any	any	DT
37681	838	13	hope	hope	NN
37681	838	14	of	of	IN
37681	838	15	success	success	NN
37681	838	16	.	.	.
37681	839	1	The	the	DT
37681	839	2	first	first	JJ
37681	839	3	is	be	VBZ
37681	839	4	the	the	DT
37681	839	5	one	one	NN
37681	839	6	with	with	IN
37681	839	7	all	all	DT
37681	839	8	or	or	CC
37681	839	9	a	a	DT
37681	839	10	large	large	JJ
37681	839	11	part	part	NN
37681	839	12	of	of	IN
37681	839	13	the	the	DT
37681	839	14	basal	basal	NN
37681	839	15	propositions	proposition	NNS
37681	839	16	demonstrated	demonstrate	VBD
37681	839	17	in	in	IN
37681	839	18	full	full	JJ
37681	839	19	,	,	,
37681	839	20	and	and	CC
37681	839	21	with	with	IN
37681	839	22	these	these	DT
37681	839	23	propositions	proposition	NNS
37681	839	24	not	not	RB
37681	839	25	unduly	unduly	RB
37681	839	26	reduced	reduce	VBN
37681	839	27	in	in	IN
37681	839	28	number	number	NN
37681	839	29	.	.	.
37681	840	1	Such	such	PDT
37681	840	2	a	a	DT
37681	840	3	book	book	NN
37681	840	4	should	should	MD
37681	840	5	give	give	VB
37681	840	6	a	a	DT
37681	840	7	large	large	JJ
37681	840	8	number	number	NN
37681	840	9	of	of	IN
37681	840	10	simple	simple	JJ
37681	840	11	exercises	exercise	NNS
37681	840	12	scattered	scatter	VBN
37681	840	13	through	through	IN
37681	840	14	the	the	DT
37681	840	15	work	work	NN
37681	840	16	,	,	,
37681	840	17	with	with	IN
37681	840	18	a	a	DT
37681	840	19	relatively	relatively	RB
37681	840	20	small	small	JJ
37681	840	21	number	number	NN
37681	840	22	of	of	IN
37681	840	23	difficult	difficult	JJ
37681	840	24	ones	one	NNS
37681	840	25	.	.	.
37681	841	1	It	-PRON-	PRP
37681	841	2	should	should	MD
37681	841	3	be	be	VB
37681	841	4	modern	modern	JJ
37681	841	5	in	in	IN
37681	841	6	its	-PRON-	PRP$
37681	841	7	spirit	spirit	NN
37681	841	8	,	,	,
37681	841	9	with	with	IN
37681	841	10	figures	figure	NNS
37681	841	11	systematically	systematically	RB
37681	841	12	lettered	letter	VBN
37681	841	13	,	,	,
37681	841	14	with	with	IN
37681	841	15	each	each	DT
37681	841	16	page	page	NN
37681	841	17	a	a	DT
37681	841	18	unit	unit	NN
37681	841	19	as	as	RB
37681	841	20	far	far	RB
37681	841	21	as	as	IN
37681	841	22	possible	possible	JJ
37681	841	23	,	,	,
37681	841	24	and	and	CC
37681	841	25	with	with	IN
37681	841	26	every	every	DT
37681	841	27	proof	proof	NN
37681	841	28	a	a	DT
37681	841	29	model	model	NN
37681	841	30	of	of	IN
37681	841	31	clearness	clearness	NN
37681	841	32	of	of	IN
37681	841	33	statement	statement	NN
37681	841	34	and	and	CC
37681	841	35	neatness	neatness	NN
37681	841	36	of	of	IN
37681	841	37	form	form	NN
37681	841	38	.	.	.
37681	842	1	Above	above	IN
37681	842	2	all	all	DT
37681	842	3	,	,	,
37681	842	4	it	-PRON-	PRP
37681	842	5	should	should	MD
37681	842	6	not	not	RB
37681	842	7	yield	yield	VB
37681	842	8	to	to	IN
37681	842	9	the	the	DT
37681	842	10	demand	demand	NN
37681	842	11	of	of	IN
37681	842	12	a	a	DT
37681	842	13	few	few	JJ
37681	842	14	who	who	WP
37681	842	15	are	be	VBP
37681	842	16	always	always	RB
37681	842	17	looking	look	VBG
37681	842	18	merely	merely	RB
37681	842	19	for	for	IN
37681	842	20	something	something	NN
37681	842	21	to	to	TO
37681	842	22	change	change	VB
37681	842	23	,	,	,
37681	842	24	nor	nor	CC
37681	842	25	should	should	MD
37681	842	26	it	-PRON-	PRP
37681	842	27	in	in	IN
37681	842	28	a	a	DT
37681	842	29	reactionary	reactionary	JJ
37681	842	30	spirit	spirit	NN
37681	842	31	return	return	NN
37681	842	32	to	to	IN
37681	842	33	the	the	DT
37681	842	34	old	old	JJ
37681	842	35	essay	essay	NN
37681	842	36	form	form	NN
37681	842	37	of	of	IN
37681	842	38	proof	proof	NN
37681	842	39	,	,	,
37681	842	40	which	which	WDT
37681	842	41	hinders	hinder	VBZ
37681	842	42	the	the	DT
37681	842	43	pupil	pupil	NN
37681	842	44	at	at	IN
37681	842	45	this	this	DT
37681	842	46	stage	stage	NN
37681	842	47	.	.	.
37681	843	1	The	the	DT
37681	843	2	second	second	JJ
37681	843	3	type	type	NN
37681	843	4	is	be	VBZ
37681	843	5	the	the	DT
37681	843	6	semisyllabus	semisyllabus	NNP
37681	843	7	,	,	,
37681	843	8	otherwise	otherwise	RB
37681	843	9	with	with	IN
37681	843	10	all	all	PDT
37681	843	11	the	the	DT
37681	843	12	spirit	spirit	NN
37681	843	13	of	of	IN
37681	843	14	the	the	DT
37681	843	15	first	first	JJ
37681	843	16	type	type	NN
37681	843	17	.	.	.
37681	844	1	In	in	IN
37681	844	2	both	both	DT
37681	844	3	there	there	EX
37681	844	4	should	should	MD
37681	844	5	be	be	VB
37681	844	6	an	an	DT
37681	844	7	honest	honest	JJ
37681	844	8	fusion	fusion	NN
37681	844	9	of	of	IN
37681	844	10	pure	pure	JJ
37681	844	11	and	and	CC
37681	844	12	applied	applied	JJ
37681	844	13	geometry	geometry	NN
37681	844	14	,	,	,
37681	844	15	with	with	IN
37681	844	16	no	no	DT
37681	844	17	exercises	exercise	NNS
37681	844	18	that	that	WDT
37681	844	19	pretend	pretend	VBP
37681	844	20	to	to	TO
37681	844	21	be	be	VB
37681	844	22	practical	practical	JJ
37681	844	23	without	without	IN
37681	844	24	being	be	VBG
37681	844	25	so	so	RB
37681	844	26	,	,	,
37681	844	27	with	with	IN
37681	844	28	no	no	DT
37681	844	29	forced	force	VBN
37681	844	30	applications	application	NNS
37681	844	31	that	that	WDT
37681	844	32	lead	lead	VBP
37681	844	33	the	the	DT
37681	844	34	pupil	pupil	NN
37681	844	35	to	to	TO
37681	844	36	measure	measure	VB
37681	844	37	things	thing	NNS
37681	844	38	in	in	IN
37681	844	39	a	a	DT
37681	844	40	way	way	NN
37681	844	41	that	that	WDT
37681	844	42	would	would	MD
37681	844	43	appeal	appeal	VB
37681	844	44	to	to	IN
37681	844	45	no	no	DT
37681	844	46	practical	practical	JJ
37681	844	47	man	man	NN
37681	844	48	,	,	,
37681	844	49	with	with	IN
37681	844	50	no	no	DT
37681	844	51	merely	merely	RB
37681	844	52	narrow	narrow	JJ
37681	844	53	range	range	NN
37681	844	54	of	of	IN
37681	844	55	applications	application	NNS
37681	844	56	,	,	,
37681	844	57	and	and	CC
37681	844	58	with	with	IN
37681	844	59	no	no	DT
37681	844	60	array	array	NN
37681	844	61	of	of	IN
37681	844	62	difficult	difficult	JJ
37681	844	63	terms	term	NNS
37681	844	64	from	from	IN
37681	844	65	physics	physics	NN
37681	844	66	and	and	CC
37681	844	67	engineering	engineering	NN
37681	844	68	that	that	DT
37681	844	69	submerge	submerge	NN
37681	844	70	all	all	DT
37681	844	71	thought	thought	NN
37681	844	72	of	of	IN
37681	844	73	mathematics	mathematic	NNS
37681	844	74	in	in	IN
37681	844	75	the	the	DT
37681	844	76	slough	slough	NN
37681	844	77	of	of	IN
37681	844	78	despond	despond	NN
37681	844	79	of	of	IN
37681	844	80	an	an	DT
37681	844	81	unknown	unknown	JJ
37681	844	82	technical	technical	JJ
37681	844	83	vocabulary	vocabulary	NN
37681	844	84	.	.	.
37681	845	1	Outdoor	outdoor	JJ
37681	845	2	exercises	exercise	NNS
37681	845	3	,	,	,
37681	845	4	even	even	RB
37681	845	5	if	if	IN
37681	845	6	somewhat	somewhat	RB
37681	845	7	primitive	primitive	JJ
37681	845	8	,	,	,
37681	845	9	may	may	MD
37681	845	10	be	be	VB
37681	845	11	introduced	introduce	VBN
37681	845	12	,	,	,
37681	845	13	but	but	CC
37681	845	14	it	-PRON-	PRP
37681	845	15	should	should	MD
37681	845	16	be	be	VB
37681	845	17	perfectly	perfectly	RB
37681	845	18	understood	understand	VBN
37681	845	19	that	that	IN
37681	845	20	such	such	JJ
37681	845	21	exercises	exercise	NNS
37681	845	22	are	be	VBP
37681	845	23	given	give	VBN
37681	845	24	for	for	IN
37681	845	25	the	the	DT
37681	845	26	purpose	purpose	NN
37681	845	27	of	of	IN
37681	845	28	increasing	increase	VBG
37681	845	29	the	the	DT
37681	845	30	interest	interest	NN
37681	845	31	in	in	IN
37681	845	32	geometry	geometry	NN
37681	845	33	,	,	,
37681	845	34	and	and	CC
37681	845	35	they	-PRON-	PRP
37681	845	36	should	should	MD
37681	845	37	be	be	VB
37681	845	38	abandoned	abandon	VBN
37681	845	39	if	if	IN
37681	845	40	they	-PRON-	PRP
37681	845	41	fail	fail	VBP
37681	845	42	of	of	IN
37681	845	43	this	this	DT
37681	845	44	purpose	purpose	NN
37681	845	45	.	.	.
37681	846	1	=	=	NFP
37681	846	2	Bibliography.=	Bibliography.=	NNP
37681	846	3	For	for	IN
37681	846	4	a	a	DT
37681	846	5	list	list	NN
37681	846	6	of	of	IN
37681	846	7	standard	standard	JJ
37681	846	8	textbooks	textbook	NNS
37681	846	9	issued	issue	VBN
37681	846	10	prior	prior	RB
37681	846	11	to	to	IN
37681	846	12	the	the	DT
37681	846	13	present	present	JJ
37681	846	14	generation	generation	NN
37681	846	15	,	,	,
37681	846	16	consult	consult	VB
37681	846	17	the	the	DT
37681	846	18	bibliography	bibliography	NN
37681	846	19	in	in	IN
37681	846	20	Stamper	Stamper	NNP
37681	846	21	,	,	,
37681	846	22	History	history	NN
37681	846	23	of	of	IN
37681	846	24	the	the	DT
37681	846	25	Teaching	Teaching	NNP
37681	846	26	of	of	IN
37681	846	27	Geometry	Geometry	NNP
37681	846	28	,	,	,
37681	846	29	New	New	NNP
37681	846	30	York	York	NNP
37681	846	31	,	,	,
37681	846	32	1908	1908	CD
37681	846	33	.	.	.
37681	847	1	FOOTNOTES	footnote	NNS
37681	847	2	:	:	:
37681	847	3	[	[	-LRB-
37681	847	4	35	35	CD
37681	847	5	]	]	-RRB-
37681	847	6	For	for	IN
37681	847	7	some	some	DT
37681	847	8	classes	class	NNS
37681	847	9	of	of	IN
37681	847	10	schools	school	NNS
37681	847	11	and	and	CC
37681	847	12	under	under	IN
37681	847	13	certain	certain	JJ
37681	847	14	circumstances	circumstance	NNS
37681	847	15	courses	course	NNS
37681	847	16	in	in	IN
37681	847	17	combined	combine	VBN
37681	847	18	mathematics	mathematic	NNS
37681	847	19	are	be	VBP
37681	847	20	very	very	RB
37681	847	21	desirable	desirable	JJ
37681	847	22	.	.	.
37681	848	1	All	all	DT
37681	848	2	that	that	WDT
37681	848	3	is	be	VBZ
37681	848	4	here	here	RB
37681	848	5	insisted	insist	VBN
37681	848	6	upon	upon	IN
37681	848	7	is	be	VBZ
37681	848	8	that	that	IN
37681	848	9	any	any	DT
37681	848	10	general	general	JJ
37681	848	11	fusion	fusion	NN
37681	848	12	all	all	RB
37681	848	13	along	along	IN
37681	848	14	the	the	DT
37681	848	15	line	line	NN
37681	848	16	would	would	MD
37681	848	17	result	result	VB
37681	848	18	in	in	IN
37681	848	19	weak	weak	JJ
37681	848	20	,	,	,
37681	848	21	insipid	insipid	JJ
37681	848	22	,	,	,
37681	848	23	and	and	CC
37681	848	24	uninteresting	unintereste	VBG
37681	848	25	mathematics	mathematic	NNS
37681	848	26	.	.	.
37681	849	1	A	a	DT
37681	849	2	beginning	beginning	NN
37681	849	3	,	,	,
37681	849	4	inspirational	inspirational	JJ
37681	849	5	course	course	NN
37681	849	6	in	in	IN
37681	849	7	combined	combine	VBN
37681	849	8	mathematics	mathematic	NNS
37681	849	9	has	have	VBZ
37681	849	10	a	a	DT
37681	849	11	good	good	JJ
37681	849	12	reason	reason	NN
37681	849	13	for	for	IN
37681	849	14	being	be	VBG
37681	849	15	in	in	IN
37681	849	16	many	many	JJ
37681	849	17	high	high	JJ
37681	849	18	schools	school	NNS
37681	849	19	in	in	IN
37681	849	20	spite	spite	NN
37681	849	21	of	of	IN
37681	849	22	its	-PRON-	PRP$
37681	849	23	manifest	manif	JJS
37681	849	24	disadvantages	disadvantage	NNS
37681	849	25	,	,	,
37681	849	26	and	and	CC
37681	849	27	such	such	PDT
37681	849	28	a	a	DT
37681	849	29	course	course	NN
37681	849	30	may	may	MD
37681	849	31	be	be	VB
37681	849	32	developed	develop	VBN
37681	849	33	to	to	TO
37681	849	34	cover	cover	VB
37681	849	35	all	all	DT
37681	849	36	of	of	IN
37681	849	37	the	the	DT
37681	849	38	required	require	VBN
37681	849	39	mathematics	mathematic	NNS
37681	849	40	given	give	VBN
37681	849	41	in	in	IN
37681	849	42	certain	certain	JJ
37681	849	43	schools	school	NNS
37681	849	44	.	.	.
37681	850	1	[	[	-LRB-
37681	850	2	36	36	CD
37681	850	3	]	]	-RRB-
37681	850	4	Carson	Carson	NNP
37681	850	5	,	,	,
37681	850	6	loc	loc	NNP
37681	850	7	.	.	.
37681	851	1	cit	cit	NNP
37681	851	2	.	.	NNP
37681	851	3	,	,	,
37681	851	4	p.	p.	NN
37681	851	5	15	15	CD
37681	851	6	.	.	.
37681	852	1	CHAPTER	chapter	NN
37681	852	2	VIII	viii	VBP
37681	852	3	THE	the	DT
37681	852	4	RELATION	relation	NN
37681	852	5	OF	of	IN
37681	852	6	ALGEBRA	algebra	NN
37681	852	7	TO	to	IN
37681	852	8	GEOMETRY	geometry	VB
37681	852	9	From	from	IN
37681	852	10	the	the	DT
37681	852	11	standpoint	standpoint	NN
37681	852	12	of	of	IN
37681	852	13	theory	theory	NN
37681	852	14	there	there	EX
37681	852	15	is	be	VBZ
37681	852	16	or	or	CC
37681	852	17	need	need	VB
37681	852	18	be	be	VB
37681	852	19	no	no	DT
37681	852	20	relation	relation	NN
37681	852	21	whatever	whatever	WDT
37681	852	22	between	between	IN
37681	852	23	algebra	algebra	NN
37681	852	24	and	and	CC
37681	852	25	geometry	geometry	NN
37681	852	26	.	.	.
37681	853	1	Algebra	algebra	NN
37681	853	2	was	be	VBD
37681	853	3	originally	originally	RB
37681	853	4	the	the	DT
37681	853	5	science	science	NN
37681	853	6	of	of	IN
37681	853	7	the	the	DT
37681	853	8	equation	equation	NN
37681	853	9	,	,	,
37681	853	10	as	as	IN
37681	853	11	its	-PRON-	PRP$
37681	853	12	name[37	name[37	NN
37681	853	13	]	]	-RRB-
37681	853	14	indicates	indicate	VBZ
37681	853	15	.	.	.
37681	854	1	This	this	DT
37681	854	2	means	mean	VBZ
37681	854	3	that	that	IN
37681	854	4	it	-PRON-	PRP
37681	854	5	was	be	VBD
37681	854	6	the	the	DT
37681	854	7	science	science	NN
37681	854	8	of	of	IN
37681	854	9	finding	find	VBG
37681	854	10	the	the	DT
37681	854	11	value	value	NN
37681	854	12	of	of	IN
37681	854	13	an	an	DT
37681	854	14	unknown	unknown	JJ
37681	854	15	quantity	quantity	NN
37681	854	16	in	in	IN
37681	854	17	a	a	DT
37681	854	18	statement	statement	NN
37681	854	19	of	of	IN
37681	854	20	equality	equality	NN
37681	854	21	.	.	.
37681	855	1	Later	later	RB
37681	855	2	it	-PRON-	PRP
37681	855	3	came	come	VBD
37681	855	4	to	to	TO
37681	855	5	mean	mean	VB
37681	855	6	much	much	RB
37681	855	7	more	more	JJR
37681	855	8	than	than	IN
37681	855	9	this	this	DT
37681	855	10	,	,	,
37681	855	11	and	and	CC
37681	855	12	Newton	Newton	NNP
37681	855	13	spoke	speak	VBD
37681	855	14	of	of	IN
37681	855	15	it	-PRON-	PRP
37681	855	16	as	as	IN
37681	855	17	universal	universal	JJ
37681	855	18	arithmetic	arithmetic	NNP
37681	855	19	,	,	,
37681	855	20	and	and	CC
37681	855	21	wrote	write	VBD
37681	855	22	an	an	DT
37681	855	23	algebra	algebra	NN
37681	855	24	with	with	IN
37681	855	25	this	this	DT
37681	855	26	title	title	NN
37681	855	27	.	.	.
37681	856	1	At	at	IN
37681	856	2	present	present	JJ
37681	856	3	the	the	DT
37681	856	4	term	term	NN
37681	856	5	is	be	VBZ
37681	856	6	applied	apply	VBN
37681	856	7	to	to	IN
37681	856	8	the	the	DT
37681	856	9	elements	element	NNS
37681	856	10	of	of	IN
37681	856	11	a	a	DT
37681	856	12	science	science	NN
37681	856	13	in	in	IN
37681	856	14	which	which	WDT
37681	856	15	numbers	number	NNS
37681	856	16	are	be	VBP
37681	856	17	represented	represent	VBN
37681	856	18	by	by	IN
37681	856	19	letters	letter	NNS
37681	856	20	and	and	CC
37681	856	21	in	in	IN
37681	856	22	which	which	WDT
37681	856	23	certain	certain	JJ
37681	856	24	functions	function	NNS
37681	856	25	are	be	VBP
37681	856	26	studied	study	VBN
37681	856	27	,	,	,
37681	856	28	functions	function	NNS
37681	856	29	which	which	WDT
37681	856	30	it	-PRON-	PRP
37681	856	31	is	be	VBZ
37681	856	32	not	not	RB
37681	856	33	necessary	necessary	JJ
37681	856	34	to	to	TO
37681	856	35	specify	specify	VB
37681	856	36	at	at	IN
37681	856	37	this	this	DT
37681	856	38	time	time	NN
37681	856	39	.	.	.
37681	857	1	The	the	DT
37681	857	2	work	work	NN
37681	857	3	relates	relate	VBZ
37681	857	4	chiefly	chiefly	RB
37681	857	5	to	to	IN
37681	857	6	functions	function	NNS
37681	857	7	involving	involve	VBG
37681	857	8	the	the	DT
37681	857	9	idea	idea	NN
37681	857	10	of	of	IN
37681	857	11	number	number	NN
37681	857	12	.	.	.
37681	858	1	In	in	IN
37681	858	2	geometry	geometry	NN
37681	858	3	,	,	,
37681	858	4	on	on	IN
37681	858	5	the	the	DT
37681	858	6	other	other	JJ
37681	858	7	hand	hand	NN
37681	858	8	,	,	,
37681	858	9	the	the	DT
37681	858	10	work	work	NN
37681	858	11	relates	relate	VBZ
37681	858	12	chiefly	chiefly	RB
37681	858	13	to	to	TO
37681	858	14	form	form	VB
37681	858	15	.	.	.
37681	859	1	Indeed	indeed	RB
37681	859	2	,	,	,
37681	859	3	in	in	IN
37681	859	4	pure	pure	JJ
37681	859	5	geometry	geometry	NN
37681	859	6	number	number	NN
37681	859	7	plays	play	VBZ
37681	859	8	practically	practically	RB
37681	859	9	no	no	DT
37681	859	10	part	part	NN
37681	859	11	,	,	,
37681	859	12	while	while	IN
37681	859	13	in	in	IN
37681	859	14	pure	pure	JJ
37681	859	15	algebra	algebra	NN
37681	859	16	form	form	NN
37681	859	17	plays	play	VBZ
37681	859	18	practically	practically	RB
37681	859	19	no	no	DT
37681	859	20	part	part	NN
37681	859	21	.	.	.
37681	860	1	In	in	IN
37681	860	2	1687	1687	CD
37681	860	3	the	the	DT
37681	860	4	great	great	JJ
37681	860	5	French	french	JJ
37681	860	6	philosopher	philosopher	NN
37681	860	7	,	,	,
37681	860	8	Descartes	Descartes	NNPS
37681	860	9	,	,	,
37681	860	10	wishing	wish	VBG
37681	860	11	to	to	TO
37681	860	12	picture	picture	VB
37681	860	13	certain	certain	JJ
37681	860	14	algebraic	algebraic	JJ
37681	860	15	functions	function	NNS
37681	860	16	,	,	,
37681	860	17	wrote	write	VBD
37681	860	18	a	a	DT
37681	860	19	work	work	NN
37681	860	20	of	of	IN
37681	860	21	about	about	RB
37681	860	22	a	a	DT
37681	860	23	hundred	hundred	CD
37681	860	24	pages	page	NNS
37681	860	25	,	,	,
37681	860	26	entitled	entitle	VBN
37681	860	27	"	"	``
37681	860	28	La	La	NNP
37681	860	29	Géométrie	Géométrie	NNP
37681	860	30	,	,	,
37681	860	31	"	"	''
37681	860	32	and	and	CC
37681	860	33	in	in	IN
37681	860	34	this	this	DT
37681	860	35	he	-PRON-	PRP
37681	860	36	showed	show	VBD
37681	860	37	a	a	DT
37681	860	38	correspondence	correspondence	NN
37681	860	39	between	between	IN
37681	860	40	the	the	DT
37681	860	41	numbers	number	NNS
37681	860	42	of	of	IN
37681	860	43	algebra	algebra	NN
37681	860	44	(	(	-LRB-
37681	860	45	which	which	WDT
37681	860	46	may	may	MD
37681	860	47	be	be	VB
37681	860	48	expressed	express	VBN
37681	860	49	by	by	IN
37681	860	50	letters	letter	NNS
37681	860	51	)	)	-RRB-
37681	860	52	and	and	CC
37681	860	53	the	the	DT
37681	860	54	concepts	concept	NNS
37681	860	55	of	of	IN
37681	860	56	geometry	geometry	NN
37681	860	57	.	.	.
37681	861	1	This	this	DT
37681	861	2	was	be	VBD
37681	861	3	the	the	DT
37681	861	4	first	first	JJ
37681	861	5	great	great	JJ
37681	861	6	step	step	NN
37681	861	7	in	in	IN
37681	861	8	the	the	DT
37681	861	9	analytic	analytic	JJ
37681	861	10	geometry	geometry	NN
37681	861	11	that	that	WDT
37681	861	12	finally	finally	RB
37681	861	13	gave	give	VBD
37681	861	14	us	-PRON-	PRP
37681	861	15	the	the	DT
37681	861	16	graph	graph	NN
37681	861	17	in	in	IN
37681	861	18	algebra	algebra	NN
37681	861	19	.	.	.
37681	862	1	Since	since	IN
37681	862	2	then	then	RB
37681	862	3	there	there	EX
37681	862	4	have	have	VBP
37681	862	5	been	be	VBN
37681	862	6	brought	bring	VBN
37681	862	7	out	out	RP
37681	862	8	from	from	IN
37681	862	9	time	time	NN
37681	862	10	to	to	IN
37681	862	11	time	time	NN
37681	862	12	other	other	JJ
37681	862	13	analogies	analogy	NNS
37681	862	14	between	between	IN
37681	862	15	algebra	algebra	NN
37681	862	16	and	and	CC
37681	862	17	geometry	geometry	NN
37681	862	18	,	,	,
37681	862	19	always	always	RB
37681	862	20	to	to	IN
37681	862	21	the	the	DT
37681	862	22	advantage	advantage	NN
37681	862	23	of	of	IN
37681	862	24	each	each	DT
37681	862	25	science	science	NN
37681	862	26	.	.	.
37681	863	1	This	this	DT
37681	863	2	has	have	VBZ
37681	863	3	led	lead	VBN
37681	863	4	to	to	IN
37681	863	5	a	a	DT
37681	863	6	desire	desire	NN
37681	863	7	on	on	IN
37681	863	8	the	the	DT
37681	863	9	part	part	NN
37681	863	10	of	of	IN
37681	863	11	some	some	DT
37681	863	12	teachers	teacher	NNS
37681	863	13	to	to	TO
37681	863	14	unite	unite	VB
37681	863	15	algebra	algebra	NN
37681	863	16	and	and	CC
37681	863	17	geometry	geometry	NN
37681	863	18	into	into	IN
37681	863	19	one	one	CD
37681	863	20	science	science	NN
37681	863	21	,	,	,
37681	863	22	having	have	VBG
37681	863	23	simply	simply	RB
37681	863	24	a	a	DT
37681	863	25	class	class	NN
37681	863	26	in	in	IN
37681	863	27	mathematics	mathematic	NNS
37681	863	28	without	without	IN
37681	863	29	these	these	DT
37681	863	30	special	special	JJ
37681	863	31	names	name	NNS
37681	863	32	.	.	.
37681	864	1	It	-PRON-	PRP
37681	864	2	is	be	VBZ
37681	864	3	well	well	JJ
37681	864	4	to	to	TO
37681	864	5	consider	consider	VB
37681	864	6	the	the	DT
37681	864	7	advantages	advantage	NNS
37681	864	8	and	and	CC
37681	864	9	the	the	DT
37681	864	10	disadvantages	disadvantage	NNS
37681	864	11	of	of	IN
37681	864	12	such	such	PDT
37681	864	13	a	a	DT
37681	864	14	plan	plan	NN
37681	864	15	,	,	,
37681	864	16	and	and	CC
37681	864	17	to	to	TO
37681	864	18	decide	decide	VB
37681	864	19	as	as	IN
37681	864	20	to	to	IN
37681	864	21	the	the	DT
37681	864	22	rational	rational	JJ
37681	864	23	attitude	attitude	NN
37681	864	24	to	to	TO
37681	864	25	be	be	VB
37681	864	26	taken	take	VBN
37681	864	27	by	by	IN
37681	864	28	teachers	teacher	NNS
37681	864	29	concerning	concern	VBG
37681	864	30	the	the	DT
37681	864	31	question	question	NN
37681	864	32	at	at	IN
37681	864	33	issue	issue	NN
37681	864	34	.	.	.
37681	865	1	On	on	IN
37681	865	2	the	the	DT
37681	865	3	side	side	NN
37681	865	4	of	of	IN
37681	865	5	advantages	advantage	NNS
37681	865	6	it	-PRON-	PRP
37681	865	7	is	be	VBZ
37681	865	8	claimed	claim	VBN
37681	865	9	that	that	IN
37681	865	10	there	there	EX
37681	865	11	is	be	VBZ
37681	865	12	economy	economy	NN
37681	865	13	of	of	IN
37681	865	14	time	time	NN
37681	865	15	and	and	CC
37681	865	16	of	of	IN
37681	865	17	energy	energy	NN
37681	865	18	.	.	.
37681	866	1	If	if	IN
37681	866	2	a	a	DT
37681	866	3	pupil	pupil	NN
37681	866	4	is	be	VBZ
37681	866	5	studying	study	VBG
37681	866	6	formulas	formula	NNS
37681	866	7	,	,	,
37681	866	8	let	let	VB
37681	866	9	the	the	DT
37681	866	10	formulas	formula	NNS
37681	866	11	of	of	IN
37681	866	12	geometry	geometry	NN
37681	866	13	be	be	VB
37681	866	14	studied	study	VBN
37681	866	15	;	;	:
37681	866	16	if	if	IN
37681	866	17	he	-PRON-	PRP
37681	866	18	is	be	VBZ
37681	866	19	taking	take	VBG
37681	866	20	up	up	RP
37681	866	21	ratio	ratio	NN
37681	866	22	and	and	CC
37681	866	23	proportion	proportion	NN
37681	866	24	;	;	:
37681	866	25	let	let	VB
37681	866	26	him	-PRON-	PRP
37681	866	27	do	do	VB
37681	866	28	so	so	RB
37681	866	29	for	for	IN
37681	866	30	algebra	algebra	NN
37681	866	31	and	and	CC
37681	866	32	geometry	geometry	NN
37681	866	33	at	at	IN
37681	866	34	the	the	DT
37681	866	35	same	same	JJ
37681	866	36	time	time	NN
37681	866	37	;	;	:
37681	866	38	if	if	IN
37681	866	39	he	-PRON-	PRP
37681	866	40	is	be	VBZ
37681	866	41	solving	solve	VBG
37681	866	42	quadratics	quadratic	NNS
37681	866	43	,	,	,
37681	866	44	let	let	VB
37681	866	45	him	-PRON-	PRP
37681	866	46	apply	apply	VB
37681	866	47	them	-PRON-	PRP
37681	866	48	at	at	IN
37681	866	49	once	once	RB
37681	866	50	to	to	IN
37681	866	51	certain	certain	JJ
37681	866	52	propositions	proposition	NNS
37681	866	53	concerning	concern	VBG
37681	866	54	secants	secant	NNS
37681	866	55	;	;	:
37681	866	56	and	and	CC
37681	866	57	if	if	IN
37681	866	58	he	-PRON-	PRP
37681	866	59	is	be	VBZ
37681	866	60	proving	prove	VBG
37681	866	61	that	that	IN
37681	866	62	(	(	-LRB-
37681	866	63	_	_	NNP
37681	866	64	a	a	DT
37681	866	65	_	_	NNP
37681	866	66	+	+	CC
37681	866	67	_	_	NNP
37681	866	68	b_)^2	b_)^2	RB
37681	866	69	equals	equal	VBZ
37681	866	70	_	_	NNP
37681	866	71	a_^2	a_^2	NNP
37681	866	72	+	+	CC
37681	866	73	2_ab	2_ab	CD
37681	866	74	_	_	NNP
37681	866	75	+	+	CC
37681	866	76	_	_	NNP
37681	866	77	b_^2	b_^2	NNP
37681	866	78	,	,	,
37681	866	79	let	let	VBD
37681	866	80	him	-PRON-	PRP
37681	866	81	do	do	VB
37681	866	82	so	so	RB
37681	866	83	by	by	IN
37681	866	84	algebra	algebra	NN
37681	866	85	and	and	CC
37681	866	86	by	by	IN
37681	866	87	geometry	geometry	NN
37681	866	88	simultaneously	simultaneously	RB
37681	866	89	.	.	.
37681	867	1	It	-PRON-	PRP
37681	867	2	is	be	VBZ
37681	867	3	claimed	claim	VBN
37681	867	4	that	that	IN
37681	867	5	not	not	RB
37681	867	6	only	only	RB
37681	867	7	is	be	VBZ
37681	867	8	there	there	EX
37681	867	9	economy	economy	NN
37681	867	10	in	in	IN
37681	867	11	this	this	DT
37681	867	12	arrangement	arrangement	NN
37681	867	13	,	,	,
37681	867	14	but	but	CC
37681	867	15	that	that	IN
37681	867	16	the	the	DT
37681	867	17	pupil	pupil	NN
37681	867	18	sees	see	VBZ
37681	867	19	mathematics	mathematic	NNS
37681	867	20	as	as	IN
37681	867	21	a	a	DT
37681	867	22	whole	whole	NN
37681	867	23	,	,	,
37681	867	24	and	and	CC
37681	867	25	thus	thus	RB
37681	867	26	acquires	acquire	VBZ
37681	867	27	more	more	JJR
37681	867	28	of	of	IN
37681	867	29	a	a	DT
37681	867	30	mastery	mastery	NN
37681	867	31	than	than	IN
37681	867	32	comes	come	VBZ
37681	867	33	by	by	IN
37681	867	34	our	-PRON-	PRP$
37681	867	35	present	present	JJ
37681	867	36	"	"	``
37681	867	37	tandem	tandem	NN
37681	867	38	arrangement	arrangement	NN
37681	867	39	.	.	.
37681	867	40	"	"	''
37681	868	1	On	on	IN
37681	868	2	the	the	DT
37681	868	3	side	side	NN
37681	868	4	of	of	IN
37681	868	5	disadvantages	disadvantage	NNS
37681	868	6	it	-PRON-	PRP
37681	868	7	may	may	MD
37681	868	8	be	be	VB
37681	868	9	asked	ask	VBN
37681	868	10	if	if	IN
37681	868	11	the	the	DT
37681	868	12	same	same	JJ
37681	868	13	arguments	argument	NNS
37681	868	14	would	would	MD
37681	868	15	not	not	RB
37681	868	16	lead	lead	VB
37681	868	17	us	-PRON-	PRP
37681	868	18	to	to	TO
37681	868	19	teach	teach	VB
37681	868	20	Latin	Latin	NNP
37681	868	21	and	and	CC
37681	868	22	Greek	Greek	NNP
37681	868	23	together	together	RB
37681	868	24	,	,	,
37681	868	25	or	or	CC
37681	868	26	Latin	Latin	NNP
37681	868	27	and	and	CC
37681	868	28	French	French	NNP
37681	868	29	,	,	,
37681	868	30	or	or	CC
37681	868	31	all	all	DT
37681	868	32	three	three	CD
37681	868	33	simultaneously	simultaneously	RB
37681	868	34	?	?	.
37681	869	1	If	if	IN
37681	869	2	pupils	pupil	NNS
37681	869	3	should	should	MD
37681	869	4	decline	decline	VB
37681	869	5	nouns	noun	NNS
37681	869	6	in	in	IN
37681	869	7	all	all	DT
37681	869	8	three	three	CD
37681	869	9	languages	language	NNS
37681	869	10	at	at	IN
37681	869	11	the	the	DT
37681	869	12	same	same	JJ
37681	869	13	time	time	NN
37681	869	14	,	,	,
37681	869	15	learn	learn	VB
37681	869	16	to	to	TO
37681	869	17	count	count	VB
37681	869	18	in	in	IN
37681	869	19	all	all	DT
37681	869	20	at	at	IN
37681	869	21	the	the	DT
37681	869	22	same	same	JJ
37681	869	23	time	time	NN
37681	869	24	,	,	,
37681	869	25	and	and	CC
37681	869	26	begin	begin	VB
37681	869	27	to	to	TO
37681	869	28	translate	translate	VB
37681	869	29	in	in	RB
37681	869	30	all	all	DT
37681	869	31	simultaneously	simultaneously	RB
37681	869	32	,	,	,
37681	869	33	would	would	MD
37681	869	34	there	there	EX
37681	869	35	not	not	RB
37681	869	36	be	be	VB
37681	869	37	an	an	DT
37681	869	38	economy	economy	NN
37681	869	39	of	of	IN
37681	869	40	time	time	NN
37681	869	41	and	and	CC
37681	869	42	effort	effort	NN
37681	869	43	,	,	,
37681	869	44	and	and	CC
37681	869	45	would	would	MD
37681	869	46	there	there	EX
37681	869	47	not	not	RB
37681	869	48	be	be	VB
37681	869	49	developed	develop	VBN
37681	869	50	a	a	DT
37681	869	51	much	much	RB
37681	869	52	broader	broad	JJR
37681	869	53	view	view	NN
37681	869	54	of	of	IN
37681	869	55	language	language	NN
37681	869	56	?	?	.
37681	870	1	Now	now	RB
37681	870	2	the	the	DT
37681	870	3	fusionist	fusionist	NN
37681	870	4	of	of	IN
37681	870	5	algebra	algebra	NN
37681	870	6	and	and	CC
37681	870	7	geometry	geometry	NN
37681	870	8	does	do	VBZ
37681	870	9	not	not	RB
37681	870	10	like	like	VB
37681	870	11	this	this	DT
37681	870	12	argument	argument	NN
37681	870	13	,	,	,
37681	870	14	and	and	CC
37681	870	15	he	-PRON-	PRP
37681	870	16	says	say	VBZ
37681	870	17	that	that	IN
37681	870	18	the	the	DT
37681	870	19	cases	case	NNS
37681	870	20	are	be	VBP
37681	870	21	not	not	RB
37681	870	22	parallel	parallel	JJ
37681	870	23	,	,	,
37681	870	24	and	and	CC
37681	870	25	he	-PRON-	PRP
37681	870	26	tries	try	VBZ
37681	870	27	to	to	TO
37681	870	28	tell	tell	VB
37681	870	29	why	why	WRB
37681	870	30	they	-PRON-	PRP
37681	870	31	are	be	VBP
37681	870	32	not	not	RB
37681	870	33	.	.	.
37681	871	1	He	-PRON-	PRP
37681	871	2	demands	demand	VBZ
37681	871	3	that	that	IN
37681	871	4	his	-PRON-	PRP$
37681	871	5	opponent	opponent	NN
37681	871	6	abandon	abandon	NNP
37681	871	7	argument	argument	NN
37681	871	8	by	by	IN
37681	871	9	analogy	analogy	NN
37681	871	10	and	and	CC
37681	871	11	advance	advance	VB
37681	871	12	some	some	DT
37681	871	13	positive	positive	JJ
37681	871	14	reason	reason	NN
37681	871	15	why	why	WRB
37681	871	16	algebra	algebra	NN
37681	871	17	and	and	CC
37681	871	18	geometry	geometry	NN
37681	871	19	should	should	MD
37681	871	20	not	not	RB
37681	871	21	be	be	VB
37681	871	22	fused	fuse	VBN
37681	871	23	.	.	.
37681	872	1	Then	then	RB
37681	872	2	his	-PRON-	PRP$
37681	872	3	opponent	opponent	NN
37681	872	4	says	say	VBZ
37681	872	5	that	that	IN
37681	872	6	it	-PRON-	PRP
37681	872	7	is	be	VBZ
37681	872	8	not	not	RB
37681	872	9	for	for	IN
37681	872	10	him	-PRON-	PRP
37681	872	11	to	to	TO
37681	872	12	advance	advance	VB
37681	872	13	any	any	DT
37681	872	14	reason	reason	NN
37681	872	15	for	for	IN
37681	872	16	what	what	WP
37681	872	17	already	already	RB
37681	872	18	exists	exist	VBZ
37681	872	19	,	,	,
37681	872	20	the	the	DT
37681	872	21	teaching	teaching	NN
37681	872	22	of	of	IN
37681	872	23	the	the	DT
37681	872	24	two	two	CD
37681	872	25	separately	separately	RB
37681	872	26	;	;	:
37681	872	27	that	that	IN
37681	872	28	he	-PRON-	PRP
37681	872	29	has	have	VBZ
37681	872	30	only	only	RB
37681	872	31	to	to	TO
37681	872	32	refute	refute	VB
37681	872	33	the	the	DT
37681	872	34	fusionist	fusionist	NN
37681	872	35	's	's	POS
37681	872	36	arguments	argument	NNS
37681	872	37	,	,	,
37681	872	38	and	and	CC
37681	872	39	that	that	IN
37681	872	40	he	-PRON-	PRP
37681	872	41	has	have	VBZ
37681	872	42	done	do	VBN
37681	872	43	so	so	RB
37681	872	44	.	.	.
37681	873	1	He	-PRON-	PRP
37681	873	2	asserts	assert	VBZ
37681	873	3	that	that	IN
37681	873	4	algebra	algebra	NN
37681	873	5	and	and	CC
37681	873	6	geometry	geometry	NN
37681	873	7	are	be	VBP
37681	873	8	as	as	RB
37681	873	9	distinct	distinct	JJ
37681	873	10	as	as	IN
37681	873	11	chemistry	chemistry	NN
37681	873	12	and	and	CC
37681	873	13	biology	biology	NN
37681	873	14	;	;	:
37681	873	15	that	that	IN
37681	873	16	they	-PRON-	PRP
37681	873	17	have	have	VBP
37681	873	18	a	a	DT
37681	873	19	few	few	JJ
37681	873	20	common	common	JJ
37681	873	21	points	point	NNS
37681	873	22	,	,	,
37681	873	23	but	but	CC
37681	873	24	not	not	RB
37681	873	25	enough	enough	JJ
37681	873	26	to	to	TO
37681	873	27	require	require	VB
37681	873	28	teaching	teach	VBG
37681	873	29	them	-PRON-	PRP
37681	873	30	together	together	RB
37681	873	31	.	.	.
37681	874	1	He	-PRON-	PRP
37681	874	2	claims	claim	VBZ
37681	874	3	that	that	IN
37681	874	4	to	to	TO
37681	874	5	begin	begin	VB
37681	874	6	Latin	Latin	NNP
37681	874	7	and	and	CC
37681	874	8	Greek	Greek	NNP
37681	874	9	at	at	IN
37681	874	10	the	the	DT
37681	874	11	same	same	JJ
37681	874	12	time	time	NN
37681	874	13	has	have	VBZ
37681	874	14	always	always	RB
37681	874	15	proved	prove	VBN
37681	874	16	to	to	TO
37681	874	17	be	be	VB
37681	874	18	confusing	confusing	JJ
37681	874	19	,	,	,
37681	874	20	and	and	CC
37681	874	21	that	that	IN
37681	874	22	the	the	DT
37681	874	23	same	same	JJ
37681	874	24	is	be	VBZ
37681	874	25	true	true	JJ
37681	874	26	of	of	IN
37681	874	27	algebra	algebra	NN
37681	874	28	and	and	CC
37681	874	29	geometry	geometry	NN
37681	874	30	.	.	.
37681	875	1	He	-PRON-	PRP
37681	875	2	grants	grant	VBZ
37681	875	3	that	that	IN
37681	875	4	unified	unified	JJ
37681	875	5	knowledge	knowledge	NN
37681	875	6	is	be	VBZ
37681	875	7	desirable	desirable	JJ
37681	875	8	,	,	,
37681	875	9	but	but	CC
37681	875	10	he	-PRON-	PRP
37681	875	11	argues	argue	VBZ
37681	875	12	that	that	IN
37681	875	13	when	when	WRB
37681	875	14	the	the	DT
37681	875	15	fine	fine	JJ
37681	875	16	arts	art	NNS
37681	875	17	of	of	IN
37681	875	18	music	music	NN
37681	875	19	and	and	CC
37681	875	20	color	color	NN
37681	875	21	work	work	NN
37681	875	22	fuse	fuse	NN
37681	875	23	,	,	,
37681	875	24	and	and	CC
37681	875	25	when	when	WRB
37681	875	26	the	the	DT
37681	875	27	natural	natural	JJ
37681	875	28	sciences	science	NNS
37681	875	29	of	of	IN
37681	875	30	chemistry	chemistry	NN
37681	875	31	and	and	CC
37681	875	32	physics	physics	NN
37681	875	33	are	be	VBP
37681	875	34	taught	teach	VBN
37681	875	35	in	in	IN
37681	875	36	the	the	DT
37681	875	37	same	same	JJ
37681	875	38	class	class	NN
37681	875	39	,	,	,
37681	875	40	and	and	CC
37681	875	41	when	when	WRB
37681	875	42	we	-PRON-	PRP
37681	875	43	follow	follow	VBP
37681	875	44	the	the	DT
37681	875	45	declension	declension	NN
37681	875	46	of	of	IN
37681	875	47	a	a	DT
37681	875	48	German	german	JJ
37681	875	49	noun	noun	NN
37681	875	50	by	by	IN
37681	875	51	that	that	DT
37681	875	52	of	of	IN
37681	875	53	a	a	DT
37681	875	54	French	french	JJ
37681	875	55	noun	noun	NN
37681	875	56	and	and	CC
37681	875	57	a	a	DT
37681	875	58	Latin	latin	JJ
37681	875	59	noun	noun	NN
37681	875	60	,	,	,
37681	875	61	and	and	CC
37681	875	62	when	when	WRB
37681	875	63	we	-PRON-	PRP
37681	875	64	teach	teach	VBP
37681	875	65	drawing	draw	VBG
37681	875	66	and	and	CC
37681	875	67	penmanship	penmanship	NN
37681	875	68	together	together	RB
37681	875	69	,	,	,
37681	875	70	then	then	RB
37681	875	71	it	-PRON-	PRP
37681	875	72	is	be	VBZ
37681	875	73	well	well	JJ
37681	875	74	to	to	TO
37681	875	75	talk	talk	VB
37681	875	76	of	of	IN
37681	875	77	mixing	mix	VBG
37681	875	78	algebra	algebra	NN
37681	875	79	and	and	CC
37681	875	80	geometry	geometry	NN
37681	875	81	.	.	.
37681	876	1	It	-PRON-	PRP
37681	876	2	is	be	VBZ
37681	876	3	well	well	RB
37681	876	4	,	,	,
37681	876	5	before	before	IN
37681	876	6	deciding	decide	VBG
37681	876	7	such	such	PDT
37681	876	8	a	a	DT
37681	876	9	question	question	NN
37681	876	10	for	for	IN
37681	876	11	ourselves	-PRON-	PRP
37681	876	12	(	(	-LRB-
37681	876	13	for	for	IN
37681	876	14	evidently	evidently	RB
37681	876	15	we	-PRON-	PRP
37681	876	16	can	can	MD
37681	876	17	not	not	RB
37681	876	18	decide	decide	VB
37681	876	19	it	-PRON-	PRP
37681	876	20	for	for	IN
37681	876	21	the	the	DT
37681	876	22	world	world	NN
37681	876	23	)	)	-RRB-
37681	876	24	,	,	,
37681	876	25	to	to	TO
37681	876	26	consider	consider	VB
37681	876	27	what	what	WP
37681	876	28	has	have	VBZ
37681	876	29	been	be	VBN
37681	876	30	the	the	DT
37681	876	31	result	result	NN
37681	876	32	of	of	IN
37681	876	33	experience	experience	NN
37681	876	34	.	.	.
37681	877	1	Algebra	algebra	NN
37681	877	2	and	and	CC
37681	877	3	geometry	geometry	NN
37681	877	4	were	be	VBD
37681	877	5	always	always	RB
37681	877	6	taught	teach	VBN
37681	877	7	together	together	RB
37681	877	8	in	in	IN
37681	877	9	early	early	JJ
37681	877	10	times	time	NNS
37681	877	11	,	,	,
37681	877	12	as	as	IN
37681	877	13	were	be	VBD
37681	877	14	trigonometry	trigonometry	NN
37681	877	15	and	and	CC
37681	877	16	astronomy	astronomy	NN
37681	877	17	.	.	.
37681	878	1	The	the	DT
37681	878	2	Ahmes	Ahmes	NNP
37681	878	3	papyrus	papyrus	NN
37681	878	4	contains	contain	VBZ
37681	878	5	both	both	CC
37681	878	6	primitive	primitive	JJ
37681	878	7	algebra	algebra	NN
37681	878	8	and	and	CC
37681	878	9	primitive	primitive	JJ
37681	878	10	geometry	geometry	NN
37681	878	11	.	.	.
37681	879	1	Euclid	Euclid	NNP
37681	879	2	's	's	POS
37681	879	3	"	"	``
37681	879	4	Elements	Elements	NNPS
37681	879	5	"	"	''
37681	879	6	contains	contain	VBZ
37681	879	7	not	not	RB
37681	879	8	only	only	RB
37681	879	9	pure	pure	JJ
37681	879	10	geometry	geometry	NN
37681	879	11	,	,	,
37681	879	12	but	but	CC
37681	879	13	also	also	RB
37681	879	14	a	a	DT
37681	879	15	geometric	geometric	JJ
37681	879	16	algebra	algebra	NN
37681	879	17	and	and	CC
37681	879	18	the	the	DT
37681	879	19	theory	theory	NN
37681	879	20	of	of	IN
37681	879	21	numbers	number	NNS
37681	879	22	.	.	.
37681	880	1	The	the	DT
37681	880	2	early	early	JJ
37681	880	3	works	work	NNS
37681	880	4	of	of	IN
37681	880	5	the	the	DT
37681	880	6	Hindus	Hindus	NNPS
37681	880	7	often	often	RB
37681	880	8	fused	fuse	VBD
37681	880	9	geometry	geometry	NN
37681	880	10	and	and	CC
37681	880	11	arithmetic	arithmetic	JJ
37681	880	12	,	,	,
37681	880	13	or	or	CC
37681	880	14	geometry	geometry	NN
37681	880	15	and	and	CC
37681	880	16	algebra	algebra	NN
37681	880	17	.	.	.
37681	881	1	Even	even	RB
37681	881	2	the	the	DT
37681	881	3	first	first	JJ
37681	881	4	great	great	JJ
37681	881	5	printed	print	VBN
37681	881	6	compendium	compendium	NN
37681	881	7	of	of	IN
37681	881	8	mathematics	mathematic	NNS
37681	881	9	,	,	,
37681	881	10	the	the	DT
37681	881	11	"	"	``
37681	881	12	S[=u]ma	S[=u]ma	NNP
37681	881	13	"	"	''
37681	881	14	of	of	IN
37681	881	15	Paciuolo	Paciuolo	NNP
37681	881	16	(	(	-LRB-
37681	881	17	1494	1494	CD
37681	881	18	)	)	-RRB-
37681	881	19	contained	contain	VBD
37681	881	20	all	all	DT
37681	881	21	of	of	IN
37681	881	22	the	the	DT
37681	881	23	branches	branch	NNS
37681	881	24	of	of	IN
37681	881	25	mathematics	mathematic	NNS
37681	881	26	.	.	.
37681	882	1	Much	much	JJ
37681	882	2	of	of	IN
37681	882	3	this	this	DT
37681	882	4	later	later	JJ
37681	882	5	attempt	attempt	NN
37681	882	6	was	be	VBD
37681	882	7	not	not	RB
37681	882	8	,	,	,
37681	882	9	however	however	RB
37681	882	10	,	,	,
37681	882	11	an	an	DT
37681	882	12	example	example	NN
37681	882	13	of	of	IN
37681	882	14	perfect	perfect	JJ
37681	882	15	fusion	fusion	NN
37681	882	16	,	,	,
37681	882	17	but	but	CC
37681	882	18	rather	rather	RB
37681	882	19	of	of	IN
37681	882	20	assigning	assign	VBG
37681	882	21	one	one	CD
37681	882	22	set	set	NN
37681	882	23	of	of	IN
37681	882	24	chapters	chapter	NNS
37681	882	25	to	to	TO
37681	882	26	algebra	algebra	VB
37681	882	27	,	,	,
37681	882	28	another	another	DT
37681	882	29	to	to	TO
37681	882	30	geometry	geometry	VB
37681	882	31	,	,	,
37681	882	32	and	and	CC
37681	882	33	another	another	DT
37681	882	34	to	to	IN
37681	882	35	arithmetic	arithmetic	JJ
37681	882	36	.	.	.
37681	883	1	So	so	RB
37681	883	2	fusion	fusion	NN
37681	883	3	,	,	,
37681	883	4	more	more	RBR
37681	883	5	or	or	CC
37681	883	6	less	less	RBR
37681	883	7	perfect	perfect	JJ
37681	883	8	,	,	,
37681	883	9	has	have	VBZ
37681	883	10	been	be	VBN
37681	883	11	tried	try	VBN
37681	883	12	over	over	IN
37681	883	13	long	long	JJ
37681	883	14	periods	period	NNS
37681	883	15	,	,	,
37681	883	16	and	and	CC
37681	883	17	abandoned	abandon	VBD
37681	883	18	as	as	IN
37681	883	19	each	each	DT
37681	883	20	subject	subject	NN
37681	883	21	grew	grow	VBD
37681	883	22	more	more	RBR
37681	883	23	complete	complete	JJ
37681	883	24	in	in	IN
37681	883	25	itself	-PRON-	PRP
37681	883	26	,	,	,
37681	883	27	with	with	IN
37681	883	28	its	-PRON-	PRP$
37681	883	29	own	own	JJ
37681	883	30	language	language	NN
37681	883	31	and	and	CC
37681	883	32	its	-PRON-	PRP$
37681	883	33	peculiar	peculiar	JJ
37681	883	34	symbols	symbol	NNS
37681	883	35	.	.	.
37681	884	1	But	but	CC
37681	884	2	it	-PRON-	PRP
37681	884	3	is	be	VBZ
37681	884	4	asserted	assert	VBN
37681	884	5	that	that	DT
37681	884	6	fusion	fusion	NN
37681	884	7	is	be	VBZ
37681	884	8	being	be	VBG
37681	884	9	carried	carry	VBN
37681	884	10	on	on	IN
37681	884	11	successfully	successfully	RB
37681	884	12	to	to	NN
37681	884	13	-	-	HYPH
37681	884	14	day	day	NN
37681	884	15	by	by	IN
37681	884	16	more	more	JJR
37681	884	17	than	than	IN
37681	884	18	one	one	CD
37681	884	19	enthusiastic	enthusiastic	JJ
37681	884	20	teacher	teacher	NN
37681	884	21	,	,	,
37681	884	22	and	and	CC
37681	884	23	that	that	IN
37681	884	24	this	this	DT
37681	884	25	proves	prove	VBZ
37681	884	26	the	the	DT
37681	884	27	contention	contention	NN
37681	884	28	that	that	IN
37681	884	29	the	the	DT
37681	884	30	plan	plan	NN
37681	884	31	is	be	VBZ
37681	884	32	a	a	DT
37681	884	33	good	good	JJ
37681	884	34	one	one	NN
37681	884	35	.	.	.
37681	885	1	Books	book	NNS
37681	885	2	are	be	VBP
37681	885	3	cited	cite	VBN
37681	885	4	to	to	TO
37681	885	5	show	show	VB
37681	885	6	that	that	IN
37681	885	7	the	the	DT
37681	885	8	arrangement	arrangement	NN
37681	885	9	is	be	VBZ
37681	885	10	feasible	feasible	JJ
37681	885	11	,	,	,
37681	885	12	and	and	CC
37681	885	13	classes	class	NNS
37681	885	14	are	be	VBP
37681	885	15	indicated	indicate	VBN
37681	885	16	where	where	WRB
37681	885	17	the	the	DT
37681	885	18	work	work	NN
37681	885	19	is	be	VBZ
37681	885	20	progressing	progress	VBG
37681	885	21	along	along	IN
37681	885	22	this	this	DT
37681	885	23	line	line	NN
37681	885	24	.	.	.
37681	886	1	What	what	WP
37681	886	2	,	,	,
37681	886	3	then	then	RB
37681	886	4	,	,	,
37681	886	5	is	be	VBZ
37681	886	6	the	the	DT
37681	886	7	conclusion	conclusion	NN
37681	886	8	?	?	.
37681	887	1	That	that	DT
37681	887	2	is	be	VBZ
37681	887	3	a	a	DT
37681	887	4	question	question	NN
37681	887	5	for	for	IN
37681	887	6	the	the	DT
37681	887	7	teacher	teacher	NN
37681	887	8	to	to	TO
37681	887	9	settle	settle	VB
37681	887	10	,	,	,
37681	887	11	but	but	CC
37681	887	12	it	-PRON-	PRP
37681	887	13	is	be	VBZ
37681	887	14	one	one	CD
37681	887	15	upon	upon	IN
37681	887	16	which	which	WDT
37681	887	17	a	a	DT
37681	887	18	writer	writer	NN
37681	887	19	on	on	IN
37681	887	20	the	the	DT
37681	887	21	teaching	teaching	NN
37681	887	22	of	of	IN
37681	887	23	mathematics	mathematic	NNS
37681	887	24	should	should	MD
37681	887	25	not	not	RB
37681	887	26	fear	fear	VB
37681	887	27	to	to	TO
37681	887	28	express	express	VB
37681	887	29	his	-PRON-	PRP$
37681	887	30	candid	candid	JJ
37681	887	31	opinion	opinion	NN
37681	887	32	.	.	.
37681	888	1	It	-PRON-	PRP
37681	888	2	is	be	VBZ
37681	888	3	a	a	DT
37681	888	4	fact	fact	NN
37681	888	5	that	that	IN
37681	888	6	the	the	DT
37681	888	7	Greek	greek	JJ
37681	888	8	and	and	CC
37681	888	9	Latin	Latin	NNP
37681	888	10	fusion	fusion	NN
37681	888	11	is	be	VBZ
37681	888	12	a	a	DT
37681	888	13	fair	fair	JJ
37681	888	14	analogy	analogy	NN
37681	888	15	.	.	.
37681	889	1	There	there	EX
37681	889	2	are	be	VBP
37681	889	3	reasons	reason	NNS
37681	889	4	for	for	IN
37681	889	5	it	-PRON-	PRP
37681	889	6	,	,	,
37681	889	7	but	but	CC
37681	889	8	there	there	EX
37681	889	9	are	be	VBP
37681	889	10	many	many	RB
37681	889	11	more	more	JJR
37681	889	12	against	against	IN
37681	889	13	it	-PRON-	PRP
37681	889	14	,	,	,
37681	889	15	the	the	DT
37681	889	16	chief	chief	JJ
37681	889	17	one	one	NN
37681	889	18	being	be	VBG
37681	889	19	the	the	DT
37681	889	20	confusion	confusion	NN
37681	889	21	of	of	IN
37681	889	22	beginning	begin	VBG
37681	889	23	two	two	CD
37681	889	24	languages	language	NNS
37681	889	25	at	at	IN
37681	889	26	once	once	RB
37681	889	27	,	,	,
37681	889	28	and	and	CC
37681	889	29	the	the	DT
37681	889	30	learning	learning	NN
37681	889	31	simultaneously	simultaneously	RB
37681	889	32	of	of	IN
37681	889	33	two	two	CD
37681	889	34	vocabularies	vocabulary	NNS
37681	889	35	that	that	WDT
37681	889	36	must	must	MD
37681	889	37	be	be	VB
37681	889	38	kept	keep	VBN
37681	889	39	separate	separate	JJ
37681	889	40	.	.	.
37681	890	1	It	-PRON-	PRP
37681	890	2	is	be	VBZ
37681	890	3	also	also	RB
37681	890	4	a	a	DT
37681	890	5	fact	fact	NN
37681	890	6	that	that	IN
37681	890	7	algebra	algebra	NN
37681	890	8	and	and	CC
37681	890	9	geometry	geometry	NN
37681	890	10	are	be	VBP
37681	890	11	fully	fully	RB
37681	890	12	as	as	RB
37681	890	13	distinct	distinct	JJ
37681	890	14	as	as	IN
37681	890	15	physics	physics	NN
37681	890	16	and	and	CC
37681	890	17	chemistry	chemistry	NN
37681	890	18	,	,	,
37681	890	19	or	or	CC
37681	890	20	chemistry	chemistry	NN
37681	890	21	and	and	CC
37681	890	22	biology	biology	NN
37681	890	23	.	.	.
37681	891	1	Life	life	NN
37681	891	2	may	may	MD
37681	891	3	be	be	VB
37681	891	4	electricity	electricity	NN
37681	891	5	,	,	,
37681	891	6	and	and	CC
37681	891	7	a	a	DT
37681	891	8	brief	brief	JJ
37681	891	9	cessation	cessation	NN
37681	891	10	of	of	IN
37681	891	11	oxidization	oxidization	NN
37681	891	12	in	in	IN
37681	891	13	the	the	DT
37681	891	14	lungs	lung	NNS
37681	891	15	brings	bring	VBZ
37681	891	16	death	death	NN
37681	891	17	,	,	,
37681	891	18	but	but	CC
37681	891	19	these	these	DT
37681	891	20	facts	fact	NNS
37681	891	21	are	be	VBP
37681	891	22	no	no	DT
37681	891	23	reasons	reason	NNS
37681	891	24	for	for	IN
37681	891	25	fusing	fuse	VBG
37681	891	26	the	the	DT
37681	891	27	sciences	science	NNS
37681	891	28	of	of	IN
37681	891	29	physics	physics	NN
37681	891	30	,	,	,
37681	891	31	biology	biology	NN
37681	891	32	,	,	,
37681	891	33	and	and	CC
37681	891	34	chemistry	chemistry	NN
37681	891	35	.	.	.
37681	892	1	Algebra	algebra	NN
37681	892	2	is	be	VBZ
37681	892	3	primarily	primarily	RB
37681	892	4	a	a	DT
37681	892	5	theory	theory	NN
37681	892	6	of	of	IN
37681	892	7	certain	certain	JJ
37681	892	8	elementary	elementary	JJ
37681	892	9	functions	function	NNS
37681	892	10	,	,	,
37681	892	11	a	a	DT
37681	892	12	generalized	generalize	VBN
37681	892	13	arithmetic	arithmetic	JJ
37681	892	14	,	,	,
37681	892	15	while	while	IN
37681	892	16	geometry	geometry	NN
37681	892	17	is	be	VBZ
37681	892	18	primarily	primarily	RB
37681	892	19	a	a	DT
37681	892	20	theory	theory	NN
37681	892	21	of	of	IN
37681	892	22	form	form	NN
37681	892	23	with	with	IN
37681	892	24	a	a	DT
37681	892	25	highly	highly	RB
37681	892	26	refined	refined	JJ
37681	892	27	logic	logic	NN
37681	892	28	to	to	TO
37681	892	29	be	be	VB
37681	892	30	used	use	VBN
37681	892	31	in	in	IN
37681	892	32	its	-PRON-	PRP$
37681	892	33	mastery	mastery	NN
37681	892	34	.	.	.
37681	893	1	They	-PRON-	PRP
37681	893	2	have	have	VBP
37681	893	3	a	a	DT
37681	893	4	few	few	JJ
37681	893	5	things	thing	NNS
37681	893	6	in	in	IN
37681	893	7	common	common	JJ
37681	893	8	,	,	,
37681	893	9	as	as	IN
37681	893	10	many	many	JJ
37681	893	11	other	other	JJ
37681	893	12	subjects	subject	NNS
37681	893	13	have	have	VBP
37681	893	14	,	,	,
37681	893	15	but	but	CC
37681	893	16	they	-PRON-	PRP
37681	893	17	have	have	VBP
37681	893	18	very	very	RB
37681	893	19	many	many	JJ
37681	893	20	more	more	JJR
37681	893	21	features	feature	NNS
37681	893	22	that	that	WDT
37681	893	23	are	be	VBP
37681	893	24	peculiar	peculiar	JJ
37681	893	25	to	to	IN
37681	893	26	the	the	DT
37681	893	27	one	one	CD
37681	893	28	or	or	CC
37681	893	29	the	the	DT
37681	893	30	other	other	JJ
37681	893	31	.	.	.
37681	894	1	The	the	DT
37681	894	2	experience	experience	NN
37681	894	3	of	of	IN
37681	894	4	the	the	DT
37681	894	5	world	world	NN
37681	894	6	has	have	VBZ
37681	894	7	led	lead	VBN
37681	894	8	it	-PRON-	PRP
37681	894	9	away	away	RB
37681	894	10	from	from	IN
37681	894	11	a	a	DT
37681	894	12	simultaneous	simultaneous	JJ
37681	894	13	treatment	treatment	NN
37681	894	14	,	,	,
37681	894	15	and	and	CC
37681	894	16	the	the	DT
37681	894	17	contrary	contrary	JJ
37681	894	18	experience	experience	NN
37681	894	19	of	of	IN
37681	894	20	a	a	DT
37681	894	21	few	few	JJ
37681	894	22	enthusiastic	enthusiastic	JJ
37681	894	23	teachers	teacher	NNS
37681	894	24	of	of	IN
37681	894	25	to	to	IN
37681	894	26	-	-	HYPH
37681	894	27	day	day	NN
37681	894	28	proves	prove	VBZ
37681	894	29	only	only	RB
37681	894	30	their	-PRON-	PRP$
37681	894	31	own	own	JJ
37681	894	32	powers	power	NNS
37681	894	33	to	to	TO
37681	894	34	succeed	succeed	VB
37681	894	35	with	with	IN
37681	894	36	any	any	DT
37681	894	37	method	method	NN
37681	894	38	.	.	.
37681	895	1	It	-PRON-	PRP
37681	895	2	is	be	VBZ
37681	895	3	easy	easy	JJ
37681	895	4	to	to	TO
37681	895	5	teach	teach	VB
37681	895	6	logarithms	logarithm	NNS
37681	895	7	in	in	IN
37681	895	8	the	the	DT
37681	895	9	seventh	seventh	JJ
37681	895	10	school	school	NN
37681	895	11	year	year	NN
37681	895	12	,	,	,
37681	895	13	but	but	CC
37681	895	14	it	-PRON-	PRP
37681	895	15	is	be	VBZ
37681	895	16	not	not	RB
37681	895	17	good	good	JJ
37681	895	18	policy	policy	NN
37681	895	19	to	to	TO
37681	895	20	do	do	VB
37681	895	21	so	so	RB
37681	895	22	under	under	IN
37681	895	23	present	present	JJ
37681	895	24	conditions	condition	NNS
37681	895	25	.	.	.
37681	896	1	So	so	RB
37681	896	2	the	the	DT
37681	896	3	experience	experience	NN
37681	896	4	of	of	IN
37681	896	5	the	the	DT
37681	896	6	world	world	NN
37681	896	7	is	be	VBZ
37681	896	8	against	against	IN
37681	896	9	the	the	DT
37681	896	10	plan	plan	NN
37681	896	11	of	of	IN
37681	896	12	strict	strict	JJ
37681	896	13	fusion	fusion	NN
37681	896	14	,	,	,
37681	896	15	and	and	CC
37681	896	16	no	no	DT
37681	896	17	arguments	argument	NNS
37681	896	18	have	have	VBP
37681	896	19	as	as	RB
37681	896	20	yet	yet	RB
37681	896	21	been	be	VBN
37681	896	22	advanced	advance	VBN
37681	896	23	that	that	WDT
37681	896	24	are	be	VBP
37681	896	25	likely	likely	JJ
37681	896	26	to	to	TO
37681	896	27	change	change	VB
37681	896	28	the	the	DT
37681	896	29	world	world	NN
37681	896	30	's	's	POS
37681	896	31	view	view	NN
37681	896	32	.	.	.
37681	897	1	No	no	DT
37681	897	2	one	one	NN
37681	897	3	has	have	VBZ
37681	897	4	written	write	VBN
37681	897	5	a	a	DT
37681	897	6	book	book	NN
37681	897	7	combining	combine	VBG
37681	897	8	algebra	algebra	NN
37681	897	9	and	and	CC
37681	897	10	geometry	geometry	NN
37681	897	11	in	in	IN
37681	897	12	this	this	DT
37681	897	13	fashion	fashion	NN
37681	897	14	that	that	WDT
37681	897	15	has	have	VBZ
37681	897	16	helped	help	VBN
37681	897	17	the	the	DT
37681	897	18	cause	cause	NN
37681	897	19	of	of	IN
37681	897	20	fusion	fusion	NN
37681	897	21	a	a	DT
37681	897	22	particle	particle	NN
37681	897	23	;	;	:
37681	897	24	on	on	IN
37681	897	25	the	the	DT
37681	897	26	contrary	contrary	NN
37681	897	27	,	,	,
37681	897	28	every	every	DT
37681	897	29	such	such	JJ
37681	897	30	work	work	NN
37681	897	31	that	that	WDT
37681	897	32	has	have	VBZ
37681	897	33	appeared	appear	VBN
37681	897	34	has	have	VBZ
37681	897	35	damaged	damage	VBN
37681	897	36	that	that	IN
37681	897	37	cause	cause	NN
37681	897	38	by	by	IN
37681	897	39	showing	show	VBG
37681	897	40	how	how	WRB
37681	897	41	unscientific	unscientific	JJ
37681	897	42	a	a	DT
37681	897	43	result	result	NN
37681	897	44	has	have	VBZ
37681	897	45	come	come	VBN
37681	897	46	from	from	IN
37681	897	47	the	the	DT
37681	897	48	labor	labor	NN
37681	897	49	of	of	IN
37681	897	50	an	an	DT
37681	897	51	enthusiastic	enthusiastic	JJ
37681	897	52	supporter	supporter	NN
37681	897	53	of	of	IN
37681	897	54	the	the	DT
37681	897	55	movement	movement	NN
37681	897	56	.	.	.
37681	898	1	But	but	CC
37681	898	2	there	there	EX
37681	898	3	is	be	VBZ
37681	898	4	one	one	CD
37681	898	5	feature	feature	NN
37681	898	6	that	that	WDT
37681	898	7	has	have	VBZ
37681	898	8	not	not	RB
37681	898	9	been	be	VBN
37681	898	10	considered	consider	VBN
37681	898	11	above	above	RB
37681	898	12	,	,	,
37681	898	13	and	and	CC
37681	898	14	that	that	DT
37681	898	15	is	be	VBZ
37681	898	16	a	a	DT
37681	898	17	serious	serious	JJ
37681	898	18	handicap	handicap	NN
37681	898	19	to	to	IN
37681	898	20	any	any	DT
37681	898	21	effort	effort	NN
37681	898	22	at	at	IN
37681	898	23	combining	combine	VBG
37681	898	24	the	the	DT
37681	898	25	two	two	CD
37681	898	26	sciences	science	NNS
37681	898	27	in	in	IN
37681	898	28	the	the	DT
37681	898	29	high	high	JJ
37681	898	30	school	school	NN
37681	898	31	,	,	,
37681	898	32	and	and	CC
37681	898	33	this	this	DT
37681	898	34	is	be	VBZ
37681	898	35	the	the	DT
37681	898	36	question	question	NN
37681	898	37	of	of	IN
37681	898	38	relative	relative	JJ
37681	898	39	difficulty	difficulty	NN
37681	898	40	.	.	.
37681	899	1	It	-PRON-	PRP
37681	899	2	is	be	VBZ
37681	899	3	sometimes	sometimes	RB
37681	899	4	said	say	VBN
37681	899	5	,	,	,
37681	899	6	in	in	IN
37681	899	7	a	a	DT
37681	899	8	doctrinaire	doctrinaire	JJ
37681	899	9	fashion	fashion	NN
37681	899	10	,	,	,
37681	899	11	that	that	DT
37681	899	12	geometry	geometry	NN
37681	899	13	is	be	VBZ
37681	899	14	easier	easy	JJR
37681	899	15	than	than	IN
37681	899	16	algebra	algebra	NN
37681	899	17	,	,	,
37681	899	18	since	since	IN
37681	899	19	form	form	NN
37681	899	20	is	be	VBZ
37681	899	21	easier	easy	JJR
37681	899	22	to	to	TO
37681	899	23	grasp	grasp	VB
37681	899	24	than	than	IN
37681	899	25	function	function	NN
37681	899	26	,	,	,
37681	899	27	and	and	CC
37681	899	28	that	that	IN
37681	899	29	therefore	therefore	RB
37681	899	30	geometry	geometry	NN
37681	899	31	should	should	MD
37681	899	32	precede	precede	VB
37681	899	33	algebra	algebra	NN
37681	899	34	.	.	.
37681	900	1	But	but	CC
37681	900	2	every	every	DT
37681	900	3	teacher	teacher	NN
37681	900	4	of	of	IN
37681	900	5	mathematics	mathematic	NNS
37681	900	6	knows	know	VBZ
37681	900	7	better	well	RBR
37681	900	8	than	than	IN
37681	900	9	this	this	DT
37681	900	10	.	.	.
37681	901	1	He	-PRON-	PRP
37681	901	2	knows	know	VBZ
37681	901	3	that	that	IN
37681	901	4	the	the	DT
37681	901	5	simplest	simple	JJS
37681	901	6	form	form	NN
37681	901	7	is	be	VBZ
37681	901	8	easier	easy	JJR
37681	901	9	to	to	TO
37681	901	10	grasp	grasp	VB
37681	901	11	than	than	IN
37681	901	12	the	the	DT
37681	901	13	simplest	simple	JJS
37681	901	14	function	function	NN
37681	901	15	,	,	,
37681	901	16	but	but	CC
37681	901	17	nevertheless	nevertheless	RB
37681	901	18	that	that	DT
37681	901	19	plane	plane	NN
37681	901	20	geometry	geometry	NN
37681	901	21	,	,	,
37681	901	22	as	as	IN
37681	901	23	we	-PRON-	PRP
37681	901	24	understand	understand	VBP
37681	901	25	the	the	DT
37681	901	26	term	term	NN
37681	901	27	to	to	IN
37681	901	28	-	-	HYPH
37681	901	29	day	day	NN
37681	901	30	,	,	,
37681	901	31	is	be	VBZ
37681	901	32	much	much	RB
37681	901	33	more	more	RBR
37681	901	34	difficult	difficult	JJ
37681	901	35	than	than	IN
37681	901	36	elementary	elementary	JJ
37681	901	37	algebra	algebra	NN
37681	901	38	for	for	IN
37681	901	39	a	a	DT
37681	901	40	pupil	pupil	NN
37681	901	41	of	of	IN
37681	901	42	fourteen	fourteen	CD
37681	901	43	.	.	.
37681	902	1	The	the	DT
37681	902	2	child	child	NN
37681	902	3	studies	study	NNS
37681	902	4	form	form	VBP
37681	902	5	in	in	IN
37681	902	6	the	the	DT
37681	902	7	kindergarten	kindergarten	NN
37681	902	8	before	before	IN
37681	902	9	he	-PRON-	PRP
37681	902	10	studies	study	VBZ
37681	902	11	number	number	NN
37681	902	12	,	,	,
37681	902	13	and	and	CC
37681	902	14	this	this	DT
37681	902	15	is	be	VBZ
37681	902	16	sound	sound	JJ
37681	902	17	educational	educational	JJ
37681	902	18	policy	policy	NN
37681	902	19	.	.	.
37681	903	1	He	-PRON-	PRP
37681	903	2	studies	study	VBZ
37681	903	3	form	form	VBP
37681	903	4	,	,	,
37681	903	5	in	in	IN
37681	903	6	mensuration	mensuration	NN
37681	903	7	,	,	,
37681	903	8	throughout	throughout	IN
37681	903	9	his	-PRON-	PRP$
37681	903	10	course	course	NN
37681	903	11	in	in	IN
37681	903	12	arithmetic	arithmetic	JJ
37681	903	13	,	,	,
37681	903	14	and	and	CC
37681	903	15	this	this	DT
37681	903	16	,	,	,
37681	903	17	too	too	RB
37681	903	18	,	,	,
37681	903	19	is	be	VBZ
37681	903	20	good	good	JJ
37681	903	21	educational	educational	JJ
37681	903	22	policy	policy	NN
37681	903	23	.	.	.
37681	904	1	This	this	DT
37681	904	2	kind	kind	NN
37681	904	3	of	of	IN
37681	904	4	geometry	geometry	NN
37681	904	5	very	very	RB
37681	904	6	properly	properly	RB
37681	904	7	precedes	precede	NNS
37681	904	8	algebra	algebra	NN
37681	904	9	.	.	.
37681	905	1	But	but	CC
37681	905	2	the	the	DT
37681	905	3	demonstrations	demonstration	NNS
37681	905	4	of	of	IN
37681	905	5	geometry	geometry	NN
37681	905	6	,	,	,
37681	905	7	the	the	DT
37681	905	8	study	study	NN
37681	905	9	by	by	IN
37681	905	10	pupils	pupil	NNS
37681	905	11	of	of	IN
37681	905	12	fourteen	fourteen	CD
37681	905	13	years	year	NNS
37681	905	14	of	of	IN
37681	905	15	a	a	DT
37681	905	16	geometry	geometry	NN
37681	905	17	that	that	WDT
37681	905	18	was	be	VBD
37681	905	19	written	write	VBN
37681	905	20	for	for	IN
37681	905	21	college	college	NN
37681	905	22	students	student	NNS
37681	905	23	and	and	CC
37681	905	24	always	always	RB
37681	905	25	studied	study	VBN
37681	905	26	by	by	IN
37681	905	27	them	-PRON-	PRP
37681	905	28	until	until	IN
37681	905	29	about	about	IN
37681	905	30	fifty	fifty	CD
37681	905	31	years	year	NNS
37681	905	32	ago,--that	ago,--that	EX
37681	905	33	is	be	VBZ
37681	905	34	by	by	IN
37681	905	35	no	no	DT
37681	905	36	means	mean	NNS
37681	905	37	as	as	RB
37681	905	38	easy	easy	JJ
37681	905	39	as	as	IN
37681	905	40	the	the	DT
37681	905	41	study	study	NN
37681	905	42	of	of	IN
37681	905	43	a	a	DT
37681	905	44	simple	simple	JJ
37681	905	45	algebraic	algebraic	JJ
37681	905	46	symbolism	symbolism	NN
37681	905	47	and	and	CC
37681	905	48	its	-PRON-	PRP$
37681	905	49	application	application	NN
37681	905	50	to	to	IN
37681	905	51	easy	easy	JJ
37681	905	52	equations	equation	NNS
37681	905	53	.	.	.
37681	906	1	If	if	IN
37681	906	2	geometry	geometry	NN
37681	906	3	is	be	VBZ
37681	906	4	to	to	TO
37681	906	5	be	be	VB
37681	906	6	taught	teach	VBN
37681	906	7	for	for	IN
37681	906	8	the	the	DT
37681	906	9	same	same	JJ
37681	906	10	reasons	reason	NNS
37681	906	11	as	as	IN
37681	906	12	at	at	IN
37681	906	13	present	present	NN
37681	906	14	,	,	,
37681	906	15	it	-PRON-	PRP
37681	906	16	can	can	MD
37681	906	17	not	not	RB
37681	906	18	advantageously	advantageously	RB
37681	906	19	be	be	VB
37681	906	20	taught	teach	VBN
37681	906	21	earlier	early	RBR
37681	906	22	than	than	IN
37681	906	23	now	now	RB
37681	906	24	without	without	IN
37681	906	25	much	much	JJ
37681	906	26	simplification	simplification	NN
37681	906	27	,	,	,
37681	906	28	and	and	CC
37681	906	29	it	-PRON-	PRP
37681	906	30	can	can	MD
37681	906	31	not	not	RB
37681	906	32	successfully	successfully	RB
37681	906	33	be	be	VB
37681	906	34	fused	fuse	VBN
37681	906	35	with	with	IN
37681	906	36	algebra	algebra	NN
37681	906	37	save	save	VB
37681	906	38	by	by	IN
37681	906	39	some	some	DT
37681	906	40	teacher	teacher	NN
37681	906	41	who	who	WP
37681	906	42	is	be	VBZ
37681	906	43	willing	willing	JJ
37681	906	44	to	to	TO
37681	906	45	sacrifice	sacrifice	VB
37681	906	46	an	an	DT
37681	906	47	undue	undue	JJ
37681	906	48	amount	amount	NN
37681	906	49	of	of	IN
37681	906	50	energy	energy	NN
37681	906	51	to	to	IN
37681	906	52	no	no	DT
37681	906	53	really	really	RB
37681	906	54	worthy	worthy	JJ
37681	906	55	purpose	purpose	NN
37681	906	56	.	.	.
37681	907	1	When	when	WRB
37681	907	2	great	great	JJ
37681	907	3	mathematicians	mathematician	NNS
37681	907	4	like	like	IN
37681	907	5	Professor	Professor	NNP
37681	907	6	Klein	Klein	NNP
37681	907	7	speak	speak	VBP
37681	907	8	of	of	IN
37681	907	9	the	the	DT
37681	907	10	fusion	fusion	NN
37681	907	11	of	of	IN
37681	907	12	all	all	DT
37681	907	13	mathematics	mathematic	NNS
37681	907	14	,	,	,
37681	907	15	they	-PRON-	PRP
37681	907	16	speak	speak	VBP
37681	907	17	from	from	IN
37681	907	18	the	the	DT
37681	907	19	standpoint	standpoint	NN
37681	907	20	of	of	IN
37681	907	21	advanced	advanced	JJ
37681	907	22	students	student	NNS
37681	907	23	,	,	,
37681	907	24	not	not	RB
37681	907	25	for	for	IN
37681	907	26	the	the	DT
37681	907	27	teacher	teacher	NN
37681	907	28	of	of	IN
37681	907	29	elementary	elementary	JJ
37681	907	30	geometry	geometry	NN
37681	907	31	.	.	.
37681	908	1	It	-PRON-	PRP
37681	908	2	is	be	VBZ
37681	908	3	therefore	therefore	RB
37681	908	4	probable	probable	JJ
37681	908	5	that	that	IN
37681	908	6	simple	simple	JJ
37681	908	7	mensuration	mensuration	NN
37681	908	8	will	will	MD
37681	908	9	continue	continue	VB
37681	908	10	,	,	,
37681	908	11	as	as	IN
37681	908	12	a	a	DT
37681	908	13	part	part	NN
37681	908	14	of	of	IN
37681	908	15	arithmetic	arithmetic	JJ
37681	908	16	,	,	,
37681	908	17	to	to	TO
37681	908	18	precede	precede	VB
37681	908	19	algebra	algebra	NN
37681	908	20	,	,	,
37681	908	21	as	as	IN
37681	908	22	at	at	IN
37681	908	23	present	present	NN
37681	908	24	;	;	:
37681	908	25	and	and	CC
37681	908	26	that	that	DT
37681	908	27	algebra	algebra	NN
37681	908	28	into	into	IN
37681	908	29	or	or	CC
37681	908	30	through	through	IN
37681	908	31	quadratics	quadratic	NNS
37681	908	32	will	will	MD
37681	908	33	precede	precede	VB
37681	908	34	geometry,[38	geometry,[38	NN
37681	908	35	]	]	-RRB-
37681	908	36	drawing	draw	VBG
37681	908	37	upon	upon	IN
37681	908	38	the	the	DT
37681	908	39	mensuration	mensuration	NN
37681	908	40	of	of	IN
37681	908	41	arithmetic	arithmetic	JJ
37681	908	42	as	as	IN
37681	908	43	may	may	MD
37681	908	44	be	be	VB
37681	908	45	needed	need	VBN
37681	908	46	;	;	:
37681	908	47	and	and	CC
37681	908	48	that	that	DT
37681	908	49	geometry	geometry	NN
37681	908	50	will	will	MD
37681	908	51	follow	follow	VB
37681	908	52	this	this	DT
37681	908	53	part	part	NN
37681	908	54	of	of	IN
37681	908	55	algebra	algebra	NN
37681	908	56	,	,	,
37681	908	57	using	use	VBG
37681	908	58	its	-PRON-	PRP$
37681	908	59	principles	principle	NNS
37681	908	60	as	as	RB
37681	908	61	far	far	RB
37681	908	62	as	as	IN
37681	908	63	possible	possible	JJ
37681	908	64	to	to	TO
37681	908	65	assist	assist	VB
37681	908	66	in	in	IN
37681	908	67	the	the	DT
37681	908	68	demonstrations	demonstration	NNS
37681	908	69	and	and	CC
37681	908	70	to	to	TO
37681	908	71	express	express	VB
37681	908	72	and	and	CC
37681	908	73	manipulate	manipulate	VB
37681	908	74	its	-PRON-	PRP$
37681	908	75	formulas	formula	NNS
37681	908	76	.	.	.
37681	909	1	Plane	plane	NN
37681	909	2	geometry	geometry	NN
37681	909	3	,	,	,
37681	909	4	or	or	CC
37681	909	5	else	else	RB
37681	909	6	a	a	DT
37681	909	7	year	year	NN
37681	909	8	of	of	IN
37681	909	9	plane	plane	NN
37681	909	10	and	and	CC
37681	909	11	solid	solid	JJ
37681	909	12	geometry	geometry	NN
37681	909	13	,	,	,
37681	909	14	will	will	MD
37681	909	15	probably	probably	RB
37681	909	16	,	,	,
37681	909	17	in	in	IN
37681	909	18	this	this	DT
37681	909	19	country	country	NN
37681	909	20	,	,	,
37681	909	21	be	be	VB
37681	909	22	followed	follow	VBN
37681	909	23	by	by	IN
37681	909	24	algebra	algebra	NN
37681	909	25	,	,	,
37681	909	26	completing	complete	VBG
37681	909	27	quadratics	quadratic	NNS
37681	909	28	and	and	CC
37681	909	29	studying	study	VBG
37681	909	30	progressions	progression	NNS
37681	909	31	;	;	:
37681	909	32	and	and	CC
37681	909	33	by	by	IN
37681	909	34	solid	solid	JJ
37681	909	35	geometry	geometry	NN
37681	909	36	,	,	,
37681	909	37	or	or	CC
37681	909	38	a	a	DT
37681	909	39	supplementary	supplementary	JJ
37681	909	40	course	course	NN
37681	909	41	in	in	IN
37681	909	42	plane	plane	NN
37681	909	43	and	and	CC
37681	909	44	solid	solid	JJ
37681	909	45	geometry	geometry	NN
37681	909	46	,	,	,
37681	909	47	this	this	DT
37681	909	48	work	work	NN
37681	909	49	being	be	VBG
37681	909	50	elective	elective	JJ
37681	909	51	in	in	IN
37681	909	52	many	many	JJ
37681	909	53	,	,	,
37681	909	54	if	if	IN
37681	909	55	not	not	RB
37681	909	56	all	all	DT
37681	909	57	,	,	,
37681	909	58	schools	school	NNS
37681	909	59	.	.	.
37681	910	1	[	[	-LRB-
37681	910	2	39	39	CD
37681	910	3	]	]	-RRB-
37681	910	4	It	-PRON-	PRP
37681	910	5	is	be	VBZ
37681	910	6	also	also	RB
37681	910	7	probable	probable	JJ
37681	910	8	that	that	IN
37681	910	9	a	a	DT
37681	910	10	general	general	JJ
37681	910	11	review	review	NN
37681	910	12	of	of	IN
37681	910	13	mathematics	mathematic	NNS
37681	910	14	,	,	,
37681	910	15	where	where	WRB
37681	910	16	the	the	DT
37681	910	17	fusion	fusion	NN
37681	910	18	idea	idea	NN
37681	910	19	may	may	MD
37681	910	20	be	be	VB
37681	910	21	carried	carry	VBN
37681	910	22	out	out	RP
37681	910	23	,	,	,
37681	910	24	will	will	MD
37681	910	25	prove	prove	VB
37681	910	26	to	to	TO
37681	910	27	be	be	VB
37681	910	28	a	a	DT
37681	910	29	feature	feature	NN
37681	910	30	of	of	IN
37681	910	31	the	the	DT
37681	910	32	last	last	JJ
37681	910	33	year	year	NN
37681	910	34	of	of	IN
37681	910	35	the	the	DT
37681	910	36	high	high	JJ
37681	910	37	school	school	NN
37681	910	38	,	,	,
37681	910	39	and	and	CC
37681	910	40	one	one	NN
37681	910	41	that	that	WDT
37681	910	42	will	will	MD
37681	910	43	grow	grow	VB
37681	910	44	in	in	IN
37681	910	45	popularity	popularity	NN
37681	910	46	as	as	IN
37681	910	47	time	time	NN
37681	910	48	goes	go	VBZ
37681	910	49	on	on	RP
37681	910	50	.	.	.
37681	911	1	Such	such	PDT
37681	911	2	a	a	DT
37681	911	3	plan	plan	NN
37681	911	4	will	will	MD
37681	911	5	keep	keep	VB
37681	911	6	algebra	algebra	NN
37681	911	7	and	and	CC
37681	911	8	geometry	geometry	NN
37681	911	9	separate	separate	VBP
37681	911	10	,	,	,
37681	911	11	but	but	CC
37681	911	12	it	-PRON-	PRP
37681	911	13	will	will	MD
37681	911	14	allow	allow	VB
37681	911	15	each	each	DT
37681	911	16	to	to	TO
37681	911	17	use	use	VB
37681	911	18	all	all	DT
37681	911	19	of	of	IN
37681	911	20	the	the	DT
37681	911	21	other	other	JJ
37681	911	22	that	that	WDT
37681	911	23	has	have	VBZ
37681	911	24	preceded	precede	VBN
37681	911	25	it	-PRON-	PRP
37681	911	26	,	,	,
37681	911	27	and	and	CC
37681	911	28	will	will	MD
37681	911	29	encourage	encourage	VB
37681	911	30	every	every	DT
37681	911	31	effort	effort	NN
37681	911	32	in	in	IN
37681	911	33	this	this	DT
37681	911	34	direction	direction	NN
37681	911	35	.	.	.
37681	912	1	It	-PRON-	PRP
37681	912	2	will	will	MD
37681	912	3	accomplish	accomplish	VB
37681	912	4	all	all	PDT
37681	912	5	that	that	WDT
37681	912	6	a	a	DT
37681	912	7	more	more	RBR
37681	912	8	complete	complete	JJ
37681	912	9	fusion	fusion	NN
37681	912	10	really	really	RB
37681	912	11	hopes	hope	VBZ
37681	912	12	to	to	TO
37681	912	13	accomplish	accomplish	VB
37681	912	14	,	,	,
37681	912	15	and	and	CC
37681	912	16	it	-PRON-	PRP
37681	912	17	will	will	MD
37681	912	18	give	give	VB
37681	912	19	encouragement	encouragement	NN
37681	912	20	to	to	IN
37681	912	21	all	all	DT
37681	912	22	who	who	WP
37681	912	23	seek	seek	VBP
37681	912	24	to	to	TO
37681	912	25	modernize	modernize	VB
37681	912	26	the	the	DT
37681	912	27	spirit	spirit	NN
37681	912	28	of	of	IN
37681	912	29	each	each	DT
37681	912	30	of	of	IN
37681	912	31	these	these	DT
37681	912	32	great	great	JJ
37681	912	33	branches	branch	NNS
37681	912	34	of	of	IN
37681	912	35	mathematics	mathematic	NNS
37681	912	36	.	.	.
37681	913	1	There	there	EX
37681	913	2	is	be	VBZ
37681	913	3	,	,	,
37681	913	4	however	however	RB
37681	913	5	,	,	,
37681	913	6	a	a	DT
37681	913	7	chance	chance	NN
37681	913	8	for	for	IN
37681	913	9	fusion	fusion	NN
37681	913	10	in	in	IN
37681	913	11	two	two	CD
37681	913	12	classes	class	NNS
37681	913	13	of	of	IN
37681	913	14	school	school	NN
37681	913	15	,	,	,
37681	913	16	neither	neither	DT
37681	913	17	of	of	IN
37681	913	18	which	which	WDT
37681	913	19	is	be	VBZ
37681	913	20	as	as	RB
37681	913	21	yet	yet	RB
37681	913	22	well	well	RB
37681	913	23	developed	develop	VBN
37681	913	24	in	in	IN
37681	913	25	this	this	DT
37681	913	26	country	country	NN
37681	913	27	.	.	.
37681	914	1	The	the	DT
37681	914	2	first	first	JJ
37681	914	3	is	be	VBZ
37681	914	4	the	the	DT
37681	914	5	technical	technical	JJ
37681	914	6	high	high	JJ
37681	914	7	school	school	NN
37681	914	8	that	that	WDT
37681	914	9	is	be	VBZ
37681	914	10	at	at	IN
37681	914	11	present	present	JJ
37681	914	12	coming	come	VBG
37681	914	13	into	into	IN
37681	914	14	some	some	DT
37681	914	15	prominence	prominence	NN
37681	914	16	.	.	.
37681	915	1	It	-PRON-	PRP
37681	915	2	is	be	VBZ
37681	915	3	not	not	RB
37681	915	4	probable	probable	JJ
37681	915	5	even	even	RB
37681	915	6	here	here	RB
37681	915	7	that	that	IN
37681	915	8	the	the	DT
37681	915	9	best	good	JJS
37681	915	10	results	result	NNS
37681	915	11	can	can	MD
37681	915	12	be	be	VB
37681	915	13	secured	secure	VBN
37681	915	14	by	by	IN
37681	915	15	eliminating	eliminate	VBG
37681	915	16	all	all	DT
37681	915	17	mathematics	mathematic	NNS
37681	915	18	save	save	VBP
37681	915	19	only	only	RB
37681	915	20	what	what	WP
37681	915	21	is	be	VBZ
37681	915	22	applicable	applicable	JJ
37681	915	23	in	in	IN
37681	915	24	the	the	DT
37681	915	25	shop	shop	NN
37681	915	26	,	,	,
37681	915	27	but	but	CC
37681	915	28	if	if	IN
37681	915	29	this	this	DT
37681	915	30	view	view	NN
37681	915	31	should	should	MD
37681	915	32	prevail	prevail	VB
37681	915	33	for	for	IN
37681	915	34	a	a	DT
37681	915	35	time	time	NN
37681	915	36	,	,	,
37681	915	37	there	there	EX
37681	915	38	would	would	MD
37681	915	39	be	be	VB
37681	915	40	so	so	RB
37681	915	41	little	little	JJ
37681	915	42	left	left	JJ
37681	915	43	of	of	IN
37681	915	44	either	either	DT
37681	915	45	algebra	algebra	NN
37681	915	46	or	or	CC
37681	915	47	geometry	geometry	VB
37681	915	48	that	that	WDT
37681	915	49	each	each	DT
37681	915	50	could	could	MD
37681	915	51	readily	readily	RB
37681	915	52	be	be	VB
37681	915	53	joined	join	VBN
37681	915	54	to	to	IN
37681	915	55	the	the	DT
37681	915	56	other	other	JJ
37681	915	57	.	.	.
37681	916	1	The	the	DT
37681	916	2	actual	actual	JJ
37681	916	3	amount	amount	NN
37681	916	4	of	of	IN
37681	916	5	algebra	algebra	NN
37681	916	6	needed	need	VBN
37681	916	7	by	by	IN
37681	916	8	a	a	DT
37681	916	9	foreman	foreman	NN
37681	916	10	in	in	IN
37681	916	11	a	a	DT
37681	916	12	machine	machine	NN
37681	916	13	shop	shop	NN
37681	916	14	can	can	MD
37681	916	15	be	be	VB
37681	916	16	taught	teach	VBN
37681	916	17	in	in	IN
37681	916	18	about	about	RB
37681	916	19	four	four	CD
37681	916	20	lessons	lesson	NNS
37681	916	21	,	,	,
37681	916	22	and	and	CC
37681	916	23	the	the	DT
37681	916	24	geometry	geometry	NN
37681	916	25	or	or	CC
37681	916	26	mensuration	mensuration	NN
37681	916	27	that	that	IN
37681	916	28	he	-PRON-	PRP
37681	916	29	needs	need	VBZ
37681	916	30	can	can	MD
37681	916	31	be	be	VB
37681	916	32	taught	teach	VBN
37681	916	33	in	in	IN
37681	916	34	eight	eight	CD
37681	916	35	lessons	lesson	NNS
37681	916	36	at	at	IN
37681	916	37	the	the	DT
37681	916	38	most	most	RBS
37681	916	39	.	.	.
37681	917	1	The	the	DT
37681	917	2	necessary	necessary	JJ
37681	917	3	trigonometry	trigonometry	NN
37681	917	4	may	may	MD
37681	917	5	take	take	VB
37681	917	6	eight	eight	CD
37681	917	7	more	more	JJR
37681	917	8	,	,	,
37681	917	9	so	so	IN
37681	917	10	that	that	IN
37681	917	11	it	-PRON-	PRP
37681	917	12	is	be	VBZ
37681	917	13	entirely	entirely	RB
37681	917	14	feasible	feasible	JJ
37681	917	15	to	to	TO
37681	917	16	unite	unite	VB
37681	917	17	these	these	DT
37681	917	18	three	three	CD
37681	917	19	subjects	subject	NNS
37681	917	20	.	.	.
37681	918	1	The	the	DT
37681	918	2	boy	boy	NN
37681	918	3	who	who	WP
37681	918	4	takes	take	VBZ
37681	918	5	such	such	PDT
37681	918	6	a	a	DT
37681	918	7	course	course	NN
37681	918	8	would	would	MD
37681	918	9	know	know	VB
37681	918	10	as	as	RB
37681	918	11	much	much	JJ
37681	918	12	about	about	IN
37681	918	13	mathematics	mathematic	NNS
37681	918	14	as	as	IN
37681	918	15	a	a	DT
37681	918	16	child	child	NN
37681	918	17	who	who	WP
37681	918	18	had	have	VBD
37681	918	19	read	read	VBN
37681	918	20	ten	ten	CD
37681	918	21	pages	page	NNS
37681	918	22	in	in	IN
37681	918	23	a	a	DT
37681	918	24	primer	primer	NN
37681	918	25	would	would	MD
37681	918	26	know	know	VB
37681	918	27	about	about	IN
37681	918	28	literature	literature	NN
37681	918	29	,	,	,
37681	918	30	but	but	CC
37681	918	31	he	-PRON-	PRP
37681	918	32	would	would	MD
37681	918	33	have	have	VB
37681	918	34	enough	enough	JJ
37681	918	35	for	for	IN
37681	918	36	his	-PRON-	PRP$
37681	918	37	immediate	immediate	JJ
37681	918	38	needs	need	NNS
37681	918	39	,	,	,
37681	918	40	even	even	RB
37681	918	41	though	though	IN
37681	918	42	he	-PRON-	PRP
37681	918	43	had	have	VBD
37681	918	44	no	no	DT
37681	918	45	appreciation	appreciation	NN
37681	918	46	of	of	IN
37681	918	47	mathematics	mathematic	NNS
37681	918	48	as	as	IN
37681	918	49	a	a	DT
37681	918	50	science	science	NN
37681	918	51	.	.	.
37681	919	1	If	if	IN
37681	919	2	any	any	DT
37681	919	3	one	one	NN
37681	919	4	asks	ask	VBZ
37681	919	5	if	if	IN
37681	919	6	this	this	DT
37681	919	7	is	be	VBZ
37681	919	8	not	not	RB
37681	919	9	all	all	DT
37681	919	10	that	that	WDT
37681	919	11	the	the	DT
37681	919	12	school	school	NN
37681	919	13	should	should	MD
37681	919	14	give	give	VB
37681	919	15	him	-PRON-	PRP
37681	919	16	,	,	,
37681	919	17	it	-PRON-	PRP
37681	919	18	might	may	MD
37681	919	19	be	be	VB
37681	919	20	well	well	JJ
37681	919	21	to	to	TO
37681	919	22	ask	ask	VB
37681	919	23	if	if	IN
37681	919	24	the	the	DT
37681	919	25	school	school	NN
37681	919	26	should	should	MD
37681	919	27	give	give	VB
37681	919	28	only	only	RB
37681	919	29	the	the	DT
37681	919	30	ability	ability	NN
37681	919	31	to	to	TO
37681	919	32	read	read	VB
37681	919	33	,	,	,
37681	919	34	without	without	IN
37681	919	35	the	the	DT
37681	919	36	knowledge	knowledge	NN
37681	919	37	of	of	IN
37681	919	38	any	any	DT
37681	919	39	good	good	JJ
37681	919	40	literature	literature	NN
37681	919	41	;	;	:
37681	919	42	if	if	IN
37681	919	43	it	-PRON-	PRP
37681	919	44	should	should	MD
37681	919	45	give	give	VB
37681	919	46	only	only	RB
37681	919	47	the	the	DT
37681	919	48	ability	ability	NN
37681	919	49	to	to	TO
37681	919	50	sing	sing	VB
37681	919	51	,	,	,
37681	919	52	without	without	IN
37681	919	53	the	the	DT
37681	919	54	knowledge	knowledge	NN
37681	919	55	of	of	IN
37681	919	56	good	good	JJ
37681	919	57	music	music	NN
37681	919	58	;	;	:
37681	919	59	if	if	IN
37681	919	60	it	-PRON-	PRP
37681	919	61	should	should	MD
37681	919	62	give	give	VB
37681	919	63	only	only	RB
37681	919	64	the	the	DT
37681	919	65	ability	ability	NN
37681	919	66	to	to	TO
37681	919	67	speak	speak	VB
37681	919	68	,	,	,
37681	919	69	without	without	IN
37681	919	70	any	any	DT
37681	919	71	training	training	NN
37681	919	72	in	in	IN
37681	919	73	the	the	DT
37681	919	74	use	use	NN
37681	919	75	of	of	IN
37681	919	76	good	good	JJ
37681	919	77	language	language	NN
37681	919	78	;	;	:
37681	919	79	and	and	CC
37681	919	80	if	if	IN
37681	919	81	it	-PRON-	PRP
37681	919	82	should	should	MD
37681	919	83	give	give	VB
37681	919	84	a	a	DT
37681	919	85	knowledge	knowledge	NN
37681	919	86	of	of	IN
37681	919	87	home	home	NN
37681	919	88	geography	geography	NN
37681	919	89	,	,	,
37681	919	90	without	without	IN
37681	919	91	any	any	DT
37681	919	92	intimation	intimation	NN
37681	919	93	that	that	IN
37681	919	94	the	the	DT
37681	919	95	world	world	NN
37681	919	96	is	be	VBZ
37681	919	97	round,--an	round,--an	NNP
37681	919	98	atom	atom	JJ
37681	919	99	in	in	IN
37681	919	100	the	the	DT
37681	919	101	unfathomable	unfathomable	JJ
37681	919	102	universe	universe	NN
37681	919	103	about	about	IN
37681	919	104	us	-PRON-	PRP
37681	919	105	.	.	.
37681	920	1	The	the	DT
37681	920	2	second	second	JJ
37681	920	3	opportunity	opportunity	NN
37681	920	4	for	for	IN
37681	920	5	fusion	fusion	NN
37681	920	6	is	be	VBZ
37681	920	7	possibly	possibly	RB
37681	920	8	(	(	-LRB-
37681	920	9	for	for	IN
37681	920	10	it	-PRON-	PRP
37681	920	11	is	be	VBZ
37681	920	12	by	by	IN
37681	920	13	no	no	DT
37681	920	14	means	mean	NNS
37681	920	15	certain	certain	JJ
37681	920	16	)	)	-RRB-
37681	920	17	to	to	TO
37681	920	18	be	be	VB
37681	920	19	found	find	VBN
37681	920	20	in	in	IN
37681	920	21	a	a	DT
37681	920	22	type	type	NN
37681	920	23	of	of	IN
37681	920	24	school	school	NN
37681	920	25	in	in	IN
37681	920	26	which	which	WDT
37681	920	27	the	the	DT
37681	920	28	only	only	JJ
37681	920	29	required	require	VBN
37681	920	30	courses	course	NNS
37681	920	31	are	be	VBP
37681	920	32	the	the	DT
37681	920	33	initial	initial	JJ
37681	920	34	ones	one	NNS
37681	920	35	.	.	.
37681	921	1	These	these	DT
37681	921	2	schools	school	NNS
37681	921	3	have	have	VBP
37681	921	4	some	some	DT
37681	921	5	strong	strong	JJ
37681	921	6	advocates	advocate	NNS
37681	921	7	,	,	,
37681	921	8	it	-PRON-	PRP
37681	921	9	being	be	VBG
37681	921	10	claimed	claim	VBN
37681	921	11	that	that	IN
37681	921	12	every	every	DT
37681	921	13	pupil	pupil	NN
37681	921	14	should	should	MD
37681	921	15	be	be	VB
37681	921	16	introduced	introduce	VBN
37681	921	17	to	to	IN
37681	921	18	the	the	DT
37681	921	19	large	large	JJ
37681	921	20	branches	branch	NNS
37681	921	21	of	of	IN
37681	921	22	knowledge	knowledge	NN
37681	921	23	and	and	CC
37681	921	24	then	then	RB
37681	921	25	allowed	allow	VBN
37681	921	26	to	to	TO
37681	921	27	elect	elect	VB
37681	921	28	the	the	DT
37681	921	29	ones	one	NNS
37681	921	30	in	in	IN
37681	921	31	which	which	WDT
37681	921	32	he	-PRON-	PRP
37681	921	33	finds	find	VBZ
37681	921	34	himself	-PRON-	PRP
37681	921	35	the	the	DT
37681	921	36	most	most	RBS
37681	921	37	interested	interested	JJ
37681	921	38	.	.	.
37681	922	1	Whether	whether	IN
37681	922	2	or	or	CC
37681	922	3	not	not	RB
37681	922	4	this	this	DT
37681	922	5	is	be	VBZ
37681	922	6	sound	sound	JJ
37681	922	7	educational	educational	JJ
37681	922	8	policy	policy	NN
37681	922	9	need	nee	MD
37681	922	10	not	not	RB
37681	922	11	be	be	VB
37681	922	12	discussed	discuss	VBN
37681	922	13	at	at	IN
37681	922	14	this	this	DT
37681	922	15	time	time	NN
37681	922	16	;	;	:
37681	922	17	but	but	CC
37681	922	18	if	if	IN
37681	922	19	such	such	PDT
37681	922	20	a	a	DT
37681	922	21	plan	plan	NN
37681	922	22	were	be	VBD
37681	922	23	developed	develop	VBN
37681	922	24	,	,	,
37681	922	25	it	-PRON-	PRP
37681	922	26	might	may	MD
37681	922	27	be	be	VB
37681	922	28	well	well	JJ
37681	922	29	to	to	TO
37681	922	30	offer	offer	VB
37681	922	31	a	a	DT
37681	922	32	somewhat	somewhat	RB
37681	922	33	superficial	superficial	JJ
37681	922	34	(	(	-LRB-
37681	922	35	in	in	IN
37681	922	36	the	the	DT
37681	922	37	sense	sense	NN
37681	922	38	of	of	IN
37681	922	39	abridged	abridge	VBN
37681	922	40	)	)	-RRB-
37681	922	41	course	course	NN
37681	922	42	that	that	WDT
37681	922	43	should	should	MD
37681	922	44	embody	embody	VB
37681	922	45	a	a	DT
37681	922	46	little	little	NN
37681	922	47	of	of	IN
37681	922	48	algebra	algebra	NN
37681	922	49	,	,	,
37681	922	50	a	a	DT
37681	922	51	little	little	JJ
37681	922	52	of	of	IN
37681	922	53	geometry	geometry	NN
37681	922	54	,	,	,
37681	922	55	and	and	CC
37681	922	56	a	a	DT
37681	922	57	little	little	JJ
37681	922	58	of	of	IN
37681	922	59	trigonometry	trigonometry	NN
37681	922	60	.	.	.
37681	923	1	This	this	DT
37681	923	2	would	would	MD
37681	923	3	unconsciously	unconsciously	RB
37681	923	4	become	become	VB
37681	923	5	a	a	DT
37681	923	6	bait	bait	NN
37681	923	7	for	for	IN
37681	923	8	students	student	NNS
37681	923	9	,	,	,
37681	923	10	and	and	CC
37681	923	11	the	the	DT
37681	923	12	result	result	NN
37681	923	13	would	would	MD
37681	923	14	probably	probably	RB
37681	923	15	be	be	VB
37681	923	16	some	some	DT
37681	923	17	good	good	JJ
37681	923	18	teaching	teaching	NN
37681	923	19	in	in	IN
37681	923	20	the	the	DT
37681	923	21	class	class	NN
37681	923	22	in	in	IN
37681	923	23	question	question	NN
37681	923	24	.	.	.
37681	924	1	It	-PRON-	PRP
37681	924	2	is	be	VBZ
37681	924	3	to	to	TO
37681	924	4	be	be	VB
37681	924	5	hoped	hope	VBN
37681	924	6	that	that	IN
37681	924	7	we	-PRON-	PRP
37681	924	8	may	may	MD
37681	924	9	have	have	VB
37681	924	10	some	some	DT
37681	924	11	strong	strong	JJ
37681	924	12	,	,	,
37681	924	13	well	well	RB
37681	924	14	-	-	HYPH
37681	924	15	considered	consider	VBN
37681	924	16	textbooks	textbook	NNS
37681	924	17	upon	upon	IN
37681	924	18	this	this	DT
37681	924	19	phase	phase	NN
37681	924	20	of	of	IN
37681	924	21	the	the	DT
37681	924	22	work	work	NN
37681	924	23	.	.	.
37681	925	1	As	as	IN
37681	925	2	to	to	IN
37681	925	3	the	the	DT
37681	925	4	fusion	fusion	NN
37681	925	5	of	of	IN
37681	925	6	trigonometry	trigonometry	NN
37681	925	7	and	and	CC
37681	925	8	plane	plane	NN
37681	925	9	geometry	geometry	NN
37681	925	10	little	little	JJ
37681	925	11	need	need	NN
37681	925	12	be	be	VB
37681	925	13	said	say	VBN
37681	925	14	,	,	,
37681	925	15	because	because	IN
37681	925	16	the	the	DT
37681	925	17	subject	subject	NN
37681	925	18	is	be	VBZ
37681	925	19	in	in	IN
37681	925	20	the	the	DT
37681	925	21	doctrinaire	doctrinaire	JJ
37681	925	22	stage	stage	NN
37681	925	23	.	.	.
37681	926	1	Trigonometry	Trigonometry	NNP
37681	926	2	naturally	naturally	RB
37681	926	3	follows	follow	VBZ
37681	926	4	the	the	DT
37681	926	5	chapter	chapter	NN
37681	926	6	on	on	IN
37681	926	7	similar	similar	JJ
37681	926	8	triangles	triangle	NNS
37681	926	9	,	,	,
37681	926	10	but	but	CC
37681	926	11	to	to	TO
37681	926	12	put	put	VB
37681	926	13	it	-PRON-	PRP
37681	926	14	there	there	EX
37681	926	15	means	mean	VBZ
37681	926	16	,	,	,
37681	926	17	in	in	IN
37681	926	18	our	-PRON-	PRP$
37681	926	19	crowded	crowded	JJ
37681	926	20	curriculum	curriculum	NN
37681	926	21	,	,	,
37681	926	22	to	to	TO
37681	926	23	eliminate	eliminate	VB
37681	926	24	something	something	NN
37681	926	25	from	from	IN
37681	926	26	geometry	geometry	NN
37681	926	27	.	.	.
37681	927	1	Which	which	WDT
37681	927	2	,	,	,
37681	927	3	then	then	RB
37681	927	4	,	,	,
37681	927	5	is	be	VBZ
37681	927	6	better,--to	better,--to	NNP
37681	927	7	give	give	VB
37681	927	8	up	up	RP
37681	927	9	the	the	DT
37681	927	10	latter	latter	JJ
37681	927	11	portion	portion	NN
37681	927	12	of	of	IN
37681	927	13	geometry	geometry	NN
37681	927	14	,	,	,
37681	927	15	or	or	CC
37681	927	16	part	part	NN
37681	927	17	of	of	IN
37681	927	18	it	-PRON-	PRP
37681	927	19	at	at	IN
37681	927	20	least	least	JJS
37681	927	21	,	,	,
37681	927	22	or	or	CC
37681	927	23	to	to	TO
37681	927	24	give	give	VB
37681	927	25	up	up	RP
37681	927	26	trigonometry	trigonometry	NN
37681	927	27	?	?	.
37681	928	1	Some	some	DT
37681	928	2	advocates	advocate	NNS
37681	928	3	have	have	VBP
37681	928	4	entered	enter	VBN
37681	928	5	a	a	DT
37681	928	6	plea	plea	NN
37681	928	7	for	for	IN
37681	928	8	two	two	CD
37681	928	9	or	or	CC
37681	928	10	three	three	CD
37681	928	11	lessons	lesson	NNS
37681	928	12	in	in	IN
37681	928	13	trigonometry	trigonometry	NN
37681	928	14	at	at	IN
37681	928	15	this	this	DT
37681	928	16	point	point	NN
37681	928	17	,	,	,
37681	928	18	and	and	CC
37681	928	19	this	this	DT
37681	928	20	is	be	VBZ
37681	928	21	a	a	DT
37681	928	22	feature	feature	NN
37681	928	23	that	that	WDT
37681	928	24	any	any	DT
37681	928	25	teacher	teacher	NN
37681	928	26	may	may	MD
37681	928	27	introduce	introduce	VB
37681	928	28	as	as	IN
37681	928	29	a	a	DT
37681	928	30	bit	bit	NN
37681	928	31	of	of	IN
37681	928	32	interest	interest	NN
37681	928	33	,	,	,
37681	928	34	as	as	IN
37681	928	35	is	be	VBZ
37681	928	36	suggested	suggest	VBN
37681	928	37	in	in	IN
37681	928	38	Chapter	Chapter	NNP
37681	928	39	XVI	XVI	NNP
37681	928	40	,	,	,
37681	928	41	just	just	RB
37681	928	42	as	as	IN
37681	928	43	he	-PRON-	PRP
37681	928	44	may	may	MD
37681	928	45	give	give	VB
37681	928	46	a	a	DT
37681	928	47	popular	popular	JJ
37681	928	48	talk	talk	NN
37681	928	49	to	to	IN
37681	928	50	his	-PRON-	PRP$
37681	928	51	class	class	NN
37681	928	52	upon	upon	IN
37681	928	53	the	the	DT
37681	928	54	fourth	fourth	JJ
37681	928	55	dimension	dimension	NN
37681	928	56	or	or	CC
37681	928	57	the	the	DT
37681	928	58	non	non	JJ
37681	928	59	-	-	JJ
37681	928	60	Euclidean	euclidean	JJ
37681	928	61	geometry	geometry	NN
37681	928	62	.	.	.
37681	929	1	The	the	DT
37681	929	2	lasting	lasting	JJ
37681	929	3	impression	impression	NN
37681	929	4	upon	upon	IN
37681	929	5	the	the	DT
37681	929	6	pupil	pupil	NN
37681	929	7	will	will	MD
37681	929	8	be	be	VB
37681	929	9	exactly	exactly	RB
37681	929	10	the	the	DT
37681	929	11	same	same	JJ
37681	929	12	as	as	IN
37681	929	13	that	that	DT
37681	929	14	of	of	IN
37681	929	15	four	four	CD
37681	929	16	lessons	lesson	NNS
37681	929	17	in	in	IN
37681	929	18	Sanskrit	Sanskrit	NNP
37681	929	19	while	while	IN
37681	929	20	he	-PRON-	PRP
37681	929	21	is	be	VBZ
37681	929	22	studying	study	VBG
37681	929	23	Latin	Latin	NNP
37681	929	24	.	.	.
37681	930	1	He	-PRON-	PRP
37681	930	2	might	may	MD
37681	930	3	remember	remember	VB
37681	930	4	each	each	DT
37681	930	5	with	with	IN
37681	930	6	pleasure	pleasure	NN
37681	930	7	,	,	,
37681	930	8	Latin	Latin	NNP
37681	930	9	being	be	VBG
37681	930	10	related	relate	VBN
37681	930	11	,	,	,
37681	930	12	as	as	IN
37681	930	13	it	-PRON-	PRP
37681	930	14	is	be	VBZ
37681	930	15	,	,	,
37681	930	16	to	to	IN
37681	930	17	Sanskrit	Sanskrit	NNP
37681	930	18	,	,	,
37681	930	19	and	and	CC
37681	930	20	trigonometry	trigonometry	NNP
37681	930	21	being	be	VBG
37681	930	22	an	an	DT
37681	930	23	outcome	outcome	NN
37681	930	24	of	of	IN
37681	930	25	the	the	DT
37681	930	26	theory	theory	NN
37681	930	27	of	of	IN
37681	930	28	similar	similar	JJ
37681	930	29	triangles	triangle	NNS
37681	930	30	.	.	.
37681	931	1	But	but	CC
37681	931	2	that	that	IN
37681	931	3	either	either	DT
37681	931	4	of	of	IN
37681	931	5	these	these	DT
37681	931	6	departures	departure	NNS
37681	931	7	from	from	IN
37681	931	8	the	the	DT
37681	931	9	regular	regular	JJ
37681	931	10	sequence	sequence	NN
37681	931	11	is	be	VBZ
37681	931	12	of	of	IN
37681	931	13	any	any	DT
37681	931	14	serious	serious	JJ
37681	931	15	mathematical	mathematical	JJ
37681	931	16	or	or	CC
37681	931	17	linguistic	linguistic	JJ
37681	931	18	significance	significance	NN
37681	931	19	no	no	DT
37681	931	20	one	one	PRP
37681	931	21	would	would	MD
37681	931	22	feel	feel	VB
37681	931	23	like	like	IN
37681	931	24	asserting	assert	VBG
37681	931	25	.	.	.
37681	932	1	Each	each	DT
37681	932	2	is	be	VBZ
37681	932	3	allowable	allowable	JJ
37681	932	4	on	on	IN
37681	932	5	the	the	DT
37681	932	6	score	score	NN
37681	932	7	of	of	IN
37681	932	8	interest	interest	NN
37681	932	9	,	,	,
37681	932	10	but	but	CC
37681	932	11	neither	neither	DT
37681	932	12	will	will	MD
37681	932	13	add	add	VB
37681	932	14	to	to	IN
37681	932	15	the	the	DT
37681	932	16	pupil	pupil	NN
37681	932	17	's	's	POS
37681	932	18	power	power	NN
37681	932	19	in	in	IN
37681	932	20	any	any	DT
37681	932	21	essential	essential	JJ
37681	932	22	feature	feature	NN
37681	932	23	.	.	.
37681	933	1	Each	each	DT
37681	933	2	of	of	IN
37681	933	3	these	these	DT
37681	933	4	subjects	subject	NNS
37681	933	5	is	be	VBZ
37681	933	6	better	well	RBR
37681	933	7	taught	teach	VBN
37681	933	8	by	by	IN
37681	933	9	itself	-PRON-	PRP
37681	933	10	,	,	,
37681	933	11	each	each	DT
37681	933	12	using	use	VBG
37681	933	13	the	the	DT
37681	933	14	other	other	JJ
37681	933	15	as	as	RB
37681	933	16	far	far	RB
37681	933	17	as	as	IN
37681	933	18	possible	possible	JJ
37681	933	19	and	and	CC
37681	933	20	being	be	VBG
37681	933	21	followed	follow	VBN
37681	933	22	by	by	IN
37681	933	23	a	a	DT
37681	933	24	review	review	NN
37681	933	25	that	that	WDT
37681	933	26	shall	shall	MD
37681	933	27	make	make	VB
37681	933	28	use	use	NN
37681	933	29	of	of	IN
37681	933	30	all	all	DT
37681	933	31	.	.	.
37681	934	1	It	-PRON-	PRP
37681	934	2	is	be	VBZ
37681	934	3	not	not	RB
37681	934	4	improbable	improbable	JJ
37681	934	5	that	that	IN
37681	934	6	we	-PRON-	PRP
37681	934	7	may	may	MD
37681	934	8	in	in	IN
37681	934	9	due	due	JJ
37681	934	10	time	time	NN
37681	934	11	have	have	VBP
37681	934	12	high	high	JJ
37681	934	13	schools	school	NNS
37681	934	14	that	that	WDT
37681	934	15	give	give	VBP
37681	934	16	less	less	RBR
37681	934	17	extended	extended	JJ
37681	934	18	courses	course	NNS
37681	934	19	in	in	IN
37681	934	20	algebra	algebra	NN
37681	934	21	and	and	CC
37681	934	22	geometry	geometry	NN
37681	934	23	,	,	,
37681	934	24	adding	add	VBG
37681	934	25	brief	brief	JJ
37681	934	26	practical	practical	JJ
37681	934	27	courses	course	NNS
37681	934	28	in	in	IN
37681	934	29	trigonometry	trigonometry	NN
37681	934	30	and	and	CC
37681	934	31	the	the	DT
37681	934	32	elements	element	NNS
37681	934	33	of	of	IN
37681	934	34	the	the	DT
37681	934	35	calculus	calculus	NN
37681	934	36	;	;	:
37681	934	37	but	but	CC
37681	934	38	even	even	RB
37681	934	39	in	in	IN
37681	934	40	such	such	JJ
37681	934	41	schools	school	NNS
37681	934	42	it	-PRON-	PRP
37681	934	43	is	be	VBZ
37681	934	44	likely	likely	JJ
37681	934	45	to	to	TO
37681	934	46	be	be	VB
37681	934	47	found	find	VBN
37681	934	48	that	that	IN
37681	934	49	geometry	geometry	NN
37681	934	50	is	be	VBZ
37681	934	51	best	well	RBS
37681	934	52	taught	teach	VBN
37681	934	53	by	by	IN
37681	934	54	itself	-PRON-	PRP
37681	934	55	,	,	,
37681	934	56	making	make	VBG
37681	934	57	use	use	NN
37681	934	58	of	of	IN
37681	934	59	all	all	PDT
37681	934	60	the	the	DT
37681	934	61	mathematics	mathematic	NNS
37681	934	62	that	that	WDT
37681	934	63	has	have	VBZ
37681	934	64	preceded	precede	VBN
37681	934	65	it	-PRON-	PRP
37681	934	66	.	.	.
37681	935	1	It	-PRON-	PRP
37681	935	2	will	will	MD
37681	935	3	of	of	IN
37681	935	4	course	course	NN
37681	935	5	be	be	VB
37681	935	6	understood	understand	VBN
37681	935	7	that	that	IN
37681	935	8	the	the	DT
37681	935	9	fusion	fusion	NN
37681	935	10	of	of	IN
37681	935	11	algebra	algebra	NN
37681	935	12	and	and	CC
37681	935	13	geometry	geometry	NN
37681	935	14	as	as	RB
37681	935	15	here	here	RB
37681	935	16	understood	understand	VBD
37681	935	17	has	have	VBZ
37681	935	18	nothing	nothing	NN
37681	935	19	to	to	TO
37681	935	20	do	do	VB
37681	935	21	with	with	IN
37681	935	22	the	the	DT
37681	935	23	question	question	NN
37681	935	24	of	of	IN
37681	935	25	teaching	teach	VBG
37681	935	26	the	the	DT
37681	935	27	two	two	CD
37681	935	28	subjects	subject	NNS
37681	935	29	simultaneously	simultaneously	RB
37681	935	30	,	,	,
37681	935	31	say	say	VBP
37681	935	32	two	two	CD
37681	935	33	days	day	NNS
37681	935	34	in	in	IN
37681	935	35	the	the	DT
37681	935	36	week	week	NN
37681	935	37	for	for	IN
37681	935	38	one	one	CD
37681	935	39	and	and	CC
37681	935	40	three	three	CD
37681	935	41	days	day	NNS
37681	935	42	for	for	IN
37681	935	43	the	the	DT
37681	935	44	other	other	JJ
37681	935	45	.	.	.
37681	936	1	This	this	DT
37681	936	2	plan	plan	NN
37681	936	3	has	have	VBZ
37681	936	4	many	many	JJ
37681	936	5	advocates	advocate	NNS
37681	936	6	,	,	,
37681	936	7	although	although	IN
37681	936	8	on	on	IN
37681	936	9	the	the	DT
37681	936	10	whole	whole	NN
37681	936	11	it	-PRON-	PRP
37681	936	12	has	have	VBZ
37681	936	13	not	not	RB
37681	936	14	been	be	VBN
37681	936	15	well	well	RB
37681	936	16	received	receive	VBN
37681	936	17	in	in	IN
37681	936	18	this	this	DT
37681	936	19	country	country	NN
37681	936	20	.	.	.
37681	937	1	But	but	CC
37681	937	2	what	what	WP
37681	937	3	is	be	VBZ
37681	937	4	meant	mean	VBN
37681	937	5	here	here	RB
37681	937	6	is	be	VBZ
37681	937	7	the	the	DT
37681	937	8	actual	actual	JJ
37681	937	9	fusing	fusing	NN
37681	937	10	of	of	IN
37681	937	11	algebra	algebra	NN
37681	937	12	and	and	CC
37681	937	13	geometry	geometry	NN
37681	937	14	day	day	NN
37681	937	15	after	after	IN
37681	937	16	day,--a	day,--a	NNP
37681	937	17	plan	plan	NN
37681	937	18	that	that	WDT
37681	937	19	has	have	VBZ
37681	937	20	as	as	RB
37681	937	21	yet	yet	RB
37681	937	22	met	meet	VBN
37681	937	23	with	with	IN
37681	937	24	only	only	RB
37681	937	25	a	a	DT
37681	937	26	sporadic	sporadic	JJ
37681	937	27	success	success	NN
37681	937	28	,	,	,
37681	937	29	but	but	CC
37681	937	30	which	which	WDT
37681	937	31	may	may	MD
37681	937	32	be	be	VB
37681	937	33	developed	develop	VBN
37681	937	34	for	for	IN
37681	937	35	beginning	begin	VBG
37681	937	36	classes	class	NNS
37681	937	37	in	in	IN
37681	937	38	due	due	JJ
37681	937	39	time	time	NN
37681	937	40	.	.	.
37681	938	1	FOOTNOTES	footnote	NNS
37681	938	2	:	:	:
37681	938	3	[	[	-LRB-
37681	938	4	37	37	CD
37681	938	5	]	]	-RRB-
37681	938	6	_	_	NNP
37681	938	7	Al	Al	NNP
37681	938	8	-	-	HYPH
37681	938	9	jabr	jabr	NNP
37681	938	10	wa'l	wa'l	NNP
37681	938	11	-	-	HYPH
37681	938	12	muq[=a]balah	muq[=a]balah	NNP
37681	938	13	_	_	NNP
37681	938	14	:	:	:
37681	938	15	"	"	``
37681	938	16	restoration	restoration	NN
37681	938	17	and	and	CC
37681	938	18	equation	equation	NN
37681	938	19	"	"	''
37681	938	20	is	be	VBZ
37681	938	21	a	a	DT
37681	938	22	fairly	fairly	RB
37681	938	23	good	good	JJ
37681	938	24	translation	translation	NN
37681	938	25	of	of	IN
37681	938	26	the	the	DT
37681	938	27	Arabic	Arabic	NNP
37681	938	28	.	.	.
37681	939	1	[	[	-LRB-
37681	939	2	38	38	CD
37681	939	3	]	]	-RRB-
37681	939	4	Or	or	CC
37681	939	5	be	be	VB
37681	939	6	carried	carry	VBN
37681	939	7	along	along	RB
37681	939	8	at	at	IN
37681	939	9	the	the	DT
37681	939	10	same	same	JJ
37681	939	11	time	time	NN
37681	939	12	as	as	IN
37681	939	13	a	a	DT
37681	939	14	distinct	distinct	JJ
37681	939	15	topic	topic	NN
37681	939	16	.	.	.
37681	940	1	[	[	-LRB-
37681	940	2	39	39	CD
37681	940	3	]	]	-RRB-
37681	940	4	With	with	IN
37681	940	5	a	a	DT
37681	940	6	single	single	JJ
37681	940	7	year	year	NN
37681	940	8	for	for	IN
37681	940	9	required	require	VBN
37681	940	10	geometry	geometry	NN
37681	940	11	it	-PRON-	PRP
37681	940	12	would	would	MD
37681	940	13	be	be	VB
37681	940	14	better	well	JJR
37681	940	15	from	from	IN
37681	940	16	every	every	DT
37681	940	17	point	point	NN
37681	940	18	of	of	IN
37681	940	19	view	view	NN
37681	940	20	to	to	TO
37681	940	21	cut	cut	VB
37681	940	22	the	the	DT
37681	940	23	plane	plane	NN
37681	940	24	geometry	geometry	NN
37681	940	25	enough	enough	RB
37681	940	26	to	to	TO
37681	940	27	admit	admit	VB
37681	940	28	a	a	DT
37681	940	29	fair	fair	JJ
37681	940	30	course	course	NN
37681	940	31	in	in	IN
37681	940	32	solid	solid	JJ
37681	940	33	geometry	geometry	NN
37681	940	34	.	.	.
37681	941	1	CHAPTER	CHAPTER	NNP
37681	941	2	IX	IX	NNP
37681	941	3	THE	the	DT
37681	941	4	INTRODUCTION	introduction	NN
37681	941	5	TO	to	IN
37681	941	6	GEOMETRY	GEOMETRY	NNP
37681	941	7	There	there	EX
37681	941	8	are	be	VBP
37681	941	9	two	two	CD
37681	941	10	difficult	difficult	JJ
37681	941	11	crises	crisis	NNS
37681	941	12	in	in	IN
37681	941	13	the	the	DT
37681	941	14	geometry	geometry	NN
37681	941	15	course	course	NN
37681	941	16	,	,	,
37681	941	17	both	both	CC
37681	941	18	for	for	IN
37681	941	19	the	the	DT
37681	941	20	pupil	pupil	NN
37681	941	21	and	and	CC
37681	941	22	for	for	IN
37681	941	23	the	the	DT
37681	941	24	teacher	teacher	NN
37681	941	25	.	.	.
37681	942	1	These	these	DT
37681	942	2	crises	crisis	NNS
37681	942	3	are	be	VBP
37681	942	4	met	meet	VBN
37681	942	5	at	at	IN
37681	942	6	the	the	DT
37681	942	7	beginning	beginning	NN
37681	942	8	of	of	IN
37681	942	9	the	the	DT
37681	942	10	subject	subject	NN
37681	942	11	and	and	CC
37681	942	12	at	at	IN
37681	942	13	the	the	DT
37681	942	14	beginning	beginning	NN
37681	942	15	of	of	IN
37681	942	16	solid	solid	JJ
37681	942	17	geometry	geometry	NN
37681	942	18	.	.	.
37681	943	1	Once	once	RB
37681	943	2	a	a	DT
37681	943	3	class	class	NN
37681	943	4	has	have	VBZ
37681	943	5	fairly	fairly	RB
37681	943	6	got	get	VBN
37681	943	7	into	into	IN
37681	943	8	Book	Book	NNP
37681	943	9	I	-PRON-	PRP
37681	943	10	,	,	,
37681	943	11	if	if	IN
37681	943	12	the	the	DT
37681	943	13	interest	interest	NN
37681	943	14	in	in	IN
37681	943	15	the	the	DT
37681	943	16	subject	subject	NN
37681	943	17	can	can	MD
37681	943	18	be	be	VB
37681	943	19	maintained	maintain	VBN
37681	943	20	,	,	,
37681	943	21	there	there	EX
37681	943	22	are	be	VBP
37681	943	23	only	only	RB
37681	943	24	the	the	DT
37681	943	25	incidental	incidental	JJ
37681	943	26	difficulties	difficulty	NNS
37681	943	27	of	of	IN
37681	943	28	logical	logical	JJ
37681	943	29	advance	advance	NN
37681	943	30	throughout	throughout	IN
37681	943	31	the	the	DT
37681	943	32	plane	plane	NN
37681	943	33	geometry	geometry	NN
37681	943	34	.	.	.
37681	944	1	When	when	WRB
37681	944	2	the	the	DT
37681	944	3	pupil	pupil	NN
37681	944	4	who	who	WP
37681	944	5	has	have	VBZ
37681	944	6	been	be	VBN
37681	944	7	seeing	see	VBG
37681	944	8	figures	figure	NNS
37681	944	9	in	in	IN
37681	944	10	one	one	CD
37681	944	11	plane	plane	NN
37681	944	12	for	for	IN
37681	944	13	a	a	DT
37681	944	14	year	year	NN
37681	944	15	attempts	attempt	NNS
37681	944	16	to	to	TO
37681	944	17	visualize	visualize	VB
37681	944	18	solids	solid	NNS
37681	944	19	from	from	IN
37681	944	20	a	a	DT
37681	944	21	flat	flat	JJ
37681	944	22	drawing	drawing	NN
37681	944	23	,	,	,
37681	944	24	the	the	DT
37681	944	25	second	second	JJ
37681	944	26	difficult	difficult	JJ
37681	944	27	place	place	NN
37681	944	28	is	be	VBZ
37681	944	29	reached	reach	VBN
37681	944	30	.	.	.
37681	945	1	Teachers	teacher	NNS
37681	945	2	going	go	VBG
37681	945	3	over	over	RP
37681	945	4	solid	solid	JJ
37681	945	5	geometry	geometry	NN
37681	945	6	from	from	IN
37681	945	7	year	year	NN
37681	945	8	to	to	IN
37681	945	9	year	year	NN
37681	945	10	often	often	RB
37681	945	11	forget	forget	VBP
37681	945	12	this	this	DT
37681	945	13	difficulty	difficulty	NN
37681	945	14	,	,	,
37681	945	15	but	but	CC
37681	945	16	most	most	JJS
37681	945	17	of	of	IN
37681	945	18	them	-PRON-	PRP
37681	945	19	can	can	MD
37681	945	20	easily	easily	RB
37681	945	21	place	place	VB
37681	945	22	themselves	-PRON-	PRP
37681	945	23	in	in	IN
37681	945	24	the	the	DT
37681	945	25	pupil	pupil	NN
37681	945	26	's	's	POS
37681	945	27	position	position	NN
37681	945	28	by	by	IN
37681	945	29	looking	look	VBG
37681	945	30	at	at	IN
37681	945	31	the	the	DT
37681	945	32	working	work	VBG
37681	945	33	drawings	drawing	NNS
37681	945	34	of	of	IN
37681	945	35	any	any	DT
37681	945	36	artisan,--usually	artisan,--usually	NNP
37681	945	37	simple	simple	JJ
37681	945	38	cases	case	NNS
37681	945	39	in	in	IN
37681	945	40	the	the	DT
37681	945	41	so	so	RB
37681	945	42	-	-	HYPH
37681	945	43	called	call	VBN
37681	945	44	descriptive	descriptive	JJ
37681	945	45	geometry	geometry	NN
37681	945	46	.	.	.
37681	946	1	They	-PRON-	PRP
37681	946	2	will	will	MD
37681	946	3	then	then	RB
37681	946	4	realize	realize	VB
37681	946	5	how	how	WRB
37681	946	6	difficult	difficult	JJ
37681	946	7	it	-PRON-	PRP
37681	946	8	is	be	VBZ
37681	946	9	to	to	TO
37681	946	10	visualize	visualize	VB
37681	946	11	a	a	DT
37681	946	12	solid	solid	JJ
37681	946	13	from	from	IN
37681	946	14	an	an	DT
37681	946	15	unfamiliar	unfamiliar	JJ
37681	946	16	kind	kind	NN
37681	946	17	of	of	IN
37681	946	18	picture	picture	NN
37681	946	19	.	.	.
37681	947	1	The	the	DT
37681	947	2	trouble	trouble	NN
37681	947	3	is	be	VBZ
37681	947	4	usually	usually	RB
37681	947	5	avoided	avoid	VBN
37681	947	6	by	by	IN
37681	947	7	the	the	DT
37681	947	8	help	help	NN
37681	947	9	of	of	IN
37681	947	10	a	a	DT
37681	947	11	couple	couple	NN
37681	947	12	of	of	IN
37681	947	13	pieces	piece	NNS
37681	947	14	of	of	IN
37681	947	15	heavy	heavy	JJ
37681	947	16	cardboard	cardboard	NN
37681	947	17	or	or	CC
37681	947	18	box	box	NNP
37681	947	19	board	board	NNP
37681	947	20	,	,	,
37681	947	21	and	and	CC
37681	947	22	a	a	DT
37681	947	23	few	few	JJ
37681	947	24	knitting	knitting	NN
37681	947	25	needles	needle	NNS
37681	947	26	with	with	IN
37681	947	27	which	which	WDT
37681	947	28	to	to	TO
37681	947	29	represent	represent	VB
37681	947	30	lines	line	NNS
37681	947	31	in	in	IN
37681	947	32	space	space	NN
37681	947	33	.	.	.
37681	948	1	If	if	IN
37681	948	2	these	these	DT
37681	948	3	are	be	VBP
37681	948	4	judiciously	judiciously	RB
37681	948	5	used	use	VBN
37681	948	6	in	in	IN
37681	948	7	class	class	NN
37681	948	8	for	for	IN
37681	948	9	a	a	DT
37681	948	10	few	few	JJ
37681	948	11	days	day	NNS
37681	948	12	,	,	,
37681	948	13	until	until	IN
37681	948	14	the	the	DT
37681	948	15	figures	figure	NNS
37681	948	16	are	be	VBP
37681	948	17	understood	understand	VBN
37681	948	18	,	,	,
37681	948	19	the	the	DT
37681	948	20	second	second	JJ
37681	948	21	crisis	crisis	NN
37681	948	22	is	be	VBZ
37681	948	23	easily	easily	RB
37681	948	24	passed	pass	VBN
37681	948	25	.	.	.
37681	949	1	The	the	DT
37681	949	2	continued	continue	VBN
37681	949	3	use	use	NN
37681	949	4	of	of	IN
37681	949	5	such	such	JJ
37681	949	6	material	material	NN
37681	949	7	,	,	,
37681	949	8	however	however	RB
37681	949	9	,	,	,
37681	949	10	or	or	CC
37681	949	11	the	the	DT
37681	949	12	daily	daily	JJ
37681	949	13	use	use	NN
37681	949	14	of	of	IN
37681	949	15	either	either	DT
37681	949	16	models	model	NNS
37681	949	17	or	or	CC
37681	949	18	photographs	photograph	NNS
37681	949	19	,	,	,
37681	949	20	weakens	weaken	VBZ
37681	949	21	the	the	DT
37681	949	22	pupil	pupil	NN
37681	949	23	,	,	,
37681	949	24	even	even	RB
37681	949	25	as	as	IN
37681	949	26	a	a	DT
37681	949	27	child	child	NN
37681	949	28	is	be	VBZ
37681	949	29	weakened	weaken	VBN
37681	949	30	by	by	IN
37681	949	31	being	be	VBG
37681	949	32	kept	keep	VBD
37681	949	33	too	too	RB
37681	949	34	long	long	RB
37681	949	35	in	in	IN
37681	949	36	a	a	DT
37681	949	37	perambulator	perambulator	NN
37681	949	38	.	.	.
37681	950	1	Such	such	JJ
37681	950	2	devices	device	NNS
37681	950	3	have	have	VBP
37681	950	4	their	-PRON-	PRP$
37681	950	5	place	place	NN
37681	950	6	;	;	:
37681	950	7	they	-PRON-	PRP
37681	950	8	are	be	VBP
37681	950	9	useful	useful	JJ
37681	950	10	when	when	WRB
37681	950	11	needed	need	VBN
37681	950	12	,	,	,
37681	950	13	but	but	CC
37681	950	14	they	-PRON-	PRP
37681	950	15	are	be	VBP
37681	950	16	pernicious	pernicious	JJ
37681	950	17	when	when	WRB
37681	950	18	unnecessary	unnecessary	JJ
37681	950	19	.	.	.
37681	951	1	Just	just	RB
37681	951	2	as	as	IN
37681	951	3	the	the	DT
37681	951	4	mechanic	mechanic	NN
37681	951	5	must	must	MD
37681	951	6	be	be	VB
37681	951	7	able	able	JJ
37681	951	8	to	to	TO
37681	951	9	make	make	VB
37681	951	10	and	and	CC
37681	951	11	to	to	TO
37681	951	12	visualize	visualize	VB
37681	951	13	his	-PRON-	PRP$
37681	951	14	working	work	VBG
37681	951	15	drawings	drawing	NNS
37681	951	16	,	,	,
37681	951	17	so	so	CC
37681	951	18	the	the	DT
37681	951	19	student	student	NN
37681	951	20	of	of	IN
37681	951	21	solid	solid	JJ
37681	951	22	geometry	geometry	NN
37681	951	23	must	must	MD
37681	951	24	be	be	VB
37681	951	25	able	able	JJ
37681	951	26	to	to	TO
37681	951	27	get	get	VB
37681	951	28	on	on	RP
37681	951	29	with	with	IN
37681	951	30	pencil	pencil	NN
37681	951	31	and	and	CC
37681	951	32	paper	paper	NN
37681	951	33	,	,	,
37681	951	34	representing	represent	VBG
37681	951	35	his	-PRON-	PRP$
37681	951	36	solid	solid	JJ
37681	951	37	figures	figure	NNS
37681	951	38	in	in	IN
37681	951	39	the	the	DT
37681	951	40	flat	flat	NN
37681	951	41	.	.	.
37681	952	1	But	but	CC
37681	952	2	the	the	DT
37681	952	3	introduction	introduction	NN
37681	952	4	to	to	IN
37681	952	5	plane	plane	NN
37681	952	6	geometry	geometry	NN
37681	952	7	is	be	VBZ
37681	952	8	not	not	RB
37681	952	9	so	so	RB
37681	952	10	easily	easily	RB
37681	952	11	disposed	dispose	VBN
37681	952	12	of	of	IN
37681	952	13	.	.	.
37681	953	1	The	the	DT
37681	953	2	pupil	pupil	NN
37681	953	3	at	at	IN
37681	953	4	that	that	DT
37681	953	5	time	time	NN
37681	953	6	is	be	VBZ
37681	953	7	entering	enter	VBG
37681	953	8	a	a	DT
37681	953	9	field	field	NN
37681	953	10	that	that	WDT
37681	953	11	is	be	VBZ
37681	953	12	entirely	entirely	RB
37681	953	13	unfamiliar	unfamiliar	JJ
37681	953	14	.	.	.
37681	954	1	He	-PRON-	PRP
37681	954	2	is	be	VBZ
37681	954	3	only	only	RB
37681	954	4	fourteen	fourteen	CD
37681	954	5	or	or	CC
37681	954	6	fifteen	fifteen	CD
37681	954	7	years	year	NNS
37681	954	8	of	of	IN
37681	954	9	age	age	NN
37681	954	10	,	,	,
37681	954	11	and	and	CC
37681	954	12	his	-PRON-	PRP$
37681	954	13	thoughts	thought	NNS
37681	954	14	are	be	VBP
37681	954	15	distinctly	distinctly	RB
37681	954	16	not	not	RB
37681	954	17	on	on	IN
37681	954	18	geometry	geometry	NN
37681	954	19	.	.	.
37681	955	1	Of	of	IN
37681	955	2	logic	logic	NN
37681	955	3	he	-PRON-	PRP
37681	955	4	knows	know	VBZ
37681	955	5	little	little	JJ
37681	955	6	and	and	CC
37681	955	7	cares	care	VBZ
37681	955	8	less	less	RBR
37681	955	9	.	.	.
37681	956	1	He	-PRON-	PRP
37681	956	2	is	be	VBZ
37681	956	3	not	not	RB
37681	956	4	interested	interested	JJ
37681	956	5	in	in	IN
37681	956	6	a	a	DT
37681	956	7	subject	subject	NN
37681	956	8	of	of	IN
37681	956	9	which	which	WDT
37681	956	10	he	-PRON-	PRP
37681	956	11	knows	know	VBZ
37681	956	12	nothing	nothing	NN
37681	956	13	,	,	,
37681	956	14	not	not	RB
37681	956	15	even	even	RB
37681	956	16	the	the	DT
37681	956	17	meaning	meaning	NN
37681	956	18	of	of	IN
37681	956	19	its	-PRON-	PRP$
37681	956	20	name	name	NN
37681	956	21	.	.	.
37681	957	1	He	-PRON-	PRP
37681	957	2	asks	ask	VBZ
37681	957	3	,	,	,
37681	957	4	naturally	naturally	RB
37681	957	5	and	and	CC
37681	957	6	properly	properly	RB
37681	957	7	,	,	,
37681	957	8	what	what	WP
37681	957	9	it	-PRON-	PRP
37681	957	10	all	all	DT
37681	957	11	signifies	signify	VBZ
37681	957	12	,	,	,
37681	957	13	what	what	WP
37681	957	14	possible	possible	JJ
37681	957	15	use	use	NN
37681	957	16	there	there	EX
37681	957	17	is	be	VBZ
37681	957	18	for	for	IN
37681	957	19	studying	study	VBG
37681	957	20	geometry	geometry	NN
37681	957	21	,	,	,
37681	957	22	and	and	CC
37681	957	23	why	why	WRB
37681	957	24	he	-PRON-	PRP
37681	957	25	should	should	MD
37681	957	26	have	have	VB
37681	957	27	to	to	TO
37681	957	28	prove	prove	VB
37681	957	29	what	what	WP
37681	957	30	seems	seem	VBZ
37681	957	31	to	to	IN
37681	957	32	him	-PRON-	PRP
37681	957	33	evident	evident	JJ
37681	957	34	without	without	IN
37681	957	35	proof	proof	NN
37681	957	36	.	.	.
37681	958	1	To	to	TO
37681	958	2	pass	pass	VB
37681	958	3	him	-PRON-	PRP
37681	958	4	successfully	successfully	RB
37681	958	5	through	through	IN
37681	958	6	this	this	DT
37681	958	7	stage	stage	NN
37681	958	8	has	have	VBZ
37681	958	9	taxed	tax	VBN
37681	958	10	the	the	DT
37681	958	11	ingenuity	ingenuity	NN
37681	958	12	of	of	IN
37681	958	13	every	every	DT
37681	958	14	real	real	JJ
37681	958	15	teacher	teacher	NN
37681	958	16	from	from	IN
37681	958	17	the	the	DT
37681	958	18	time	time	NN
37681	958	19	of	of	IN
37681	958	20	Euclid	Euclid	NNP
37681	958	21	to	to	IN
37681	958	22	the	the	DT
37681	958	23	present	present	NN
37681	958	24	;	;	:
37681	958	25	and	and	CC
37681	958	26	just	just	RB
37681	958	27	as	as	IN
37681	958	28	Euclid	Euclid	NNP
37681	958	29	remarked	remark	VBD
37681	958	30	to	to	IN
37681	958	31	King	King	NNP
37681	958	32	Ptolemy	Ptolemy	NNP
37681	958	33	,	,	,
37681	958	34	his	-PRON-	PRP$
37681	958	35	patron	patron	NN
37681	958	36	,	,	,
37681	958	37	that	that	IN
37681	958	38	there	there	EX
37681	958	39	is	be	VBZ
37681	958	40	no	no	DT
37681	958	41	royal	royal	JJ
37681	958	42	road	road	NN
37681	958	43	to	to	IN
37681	958	44	geometry	geometry	NN
37681	958	45	,	,	,
37681	958	46	so	so	RB
37681	958	47	we	-PRON-	PRP
37681	958	48	may	may	MD
37681	958	49	affirm	affirm	VB
37681	958	50	that	that	IN
37681	958	51	there	there	EX
37681	958	52	is	be	VBZ
37681	958	53	no	no	DT
37681	958	54	royal	royal	JJ
37681	958	55	road	road	NN
37681	958	56	to	to	IN
37681	958	57	the	the	DT
37681	958	58	teaching	teaching	NN
37681	958	59	of	of	IN
37681	958	60	geometry	geometry	NN
37681	958	61	.	.	.
37681	959	1	Nevertheless	nevertheless	RB
37681	959	2	the	the	DT
37681	959	3	experience	experience	NN
37681	959	4	of	of	IN
37681	959	5	teachers	teacher	NNS
37681	959	6	counts	count	VBZ
37681	959	7	for	for	IN
37681	959	8	a	a	DT
37681	959	9	great	great	JJ
37681	959	10	deal	deal	NN
37681	959	11	,	,	,
37681	959	12	and	and	CC
37681	959	13	this	this	DT
37681	959	14	experience	experience	NN
37681	959	15	has	have	VBZ
37681	959	16	shown	show	VBN
37681	959	17	that	that	IN
37681	959	18	,	,	,
37681	959	19	aside	aside	RB
37681	959	20	from	from	IN
37681	959	21	the	the	DT
37681	959	22	matter	matter	NN
37681	959	23	of	of	IN
37681	959	24	technic	technic	NN
37681	959	25	in	in	IN
37681	959	26	handling	handle	VBG
37681	959	27	the	the	DT
37681	959	28	class	class	NN
37681	959	29	,	,	,
37681	959	30	certain	certain	JJ
37681	959	31	suggestions	suggestion	NNS
37681	959	32	are	be	VBP
37681	959	33	of	of	IN
37681	959	34	value	value	NN
37681	959	35	,	,	,
37681	959	36	and	and	CC
37681	959	37	a	a	DT
37681	959	38	few	few	JJ
37681	959	39	of	of	IN
37681	959	40	these	these	DT
37681	959	41	will	will	MD
37681	959	42	now	now	RB
37681	959	43	be	be	VB
37681	959	44	set	set	VBN
37681	959	45	forth	forth	RB
37681	959	46	.	.	.
37681	960	1	First	first	RB
37681	960	2	,	,	,
37681	960	3	as	as	IN
37681	960	4	to	to	IN
37681	960	5	why	why	WRB
37681	960	6	geometry	geometry	NNP
37681	960	7	is	be	VBZ
37681	960	8	studied	study	VBN
37681	960	9	,	,	,
37681	960	10	it	-PRON-	PRP
37681	960	11	is	be	VBZ
37681	960	12	manifestly	manifestly	RB
37681	960	13	impossible	impossible	JJ
37681	960	14	successfully	successfully	RB
37681	960	15	to	to	TO
37681	960	16	explain	explain	VB
37681	960	17	to	to	IN
37681	960	18	a	a	DT
37681	960	19	boy	boy	NN
37681	960	20	of	of	IN
37681	960	21	fourteen	fourteen	CD
37681	960	22	or	or	CC
37681	960	23	fifteen	fifteen	CD
37681	960	24	the	the	DT
37681	960	25	larger	large	JJR
37681	960	26	reasons	reason	NNS
37681	960	27	for	for	IN
37681	960	28	studying	study	VBG
37681	960	29	anything	anything	NN
37681	960	30	whatever	whatever	WDT
37681	960	31	.	.	.
37681	961	1	When	when	WRB
37681	961	2	we	-PRON-	PRP
37681	961	3	confess	confess	VBP
37681	961	4	ourselves	-PRON-	PRP
37681	961	5	honestly	honestly	RB
37681	961	6	we	-PRON-	PRP
37681	961	7	find	find	VBP
37681	961	8	that	that	IN
37681	961	9	these	these	DT
37681	961	10	reasons	reason	NNS
37681	961	11	,	,	,
37681	961	12	whether	whether	IN
37681	961	13	in	in	IN
37681	961	14	mathematics	mathematic	NNS
37681	961	15	,	,	,
37681	961	16	the	the	DT
37681	961	17	natural	natural	JJ
37681	961	18	sciences	science	NNS
37681	961	19	,	,	,
37681	961	20	handwork	handwork	NN
37681	961	21	,	,	,
37681	961	22	letters	letter	NNS
37681	961	23	,	,	,
37681	961	24	the	the	DT
37681	961	25	vocations	vocation	NNS
37681	961	26	,	,	,
37681	961	27	or	or	CC
37681	961	28	the	the	DT
37681	961	29	fine	fine	JJ
37681	961	30	arts	art	NNS
37681	961	31	,	,	,
37681	961	32	are	be	VBP
37681	961	33	none	none	NN
37681	961	34	too	too	RB
37681	961	35	clear	clear	JJ
37681	961	36	in	in	IN
37681	961	37	our	-PRON-	PRP$
37681	961	38	own	own	JJ
37681	961	39	minds	mind	NNS
37681	961	40	,	,	,
37681	961	41	in	in	IN
37681	961	42	spite	spite	NN
37681	961	43	of	of	IN
37681	961	44	any	any	DT
37681	961	45	pretentious	pretentious	JJ
37681	961	46	language	language	NN
37681	961	47	that	that	WDT
37681	961	48	we	-PRON-	PRP
37681	961	49	may	may	MD
37681	961	50	use	use	VB
37681	961	51	.	.	.
37681	962	1	It	-PRON-	PRP
37681	962	2	is	be	VBZ
37681	962	3	therefore	therefore	RB
37681	962	4	most	most	RBS
37681	962	5	satisfactory	satisfactory	JJ
37681	962	6	to	to	TO
37681	962	7	anticipate	anticipate	VB
37681	962	8	the	the	DT
37681	962	9	question	question	NN
37681	962	10	at	at	IN
37681	962	11	once	once	RB
37681	962	12	,	,	,
37681	962	13	and	and	CC
37681	962	14	to	to	TO
37681	962	15	set	set	VB
37681	962	16	the	the	DT
37681	962	17	pupils	pupil	NNS
37681	962	18	,	,	,
37681	962	19	for	for	IN
37681	962	20	a	a	DT
37681	962	21	few	few	JJ
37681	962	22	days	day	NNS
37681	962	23	,	,	,
37681	962	24	at	at	IN
37681	962	25	using	use	VBG
37681	962	26	the	the	DT
37681	962	27	compasses	compass	NNS
37681	962	28	and	and	CC
37681	962	29	ruler	ruler	NN
37681	962	30	in	in	IN
37681	962	31	the	the	DT
37681	962	32	drawing	drawing	NN
37681	962	33	of	of	IN
37681	962	34	geometric	geometric	JJ
37681	962	35	designs	design	NNS
37681	962	36	and	and	CC
37681	962	37	of	of	IN
37681	962	38	the	the	DT
37681	962	39	most	most	RBS
37681	962	40	common	common	JJ
37681	962	41	figures	figure	NNS
37681	962	42	that	that	IN
37681	962	43	they	-PRON-	PRP
37681	962	44	will	will	MD
37681	962	45	use	use	VB
37681	962	46	.	.	.
37681	963	1	This	this	DT
37681	963	2	serves	serve	VBZ
37681	963	3	several	several	JJ
37681	963	4	purposes	purpose	NNS
37681	963	5	:	:	:
37681	963	6	it	-PRON-	PRP
37681	963	7	excites	excite	VBZ
37681	963	8	their	-PRON-	PRP$
37681	963	9	interest	interest	NN
37681	963	10	,	,	,
37681	963	11	it	-PRON-	PRP
37681	963	12	guards	guard	VBZ
37681	963	13	against	against	IN
37681	963	14	the	the	DT
37681	963	15	slovenly	slovenly	JJ
37681	963	16	figures	figure	NNS
37681	963	17	that	that	WDT
37681	963	18	so	so	RB
37681	963	19	often	often	RB
37681	963	20	lead	lead	VBP
37681	963	21	them	-PRON-	PRP
37681	963	22	to	to	IN
37681	963	23	erroneous	erroneous	JJ
37681	963	24	conclusions	conclusion	NNS
37681	963	25	,	,	,
37681	963	26	it	-PRON-	PRP
37681	963	27	has	have	VBZ
37681	963	28	a	a	DT
37681	963	29	genuine	genuine	JJ
37681	963	30	value	value	NN
37681	963	31	for	for	IN
37681	963	32	the	the	DT
37681	963	33	future	future	JJ
37681	963	34	artisan	artisan	NNP
37681	963	35	,	,	,
37681	963	36	and	and	CC
37681	963	37	it	-PRON-	PRP
37681	963	38	shows	show	VBZ
37681	963	39	that	that	IN
37681	963	40	geometry	geometry	NN
37681	963	41	is	be	VBZ
37681	963	42	something	something	NN
37681	963	43	besides	besides	IN
37681	963	44	mere	mere	JJ
37681	963	45	theory	theory	NN
37681	963	46	.	.	.
37681	964	1	Whether	whether	IN
37681	964	2	the	the	DT
37681	964	3	textbook	textbook	NN
37681	964	4	provides	provide	VBZ
37681	964	5	for	for	IN
37681	964	6	it	-PRON-	PRP
37681	964	7	or	or	CC
37681	964	8	not	not	RB
37681	964	9	,	,	,
37681	964	10	the	the	DT
37681	964	11	teacher	teacher	NN
37681	964	12	will	will	MD
37681	964	13	find	find	VB
37681	964	14	a	a	DT
37681	964	15	few	few	JJ
37681	964	16	days	day	NNS
37681	964	17	of	of	IN
37681	964	18	such	such	JJ
37681	964	19	work	work	NN
37681	964	20	well	well	RB
37681	964	21	spent	spend	VBN
37681	964	22	,	,	,
37681	964	23	it	-PRON-	PRP
37681	964	24	being	be	VBG
37681	964	25	a	a	DT
37681	964	26	simple	simple	JJ
37681	964	27	matter	matter	NN
37681	964	28	to	to	TO
37681	964	29	supplement	supplement	VB
37681	964	30	the	the	DT
37681	964	31	book	book	NN
37681	964	32	in	in	IN
37681	964	33	this	this	DT
37681	964	34	respect	respect	NN
37681	964	35	.	.	.
37681	965	1	There	there	EX
37681	965	2	was	be	VBD
37681	965	3	a	a	DT
37681	965	4	time	time	NN
37681	965	5	when	when	WRB
37681	965	6	some	some	DT
37681	965	7	form	form	NN
37681	965	8	of	of	IN
37681	965	9	mechanical	mechanical	JJ
37681	965	10	drawing	drawing	NN
37681	965	11	was	be	VBD
37681	965	12	generally	generally	RB
37681	965	13	taught	teach	VBN
37681	965	14	in	in	IN
37681	965	15	the	the	DT
37681	965	16	schools	school	NNS
37681	965	17	,	,	,
37681	965	18	but	but	CC
37681	965	19	this	this	DT
37681	965	20	has	have	VBZ
37681	965	21	given	give	VBN
37681	965	22	place	place	NN
37681	965	23	to	to	IN
37681	965	24	more	more	RBR
37681	965	25	genuine	genuine	JJ
37681	965	26	art	art	NN
37681	965	27	work	work	NN
37681	965	28	,	,	,
37681	965	29	leaving	leave	VBG
37681	965	30	it	-PRON-	PRP
37681	965	31	to	to	IN
37681	965	32	the	the	DT
37681	965	33	teacher	teacher	NN
37681	965	34	of	of	IN
37681	965	35	geometry	geometry	NN
37681	965	36	to	to	TO
37681	965	37	impart	impart	VB
37681	965	38	such	such	JJ
37681	965	39	knowledge	knowledge	NN
37681	965	40	of	of	IN
37681	965	41	drawing	drawing	NN
37681	965	42	as	as	IN
37681	965	43	is	be	VBZ
37681	965	44	a	a	DT
37681	965	45	necessary	necessary	JJ
37681	965	46	preliminary	preliminary	JJ
37681	965	47	to	to	IN
37681	965	48	the	the	DT
37681	965	49	regular	regular	JJ
37681	965	50	study	study	NN
37681	965	51	of	of	IN
37681	965	52	the	the	DT
37681	965	53	subject	subject	NN
37681	965	54	.	.	.
37681	966	1	Such	such	JJ
37681	966	2	work	work	NN
37681	966	3	in	in	IN
37681	966	4	drawing	drawing	NN
37681	966	5	should	should	MD
37681	966	6	go	go	VB
37681	966	7	so	so	RB
37681	966	8	far	far	RB
37681	966	9	,	,	,
37681	966	10	and	and	CC
37681	966	11	only	only	RB
37681	966	12	so	so	RB
37681	966	13	far	far	RB
37681	966	14	,	,	,
37681	966	15	as	as	IN
37681	966	16	to	to	TO
37681	966	17	arouse	arouse	VB
37681	966	18	an	an	DT
37681	966	19	interest	interest	NN
37681	966	20	in	in	IN
37681	966	21	geometric	geometric	JJ
37681	966	22	form	form	NN
37681	966	23	without	without	IN
37681	966	24	becoming	become	VBG
37681	966	25	wearisome	wearisome	VBN
37681	966	26	,	,	,
37681	966	27	and	and	CC
37681	966	28	to	to	TO
37681	966	29	familiarize	familiarize	VB
37681	966	30	the	the	DT
37681	966	31	pupil	pupil	NN
37681	966	32	with	with	IN
37681	966	33	the	the	DT
37681	966	34	use	use	NN
37681	966	35	of	of	IN
37681	966	36	the	the	DT
37681	966	37	instruments	instrument	NNS
37681	966	38	.	.	.
37681	967	1	He	-PRON-	PRP
37681	967	2	should	should	MD
37681	967	3	be	be	VB
37681	967	4	counseled	counsel	VBN
37681	967	5	about	about	IN
37681	967	6	making	make	VBG
37681	967	7	fine	fine	JJ
37681	967	8	lines	line	NNS
37681	967	9	,	,	,
37681	967	10	about	about	IN
37681	967	11	being	be	VBG
37681	967	12	careful	careful	JJ
37681	967	13	in	in	IN
37681	967	14	setting	set	VBG
37681	967	15	the	the	DT
37681	967	16	point	point	NN
37681	967	17	of	of	IN
37681	967	18	his	-PRON-	PRP$
37681	967	19	compasses	compass	NNS
37681	967	20	on	on	IN
37681	967	21	the	the	DT
37681	967	22	exact	exact	JJ
37681	967	23	center	center	NN
37681	967	24	that	that	WDT
37681	967	25	he	-PRON-	PRP
37681	967	26	wishes	wish	VBZ
37681	967	27	to	to	TO
37681	967	28	use	use	VB
37681	967	29	,	,	,
37681	967	30	and	and	CC
37681	967	31	about	about	IN
37681	967	32	representing	represent	VBG
37681	967	33	a	a	DT
37681	967	34	point	point	NN
37681	967	35	by	by	IN
37681	967	36	a	a	DT
37681	967	37	very	very	RB
37681	967	38	fine	fine	JJ
37681	967	39	dot	dot	NN
37681	967	40	,	,	,
37681	967	41	or	or	CC
37681	967	42	,	,	,
37681	967	43	preferably	preferably	RB
37681	967	44	at	at	IN
37681	967	45	first	first	RB
37681	967	46	,	,	,
37681	967	47	by	by	IN
37681	967	48	two	two	CD
37681	967	49	crossed	cross	VBN
37681	967	50	lines	line	NNS
37681	967	51	.	.	.
37681	968	1	Unless	unless	IN
37681	968	2	these	these	DT
37681	968	3	details	detail	NNS
37681	968	4	are	be	VBP
37681	968	5	carefully	carefully	RB
37681	968	6	considered	consider	VBN
37681	968	7	,	,	,
37681	968	8	the	the	DT
37681	968	9	pupil	pupil	NN
37681	968	10	will	will	MD
37681	968	11	soon	soon	RB
37681	968	12	find	find	VB
37681	968	13	that	that	IN
37681	968	14	the	the	DT
37681	968	15	lines	line	NNS
37681	968	16	of	of	IN
37681	968	17	his	-PRON-	PRP$
37681	968	18	drawings	drawing	NNS
37681	968	19	do	do	VBP
37681	968	20	not	not	RB
37681	968	21	fit	fit	VB
37681	968	22	together	together	RB
37681	968	23	,	,	,
37681	968	24	and	and	CC
37681	968	25	that	that	IN
37681	968	26	the	the	DT
37681	968	27	result	result	NN
37681	968	28	is	be	VBZ
37681	968	29	not	not	RB
37681	968	30	pleasing	pleasing	JJ
37681	968	31	to	to	IN
37681	968	32	the	the	DT
37681	968	33	eye	eye	NN
37681	968	34	.	.	.
37681	969	1	The	the	DT
37681	969	2	figures	figure	NNS
37681	969	3	here	here	RB
37681	969	4	given	give	VBN
37681	969	5	are	be	VBP
37681	969	6	good	good	JJ
37681	969	7	ones	one	NNS
37681	969	8	upon	upon	IN
37681	969	9	which	which	WDT
37681	969	10	to	to	TO
37681	969	11	begin	begin	VB
37681	969	12	,	,	,
37681	969	13	the	the	DT
37681	969	14	dotted	dotted	JJ
37681	969	15	construction	construction	NN
37681	969	16	lines	line	NNS
37681	969	17	being	be	VBG
37681	969	18	erased	erase	VBN
37681	969	19	after	after	IN
37681	969	20	the	the	DT
37681	969	21	work	work	NN
37681	969	22	is	be	VBZ
37681	969	23	completed	complete	VBN
37681	969	24	.	.	.
37681	970	1	They	-PRON-	PRP
37681	970	2	may	may	MD
37681	970	3	be	be	VB
37681	970	4	constructed	construct	VBN
37681	970	5	with	with	IN
37681	970	6	the	the	DT
37681	970	7	compasses	compass	NNS
37681	970	8	and	and	CC
37681	970	9	ruler	ruler	NN
37681	970	10	alone	alone	RB
37681	970	11	,	,	,
37681	970	12	or	or	CC
37681	970	13	the	the	DT
37681	970	14	draftsman	draftsman	NN
37681	970	15	's	's	POS
37681	970	16	T	T	NNP
37681	970	17	-	-	HYPH
37681	970	18	square	square	NNP
37681	970	19	,	,	,
37681	970	20	triangle	triangle	NNP
37681	970	21	,	,	,
37681	970	22	and	and	CC
37681	970	23	protractor	protractor	NN
37681	970	24	may	may	MD
37681	970	25	be	be	VB
37681	970	26	used	use	VBN
37681	970	27	,	,	,
37681	970	28	although	although	IN
37681	970	29	these	these	DT
37681	970	30	latter	latter	JJ
37681	970	31	instruments	instrument	NNS
37681	970	32	are	be	VBP
37681	970	33	not	not	RB
37681	970	34	necessary	necessary	JJ
37681	970	35	.	.	.
37681	971	1	We	-PRON-	PRP
37681	971	2	should	should	MD
37681	971	3	constantly	constantly	RB
37681	971	4	remember	remember	VB
37681	971	5	that	that	IN
37681	971	6	there	there	EX
37681	971	7	is	be	VBZ
37681	971	8	a	a	DT
37681	971	9	danger	danger	NN
37681	971	10	in	in	IN
37681	971	11	the	the	DT
37681	971	12	slavish	slavish	JJ
37681	971	13	use	use	NN
37681	971	14	of	of	IN
37681	971	15	instruments	instrument	NNS
37681	971	16	and	and	CC
37681	971	17	of	of	IN
37681	971	18	such	such	JJ
37681	971	19	helps	help	NNS
37681	971	20	as	as	IN
37681	971	21	squared	square	VBN
37681	971	22	paper	paper	NN
37681	971	23	.	.	.
37681	972	1	Just	just	RB
37681	972	2	as	as	IN
37681	972	3	Euclid	Euclid	NNP
37681	972	4	rode	ride	VBD
37681	972	5	roughshod	roughshod	RB
37681	972	6	over	over	IN
37681	972	7	the	the	DT
37681	972	8	growing	grow	VBG
37681	972	9	intellects	intellect	NNS
37681	972	10	of	of	IN
37681	972	11	boys	boy	NNS
37681	972	12	and	and	CC
37681	972	13	girls	girl	NNS
37681	972	14	,	,	,
37681	972	15	so	so	RB
37681	972	16	may	may	MD
37681	972	17	instruments	instrument	NNS
37681	972	18	ride	ride	VB
37681	972	19	roughshod	roughshod	RB
37681	972	20	over	over	IN
37681	972	21	their	-PRON-	PRP$
37681	972	22	growing	grow	VBG
37681	972	23	perceptions	perception	NNS
37681	972	24	by	by	IN
37681	972	25	interfering	interfere	VBG
37681	972	26	with	with	IN
37681	972	27	natural	natural	JJ
37681	972	28	and	and	CC
37681	972	29	healthy	healthy	JJ
37681	972	30	intuitions	intuition	NNS
37681	972	31	,	,	,
37681	972	32	and	and	CC
37681	972	33	making	make	VBG
37681	972	34	them	-PRON-	PRP
37681	972	35	the	the	DT
37681	972	36	subject	subject	NN
37681	972	37	of	of	IN
37681	972	38	laborious	laborious	JJ
37681	972	39	measurement	measurement	NN
37681	972	40	.	.	.
37681	973	1	[	[	-LRB-
37681	973	2	40	40	CD
37681	973	3	]	]	-RRB-
37681	973	4	[	[	-LRB-
37681	973	5	Illustration	illustration	NN
37681	973	6	]	]	-RRB-
37681	973	7	The	the	DT
37681	973	8	pupil	pupil	NN
37681	973	9	who	who	WP
37681	973	10	can	can	MD
37681	973	11	not	not	RB
37681	973	12	see	see	VB
37681	973	13	the	the	DT
37681	973	14	equality	equality	NN
37681	973	15	of	of	IN
37681	973	16	vertical	vertical	JJ
37681	973	17	angles	angle	NNS
37681	973	18	intuitively	intuitively	RB
37681	973	19	better	well	RBR
37681	973	20	than	than	IN
37681	973	21	by	by	IN
37681	973	22	the	the	DT
37681	973	23	use	use	NN
37681	973	24	of	of	IN
37681	973	25	the	the	DT
37681	973	26	protractor	protractor	NN
37681	973	27	is	be	VBZ
37681	973	28	abnormal	abnormal	JJ
37681	973	29	.	.	.
37681	974	1	Nevertheless	nevertheless	RB
37681	974	2	it	-PRON-	PRP
37681	974	3	is	be	VBZ
37681	974	4	the	the	DT
37681	974	5	pupil	pupil	NN
37681	974	6	's	's	POS
37681	974	7	interest	interest	NN
37681	974	8	that	that	WDT
37681	974	9	is	be	VBZ
37681	974	10	at	at	IN
37681	974	11	stake	stake	NN
37681	974	12	,	,	,
37681	974	13	together	together	RB
37681	974	14	with	with	IN
37681	974	15	his	-PRON-	PRP$
37681	974	16	ability	ability	NN
37681	974	17	to	to	TO
37681	974	18	use	use	VB
37681	974	19	the	the	DT
37681	974	20	instruments	instrument	NNS
37681	974	21	of	of	IN
37681	974	22	daily	daily	JJ
37681	974	23	life	life	NN
37681	974	24	.	.	.
37681	975	1	If	if	IN
37681	975	2	,	,	,
37681	975	3	therefore	therefore	RB
37681	975	4	,	,	,
37681	975	5	he	-PRON-	PRP
37681	975	6	can	can	MD
37681	975	7	readily	readily	RB
37681	975	8	be	be	VB
37681	975	9	supplied	supply	VBN
37681	975	10	with	with	IN
37681	975	11	draftsmen	draftsman	NNS
37681	975	12	's	's	POS
37681	975	13	materials	material	NNS
37681	975	14	,	,	,
37681	975	15	and	and	CC
37681	975	16	is	be	VBZ
37681	975	17	not	not	RB
37681	975	18	compelled	compel	VBN
37681	975	19	to	to	TO
37681	975	20	use	use	VB
37681	975	21	them	-PRON-	PRP
37681	975	22	in	in	IN
37681	975	23	a	a	DT
37681	975	24	foolish	foolish	JJ
37681	975	25	manner	manner	NN
37681	975	26	,	,	,
37681	975	27	so	so	RB
37681	975	28	much	much	RB
37681	975	29	the	the	DT
37681	975	30	better	well	JJR
37681	975	31	.	.	.
37681	976	1	They	-PRON-	PRP
37681	976	2	will	will	MD
37681	976	3	not	not	RB
37681	976	4	hurt	hurt	VB
37681	976	5	his	-PRON-	PRP$
37681	976	6	geometry	geometry	NN
37681	976	7	if	if	IN
37681	976	8	the	the	DT
37681	976	9	teacher	teacher	NN
37681	976	10	does	do	VBZ
37681	976	11	not	not	RB
37681	976	12	interfere	interfere	VB
37681	976	13	,	,	,
37681	976	14	and	and	CC
37681	976	15	they	-PRON-	PRP
37681	976	16	will	will	MD
37681	976	17	help	help	VB
37681	976	18	his	-PRON-	PRP$
37681	976	19	practical	practical	JJ
37681	976	20	drawing	drawing	NN
37681	976	21	;	;	:
37681	976	22	but	but	CC
37681	976	23	for	for	IN
37681	976	24	obvious	obvious	JJ
37681	976	25	reasons	reason	NNS
37681	976	26	we	-PRON-	PRP
37681	976	27	can	can	MD
37681	976	28	not	not	RB
37681	976	29	demand	demand	VB
37681	976	30	that	that	IN
37681	976	31	the	the	DT
37681	976	32	pupil	pupil	NN
37681	976	33	purchase	purchase	NN
37681	976	34	what	what	WP
37681	976	35	is	be	VBZ
37681	976	36	not	not	RB
37681	976	37	really	really	RB
37681	976	38	essential	essential	JJ
37681	976	39	to	to	IN
37681	976	40	his	-PRON-	PRP$
37681	976	41	study	study	NN
37681	976	42	of	of	IN
37681	976	43	the	the	DT
37681	976	44	subject	subject	NN
37681	976	45	.	.	.
37681	977	1	The	the	DT
37681	977	2	most	most	RBS
37681	977	3	valuable	valuable	JJ
37681	977	4	single	single	JJ
37681	977	5	instrument	instrument	NN
37681	977	6	of	of	IN
37681	977	7	the	the	DT
37681	977	8	three	three	CD
37681	977	9	just	just	RB
37681	977	10	mentioned	mention	VBN
37681	977	11	is	be	VBZ
37681	977	12	the	the	DT
37681	977	13	protractor	protractor	NN
37681	977	14	,	,	,
37681	977	15	and	and	CC
37681	977	16	since	since	IN
37681	977	17	a	a	DT
37681	977	18	paper	paper	NN
37681	977	19	one	one	CD
37681	977	20	costs	cost	VBZ
37681	977	21	only	only	RB
37681	977	22	a	a	DT
37681	977	23	few	few	JJ
37681	977	24	cents	cent	NNS
37681	977	25	and	and	CC
37681	977	26	is	be	VBZ
37681	977	27	often	often	RB
37681	977	28	helpful	helpful	JJ
37681	977	29	in	in	IN
37681	977	30	the	the	DT
37681	977	31	drawing	drawing	NN
37681	977	32	of	of	IN
37681	977	33	figures	figure	NNS
37681	977	34	,	,	,
37681	977	35	it	-PRON-	PRP
37681	977	36	should	should	MD
37681	977	37	be	be	VB
37681	977	38	recommended	recommend	VBN
37681	977	39	to	to	IN
37681	977	40	pupils	pupil	NNS
37681	977	41	.	.	.
37681	978	1	There	there	EX
37681	978	2	is	be	VBZ
37681	978	3	also	also	RB
37681	978	4	another	another	DT
37681	978	5	line	line	NN
37681	978	6	of	of	IN
37681	978	7	work	work	NN
37681	978	8	that	that	WDT
37681	978	9	often	often	RB
37681	978	10	arouses	arouse	VBZ
37681	978	11	a	a	DT
37681	978	12	good	good	JJ
37681	978	13	deal	deal	NN
37681	978	14	of	of	IN
37681	978	15	interest	interest	NN
37681	978	16	,	,	,
37681	978	17	namely	namely	RB
37681	978	18	,	,	,
37681	978	19	the	the	DT
37681	978	20	simple	simple	JJ
37681	978	21	field	field	NN
37681	978	22	measures	measure	NNS
37681	978	23	that	that	WDT
37681	978	24	can	can	MD
37681	978	25	easily	easily	RB
37681	978	26	be	be	VB
37681	978	27	made	make	VBN
37681	978	28	about	about	IN
37681	978	29	the	the	DT
37681	978	30	school	school	NN
37681	978	31	grounds	ground	NNS
37681	978	32	.	.	.
37681	979	1	Guarding	guard	VBG
37681	979	2	against	against	IN
37681	979	3	the	the	DT
37681	979	4	ever	ever	RB
37681	979	5	-	-	HYPH
37681	979	6	present	present	JJ
37681	979	7	danger	danger	NN
37681	979	8	of	of	IN
37681	979	9	doing	do	VBG
37681	979	10	too	too	RB
37681	979	11	much	much	JJ
37681	979	12	of	of	IN
37681	979	13	such	such	JJ
37681	979	14	work	work	NN
37681	979	15	,	,	,
37681	979	16	of	of	IN
37681	979	17	doing	do	VBG
37681	979	18	work	work	NN
37681	979	19	that	that	WDT
37681	979	20	has	have	VBZ
37681	979	21	no	no	DT
37681	979	22	interest	interest	NN
37681	979	23	for	for	IN
37681	979	24	the	the	DT
37681	979	25	pupil	pupil	NN
37681	979	26	,	,	,
37681	979	27	of	of	IN
37681	979	28	requiring	require	VBG
37681	979	29	it	-PRON-	PRP
37681	979	30	done	do	VBN
37681	979	31	in	in	IN
37681	979	32	a	a	DT
37681	979	33	way	way	NN
37681	979	34	that	that	WDT
37681	979	35	seems	seem	VBZ
37681	979	36	unreal	unreal	JJ
37681	979	37	to	to	IN
37681	979	38	a	a	DT
37681	979	39	class	class	NN
37681	979	40	,	,	,
37681	979	41	and	and	CC
37681	979	42	of	of	IN
37681	979	43	neglecting	neglect	VBG
37681	979	44	the	the	DT
37681	979	45	essence	essence	NN
37681	979	46	of	of	IN
37681	979	47	geometry	geometry	NN
37681	979	48	by	by	IN
37681	979	49	a	a	DT
37681	979	50	line	line	NN
37681	979	51	of	of	IN
37681	979	52	work	work	NN
37681	979	53	that	that	WDT
37681	979	54	involves	involve	VBZ
37681	979	55	no	no	DT
37681	979	56	new	new	JJ
37681	979	57	principles,--such	principles,--such	JJ
37681	979	58	outdoor	outdoor	JJ
37681	979	59	exercises	exercise	NNS
37681	979	60	in	in	IN
37681	979	61	measurement	measurement	NN
37681	979	62	have	have	VBP
37681	979	63	a	a	DT
37681	979	64	positive	positive	JJ
37681	979	65	value	value	NN
37681	979	66	,	,	,
37681	979	67	and	and	CC
37681	979	68	a	a	DT
37681	979	69	plentiful	plentiful	JJ
37681	979	70	supply	supply	NN
37681	979	71	of	of	IN
37681	979	72	suggestions	suggestion	NNS
37681	979	73	in	in	IN
37681	979	74	this	this	DT
37681	979	75	line	line	NN
37681	979	76	is	be	VBZ
37681	979	77	given	give	VBN
37681	979	78	in	in	IN
37681	979	79	the	the	DT
37681	979	80	subsequent	subsequent	JJ
37681	979	81	chapters	chapter	NNS
37681	979	82	.	.	.
37681	980	1	The	the	DT
37681	980	2	object	object	NN
37681	980	3	is	be	VBZ
37681	980	4	chiefly	chiefly	JJ
37681	980	5	to	to	TO
37681	980	6	furnish	furnish	VB
37681	980	7	a	a	DT
37681	980	8	motive	motive	NN
37681	980	9	for	for	IN
37681	980	10	geometry	geometry	NN
37681	980	11	,	,	,
37681	980	12	and	and	CC
37681	980	13	for	for	IN
37681	980	14	many	many	JJ
37681	980	15	pupils	pupil	NNS
37681	980	16	this	this	DT
37681	980	17	is	be	VBZ
37681	980	18	quite	quite	RB
37681	980	19	unnecessary	unnecessary	JJ
37681	980	20	.	.	.
37681	981	1	For	for	IN
37681	981	2	some	some	DT
37681	981	3	,	,	,
37681	981	4	however	however	RB
37681	981	5	,	,	,
37681	981	6	and	and	CC
37681	981	7	particularly	particularly	RB
37681	981	8	for	for	IN
37681	981	9	the	the	DT
37681	981	10	energetic	energetic	JJ
37681	981	11	,	,	,
37681	981	12	restless	restless	JJ
37681	981	13	boy	boy	NN
37681	981	14	,	,	,
37681	981	15	such	such	JJ
37681	981	16	work	work	NN
37681	981	17	has	have	VBZ
37681	981	18	been	be	VBN
37681	981	19	successfully	successfully	RB
37681	981	20	offered	offer	VBN
37681	981	21	by	by	IN
37681	981	22	various	various	JJ
37681	981	23	teachers	teacher	NNS
37681	981	24	as	as	IN
37681	981	25	an	an	DT
37681	981	26	alternative	alternative	NN
37681	981	27	to	to	IN
37681	981	28	some	some	DT
37681	981	29	of	of	IN
37681	981	30	the	the	DT
37681	981	31	book	book	NN
37681	981	32	work	work	NN
37681	981	33	.	.	.
37681	982	1	Because	because	IN
37681	982	2	of	of	IN
37681	982	3	this	this	DT
37681	982	4	value	value	NN
37681	982	5	a	a	DT
37681	982	6	considerable	considerable	JJ
37681	982	7	amount	amount	NN
37681	982	8	of	of	IN
37681	982	9	such	such	JJ
37681	982	10	work	work	NN
37681	982	11	will	will	MD
37681	982	12	be	be	VB
37681	982	13	suggested	suggest	VBN
37681	982	14	for	for	IN
37681	982	15	teachers	teacher	NNS
37681	982	16	who	who	WP
37681	982	17	may	may	MD
37681	982	18	care	care	VB
37681	982	19	to	to	TO
37681	982	20	use	use	VB
37681	982	21	it	-PRON-	PRP
37681	982	22	,	,	,
37681	982	23	the	the	DT
37681	982	24	textbook	textbook	NN
37681	982	25	being	be	VBG
37681	982	26	manifestly	manifestly	RB
37681	982	27	not	not	RB
37681	982	28	the	the	DT
37681	982	29	place	place	NN
37681	982	30	for	for	IN
37681	982	31	occasional	occasional	JJ
37681	982	32	topics	topic	NNS
37681	982	33	of	of	IN
37681	982	34	this	this	DT
37681	982	35	nature	nature	NN
37681	982	36	.	.	.
37681	983	1	For	for	IN
37681	983	2	the	the	DT
37681	983	3	purposes	purpose	NNS
37681	983	4	of	of	IN
37681	983	5	an	an	DT
37681	983	6	introduction	introduction	NN
37681	983	7	only	only	RB
37681	983	8	a	a	DT
37681	983	9	tape	tape	NN
37681	983	10	line	line	NN
37681	983	11	need	nee	MD
37681	983	12	be	be	VB
37681	983	13	purchased	purchase	VBN
37681	983	14	.	.	.
37681	984	1	Wooden	wooden	JJ
37681	984	2	pins	pin	NNS
37681	984	3	and	and	CC
37681	984	4	a	a	DT
37681	984	5	plumb	plumb	JJ
37681	984	6	line	line	NN
37681	984	7	can	can	MD
37681	984	8	easily	easily	RB
37681	984	9	be	be	VB
37681	984	10	made	make	VBN
37681	984	11	.	.	.
37681	985	1	Even	even	RB
37681	985	2	before	before	IN
37681	985	3	he	-PRON-	PRP
37681	985	4	comes	come	VBZ
37681	985	5	to	to	IN
37681	985	6	the	the	DT
37681	985	7	propositions	proposition	NNS
37681	985	8	in	in	IN
37681	985	9	mensuration	mensuration	NN
37681	985	10	in	in	IN
37681	985	11	geometry	geometry	NN
37681	985	12	the	the	DT
37681	985	13	pupil	pupil	NN
37681	985	14	knows	know	VBZ
37681	985	15	,	,	,
37681	985	16	from	from	IN
37681	985	17	his	-PRON-	PRP$
37681	985	18	arithmetic	arithmetic	JJ
37681	985	19	,	,	,
37681	985	20	how	how	WRB
37681	985	21	to	to	TO
37681	985	22	find	find	VB
37681	985	23	ordinary	ordinary	JJ
37681	985	24	areas	area	NNS
37681	985	25	and	and	CC
37681	985	26	volumes	volume	NNS
37681	985	27	,	,	,
37681	985	28	and	and	CC
37681	985	29	he	-PRON-	PRP
37681	985	30	may	may	MD
37681	985	31	therefore	therefore	RB
37681	985	32	be	be	VB
37681	985	33	set	set	VBN
37681	985	34	at	at	IN
37681	985	35	work	work	NN
37681	985	36	to	to	TO
37681	985	37	find	find	VB
37681	985	38	the	the	DT
37681	985	39	area	area	NN
37681	985	40	of	of	IN
37681	985	41	the	the	DT
37681	985	42	school	school	NN
37681	985	43	ground	ground	NN
37681	985	44	,	,	,
37681	985	45	or	or	CC
37681	985	46	of	of	IN
37681	985	47	a	a	DT
37681	985	48	field	field	NN
37681	985	49	,	,	,
37681	985	50	or	or	CC
37681	985	51	of	of	IN
37681	985	52	a	a	DT
37681	985	53	city	city	NN
37681	985	54	block	block	NN
37681	985	55	.	.	.
37681	986	1	The	the	DT
37681	986	2	following	follow	VBG
37681	986	3	are	be	VBP
37681	986	4	among	among	IN
37681	986	5	the	the	DT
37681	986	6	simple	simple	JJ
37681	986	7	exercises	exercise	NNS
37681	986	8	for	for	IN
37681	986	9	a	a	DT
37681	986	10	beginner	beginner	NN
37681	986	11	:	:	:
37681	986	12	[	[	-LRB-
37681	986	13	Illustration	illustration	NN
37681	986	14	]	]	-RRB-
37681	986	15	1	1	CD
37681	986	16	.	.	.
37681	987	1	Drive	drive	NN
37681	987	2	stakes	stake	NNS
37681	987	3	at	at	IN
37681	987	4	two	two	CD
37681	987	5	corners	corner	NNS
37681	987	6	,	,	,
37681	987	7	_	_	NNP
37681	987	8	A	A	NNP
37681	987	9	_	_	NNP
37681	987	10	and	and	CC
37681	987	11	_	_	NNP
37681	987	12	B	B	NNP
37681	987	13	_	_	NNP
37681	987	14	,	,	,
37681	987	15	of	of	IN
37681	987	16	the	the	DT
37681	987	17	school	school	NN
37681	987	18	grounds	ground	NNS
37681	987	19	,	,	,
37681	987	20	putting	put	VBG
37681	987	21	a	a	DT
37681	987	22	cross	cross	NN
37681	987	23	on	on	IN
37681	987	24	top	top	NN
37681	987	25	of	of	IN
37681	987	26	each	each	DT
37681	987	27	;	;	:
37681	987	28	or	or	CC
37681	987	29	make	make	VB
37681	987	30	the	the	DT
37681	987	31	crosses	crosse	NNS
37681	987	32	on	on	IN
37681	987	33	the	the	DT
37681	987	34	sidewalk	sidewalk	NN
37681	987	35	,	,	,
37681	987	36	so	so	IN
37681	987	37	as	as	IN
37681	987	38	to	to	TO
37681	987	39	get	get	VB
37681	987	40	two	two	CD
37681	987	41	points	point	NNS
37681	987	42	between	between	IN
37681	987	43	which	which	WDT
37681	987	44	to	to	TO
37681	987	45	measure	measure	VB
37681	987	46	.	.	.
37681	988	1	Measure	measure	NN
37681	988	2	from	from	IN
37681	988	3	_	_	NNP
37681	988	4	A	A	NNP
37681	988	5	_	_	NNP
37681	988	6	to	to	IN
37681	988	7	_	_	NNP
37681	988	8	B	B	NNP
37681	988	9	_	_	NNP
37681	988	10	by	by	IN
37681	988	11	holding	hold	VBG
37681	988	12	the	the	DT
37681	988	13	tape	tape	NN
37681	988	14	taut	taut	JJ
37681	988	15	and	and	CC
37681	988	16	level	level	NN
37681	988	17	,	,	,
37681	988	18	dropping	drop	VBG
37681	988	19	perpendiculars	perpendicular	NNS
37681	988	20	when	when	WRB
37681	988	21	necessary	necessary	JJ
37681	988	22	by	by	IN
37681	988	23	means	mean	NNS
37681	988	24	of	of	IN
37681	988	25	the	the	DT
37681	988	26	plumb	plumb	JJ
37681	988	27	line	line	NN
37681	988	28	,	,	,
37681	988	29	as	as	IN
37681	988	30	shown	show	VBN
37681	988	31	in	in	IN
37681	988	32	the	the	DT
37681	988	33	figure	figure	NN
37681	988	34	.	.	.
37681	989	1	Check	check	VB
37681	989	2	the	the	DT
37681	989	3	work	work	NN
37681	989	4	by	by	IN
37681	989	5	measuring	measure	VBG
37681	989	6	from	from	IN
37681	989	7	_	_	NNP
37681	989	8	B	B	NNP
37681	989	9	_	_	NNP
37681	989	10	back	back	RB
37681	989	11	to	to	IN
37681	989	12	_	_	NNP
37681	989	13	A	A	NNP
37681	989	14	_	_	NNP
37681	989	15	in	in	IN
37681	989	16	the	the	DT
37681	989	17	same	same	JJ
37681	989	18	way	way	NN
37681	989	19	.	.	.
37681	990	1	Pupils	pupil	NNS
37681	990	2	will	will	MD
37681	990	3	find	find	VB
37681	990	4	that	that	IN
37681	990	5	their	-PRON-	PRP$
37681	990	6	work	work	NN
37681	990	7	should	should	MD
37681	990	8	always	always	RB
37681	990	9	be	be	VB
37681	990	10	checked	check	VBN
37681	990	11	,	,	,
37681	990	12	and	and	CC
37681	990	13	they	-PRON-	PRP
37681	990	14	will	will	MD
37681	990	15	be	be	VB
37681	990	16	surprised	surprised	JJ
37681	990	17	to	to	TO
37681	990	18	see	see	VB
37681	990	19	how	how	WRB
37681	990	20	the	the	DT
37681	990	21	results	result	NNS
37681	990	22	will	will	MD
37681	990	23	vary	vary	VB
37681	990	24	in	in	IN
37681	990	25	such	such	PDT
37681	990	26	a	a	DT
37681	990	27	simple	simple	JJ
37681	990	28	measurement	measurement	NN
37681	990	29	as	as	IN
37681	990	30	this	this	DT
37681	990	31	,	,	,
37681	990	32	unless	unless	IN
37681	990	33	very	very	RB
37681	990	34	great	great	JJ
37681	990	35	care	care	NN
37681	990	36	is	be	VBZ
37681	990	37	taken	take	VBN
37681	990	38	.	.	.
37681	991	1	If	if	IN
37681	991	2	they	-PRON-	PRP
37681	991	3	learn	learn	VBP
37681	991	4	the	the	DT
37681	991	5	lesson	lesson	NN
37681	991	6	of	of	IN
37681	991	7	accuracy	accuracy	NN
37681	991	8	thus	thus	RB
37681	991	9	early	early	RB
37681	991	10	,	,	,
37681	991	11	they	-PRON-	PRP
37681	991	12	will	will	MD
37681	991	13	have	have	VB
37681	991	14	gained	gain	VBN
37681	991	15	much	much	JJ
37681	991	16	.	.	.
37681	992	1	[	[	-LRB-
37681	992	2	Illustration	illustration	NN
37681	992	3	]	]	-RRB-
37681	992	4	2	2	CD
37681	992	5	.	.	.
37681	993	1	Take	take	VB
37681	993	2	two	two	CD
37681	993	3	stakes	stake	NNS
37681	993	4	,	,	,
37681	993	5	_	_	NNP
37681	993	6	X	X	NNP
37681	993	7	_	_	NNP
37681	993	8	,	,	,
37681	993	9	_	_	NNP
37681	993	10	Y	Y	NNP
37681	993	11	_	_	NNP
37681	993	12	,	,	,
37681	993	13	in	in	IN
37681	993	14	a	a	DT
37681	993	15	field	field	NN
37681	993	16	,	,	,
37681	993	17	preferably	preferably	RB
37681	993	18	two	two	CD
37681	993	19	or	or	CC
37681	993	20	three	three	CD
37681	993	21	hundred	hundred	CD
37681	993	22	feet	foot	NNS
37681	993	23	apart	apart	RB
37681	993	24	,	,	,
37681	993	25	always	always	RB
37681	993	26	marked	mark	VBN
37681	993	27	on	on	IN
37681	993	28	top	top	NN
37681	993	29	with	with	IN
37681	993	30	crosses	crosse	NNS
37681	993	31	so	so	IN
37681	993	32	as	as	IN
37681	993	33	to	to	TO
37681	993	34	have	have	VB
37681	993	35	exact	exact	JJ
37681	993	36	points	point	NNS
37681	993	37	from	from	IN
37681	993	38	which	which	WDT
37681	993	39	to	to	IN
37681	993	40	work	work	VB
37681	993	41	.	.	.
37681	994	1	Let	let	VB
37681	994	2	it	-PRON-	PRP
37681	994	3	then	then	RB
37681	994	4	be	be	VB
37681	994	5	required	require	VBN
37681	994	6	to	to	TO
37681	994	7	stake	stake	VB
37681	994	8	out	out	RP
37681	994	9	or	or	CC
37681	994	10	"	"	``
37681	994	11	range	range	VB
37681	994	12	"	"	''
37681	994	13	the	the	DT
37681	994	14	line	line	NN
37681	994	15	from	from	IN
37681	994	16	_	_	NNP
37681	994	17	X	X	NNP
37681	994	18	_	_	NNP
37681	994	19	to	to	IN
37681	994	20	_	_	NNP
37681	994	21	Y	Y	NNP
37681	994	22	_	_	NNP
37681	994	23	by	by	IN
37681	994	24	placing	place	VBG
37681	994	25	stakes	stake	NNS
37681	994	26	at	at	IN
37681	994	27	specified	specified	JJ
37681	994	28	distances	distance	NNS
37681	994	29	.	.	.
37681	995	1	One	one	CD
37681	995	2	boy	boy	NN
37681	995	3	stands	stand	VBZ
37681	995	4	at	at	IN
37681	995	5	_	_	NNP
37681	995	6	Y	Y	NNP
37681	995	7	_	_	NNP
37681	995	8	and	and	CC
37681	995	9	another	another	DT
37681	995	10	at	at	IN
37681	995	11	_	_	NNP
37681	995	12	X	X	NNP
37681	995	13	_	_	NNP
37681	995	14	,	,	,
37681	995	15	each	each	DT
37681	995	16	with	with	IN
37681	995	17	a	a	DT
37681	995	18	plumb	plumb	JJ
37681	995	19	line	line	NN
37681	995	20	.	.	.
37681	996	1	A	a	DT
37681	996	2	third	third	JJ
37681	996	3	one	one	NN
37681	996	4	takes	take	VBZ
37681	996	5	a	a	DT
37681	996	6	plumb	plumb	JJ
37681	996	7	line	line	NN
37681	996	8	and	and	CC
37681	996	9	stands	stand	VBZ
37681	996	10	at	at	IN
37681	996	11	_	_	NNP
37681	996	12	P	P	NNP
37681	996	13	_	_	NNP
37681	996	14	,	,	,
37681	996	15	the	the	DT
37681	996	16	observer	observer	NN
37681	996	17	at	at	IN
37681	996	18	_	_	NNP
37681	996	19	X	X	NNP
37681	996	20	_	_	NNP
37681	996	21	motioning	motioning	NN
37681	996	22	to	to	IN
37681	996	23	him	-PRON-	PRP
37681	996	24	to	to	TO
37681	996	25	move	move	VB
37681	996	26	his	-PRON-	PRP$
37681	996	27	plumb	plumb	JJ
37681	996	28	line	line	NN
37681	996	29	to	to	IN
37681	996	30	the	the	DT
37681	996	31	right	right	NN
37681	996	32	or	or	CC
37681	996	33	the	the	DT
37681	996	34	left	left	NN
37681	996	35	until	until	IN
37681	996	36	it	-PRON-	PRP
37681	996	37	is	be	VBZ
37681	996	38	exactly	exactly	RB
37681	996	39	in	in	IN
37681	996	40	line	line	NN
37681	996	41	with	with	IN
37681	996	42	_	_	NNP
37681	996	43	X	X	NNP
37681	996	44	_	_	NNP
37681	996	45	and	and	CC
37681	996	46	_	_	NNP
37681	996	47	Y	Y	NNP
37681	996	48	_	_	NNP
37681	996	49	.	.	.
37681	997	1	A	a	DT
37681	997	2	stake	stake	NN
37681	997	3	is	be	VBZ
37681	997	4	then	then	RB
37681	997	5	driven	drive	VBN
37681	997	6	at	at	IN
37681	997	7	_	_	NNP
37681	997	8	P	P	NNP
37681	997	9	_	_	NNP
37681	997	10	,	,	,
37681	997	11	and	and	CC
37681	997	12	the	the	DT
37681	997	13	pupil	pupil	NN
37681	997	14	at	at	IN
37681	997	15	_	_	NNP
37681	997	16	X	X	NNP
37681	997	17	_	_	NNP
37681	997	18	moves	move	VBZ
37681	997	19	on	on	RP
37681	997	20	to	to	IN
37681	997	21	the	the	DT
37681	997	22	stake	stake	NN
37681	997	23	_	_	NNP
37681	997	24	P	P	NNP
37681	997	25	_	_	NNP
37681	997	26	.	.	.
37681	998	1	Then	then	RB
37681	998	2	_	_	NNP
37681	998	3	Q	Q	NNP
37681	998	4	_	_	NNP
37681	998	5	is	be	VBZ
37681	998	6	located	locate	VBN
37681	998	7	in	in	IN
37681	998	8	the	the	DT
37681	998	9	same	same	JJ
37681	998	10	way	way	NN
37681	998	11	,	,	,
37681	998	12	and	and	CC
37681	998	13	then	then	RB
37681	998	14	_	_	NNP
37681	998	15	R	R	NNP
37681	998	16	_	_	NNP
37681	998	17	,	,	,
37681	998	18	and	and	CC
37681	998	19	so	so	RB
37681	998	20	on	on	RB
37681	998	21	.	.	.
37681	999	1	The	the	DT
37681	999	2	work	work	NN
37681	999	3	is	be	VBZ
37681	999	4	checked	check	VBN
37681	999	5	by	by	IN
37681	999	6	ranging	range	VBG
37681	999	7	back	back	RB
37681	999	8	from	from	IN
37681	999	9	_	_	NNP
37681	999	10	Y	Y	NNP
37681	999	11	_	_	NNP
37681	999	12	to	to	IN
37681	999	13	_	_	NNP
37681	999	14	X	X	NNP
37681	999	15	_	_	NNP
37681	999	16	.	.	.
37681	1000	1	In	in	IN
37681	1000	2	some	some	DT
37681	1000	3	of	of	IN
37681	1000	4	the	the	DT
37681	1000	5	simple	simple	JJ
37681	1000	6	exercises	exercise	NNS
37681	1000	7	suggested	suggest	VBN
37681	1000	8	later	later	RB
37681	1000	9	it	-PRON-	PRP
37681	1000	10	is	be	VBZ
37681	1000	11	necessary	necessary	JJ
37681	1000	12	to	to	TO
37681	1000	13	range	range	VB
37681	1000	14	a	a	DT
37681	1000	15	line	line	NN
37681	1000	16	so	so	IN
37681	1000	17	that	that	IN
37681	1000	18	this	this	DT
37681	1000	19	work	work	NN
37681	1000	20	is	be	VBZ
37681	1000	21	useful	useful	JJ
37681	1000	22	in	in	IN
37681	1000	23	making	make	VBG
37681	1000	24	measurements	measurement	NNS
37681	1000	25	.	.	.
37681	1001	1	The	the	DT
37681	1001	2	geometric	geometric	JJ
37681	1001	3	principle	principle	NN
37681	1001	4	involved	involve	VBN
37681	1001	5	is	be	VBZ
37681	1001	6	that	that	IN
37681	1001	7	two	two	CD
37681	1001	8	points	point	NNS
37681	1001	9	determine	determine	VBP
37681	1001	10	a	a	DT
37681	1001	11	straight	straight	JJ
37681	1001	12	line	line	NN
37681	1001	13	.	.	.
37681	1002	1	[	[	-LRB-
37681	1002	2	Illustration	illustration	NN
37681	1002	3	]	]	-RRB-
37681	1002	4	[	[	-LRB-
37681	1002	5	Illustration	illustration	NN
37681	1002	6	]	]	-RRB-
37681	1002	7	3	3	CD
37681	1002	8	.	.	.
37681	1003	1	To	to	TO
37681	1003	2	test	test	VB
37681	1003	3	a	a	DT
37681	1003	4	perpendicular	perpendicular	NN
37681	1003	5	or	or	CC
37681	1003	6	to	to	TO
37681	1003	7	draw	draw	VB
37681	1003	8	one	one	CD
37681	1003	9	line	line	NN
37681	1003	10	perpendicular	perpendicular	JJ
37681	1003	11	to	to	IN
37681	1003	12	another	another	DT
37681	1003	13	in	in	IN
37681	1003	14	a	a	DT
37681	1003	15	field	field	NN
37681	1003	16	,	,	,
37681	1003	17	we	-PRON-	PRP
37681	1003	18	may	may	MD
37681	1003	19	take	take	VB
37681	1003	20	a	a	DT
37681	1003	21	stout	stout	JJ
37681	1003	22	cord	cord	NN
37681	1003	23	twelve	twelve	CD
37681	1003	24	feet	foot	NNS
37681	1003	25	long	long	JJ
37681	1003	26	,	,	,
37681	1003	27	having	have	VBG
37681	1003	28	a	a	DT
37681	1003	29	knot	knot	NN
37681	1003	30	at	at	IN
37681	1003	31	the	the	DT
37681	1003	32	end	end	NN
37681	1003	33	of	of	IN
37681	1003	34	every	every	DT
37681	1003	35	foot	foot	NN
37681	1003	36	.	.	.
37681	1004	1	If	if	IN
37681	1004	2	this	this	DT
37681	1004	3	is	be	VBZ
37681	1004	4	laid	lay	VBN
37681	1004	5	along	along	IN
37681	1004	6	four	four	CD
37681	1004	7	feet	foot	NNS
37681	1004	8	,	,	,
37681	1004	9	the	the	DT
37681	1004	10	ends	end	NNS
37681	1004	11	of	of	IN
37681	1004	12	this	this	DT
37681	1004	13	part	part	NN
37681	1004	14	being	be	VBG
37681	1004	15	fixed	fix	VBN
37681	1004	16	,	,	,
37681	1004	17	and	and	CC
37681	1004	18	it	-PRON-	PRP
37681	1004	19	is	be	VBZ
37681	1004	20	stretched	stretch	VBN
37681	1004	21	as	as	IN
37681	1004	22	here	here	RB
37681	1004	23	shown	show	VBN
37681	1004	24	,	,	,
37681	1004	25	so	so	IN
37681	1004	26	that	that	IN
37681	1004	27	the	the	DT
37681	1004	28	next	next	JJ
37681	1004	29	vertex	vertex	NN
37681	1004	30	is	be	VBZ
37681	1004	31	five	five	CD
37681	1004	32	feet	foot	NNS
37681	1004	33	from	from	IN
37681	1004	34	one	one	CD
37681	1004	35	of	of	IN
37681	1004	36	these	these	DT
37681	1004	37	ends	end	NNS
37681	1004	38	and	and	CC
37681	1004	39	three	three	CD
37681	1004	40	feet	foot	NNS
37681	1004	41	from	from	IN
37681	1004	42	the	the	DT
37681	1004	43	other	other	JJ
37681	1004	44	end	end	NN
37681	1004	45	,	,	,
37681	1004	46	a	a	DT
37681	1004	47	right	right	JJ
37681	1004	48	angle	angle	NN
37681	1004	49	will	will	MD
37681	1004	50	be	be	VB
37681	1004	51	formed	form	VBN
37681	1004	52	.	.	.
37681	1005	1	A	a	DT
37681	1005	2	right	right	JJ
37681	1005	3	angle	angle	NN
37681	1005	4	can	can	MD
37681	1005	5	also	also	RB
37681	1005	6	be	be	VB
37681	1005	7	run	run	VBN
37681	1005	8	by	by	IN
37681	1005	9	making	make	VBG
37681	1005	10	a	a	DT
37681	1005	11	simple	simple	JJ
37681	1005	12	instrument	instrument	NN
37681	1005	13	,	,	,
37681	1005	14	such	such	JJ
37681	1005	15	as	as	IN
37681	1005	16	is	be	VBZ
37681	1005	17	described	describe	VBN
37681	1005	18	in	in	IN
37681	1005	19	Chapter	Chapter	NNP
37681	1005	20	XV	XV	NNP
37681	1005	21	.	.	.
37681	1006	1	Still	still	RB
37681	1006	2	another	another	DT
37681	1006	3	plan	plan	NN
37681	1006	4	of	of	IN
37681	1006	5	drawing	draw	VBG
37681	1006	6	a	a	DT
37681	1006	7	line	line	NN
37681	1006	8	perpendicular	perpendicular	JJ
37681	1006	9	to	to	IN
37681	1006	10	another	another	DT
37681	1006	11	line	line	NN
37681	1006	12	_	_	NNP
37681	1006	13	AB	AB	NNP
37681	1006	14	_	_	NNP
37681	1006	15	,	,	,
37681	1006	16	from	from	IN
37681	1006	17	a	a	DT
37681	1006	18	point	point	NN
37681	1006	19	_	_	NNP
37681	1006	20	P	P	NNP
37681	1006	21	_	_	NNP
37681	1006	22	,	,	,
37681	1006	23	consists	consist	VBZ
37681	1006	24	in	in	IN
37681	1006	25	swinging	swinge	VBG
37681	1006	26	a	a	DT
37681	1006	27	tape	tape	NN
37681	1006	28	from	from	IN
37681	1006	29	_	_	NNP
37681	1006	30	P	P	NNP
37681	1006	31	_	_	NNP
37681	1006	32	,	,	,
37681	1006	33	cutting	cut	VBG
37681	1006	34	_	_	NNP
37681	1006	35	AB	AB	NNP
37681	1006	36	_	_	NNP
37681	1006	37	at	at	IN
37681	1006	38	_	_	NNP
37681	1006	39	X	X	NNP
37681	1006	40	_	_	NNP
37681	1006	41	and	and	CC
37681	1006	42	_	_	NNP
37681	1006	43	Y	Y	NNP
37681	1006	44	_	_	NNP
37681	1006	45	,	,	,
37681	1006	46	and	and	CC
37681	1006	47	then	then	RB
37681	1006	48	bisecting	bisect	VBG
37681	1006	49	_	_	NNP
37681	1006	50	XY	XY	NNP
37681	1006	51	_	_	NNP
37681	1006	52	by	by	IN
37681	1006	53	doubling	double	VBG
37681	1006	54	the	the	DT
37681	1006	55	tape	tape	NN
37681	1006	56	.	.	.
37681	1007	1	This	this	DT
37681	1007	2	fixes	fix	VBZ
37681	1007	3	the	the	DT
37681	1007	4	foot	foot	NN
37681	1007	5	of	of	IN
37681	1007	6	the	the	DT
37681	1007	7	perpendicular	perpendicular	NN
37681	1007	8	.	.	.
37681	1008	1	[	[	-LRB-
37681	1008	2	Illustration	illustration	NN
37681	1008	3	]	]	-RRB-
37681	1008	4	4	4	CD
37681	1008	5	.	.	.
37681	1009	1	It	-PRON-	PRP
37681	1009	2	is	be	VBZ
37681	1009	3	now	now	RB
37681	1009	4	possible	possible	JJ
37681	1009	5	to	to	TO
37681	1009	6	find	find	VB
37681	1009	7	the	the	DT
37681	1009	8	area	area	NN
37681	1009	9	of	of	IN
37681	1009	10	a	a	DT
37681	1009	11	field	field	NN
37681	1009	12	of	of	IN
37681	1009	13	irregular	irregular	JJ
37681	1009	14	shape	shape	NN
37681	1009	15	by	by	IN
37681	1009	16	dividing	divide	VBG
37681	1009	17	it	-PRON-	PRP
37681	1009	18	into	into	IN
37681	1009	19	triangles	triangle	NNS
37681	1009	20	and	and	CC
37681	1009	21	trapezoids	trapezoid	NNS
37681	1009	22	,	,	,
37681	1009	23	as	as	IN
37681	1009	24	shown	show	VBN
37681	1009	25	in	in	IN
37681	1009	26	the	the	DT
37681	1009	27	figure	figure	NN
37681	1009	28	.	.	.
37681	1010	1	Pupils	pupil	NNS
37681	1010	2	know	know	VBP
37681	1010	3	from	from	IN
37681	1010	4	their	-PRON-	PRP$
37681	1010	5	work	work	NN
37681	1010	6	in	in	IN
37681	1010	7	arithmetic	arithmetic	JJ
37681	1010	8	how	how	WRB
37681	1010	9	to	to	TO
37681	1010	10	find	find	VB
37681	1010	11	the	the	DT
37681	1010	12	area	area	NN
37681	1010	13	of	of	IN
37681	1010	14	a	a	DT
37681	1010	15	triangle	triangle	NN
37681	1010	16	or	or	CC
37681	1010	17	a	a	DT
37681	1010	18	trapezoid	trapezoid	NN
37681	1010	19	,	,	,
37681	1010	20	so	so	IN
37681	1010	21	that	that	IN
37681	1010	22	the	the	DT
37681	1010	23	area	area	NN
37681	1010	24	of	of	IN
37681	1010	25	the	the	DT
37681	1010	26	field	field	NN
37681	1010	27	is	be	VBZ
37681	1010	28	easily	easily	RB
37681	1010	29	found	find	VBN
37681	1010	30	.	.	.
37681	1011	1	The	the	DT
37681	1011	2	work	work	NN
37681	1011	3	may	may	MD
37681	1011	4	be	be	VB
37681	1011	5	checked	check	VBN
37681	1011	6	by	by	IN
37681	1011	7	comparing	compare	VBG
37681	1011	8	the	the	DT
37681	1011	9	results	result	NNS
37681	1011	10	of	of	IN
37681	1011	11	different	different	JJ
37681	1011	12	groups	group	NNS
37681	1011	13	of	of	IN
37681	1011	14	pupils	pupil	NNS
37681	1011	15	,	,	,
37681	1011	16	or	or	CC
37681	1011	17	by	by	IN
37681	1011	18	drawing	draw	VBG
37681	1011	19	another	another	DT
37681	1011	20	diagonal	diagonal	JJ
37681	1011	21	and	and	CC
37681	1011	22	dividing	divide	VBG
37681	1011	23	the	the	DT
37681	1011	24	field	field	NN
37681	1011	25	into	into	IN
37681	1011	26	other	other	JJ
37681	1011	27	triangles	triangle	NNS
37681	1011	28	and	and	CC
37681	1011	29	trapezoids	trapezoid	NNS
37681	1011	30	.	.	.
37681	1012	1	These	these	DT
37681	1012	2	are	be	VBP
37681	1012	3	about	about	IN
37681	1012	4	as	as	RB
37681	1012	5	many	many	JJ
37681	1012	6	types	type	NNS
37681	1012	7	of	of	IN
37681	1012	8	field	field	NN
37681	1012	9	work	work	NN
37681	1012	10	as	as	IN
37681	1012	11	there	there	EX
37681	1012	12	is	be	VBZ
37681	1012	13	any	any	DT
37681	1012	14	advantage	advantage	NN
37681	1012	15	in	in	IN
37681	1012	16	undertaking	undertaking	NN
37681	1012	17	for	for	IN
37681	1012	18	the	the	DT
37681	1012	19	purpose	purpose	NN
37681	1012	20	of	of	IN
37681	1012	21	securing	secure	VBG
37681	1012	22	the	the	DT
37681	1012	23	interest	interest	NN
37681	1012	24	of	of	IN
37681	1012	25	pupils	pupil	NNS
37681	1012	26	as	as	IN
37681	1012	27	a	a	DT
37681	1012	28	preliminary	preliminary	NN
37681	1012	29	to	to	IN
37681	1012	30	the	the	DT
37681	1012	31	work	work	NN
37681	1012	32	in	in	IN
37681	1012	33	geometry	geometry	NN
37681	1012	34	.	.	.
37681	1013	1	Whether	whether	IN
37681	1013	2	any	any	DT
37681	1013	3	of	of	IN
37681	1013	4	it	-PRON-	PRP
37681	1013	5	is	be	VBZ
37681	1013	6	necessary	necessary	JJ
37681	1013	7	,	,	,
37681	1013	8	and	and	CC
37681	1013	9	for	for	IN
37681	1013	10	what	what	WP
37681	1013	11	pupils	pupil	NNS
37681	1013	12	it	-PRON-	PRP
37681	1013	13	is	be	VBZ
37681	1013	14	necessary	necessary	JJ
37681	1013	15	,	,	,
37681	1013	16	and	and	CC
37681	1013	17	how	how	WRB
37681	1013	18	much	much	JJ
37681	1013	19	it	-PRON-	PRP
37681	1013	20	should	should	MD
37681	1013	21	trespass	trespass	VB
37681	1013	22	upon	upon	IN
37681	1013	23	the	the	DT
37681	1013	24	time	time	NN
37681	1013	25	of	of	IN
37681	1013	26	scientific	scientific	JJ
37681	1013	27	geometry	geometry	NN
37681	1013	28	are	be	VBP
37681	1013	29	matters	matter	NNS
37681	1013	30	that	that	WDT
37681	1013	31	can	can	MD
37681	1013	32	be	be	VB
37681	1013	33	decided	decide	VBN
37681	1013	34	only	only	RB
37681	1013	35	by	by	IN
37681	1013	36	the	the	DT
37681	1013	37	teacher	teacher	NN
37681	1013	38	of	of	IN
37681	1013	39	a	a	DT
37681	1013	40	particular	particular	JJ
37681	1013	41	class	class	NN
37681	1013	42	.	.	.
37681	1014	1	[	[	-LRB-
37681	1014	2	Illustration	illustration	NN
37681	1014	3	]	]	-RRB-
37681	1014	4	[	[	-LRB-
37681	1014	5	Illustration	illustration	NN
37681	1014	6	]	]	-RRB-
37681	1014	7	[	[	-LRB-
37681	1014	8	Illustration	illustration	NN
37681	1014	9	]	]	-RRB-
37681	1014	10	[	[	-LRB-
37681	1014	11	Illustration	illustration	NN
37681	1014	12	]	]	-RRB-
37681	1014	13	[	[	-LRB-
37681	1014	14	Illustration	illustration	NN
37681	1014	15	]	]	-RRB-
37681	1014	16	[	[	-LRB-
37681	1014	17	Illustration	illustration	NN
37681	1014	18	]	]	-RRB-
37681	1014	19	[	[	-LRB-
37681	1014	20	Illustration	illustration	NN
37681	1014	21	]	]	-RRB-
37681	1014	22	A	a	DT
37681	1014	23	second	second	JJ
37681	1014	24	difficulty	difficulty	NN
37681	1014	25	of	of	IN
37681	1014	26	the	the	DT
37681	1014	27	pupil	pupil	NN
37681	1014	28	is	be	VBZ
37681	1014	29	seen	see	VBN
37681	1014	30	in	in	IN
37681	1014	31	his	-PRON-	PRP$
37681	1014	32	attitude	attitude	NN
37681	1014	33	of	of	IN
37681	1014	34	mind	mind	NN
37681	1014	35	towards	towards	IN
37681	1014	36	proofs	proof	NNS
37681	1014	37	in	in	IN
37681	1014	38	general	general	JJ
37681	1014	39	.	.	.
37681	1015	1	He	-PRON-	PRP
37681	1015	2	does	do	VBZ
37681	1015	3	not	not	RB
37681	1015	4	see	see	VB
37681	1015	5	why	why	WRB
37681	1015	6	vertical	vertical	JJ
37681	1015	7	angles	angle	NNS
37681	1015	8	should	should	MD
37681	1015	9	be	be	VB
37681	1015	10	proved	prove	VBN
37681	1015	11	equal	equal	JJ
37681	1015	12	when	when	WRB
37681	1015	13	he	-PRON-	PRP
37681	1015	14	knows	know	VBZ
37681	1015	15	that	that	IN
37681	1015	16	they	-PRON-	PRP
37681	1015	17	are	be	VBP
37681	1015	18	so	so	RB
37681	1015	19	by	by	IN
37681	1015	20	looking	look	VBG
37681	1015	21	at	at	IN
37681	1015	22	the	the	DT
37681	1015	23	figure	figure	NN
37681	1015	24	.	.	.
37681	1016	1	This	this	DT
37681	1016	2	difficulty	difficulty	NN
37681	1016	3	should	should	MD
37681	1016	4	also	also	RB
37681	1016	5	be	be	VB
37681	1016	6	anticipated	anticipate	VBN
37681	1016	7	by	by	IN
37681	1016	8	giving	give	VBG
37681	1016	9	him	-PRON-	PRP
37681	1016	10	some	some	DT
37681	1016	11	opportunity	opportunity	NN
37681	1016	12	to	to	TO
37681	1016	13	know	know	VB
37681	1016	14	the	the	DT
37681	1016	15	weakness	weakness	NN
37681	1016	16	of	of	IN
37681	1016	17	his	-PRON-	PRP$
37681	1016	18	judgment	judgment	NN
37681	1016	19	,	,	,
37681	1016	20	and	and	CC
37681	1016	21	for	for	IN
37681	1016	22	this	this	DT
37681	1016	23	purpose	purpose	NN
37681	1016	24	figures	figure	NNS
37681	1016	25	like	like	IN
37681	1016	26	the	the	DT
37681	1016	27	following	follow	VBG
37681	1016	28	should	should	MD
37681	1016	29	be	be	VB
37681	1016	30	placed	place	VBN
37681	1016	31	before	before	IN
37681	1016	32	him	-PRON-	PRP
37681	1016	33	.	.	.
37681	1017	1	He	-PRON-	PRP
37681	1017	2	should	should	MD
37681	1017	3	be	be	VB
37681	1017	4	asked	ask	VBN
37681	1017	5	which	which	WDT
37681	1017	6	of	of	IN
37681	1017	7	these	these	DT
37681	1017	8	lines	line	NNS
37681	1017	9	is	be	VBZ
37681	1017	10	longer	long	JJR
37681	1017	11	,	,	,
37681	1017	12	_	_	NNP
37681	1017	13	AB	AB	NNP
37681	1017	14	_	_	NNP
37681	1017	15	or	or	CC
37681	1017	16	_	_	NNP
37681	1017	17	XY	XY	NNP
37681	1017	18	_	_	NNP
37681	1017	19	.	.	.
37681	1018	1	Two	two	CD
37681	1018	2	equal	equal	JJ
37681	1018	3	lines	line	NNS
37681	1018	4	should	should	MD
37681	1018	5	then	then	RB
37681	1018	6	be	be	VB
37681	1018	7	arranged	arrange	VBN
37681	1018	8	in	in	IN
37681	1018	9	the	the	DT
37681	1018	10	form	form	NN
37681	1018	11	of	of	IN
37681	1018	12	a	a	DT
37681	1018	13	letter	letter	NN
37681	1018	14	T	T	NNP
37681	1018	15	,	,	,
37681	1018	16	as	as	IN
37681	1018	17	here	here	RB
37681	1018	18	shown	show	VBN
37681	1018	19	,	,	,
37681	1018	20	and	and	CC
37681	1018	21	he	-PRON-	PRP
37681	1018	22	should	should	MD
37681	1018	23	be	be	VB
37681	1018	24	asked	ask	VBN
37681	1018	25	which	which	WDT
37681	1018	26	is	be	VBZ
37681	1018	27	the	the	DT
37681	1018	28	longer	long	JJR
37681	1018	29	,	,	,
37681	1018	30	_	_	NNP
37681	1018	31	AB	AB	NNP
37681	1018	32	_	_	NNP
37681	1018	33	or	or	CC
37681	1018	34	_	_	NNP
37681	1018	35	CD	CD	NNP
37681	1018	36	_	_	NNP
37681	1018	37	.	.	.
37681	1019	1	A	a	DT
37681	1019	2	figure	figure	NN
37681	1019	3	that	that	WDT
37681	1019	4	is	be	VBZ
37681	1019	5	very	very	RB
37681	1019	6	deceptive	deceptive	JJ
37681	1019	7	,	,	,
37681	1019	8	particularly	particularly	RB
37681	1019	9	if	if	IN
37681	1019	10	drawn	draw	VBN
37681	1019	11	larger	larger	RBR
37681	1019	12	and	and	CC
37681	1019	13	with	with	IN
37681	1019	14	heavy	heavy	JJ
37681	1019	15	cross	cross	NN
37681	1019	16	lines	line	NNS
37681	1019	17	,	,	,
37681	1019	18	is	be	VBZ
37681	1019	19	this	this	DT
37681	1019	20	one	one	CD
37681	1019	21	in	in	IN
37681	1019	22	which	which	WDT
37681	1019	23	_	_	NNP
37681	1019	24	AB	AB	NNP
37681	1019	25	_	_	NNP
37681	1019	26	and	and	CC
37681	1019	27	_	_	NNP
37681	1019	28	CD	CD	NNP
37681	1019	29	_	_	NNP
37681	1019	30	are	be	VBP
37681	1019	31	really	really	RB
37681	1019	32	parallel	parallel	JJ
37681	1019	33	,	,	,
37681	1019	34	but	but	CC
37681	1019	35	do	do	VBP
37681	1019	36	not	not	RB
37681	1019	37	seem	seem	VB
37681	1019	38	to	to	TO
37681	1019	39	be	be	VB
37681	1019	40	so	so	RB
37681	1019	41	.	.	.
37681	1020	1	Other	other	JJ
37681	1020	2	interesting	interesting	JJ
37681	1020	3	deceptions	deception	NNS
37681	1020	4	have	have	VBP
37681	1020	5	to	to	TO
37681	1020	6	do	do	VB
37681	1020	7	with	with	IN
37681	1020	8	producing	produce	VBG
37681	1020	9	lines	line	NNS
37681	1020	10	,	,	,
37681	1020	11	as	as	IN
37681	1020	12	in	in	IN
37681	1020	13	these	these	DT
37681	1020	14	figures	figure	NNS
37681	1020	15	,	,	,
37681	1020	16	where	where	WRB
37681	1020	17	it	-PRON-	PRP
37681	1020	18	is	be	VBZ
37681	1020	19	quite	quite	RB
37681	1020	20	difficult	difficult	JJ
37681	1020	21	in	in	IN
37681	1020	22	advance	advance	NN
37681	1020	23	to	to	TO
37681	1020	24	tell	tell	VB
37681	1020	25	whether	whether	IN
37681	1020	26	_	_	NNP
37681	1020	27	AB	AB	NNP
37681	1020	28	_	_	NNP
37681	1020	29	and	and	CC
37681	1020	30	_	_	NNP
37681	1020	31	CD	CD	NNP
37681	1020	32	_	_	NNP
37681	1020	33	are	be	VBP
37681	1020	34	in	in	IN
37681	1020	35	the	the	DT
37681	1020	36	same	same	JJ
37681	1020	37	line	line	NN
37681	1020	38	,	,	,
37681	1020	39	and	and	CC
37681	1020	40	similarly	similarly	RB
37681	1020	41	for	for	IN
37681	1020	42	_	_	NNP
37681	1020	43	WX	WX	NNP
37681	1020	44	_	_	NNP
37681	1020	45	and	and	CC
37681	1020	46	_	_	NNP
37681	1020	47	YZ	YZ	NNP
37681	1020	48	_	_	NNP
37681	1020	49	.	.	.
37681	1021	1	Equally	equally	RB
37681	1021	2	deceptive	deceptive	JJ
37681	1021	3	is	be	VBZ
37681	1021	4	this	this	DT
37681	1021	5	figure	figure	NN
37681	1021	6	,	,	,
37681	1021	7	in	in	IN
37681	1021	8	which	which	WDT
37681	1021	9	it	-PRON-	PRP
37681	1021	10	is	be	VBZ
37681	1021	11	difficult	difficult	JJ
37681	1021	12	to	to	TO
37681	1021	13	tell	tell	VB
37681	1021	14	which	which	WDT
37681	1021	15	line	line	NN
37681	1021	16	_	_	NNP
37681	1021	17	AB	AB	NNP
37681	1021	18	_	_	NNP
37681	1021	19	will	will	MD
37681	1021	20	lie	lie	VB
37681	1021	21	along	along	RB
37681	1021	22	when	when	WRB
37681	1021	23	produced	produce	VBN
37681	1021	24	.	.	.
37681	1022	1	In	in	IN
37681	1022	2	the	the	DT
37681	1022	3	next	next	JJ
37681	1022	4	figure	figure	NN
37681	1022	5	_	_	NNP
37681	1022	6	AB	AB	NNP
37681	1022	7	_	_	NNP
37681	1022	8	appears	appear	VBZ
37681	1022	9	to	to	TO
37681	1022	10	be	be	VB
37681	1022	11	curved	curve	VBN
37681	1022	12	when	when	WRB
37681	1022	13	in	in	IN
37681	1022	14	reality	reality	NN
37681	1022	15	it	-PRON-	PRP
37681	1022	16	is	be	VBZ
37681	1022	17	straight	straight	JJ
37681	1022	18	,	,	,
37681	1022	19	and	and	CC
37681	1022	20	_	_	NNP
37681	1022	21	CD	CD	NNP
37681	1022	22	_	_	NNP
37681	1022	23	appears	appear	VBZ
37681	1022	24	straight	straight	RB
37681	1022	25	when	when	WRB
37681	1022	26	in	in	IN
37681	1022	27	reality	reality	NN
37681	1022	28	it	-PRON-	PRP
37681	1022	29	is	be	VBZ
37681	1022	30	curved	curved	JJ
37681	1022	31	.	.	.
37681	1023	1	The	the	DT
37681	1023	2	first	first	JJ
37681	1023	3	of	of	IN
37681	1023	4	the	the	DT
37681	1023	5	following	follow	VBG
37681	1023	6	circles	circle	NNS
37681	1023	7	seems	seem	VBZ
37681	1023	8	to	to	TO
37681	1023	9	be	be	VB
37681	1023	10	slightly	slightly	RB
37681	1023	11	flattened	flatten	VBN
37681	1023	12	at	at	IN
37681	1023	13	the	the	DT
37681	1023	14	points	point	NNS
37681	1023	15	_	_	NNP
37681	1023	16	P	P	NNP
37681	1023	17	_	_	NNP
37681	1023	18	,	,	,
37681	1023	19	_	_	NNP
37681	1023	20	Q	Q	NNP
37681	1023	21	_	_	NNP
37681	1023	22	,	,	,
37681	1023	23	_	_	NNP
37681	1023	24	R	R	NNP
37681	1023	25	_	_	NNP
37681	1023	26	,	,	,
37681	1023	27	_	_	NNP
37681	1023	28	S	S	NNP
37681	1023	29	_	_	NNP
37681	1023	30	,	,	,
37681	1023	31	and	and	CC
37681	1023	32	in	in	IN
37681	1023	33	the	the	DT
37681	1023	34	second	second	JJ
37681	1023	35	one	one	NN
37681	1023	36	the	the	DT
37681	1023	37	distance	distance	NN
37681	1023	38	_	_	NNP
37681	1023	39	BD	BD	NNP
37681	1023	40	_	_	NNP
37681	1023	41	seems	seem	VBZ
37681	1023	42	greater	great	JJR
37681	1023	43	than	than	IN
37681	1023	44	the	the	DT
37681	1023	45	distance	distance	NN
37681	1023	46	_	_	NNP
37681	1023	47	AC	AC	NNP
37681	1023	48	_	_	NNP
37681	1023	49	.	.	.
37681	1024	1	There	there	EX
37681	1024	2	are	be	VBP
37681	1024	3	many	many	JJ
37681	1024	4	equally	equally	RB
37681	1024	5	deceptive	deceptive	JJ
37681	1024	6	figures	figure	NNS
37681	1024	7	,	,	,
37681	1024	8	and	and	CC
37681	1024	9	a	a	DT
37681	1024	10	few	few	JJ
37681	1024	11	of	of	IN
37681	1024	12	them	-PRON-	PRP
37681	1024	13	will	will	MD
37681	1024	14	convince	convince	VB
37681	1024	15	the	the	DT
37681	1024	16	beginner	beginner	NN
37681	1024	17	that	that	IN
37681	1024	18	the	the	DT
37681	1024	19	proofs	proof	NNS
37681	1024	20	are	be	VBP
37681	1024	21	necessary	necessary	JJ
37681	1024	22	features	feature	NNS
37681	1024	23	of	of	IN
37681	1024	24	geometry	geometry	NN
37681	1024	25	.	.	.
37681	1025	1	It	-PRON-	PRP
37681	1025	2	is	be	VBZ
37681	1025	3	interesting	interesting	JJ
37681	1025	4	,	,	,
37681	1025	5	in	in	IN
37681	1025	6	connection	connection	NN
37681	1025	7	with	with	IN
37681	1025	8	the	the	DT
37681	1025	9	tendency	tendency	NN
37681	1025	10	to	to	TO
37681	1025	11	feel	feel	VB
37681	1025	12	that	that	IN
37681	1025	13	a	a	DT
37681	1025	14	statement	statement	NN
37681	1025	15	is	be	VBZ
37681	1025	16	apparent	apparent	JJ
37681	1025	17	without	without	IN
37681	1025	18	proof	proof	NN
37681	1025	19	,	,	,
37681	1025	20	to	to	TO
37681	1025	21	recall	recall	VB
37681	1025	22	an	an	DT
37681	1025	23	anecdote	anecdote	NN
37681	1025	24	related	relate	VBN
37681	1025	25	by	by	IN
37681	1025	26	the	the	DT
37681	1025	27	French	french	JJ
37681	1025	28	mathematician	mathematician	NN
37681	1025	29	,	,	,
37681	1025	30	Biot	Biot	NNP
37681	1025	31	,	,	,
37681	1025	32	concerning	concern	VBG
37681	1025	33	the	the	DT
37681	1025	34	great	great	JJ
37681	1025	35	scientist	scientist	NN
37681	1025	36	,	,	,
37681	1025	37	Laplace	Laplace	NNP
37681	1025	38	:	:	:
37681	1025	39	Once	once	RB
37681	1025	40	Laplace	Laplace	NNP
37681	1025	41	,	,	,
37681	1025	42	having	have	VBG
37681	1025	43	been	be	VBN
37681	1025	44	asked	ask	VBN
37681	1025	45	about	about	IN
37681	1025	46	a	a	DT
37681	1025	47	certain	certain	JJ
37681	1025	48	point	point	NN
37681	1025	49	in	in	IN
37681	1025	50	his	-PRON-	PRP$
37681	1025	51	"	"	``
37681	1025	52	Celestial	Celestial	NNP
37681	1025	53	Mechanics	Mechanics	NNPS
37681	1025	54	,	,	,
37681	1025	55	"	"	''
37681	1025	56	spent	spend	VBD
37681	1025	57	nearly	nearly	RB
37681	1025	58	an	an	DT
37681	1025	59	hour	hour	NN
37681	1025	60	in	in	IN
37681	1025	61	trying	try	VBG
37681	1025	62	to	to	TO
37681	1025	63	recall	recall	VB
37681	1025	64	the	the	DT
37681	1025	65	chain	chain	NN
37681	1025	66	of	of	IN
37681	1025	67	reasoning	reasoning	NN
37681	1025	68	which	which	WDT
37681	1025	69	he	-PRON-	PRP
37681	1025	70	had	have	VBD
37681	1025	71	carelessly	carelessly	RB
37681	1025	72	concealed	conceal	VBN
37681	1025	73	by	by	IN
37681	1025	74	the	the	DT
37681	1025	75	words	word	NNS
37681	1025	76	"	"	``
37681	1025	77	It	-PRON-	PRP
37681	1025	78	is	be	VBZ
37681	1025	79	easy	easy	JJ
37681	1025	80	to	to	TO
37681	1025	81	see	see	VB
37681	1025	82	.	.	.
37681	1025	83	"	"	''
37681	1026	1	A	a	DT
37681	1026	2	third	third	JJ
37681	1026	3	difficulty	difficulty	NN
37681	1026	4	lies	lie	VBZ
37681	1026	5	in	in	IN
37681	1026	6	the	the	DT
37681	1026	7	necessity	necessity	NN
37681	1026	8	for	for	IN
37681	1026	9	putting	put	VBG
37681	1026	10	a	a	DT
37681	1026	11	considerable	considerable	JJ
37681	1026	12	number	number	NN
37681	1026	13	of	of	IN
37681	1026	14	definitions	definition	NNS
37681	1026	15	at	at	IN
37681	1026	16	the	the	DT
37681	1026	17	beginning	beginning	NN
37681	1026	18	of	of	IN
37681	1026	19	geometry	geometry	NN
37681	1026	20	,	,	,
37681	1026	21	in	in	IN
37681	1026	22	order	order	NN
37681	1026	23	to	to	TO
37681	1026	24	get	get	VB
37681	1026	25	a	a	DT
37681	1026	26	working	work	VBG
37681	1026	27	vocabulary	vocabulary	NN
37681	1026	28	.	.	.
37681	1027	1	Although	although	IN
37681	1027	2	practically	practically	RB
37681	1027	3	all	all	DT
37681	1027	4	writers	writer	NNS
37681	1027	5	scatter	scatter	VBP
37681	1027	6	the	the	DT
37681	1027	7	definitions	definition	NNS
37681	1027	8	as	as	RB
37681	1027	9	much	much	RB
37681	1027	10	as	as	IN
37681	1027	11	possible	possible	JJ
37681	1027	12	,	,	,
37681	1027	13	there	there	EX
37681	1027	14	must	must	MD
37681	1027	15	necessarily	necessarily	RB
37681	1027	16	be	be	VB
37681	1027	17	some	some	DT
37681	1027	18	vocabulary	vocabulary	NN
37681	1027	19	at	at	IN
37681	1027	20	the	the	DT
37681	1027	21	beginning	beginning	NN
37681	1027	22	.	.	.
37681	1028	1	In	in	IN
37681	1028	2	order	order	NN
37681	1028	3	to	to	TO
37681	1028	4	minimize	minimize	VB
37681	1028	5	the	the	DT
37681	1028	6	difficulty	difficulty	NN
37681	1028	7	of	of	IN
37681	1028	8	remembering	remember	VBG
37681	1028	9	so	so	RB
37681	1028	10	many	many	JJ
37681	1028	11	new	new	JJ
37681	1028	12	terms	term	NNS
37681	1028	13	,	,	,
37681	1028	14	it	-PRON-	PRP
37681	1028	15	is	be	VBZ
37681	1028	16	helpful	helpful	JJ
37681	1028	17	to	to	TO
37681	1028	18	mingle	mingle	VB
37681	1028	19	with	with	IN
37681	1028	20	them	-PRON-	PRP
37681	1028	21	a	a	DT
37681	1028	22	considerable	considerable	JJ
37681	1028	23	number	number	NN
37681	1028	24	of	of	IN
37681	1028	25	exercises	exercise	NNS
37681	1028	26	in	in	IN
37681	1028	27	which	which	WDT
37681	1028	28	these	these	DT
37681	1028	29	terms	term	NNS
37681	1028	30	are	be	VBP
37681	1028	31	employed	employ	VBN
37681	1028	32	,	,	,
37681	1028	33	so	so	IN
37681	1028	34	that	that	IN
37681	1028	35	they	-PRON-	PRP
37681	1028	36	may	may	MD
37681	1028	37	become	become	VB
37681	1028	38	fixed	fixed	JJ
37681	1028	39	in	in	IN
37681	1028	40	mind	mind	NN
37681	1028	41	through	through	IN
37681	1028	42	actual	actual	JJ
37681	1028	43	use	use	NN
37681	1028	44	.	.	.
37681	1029	1	Thus	thus	RB
37681	1029	2	it	-PRON-	PRP
37681	1029	3	is	be	VBZ
37681	1029	4	of	of	IN
37681	1029	5	value	value	NN
37681	1029	6	to	to	TO
37681	1029	7	have	have	VB
37681	1029	8	a	a	DT
37681	1029	9	class	class	NN
37681	1029	10	find	find	VB
37681	1029	11	the	the	DT
37681	1029	12	complements	complement	NNS
37681	1029	13	of	of	IN
37681	1029	14	27	27	CD
37681	1029	15	°	°	NNS
37681	1029	16	,	,	,
37681	1029	17	32	32	CD
37681	1029	18	°	°	,
37681	1029	19	20	20	CD
37681	1029	20	'	'	CD
37681	1029	21	,	,	,
37681	1029	22	41	41	CD
37681	1029	23	°	°	,
37681	1029	24	32	32	CD
37681	1029	25	'	'	CD
37681	1029	26	48	48	CD
37681	1029	27	"	"	''
37681	1029	28	,	,	,
37681	1029	29	26.75	26.75	CD
37681	1029	30	°	°	NNS
37681	1029	31	,	,	,
37681	1029	32	33	33	CD
37681	1029	33	1/3	1/3	CD
37681	1029	34	°	°	NNS
37681	1029	35	,	,	,
37681	1029	36	and	and	CC
37681	1029	37	0	0	CD
37681	1029	38	°	°	NNS
37681	1029	39	.	.	.
37681	1030	1	It	-PRON-	PRP
37681	1030	2	is	be	VBZ
37681	1030	3	true	true	JJ
37681	1030	4	that	that	IN
37681	1030	5	into	into	IN
37681	1030	6	the	the	DT
37681	1030	7	pure	pure	JJ
37681	1030	8	geometry	geometry	NN
37681	1030	9	of	of	IN
37681	1030	10	Euclid	Euclid	NNP
37681	1030	11	the	the	DT
37681	1030	12	measuring	measuring	NN
37681	1030	13	of	of	IN
37681	1030	14	angles	angle	NNS
37681	1030	15	in	in	IN
37681	1030	16	degrees	degree	NNS
37681	1030	17	does	do	VBZ
37681	1030	18	not	not	RB
37681	1030	19	enter	enter	VB
37681	1030	20	,	,	,
37681	1030	21	but	but	CC
37681	1030	22	it	-PRON-	PRP
37681	1030	23	has	have	VBZ
37681	1030	24	place	place	NN
37681	1030	25	in	in	IN
37681	1030	26	the	the	DT
37681	1030	27	practical	practical	JJ
37681	1030	28	applications	application	NNS
37681	1030	29	,	,	,
37681	1030	30	and	and	CC
37681	1030	31	it	-PRON-	PRP
37681	1030	32	serves	serve	VBZ
37681	1030	33	at	at	IN
37681	1030	34	this	this	DT
37681	1030	35	juncture	juncture	NN
37681	1030	36	to	to	TO
37681	1030	37	fix	fix	VB
37681	1030	38	the	the	DT
37681	1030	39	meaning	meaning	NN
37681	1030	40	of	of	IN
37681	1030	41	a	a	DT
37681	1030	42	new	new	JJ
37681	1030	43	term	term	NN
37681	1030	44	like	like	IN
37681	1030	45	"	"	``
37681	1030	46	complement	complement	NN
37681	1030	47	.	.	.
37681	1030	48	"	"	''
37681	1031	1	The	the	DT
37681	1031	2	teacher	teacher	NN
37681	1031	3	who	who	WP
37681	1031	4	thus	thus	RB
37681	1031	5	anticipates	anticipate	VBZ
37681	1031	6	the	the	DT
37681	1031	7	question	question	NN
37681	1031	8	as	as	IN
37681	1031	9	to	to	IN
37681	1031	10	the	the	DT
37681	1031	11	reason	reason	NN
37681	1031	12	for	for	IN
37681	1031	13	studying	study	VBG
37681	1031	14	geometry	geometry	NN
37681	1031	15	,	,	,
37681	1031	16	the	the	DT
37681	1031	17	mental	mental	JJ
37681	1031	18	opposition	opposition	NN
37681	1031	19	to	to	IN
37681	1031	20	proving	proving	NN
37681	1031	21	statements	statement	NNS
37681	1031	22	,	,	,
37681	1031	23	and	and	CC
37681	1031	24	the	the	DT
37681	1031	25	forgetfulness	forgetfulness	NN
37681	1031	26	of	of	IN
37681	1031	27	the	the	DT
37681	1031	28	meaning	meaning	NN
37681	1031	29	of	of	IN
37681	1031	30	common	common	JJ
37681	1031	31	terms	term	NNS
37681	1031	32	will	will	MD
37681	1031	33	find	find	VB
37681	1031	34	that	that	IN
37681	1031	35	much	much	JJ
37681	1031	36	of	of	IN
37681	1031	37	the	the	DT
37681	1031	38	initial	initial	JJ
37681	1031	39	difficulty	difficulty	NN
37681	1031	40	is	be	VBZ
37681	1031	41	avoided	avoid	VBN
37681	1031	42	.	.	.
37681	1032	1	If	if	IN
37681	1032	2	,	,	,
37681	1032	3	now	now	RB
37681	1032	4	,	,	,
37681	1032	5	great	great	JJ
37681	1032	6	care	care	NN
37681	1032	7	is	be	VBZ
37681	1032	8	given	give	VBN
37681	1032	9	to	to	IN
37681	1032	10	the	the	DT
37681	1032	11	first	first	JJ
37681	1032	12	half	half	JJ
37681	1032	13	dozen	dozen	NN
37681	1032	14	propositions	proposition	NNS
37681	1032	15	,	,	,
37681	1032	16	the	the	DT
37681	1032	17	pupil	pupil	NN
37681	1032	18	will	will	MD
37681	1032	19	be	be	VB
37681	1032	20	well	well	JJ
37681	1032	21	on	on	IN
37681	1032	22	his	-PRON-	PRP$
37681	1032	23	way	way	NN
37681	1032	24	in	in	IN
37681	1032	25	geometry	geometry	NN
37681	1032	26	.	.	.
37681	1033	1	As	as	IN
37681	1033	2	to	to	IN
37681	1033	3	these	these	DT
37681	1033	4	propositions	proposition	NNS
37681	1033	5	,	,	,
37681	1033	6	two	two	CD
37681	1033	7	plans	plan	NNS
37681	1033	8	of	of	IN
37681	1033	9	selection	selection	NN
37681	1033	10	are	be	VBP
37681	1033	11	employed	employ	VBN
37681	1033	12	.	.	.
37681	1034	1	The	the	DT
37681	1034	2	first	first	JJ
37681	1034	3	takes	take	VBZ
37681	1034	4	a	a	DT
37681	1034	5	few	few	JJ
37681	1034	6	preliminary	preliminary	JJ
37681	1034	7	propositions	proposition	NNS
37681	1034	8	,	,	,
37681	1034	9	easily	easily	RB
37681	1034	10	demonstrated	demonstrate	VBD
37681	1034	11	,	,	,
37681	1034	12	and	and	CC
37681	1034	13	seeks	seek	VBZ
37681	1034	14	thus	thus	RB
37681	1034	15	to	to	TO
37681	1034	16	introduce	introduce	VB
37681	1034	17	the	the	DT
37681	1034	18	pupil	pupil	NN
37681	1034	19	to	to	IN
37681	1034	20	the	the	DT
37681	1034	21	nature	nature	NN
37681	1034	22	of	of	IN
37681	1034	23	a	a	DT
37681	1034	24	proof	proof	NN
37681	1034	25	.	.	.
37681	1035	1	This	this	DT
37681	1035	2	has	have	VBZ
37681	1035	3	the	the	DT
37681	1035	4	advantage	advantage	NN
37681	1035	5	of	of	IN
37681	1035	6	inspiring	inspire	VBG
37681	1035	7	confidence	confidence	NN
37681	1035	8	and	and	CC
37681	1035	9	the	the	DT
37681	1035	10	disadvantage	disadvantage	NN
37681	1035	11	of	of	IN
37681	1035	12	appearing	appear	VBG
37681	1035	13	to	to	TO
37681	1035	14	prove	prove	VB
37681	1035	15	the	the	DT
37681	1035	16	obvious	obvious	JJ
37681	1035	17	.	.	.
37681	1036	1	The	the	DT
37681	1036	2	second	second	JJ
37681	1036	3	plan	plan	NN
37681	1036	4	discards	discard	VBZ
37681	1036	5	all	all	DT
37681	1036	6	such	such	JJ
37681	1036	7	apparently	apparently	RB
37681	1036	8	obvious	obvious	JJ
37681	1036	9	propositions	proposition	NNS
37681	1036	10	as	as	IN
37681	1036	11	those	those	DT
37681	1036	12	about	about	IN
37681	1036	13	the	the	DT
37681	1036	14	equality	equality	NN
37681	1036	15	of	of	IN
37681	1036	16	right	right	JJ
37681	1036	17	angles	angle	NNS
37681	1036	18	,	,	,
37681	1036	19	and	and	CC
37681	1036	20	the	the	DT
37681	1036	21	sum	sum	NN
37681	1036	22	of	of	IN
37681	1036	23	two	two	CD
37681	1036	24	adjacent	adjacent	JJ
37681	1036	25	angles	angle	NNS
37681	1036	26	formed	form	VBN
37681	1036	27	by	by	IN
37681	1036	28	one	one	CD
37681	1036	29	line	line	NN
37681	1036	30	meeting	meet	VBG
37681	1036	31	another	another	DT
37681	1036	32	,	,	,
37681	1036	33	and	and	CC
37681	1036	34	begins	begin	VBZ
37681	1036	35	at	at	IN
37681	1036	36	once	once	RB
37681	1036	37	on	on	IN
37681	1036	38	things	thing	NNS
37681	1036	39	that	that	WDT
37681	1036	40	seem	seem	VBP
37681	1036	41	to	to	IN
37681	1036	42	the	the	DT
37681	1036	43	pupil	pupil	NN
37681	1036	44	as	as	IN
37681	1036	45	worth	worth	JJ
37681	1036	46	the	the	DT
37681	1036	47	proving	proving	NN
37681	1036	48	.	.	.
37681	1037	1	In	in	IN
37681	1037	2	this	this	DT
37681	1037	3	latter	latter	JJ
37681	1037	4	plan	plan	NN
37681	1037	5	the	the	DT
37681	1037	6	introduction	introduction	NN
37681	1037	7	is	be	VBZ
37681	1037	8	usually	usually	RB
37681	1037	9	made	make	VBN
37681	1037	10	with	with	IN
37681	1037	11	the	the	DT
37681	1037	12	proposition	proposition	NN
37681	1037	13	concerning	concern	VBG
37681	1037	14	vertical	vertical	JJ
37681	1037	15	angles	angle	NNS
37681	1037	16	,	,	,
37681	1037	17	and	and	CC
37681	1037	18	the	the	DT
37681	1037	19	two	two	CD
37681	1037	20	simplest	simple	JJS
37681	1037	21	cases	case	NNS
37681	1037	22	of	of	IN
37681	1037	23	congruent	congruent	JJ
37681	1037	24	triangles	triangle	NNS
37681	1037	25	.	.	.
37681	1038	1	Whichever	whichever	WDT
37681	1038	2	plan	plan	NN
37681	1038	3	of	of	IN
37681	1038	4	selection	selection	NN
37681	1038	5	is	be	VBZ
37681	1038	6	taken	take	VBN
37681	1038	7	,	,	,
37681	1038	8	it	-PRON-	PRP
37681	1038	9	is	be	VBZ
37681	1038	10	important	important	JJ
37681	1038	11	to	to	TO
37681	1038	12	introduce	introduce	VB
37681	1038	13	a	a	DT
37681	1038	14	considerable	considerable	JJ
37681	1038	15	number	number	NN
37681	1038	16	of	of	IN
37681	1038	17	one	one	CD
37681	1038	18	-	-	HYPH
37681	1038	19	step	step	NN
37681	1038	20	exercises	exercise	NNS
37681	1038	21	immediately	immediately	RB
37681	1038	22	,	,	,
37681	1038	23	that	that	RB
37681	1038	24	is	is	RB
37681	1038	25	,	,	,
37681	1038	26	exercises	exercise	VBZ
37681	1038	27	that	that	WDT
37681	1038	28	require	require	VBP
37681	1038	29	only	only	RB
37681	1038	30	one	one	CD
37681	1038	31	significant	significant	JJ
37681	1038	32	step	step	NN
37681	1038	33	in	in	IN
37681	1038	34	the	the	DT
37681	1038	35	proof	proof	NN
37681	1038	36	.	.	.
37681	1039	1	In	in	IN
37681	1039	2	this	this	DT
37681	1039	3	way	way	NN
37681	1039	4	the	the	DT
37681	1039	5	pupil	pupil	NN
37681	1039	6	acquires	acquire	VBZ
37681	1039	7	confidence	confidence	NN
37681	1039	8	in	in	IN
37681	1039	9	his	-PRON-	PRP$
37681	1039	10	own	own	JJ
37681	1039	11	powers	power	NNS
37681	1039	12	,	,	,
37681	1039	13	he	-PRON-	PRP
37681	1039	14	finds	find	VBZ
37681	1039	15	that	that	IN
37681	1039	16	geometry	geometry	NN
37681	1039	17	is	be	VBZ
37681	1039	18	not	not	RB
37681	1039	19	mere	mere	JJ
37681	1039	20	memorizing	memorizing	NN
37681	1039	21	,	,	,
37681	1039	22	and	and	CC
37681	1039	23	he	-PRON-	PRP
37681	1039	24	sees	see	VBZ
37681	1039	25	that	that	IN
37681	1039	26	each	each	DT
37681	1039	27	proposition	proposition	NN
37681	1039	28	makes	make	VBZ
37681	1039	29	him	-PRON-	PRP
37681	1039	30	the	the	DT
37681	1039	31	master	master	NN
37681	1039	32	of	of	IN
37681	1039	33	a	a	DT
37681	1039	34	large	large	JJ
37681	1039	35	field	field	NN
37681	1039	36	.	.	.
37681	1040	1	To	to	TO
37681	1040	2	delay	delay	VB
37681	1040	3	the	the	DT
37681	1040	4	exercises	exercise	NNS
37681	1040	5	to	to	IN
37681	1040	6	the	the	DT
37681	1040	7	end	end	NN
37681	1040	8	of	of	IN
37681	1040	9	each	each	DT
37681	1040	10	book	book	NN
37681	1040	11	,	,	,
37681	1040	12	or	or	CC
37681	1040	13	even	even	RB
37681	1040	14	to	to	TO
37681	1040	15	delay	delay	VB
37681	1040	16	them	-PRON-	PRP
37681	1040	17	for	for	IN
37681	1040	18	several	several	JJ
37681	1040	19	lessons	lesson	NNS
37681	1040	20	,	,	,
37681	1040	21	is	be	VBZ
37681	1040	22	to	to	TO
37681	1040	23	sow	sow	VB
37681	1040	24	seeds	seed	NNS
37681	1040	25	that	that	WDT
37681	1040	26	will	will	MD
37681	1040	27	result	result	VB
37681	1040	28	in	in	IN
37681	1040	29	the	the	DT
37681	1040	30	attempt	attempt	NN
37681	1040	31	to	to	TO
37681	1040	32	master	master	VB
37681	1040	33	geometry	geometry	NN
37681	1040	34	by	by	IN
37681	1040	35	the	the	DT
37681	1040	36	sheer	sheer	JJ
37681	1040	37	process	process	NN
37681	1040	38	of	of	IN
37681	1040	39	memorizing	memorize	VBG
37681	1040	40	.	.	.
37681	1041	1	As	as	IN
37681	1041	2	to	to	IN
37681	1041	3	the	the	DT
37681	1041	4	nature	nature	NN
37681	1041	5	of	of	IN
37681	1041	6	these	these	DT
37681	1041	7	exercises	exercise	NNS
37681	1041	8	,	,	,
37681	1041	9	however	however	RB
37681	1041	10	,	,	,
37681	1041	11	the	the	DT
37681	1041	12	mistake	mistake	NN
37681	1041	13	must	must	MD
37681	1041	14	not	not	RB
37681	1041	15	be	be	VB
37681	1041	16	made	make	VBN
37681	1041	17	of	of	IN
37681	1041	18	feeling	feeling	NN
37681	1041	19	that	that	IN
37681	1041	20	only	only	RB
37681	1041	21	those	those	DT
37681	1041	22	have	have	VBP
37681	1041	23	any	any	DT
37681	1041	24	value	value	NN
37681	1041	25	that	that	WDT
37681	1041	26	relate	relate	VBP
37681	1041	27	to	to	IN
37681	1041	28	football	football	NN
37681	1041	29	or	or	CC
37681	1041	30	the	the	DT
37681	1041	31	laying	lay	VBG
37681	1041	32	out	out	IN
37681	1041	33	of	of	IN
37681	1041	34	a	a	DT
37681	1041	35	tennis	tennis	NN
37681	1041	36	court	court	NN
37681	1041	37	.	.	.
37681	1042	1	Such	such	JJ
37681	1042	2	exercises	exercise	NNS
37681	1042	3	are	be	VBP
37681	1042	4	valuable	valuable	JJ
37681	1042	5	,	,	,
37681	1042	6	but	but	CC
37681	1042	7	such	such	JJ
37681	1042	8	exercises	exercise	NNS
37681	1042	9	alone	alone	RB
37681	1042	10	are	be	VBP
37681	1042	11	one	one	CD
37681	1042	12	-	-	HYPH
37681	1042	13	sided	sided	JJ
37681	1042	14	.	.	.
37681	1043	1	Moreover	moreover	RB
37681	1043	2	,	,	,
37681	1043	3	any	any	DT
37681	1043	4	one	one	NN
37681	1043	5	who	who	WP
37681	1043	6	examines	examine	VBZ
37681	1043	7	the	the	DT
37681	1043	8	hundreds	hundred	NNS
37681	1043	9	of	of	IN
37681	1043	10	suggested	suggest	VBN
37681	1043	11	exercises	exercise	NNS
37681	1043	12	that	that	WDT
37681	1043	13	are	be	VBP
37681	1043	14	constantly	constantly	RB
37681	1043	15	appearing	appear	VBG
37681	1043	16	in	in	IN
37681	1043	17	various	various	JJ
37681	1043	18	journals	journal	NNS
37681	1043	19	,	,	,
37681	1043	20	or	or	CC
37681	1043	21	who	who	WP
37681	1043	22	,	,	,
37681	1043	23	in	in	IN
37681	1043	24	the	the	DT
37681	1043	25	preparation	preparation	NN
37681	1043	26	of	of	IN
37681	1043	27	teachers	teacher	NNS
37681	1043	28	,	,	,
37681	1043	29	looks	look	VBZ
37681	1043	30	through	through	IN
37681	1043	31	the	the	DT
37681	1043	32	thousands	thousand	NNS
37681	1043	33	of	of	IN
37681	1043	34	exercises	exercise	NNS
37681	1043	35	that	that	WDT
37681	1043	36	come	come	VBP
37681	1043	37	to	to	IN
37681	1043	38	him	-PRON-	PRP
37681	1043	39	in	in	IN
37681	1043	40	the	the	DT
37681	1043	41	papers	paper	NNS
37681	1043	42	of	of	IN
37681	1043	43	his	-PRON-	PRP$
37681	1043	44	students	student	NNS
37681	1043	45	,	,	,
37681	1043	46	comes	come	VBZ
37681	1043	47	very	very	RB
37681	1043	48	soon	soon	RB
37681	1043	49	to	to	TO
37681	1043	50	see	see	VB
37681	1043	51	how	how	WRB
37681	1043	52	hollow	hollow	JJ
37681	1043	53	is	be	VBZ
37681	1043	54	the	the	DT
37681	1043	55	pretense	pretense	NN
37681	1043	56	of	of	IN
37681	1043	57	most	most	JJS
37681	1043	58	of	of	IN
37681	1043	59	them	-PRON-	PRP
37681	1043	60	.	.	.
37681	1044	1	As	as	IN
37681	1044	2	has	have	VBZ
37681	1044	3	already	already	RB
37681	1044	4	been	be	VBN
37681	1044	5	said	say	VBN
37681	1044	6	,	,	,
37681	1044	7	there	there	EX
37681	1044	8	are	be	VBP
37681	1044	9	relatively	relatively	RB
37681	1044	10	few	few	JJ
37681	1044	11	propositions	proposition	NNS
37681	1044	12	in	in	IN
37681	1044	13	geometry	geometry	NN
37681	1044	14	that	that	WDT
37681	1044	15	have	have	VBP
37681	1044	16	any	any	DT
37681	1044	17	practical	practical	JJ
37681	1044	18	applications	application	NNS
37681	1044	19	,	,	,
37681	1044	20	applications	application	NNS
37681	1044	21	that	that	WDT
37681	1044	22	are	be	VBP
37681	1044	23	even	even	RB
37681	1044	24	honest	honest	JJ
37681	1044	25	in	in	IN
37681	1044	26	their	-PRON-	PRP$
37681	1044	27	pretense	pretense	NN
37681	1044	28	.	.	.
37681	1045	1	The	the	DT
37681	1045	2	principle	principle	NN
37681	1045	3	that	that	IN
37681	1045	4	the	the	DT
37681	1045	5	writer	writer	NN
37681	1045	6	has	have	VBZ
37681	1045	7	so	so	RB
37681	1045	8	often	often	RB
37681	1045	9	laid	lay	VBN
37681	1045	10	down	down	RP
37681	1045	11	in	in	IN
37681	1045	12	other	other	JJ
37681	1045	13	works	work	NNS
37681	1045	14	,	,	,
37681	1045	15	that	that	IN
37681	1045	16	whatever	whatever	WDT
37681	1045	17	pretends	pretend	NNS
37681	1045	18	to	to	TO
37681	1045	19	be	be	VB
37681	1045	20	practical	practical	JJ
37681	1045	21	should	should	MD
37681	1045	22	really	really	RB
37681	1045	23	be	be	VB
37681	1045	24	so	so	RB
37681	1045	25	,	,	,
37681	1045	26	applies	apply	VBZ
37681	1045	27	with	with	IN
37681	1045	28	much	much	JJ
37681	1045	29	force	force	NN
37681	1045	30	to	to	IN
37681	1045	31	these	these	DT
37681	1045	32	exercises	exercise	NNS
37681	1045	33	.	.	.
37681	1046	1	When	when	WRB
37681	1046	2	we	-PRON-	PRP
37681	1046	3	can	can	MD
37681	1046	4	find	find	VB
37681	1046	5	the	the	DT
37681	1046	6	genuine	genuine	JJ
37681	1046	7	application	application	NN
37681	1046	8	,	,	,
37681	1046	9	if	if	IN
37681	1046	10	it	-PRON-	PRP
37681	1046	11	is	be	VBZ
37681	1046	12	within	within	IN
37681	1046	13	reasonable	reasonable	JJ
37681	1046	14	grasp	grasp	NN
37681	1046	15	of	of	IN
37681	1046	16	the	the	DT
37681	1046	17	pupil	pupil	NN
37681	1046	18	,	,	,
37681	1046	19	by	by	IN
37681	1046	20	all	all	DT
37681	1046	21	means	mean	NNS
37681	1046	22	let	let	VB
37681	1046	23	us	-PRON-	PRP
37681	1046	24	use	use	VB
37681	1046	25	it	-PRON-	PRP
37681	1046	26	.	.	.
37681	1047	1	But	but	CC
37681	1047	2	to	to	TO
37681	1047	3	put	put	VB
37681	1047	4	before	before	IN
37681	1047	5	a	a	DT
37681	1047	6	class	class	NN
37681	1047	7	of	of	IN
37681	1047	8	girls	girl	NNS
37681	1047	9	some	some	DT
37681	1047	10	technicality	technicality	NN
37681	1047	11	of	of	IN
37681	1047	12	the	the	DT
37681	1047	13	steam	steam	NN
37681	1047	14	engine	engine	NN
37681	1047	15	that	that	WDT
37681	1047	16	only	only	RB
37681	1047	17	a	a	DT
37681	1047	18	skilled	skilled	JJ
37681	1047	19	mechanic	mechanic	NN
37681	1047	20	would	would	MD
37681	1047	21	be	be	VB
37681	1047	22	expected	expect	VBN
37681	1047	23	to	to	TO
37681	1047	24	know	know	VB
37681	1047	25	is	be	VBZ
37681	1047	26	not	not	RB
37681	1047	27	education,--it	education,--it	NNP
37681	1047	28	is	be	VBZ
37681	1047	29	mere	mere	NNP
37681	1047	30	sham	sham	NNP
37681	1047	31	.	.	.
37681	1048	1	There	there	EX
37681	1048	2	is	be	VBZ
37681	1048	3	a	a	DT
37681	1048	4	noble	noble	JJ
37681	1048	5	dignity	dignity	NN
37681	1048	6	to	to	TO
37681	1048	7	geometry	geometry	VB
37681	1048	8	,	,	,
37681	1048	9	a	a	DT
37681	1048	10	dignity	dignity	NN
37681	1048	11	that	that	IN
37681	1048	12	a	a	DT
37681	1048	13	large	large	JJ
37681	1048	14	majority	majority	NN
37681	1048	15	of	of	IN
37681	1048	16	any	any	DT
37681	1048	17	class	class	NN
37681	1048	18	comes	come	VBZ
37681	1048	19	to	to	TO
37681	1048	20	appreciate	appreciate	VB
37681	1048	21	when	when	WRB
37681	1048	22	guided	guide	VBN
37681	1048	23	by	by	IN
37681	1048	24	an	an	DT
37681	1048	25	earnest	earnest	JJ
37681	1048	26	teacher	teacher	NN
37681	1048	27	;	;	:
37681	1048	28	but	but	CC
37681	1048	29	the	the	DT
37681	1048	30	best	good	JJS
37681	1048	31	way	way	NN
37681	1048	32	to	to	TO
37681	1048	33	destroy	destroy	VB
37681	1048	34	this	this	DT
37681	1048	35	dignity	dignity	NN
37681	1048	36	,	,	,
37681	1048	37	to	to	TO
37681	1048	38	take	take	VB
37681	1048	39	away	away	RB
37681	1048	40	the	the	DT
37681	1048	41	appreciation	appreciation	NN
37681	1048	42	of	of	IN
37681	1048	43	pure	pure	JJ
37681	1048	44	mathematics	mathematic	NNS
37681	1048	45	,	,	,
37681	1048	46	and	and	CC
37681	1048	47	to	to	TO
37681	1048	48	furnish	furnish	VB
37681	1048	49	weaker	weak	JJR
37681	1048	50	candidates	candidate	NNS
37681	1048	51	than	than	IN
37681	1048	52	now	now	RB
37681	1048	53	for	for	IN
37681	1048	54	advance	advance	NN
37681	1048	55	in	in	IN
37681	1048	56	this	this	DT
37681	1048	57	field	field	NN
37681	1048	58	is	be	VBZ
37681	1048	59	to	to	TO
37681	1048	60	deceive	deceive	VB
37681	1048	61	our	-PRON-	PRP$
37681	1048	62	pupils	pupil	NNS
37681	1048	63	and	and	CC
37681	1048	64	ourselves	-PRON-	PRP
37681	1048	65	into	into	IN
37681	1048	66	believing	believe	VBG
37681	1048	67	that	that	IN
37681	1048	68	the	the	DT
37681	1048	69	ultimate	ultimate	JJ
37681	1048	70	purpose	purpose	NN
37681	1048	71	of	of	IN
37681	1048	72	mathematics	mathematic	NNS
37681	1048	73	is	be	VBZ
37681	1048	74	to	to	TO
37681	1048	75	measure	measure	VB
37681	1048	76	things	thing	NNS
37681	1048	77	in	in	IN
37681	1048	78	a	a	DT
37681	1048	79	way	way	NN
37681	1048	80	in	in	IN
37681	1048	81	which	which	WDT
37681	1048	82	no	no	DT
37681	1048	83	one	one	NN
37681	1048	84	else	else	RB
37681	1048	85	measures	measure	VBZ
37681	1048	86	them	-PRON-	PRP
37681	1048	87	or	or	CC
37681	1048	88	has	have	VBZ
37681	1048	89	ever	ever	RB
37681	1048	90	measured	measure	VBN
37681	1048	91	them	-PRON-	PRP
37681	1048	92	.	.	.
37681	1049	1	In	in	IN
37681	1049	2	the	the	DT
37681	1049	3	proof	proof	NN
37681	1049	4	of	of	IN
37681	1049	5	the	the	DT
37681	1049	6	early	early	JJ
37681	1049	7	propositions	proposition	NNS
37681	1049	8	of	of	IN
37681	1049	9	plane	plane	NN
37681	1049	10	geometry	geometry	NN
37681	1049	11	,	,	,
37681	1049	12	and	and	CC
37681	1049	13	again	again	RB
37681	1049	14	at	at	IN
37681	1049	15	the	the	DT
37681	1049	16	beginning	beginning	NN
37681	1049	17	of	of	IN
37681	1049	18	solid	solid	JJ
37681	1049	19	geometry	geometry	NN
37681	1049	20	,	,	,
37681	1049	21	there	there	EX
37681	1049	22	is	be	VBZ
37681	1049	23	a	a	DT
37681	1049	24	little	little	JJ
37681	1049	25	advantage	advantage	NN
37681	1049	26	in	in	IN
37681	1049	27	using	use	VBG
37681	1049	28	colored	colored	JJ
37681	1049	29	crayon	crayon	NN
37681	1049	30	to	to	TO
37681	1049	31	bring	bring	VB
37681	1049	32	out	out	RP
37681	1049	33	more	more	RBR
37681	1049	34	distinctly	distinctly	RB
37681	1049	35	the	the	DT
37681	1049	36	equal	equal	JJ
37681	1049	37	parts	part	NNS
37681	1049	38	of	of	IN
37681	1049	39	two	two	CD
37681	1049	40	figures	figure	NNS
37681	1049	41	,	,	,
37681	1049	42	or	or	CC
37681	1049	43	the	the	DT
37681	1049	44	lines	line	NNS
37681	1049	45	outside	outside	IN
37681	1049	46	the	the	DT
37681	1049	47	plane	plane	NN
37681	1049	48	,	,	,
37681	1049	49	or	or	CC
37681	1049	50	to	to	TO
37681	1049	51	differentiate	differentiate	VB
37681	1049	52	one	one	CD
37681	1049	53	plane	plane	NN
37681	1049	54	from	from	IN
37681	1049	55	another	another	DT
37681	1049	56	.	.	.
37681	1050	1	This	this	DT
37681	1050	2	device	device	NN
37681	1050	3	,	,	,
37681	1050	4	however	however	RB
37681	1050	5	,	,	,
37681	1050	6	like	like	IN
37681	1050	7	that	that	DT
37681	1050	8	of	of	IN
37681	1050	9	models	model	NNS
37681	1050	10	in	in	IN
37681	1050	11	solid	solid	JJ
37681	1050	12	geometry	geometry	NN
37681	1050	13	,	,	,
37681	1050	14	can	can	MD
37681	1050	15	easily	easily	RB
37681	1050	16	be	be	VB
37681	1050	17	abused	abuse	VBN
37681	1050	18	,	,	,
37681	1050	19	and	and	CC
37681	1050	20	hence	hence	RB
37681	1050	21	should	should	MD
37681	1050	22	be	be	VB
37681	1050	23	used	use	VBN
37681	1050	24	sparingly	sparingly	RB
37681	1050	25	,	,	,
37681	1050	26	and	and	CC
37681	1050	27	only	only	RB
37681	1050	28	until	until	IN
37681	1050	29	the	the	DT
37681	1050	30	purpose	purpose	NN
37681	1050	31	is	be	VBZ
37681	1050	32	accomplished	accomplish	VBN
37681	1050	33	.	.	.
37681	1051	1	The	the	DT
37681	1051	2	student	student	NN
37681	1051	3	of	of	IN
37681	1051	4	mathematics	mathematic	NNS
37681	1051	5	must	must	MD
37681	1051	6	learn	learn	VB
37681	1051	7	to	to	TO
37681	1051	8	grasp	grasp	VB
37681	1051	9	the	the	DT
37681	1051	10	meaning	meaning	NN
37681	1051	11	of	of	IN
37681	1051	12	a	a	DT
37681	1051	13	figure	figure	NN
37681	1051	14	drawn	draw	VBN
37681	1051	15	in	in	IN
37681	1051	16	black	black	NN
37681	1051	17	on	on	IN
37681	1051	18	white	white	JJ
37681	1051	19	paper	paper	NN
37681	1051	20	,	,	,
37681	1051	21	or	or	CC
37681	1051	22	,	,	,
37681	1051	23	more	more	RBR
37681	1051	24	rarely	rarely	RB
37681	1051	25	,	,	,
37681	1051	26	in	in	IN
37681	1051	27	white	white	NN
37681	1051	28	on	on	IN
37681	1051	29	a	a	DT
37681	1051	30	blackboard	blackboard	NN
37681	1051	31	,	,	,
37681	1051	32	and	and	CC
37681	1051	33	the	the	DT
37681	1051	34	sooner	soon	RBR
37681	1051	35	he	-PRON-	PRP
37681	1051	36	is	be	VBZ
37681	1051	37	able	able	JJ
37681	1051	38	to	to	TO
37681	1051	39	do	do	VB
37681	1051	40	this	this	DT
37681	1051	41	the	the	DT
37681	1051	42	better	well	JJR
37681	1051	43	for	for	IN
37681	1051	44	him	-PRON-	PRP
37681	1051	45	.	.	.
37681	1052	1	The	the	DT
37681	1052	2	same	same	JJ
37681	1052	3	thing	thing	NN
37681	1052	4	may	may	MD
37681	1052	5	be	be	VB
37681	1052	6	said	say	VBN
37681	1052	7	of	of	IN
37681	1052	8	the	the	DT
37681	1052	9	constructing	constructing	NN
37681	1052	10	of	of	IN
37681	1052	11	models	model	NNS
37681	1052	12	for	for	IN
37681	1052	13	any	any	DT
37681	1052	14	considerable	considerable	JJ
37681	1052	15	number	number	NN
37681	1052	16	of	of	IN
37681	1052	17	figures	figure	NNS
37681	1052	18	in	in	IN
37681	1052	19	solid	solid	JJ
37681	1052	20	geometry	geometry	NN
37681	1052	21	;	;	:
37681	1052	22	enough	enough	JJ
37681	1052	23	work	work	NN
37681	1052	24	of	of	IN
37681	1052	25	this	this	DT
37681	1052	26	kind	kind	NN
37681	1052	27	to	to	TO
37681	1052	28	enable	enable	VB
37681	1052	29	a	a	DT
37681	1052	30	pupil	pupil	NN
37681	1052	31	clearly	clearly	RB
37681	1052	32	to	to	TO
37681	1052	33	visualize	visualize	VB
37681	1052	34	the	the	DT
37681	1052	35	solids	solid	NNS
37681	1052	36	is	be	VBZ
37681	1052	37	valuable	valuable	JJ
37681	1052	38	,	,	,
37681	1052	39	but	but	CC
37681	1052	40	thereafter	thereafter	RB
37681	1052	41	the	the	DT
37681	1052	42	value	value	NN
37681	1052	43	is	be	VBZ
37681	1052	44	usually	usually	RB
37681	1052	45	more	more	JJR
37681	1052	46	than	than	IN
37681	1052	47	offset	offset	VBN
37681	1052	48	by	by	IN
37681	1052	49	the	the	DT
37681	1052	50	time	time	NN
37681	1052	51	consumed	consume	VBN
37681	1052	52	and	and	CC
37681	1052	53	the	the	DT
37681	1052	54	weakened	weakened	JJ
37681	1052	55	power	power	NN
37681	1052	56	to	to	TO
37681	1052	57	grasp	grasp	VB
37681	1052	58	the	the	DT
37681	1052	59	meaning	meaning	NN
37681	1052	60	of	of	IN
37681	1052	61	a	a	DT
37681	1052	62	geometric	geometric	JJ
37681	1052	63	drawing	drawing	NN
37681	1052	64	.	.	.
37681	1053	1	There	there	EX
37681	1053	2	is	be	VBZ
37681	1053	3	often	often	RB
37681	1053	4	a	a	DT
37681	1053	5	tendency	tendency	NN
37681	1053	6	on	on	IN
37681	1053	7	the	the	DT
37681	1053	8	part	part	NN
37681	1053	9	of	of	IN
37681	1053	10	teachers	teacher	NNS
37681	1053	11	in	in	IN
37681	1053	12	their	-PRON-	PRP$
37681	1053	13	first	first	JJ
37681	1053	14	years	year	NNS
37681	1053	15	of	of	IN
37681	1053	16	work	work	NN
37681	1053	17	to	to	TO
37681	1053	18	overestimate	overestimate	VB
37681	1053	19	the	the	DT
37681	1053	20	logical	logical	JJ
37681	1053	21	powers	power	NNS
37681	1053	22	of	of	IN
37681	1053	23	their	-PRON-	PRP$
37681	1053	24	pupils	pupil	NNS
37681	1053	25	and	and	CC
37681	1053	26	to	to	TO
37681	1053	27	introduce	introduce	VB
37681	1053	28	forms	form	NNS
37681	1053	29	of	of	IN
37681	1053	30	reasoning	reasoning	NN
37681	1053	31	and	and	CC
37681	1053	32	technical	technical	JJ
37681	1053	33	terms	term	NNS
37681	1053	34	that	that	WDT
37681	1053	35	experience	experience	NN
37681	1053	36	has	have	VBZ
37681	1053	37	proved	prove	VBN
37681	1053	38	to	to	TO
37681	1053	39	be	be	VB
37681	1053	40	unsuited	unsuited	JJ
37681	1053	41	to	to	IN
37681	1053	42	one	one	CD
37681	1053	43	who	who	WP
37681	1053	44	is	be	VBZ
37681	1053	45	beginning	begin	VBG
37681	1053	46	geometry	geometry	NN
37681	1053	47	.	.	.
37681	1054	1	Usually	usually	RB
37681	1054	2	but	but	CC
37681	1054	3	little	little	JJ
37681	1054	4	harm	harm	NN
37681	1054	5	is	be	VBZ
37681	1054	6	done	do	VBN
37681	1054	7	,	,	,
37681	1054	8	because	because	IN
37681	1054	9	the	the	DT
37681	1054	10	enthusiasm	enthusiasm	NN
37681	1054	11	of	of	IN
37681	1054	12	any	any	DT
37681	1054	13	teacher	teacher	NN
37681	1054	14	who	who	WP
37681	1054	15	would	would	MD
37681	1054	16	use	use	VB
37681	1054	17	this	this	DT
37681	1054	18	work	work	NN
37681	1054	19	would	would	MD
37681	1054	20	carry	carry	VB
37681	1054	21	the	the	DT
37681	1054	22	pupils	pupil	NNS
37681	1054	23	over	over	IN
37681	1054	24	the	the	DT
37681	1054	25	difficulties	difficulty	NNS
37681	1054	26	without	without	IN
37681	1054	27	much	much	JJ
37681	1054	28	waste	waste	NN
37681	1054	29	of	of	IN
37681	1054	30	energy	energy	NN
37681	1054	31	on	on	IN
37681	1054	32	their	-PRON-	PRP$
37681	1054	33	part	part	NN
37681	1054	34	.	.	.
37681	1055	1	In	in	IN
37681	1055	2	the	the	DT
37681	1055	3	long	long	JJ
37681	1055	4	run	run	NN
37681	1055	5	,	,	,
37681	1055	6	however	however	RB
37681	1055	7	,	,	,
37681	1055	8	the	the	DT
37681	1055	9	attempt	attempt	NN
37681	1055	10	is	be	VBZ
37681	1055	11	usually	usually	RB
37681	1055	12	abandoned	abandon	VBN
37681	1055	13	as	as	IN
37681	1055	14	not	not	RB
37681	1055	15	worth	worth	JJ
37681	1055	16	the	the	DT
37681	1055	17	effort	effort	NN
37681	1055	18	.	.	.
37681	1056	1	Such	such	PDT
37681	1056	2	a	a	DT
37681	1056	3	term	term	NN
37681	1056	4	as	as	IN
37681	1056	5	"	"	``
37681	1056	6	contrapositive	contrapositive	JJ
37681	1056	7	,	,	,
37681	1056	8	"	"	''
37681	1056	9	such	such	JJ
37681	1056	10	distinctions	distinction	NNS
37681	1056	11	as	as	IN
37681	1056	12	that	that	DT
37681	1056	13	between	between	IN
37681	1056	14	the	the	DT
37681	1056	15	logical	logical	JJ
37681	1056	16	and	and	CC
37681	1056	17	the	the	DT
37681	1056	18	geometric	geometric	JJ
37681	1056	19	converse	converse	NN
37681	1056	20	,	,	,
37681	1056	21	or	or	CC
37681	1056	22	between	between	IN
37681	1056	23	perfect	perfect	JJ
37681	1056	24	and	and	CC
37681	1056	25	partial	partial	JJ
37681	1056	26	geometric	geometric	JJ
37681	1056	27	conversion	conversion	NN
37681	1056	28	,	,	,
37681	1056	29	and	and	CC
37681	1056	30	such	such	JJ
37681	1056	31	pronounced	pronounced	JJ
37681	1056	32	formalism	formalism	NN
37681	1056	33	as	as	IN
37681	1056	34	the	the	DT
37681	1056	35	"	"	``
37681	1056	36	syllogistic	syllogistic	JJ
37681	1056	37	method,"--all	method,"--all	NN
37681	1056	38	these	these	DT
37681	1056	39	are	be	VBP
37681	1056	40	happily	happily	RB
37681	1056	41	unknown	unknown	JJ
37681	1056	42	to	to	IN
37681	1056	43	most	most	JJS
37681	1056	44	teachers	teacher	NNS
37681	1056	45	and	and	CC
37681	1056	46	might	may	MD
37681	1056	47	profitably	profitably	RB
37681	1056	48	be	be	VB
37681	1056	49	unknown	unknown	JJ
37681	1056	50	to	to	IN
37681	1056	51	all	all	DT
37681	1056	52	pupils	pupil	NNS
37681	1056	53	.	.	.
37681	1057	1	The	the	DT
37681	1057	2	modern	modern	JJ
37681	1057	3	American	american	JJ
37681	1057	4	textbook	textbook	NN
37681	1057	5	in	in	IN
37681	1057	6	geometry	geometry	NN
37681	1057	7	does	do	VBZ
37681	1057	8	not	not	RB
37681	1057	9	begin	begin	VB
37681	1057	10	to	to	TO
37681	1057	11	be	be	VB
37681	1057	12	as	as	RB
37681	1057	13	good	good	JJ
37681	1057	14	a	a	DT
37681	1057	15	piece	piece	NN
37681	1057	16	of	of	IN
37681	1057	17	logic	logic	NN
37681	1057	18	as	as	IN
37681	1057	19	Euclid	Euclid	NNP
37681	1057	20	's	's	POS
37681	1057	21	"	"	``
37681	1057	22	Elements	Elements	NNPS
37681	1057	23	,	,	,
37681	1057	24	"	"	''
37681	1057	25	and	and	CC
37681	1057	26	yet	yet	RB
37681	1057	27	it	-PRON-	PRP
37681	1057	28	is	be	VBZ
37681	1057	29	to	to	TO
37681	1057	30	be	be	VB
37681	1057	31	observed	observe	VBN
37681	1057	32	that	that	IN
37681	1057	33	none	none	NN
37681	1057	34	of	of	IN
37681	1057	35	these	these	DT
37681	1057	36	terms	term	NNS
37681	1057	37	is	be	VBZ
37681	1057	38	found	find	VBN
37681	1057	39	in	in	IN
37681	1057	40	this	this	DT
37681	1057	41	classic	classic	JJ
37681	1057	42	work	work	NN
37681	1057	43	,	,	,
37681	1057	44	so	so	IN
37681	1057	45	that	that	IN
37681	1057	46	they	-PRON-	PRP
37681	1057	47	can	can	MD
37681	1057	48	not	not	RB
37681	1057	49	be	be	VB
37681	1057	50	thought	think	VBN
37681	1057	51	to	to	TO
37681	1057	52	be	be	VB
37681	1057	53	necessary	necessary	JJ
37681	1057	54	to	to	IN
37681	1057	55	a	a	DT
37681	1057	56	logical	logical	JJ
37681	1057	57	treatment	treatment	NN
37681	1057	58	of	of	IN
37681	1057	59	the	the	DT
37681	1057	60	subject	subject	NN
37681	1057	61	.	.	.
37681	1058	1	We	-PRON-	PRP
37681	1058	2	need	need	VBP
37681	1058	3	the	the	DT
37681	1058	4	word	word	NN
37681	1058	5	"	"	``
37681	1058	6	converse	converse	NN
37681	1058	7	,	,	,
37681	1058	8	"	"	''
37681	1058	9	and	and	CC
37681	1058	10	some	some	DT
37681	1058	11	reference	reference	NN
37681	1058	12	to	to	IN
37681	1058	13	the	the	DT
37681	1058	14	law	law	NN
37681	1058	15	of	of	IN
37681	1058	16	converse	converse	NN
37681	1058	17	is	be	VBZ
37681	1058	18	therefore	therefore	RB
37681	1058	19	permissible	permissible	JJ
37681	1058	20	;	;	:
37681	1058	21	the	the	DT
37681	1058	22	meaning	meaning	NN
37681	1058	23	of	of	IN
37681	1058	24	the	the	DT
37681	1058	25	_	_	NNP
37681	1058	26	reductio	reductio	NN
37681	1058	27	ad	ad	NN
37681	1058	28	absurdum	absurdum	NN
37681	1058	29	_	_	NNP
37681	1058	30	,	,	,
37681	1058	31	of	of	IN
37681	1058	32	a	a	DT
37681	1058	33	necessary	necessary	JJ
37681	1058	34	and	and	CC
37681	1058	35	sufficient	sufficient	JJ
37681	1058	36	condition	condition	NN
37681	1058	37	,	,	,
37681	1058	38	and	and	CC
37681	1058	39	of	of	IN
37681	1058	40	the	the	DT
37681	1058	41	terms	term	NNS
37681	1058	42	"	"	``
37681	1058	43	synthesis	synthesis	NN
37681	1058	44	"	"	''
37681	1058	45	and	and	CC
37681	1058	46	"	"	``
37681	1058	47	analysis	analysis	NN
37681	1058	48	"	"	''
37681	1058	49	may	may	MD
37681	1058	50	properly	properly	RB
37681	1058	51	form	form	VB
37681	1058	52	part	part	NN
37681	1058	53	of	of	IN
37681	1058	54	the	the	DT
37681	1058	55	pupil	pupil	NN
37681	1058	56	's	's	POS
37681	1058	57	equipment	equipment	NN
37681	1058	58	because	because	IN
37681	1058	59	of	of	IN
37681	1058	60	their	-PRON-	PRP$
37681	1058	61	universal	universal	JJ
37681	1058	62	use	use	NN
37681	1058	63	;	;	:
37681	1058	64	but	but	CC
37681	1058	65	any	any	DT
37681	1058	66	extended	extended	JJ
37681	1058	67	incursion	incursion	NN
37681	1058	68	into	into	IN
37681	1058	69	the	the	DT
37681	1058	70	domain	domain	NN
37681	1058	71	of	of	IN
37681	1058	72	logic	logic	NN
37681	1058	73	will	will	MD
37681	1058	74	be	be	VB
37681	1058	75	found	find	VBN
37681	1058	76	unprofitable	unprofitable	JJ
37681	1058	77	,	,	,
37681	1058	78	and	and	CC
37681	1058	79	it	-PRON-	PRP
37681	1058	80	is	be	VBZ
37681	1058	81	liable	liable	JJ
37681	1058	82	to	to	TO
37681	1058	83	be	be	VB
37681	1058	84	positively	positively	RB
37681	1058	85	harmful	harmful	JJ
37681	1058	86	to	to	IN
37681	1058	87	a	a	DT
37681	1058	88	beginner	beginner	NN
37681	1058	89	in	in	IN
37681	1058	90	geometry	geometry	NN
37681	1058	91	.	.	.
37681	1059	1	A	a	DT
37681	1059	2	word	word	NN
37681	1059	3	should	should	MD
37681	1059	4	be	be	VB
37681	1059	5	said	say	VBN
37681	1059	6	as	as	IN
37681	1059	7	to	to	IN
37681	1059	8	the	the	DT
37681	1059	9	lettering	lettering	NN
37681	1059	10	of	of	IN
37681	1059	11	the	the	DT
37681	1059	12	figures	figure	NNS
37681	1059	13	in	in	IN
37681	1059	14	the	the	DT
37681	1059	15	early	early	JJ
37681	1059	16	stages	stage	NNS
37681	1059	17	of	of	IN
37681	1059	18	geometry	geometry	NN
37681	1059	19	.	.	.
37681	1060	1	In	in	IN
37681	1060	2	general	general	JJ
37681	1060	3	,	,	,
37681	1060	4	it	-PRON-	PRP
37681	1060	5	is	be	VBZ
37681	1060	6	a	a	DT
37681	1060	7	great	great	JJ
37681	1060	8	aid	aid	NN
37681	1060	9	to	to	IN
37681	1060	10	the	the	DT
37681	1060	11	eye	eye	NN
37681	1060	12	if	if	IN
37681	1060	13	this	this	DT
37681	1060	14	is	be	VBZ
37681	1060	15	carried	carry	VBN
37681	1060	16	out	out	RP
37681	1060	17	with	with	IN
37681	1060	18	some	some	DT
37681	1060	19	system	system	NN
37681	1060	20	,	,	,
37681	1060	21	and	and	CC
37681	1060	22	the	the	DT
37681	1060	23	following	follow	VBG
37681	1060	24	suggestions	suggestion	NNS
37681	1060	25	are	be	VBP
37681	1060	26	given	give	VBN
37681	1060	27	as	as	IN
37681	1060	28	in	in	IN
37681	1060	29	accord	accord	NN
37681	1060	30	with	with	IN
37681	1060	31	the	the	DT
37681	1060	32	best	good	JJS
37681	1060	33	authors	author	NNS
37681	1060	34	who	who	WP
37681	1060	35	have	have	VBP
37681	1060	36	given	give	VBN
37681	1060	37	any	any	DT
37681	1060	38	attention	attention	NN
37681	1060	39	to	to	IN
37681	1060	40	the	the	DT
37681	1060	41	subject	subject	NN
37681	1060	42	:	:	:
37681	1060	43	1	1	CD
37681	1060	44	.	.	.
37681	1061	1	In	in	IN
37681	1061	2	general	general	JJ
37681	1061	3	,	,	,
37681	1061	4	letter	letter	VB
37681	1061	5	a	a	DT
37681	1061	6	figure	figure	NN
37681	1061	7	counterclockwise	counterclockwise	NN
37681	1061	8	,	,	,
37681	1061	9	for	for	IN
37681	1061	10	the	the	DT
37681	1061	11	reason	reason	NN
37681	1061	12	that	that	WDT
37681	1061	13	we	-PRON-	PRP
37681	1061	14	read	read	VBP
37681	1061	15	angles	angle	NNS
37681	1061	16	in	in	IN
37681	1061	17	this	this	DT
37681	1061	18	way	way	NN
37681	1061	19	in	in	IN
37681	1061	20	higher	high	JJR
37681	1061	21	mathematics	mathematic	NNS
37681	1061	22	,	,	,
37681	1061	23	and	and	CC
37681	1061	24	it	-PRON-	PRP
37681	1061	25	is	be	VBZ
37681	1061	26	as	as	RB
37681	1061	27	easy	easy	JJ
37681	1061	28	to	to	TO
37681	1061	29	form	form	VB
37681	1061	30	this	this	DT
37681	1061	31	habit	habit	NN
37681	1061	32	now	now	RB
37681	1061	33	as	as	IN
37681	1061	34	to	to	TO
37681	1061	35	form	form	VB
37681	1061	36	one	one	NN
37681	1061	37	that	that	WDT
37681	1061	38	may	may	MD
37681	1061	39	have	have	VB
37681	1061	40	to	to	TO
37681	1061	41	be	be	VB
37681	1061	42	changed	change	VBN
37681	1061	43	.	.	.
37681	1062	1	Where	where	WRB
37681	1062	2	two	two	CD
37681	1062	3	triangles	triangle	NNS
37681	1062	4	are	be	VBP
37681	1062	5	congruent	congruent	JJ
37681	1062	6	,	,	,
37681	1062	7	however	however	RB
37681	1062	8	,	,	,
37681	1062	9	but	but	CC
37681	1062	10	have	have	VBP
37681	1062	11	their	-PRON-	PRP$
37681	1062	12	sides	side	NNS
37681	1062	13	arranged	arrange	VBN
37681	1062	14	in	in	IN
37681	1062	15	opposite	opposite	JJ
37681	1062	16	order	order	NN
37681	1062	17	,	,	,
37681	1062	18	it	-PRON-	PRP
37681	1062	19	is	be	VBZ
37681	1062	20	better	well	JJR
37681	1062	21	to	to	TO
37681	1062	22	letter	letter	VB
37681	1062	23	them	-PRON-	PRP
37681	1062	24	so	so	IN
37681	1062	25	that	that	IN
37681	1062	26	their	-PRON-	PRP$
37681	1062	27	corresponding	corresponding	JJ
37681	1062	28	parts	part	NNS
37681	1062	29	appear	appear	VBP
37681	1062	30	in	in	IN
37681	1062	31	the	the	DT
37681	1062	32	same	same	JJ
37681	1062	33	order	order	NN
37681	1062	34	,	,	,
37681	1062	35	although	although	IN
37681	1062	36	this	this	DT
37681	1062	37	makes	make	VBZ
37681	1062	38	one	one	CD
37681	1062	39	read	read	VB
37681	1062	40	clockwise	clockwise	NN
37681	1062	41	.	.	.
37681	1063	1	[	[	-LRB-
37681	1063	2	Illustration	illustration	NN
37681	1063	3	]	]	-RRB-
37681	1063	4	2	2	CD
37681	1063	5	.	.	.
37681	1064	1	For	for	IN
37681	1064	2	the	the	DT
37681	1064	3	same	same	JJ
37681	1064	4	reason	reason	NN
37681	1064	5	,	,	,
37681	1064	6	read	read	VB
37681	1064	7	angles	angle	NNS
37681	1064	8	counterclockwise	counterclockwise	NN
37681	1064	9	.	.	.
37681	1065	1	Thus	thus	RB
37681	1065	2	[	[	-LRB-
37681	1065	3	L]_A	L]_A	NNS
37681	1065	4	_	_	NNP
37681	1065	5	is	be	VBZ
37681	1065	6	read	read	VBN
37681	1065	7	"	"	``
37681	1065	8	_	_	NNP
37681	1065	9	BAC	BAC	NNP
37681	1065	10	_	_	NNP
37681	1065	11	,	,	,
37681	1065	12	"	"	''
37681	1065	13	the	the	DT
37681	1065	14	reflex	reflex	JJ
37681	1065	15	angle	angle	NN
37681	1065	16	on	on	IN
37681	1065	17	the	the	DT
37681	1065	18	outside	outside	NN
37681	1065	19	of	of	IN
37681	1065	20	the	the	DT
37681	1065	21	triangle	triangle	NN
37681	1065	22	being	be	VBG
37681	1065	23	read	read	VBN
37681	1065	24	"	"	``
37681	1065	25	_	_	NNP
37681	1065	26	CAB	CAB	NNP
37681	1065	27	_	_	NNP
37681	1065	28	.	.	.
37681	1065	29	"	"	''
37681	1066	1	Of	of	RB
37681	1066	2	course	course	RB
37681	1066	3	this	this	DT
37681	1066	4	is	be	VBZ
37681	1066	5	not	not	RB
37681	1066	6	vital	vital	JJ
37681	1066	7	,	,	,
37681	1066	8	and	and	CC
37681	1066	9	many	many	JJ
37681	1066	10	authors	author	NNS
37681	1066	11	pay	pay	VBP
37681	1066	12	no	no	DT
37681	1066	13	attention	attention	NN
37681	1066	14	to	to	IN
37681	1066	15	it	-PRON-	PRP
37681	1066	16	;	;	:
37681	1066	17	but	but	CC
37681	1066	18	it	-PRON-	PRP
37681	1066	19	is	be	VBZ
37681	1066	20	convenient	convenient	JJ
37681	1066	21	,	,	,
37681	1066	22	and	and	CC
37681	1066	23	if	if	IN
37681	1066	24	the	the	DT
37681	1066	25	teacher	teacher	NN
37681	1066	26	habitually	habitually	RB
37681	1066	27	does	do	VBZ
37681	1066	28	it	-PRON-	PRP
37681	1066	29	,	,	,
37681	1066	30	the	the	DT
37681	1066	31	pupils	pupil	NNS
37681	1066	32	will	will	MD
37681	1066	33	also	also	RB
37681	1066	34	tend	tend	VB
37681	1066	35	to	to	TO
37681	1066	36	do	do	VB
37681	1066	37	it	-PRON-	PRP
37681	1066	38	.	.	.
37681	1067	1	It	-PRON-	PRP
37681	1067	2	is	be	VBZ
37681	1067	3	helpful	helpful	JJ
37681	1067	4	in	in	IN
37681	1067	5	trigonometry	trigonometry	NN
37681	1067	6	,	,	,
37681	1067	7	and	and	CC
37681	1067	8	it	-PRON-	PRP
37681	1067	9	saves	save	VBZ
37681	1067	10	confusion	confusion	NN
37681	1067	11	in	in	IN
37681	1067	12	the	the	DT
37681	1067	13	case	case	NN
37681	1067	14	of	of	IN
37681	1067	15	a	a	DT
37681	1067	16	reflex	reflex	JJ
37681	1067	17	angle	angle	NN
37681	1067	18	in	in	IN
37681	1067	19	a	a	DT
37681	1067	20	polygon	polygon	NN
37681	1067	21	.	.	.
37681	1068	1	Designate	designate	VB
37681	1068	2	an	an	DT
37681	1068	3	angle	angle	NN
37681	1068	4	by	by	IN
37681	1068	5	a	a	DT
37681	1068	6	single	single	JJ
37681	1068	7	letter	letter	NN
37681	1068	8	if	if	IN
37681	1068	9	this	this	DT
37681	1068	10	can	can	MD
37681	1068	11	conveniently	conveniently	RB
37681	1068	12	be	be	VB
37681	1068	13	done	do	VBN
37681	1068	14	.	.	.
37681	1069	1	3	3	LS
37681	1069	2	.	.	.
37681	1070	1	Designate	designate	VB
37681	1070	2	the	the	DT
37681	1070	3	sides	side	NNS
37681	1070	4	opposite	opposite	IN
37681	1070	5	angles	angle	NNS
37681	1070	6	_	_	NNP
37681	1070	7	A	A	NNP
37681	1070	8	_	_	NNP
37681	1070	9	,	,	,
37681	1070	10	_	_	NNP
37681	1070	11	B	B	NNP
37681	1070	12	_	_	NNP
37681	1070	13	,	,	,
37681	1070	14	_	_	NNP
37681	1070	15	C	C	NNP
37681	1070	16	_	_	NNP
37681	1070	17	,	,	,
37681	1070	18	in	in	IN
37681	1070	19	a	a	DT
37681	1070	20	triangle	triangle	NN
37681	1070	21	,	,	,
37681	1070	22	by	by	IN
37681	1070	23	_	_	NNP
37681	1070	24	a	a	DT
37681	1070	25	_	_	NNP
37681	1070	26	,	,	,
37681	1070	27	_	_	NNP
37681	1070	28	b	b	NNP
37681	1070	29	_	_	NNP
37681	1070	30	,	,	,
37681	1070	31	_	_	NNP
37681	1070	32	c	c	NNP
37681	1070	33	_	_	NNP
37681	1070	34	,	,	,
37681	1070	35	and	and	CC
37681	1070	36	use	use	VB
37681	1070	37	these	these	DT
37681	1070	38	letters	letter	NNS
37681	1070	39	in	in	IN
37681	1070	40	writing	write	VBG
37681	1070	41	proofs	proof	NNS
37681	1070	42	.	.	.
37681	1071	1	4	4	LS
37681	1071	2	.	.	.
37681	1072	1	In	in	IN
37681	1072	2	the	the	DT
37681	1072	3	case	case	NN
37681	1072	4	of	of	IN
37681	1072	5	two	two	CD
37681	1072	6	congruent	congruent	JJ
37681	1072	7	triangles	triangle	NNS
37681	1072	8	use	use	VBP
37681	1072	9	the	the	DT
37681	1072	10	letters	letter	NNS
37681	1072	11	_	_	NNP
37681	1072	12	A	A	NNP
37681	1072	13	_	_	NNP
37681	1072	14	,	,	,
37681	1072	15	_	_	NNP
37681	1072	16	B	B	NNP
37681	1072	17	_	_	NNP
37681	1072	18	,	,	,
37681	1072	19	_	_	NNP
37681	1072	20	C	C	NNP
37681	1072	21	_	_	NNP
37681	1072	22	and	and	CC
37681	1072	23	_	_	NNP
37681	1072	24	A	A	NNP
37681	1072	25	'	'	''
37681	1072	26	_	_	NNP
37681	1072	27	,	,	,
37681	1072	28	_	_	NNP
37681	1072	29	B	B	NNP
37681	1072	30	'	'	''
37681	1072	31	_	_	NNP
37681	1072	32	,	,	,
37681	1072	33	_	_	NNP
37681	1072	34	C	C	NNP
37681	1072	35	'	'	''
37681	1072	36	_	_	NNP
37681	1072	37	,	,	,
37681	1072	38	or	or	CC
37681	1072	39	_	_	NNP
37681	1072	40	X	X	NNP
37681	1072	41	_	_	NNP
37681	1072	42	,	,	,
37681	1072	43	_	_	NNP
37681	1072	44	Y	Y	NNP
37681	1072	45	_	_	NNP
37681	1072	46	,	,	,
37681	1072	47	_	_	NNP
37681	1072	48	Z	Z	NNP
37681	1072	49	_	_	NNP
37681	1072	50	,	,	,
37681	1072	51	instead	instead	RB
37681	1072	52	of	of	IN
37681	1072	53	letters	letter	NNS
37681	1072	54	chosen	choose	VBN
37681	1072	55	at	at	IN
37681	1072	56	random	random	JJ
37681	1072	57	,	,	,
37681	1072	58	like	like	IN
37681	1072	59	_	_	NNP
37681	1072	60	D	D	NNP
37681	1072	61	_	_	NNP
37681	1072	62	,	,	,
37681	1072	63	_	_	NNP
37681	1072	64	K	K	NNP
37681	1072	65	_	_	NNP
37681	1072	66	,	,	,
37681	1072	67	_	_	NNP
37681	1072	68	L	L	NNP
37681	1072	69	_	_	NNP
37681	1072	70	.	.	.
37681	1073	1	It	-PRON-	PRP
37681	1073	2	is	be	VBZ
37681	1073	3	easier	easy	JJR
37681	1073	4	to	to	TO
37681	1073	5	follow	follow	VB
37681	1073	6	a	a	DT
37681	1073	7	proof	proof	NN
37681	1073	8	where	where	WRB
37681	1073	9	some	some	DT
37681	1073	10	system	system	NN
37681	1073	11	is	be	VBZ
37681	1073	12	shown	show	VBN
37681	1073	13	in	in	IN
37681	1073	14	lettering	letter	VBG
37681	1073	15	the	the	DT
37681	1073	16	figures	figure	NNS
37681	1073	17	.	.	.
37681	1074	1	Some	some	DT
37681	1074	2	teachers	teacher	NNS
37681	1074	3	insist	insist	VBP
37681	1074	4	that	that	IN
37681	1074	5	a	a	DT
37681	1074	6	pupil	pupil	NN
37681	1074	7	at	at	IN
37681	1074	8	the	the	DT
37681	1074	9	blackboard	blackboard	NN
37681	1074	10	should	should	MD
37681	1074	11	not	not	RB
37681	1074	12	use	use	VB
37681	1074	13	the	the	DT
37681	1074	14	letters	letter	NNS
37681	1074	15	given	give	VBN
37681	1074	16	in	in	IN
37681	1074	17	the	the	DT
37681	1074	18	textbook	textbook	NN
37681	1074	19	,	,	,
37681	1074	20	hoping	hope	VBG
37681	1074	21	thereby	thereby	RB
37681	1074	22	to	to	TO
37681	1074	23	avoid	avoid	VB
37681	1074	24	memorizing	memorize	VBG
37681	1074	25	.	.	.
37681	1075	1	While	while	IN
37681	1075	2	the	the	DT
37681	1075	3	danger	danger	NN
37681	1075	4	is	be	VBZ
37681	1075	5	probably	probably	RB
37681	1075	6	exaggerated	exaggerated	JJ
37681	1075	7	,	,	,
37681	1075	8	it	-PRON-	PRP
37681	1075	9	is	be	VBZ
37681	1075	10	easy	easy	JJ
37681	1075	11	to	to	TO
37681	1075	12	change	change	VB
37681	1075	13	with	with	IN
37681	1075	14	some	some	DT
37681	1075	15	system	system	NN
37681	1075	16	,	,	,
37681	1075	17	using	use	VBG
37681	1075	18	_	_	NNP
37681	1075	19	P	P	NNP
37681	1075	20	_	_	NNP
37681	1075	21	,	,	,
37681	1075	22	_	_	NNP
37681	1075	23	Q	Q	NNP
37681	1075	24	_	_	NNP
37681	1075	25	,	,	,
37681	1075	26	_	_	NNP
37681	1075	27	R	R	NNP
37681	1075	28	_	_	NNP
37681	1075	29	and	and	CC
37681	1075	30	_	_	NNP
37681	1075	31	P	P	NNP
37681	1075	32	'	'	''
37681	1075	33	_	_	NNP
37681	1075	34	,	,	,
37681	1075	35	_	_	NNP
37681	1075	36	Q	Q	NNP
37681	1075	37	'	'	''
37681	1075	38	_	_	NNP
37681	1075	39	,	,	,
37681	1075	40	_	_	NNP
37681	1075	41	R	R	NNP
37681	1075	42	'	'	''
37681	1075	43	_	_	NNP
37681	1075	44	,	,	,
37681	1075	45	for	for	IN
37681	1075	46	example	example	NN
37681	1075	47	.	.	.
37681	1076	1	5	5	CD
37681	1076	2	.	.	.
37681	1077	1	Use	use	VB
37681	1077	2	small	small	JJ
37681	1077	3	letters	letter	NNS
37681	1077	4	for	for	IN
37681	1077	5	lines	line	NNS
37681	1077	6	,	,	,
37681	1077	7	as	as	IN
37681	1077	8	above	above	IN
37681	1077	9	stated	state	VBN
37681	1077	10	,	,	,
37681	1077	11	and	and	CC
37681	1077	12	also	also	RB
37681	1077	13	place	place	VB
37681	1077	14	them	-PRON-	PRP
37681	1077	15	within	within	IN
37681	1077	16	angles	angle	NNS
37681	1077	17	,	,	,
37681	1077	18	it	-PRON-	PRP
37681	1077	19	being	be	VBG
37681	1077	20	easier	easy	JJR
37681	1077	21	to	to	TO
37681	1077	22	speak	speak	VB
37681	1077	23	of	of	IN
37681	1077	24	and	and	CC
37681	1077	25	to	to	TO
37681	1077	26	see	see	VB
37681	1077	27	[	[	-LRB-
37681	1077	28	L]_m	L]_m	NNP
37681	1077	29	_	_	NNP
37681	1077	30	than	than	IN
37681	1077	31	[	[	-LRB-
37681	1077	32	L]_DEF	L]_DEF	NNP
37681	1077	33	_	_	NNP
37681	1077	34	.	.	.
37681	1078	1	The	the	DT
37681	1078	2	Germans	Germans	NNPS
37681	1078	3	have	have	VBP
37681	1078	4	a	a	DT
37681	1078	5	convenient	convenient	JJ
37681	1078	6	system	system	NN
37681	1078	7	that	that	WDT
37681	1078	8	some	some	DT
37681	1078	9	American	american	JJ
37681	1078	10	teachers	teacher	NNS
37681	1078	11	follow	follow	VBP
37681	1078	12	to	to	IN
37681	1078	13	advantage	advantage	NN
37681	1078	14	,	,	,
37681	1078	15	but	but	CC
37681	1078	16	that	that	IN
37681	1078	17	a	a	DT
37681	1078	18	textbook	textbook	NN
37681	1078	19	has	have	VBZ
37681	1078	20	no	no	DT
37681	1078	21	right	right	NN
37681	1078	22	to	to	TO
37681	1078	23	require	require	VB
37681	1078	24	.	.	.
37681	1079	1	They	-PRON-	PRP
37681	1079	2	use	use	VBP
37681	1079	3	,	,	,
37681	1079	4	as	as	IN
37681	1079	5	in	in	IN
37681	1079	6	the	the	DT
37681	1079	7	following	following	JJ
37681	1079	8	figure	figure	NN
37681	1079	9	,	,	,
37681	1079	10	_	_	NNP
37681	1079	11	A	A	NNP
37681	1079	12	_	_	NNP
37681	1079	13	for	for	IN
37681	1079	14	the	the	DT
37681	1079	15	point	point	NN
37681	1079	16	,	,	,
37681	1079	17	_	_	NNP
37681	1079	18	a	a	DT
37681	1079	19	_	_	NNP
37681	1079	20	for	for	IN
37681	1079	21	the	the	DT
37681	1079	22	opposite	opposite	JJ
37681	1079	23	side	side	NN
37681	1079	24	,	,	,
37681	1079	25	and	and	CC
37681	1079	26	the	the	DT
37681	1079	27	Greek	greek	JJ
37681	1079	28	letter	letter	NN
37681	1079	29	[	[	-LRB-
37681	1079	30	alpha	alpha	NN
37681	1079	31	]	]	-RRB-
37681	1079	32	(	(	-LRB-
37681	1079	33	alpha	alpha	NN
37681	1079	34	)	)	-RRB-
37681	1079	35	for	for	IN
37681	1079	36	the	the	DT
37681	1079	37	angle	angle	NN
37681	1079	38	.	.	.
37681	1080	1	The	the	DT
37681	1080	2	learning	learning	NN
37681	1080	3	of	of	IN
37681	1080	4	the	the	DT
37681	1080	5	first	first	JJ
37681	1080	6	three	three	CD
37681	1080	7	Greek	greek	JJ
37681	1080	8	letters	letter	NNS
37681	1080	9	,	,	,
37681	1080	10	alpha	alpha	NN
37681	1080	11	(	(	-LRB-
37681	1080	12	[	[	-LRB-
37681	1080	13	alpha	alpha	NN
37681	1080	14	]	]	-RRB-
37681	1080	15	)	)	-RRB-
37681	1080	16	,	,	,
37681	1080	17	beta	beta	NN
37681	1080	18	(	(	-LRB-
37681	1080	19	[	[	-LRB-
37681	1080	20	beta	beta	NN
37681	1080	21	]	]	-RRB-
37681	1080	22	)	)	-RRB-
37681	1080	23	,	,	,
37681	1080	24	and	and	CC
37681	1080	25	gamma	gamma	NN
37681	1080	26	(	(	-LRB-
37681	1080	27	[	[	-LRB-
37681	1080	28	gamma	gamma	NN
37681	1080	29	]	]	-RRB-
37681	1080	30	)	)	-RRB-
37681	1080	31	,	,	,
37681	1080	32	is	be	VBZ
37681	1080	33	not	not	RB
37681	1080	34	a	a	DT
37681	1080	35	hardship	hardship	NN
37681	1080	36	,	,	,
37681	1080	37	and	and	CC
37681	1080	38	they	-PRON-	PRP
37681	1080	39	are	be	VBP
37681	1080	40	worth	worth	JJ
37681	1080	41	using	use	VBG
37681	1080	42	,	,	,
37681	1080	43	although	although	IN
37681	1080	44	Greek	Greek	NNP
37681	1080	45	is	be	VBZ
37681	1080	46	so	so	RB
37681	1080	47	little	little	RB
37681	1080	48	known	know	VBN
37681	1080	49	in	in	IN
37681	1080	50	this	this	DT
37681	1080	51	country	country	NN
37681	1080	52	to	to	IN
37681	1080	53	-	-	HYPH
37681	1080	54	day	day	NN
37681	1080	55	that	that	IN
37681	1080	56	the	the	DT
37681	1080	57	alphabet	alphabet	NN
37681	1080	58	can	can	MD
37681	1080	59	not	not	RB
37681	1080	60	be	be	VB
37681	1080	61	demanded	demand	VBN
37681	1080	62	of	of	IN
37681	1080	63	teachers	teacher	NNS
37681	1080	64	who	who	WP
37681	1080	65	do	do	VBP
37681	1080	66	not	not	RB
37681	1080	67	care	care	VB
37681	1080	68	to	to	TO
37681	1080	69	use	use	VB
37681	1080	70	it	-PRON-	PRP
37681	1080	71	.	.	.
37681	1081	1	[	[	-LRB-
37681	1081	2	Illustration	illustration	NN
37681	1081	3	]	]	-RRB-
37681	1081	4	6	6	CD
37681	1081	5	.	.	.
37681	1082	1	Also	also	RB
37681	1082	2	use	use	VB
37681	1082	3	small	small	JJ
37681	1082	4	letters	letter	NNS
37681	1082	5	to	to	TO
37681	1082	6	represent	represent	VB
37681	1082	7	numerical	numerical	JJ
37681	1082	8	values	value	NNS
37681	1082	9	.	.	.
37681	1083	1	For	for	IN
37681	1083	2	example	example	NN
37681	1083	3	,	,	,
37681	1083	4	write	write	VB
37681	1083	5	_	_	NNP
37681	1083	6	c	c	NNP
37681	1083	7	_	_	NNP
37681	1083	8	=	=	SYM
37681	1083	9	2[pi]_r	2[pi]_r	CD
37681	1083	10	_	_	NNP
37681	1083	11	instead	instead	RB
37681	1083	12	of	of	IN
37681	1083	13	_	_	NNP
37681	1083	14	C	C	NNP
37681	1083	15	_	_	NNP
37681	1083	16	=	=	SYM
37681	1083	17	2[pi]_R	2[pi]_r	CD
37681	1083	18	_	_	NNP
37681	1083	19	.	.	.
37681	1084	1	This	this	DT
37681	1084	2	is	be	VBZ
37681	1084	3	in	in	IN
37681	1084	4	accord	accord	NN
37681	1084	5	with	with	IN
37681	1084	6	the	the	DT
37681	1084	7	usage	usage	NN
37681	1084	8	in	in	IN
37681	1084	9	algebra	algebra	NN
37681	1084	10	to	to	TO
37681	1084	11	which	which	WDT
37681	1084	12	the	the	DT
37681	1084	13	pupil	pupil	NN
37681	1084	14	is	be	VBZ
37681	1084	15	accustomed	accustom	VBN
37681	1084	16	.	.	.
37681	1085	1	7	7	LS
37681	1085	2	.	.	.
37681	1086	1	Use	use	VB
37681	1086	2	initial	initial	JJ
37681	1086	3	letters	letter	NNS
37681	1086	4	whenever	whenever	WRB
37681	1086	5	convenient	convenient	RB
37681	1086	6	,	,	,
37681	1086	7	as	as	IN
37681	1086	8	in	in	IN
37681	1086	9	the	the	DT
37681	1086	10	case	case	NN
37681	1086	11	of	of	IN
37681	1086	12	_	_	NNP
37681	1086	13	a	a	DT
37681	1086	14	_	_	NNP
37681	1086	15	for	for	IN
37681	1086	16	area	area	NN
37681	1086	17	,	,	,
37681	1086	18	_	_	NNP
37681	1086	19	b	b	NNP
37681	1086	20	_	_	NNP
37681	1086	21	for	for	IN
37681	1086	22	base	base	NN
37681	1086	23	,	,	,
37681	1086	24	_	_	NNP
37681	1086	25	c	c	NNP
37681	1086	26	_	_	NNP
37681	1086	27	for	for	IN
37681	1086	28	circumference	circumference	NN
37681	1086	29	,	,	,
37681	1086	30	_	_	NNP
37681	1086	31	d	d	NNP
37681	1086	32	_	_	NNP
37681	1086	33	for	for	IN
37681	1086	34	diameter	diameter	NN
37681	1086	35	,	,	,
37681	1086	36	_	_	NNP
37681	1086	37	h	h	NNP
37681	1086	38	_	_	NNP
37681	1086	39	for	for	IN
37681	1086	40	height	height	NN
37681	1086	41	(	(	-LRB-
37681	1086	42	altitude	altitude	NN
37681	1086	43	)	)	-RRB-
37681	1086	44	,	,	,
37681	1086	45	and	and	CC
37681	1086	46	so	so	RB
37681	1086	47	on	on	RB
37681	1086	48	.	.	.
37681	1087	1	Many	many	JJ
37681	1087	2	of	of	IN
37681	1087	3	these	these	DT
37681	1087	4	suggestions	suggestion	NNS
37681	1087	5	seem	seem	VBP
37681	1087	6	of	of	IN
37681	1087	7	slight	slight	JJ
37681	1087	8	importance	importance	NN
37681	1087	9	in	in	IN
37681	1087	10	themselves	-PRON-	PRP
37681	1087	11	,	,	,
37681	1087	12	and	and	CC
37681	1087	13	some	some	DT
37681	1087	14	teachers	teacher	NNS
37681	1087	15	will	will	MD
37681	1087	16	be	be	VB
37681	1087	17	disposed	dispose	VBN
37681	1087	18	to	to	TO
37681	1087	19	object	object	VB
37681	1087	20	to	to	IN
37681	1087	21	any	any	DT
37681	1087	22	attempt	attempt	NN
37681	1087	23	at	at	IN
37681	1087	24	lettering	letter	VBG
37681	1087	25	a	a	DT
37681	1087	26	figure	figure	NN
37681	1087	27	with	with	IN
37681	1087	28	any	any	DT
37681	1087	29	regard	regard	NN
37681	1087	30	to	to	IN
37681	1087	31	system	system	NN
37681	1087	32	.	.	.
37681	1088	1	If	if	IN
37681	1088	2	,	,	,
37681	1088	3	however	however	RB
37681	1088	4	,	,	,
37681	1088	5	they	-PRON-	PRP
37681	1088	6	will	will	MD
37681	1088	7	notice	notice	VB
37681	1088	8	how	how	WRB
37681	1088	9	a	a	DT
37681	1088	10	class	class	NN
37681	1088	11	struggles	struggle	VBZ
37681	1088	12	to	to	TO
37681	1088	13	follow	follow	VB
37681	1088	14	a	a	DT
37681	1088	15	demonstration	demonstration	NN
37681	1088	16	given	give	VBN
37681	1088	17	with	with	IN
37681	1088	18	reference	reference	NN
37681	1088	19	to	to	IN
37681	1088	20	a	a	DT
37681	1088	21	figure	figure	NN
37681	1088	22	on	on	IN
37681	1088	23	the	the	DT
37681	1088	24	blackboard	blackboard	NN
37681	1088	25	,	,	,
37681	1088	26	they	-PRON-	PRP
37681	1088	27	will	will	MD
37681	1088	28	see	see	VB
37681	1088	29	how	how	WRB
37681	1088	30	helpful	helpful	JJ
37681	1088	31	it	-PRON-	PRP
37681	1088	32	is	be	VBZ
37681	1088	33	to	to	TO
37681	1088	34	have	have	VB
37681	1088	35	some	some	DT
37681	1088	36	simple	simple	JJ
37681	1088	37	standards	standard	NNS
37681	1088	38	of	of	IN
37681	1088	39	lettering	lettering	NN
37681	1088	40	.	.	.
37681	1089	1	It	-PRON-	PRP
37681	1089	2	is	be	VBZ
37681	1089	3	hardly	hardly	RB
37681	1089	4	necessary	necessary	JJ
37681	1089	5	to	to	TO
37681	1089	6	add	add	VB
37681	1089	7	that	that	DT
37681	1089	8	in	in	IN
37681	1089	9	demonstrating	demonstrate	VBG
37681	1089	10	from	from	IN
37681	1089	11	a	a	DT
37681	1089	12	figure	figure	NN
37681	1089	13	on	on	IN
37681	1089	14	a	a	DT
37681	1089	15	blackboard	blackboard	NN
37681	1089	16	it	-PRON-	PRP
37681	1089	17	is	be	VBZ
37681	1089	18	usually	usually	RB
37681	1089	19	better	well	JJR
37681	1089	20	to	to	TO
37681	1089	21	say	say	VB
37681	1089	22	"	"	``
37681	1089	23	this	this	DT
37681	1089	24	line	line	NN
37681	1089	25	,	,	,
37681	1089	26	"	"	''
37681	1089	27	or	or	CC
37681	1089	28	"	"	``
37681	1089	29	the	the	DT
37681	1089	30	red	red	JJ
37681	1089	31	line	line	NN
37681	1089	32	,	,	,
37681	1089	33	"	"	''
37681	1089	34	than	than	IN
37681	1089	35	to	to	TO
37681	1089	36	say	say	VB
37681	1089	37	,	,	,
37681	1089	38	without	without	IN
37681	1089	39	pointing	point	VBG
37681	1089	40	to	to	IN
37681	1089	41	it	-PRON-	PRP
37681	1089	42	,	,	,
37681	1089	43	"	"	''
37681	1089	44	the	the	DT
37681	1089	45	line	line	NN
37681	1089	46	_	_	NNP
37681	1089	47	AB	AB	NNP
37681	1089	48	_	_	NNP
37681	1089	49	.	.	.
37681	1089	50	"	"	''
37681	1090	1	It	-PRON-	PRP
37681	1090	2	is	be	VBZ
37681	1090	3	by	by	IN
37681	1090	4	such	such	JJ
37681	1090	5	simplicity	simplicity	NN
37681	1090	6	of	of	IN
37681	1090	7	statement	statement	NN
37681	1090	8	and	and	CC
37681	1090	9	by	by	IN
37681	1090	10	such	such	JJ
37681	1090	11	efforts	effort	NNS
37681	1090	12	to	to	TO
37681	1090	13	help	help	VB
37681	1090	14	the	the	DT
37681	1090	15	class	class	NN
37681	1090	16	to	to	TO
37681	1090	17	follow	follow	VB
37681	1090	18	demonstrations	demonstration	NNS
37681	1090	19	that	that	IN
37681	1090	20	pupils	pupil	NNS
37681	1090	21	are	be	VBP
37681	1090	22	led	lead	VBN
37681	1090	23	through	through	IN
37681	1090	24	many	many	JJ
37681	1090	25	of	of	IN
37681	1090	26	the	the	DT
37681	1090	27	initial	initial	JJ
37681	1090	28	discouragements	discouragement	NNS
37681	1090	29	of	of	IN
37681	1090	30	the	the	DT
37681	1090	31	subject	subject	NN
37681	1090	32	.	.	.
37681	1091	1	FOOTNOTES	footnote	NNS
37681	1091	2	:	:	:
37681	1091	3	[	[	-LRB-
37681	1091	4	40	40	CD
37681	1091	5	]	]	-RRB-
37681	1091	6	Carson	Carson	NNP
37681	1091	7	,	,	,
37681	1091	8	loc	loc	NNP
37681	1091	9	.	.	.
37681	1092	1	cit	cit	NNP
37681	1092	2	.	.	NNP
37681	1092	3	,	,	,
37681	1092	4	p.	p.	NN
37681	1092	5	13	13	CD
37681	1092	6	.	.	.
37681	1093	1	CHAPTER	chapter	NN
37681	1093	2	X	X	NNP
37681	1093	3	THE	the	DT
37681	1093	4	CONDUCT	conduct	NN
37681	1093	5	OF	of	IN
37681	1093	6	A	a	DT
37681	1093	7	CLASS	class	NN
37681	1093	8	IN	in	IN
37681	1093	9	GEOMETRY	GEOMETRY	NNP
37681	1093	10	No	no	DT
37681	1093	11	definite	definite	JJ
37681	1093	12	rules	rule	NNS
37681	1093	13	can	can	MD
37681	1093	14	be	be	VB
37681	1093	15	given	give	VBN
37681	1093	16	for	for	IN
37681	1093	17	the	the	DT
37681	1093	18	detailed	detailed	JJ
37681	1093	19	conduct	conduct	NN
37681	1093	20	of	of	IN
37681	1093	21	a	a	DT
37681	1093	22	class	class	NN
37681	1093	23	in	in	IN
37681	1093	24	any	any	DT
37681	1093	25	subject	subject	NN
37681	1093	26	.	.	.
37681	1094	1	If	if	IN
37681	1094	2	it	-PRON-	PRP
37681	1094	3	were	be	VBD
37681	1094	4	possible	possible	JJ
37681	1094	5	to	to	TO
37681	1094	6	formulate	formulate	VB
37681	1094	7	such	such	JJ
37681	1094	8	rules	rule	NNS
37681	1094	9	,	,	,
37681	1094	10	all	all	PDT
37681	1094	11	the	the	DT
37681	1094	12	personal	personal	JJ
37681	1094	13	magnetism	magnetism	NN
37681	1094	14	of	of	IN
37681	1094	15	the	the	DT
37681	1094	16	teacher	teacher	NN
37681	1094	17	,	,	,
37681	1094	18	all	all	PDT
37681	1094	19	the	the	DT
37681	1094	20	enthusiasm	enthusiasm	NN
37681	1094	21	,	,	,
37681	1094	22	all	all	PDT
37681	1094	23	the	the	DT
37681	1094	24	originality	originality	NN
37681	1094	25	,	,	,
37681	1094	26	all	all	PDT
37681	1094	27	the	the	DT
37681	1094	28	spirit	spirit	NN
37681	1094	29	of	of	IN
37681	1094	30	the	the	DT
37681	1094	31	class	class	NN
37681	1094	32	,	,	,
37681	1094	33	would	would	MD
37681	1094	34	depart	depart	VB
37681	1094	35	,	,	,
37681	1094	36	and	and	CC
37681	1094	37	we	-PRON-	PRP
37681	1094	38	should	should	MD
37681	1094	39	have	have	VB
37681	1094	40	a	a	DT
37681	1094	41	dull	dull	JJ
37681	1094	42	,	,	,
37681	1094	43	dry	dry	JJ
37681	1094	44	mechanism	mechanism	NN
37681	1094	45	.	.	.
37681	1095	1	There	there	EX
37681	1095	2	is	be	VBZ
37681	1095	3	no	no	DT
37681	1095	4	one	one	NN
37681	1095	5	best	good	JJS
37681	1095	6	method	method	NN
37681	1095	7	of	of	IN
37681	1095	8	teaching	teach	VBG
37681	1095	9	geometry	geometry	NN
37681	1095	10	or	or	CC
37681	1095	11	anything	anything	NN
37681	1095	12	else	else	RB
37681	1095	13	.	.	.
37681	1096	1	The	the	DT
37681	1096	2	experience	experience	NN
37681	1096	3	of	of	IN
37681	1096	4	the	the	DT
37681	1096	5	schools	school	NNS
37681	1096	6	has	have	VBZ
37681	1096	7	shown	show	VBN
37681	1096	8	that	that	IN
37681	1096	9	a	a	DT
37681	1096	10	few	few	JJ
37681	1096	11	great	great	JJ
37681	1096	12	principles	principle	NNS
37681	1096	13	stand	stand	VBP
37681	1096	14	out	out	RP
37681	1096	15	as	as	IN
37681	1096	16	generally	generally	RB
37681	1096	17	accepted	accept	VBN
37681	1096	18	,	,	,
37681	1096	19	but	but	CC
37681	1096	20	as	as	IN
37681	1096	21	to	to	IN
37681	1096	22	the	the	DT
37681	1096	23	carrying	carrying	NN
37681	1096	24	out	out	IN
37681	1096	25	of	of	IN
37681	1096	26	these	these	DT
37681	1096	27	principles	principle	NNS
37681	1096	28	there	there	EX
37681	1096	29	can	can	MD
37681	1096	30	be	be	VB
37681	1096	31	no	no	DT
37681	1096	32	definite	definite	JJ
37681	1096	33	rules	rule	NNS
37681	1096	34	.	.	.
37681	1097	1	Let	let	VB
37681	1097	2	us	-PRON-	PRP
37681	1097	3	first	first	RB
37681	1097	4	consider	consider	VB
37681	1097	5	the	the	DT
37681	1097	6	general	general	JJ
37681	1097	7	question	question	NN
37681	1097	8	of	of	IN
37681	1097	9	the	the	DT
37681	1097	10	employment	employment	NN
37681	1097	11	of	of	IN
37681	1097	12	time	time	NN
37681	1097	13	in	in	IN
37681	1097	14	a	a	DT
37681	1097	15	recitation	recitation	NN
37681	1097	16	in	in	IN
37681	1097	17	geometry	geometry	NN
37681	1097	18	.	.	.
37681	1098	1	We	-PRON-	PRP
37681	1098	2	might	may	MD
37681	1098	3	all	all	RB
37681	1098	4	agree	agree	VB
37681	1098	5	on	on	IN
37681	1098	6	certain	certain	JJ
37681	1098	7	general	general	JJ
37681	1098	8	principles	principle	NNS
37681	1098	9	,	,	,
37681	1098	10	and	and	CC
37681	1098	11	yet	yet	RB
37681	1098	12	no	no	DT
37681	1098	13	two	two	CD
37681	1098	14	teachers	teacher	NNS
37681	1098	15	ever	ever	RB
37681	1098	16	would	would	MD
37681	1098	17	or	or	CC
37681	1098	18	ever	ever	RB
37681	1098	19	should	should	MD
37681	1098	20	divide	divide	VB
37681	1098	21	the	the	DT
37681	1098	22	period	period	NN
37681	1098	23	even	even	RB
37681	1098	24	approximately	approximately	RB
37681	1098	25	in	in	IN
37681	1098	26	the	the	DT
37681	1098	27	same	same	JJ
37681	1098	28	way	way	NN
37681	1098	29	.	.	.
37681	1099	1	First	first	RB
37681	1099	2	,	,	,
37681	1099	3	a	a	DT
37681	1099	4	class	class	NN
37681	1099	5	should	should	MD
37681	1099	6	have	have	VB
37681	1099	7	an	an	DT
37681	1099	8	opportunity	opportunity	NN
37681	1099	9	to	to	TO
37681	1099	10	ask	ask	VB
37681	1099	11	questions	question	NNS
37681	1099	12	.	.	.
37681	1100	1	A	a	DT
37681	1100	2	teacher	teacher	NN
37681	1100	3	here	here	RB
37681	1100	4	shows	show	VBZ
37681	1100	5	his	-PRON-	PRP$
37681	1100	6	power	power	NN
37681	1100	7	at	at	IN
37681	1100	8	its	-PRON-	PRP$
37681	1100	9	best	good	JJS
37681	1100	10	,	,	,
37681	1100	11	listening	listen	VBG
37681	1100	12	sympathetically	sympathetically	RB
37681	1100	13	to	to	IN
37681	1100	14	any	any	DT
37681	1100	15	good	good	JJ
37681	1100	16	question	question	NN
37681	1100	17	,	,	,
37681	1100	18	quickly	quickly	RB
37681	1100	19	seeing	see	VBG
37681	1100	20	the	the	DT
37681	1100	21	essential	essential	JJ
37681	1100	22	point	point	NN
37681	1100	23	,	,	,
37681	1100	24	and	and	CC
37681	1100	25	either	either	CC
37681	1100	26	answering	answer	VBG
37681	1100	27	it	-PRON-	PRP
37681	1100	28	or	or	CC
37681	1100	29	restating	restate	VBG
37681	1100	30	it	-PRON-	PRP
37681	1100	31	in	in	IN
37681	1100	32	such	such	PDT
37681	1100	33	a	a	DT
37681	1100	34	way	way	NN
37681	1100	35	that	that	WDT
37681	1100	36	the	the	DT
37681	1100	37	pupil	pupil	NN
37681	1100	38	can	can	MD
37681	1100	39	answer	answer	VB
37681	1100	40	it	-PRON-	PRP
37681	1100	41	for	for	IN
37681	1100	42	himself	-PRON-	PRP
37681	1100	43	.	.	.
37681	1101	1	Certain	certain	JJ
37681	1101	2	questions	question	NNS
37681	1101	3	should	should	MD
37681	1101	4	be	be	VB
37681	1101	5	answered	answer	VBN
37681	1101	6	by	by	IN
37681	1101	7	the	the	DT
37681	1101	8	teacher	teacher	NN
37681	1101	9	;	;	:
37681	1101	10	he	-PRON-	PRP
37681	1101	11	is	be	VBZ
37681	1101	12	there	there	RB
37681	1101	13	for	for	IN
37681	1101	14	that	that	DT
37681	1101	15	purpose	purpose	NN
37681	1101	16	.	.	.
37681	1102	1	Others	other	NNS
37681	1102	2	can	can	MD
37681	1102	3	at	at	IN
37681	1102	4	once	once	RB
37681	1102	5	be	be	VB
37681	1102	6	put	put	VBN
37681	1102	7	in	in	IN
37681	1102	8	such	such	PDT
37681	1102	9	a	a	DT
37681	1102	10	light	light	NN
37681	1102	11	that	that	IN
37681	1102	12	the	the	DT
37681	1102	13	pupil	pupil	NN
37681	1102	14	can	can	MD
37681	1102	15	himself	-PRON-	PRP
37681	1102	16	answer	answer	VB
37681	1102	17	them	-PRON-	PRP
37681	1102	18	.	.	.
37681	1103	1	Others	other	NNS
37681	1103	2	may	may	MD
37681	1103	3	better	better	RB
37681	1103	4	be	be	VB
37681	1103	5	answered	answer	VBN
37681	1103	6	by	by	IN
37681	1103	7	the	the	DT
37681	1103	8	class	class	NN
37681	1103	9	.	.	.
37681	1104	1	Occasionally	occasionally	RB
37681	1104	2	,	,	,
37681	1104	3	but	but	CC
37681	1104	4	more	more	RBR
37681	1104	5	rarely	rarely	RB
37681	1104	6	,	,	,
37681	1104	7	a	a	DT
37681	1104	8	pupil	pupil	NN
37681	1104	9	may	may	MD
37681	1104	10	be	be	VB
37681	1104	11	told	tell	VBN
37681	1104	12	to	to	TO
37681	1104	13	"	"	``
37681	1104	14	look	look	VB
37681	1104	15	that	that	DT
37681	1104	16	up	up	RB
37681	1104	17	for	for	IN
37681	1104	18	to	to	IN
37681	1104	19	-	-	HYPH
37681	1104	20	morrow	morrow	NNP
37681	1104	21	,	,	,
37681	1104	22	"	"	''
37681	1104	23	a	a	DT
37681	1104	24	plan	plan	NN
37681	1104	25	that	that	WDT
37681	1104	26	is	be	VBZ
37681	1104	27	commonly	commonly	RB
37681	1104	28	considered	consider	VBN
37681	1104	29	by	by	IN
37681	1104	30	students	student	NNS
37681	1104	31	as	as	IN
37681	1104	32	a	a	DT
37681	1104	33	confession	confession	NN
37681	1104	34	of	of	IN
37681	1104	35	weakness	weakness	NN
37681	1104	36	on	on	IN
37681	1104	37	the	the	DT
37681	1104	38	part	part	NN
37681	1104	39	of	of	IN
37681	1104	40	the	the	DT
37681	1104	41	teacher	teacher	NN
37681	1104	42	,	,	,
37681	1104	43	as	as	IN
37681	1104	44	it	-PRON-	PRP
37681	1104	45	probably	probably	RB
37681	1104	46	is	be	VBZ
37681	1104	47	.	.	.
37681	1105	1	Of	of	RB
37681	1105	2	course	course	RB
37681	1105	3	a	a	DT
37681	1105	4	class	class	NN
37681	1105	5	will	will	MD
37681	1105	6	waste	waste	VB
37681	1105	7	time	time	NN
37681	1105	8	in	in	IN
37681	1105	9	questioning	question	VBG
37681	1105	10	a	a	DT
37681	1105	11	weak	weak	JJ
37681	1105	12	teacher	teacher	NN
37681	1105	13	,	,	,
37681	1105	14	but	but	CC
37681	1105	15	a	a	DT
37681	1105	16	strong	strong	JJ
37681	1105	17	one	one	CD
37681	1105	18	need	need	NN
37681	1105	19	have	have	VB
37681	1105	20	no	no	DT
37681	1105	21	fear	fear	NN
37681	1105	22	on	on	IN
37681	1105	23	this	this	DT
37681	1105	24	account	account	NN
37681	1105	25	.	.	.
37681	1106	1	Five	five	CD
37681	1106	2	minutes	minute	NNS
37681	1106	3	given	give	VBN
37681	1106	4	at	at	IN
37681	1106	5	the	the	DT
37681	1106	6	opening	opening	NN
37681	1106	7	of	of	IN
37681	1106	8	a	a	DT
37681	1106	9	recitation	recitation	NN
37681	1106	10	to	to	IN
37681	1106	11	brisk	brisk	JJ
37681	1106	12	,	,	,
37681	1106	13	pointed	pointed	JJ
37681	1106	14	questions	question	NNS
37681	1106	15	by	by	IN
37681	1106	16	the	the	DT
37681	1106	17	class	class	NN
37681	1106	18	,	,	,
37681	1106	19	with	with	IN
37681	1106	20	the	the	DT
37681	1106	21	same	same	JJ
37681	1106	22	credit	credit	NN
37681	1106	23	given	give	VBN
37681	1106	24	to	to	IN
37681	1106	25	a	a	DT
37681	1106	26	good	good	JJ
37681	1106	27	question	question	NN
37681	1106	28	as	as	IN
37681	1106	29	to	to	IN
37681	1106	30	a	a	DT
37681	1106	31	good	good	JJ
37681	1106	32	answer	answer	NN
37681	1106	33	,	,	,
37681	1106	34	will	will	MD
37681	1106	35	do	do	VB
37681	1106	36	a	a	DT
37681	1106	37	great	great	JJ
37681	1106	38	deal	deal	NN
37681	1106	39	to	to	TO
37681	1106	40	create	create	VB
37681	1106	41	a	a	DT
37681	1106	42	spirit	spirit	NN
37681	1106	43	of	of	IN
37681	1106	44	comradeship	comradeship	NN
37681	1106	45	,	,	,
37681	1106	46	of	of	IN
37681	1106	47	frankness	frankness	NN
37681	1106	48	,	,	,
37681	1106	49	and	and	CC
37681	1106	50	of	of	IN
37681	1106	51	honesty	honesty	NN
37681	1106	52	,	,	,
37681	1106	53	and	and	CC
37681	1106	54	will	will	MD
37681	1106	55	reveal	reveal	VB
37681	1106	56	to	to	IN
37681	1106	57	a	a	DT
37681	1106	58	sympathetic	sympathetic	JJ
37681	1106	59	teacher	teacher	NN
37681	1106	60	the	the	DT
37681	1106	61	difficulties	difficulty	NNS
37681	1106	62	of	of	IN
37681	1106	63	a	a	DT
37681	1106	64	class	class	NN
37681	1106	65	much	much	RB
37681	1106	66	better	well	JJR
37681	1106	67	than	than	IN
37681	1106	68	the	the	DT
37681	1106	69	same	same	JJ
37681	1106	70	amount	amount	NN
37681	1106	71	of	of	IN
37681	1106	72	time	time	NN
37681	1106	73	devoted	devote	VBN
37681	1106	74	to	to	IN
37681	1106	75	blackboard	blackboard	NN
37681	1106	76	work	work	NN
37681	1106	77	.	.	.
37681	1107	1	But	but	CC
37681	1107	2	there	there	EX
37681	1107	3	must	must	MD
37681	1107	4	be	be	VB
37681	1107	5	no	no	DT
37681	1107	6	dawdling	dawdling	NN
37681	1107	7	,	,	,
37681	1107	8	and	and	CC
37681	1107	9	the	the	DT
37681	1107	10	class	class	NN
37681	1107	11	must	must	MD
37681	1107	12	feel	feel	VB
37681	1107	13	that	that	IN
37681	1107	14	it	-PRON-	PRP
37681	1107	15	has	have	VBZ
37681	1107	16	only	only	RB
37681	1107	17	a	a	DT
37681	1107	18	limited	limit	VBN
37681	1107	19	time	time	NN
37681	1107	20	,	,	,
37681	1107	21	say	say	VBP
37681	1107	22	five	five	CD
37681	1107	23	minutes	minute	NNS
37681	1107	24	at	at	IN
37681	1107	25	the	the	DT
37681	1107	26	most	most	JJS
37681	1107	27	,	,	,
37681	1107	28	to	to	TO
37681	1107	29	get	get	VB
37681	1107	30	the	the	DT
37681	1107	31	help	help	NN
37681	1107	32	it	-PRON-	PRP
37681	1107	33	needs	need	VBZ
37681	1107	34	.	.	.
37681	1108	1	Next	next	RB
37681	1108	2	in	in	IN
37681	1108	3	order	order	NN
37681	1108	4	of	of	IN
37681	1108	5	the	the	DT
37681	1108	6	division	division	NN
37681	1108	7	of	of	IN
37681	1108	8	the	the	DT
37681	1108	9	time	time	NN
37681	1108	10	may	may	MD
37681	1108	11	be	be	VB
37681	1108	12	the	the	DT
37681	1108	13	teacher	teacher	NN
37681	1108	14	's	's	POS
37681	1108	15	report	report	NN
37681	1108	16	on	on	IN
37681	1108	17	any	any	DT
37681	1108	18	papers	paper	NNS
37681	1108	19	that	that	WDT
37681	1108	20	the	the	DT
37681	1108	21	class	class	NN
37681	1108	22	has	have	VBZ
37681	1108	23	handed	hand	VBN
37681	1108	24	in	in	RP
37681	1108	25	.	.	.
37681	1109	1	It	-PRON-	PRP
37681	1109	2	is	be	VBZ
37681	1109	3	impossible	impossible	JJ
37681	1109	4	to	to	TO
37681	1109	5	tell	tell	VB
37681	1109	6	how	how	WRB
37681	1109	7	much	much	JJ
37681	1109	8	of	of	IN
37681	1109	9	this	this	DT
37681	1109	10	paper	paper	NN
37681	1109	11	work	work	NN
37681	1109	12	should	should	MD
37681	1109	13	be	be	VB
37681	1109	14	demanded	demand	VBN
37681	1109	15	.	.	.
37681	1110	1	The	the	DT
37681	1110	2	local	local	JJ
37681	1110	3	school	school	NN
37681	1110	4	conditions	condition	NNS
37681	1110	5	,	,	,
37681	1110	6	the	the	DT
37681	1110	7	mental	mental	JJ
37681	1110	8	condition	condition	NN
37681	1110	9	of	of	IN
37681	1110	10	the	the	DT
37681	1110	11	class	class	NN
37681	1110	12	,	,	,
37681	1110	13	and	and	CC
37681	1110	14	the	the	DT
37681	1110	15	time	time	NN
37681	1110	16	at	at	IN
37681	1110	17	the	the	DT
37681	1110	18	disposal	disposal	NN
37681	1110	19	of	of	IN
37681	1110	20	the	the	DT
37681	1110	21	teacher	teacher	NN
37681	1110	22	are	be	VBP
37681	1110	23	all	all	DT
37681	1110	24	factors	factor	NNS
37681	1110	25	in	in	IN
37681	1110	26	the	the	DT
37681	1110	27	case	case	NN
37681	1110	28	.	.	.
37681	1111	1	In	in	IN
37681	1111	2	general	general	JJ
37681	1111	3	,	,	,
37681	1111	4	it	-PRON-	PRP
37681	1111	5	may	may	MD
37681	1111	6	be	be	VB
37681	1111	7	said	say	VBN
37681	1111	8	that	that	IN
37681	1111	9	enough	enough	JJ
37681	1111	10	of	of	IN
37681	1111	11	this	this	DT
37681	1111	12	kind	kind	NN
37681	1111	13	of	of	IN
37681	1111	14	work	work	NN
37681	1111	15	is	be	VBZ
37681	1111	16	necessary	necessary	JJ
37681	1111	17	to	to	TO
37681	1111	18	see	see	VB
37681	1111	19	that	that	IN
37681	1111	20	pupils	pupil	NNS
37681	1111	21	are	be	VBP
37681	1111	22	neat	neat	JJ
37681	1111	23	and	and	CC
37681	1111	24	accurate	accurate	JJ
37681	1111	25	in	in	IN
37681	1111	26	setting	set	VBG
37681	1111	27	down	down	RP
37681	1111	28	their	-PRON-	PRP$
37681	1111	29	demonstrations	demonstration	NNS
37681	1111	30	.	.	.
37681	1112	1	On	on	IN
37681	1112	2	the	the	DT
37681	1112	3	other	other	JJ
37681	1112	4	hand	hand	NN
37681	1112	5	,	,	,
37681	1112	6	paper	paper	NN
37681	1112	7	work	work	NN
37681	1112	8	gives	give	VBZ
37681	1112	9	an	an	DT
37681	1112	10	opportunity	opportunity	NN
37681	1112	11	for	for	IN
37681	1112	12	dishonesty	dishonesty	NN
37681	1112	13	,	,	,
37681	1112	14	and	and	CC
37681	1112	15	it	-PRON-	PRP
37681	1112	16	consumes	consume	VBZ
37681	1112	17	a	a	DT
37681	1112	18	great	great	JJ
37681	1112	19	deal	deal	NN
37681	1112	20	of	of	IN
37681	1112	21	the	the	DT
37681	1112	22	teacher	teacher	NN
37681	1112	23	's	's	POS
37681	1112	24	time	time	NN
37681	1112	25	that	that	WDT
37681	1112	26	might	may	MD
37681	1112	27	better	better	RB
37681	1112	28	be	be	VB
37681	1112	29	given	give	VBN
37681	1112	30	to	to	IN
37681	1112	31	reading	read	VBG
37681	1112	32	good	good	JJ
37681	1112	33	books	book	NNS
37681	1112	34	on	on	IN
37681	1112	35	the	the	DT
37681	1112	36	subject	subject	NN
37681	1112	37	that	that	IN
37681	1112	38	he	-PRON-	PRP
37681	1112	39	is	be	VBZ
37681	1112	40	teaching	teach	VBG
37681	1112	41	.	.	.
37681	1113	1	If	if	IN
37681	1113	2	,	,	,
37681	1113	3	however	however	RB
37681	1113	4	,	,	,
37681	1113	5	any	any	DT
37681	1113	6	papers	paper	NNS
37681	1113	7	have	have	VBP
37681	1113	8	been	be	VBN
37681	1113	9	submitted	submit	VBN
37681	1113	10	,	,	,
37681	1113	11	about	about	RB
37681	1113	12	five	five	CD
37681	1113	13	minutes	minute	NNS
37681	1113	14	may	may	MD
37681	1113	15	well	well	RB
37681	1113	16	be	be	VB
37681	1113	17	given	give	VBN
37681	1113	18	to	to	IN
37681	1113	19	a	a	DT
37681	1113	20	rapid	rapid	JJ
37681	1113	21	review	review	NN
37681	1113	22	of	of	IN
37681	1113	23	the	the	DT
37681	1113	24	failures	failure	NNS
37681	1113	25	and	and	CC
37681	1113	26	the	the	DT
37681	1113	27	successes	success	NNS
37681	1113	28	.	.	.
37681	1114	1	In	in	IN
37681	1114	2	general	general	JJ
37681	1114	3	,	,	,
37681	1114	4	it	-PRON-	PRP
37681	1114	5	is	be	VBZ
37681	1114	6	good	good	JJ
37681	1114	7	educational	educational	JJ
37681	1114	8	policy	policy	NN
37681	1114	9	to	to	TO
37681	1114	10	speak	speak	VB
37681	1114	11	of	of	IN
37681	1114	12	the	the	DT
37681	1114	13	errors	error	NNS
37681	1114	14	and	and	CC
37681	1114	15	failures	failure	NNS
37681	1114	16	impersonally	impersonally	RB
37681	1114	17	,	,	,
37681	1114	18	but	but	CC
37681	1114	19	occasionally	occasionally	RB
37681	1114	20	to	to	TO
37681	1114	21	mention	mention	VB
37681	1114	22	by	by	IN
37681	1114	23	name	name	NN
37681	1114	24	any	any	DT
37681	1114	25	one	one	NN
37681	1114	26	who	who	WP
37681	1114	27	has	have	VBZ
37681	1114	28	done	do	VBN
37681	1114	29	a	a	DT
37681	1114	30	piece	piece	NN
37681	1114	31	of	of	IN
37681	1114	32	work	work	NN
37681	1114	33	that	that	WDT
37681	1114	34	is	be	VBZ
37681	1114	35	worthy	worthy	JJ
37681	1114	36	of	of	IN
37681	1114	37	special	special	JJ
37681	1114	38	comment	comment	NN
37681	1114	39	.	.	.
37681	1115	1	Pupils	pupil	NNS
37681	1115	2	may	may	MD
37681	1115	3	better	better	RB
37681	1115	4	be	be	VB
37681	1115	5	praised	praise	VBN
37681	1115	6	in	in	IN
37681	1115	7	public	public	NN
37681	1115	8	and	and	CC
37681	1115	9	blamed	blame	VBN
37681	1115	10	in	in	IN
37681	1115	11	private	private	JJ
37681	1115	12	.	.	.
37681	1116	1	There	there	EX
37681	1116	2	is	be	VBZ
37681	1116	3	such	such	PDT
37681	1116	4	a	a	DT
37681	1116	5	thing	thing	NN
37681	1116	6	,	,	,
37681	1116	7	however	however	RB
37681	1116	8	,	,	,
37681	1116	9	as	as	IN
37681	1116	10	praising	praise	VBG
37681	1116	11	too	too	RB
37681	1116	12	much	much	RB
37681	1116	13	,	,	,
37681	1116	14	when	when	WRB
37681	1116	15	nothing	nothing	NN
37681	1116	16	worthy	worthy	JJ
37681	1116	17	of	of	IN
37681	1116	18	note	note	NN
37681	1116	19	has	have	VBZ
37681	1116	20	been	be	VBN
37681	1116	21	done	do	VBN
37681	1116	22	,	,	,
37681	1116	23	just	just	RB
37681	1116	24	as	as	IN
37681	1116	25	there	there	EX
37681	1116	26	is	be	VBZ
37681	1116	27	danger	danger	NN
37681	1116	28	of	of	IN
37681	1116	29	blaming	blame	VBG
37681	1116	30	too	too	RB
37681	1116	31	much	much	RB
37681	1116	32	,	,	,
37681	1116	33	resulting	result	VBG
37681	1116	34	in	in	IN
37681	1116	35	mere	mere	JJ
37681	1116	36	"	"	``
37681	1116	37	nagging	nagging	NN
37681	1116	38	.	.	.
37681	1116	39	"	"	''
37681	1117	1	The	the	DT
37681	1117	2	third	third	JJ
37681	1117	3	division	division	NN
37681	1117	4	of	of	IN
37681	1117	5	the	the	DT
37681	1117	6	recitation	recitation	NN
37681	1117	7	period	period	NN
37681	1117	8	may	may	MD
37681	1117	9	profitably	profitably	RB
37681	1117	10	go	go	VB
37681	1117	11	to	to	IN
37681	1117	12	assigning	assign	VBG
37681	1117	13	the	the	DT
37681	1117	14	advance	advance	NN
37681	1117	15	lesson	lesson	NN
37681	1117	16	.	.	.
37681	1118	1	The	the	DT
37681	1118	2	class	class	NN
37681	1118	3	questions	question	NNS
37681	1118	4	and	and	CC
37681	1118	5	the	the	DT
37681	1118	6	teacher	teacher	NN
37681	1118	7	's	's	POS
37681	1118	8	report	report	NN
37681	1118	9	on	on	IN
37681	1118	10	written	write	VBN
37681	1118	11	work	work	NN
37681	1118	12	have	have	VBP
37681	1118	13	shown	show	VBN
37681	1118	14	the	the	DT
37681	1118	15	mental	mental	JJ
37681	1118	16	status	status	NN
37681	1118	17	of	of	IN
37681	1118	18	the	the	DT
37681	1118	19	pupils	pupil	NNS
37681	1118	20	,	,	,
37681	1118	21	so	so	IN
37681	1118	22	that	that	IN
37681	1118	23	the	the	DT
37681	1118	24	teacher	teacher	NN
37681	1118	25	now	now	RB
37681	1118	26	knows	know	VBZ
37681	1118	27	what	what	WP
37681	1118	28	he	-PRON-	PRP
37681	1118	29	may	may	MD
37681	1118	30	expect	expect	VB
37681	1118	31	for	for	IN
37681	1118	32	the	the	DT
37681	1118	33	next	next	JJ
37681	1118	34	lesson	lesson	NN
37681	1118	35	.	.	.
37681	1119	1	If	if	IN
37681	1119	2	he	-PRON-	PRP
37681	1119	3	assigns	assign	VBZ
37681	1119	4	his	-PRON-	PRP$
37681	1119	5	lesson	lesson	NN
37681	1119	6	at	at	IN
37681	1119	7	the	the	DT
37681	1119	8	beginning	beginning	NN
37681	1119	9	of	of	IN
37681	1119	10	the	the	DT
37681	1119	11	period	period	NN
37681	1119	12	,	,	,
37681	1119	13	he	-PRON-	PRP
37681	1119	14	does	do	VBZ
37681	1119	15	not	not	RB
37681	1119	16	have	have	VB
37681	1119	17	this	this	DT
37681	1119	18	information	information	NN
37681	1119	19	.	.	.
37681	1120	1	If	if	IN
37681	1120	2	he	-PRON-	PRP
37681	1120	3	waits	wait	VBZ
37681	1120	4	to	to	IN
37681	1120	5	the	the	DT
37681	1120	6	end	end	NN
37681	1120	7	,	,	,
37681	1120	8	he	-PRON-	PRP
37681	1120	9	may	may	MD
37681	1120	10	be	be	VB
37681	1120	11	too	too	RB
37681	1120	12	hurried	hurried	JJ
37681	1120	13	to	to	TO
37681	1120	14	give	give	VB
37681	1120	15	any	any	DT
37681	1120	16	"	"	``
37681	1120	17	development	development	NN
37681	1120	18	"	"	''
37681	1120	19	that	that	WDT
37681	1120	20	the	the	DT
37681	1120	21	new	new	JJ
37681	1120	22	lesson	lesson	NN
37681	1120	23	may	may	MD
37681	1120	24	require	require	VB
37681	1120	25	.	.	.
37681	1121	1	There	there	EX
37681	1121	2	can	can	MD
37681	1121	3	be	be	VB
37681	1121	4	no	no	DT
37681	1121	5	rule	rule	NN
37681	1121	6	as	as	IN
37681	1121	7	to	to	IN
37681	1121	8	how	how	WRB
37681	1121	9	to	to	TO
37681	1121	10	assign	assign	VB
37681	1121	11	a	a	DT
37681	1121	12	new	new	JJ
37681	1121	13	lesson	lesson	NN
37681	1121	14	;	;	:
37681	1121	15	it	-PRON-	PRP
37681	1121	16	all	all	DT
37681	1121	17	depends	depend	VBZ
37681	1121	18	upon	upon	IN
37681	1121	19	what	what	WP
37681	1121	20	the	the	DT
37681	1121	21	lesson	lesson	NN
37681	1121	22	is	be	VBZ
37681	1121	23	,	,	,
37681	1121	24	upon	upon	IN
37681	1121	25	the	the	DT
37681	1121	26	mental	mental	JJ
37681	1121	27	state	state	NN
37681	1121	28	of	of	IN
37681	1121	29	the	the	DT
37681	1121	30	class	class	NN
37681	1121	31	,	,	,
37681	1121	32	and	and	CC
37681	1121	33	not	not	RB
37681	1121	34	a	a	DT
37681	1121	35	little	little	JJ
37681	1121	36	upon	upon	IN
37681	1121	37	the	the	DT
37681	1121	38	idiosyncrasy	idiosyncrasy	NN
37681	1121	39	of	of	IN
37681	1121	40	the	the	DT
37681	1121	41	teacher	teacher	NN
37681	1121	42	.	.	.
37681	1122	1	The	the	DT
37681	1122	2	German	german	JJ
37681	1122	3	educator	educator	NN
37681	1122	4	,	,	,
37681	1122	5	Herbart	Herbart	NNP
37681	1122	6	,	,	,
37681	1122	7	laid	lay	VBD
37681	1122	8	down	down	RP
37681	1122	9	certain	certain	JJ
37681	1122	10	formal	formal	JJ
37681	1122	11	steps	step	NNS
37681	1122	12	in	in	IN
37681	1122	13	developing	develop	VBG
37681	1122	14	a	a	DT
37681	1122	15	new	new	JJ
37681	1122	16	lesson	lesson	NN
37681	1122	17	,	,	,
37681	1122	18	and	and	CC
37681	1122	19	his	-PRON-	PRP$
37681	1122	20	successors	successor	NNS
37681	1122	21	have	have	VBP
37681	1122	22	elaborated	elaborate	VBN
37681	1122	23	these	these	DT
37681	1122	24	somewhat	somewhat	RB
37681	1122	25	as	as	IN
37681	1122	26	follows	follow	VBZ
37681	1122	27	:	:	:
37681	1122	28	1	1	CD
37681	1122	29	.	.	.
37681	1123	1	_	_	NNP
37681	1123	2	Aim	Aim	NNP
37681	1123	3	.	.	.
37681	1123	4	_	_	NNP
37681	1123	5	Always	always	RB
37681	1123	6	take	take	VB
37681	1123	7	a	a	DT
37681	1123	8	class	class	NN
37681	1123	9	into	into	IN
37681	1123	10	your	-PRON-	PRP$
37681	1123	11	confidence	confidence	NN
37681	1123	12	.	.	.
37681	1124	1	Tell	tell	VB
37681	1124	2	the	the	DT
37681	1124	3	members	member	NNS
37681	1124	4	at	at	IN
37681	1124	5	the	the	DT
37681	1124	6	outset	outset	NN
37681	1124	7	the	the	DT
37681	1124	8	goal	goal	NN
37681	1124	9	.	.	.
37681	1125	1	No	no	DT
37681	1125	2	one	one	NN
37681	1125	3	likes	like	VBZ
37681	1125	4	to	to	TO
37681	1125	5	be	be	VB
37681	1125	6	led	lead	VBN
37681	1125	7	blindfolded	blindfolded	JJ
37681	1125	8	.	.	.
37681	1126	1	2	2	LS
37681	1126	2	.	.	.
37681	1127	1	_	_	NNP
37681	1127	2	Preparation	Preparation	NNP
37681	1127	3	.	.	.
37681	1127	4	_	_	NNP
37681	1127	5	A	a	DT
37681	1127	6	few	few	JJ
37681	1127	7	brief	brief	JJ
37681	1127	8	questions	question	NNS
37681	1127	9	to	to	TO
37681	1127	10	bring	bring	VB
37681	1127	11	the	the	DT
37681	1127	12	class	class	NN
37681	1127	13	to	to	TO
37681	1127	14	think	think	VB
37681	1127	15	of	of	IN
37681	1127	16	what	what	WP
37681	1127	17	is	be	VBZ
37681	1127	18	to	to	TO
37681	1127	19	be	be	VB
37681	1127	20	considered	consider	VBN
37681	1127	21	.	.	.
37681	1128	1	3	3	LS
37681	1128	2	.	.	.
37681	1129	1	_	_	NNP
37681	1129	2	Presentation	Presentation	NNP
37681	1129	3	of	of	IN
37681	1129	4	the	the	DT
37681	1129	5	new	new	JJ
37681	1129	6	.	.	.
37681	1129	7	_	_	NNP
37681	1129	8	Preferably	preferably	RB
37681	1129	9	this	this	DT
37681	1129	10	is	be	VBZ
37681	1129	11	done	do	VBN
37681	1129	12	by	by	IN
37681	1129	13	questions	question	NNS
37681	1129	14	,	,	,
37681	1129	15	the	the	DT
37681	1129	16	answers	answer	NNS
37681	1129	17	leading	lead	VBG
37681	1129	18	the	the	DT
37681	1129	19	members	member	NNS
37681	1129	20	of	of	IN
37681	1129	21	the	the	DT
37681	1129	22	class	class	NN
37681	1129	23	to	to	TO
37681	1129	24	discover	discover	VB
37681	1129	25	the	the	DT
37681	1129	26	new	new	JJ
37681	1129	27	truth	truth	NN
37681	1129	28	for	for	IN
37681	1129	29	themselves	-PRON-	PRP
37681	1129	30	.	.	.
37681	1130	1	4	4	LS
37681	1130	2	.	.	.
37681	1131	1	_	_	NNP
37681	1131	2	Apperception	Apperception	NNP
37681	1131	3	.	.	.
37681	1131	4	_	_	NNP
37681	1131	5	Calling	call	VBG
37681	1131	6	attention	attention	NN
37681	1131	7	to	to	IN
37681	1131	8	the	the	DT
37681	1131	9	fact	fact	NN
37681	1131	10	that	that	IN
37681	1131	11	this	this	DT
37681	1131	12	new	new	JJ
37681	1131	13	fact	fact	NN
37681	1131	14	was	be	VBD
37681	1131	15	known	know	VBN
37681	1131	16	before	before	IN
37681	1131	17	,	,	,
37681	1131	18	in	in	IN
37681	1131	19	part	part	NN
37681	1131	20	,	,	,
37681	1131	21	and	and	CC
37681	1131	22	that	that	IN
37681	1131	23	it	-PRON-	PRP
37681	1131	24	relates	relate	VBZ
37681	1131	25	to	to	IN
37681	1131	26	a	a	DT
37681	1131	27	number	number	NN
37681	1131	28	of	of	IN
37681	1131	29	things	thing	NNS
37681	1131	30	already	already	RB
37681	1131	31	in	in	IN
37681	1131	32	the	the	DT
37681	1131	33	mind	mind	NN
37681	1131	34	.	.	.
37681	1132	1	The	the	DT
37681	1132	2	more	more	RBR
37681	1132	3	the	the	DT
37681	1132	4	new	new	JJ
37681	1132	5	can	can	MD
37681	1132	6	be	be	VB
37681	1132	7	tied	tie	VBN
37681	1132	8	up	up	RP
37681	1132	9	to	to	IN
37681	1132	10	the	the	DT
37681	1132	11	old	old	JJ
37681	1132	12	the	the	DT
37681	1132	13	more	more	RBR
37681	1132	14	tenaciously	tenaciously	RB
37681	1132	15	it	-PRON-	PRP
37681	1132	16	will	will	MD
37681	1132	17	be	be	VB
37681	1132	18	held	hold	VBN
37681	1132	19	.	.	.
37681	1133	1	5	5	CD
37681	1133	2	.	.	.
37681	1134	1	_	_	NNP
37681	1134	2	Generalization	Generalization	NNP
37681	1134	3	and	and	CC
37681	1134	4	application	application	NN
37681	1134	5	.	.	.
37681	1134	6	_	_	NNP
37681	1134	7	It	-PRON-	PRP
37681	1134	8	is	be	VBZ
37681	1134	9	evident	evident	JJ
37681	1134	10	at	at	IN
37681	1134	11	once	once	RB
37681	1134	12	that	that	IN
37681	1134	13	a	a	DT
37681	1134	14	great	great	JJ
37681	1134	15	deal	deal	NN
37681	1134	16	of	of	IN
37681	1134	17	time	time	NN
37681	1134	18	may	may	MD
37681	1134	19	be	be	VB
37681	1134	20	wasted	waste	VBN
37681	1134	21	in	in	IN
37681	1134	22	always	always	RB
37681	1134	23	following	follow	VBG
37681	1134	24	such	such	PDT
37681	1134	25	a	a	DT
37681	1134	26	plan	plan	NN
37681	1134	27	,	,	,
37681	1134	28	perhaps	perhaps	RB
37681	1134	29	in	in	IN
37681	1134	30	ever	ever	RB
37681	1134	31	following	follow	VBG
37681	1134	32	it	-PRON-	PRP
37681	1134	33	consciously	consciously	RB
37681	1134	34	.	.	.
37681	1135	1	But	but	CC
37681	1135	2	,	,	,
37681	1135	3	on	on	IN
37681	1135	4	the	the	DT
37681	1135	5	other	other	JJ
37681	1135	6	hand	hand	NN
37681	1135	7	,	,	,
37681	1135	8	probably	probably	RB
37681	1135	9	every	every	DT
37681	1135	10	good	good	JJ
37681	1135	11	teacher	teacher	NN
37681	1135	12	,	,	,
37681	1135	13	whether	whether	IN
37681	1135	14	he	-PRON-	PRP
37681	1135	15	has	have	VBZ
37681	1135	16	heard	hear	VBN
37681	1135	17	of	of	IN
37681	1135	18	Herbart	Herbart	NNP
37681	1135	19	or	or	CC
37681	1135	20	not	not	RB
37681	1135	21	,	,	,
37681	1135	22	naturally	naturally	RB
37681	1135	23	covers	cover	VBZ
37681	1135	24	these	these	DT
37681	1135	25	points	point	NNS
37681	1135	26	in	in	IN
37681	1135	27	substantially	substantially	RB
37681	1135	28	this	this	DT
37681	1135	29	order	order	NN
37681	1135	30	.	.	.
37681	1136	1	For	for	IN
37681	1136	2	an	an	DT
37681	1136	3	inexperienced	inexperienced	JJ
37681	1136	4	teacher	teacher	NN
37681	1136	5	it	-PRON-	PRP
37681	1136	6	is	be	VBZ
37681	1136	7	helpful	helpful	JJ
37681	1136	8	to	to	TO
37681	1136	9	be	be	VB
37681	1136	10	familiar	familiar	JJ
37681	1136	11	with	with	IN
37681	1136	12	them	-PRON-	PRP
37681	1136	13	,	,	,
37681	1136	14	that	that	IN
37681	1136	15	he	-PRON-	PRP
37681	1136	16	may	may	MD
37681	1136	17	call	call	VB
37681	1136	18	to	to	TO
37681	1136	19	mind	mind	VB
37681	1136	20	the	the	DT
37681	1136	21	steps	step	NNS
37681	1136	22	,	,	,
37681	1136	23	arranged	arrange	VBN
37681	1136	24	in	in	IN
37681	1136	25	a	a	DT
37681	1136	26	psychological	psychological	JJ
37681	1136	27	sequence	sequence	NN
37681	1136	28	,	,	,
37681	1136	29	that	that	IN
37681	1136	30	he	-PRON-	PRP
37681	1136	31	would	would	MD
37681	1136	32	do	do	VB
37681	1136	33	well	well	RB
37681	1136	34	to	to	TO
37681	1136	35	follow	follow	VB
37681	1136	36	.	.	.
37681	1137	1	It	-PRON-	PRP
37681	1137	2	must	must	MD
37681	1137	3	always	always	RB
37681	1137	4	be	be	VB
37681	1137	5	remembered	remember	VBN
37681	1137	6	that	that	IN
37681	1137	7	there	there	EX
37681	1137	8	is	be	VBZ
37681	1137	9	quite	quite	RB
37681	1137	10	as	as	RB
37681	1137	11	much	much	JJ
37681	1137	12	danger	danger	NN
37681	1137	13	in	in	IN
37681	1137	14	"	"	``
37681	1137	15	developing	develop	VBG
37681	1137	16	"	"	''
37681	1137	17	too	too	RB
37681	1137	18	much	much	JJ
37681	1137	19	as	as	IN
37681	1137	20	in	in	IN
37681	1137	21	taking	take	VBG
37681	1137	22	the	the	DT
37681	1137	23	opposite	opposite	JJ
37681	1137	24	extreme	extreme	NN
37681	1137	25	.	.	.
37681	1138	1	A	a	DT
37681	1138	2	mechanical	mechanical	JJ
37681	1138	3	teacher	teacher	NN
37681	1138	4	may	may	MD
37681	1138	5	develop	develop	VB
37681	1138	6	a	a	DT
37681	1138	7	new	new	JJ
37681	1138	8	lesson	lesson	NN
37681	1138	9	where	where	WRB
37681	1138	10	there	there	EX
37681	1138	11	is	be	VBZ
37681	1138	12	need	need	NN
37681	1138	13	for	for	IN
37681	1138	14	only	only	RB
37681	1138	15	a	a	DT
37681	1138	16	question	question	NN
37681	1138	17	or	or	CC
37681	1138	18	two	two	CD
37681	1138	19	or	or	CC
37681	1138	20	a	a	DT
37681	1138	21	mere	mere	JJ
37681	1138	22	suggestion	suggestion	NN
37681	1138	23	.	.	.
37681	1139	1	It	-PRON-	PRP
37681	1139	2	should	should	MD
37681	1139	3	also	also	RB
37681	1139	4	be	be	VB
37681	1139	5	recognized	recognize	VBN
37681	1139	6	that	that	IN
37681	1139	7	students	student	NNS
37681	1139	8	need	need	VBP
37681	1139	9	to	to	TO
37681	1139	10	learn	learn	VB
37681	1139	11	to	to	TO
37681	1139	12	read	read	VB
37681	1139	13	mathematics	mathematic	NNS
37681	1139	14	for	for	IN
37681	1139	15	themselves	-PRON-	PRP
37681	1139	16	,	,	,
37681	1139	17	and	and	CC
37681	1139	18	that	that	IN
37681	1139	19	always	always	RB
37681	1139	20	to	to	TO
37681	1139	21	take	take	VB
37681	1139	22	away	away	RB
37681	1139	23	every	every	DT
37681	1139	24	difficulty	difficulty	NN
37681	1139	25	by	by	IN
37681	1139	26	explanations	explanation	NNS
37681	1139	27	given	give	VBN
37681	1139	28	in	in	IN
37681	1139	29	advance	advance	NN
37681	1139	30	is	be	VBZ
37681	1139	31	weakening	weaken	VBG
37681	1139	32	to	to	IN
37681	1139	33	any	any	DT
37681	1139	34	one	one	CD
37681	1139	35	.	.	.
37681	1140	1	Therefore	therefore	RB
37681	1140	2	,	,	,
37681	1140	3	in	in	IN
37681	1140	4	assigning	assign	VBG
37681	1140	5	the	the	DT
37681	1140	6	new	new	JJ
37681	1140	7	lesson	lesson	NN
37681	1140	8	we	-PRON-	PRP
37681	1140	9	may	may	MD
37681	1140	10	say	say	VB
37681	1140	11	"	"	``
37681	1140	12	Take	take	VB
37681	1140	13	the	the	DT
37681	1140	14	next	next	JJ
37681	1140	15	two	two	CD
37681	1140	16	pages	page	NNS
37681	1140	17	,	,	,
37681	1140	18	"	"	''
37681	1140	19	and	and	CC
37681	1140	20	thus	thus	RB
37681	1140	21	discourage	discourage	VB
37681	1140	22	most	most	JJS
37681	1140	23	of	of	IN
37681	1140	24	the	the	DT
37681	1140	25	class	class	NN
37681	1140	26	.	.	.
37681	1141	1	On	on	IN
37681	1141	2	the	the	DT
37681	1141	3	other	other	JJ
37681	1141	4	hand	hand	NN
37681	1141	5	,	,	,
37681	1141	6	we	-PRON-	PRP
37681	1141	7	may	may	MD
37681	1141	8	spend	spend	VB
37681	1141	9	an	an	DT
37681	1141	10	unnecessary	unnecessary	JJ
37681	1141	11	amount	amount	NN
37681	1141	12	of	of	IN
37681	1141	13	time	time	NN
37681	1141	14	and	and	CC
37681	1141	15	overdevelop	overdevelop	VB
37681	1141	16	the	the	DT
37681	1141	17	work	work	NN
37681	1141	18	of	of	IN
37681	1141	19	those	those	DT
37681	1141	20	same	same	JJ
37681	1141	21	pages	page	NNS
37681	1141	22	,	,	,
37681	1141	23	and	and	CC
37681	1141	24	have	have	VB
37681	1141	25	the	the	DT
37681	1141	26	whole	whole	JJ
37681	1141	27	lesson	lesson	NN
37681	1141	28	lose	lose	VB
37681	1141	29	all	all	DT
37681	1141	30	its	-PRON-	PRP$
37681	1141	31	zest	zest	NN
37681	1141	32	.	.	.
37681	1142	1	It	-PRON-	PRP
37681	1142	2	is	be	VBZ
37681	1142	3	here	here	RB
37681	1142	4	that	that	IN
37681	1142	5	the	the	DT
37681	1142	6	genius	genius	NN
37681	1142	7	of	of	IN
37681	1142	8	the	the	DT
37681	1142	9	teacher	teacher	NN
37681	1142	10	comes	come	VBZ
37681	1142	11	forth	forth	RB
37681	1142	12	to	to	TO
37681	1142	13	find	find	VB
37681	1142	14	the	the	DT
37681	1142	15	happy	happy	JJ
37681	1142	16	mean	mean	NN
37681	1142	17	.	.	.
37681	1143	1	The	the	DT
37681	1143	2	fourth	fourth	JJ
37681	1143	3	division	division	NN
37681	1143	4	of	of	IN
37681	1143	5	the	the	DT
37681	1143	6	hour	hour	NN
37681	1143	7	should	should	MD
37681	1143	8	be	be	VB
37681	1143	9	reached	reach	VBN
37681	1143	10	,	,	,
37681	1143	11	in	in	IN
37681	1143	12	general	general	JJ
37681	1143	13	,	,	,
37681	1143	14	in	in	IN
37681	1143	15	about	about	RB
37681	1143	16	ten	ten	CD
37681	1143	17	minutes	minute	NNS
37681	1143	18	.	.	.
37681	1144	1	This	this	DT
37681	1144	2	includes	include	VBZ
37681	1144	3	the	the	DT
37681	1144	4	recitation	recitation	NN
37681	1144	5	proper	proper	JJ
37681	1144	6	.	.	.
37681	1145	1	But	but	CC
37681	1145	2	as	as	IN
37681	1145	3	to	to	IN
37681	1145	4	the	the	DT
37681	1145	5	nature	nature	NN
37681	1145	6	of	of	IN
37681	1145	7	this	this	DT
37681	1145	8	work	work	NN
37681	1145	9	no	no	DT
37681	1145	10	definite	definite	JJ
37681	1145	11	instructions	instruction	NNS
37681	1145	12	should	should	MD
37681	1145	13	be	be	VB
37681	1145	14	attempted	attempt	VBN
37681	1145	15	.	.	.
37681	1146	1	To	to	IN
37681	1146	2	a	a	DT
37681	1146	3	good	good	JJ
37681	1146	4	teacher	teacher	NN
37681	1146	5	they	-PRON-	PRP
37681	1146	6	would	would	MD
37681	1146	7	be	be	VB
37681	1146	8	unnecessary	unnecessary	JJ
37681	1146	9	,	,	,
37681	1146	10	to	to	IN
37681	1146	11	a	a	DT
37681	1146	12	poor	poor	JJ
37681	1146	13	one	one	NN
37681	1146	14	they	-PRON-	PRP
37681	1146	15	would	would	MD
37681	1146	16	be	be	VB
37681	1146	17	harmful	harmful	JJ
37681	1146	18	.	.	.
37681	1147	1	Part	part	NN
37681	1147	2	of	of	IN
37681	1147	3	the	the	DT
37681	1147	4	class	class	NN
37681	1147	5	may	may	MD
37681	1147	6	go	go	VB
37681	1147	7	to	to	IN
37681	1147	8	the	the	DT
37681	1147	9	board	board	NN
37681	1147	10	,	,	,
37681	1147	11	and	and	CC
37681	1147	12	as	as	IN
37681	1147	13	they	-PRON-	PRP
37681	1147	14	are	be	VBP
37681	1147	15	working	work	VBG
37681	1147	16	,	,	,
37681	1147	17	the	the	DT
37681	1147	18	rest	rest	NN
37681	1147	19	may	may	MD
37681	1147	20	be	be	VB
37681	1147	21	reciting	recite	VBG
37681	1147	22	.	.	.
37681	1148	1	Those	those	DT
37681	1148	2	at	at	IN
37681	1148	3	the	the	DT
37681	1148	4	board	board	NN
37681	1148	5	should	should	MD
37681	1148	6	be	be	VB
37681	1148	7	limited	limit	VBN
37681	1148	8	as	as	IN
37681	1148	9	to	to	IN
37681	1148	10	time	time	NN
37681	1148	11	,	,	,
37681	1148	12	for	for	IN
37681	1148	13	otherwise	otherwise	RB
37681	1148	14	a	a	DT
37681	1148	15	premium	premium	NN
37681	1148	16	is	be	VBZ
37681	1148	17	placed	place	VBN
37681	1148	18	on	on	IN
37681	1148	19	mere	mere	JJ
37681	1148	20	dawdling	dawdling	NN
37681	1148	21	.	.	.
37681	1149	1	They	-PRON-	PRP
37681	1149	2	should	should	MD
37681	1149	3	be	be	VB
37681	1149	4	so	so	RB
37681	1149	5	arranged	arrange	VBN
37681	1149	6	as	as	IN
37681	1149	7	to	to	TO
37681	1149	8	prevent	prevent	VB
37681	1149	9	copying	copying	NN
37681	1149	10	,	,	,
37681	1149	11	but	but	CC
37681	1149	12	the	the	DT
37681	1149	13	teacher	teacher	NN
37681	1149	14	's	's	POS
37681	1149	15	eye	eye	NN
37681	1149	16	is	be	VBZ
37681	1149	17	the	the	DT
37681	1149	18	best	good	JJS
37681	1149	19	preventive	preventive	NN
37681	1149	20	of	of	IN
37681	1149	21	this	this	DT
37681	1149	22	annoying	annoying	JJ
37681	1149	23	feature	feature	NN
37681	1149	24	.	.	.
37681	1150	1	Those	those	DT
37681	1150	2	at	at	IN
37681	1150	3	their	-PRON-	PRP$
37681	1150	4	seats	seat	NNS
37681	1150	5	may	may	MD
37681	1150	6	be	be	VB
37681	1150	7	called	call	VBN
37681	1150	8	upon	upon	IN
37681	1150	9	one	one	CD
37681	1150	10	at	at	IN
37681	1150	11	a	a	DT
37681	1150	12	time	time	NN
37681	1150	13	to	to	TO
37681	1150	14	demonstrate	demonstrate	VB
37681	1150	15	at	at	IN
37681	1150	16	the	the	DT
37681	1150	17	blackboard	blackboard	NN
37681	1150	18	,	,	,
37681	1150	19	the	the	DT
37681	1150	20	rest	rest	NN
37681	1150	21	being	being	NN
37681	1150	22	called	call	VBN
37681	1150	23	upon	upon	IN
37681	1150	24	for	for	IN
37681	1150	25	quick	quick	JJ
37681	1150	26	responses	response	NNS
37681	1150	27	,	,	,
37681	1150	28	as	as	IN
37681	1150	29	occasion	occasion	NN
37681	1150	30	demands	demand	VBZ
37681	1150	31	.	.	.
37681	1151	1	The	the	DT
37681	1151	2	European	european	JJ
37681	1151	3	plan	plan	NN
37681	1151	4	of	of	IN
37681	1151	5	having	have	VBG
37681	1151	6	small	small	JJ
37681	1151	7	blackboards	blackboard	NNS
37681	1151	8	is	be	VBZ
37681	1151	9	in	in	IN
37681	1151	10	many	many	JJ
37681	1151	11	respects	respect	NNS
37681	1151	12	better	well	RBR
37681	1151	13	than	than	IN
37681	1151	14	ours	our	NNS
37681	1151	15	,	,	,
37681	1151	16	since	since	IN
37681	1151	17	pupils	pupil	NNS
37681	1151	18	can	can	MD
37681	1151	19	not	not	RB
37681	1151	20	so	so	RB
37681	1151	21	easily	easily	RB
37681	1151	22	waste	waste	VB
37681	1151	23	time	time	NN
37681	1151	24	.	.	.
37681	1152	1	They	-PRON-	PRP
37681	1152	2	have	have	VBP
37681	1152	3	to	to	TO
37681	1152	4	work	work	VB
37681	1152	5	rapidly	rapidly	RB
37681	1152	6	and	and	CC
37681	1152	7	talk	talk	VB
37681	1152	8	rapidly	rapidly	RB
37681	1152	9	,	,	,
37681	1152	10	or	or	CC
37681	1152	11	else	else	RB
37681	1152	12	take	take	VBP
37681	1152	13	their	-PRON-	PRP$
37681	1152	14	seats	seat	NNS
37681	1152	15	.	.	.
37681	1153	1	What	what	WP
37681	1153	2	should	should	MD
37681	1153	3	be	be	VB
37681	1153	4	put	put	VBN
37681	1153	5	on	on	IN
37681	1153	6	the	the	DT
37681	1153	7	board	board	NN
37681	1153	8	,	,	,
37681	1153	9	whether	whether	IN
37681	1153	10	the	the	DT
37681	1153	11	figure	figure	NN
37681	1153	12	alone	alone	RB
37681	1153	13	,	,	,
37681	1153	14	or	or	CC
37681	1153	15	the	the	DT
37681	1153	16	figure	figure	NN
37681	1153	17	and	and	CC
37681	1153	18	the	the	DT
37681	1153	19	proof	proof	NN
37681	1153	20	,	,	,
37681	1153	21	depends	depend	VBZ
37681	1153	22	upon	upon	IN
37681	1153	23	the	the	DT
37681	1153	24	proposition	proposition	NN
37681	1153	25	.	.	.
37681	1154	1	In	in	IN
37681	1154	2	general	general	JJ
37681	1154	3	,	,	,
37681	1154	4	there	there	EX
37681	1154	5	should	should	MD
37681	1154	6	be	be	VB
37681	1154	7	a	a	DT
37681	1154	8	certain	certain	JJ
37681	1154	9	number	number	NN
37681	1154	10	of	of	IN
37681	1154	11	figures	figure	NNS
37681	1154	12	put	put	VBN
37681	1154	13	on	on	IN
37681	1154	14	the	the	DT
37681	1154	15	board	board	NN
37681	1154	16	for	for	IN
37681	1154	17	the	the	DT
37681	1154	18	sake	sake	NN
37681	1154	19	of	of	IN
37681	1154	20	rapid	rapid	JJ
37681	1154	21	work	work	NN
37681	1154	22	and	and	CC
37681	1154	23	as	as	IN
37681	1154	24	a	a	DT
37681	1154	25	basis	basis	NN
37681	1154	26	for	for	IN
37681	1154	27	the	the	DT
37681	1154	28	proofs	proof	NNS
37681	1154	29	of	of	IN
37681	1154	30	the	the	DT
37681	1154	31	day	day	NN
37681	1154	32	.	.	.
37681	1155	1	There	there	EX
37681	1155	2	should	should	MD
37681	1155	3	also	also	RB
37681	1155	4	be	be	VB
37681	1155	5	a	a	DT
37681	1155	6	certain	certain	JJ
37681	1155	7	amount	amount	NN
37681	1155	8	of	of	IN
37681	1155	9	written	write	VBN
37681	1155	10	work	work	NN
37681	1155	11	for	for	IN
37681	1155	12	the	the	DT
37681	1155	13	sake	sake	NN
37681	1155	14	of	of	IN
37681	1155	15	commending	commending	NN
37681	1155	16	or	or	CC
37681	1155	17	of	of	IN
37681	1155	18	criticizing	criticize	VBG
37681	1155	19	adversely	adversely	RB
37681	1155	20	the	the	DT
37681	1155	21	proof	proof	NN
37681	1155	22	used	use	VBD
37681	1155	23	.	.	.
37681	1156	1	There	there	EX
37681	1156	2	are	be	VBP
37681	1156	3	some	some	DT
37681	1156	4	figures	figure	NNS
37681	1156	5	that	that	WDT
37681	1156	6	are	be	VBP
37681	1156	7	so	so	RB
37681	1156	8	complicated	complicated	JJ
37681	1156	9	as	as	IN
37681	1156	10	to	to	TO
37681	1156	11	warrant	warrant	VB
37681	1156	12	being	be	VBG
37681	1156	13	put	put	VBN
37681	1156	14	upon	upon	IN
37681	1156	15	sheets	sheet	NNS
37681	1156	16	of	of	IN
37681	1156	17	paper	paper	NN
37681	1156	18	and	and	CC
37681	1156	19	hung	hang	VBD
37681	1156	20	before	before	IN
37681	1156	21	the	the	DT
37681	1156	22	class	class	NN
37681	1156	23	.	.	.
37681	1157	1	Thus	thus	RB
37681	1157	2	there	there	EX
37681	1157	3	is	be	VBZ
37681	1157	4	no	no	DT
37681	1157	5	rule	rule	NN
37681	1157	6	upon	upon	IN
37681	1157	7	the	the	DT
37681	1157	8	subject	subject	NN
37681	1157	9	,	,	,
37681	1157	10	and	and	CC
37681	1157	11	the	the	DT
37681	1157	12	teacher	teacher	NN
37681	1157	13	must	must	MD
37681	1157	14	use	use	VB
37681	1157	15	his	-PRON-	PRP$
37681	1157	16	judgment	judgment	NN
37681	1157	17	according	accord	VBG
37681	1157	18	to	to	IN
37681	1157	19	the	the	DT
37681	1157	20	circumstances	circumstance	NNS
37681	1157	21	and	and	CC
37681	1157	22	the	the	DT
37681	1157	23	propositions	proposition	NNS
37681	1157	24	.	.	.
37681	1158	1	If	if	IN
37681	1158	2	the	the	DT
37681	1158	3	early	early	JJ
37681	1158	4	"	"	``
37681	1158	5	originals	original	NNS
37681	1158	6	"	"	''
37681	1158	7	are	be	VBP
37681	1158	8	one	one	CD
37681	1158	9	-	-	HYPH
37681	1158	10	step	step	NN
37681	1158	11	exercises	exercise	NNS
37681	1158	12	,	,	,
37681	1158	13	and	and	CC
37681	1158	14	a	a	DT
37681	1158	15	pupil	pupil	NN
37681	1158	16	is	be	VBZ
37681	1158	17	required	require	VBN
37681	1158	18	to	to	TO
37681	1158	19	recite	recite	VB
37681	1158	20	rapidly	rapidly	RB
37681	1158	21	,	,	,
37681	1158	22	a	a	DT
37681	1158	23	habit	habit	NN
37681	1158	24	of	of	IN
37681	1158	25	quick	quick	JJ
37681	1158	26	expression	expression	NN
37681	1158	27	is	be	VBZ
37681	1158	28	easily	easily	RB
37681	1158	29	acquired	acquire	VBN
37681	1158	30	that	that	IN
37681	1158	31	leads	lead	VBZ
37681	1158	32	to	to	TO
37681	1158	33	close	close	VB
37681	1158	34	attention	attention	NN
37681	1158	35	on	on	IN
37681	1158	36	the	the	DT
37681	1158	37	part	part	NN
37681	1158	38	of	of	IN
37681	1158	39	all	all	PDT
37681	1158	40	the	the	DT
37681	1158	41	class	class	NN
37681	1158	42	.	.	.
37681	1159	1	Students	student	NNS
37681	1159	2	as	as	IN
37681	1159	3	a	a	DT
37681	1159	4	rule	rule	NN
37681	1159	5	recite	recite	NN
37681	1159	6	slower	slow	JJR
37681	1159	7	than	than	IN
37681	1159	8	they	-PRON-	PRP
37681	1159	9	need	need	VBP
37681	1159	10	to	to	TO
37681	1159	11	,	,	,
37681	1159	12	from	from	IN
37681	1159	13	mere	mere	JJ
37681	1159	14	habit	habit	NN
37681	1159	15	.	.	.
37681	1160	1	Phlegmatic	phlegmatic	JJ
37681	1160	2	as	as	IN
37681	1160	3	we	-PRON-	PRP
37681	1160	4	think	think	VBP
37681	1160	5	the	the	DT
37681	1160	6	German	German	NNP
37681	1160	7	is	be	VBZ
37681	1160	8	,	,	,
37681	1160	9	and	and	CC
37681	1160	10	nervous	nervous	JJ
37681	1160	11	as	as	IN
37681	1160	12	is	be	VBZ
37681	1160	13	the	the	DT
37681	1160	14	American	american	JJ
37681	1160	15	temperament	temperament	NN
37681	1160	16	,	,	,
37681	1160	17	a	a	DT
37681	1160	18	student	student	NN
37681	1160	19	in	in	IN
37681	1160	20	geometry	geometry	NN
37681	1160	21	in	in	IN
37681	1160	22	a	a	DT
37681	1160	23	German	german	JJ
37681	1160	24	school	school	NN
37681	1160	25	will	will	MD
37681	1160	26	usually	usually	RB
37681	1160	27	recite	recite	VB
37681	1160	28	more	more	RBR
37681	1160	29	quickly	quickly	RB
37681	1160	30	and	and	CC
37681	1160	31	with	with	IN
37681	1160	32	more	more	JJR
37681	1160	33	vigor	vigor	NN
37681	1160	34	than	than	IN
37681	1160	35	one	one	CD
37681	1160	36	with	with	IN
37681	1160	37	us	-PRON-	PRP
37681	1160	38	.	.	.
37681	1161	1	Our	-PRON-	PRP$
37681	1161	2	extensive	extensive	JJ
37681	1161	3	blackboards	blackboard	NNS
37681	1161	4	have	have	VBP
37681	1161	5	something	something	NN
37681	1161	6	to	to	TO
37681	1161	7	do	do	VB
37681	1161	8	with	with	IN
37681	1161	9	this	this	DT
37681	1161	10	,	,	,
37681	1161	11	allowing	allow	VBG
37681	1161	12	so	so	RB
37681	1161	13	many	many	JJ
37681	1161	14	pupils	pupil	NNS
37681	1161	15	to	to	TO
37681	1161	16	be	be	VB
37681	1161	17	working	work	VBG
37681	1161	18	at	at	IN
37681	1161	19	the	the	DT
37681	1161	20	board	board	NN
37681	1161	21	that	that	WDT
37681	1161	22	a	a	DT
37681	1161	23	teacher	teacher	NN
37681	1161	24	can	can	MD
37681	1161	25	not	not	RB
37681	1161	26	attend	attend	VB
37681	1161	27	to	to	IN
37681	1161	28	them	-PRON-	PRP
37681	1161	29	all	all	DT
37681	1161	30	.	.	.
37681	1162	1	The	the	DT
37681	1162	2	result	result	NN
37681	1162	3	is	be	VBZ
37681	1162	4	a	a	DT
37681	1162	5	habit	habit	NN
37681	1162	6	of	of	IN
37681	1162	7	wasting	waste	VBG
37681	1162	8	the	the	DT
37681	1162	9	minutes	minute	NNS
37681	1162	10	that	that	WDT
37681	1162	11	can	can	MD
37681	1162	12	only	only	RB
37681	1162	13	be	be	VB
37681	1162	14	overcome	overcome	VBN
37681	1162	15	by	by	IN
37681	1162	16	the	the	DT
37681	1162	17	teacher	teacher	NN
37681	1162	18	setting	set	VBG
37681	1162	19	a	a	DT
37681	1162	20	definite	definite	JJ
37681	1162	21	but	but	CC
37681	1162	22	reasonable	reasonable	JJ
37681	1162	23	time	time	NN
37681	1162	24	limit	limit	NN
37681	1162	25	,	,	,
37681	1162	26	and	and	CC
37681	1162	27	holding	hold	VBG
37681	1162	28	the	the	DT
37681	1162	29	pupil	pupil	NN
37681	1162	30	responsible	responsible	JJ
37681	1162	31	if	if	IN
37681	1162	32	the	the	DT
37681	1162	33	work	work	NN
37681	1162	34	is	be	VBZ
37681	1162	35	not	not	RB
37681	1162	36	done	do	VBN
37681	1162	37	in	in	IN
37681	1162	38	the	the	DT
37681	1162	39	time	time	NN
37681	1162	40	specified	specify	VBD
37681	1162	41	.	.	.
37681	1163	1	If	if	IN
37681	1163	2	this	this	DT
37681	1163	3	matter	matter	NN
37681	1163	4	is	be	VBZ
37681	1163	5	taken	take	VBN
37681	1163	6	in	in	IN
37681	1163	7	hand	hand	NN
37681	1163	8	the	the	DT
37681	1163	9	first	first	JJ
37681	1163	10	day	day	NN
37681	1163	11	,	,	,
37681	1163	12	and	and	CC
37681	1163	13	special	special	JJ
37681	1163	14	effort	effort	NN
37681	1163	15	made	make	VBN
37681	1163	16	in	in	IN
37681	1163	17	the	the	DT
37681	1163	18	early	early	JJ
37681	1163	19	weeks	week	NNS
37681	1163	20	of	of	IN
37681	1163	21	the	the	DT
37681	1163	22	year	year	NN
37681	1163	23	,	,	,
37681	1163	24	much	much	JJ
37681	1163	25	of	of	IN
37681	1163	26	the	the	DT
37681	1163	27	difficulty	difficulty	NN
37681	1163	28	can	can	MD
37681	1163	29	be	be	VB
37681	1163	30	overcome	overcome	VBN
37681	1163	31	.	.	.
37681	1164	1	As	as	IN
37681	1164	2	to	to	IN
37681	1164	3	the	the	DT
37681	1164	4	nature	nature	NN
37681	1164	5	of	of	IN
37681	1164	6	the	the	DT
37681	1164	7	recitation	recitation	NN
37681	1164	8	to	to	TO
37681	1164	9	be	be	VB
37681	1164	10	expected	expect	VBN
37681	1164	11	from	from	IN
37681	1164	12	the	the	DT
37681	1164	13	pupil	pupil	NN
37681	1164	14	,	,	,
37681	1164	15	no	no	DT
37681	1164	16	definite	definite	JJ
37681	1164	17	rule	rule	NN
37681	1164	18	can	can	MD
37681	1164	19	be	be	VB
37681	1164	20	laid	lay	VBN
37681	1164	21	down	down	RP
37681	1164	22	,	,	,
37681	1164	23	since	since	IN
37681	1164	24	it	-PRON-	PRP
37681	1164	25	varies	vary	VBZ
37681	1164	26	so	so	RB
37681	1164	27	much	much	RB
37681	1164	28	with	with	IN
37681	1164	29	the	the	DT
37681	1164	30	work	work	NN
37681	1164	31	of	of	IN
37681	1164	32	the	the	DT
37681	1164	33	day	day	NN
37681	1164	34	.	.	.
37681	1165	1	In	in	IN
37681	1165	2	general	general	JJ
37681	1165	3	,	,	,
37681	1165	4	however	however	RB
37681	1165	5	,	,	,
37681	1165	6	a	a	DT
37681	1165	7	pupil	pupil	NN
37681	1165	8	should	should	MD
37681	1165	9	state	state	VB
37681	1165	10	the	the	DT
37681	1165	11	theorem	theorem	NN
37681	1165	12	quickly	quickly	RB
37681	1165	13	,	,	,
37681	1165	14	state	state	NN
37681	1165	15	exactly	exactly	RB
37681	1165	16	what	what	WP
37681	1165	17	is	be	VBZ
37681	1165	18	given	give	VBN
37681	1165	19	and	and	CC
37681	1165	20	what	what	WP
37681	1165	21	is	be	VBZ
37681	1165	22	to	to	TO
37681	1165	23	be	be	VB
37681	1165	24	proved	prove	VBN
37681	1165	25	,	,	,
37681	1165	26	with	with	IN
37681	1165	27	respect	respect	NN
37681	1165	28	to	to	IN
37681	1165	29	the	the	DT
37681	1165	30	figure	figure	NN
37681	1165	31	,	,	,
37681	1165	32	and	and	CC
37681	1165	33	then	then	RB
37681	1165	34	give	give	VB
37681	1165	35	the	the	DT
37681	1165	36	proof	proof	NN
37681	1165	37	.	.	.
37681	1166	1	At	at	IN
37681	1166	2	first	first	RB
37681	1166	3	it	-PRON-	PRP
37681	1166	4	is	be	VBZ
37681	1166	5	desirable	desirable	JJ
37681	1166	6	that	that	IN
37681	1166	7	he	-PRON-	PRP
37681	1166	8	should	should	MD
37681	1166	9	give	give	VB
37681	1166	10	the	the	DT
37681	1166	11	authorities	authority	NNS
37681	1166	12	in	in	IN
37681	1166	13	full	full	JJ
37681	1166	14	,	,	,
37681	1166	15	and	and	CC
37681	1166	16	later	later	RB
37681	1166	17	give	give	VB
37681	1166	18	only	only	RB
37681	1166	19	the	the	DT
37681	1166	20	essential	essential	JJ
37681	1166	21	part	part	NN
37681	1166	22	in	in	IN
37681	1166	23	a	a	DT
37681	1166	24	few	few	JJ
37681	1166	25	words	word	NNS
37681	1166	26	.	.	.
37681	1167	1	It	-PRON-	PRP
37681	1167	2	is	be	VBZ
37681	1167	3	better	well	JJR
37681	1167	4	to	to	TO
37681	1167	5	avoid	avoid	VB
37681	1167	6	the	the	DT
37681	1167	7	expression	expression	NN
37681	1167	8	"	"	''
37681	1167	9	by	by	IN
37681	1167	10	previous	previous	JJ
37681	1167	11	proposition	proposition	NN
37681	1167	12	,	,	,
37681	1167	13	"	"	''
37681	1167	14	for	for	IN
37681	1167	15	it	-PRON-	PRP
37681	1167	16	soon	soon	RB
37681	1167	17	comes	come	VBZ
37681	1167	18	to	to	TO
37681	1167	19	be	be	VB
37681	1167	20	abused	abuse	VBN
37681	1167	21	,	,	,
37681	1167	22	and	and	CC
37681	1167	23	of	of	IN
37681	1167	24	course	course	NN
37681	1167	25	the	the	DT
37681	1167	26	learning	learning	NN
37681	1167	27	of	of	IN
37681	1167	28	section	section	NN
37681	1167	29	numbers	number	NNS
37681	1167	30	in	in	IN
37681	1167	31	a	a	DT
37681	1167	32	book	book	NN
37681	1167	33	is	be	VBZ
37681	1167	34	a	a	DT
37681	1167	35	barbarism	barbarism	NN
37681	1167	36	.	.	.
37681	1168	1	It	-PRON-	PRP
37681	1168	2	is	be	VBZ
37681	1168	3	only	only	RB
37681	1168	4	by	by	IN
37681	1168	5	continually	continually	RB
37681	1168	6	stating	state	VBG
37681	1168	7	the	the	DT
37681	1168	8	propositions	proposition	NNS
37681	1168	9	used	use	VBN
37681	1168	10	that	that	IN
37681	1168	11	a	a	DT
37681	1168	12	pupil	pupil	NN
37681	1168	13	comes	come	VBZ
37681	1168	14	to	to	TO
37681	1168	15	have	have	VB
37681	1168	16	well	well	RB
37681	1168	17	fixed	fix	VBN
37681	1168	18	in	in	IN
37681	1168	19	his	-PRON-	PRP$
37681	1168	20	memory	memory	NN
37681	1168	21	the	the	DT
37681	1168	22	basal	basal	NN
37681	1168	23	theorems	theorem	NNS
37681	1168	24	of	of	IN
37681	1168	25	geometry	geometry	NN
37681	1168	26	,	,	,
37681	1168	27	and	and	CC
37681	1168	28	without	without	IN
37681	1168	29	these	these	DT
37681	1168	30	he	-PRON-	PRP
37681	1168	31	can	can	MD
37681	1168	32	not	not	RB
37681	1168	33	make	make	VB
37681	1168	34	progress	progress	NN
37681	1168	35	in	in	IN
37681	1168	36	his	-PRON-	PRP$
37681	1168	37	subsequent	subsequent	JJ
37681	1168	38	mathematics	mathematic	NNS
37681	1168	39	.	.	.
37681	1169	1	In	in	IN
37681	1169	2	general	general	JJ
37681	1169	3	,	,	,
37681	1169	4	it	-PRON-	PRP
37681	1169	5	is	be	VBZ
37681	1169	6	better	well	JJR
37681	1169	7	to	to	TO
37681	1169	8	allow	allow	VB
37681	1169	9	a	a	DT
37681	1169	10	pupil	pupil	NN
37681	1169	11	to	to	TO
37681	1169	12	finish	finish	VB
37681	1169	13	his	-PRON-	PRP$
37681	1169	14	proof	proof	NN
37681	1169	15	before	before	IN
37681	1169	16	asking	ask	VBG
37681	1169	17	him	-PRON-	PRP
37681	1169	18	any	any	DT
37681	1169	19	questions	question	NNS
37681	1169	20	,	,	,
37681	1169	21	the	the	DT
37681	1169	22	constant	constant	JJ
37681	1169	23	interruptions	interruption	NNS
37681	1169	24	indulged	indulge	VBN
37681	1169	25	in	in	RP
37681	1169	26	by	by	IN
37681	1169	27	some	some	DT
37681	1169	28	teachers	teacher	NNS
37681	1169	29	being	be	VBG
37681	1169	30	the	the	DT
37681	1169	31	cause	cause	NN
37681	1169	32	of	of	IN
37681	1169	33	no	no	DT
37681	1169	34	little	little	JJ
37681	1169	35	confusion	confusion	NN
37681	1169	36	and	and	CC
37681	1169	37	hesitancy	hesitancy	NN
37681	1169	38	on	on	IN
37681	1169	39	the	the	DT
37681	1169	40	part	part	NN
37681	1169	41	of	of	IN
37681	1169	42	pupils	pupil	NNS
37681	1169	43	.	.	.
37681	1170	1	Sometimes	sometimes	RB
37681	1170	2	it	-PRON-	PRP
37681	1170	3	is	be	VBZ
37681	1170	4	well	well	JJ
37681	1170	5	to	to	TO
37681	1170	6	have	have	VB
37681	1170	7	a	a	DT
37681	1170	8	figure	figure	NN
37681	1170	9	drawn	draw	VBN
37681	1170	10	differently	differently	RB
37681	1170	11	from	from	IN
37681	1170	12	the	the	DT
37681	1170	13	one	one	CD
37681	1170	14	in	in	IN
37681	1170	15	the	the	DT
37681	1170	16	book	book	NN
37681	1170	17	,	,	,
37681	1170	18	or	or	CC
37681	1170	19	lettered	letter	VBD
37681	1170	20	differently	differently	RB
37681	1170	21	,	,	,
37681	1170	22	so	so	IN
37681	1170	23	as	as	IN
37681	1170	24	to	to	TO
37681	1170	25	make	make	VB
37681	1170	26	sure	sure	JJ
37681	1170	27	that	that	IN
37681	1170	28	the	the	DT
37681	1170	29	pupil	pupil	NN
37681	1170	30	has	have	VBZ
37681	1170	31	not	not	RB
37681	1170	32	memorized	memorize	VBN
37681	1170	33	the	the	DT
37681	1170	34	proof	proof	NN
37681	1170	35	,	,	,
37681	1170	36	but	but	CC
37681	1170	37	in	in	IN
37681	1170	38	general	general	JJ
37681	1170	39	such	such	JJ
37681	1170	40	devices	device	NNS
37681	1170	41	are	be	VBP
37681	1170	42	unnecessary	unnecessary	JJ
37681	1170	43	,	,	,
37681	1170	44	for	for	IN
37681	1170	45	a	a	DT
37681	1170	46	teacher	teacher	NN
37681	1170	47	can	can	MD
37681	1170	48	easily	easily	RB
37681	1170	49	discover	discover	VB
37681	1170	50	whether	whether	IN
37681	1170	51	the	the	DT
37681	1170	52	proof	proof	NN
37681	1170	53	is	be	VBZ
37681	1170	54	thoroughly	thoroughly	RB
37681	1170	55	understood	understand	VBN
37681	1170	56	,	,	,
37681	1170	57	either	either	CC
37681	1170	58	by	by	IN
37681	1170	59	the	the	DT
37681	1170	60	manner	manner	NN
37681	1170	61	of	of	IN
37681	1170	62	the	the	DT
37681	1170	63	pupil	pupil	NN
37681	1170	64	or	or	CC
37681	1170	65	by	by	IN
37681	1170	66	some	some	DT
37681	1170	67	slight	slight	JJ
37681	1170	68	questioning	questioning	NN
37681	1170	69	.	.	.
37681	1171	1	A	a	DT
37681	1171	2	good	good	JJ
37681	1171	3	textbook	textbook	NN
37681	1171	4	has	have	VBZ
37681	1171	5	the	the	DT
37681	1171	6	figures	figure	NNS
37681	1171	7	systematically	systematically	RB
37681	1171	8	lettered	letter	VBN
37681	1171	9	in	in	IN
37681	1171	10	some	some	DT
37681	1171	11	helpful	helpful	JJ
37681	1171	12	way	way	NN
37681	1171	13	that	that	WDT
37681	1171	14	is	be	VBZ
37681	1171	15	easily	easily	RB
37681	1171	16	followed	follow	VBN
37681	1171	17	by	by	IN
37681	1171	18	the	the	DT
37681	1171	19	class	class	NN
37681	1171	20	that	that	WDT
37681	1171	21	is	be	VBZ
37681	1171	22	listening	listen	VBG
37681	1171	23	to	to	IN
37681	1171	24	the	the	DT
37681	1171	25	recitation	recitation	NN
37681	1171	26	,	,	,
37681	1171	27	and	and	CC
37681	1171	28	it	-PRON-	PRP
37681	1171	29	is	be	VBZ
37681	1171	30	not	not	RB
37681	1171	31	advisable	advisable	JJ
37681	1171	32	to	to	TO
37681	1171	33	abandon	abandon	VB
37681	1171	34	this	this	DT
37681	1171	35	for	for	IN
37681	1171	36	a	a	DT
37681	1171	37	random	random	JJ
37681	1171	38	set	set	NN
37681	1171	39	of	of	IN
37681	1171	40	letters	letter	NNS
37681	1171	41	arranged	arrange	VBN
37681	1171	42	in	in	IN
37681	1171	43	no	no	DT
37681	1171	44	proper	proper	JJ
37681	1171	45	order	order	NN
37681	1171	46	.	.	.
37681	1172	1	It	-PRON-	PRP
37681	1172	2	is	be	VBZ
37681	1172	3	good	good	JJ
37681	1172	4	educational	educational	JJ
37681	1172	5	policy	policy	NN
37681	1172	6	for	for	IN
37681	1172	7	the	the	DT
37681	1172	8	teacher	teacher	NN
37681	1172	9	to	to	TO
37681	1172	10	commend	commend	VB
37681	1172	11	at	at	IN
37681	1172	12	least	least	JJS
37681	1172	13	as	as	RB
37681	1172	14	often	often	RB
37681	1172	15	as	as	IN
37681	1172	16	he	-PRON-	PRP
37681	1172	17	finds	find	VBZ
37681	1172	18	fault	fault	NN
37681	1172	19	when	when	WRB
37681	1172	20	criticizing	criticize	VBG
37681	1172	21	a	a	DT
37681	1172	22	recitation	recitation	NN
37681	1172	23	at	at	IN
37681	1172	24	the	the	DT
37681	1172	25	blackboard	blackboard	NN
37681	1172	26	and	and	CC
37681	1172	27	when	when	WRB
37681	1172	28	discussing	discuss	VBG
37681	1172	29	the	the	DT
37681	1172	30	pupils	pupil	NNS
37681	1172	31	'	'	POS
37681	1172	32	papers	paper	NNS
37681	1172	33	.	.	.
37681	1173	1	Optimism	optimism	NN
37681	1173	2	,	,	,
37681	1173	3	encouragement	encouragement	NN
37681	1173	4	,	,	,
37681	1173	5	sympathy	sympathy	NN
37681	1173	6	,	,	,
37681	1173	7	the	the	DT
37681	1173	8	genuine	genuine	JJ
37681	1173	9	desire	desire	NN
37681	1173	10	to	to	TO
37681	1173	11	help	help	VB
37681	1173	12	,	,	,
37681	1173	13	the	the	DT
37681	1173	14	putting	putting	NN
37681	1173	15	of	of	IN
37681	1173	16	one	one	NN
37681	1173	17	's	's	POS
37681	1173	18	self	self	NN
37681	1173	19	in	in	IN
37681	1173	20	the	the	DT
37681	1173	21	pupil	pupil	NN
37681	1173	22	's	's	POS
37681	1173	23	place	place	NN
37681	1173	24	,	,	,
37681	1173	25	the	the	DT
37681	1173	26	doing	doing	NN
37681	1173	27	to	to	IN
37681	1173	28	the	the	DT
37681	1173	29	pupil	pupil	NN
37681	1173	30	as	as	IN
37681	1173	31	the	the	DT
37681	1173	32	teacher	teacher	NN
37681	1173	33	would	would	MD
37681	1173	34	that	that	IN
37681	1173	35	he	-PRON-	PRP
37681	1173	36	should	should	MD
37681	1173	37	do	do	VB
37681	1173	38	in	in	IN
37681	1173	39	return,--these	return,--these	NNPS
37681	1173	40	are	be	VBP
37681	1173	41	educational	educational	JJ
37681	1173	42	policies	policy	NNS
37681	1173	43	that	that	WDT
37681	1173	44	make	make	VBP
37681	1173	45	for	for	IN
37681	1173	46	better	well	JJR
37681	1173	47	geometry	geometry	NN
37681	1173	48	as	as	IN
37681	1173	49	they	-PRON-	PRP
37681	1173	50	make	make	VBP
37681	1173	51	for	for	IN
37681	1173	52	better	well	JJR
37681	1173	53	life	life	NN
37681	1173	54	.	.	.
37681	1174	1	The	the	DT
37681	1174	2	prime	prime	JJ
37681	1174	3	failure	failure	NN
37681	1174	4	in	in	IN
37681	1174	5	teaching	teach	VBG
37681	1174	6	geometry	geometry	NN
37681	1174	7	lies	lie	VBZ
37681	1174	8	unquestionably	unquestionably	RB
37681	1174	9	in	in	IN
37681	1174	10	the	the	DT
37681	1174	11	lack	lack	NN
37681	1174	12	of	of	IN
37681	1174	13	interest	interest	NN
37681	1174	14	on	on	IN
37681	1174	15	the	the	DT
37681	1174	16	part	part	NN
37681	1174	17	of	of	IN
37681	1174	18	the	the	DT
37681	1174	19	pupil	pupil	NN
37681	1174	20	,	,	,
37681	1174	21	and	and	CC
37681	1174	22	this	this	DT
37681	1174	23	has	have	VBZ
37681	1174	24	been	be	VBN
37681	1174	25	brought	bring	VBN
37681	1174	26	about	about	RP
37681	1174	27	by	by	IN
37681	1174	28	the	the	DT
37681	1174	29	ancient	ancient	JJ
37681	1174	30	plan	plan	NN
37681	1174	31	of	of	IN
37681	1174	32	simply	simply	RB
37681	1174	33	reading	read	VBG
37681	1174	34	and	and	CC
37681	1174	35	memorizing	memorize	VBG
37681	1174	36	proofs	proof	NNS
37681	1174	37	.	.	.
37681	1175	1	It	-PRON-	PRP
37681	1175	2	is	be	VBZ
37681	1175	3	to	to	TO
37681	1175	4	get	get	VB
37681	1175	5	away	away	RB
37681	1175	6	from	from	IN
37681	1175	7	this	this	DT
37681	1175	8	that	that	IN
37681	1175	9	teachers	teacher	NNS
37681	1175	10	resort	resort	VBP
37681	1175	11	to	to	IN
37681	1175	12	some	some	DT
37681	1175	13	such	such	JJ
37681	1175	14	development	development	NN
37681	1175	15	of	of	IN
37681	1175	16	the	the	DT
37681	1175	17	lesson	lesson	NN
37681	1175	18	in	in	IN
37681	1175	19	advance	advance	NN
37681	1175	20	,	,	,
37681	1175	21	as	as	IN
37681	1175	22	has	have	VBZ
37681	1175	23	been	be	VBN
37681	1175	24	suggested	suggest	VBN
37681	1175	25	above	above	RB
37681	1175	26	.	.	.
37681	1176	1	It	-PRON-	PRP
37681	1176	2	is	be	VBZ
37681	1176	3	usually	usually	RB
37681	1176	4	a	a	DT
37681	1176	5	good	good	JJ
37681	1176	6	plan	plan	NN
37681	1176	7	to	to	TO
37681	1176	8	give	give	VB
37681	1176	9	the	the	DT
37681	1176	10	easier	easy	JJR
37681	1176	11	propositions	proposition	NNS
37681	1176	12	as	as	IN
37681	1176	13	exercises	exercise	NNS
37681	1176	14	before	before	IN
37681	1176	15	they	-PRON-	PRP
37681	1176	16	are	be	VBP
37681	1176	17	reached	reach	VBN
37681	1176	18	in	in	IN
37681	1176	19	the	the	DT
37681	1176	20	text	text	NN
37681	1176	21	,	,	,
37681	1176	22	where	where	WRB
37681	1176	23	this	this	DT
37681	1176	24	can	can	MD
37681	1176	25	be	be	VB
37681	1176	26	done	do	VBN
37681	1176	27	.	.	.
37681	1177	1	An	an	DT
37681	1177	2	English	english	JJ
37681	1177	3	writer	writer	NN
37681	1177	4	has	have	VBZ
37681	1177	5	recently	recently	RB
37681	1177	6	contributed	contribute	VBN
37681	1177	7	this	this	DT
37681	1177	8	further	further	JJ
37681	1177	9	idea	idea	NN
37681	1177	10	:	:	:
37681	1177	11	It	-PRON-	PRP
37681	1177	12	might	may	MD
37681	1177	13	be	be	VB
37681	1177	14	more	more	RBR
37681	1177	15	stimulating	stimulating	JJ
37681	1177	16	to	to	TO
37681	1177	17	encourage	encourage	VB
37681	1177	18	investigation	investigation	NN
37681	1177	19	than	than	IN
37681	1177	20	to	to	TO
37681	1177	21	demand	demand	VB
37681	1177	22	proofs	proof	NNS
37681	1177	23	of	of	IN
37681	1177	24	stated	stated	JJ
37681	1177	25	facts	fact	NNS
37681	1177	26	;	;	:
37681	1177	27	that	that	DT
37681	1177	28	is	be	VBZ
37681	1177	29	to	to	TO
37681	1177	30	say	say	VB
37681	1177	31	,	,	,
37681	1177	32	"	"	``
37681	1177	33	Here	here	RB
37681	1177	34	is	be	VBZ
37681	1177	35	a	a	DT
37681	1177	36	figure	figure	NN
37681	1177	37	drawn	draw	VBN
37681	1177	38	in	in	IN
37681	1177	39	this	this	DT
37681	1177	40	way	way	NN
37681	1177	41	,	,	,
37681	1177	42	find	find	VB
37681	1177	43	out	out	RP
37681	1177	44	anything	anything	NN
37681	1177	45	you	-PRON-	PRP
37681	1177	46	can	can	MD
37681	1177	47	about	about	IN
37681	1177	48	it	-PRON-	PRP
37681	1177	49	.	.	.
37681	1177	50	"	"	''
37681	1178	1	Some	some	DT
37681	1178	2	such	such	JJ
37681	1178	3	exercises	exercise	NNS
37681	1178	4	having	have	VBG
37681	1178	5	been	be	VBN
37681	1178	6	performed	perform	VBN
37681	1178	7	jointly	jointly	RB
37681	1178	8	by	by	IN
37681	1178	9	teachers	teacher	NNS
37681	1178	10	and	and	CC
37681	1178	11	pupils	pupil	NNS
37681	1178	12	,	,	,
37681	1178	13	the	the	DT
37681	1178	14	lust	lust	NN
37681	1178	15	of	of	IN
37681	1178	16	investigation	investigation	NN
37681	1178	17	and	and	CC
37681	1178	18	healthy	healthy	JJ
37681	1178	19	competition	competition	NN
37681	1178	20	which	which	WDT
37681	1178	21	is	be	VBZ
37681	1178	22	present	present	JJ
37681	1178	23	in	in	IN
37681	1178	24	every	every	DT
37681	1178	25	normal	normal	JJ
37681	1178	26	boy	boy	NN
37681	1178	27	or	or	CC
37681	1178	28	girl	girl	NN
37681	1178	29	might	may	MD
37681	1178	30	be	be	VB
37681	1178	31	awakened	awaken	VBN
37681	1178	32	so	so	RB
37681	1178	33	far	far	RB
37681	1178	34	as	as	IN
37681	1178	35	to	to	TO
37681	1178	36	make	make	VB
37681	1178	37	such	such	JJ
37681	1178	38	little	little	JJ
37681	1178	39	researches	research	NNS
37681	1178	40	really	really	RB
37681	1178	41	attractive	attractive	JJ
37681	1178	42	;	;	:
37681	1178	43	moreover	moreover	RB
37681	1178	44	,	,	,
37681	1178	45	the	the	DT
37681	1178	46	training	training	NN
37681	1178	47	thus	thus	RB
37681	1178	48	given	give	VBN
37681	1178	49	is	be	VBZ
37681	1178	50	of	of	IN
37681	1178	51	far	far	RB
37681	1178	52	more	more	JJR
37681	1178	53	value	value	NN
37681	1178	54	than	than	IN
37681	1178	55	that	that	DT
37681	1178	56	obtained	obtain	VBN
37681	1178	57	by	by	IN
37681	1178	58	proving	prove	VBG
37681	1178	59	facts	fact	NNS
37681	1178	60	which	which	WDT
37681	1178	61	are	be	VBP
37681	1178	62	stated	state	VBN
37681	1178	63	in	in	IN
37681	1178	64	advance	advance	NN
37681	1178	65	,	,	,
37681	1178	66	for	for	IN
37681	1178	67	it	-PRON-	PRP
37681	1178	68	is	be	VBZ
37681	1178	69	seldom	seldom	JJ
37681	1178	70	,	,	,
37681	1178	71	if	if	IN
37681	1178	72	ever	ever	RB
37681	1178	73	,	,	,
37681	1178	74	that	that	IN
37681	1178	75	the	the	DT
37681	1178	76	problems	problem	NNS
37681	1178	77	of	of	IN
37681	1178	78	adult	adult	NN
37681	1178	79	life	life	NN
37681	1178	80	present	present	VBP
37681	1178	81	themselves	-PRON-	PRP
37681	1178	82	in	in	IN
37681	1178	83	this	this	DT
37681	1178	84	manner	manner	NN
37681	1178	85	.	.	.
37681	1179	1	The	the	DT
37681	1179	2	spirit	spirit	NN
37681	1179	3	of	of	IN
37681	1179	4	the	the	DT
37681	1179	5	question	question	NN
37681	1179	6	,	,	,
37681	1179	7	"	"	``
37681	1179	8	What	what	WP
37681	1179	9	is	be	VBZ
37681	1179	10	true	true	JJ
37681	1179	11	?	?	.
37681	1179	12	"	"	''
37681	1180	1	is	be	VBZ
37681	1180	2	positive	positive	JJ
37681	1180	3	and	and	CC
37681	1180	4	constructive	constructive	JJ
37681	1180	5	,	,	,
37681	1180	6	but	but	CC
37681	1180	7	that	that	DT
37681	1180	8	involved	involve	VBN
37681	1180	9	in	in	IN
37681	1180	10	"	"	``
37681	1180	11	Is	be	VBZ
37681	1180	12	this	this	DT
37681	1180	13	true	true	JJ
37681	1180	14	?	?	.
37681	1180	15	"	"	''
37681	1181	1	is	be	VBZ
37681	1181	2	negative	negative	JJ
37681	1181	3	and	and	CC
37681	1181	4	destructive	destructive	JJ
37681	1181	5	.	.	.
37681	1182	1	[	[	-LRB-
37681	1182	2	41	41	CD
37681	1182	3	]	]	-RRB-
37681	1182	4	When	when	WRB
37681	1182	5	the	the	DT
37681	1182	6	question	question	NN
37681	1182	7	is	be	VBZ
37681	1182	8	asked	ask	VBN
37681	1182	9	,	,	,
37681	1182	10	"	"	``
37681	1182	11	How	how	WRB
37681	1182	12	shall	shall	MD
37681	1182	13	I	-PRON-	PRP
37681	1182	14	teach	teach	VB
37681	1182	15	?	?	.
37681	1182	16	"	"	''
37681	1183	1	or	or	CC
37681	1183	2	"	"	``
37681	1183	3	What	what	WP
37681	1183	4	is	be	VBZ
37681	1183	5	the	the	DT
37681	1183	6	Method	Method	NNP
37681	1183	7	?	?	.
37681	1183	8	"	"	''
37681	1184	1	there	there	EX
37681	1184	2	is	be	VBZ
37681	1184	3	no	no	DT
37681	1184	4	answer	answer	NN
37681	1184	5	such	such	JJ
37681	1184	6	as	as	IN
37681	1184	7	the	the	DT
37681	1184	8	questioner	questioner	NN
37681	1184	9	expects	expect	VBZ
37681	1184	10	.	.	.
37681	1185	1	A	a	DT
37681	1185	2	Japanese	japanese	JJ
37681	1185	3	writer	writer	NN
37681	1185	4	,	,	,
37681	1185	5	Motowori	Motowori	NNP
37681	1185	6	,	,	,
37681	1185	7	a	a	DT
37681	1185	8	great	great	JJ
37681	1185	9	authority	authority	NN
37681	1185	10	upon	upon	IN
37681	1185	11	the	the	DT
37681	1185	12	Shinto	Shinto	NNP
37681	1185	13	faith	faith	NN
37681	1185	14	of	of	IN
37681	1185	15	his	-PRON-	PRP$
37681	1185	16	people	people	NNS
37681	1185	17	,	,	,
37681	1185	18	once	once	RB
37681	1185	19	wrote	write	VBD
37681	1185	20	these	these	DT
37681	1185	21	words	word	NNS
37681	1185	22	:	:	:
37681	1185	23	"	"	``
37681	1185	24	To	to	TO
37681	1185	25	have	have	VB
37681	1185	26	learned	learn	VBN
37681	1185	27	that	that	IN
37681	1185	28	there	there	EX
37681	1185	29	is	be	VBZ
37681	1185	30	no	no	DT
37681	1185	31	way	way	NN
37681	1185	32	to	to	TO
37681	1185	33	be	be	VB
37681	1185	34	learned	learn	VBN
37681	1185	35	and	and	CC
37681	1185	36	practiced	practice	VBN
37681	1185	37	is	be	VBZ
37681	1185	38	really	really	RB
37681	1185	39	to	to	TO
37681	1185	40	have	have	VB
37681	1185	41	learned	learn	VBN
37681	1185	42	the	the	DT
37681	1185	43	way	way	NN
37681	1185	44	of	of	IN
37681	1185	45	the	the	DT
37681	1185	46	gods	god	NNS
37681	1185	47	.	.	.
37681	1185	48	"	"	''
37681	1186	1	FOOTNOTES	footnote	NNS
37681	1186	2	:	:	:
37681	1186	3	[	[	-LRB-
37681	1186	4	41	41	CD
37681	1186	5	]	]	-RRB-
37681	1186	6	Carson	Carson	NNP
37681	1186	7	,	,	,
37681	1186	8	loc	loc	NNP
37681	1186	9	.	.	.
37681	1187	1	cit	cit	NNP
37681	1187	2	.	.	NNP
37681	1187	3	,	,	,
37681	1187	4	p.	p.	NN
37681	1187	5	12	12	CD
37681	1187	6	.	.	.
37681	1188	1	CHAPTER	chapter	NN
37681	1188	2	XI	XI	NNP
37681	1188	3	THE	the	DT
37681	1188	4	AXIOMS	axiom	NNS
37681	1188	5	AND	and	CC
37681	1188	6	POSTULATES	postulate	NNS
37681	1188	7	The	the	DT
37681	1188	8	interest	interest	NN
37681	1188	9	as	as	RB
37681	1188	10	well	well	RB
37681	1188	11	as	as	IN
37681	1188	12	the	the	DT
37681	1188	13	value	value	NN
37681	1188	14	of	of	IN
37681	1188	15	geometry	geometry	NN
37681	1188	16	lies	lie	VBZ
37681	1188	17	chiefly	chiefly	RB
37681	1188	18	in	in	IN
37681	1188	19	the	the	DT
37681	1188	20	fact	fact	NN
37681	1188	21	that	that	IN
37681	1188	22	from	from	IN
37681	1188	23	a	a	DT
37681	1188	24	small	small	JJ
37681	1188	25	number	number	NN
37681	1188	26	of	of	IN
37681	1188	27	assumptions	assumption	NNS
37681	1188	28	it	-PRON-	PRP
37681	1188	29	is	be	VBZ
37681	1188	30	possible	possible	JJ
37681	1188	31	to	to	TO
37681	1188	32	deduce	deduce	VB
37681	1188	33	an	an	DT
37681	1188	34	unlimited	unlimited	JJ
37681	1188	35	number	number	NN
37681	1188	36	of	of	IN
37681	1188	37	conclusions	conclusion	NNS
37681	1188	38	.	.	.
37681	1189	1	With	with	IN
37681	1189	2	the	the	DT
37681	1189	3	truth	truth	NN
37681	1189	4	of	of	IN
37681	1189	5	these	these	DT
37681	1189	6	assumptions	assumption	NNS
37681	1189	7	we	-PRON-	PRP
37681	1189	8	are	be	VBP
37681	1189	9	not	not	RB
37681	1189	10	so	so	RB
37681	1189	11	much	much	RB
37681	1189	12	concerned	concern	VBN
37681	1189	13	as	as	IN
37681	1189	14	with	with	IN
37681	1189	15	the	the	DT
37681	1189	16	reasoning	reasoning	NN
37681	1189	17	by	by	IN
37681	1189	18	which	which	WDT
37681	1189	19	we	-PRON-	PRP
37681	1189	20	draw	draw	VBP
37681	1189	21	the	the	DT
37681	1189	22	conclusions	conclusion	NNS
37681	1189	23	,	,	,
37681	1189	24	although	although	IN
37681	1189	25	it	-PRON-	PRP
37681	1189	26	is	be	VBZ
37681	1189	27	manifestly	manifestly	RB
37681	1189	28	desirable	desirable	JJ
37681	1189	29	that	that	IN
37681	1189	30	the	the	DT
37681	1189	31	assumptions	assumption	NNS
37681	1189	32	should	should	MD
37681	1189	33	not	not	RB
37681	1189	34	be	be	VB
37681	1189	35	false	false	JJ
37681	1189	36	,	,	,
37681	1189	37	and	and	CC
37681	1189	38	that	that	IN
37681	1189	39	they	-PRON-	PRP
37681	1189	40	should	should	MD
37681	1189	41	be	be	VB
37681	1189	42	as	as	RB
37681	1189	43	few	few	JJ
37681	1189	44	as	as	IN
37681	1189	45	possible	possible	JJ
37681	1189	46	.	.	.
37681	1190	1	It	-PRON-	PRP
37681	1190	2	would	would	MD
37681	1190	3	be	be	VB
37681	1190	4	natural	natural	JJ
37681	1190	5	,	,	,
37681	1190	6	and	and	CC
37681	1190	7	in	in	IN
37681	1190	8	some	some	DT
37681	1190	9	respects	respect	NNS
37681	1190	10	desirable	desirable	JJ
37681	1190	11	,	,	,
37681	1190	12	to	to	TO
37681	1190	13	call	call	VB
37681	1190	14	these	these	DT
37681	1190	15	foundations	foundation	NNS
37681	1190	16	of	of	IN
37681	1190	17	geometry	geometry	NN
37681	1190	18	by	by	IN
37681	1190	19	the	the	DT
37681	1190	20	name	name	NN
37681	1190	21	"	"	``
37681	1190	22	assumptions	assumption	NNS
37681	1190	23	,	,	,
37681	1190	24	"	"	''
37681	1190	25	since	since	IN
37681	1190	26	they	-PRON-	PRP
37681	1190	27	are	be	VBP
37681	1190	28	simply	simply	RB
37681	1190	29	statements	statement	NNS
37681	1190	30	that	that	WDT
37681	1190	31	are	be	VBP
37681	1190	32	assumed	assume	VBN
37681	1190	33	to	to	TO
37681	1190	34	be	be	VB
37681	1190	35	true	true	JJ
37681	1190	36	.	.	.
37681	1191	1	The	the	DT
37681	1191	2	real	real	JJ
37681	1191	3	foundation	foundation	NN
37681	1191	4	principles	principle	NNS
37681	1191	5	can	can	MD
37681	1191	6	not	not	RB
37681	1191	7	be	be	VB
37681	1191	8	proved	prove	VBN
37681	1191	9	;	;	:
37681	1191	10	they	-PRON-	PRP
37681	1191	11	are	be	VBP
37681	1191	12	the	the	DT
37681	1191	13	means	mean	NNS
37681	1191	14	by	by	IN
37681	1191	15	which	which	WDT
37681	1191	16	we	-PRON-	PRP
37681	1191	17	prove	prove	VBP
37681	1191	18	other	other	JJ
37681	1191	19	statements	statement	NNS
37681	1191	20	.	.	.
37681	1192	1	But	but	CC
37681	1192	2	as	as	IN
37681	1192	3	with	with	IN
37681	1192	4	most	most	JJS
37681	1192	5	names	name	NNS
37681	1192	6	of	of	IN
37681	1192	7	men	man	NNS
37681	1192	8	or	or	CC
37681	1192	9	things	thing	NNS
37681	1192	10	,	,	,
37681	1192	11	they	-PRON-	PRP
37681	1192	12	have	have	VBP
37681	1192	13	received	receive	VBN
37681	1192	14	certain	certain	JJ
37681	1192	15	titles	title	NNS
37681	1192	16	that	that	WDT
37681	1192	17	are	be	VBP
37681	1192	18	time	time	NN
37681	1192	19	-	-	HYPH
37681	1192	20	honored	honor	VBN
37681	1192	21	,	,	,
37681	1192	22	and	and	CC
37681	1192	23	that	that	IN
37681	1192	24	it	-PRON-	PRP
37681	1192	25	is	be	VBZ
37681	1192	26	not	not	RB
37681	1192	27	worth	worth	JJ
37681	1192	28	the	the	DT
37681	1192	29	while	while	NN
37681	1192	30	to	to	TO
37681	1192	31	attempt	attempt	VB
37681	1192	32	to	to	TO
37681	1192	33	change	change	VB
37681	1192	34	.	.	.
37681	1193	1	In	in	IN
37681	1193	2	English	English	NNP
37681	1193	3	we	-PRON-	PRP
37681	1193	4	call	call	VBP
37681	1193	5	them	-PRON-	PRP
37681	1193	6	axioms	axiom	NNS
37681	1193	7	and	and	CC
37681	1193	8	postulates	postulate	NNS
37681	1193	9	,	,	,
37681	1193	10	and	and	CC
37681	1193	11	there	there	EX
37681	1193	12	is	be	VBZ
37681	1193	13	no	no	DT
37681	1193	14	more	more	JJR
37681	1193	15	reason	reason	NN
37681	1193	16	for	for	IN
37681	1193	17	attempting	attempt	VBG
37681	1193	18	to	to	TO
37681	1193	19	change	change	VB
37681	1193	20	these	these	DT
37681	1193	21	terms	term	NNS
37681	1193	22	than	than	IN
37681	1193	23	there	there	EX
37681	1193	24	is	be	VBZ
37681	1193	25	for	for	IN
37681	1193	26	attempting	attempt	VBG
37681	1193	27	to	to	TO
37681	1193	28	change	change	VB
37681	1193	29	the	the	DT
37681	1193	30	names	name	NNS
37681	1193	31	of	of	IN
37681	1193	32	geometry[42	geometry[42	NNP
37681	1193	33	]	]	-RRB-
37681	1193	34	and	and	CC
37681	1193	35	of	of	IN
37681	1193	36	algebra	algebra	NN
37681	1193	37	.	.	.
37681	1194	1	[	[	-LRB-
37681	1194	2	43	43	CD
37681	1194	3	]	]	-RRB-
37681	1194	4	Since	since	IN
37681	1194	5	these	these	DT
37681	1194	6	terms	term	NNS
37681	1194	7	are	be	VBP
37681	1194	8	likely	likely	JJ
37681	1194	9	to	to	TO
37681	1194	10	continue	continue	VB
37681	1194	11	,	,	,
37681	1194	12	it	-PRON-	PRP
37681	1194	13	is	be	VBZ
37681	1194	14	necessary	necessary	JJ
37681	1194	15	to	to	TO
37681	1194	16	distinguish	distinguish	VB
37681	1194	17	between	between	IN
37681	1194	18	them	-PRON-	PRP
37681	1194	19	more	more	RBR
37681	1194	20	carefully	carefully	RB
37681	1194	21	than	than	IN
37681	1194	22	is	be	VBZ
37681	1194	23	often	often	RB
37681	1194	24	done	do	VBN
37681	1194	25	,	,	,
37681	1194	26	and	and	CC
37681	1194	27	to	to	TO
37681	1194	28	consider	consider	VB
37681	1194	29	what	what	WP
37681	1194	30	assumptions	assumption	NNS
37681	1194	31	we	-PRON-	PRP
37681	1194	32	are	be	VBP
37681	1194	33	justified	justify	VBN
37681	1194	34	in	in	IN
37681	1194	35	including	include	VBG
37681	1194	36	under	under	IN
37681	1194	37	each	each	DT
37681	1194	38	.	.	.
37681	1195	1	In	in	IN
37681	1195	2	the	the	DT
37681	1195	3	first	first	JJ
37681	1195	4	place	place	NN
37681	1195	5	,	,	,
37681	1195	6	these	these	DT
37681	1195	7	names	name	NNS
37681	1195	8	do	do	VBP
37681	1195	9	not	not	RB
37681	1195	10	go	go	VB
37681	1195	11	back	back	RB
37681	1195	12	to	to	IN
37681	1195	13	Euclid	Euclid	NNP
37681	1195	14	,	,	,
37681	1195	15	as	as	IN
37681	1195	16	is	be	VBZ
37681	1195	17	ordinarily	ordinarily	RB
37681	1195	18	supposed	suppose	VBN
37681	1195	19	,	,	,
37681	1195	20	although	although	IN
37681	1195	21	the	the	DT
37681	1195	22	ideas	idea	NNS
37681	1195	23	and	and	CC
37681	1195	24	the	the	DT
37681	1195	25	statements	statement	NNS
37681	1195	26	are	be	VBP
37681	1195	27	his	-PRON-	PRP$
37681	1195	28	.	.	.
37681	1196	1	"	"	``
37681	1196	2	Postulate	Postulate	NNP
37681	1196	3	"	"	''
37681	1196	4	is	be	VBZ
37681	1196	5	a	a	DT
37681	1196	6	Latin	latin	JJ
37681	1196	7	form	form	NN
37681	1196	8	of	of	IN
37681	1196	9	the	the	DT
37681	1196	10	Greek	greek	JJ
37681	1196	11	[	[	-LRB-
37681	1196	12	Greek	Greek	NNP
37681	1196	13	:	:	:
37681	1196	14	aitêma	aitêma	NN
37681	1196	15	]	]	-RRB-
37681	1196	16	(	(	-LRB-
37681	1196	17	_	_	NNP
37681	1196	18	aitema	aitema	NNP
37681	1196	19	_	_	NNP
37681	1196	20	)	)	-RRB-
37681	1196	21	,	,	,
37681	1196	22	and	and	CC
37681	1196	23	appears	appear	VBZ
37681	1196	24	only	only	RB
37681	1196	25	in	in	IN
37681	1196	26	late	late	JJ
37681	1196	27	translations	translation	NNS
37681	1196	28	.	.	.
37681	1197	1	Euclid	Euclid	NNP
37681	1197	2	stated	state	VBN
37681	1197	3	in	in	IN
37681	1197	4	substance	substance	NN
37681	1197	5	,	,	,
37681	1197	6	"	"	``
37681	1197	7	Let	let	VB
37681	1197	8	the	the	DT
37681	1197	9	following	following	NN
37681	1197	10	be	be	VB
37681	1197	11	assumed	assume	VBN
37681	1197	12	.	.	.
37681	1197	13	"	"	''
37681	1198	1	"	"	``
37681	1198	2	Axiom	Axiom	NNP
37681	1198	3	"	"	''
37681	1198	4	(	(	-LRB-
37681	1198	5	[	[	-LRB-
37681	1198	6	Greek	Greek	NNP
37681	1198	7	:	:	:
37681	1198	8	axiôma	axiôma	NN
37681	1198	9	]	]	-RRB-
37681	1198	10	,	,	,
37681	1198	11	_	_	NNP
37681	1198	12	axioma	axioma	NNP
37681	1198	13	_	_	NNP
37681	1198	14	)	)	-RRB-
37681	1198	15	dates	date	VBZ
37681	1198	16	perhaps	perhaps	RB
37681	1198	17	only	only	RB
37681	1198	18	from	from	IN
37681	1198	19	Proclus	Proclus	NNP
37681	1198	20	(	(	-LRB-
37681	1198	21	fifth	fifth	JJ
37681	1198	22	century	century	NN
37681	1198	23	A.D.	A.D.	NNP
37681	1198	24	)	)	-RRB-
37681	1198	25	,	,	,
37681	1198	26	Euclid	Euclid	NNP
37681	1198	27	using	use	VBG
37681	1198	28	the	the	DT
37681	1198	29	words	word	NNS
37681	1198	30	"	"	``
37681	1198	31	common	common	JJ
37681	1198	32	notions	notion	NNS
37681	1198	33	"	"	''
37681	1198	34	(	(	-LRB-
37681	1198	35	[	[	-LRB-
37681	1198	36	Greek	Greek	NNP
37681	1198	37	:	:	:
37681	1198	38	koinai	koinai	NNP
37681	1198	39	ennoiai	ennoiai	NNP
37681	1198	40	]	]	-RRB-
37681	1198	41	,	,	,
37681	1198	42	_	_	NNP
37681	1198	43	koinai	koinai	NNP
37681	1198	44	ennoiai	ennoiai	NNP
37681	1198	45	_	_	NNP
37681	1198	46	)	)	-RRB-
37681	1198	47	for	for	IN
37681	1198	48	"	"	``
37681	1198	49	axioms	axiom	NNS
37681	1198	50	,	,	,
37681	1198	51	"	"	''
37681	1198	52	as	as	IN
37681	1198	53	Aristotle	Aristotle	NNP
37681	1198	54	before	before	IN
37681	1198	55	him	-PRON-	PRP
37681	1198	56	had	have	VBD
37681	1198	57	used	use	VBN
37681	1198	58	"	"	``
37681	1198	59	common	common	JJ
37681	1198	60	things	thing	NNS
37681	1198	61	,	,	,
37681	1198	62	"	"	''
37681	1198	63	"	"	``
37681	1198	64	common	common	JJ
37681	1198	65	principles	principle	NNS
37681	1198	66	,	,	,
37681	1198	67	"	"	''
37681	1198	68	and	and	CC
37681	1198	69	"	"	``
37681	1198	70	common	common	JJ
37681	1198	71	opinions	opinion	NNS
37681	1198	72	.	.	.
37681	1198	73	"	"	''
37681	1199	1	The	the	DT
37681	1199	2	distinction	distinction	NN
37681	1199	3	between	between	IN
37681	1199	4	axiom	axiom	NN
37681	1199	5	and	and	CC
37681	1199	6	postulate	postulate	NN
37681	1199	7	was	be	VBD
37681	1199	8	not	not	RB
37681	1199	9	clearly	clearly	RB
37681	1199	10	made	make	VBN
37681	1199	11	by	by	IN
37681	1199	12	ancient	ancient	JJ
37681	1199	13	writers	writer	NNS
37681	1199	14	.	.	.
37681	1200	1	Probably	probably	RB
37681	1200	2	what	what	WP
37681	1200	3	was	be	VBD
37681	1200	4	in	in	IN
37681	1200	5	Euclid	Euclid	NNP
37681	1200	6	's	's	POS
37681	1200	7	mind	mind	NN
37681	1200	8	was	be	VBD
37681	1200	9	the	the	DT
37681	1200	10	Aristotelian	aristotelian	JJ
37681	1200	11	distinction	distinction	NN
37681	1200	12	that	that	IN
37681	1200	13	an	an	DT
37681	1200	14	axiom	axiom	NN
37681	1200	15	was	be	VBD
37681	1200	16	a	a	DT
37681	1200	17	principle	principle	NN
37681	1200	18	common	common	JJ
37681	1200	19	to	to	IN
37681	1200	20	all	all	DT
37681	1200	21	sciences	science	NNS
37681	1200	22	,	,	,
37681	1200	23	self	self	NN
37681	1200	24	-	-	HYPH
37681	1200	25	evident	evident	JJ
37681	1200	26	but	but	CC
37681	1200	27	incapable	incapable	JJ
37681	1200	28	of	of	IN
37681	1200	29	proof	proof	NN
37681	1200	30	,	,	,
37681	1200	31	while	while	IN
37681	1200	32	the	the	DT
37681	1200	33	postulates	postulate	NNS
37681	1200	34	were	be	VBD
37681	1200	35	the	the	DT
37681	1200	36	assumptions	assumption	NNS
37681	1200	37	necessary	necessary	JJ
37681	1200	38	for	for	IN
37681	1200	39	building	build	VBG
37681	1200	40	up	up	RP
37681	1200	41	the	the	DT
37681	1200	42	particular	particular	JJ
37681	1200	43	science	science	NN
37681	1200	44	under	under	IN
37681	1200	45	consideration	consideration	NN
37681	1200	46	,	,	,
37681	1200	47	in	in	IN
37681	1200	48	this	this	DT
37681	1200	49	case	case	NN
37681	1200	50	geometry	geometry	NN
37681	1200	51	.	.	.
37681	1201	1	[	[	-LRB-
37681	1201	2	44	44	CD
37681	1201	3	]	]	-RRB-
37681	1201	4	We	-PRON-	PRP
37681	1201	5	thus	thus	RB
37681	1201	6	come	come	VBP
37681	1201	7	to	to	IN
37681	1201	8	the	the	DT
37681	1201	9	modern	modern	JJ
37681	1201	10	distinction	distinction	NN
37681	1201	11	between	between	IN
37681	1201	12	axiom	axiom	NN
37681	1201	13	and	and	CC
37681	1201	14	postulate	postulate	NN
37681	1201	15	,	,	,
37681	1201	16	and	and	CC
37681	1201	17	say	say	VB
37681	1201	18	that	that	IN
37681	1201	19	a	a	DT
37681	1201	20	general	general	JJ
37681	1201	21	statement	statement	NN
37681	1201	22	admitted	admit	VBD
37681	1201	23	to	to	TO
37681	1201	24	be	be	VB
37681	1201	25	true	true	JJ
37681	1201	26	without	without	IN
37681	1201	27	proof	proof	NN
37681	1201	28	is	be	VBZ
37681	1201	29	an	an	DT
37681	1201	30	axiom	axiom	NN
37681	1201	31	,	,	,
37681	1201	32	while	while	IN
37681	1201	33	a	a	DT
37681	1201	34	postulate	postulate	NN
37681	1201	35	in	in	IN
37681	1201	36	geometry	geometry	NN
37681	1201	37	is	be	VBZ
37681	1201	38	a	a	DT
37681	1201	39	geometric	geometric	JJ
37681	1201	40	statement	statement	NN
37681	1201	41	admitted	admit	VBN
37681	1201	42	to	to	TO
37681	1201	43	be	be	VB
37681	1201	44	true	true	JJ
37681	1201	45	,	,	,
37681	1201	46	without	without	IN
37681	1201	47	proof	proof	NN
37681	1201	48	.	.	.
37681	1202	1	For	for	IN
37681	1202	2	example	example	NN
37681	1202	3	,	,	,
37681	1202	4	when	when	WRB
37681	1202	5	we	-PRON-	PRP
37681	1202	6	say	say	VBP
37681	1202	7	"	"	``
37681	1202	8	If	if	IN
37681	1202	9	equals	equal	NNS
37681	1202	10	are	be	VBP
37681	1202	11	added	add	VBN
37681	1202	12	to	to	IN
37681	1202	13	equals	equal	NNS
37681	1202	14	,	,	,
37681	1202	15	the	the	DT
37681	1202	16	sums	sum	NNS
37681	1202	17	are	be	VBP
37681	1202	18	equal	equal	JJ
37681	1202	19	,	,	,
37681	1202	20	"	"	``
37681	1202	21	we	-PRON-	PRP
37681	1202	22	state	state	VBP
37681	1202	23	an	an	DT
37681	1202	24	assumption	assumption	NN
37681	1202	25	that	that	WDT
37681	1202	26	is	be	VBZ
37681	1202	27	taken	take	VBN
37681	1202	28	also	also	RB
37681	1202	29	as	as	RB
37681	1202	30	true	true	JJ
37681	1202	31	in	in	IN
37681	1202	32	arithmetic	arithmetic	JJ
37681	1202	33	,	,	,
37681	1202	34	in	in	IN
37681	1202	35	algebra	algebra	NN
37681	1202	36	,	,	,
37681	1202	37	and	and	CC
37681	1202	38	in	in	IN
37681	1202	39	elementary	elementary	JJ
37681	1202	40	mathematics	mathematic	NNS
37681	1202	41	in	in	IN
37681	1202	42	general	general	JJ
37681	1202	43	.	.	.
37681	1203	1	This	this	DT
37681	1203	2	is	be	VBZ
37681	1203	3	therefore	therefore	RB
37681	1203	4	an	an	DT
37681	1203	5	axiom	axiom	NN
37681	1203	6	.	.	.
37681	1204	1	At	at	IN
37681	1204	2	one	one	CD
37681	1204	3	time	time	NN
37681	1204	4	such	such	PDT
37681	1204	5	a	a	DT
37681	1204	6	statement	statement	NN
37681	1204	7	was	be	VBD
37681	1204	8	defined	define	VBN
37681	1204	9	as	as	IN
37681	1204	10	"	"	``
37681	1204	11	a	a	DT
37681	1204	12	self	self	NN
37681	1204	13	-	-	HYPH
37681	1204	14	evident	evident	JJ
37681	1204	15	truth	truth	NN
37681	1204	16	,	,	,
37681	1204	17	"	"	''
37681	1204	18	but	but	CC
37681	1204	19	this	this	DT
37681	1204	20	has	have	VBZ
37681	1204	21	in	in	IN
37681	1204	22	recent	recent	JJ
37681	1204	23	years	year	NNS
37681	1204	24	been	be	VBN
37681	1204	25	abandoned	abandon	VBN
37681	1204	26	,	,	,
37681	1204	27	since	since	IN
37681	1204	28	what	what	WP
37681	1204	29	is	be	VBZ
37681	1204	30	evident	evident	JJ
37681	1204	31	to	to	IN
37681	1204	32	one	one	CD
37681	1204	33	person	person	NN
37681	1204	34	is	be	VBZ
37681	1204	35	not	not	RB
37681	1204	36	necessarily	necessarily	RB
37681	1204	37	evident	evident	JJ
37681	1204	38	to	to	IN
37681	1204	39	another	another	DT
37681	1204	40	,	,	,
37681	1204	41	and	and	CC
37681	1204	42	since	since	IN
37681	1204	43	all	all	DT
37681	1204	44	such	such	JJ
37681	1204	45	statements	statement	NNS
37681	1204	46	are	be	VBP
37681	1204	47	mere	mere	JJ
37681	1204	48	matters	matter	NNS
37681	1204	49	of	of	IN
37681	1204	50	assumption	assumption	NN
37681	1204	51	in	in	IN
37681	1204	52	any	any	DT
37681	1204	53	case	case	NN
37681	1204	54	.	.	.
37681	1205	1	On	on	IN
37681	1205	2	the	the	DT
37681	1205	3	other	other	JJ
37681	1205	4	hand	hand	NN
37681	1205	5	,	,	,
37681	1205	6	when	when	WRB
37681	1205	7	we	-PRON-	PRP
37681	1205	8	say	say	VBP
37681	1205	9	,	,	,
37681	1205	10	"	"	''
37681	1205	11	A	a	DT
37681	1205	12	circle	circle	NN
37681	1205	13	may	may	MD
37681	1205	14	be	be	VB
37681	1205	15	described	describe	VBN
37681	1205	16	with	with	IN
37681	1205	17	any	any	DT
37681	1205	18	given	give	VBN
37681	1205	19	point	point	NN
37681	1205	20	as	as	IN
37681	1205	21	a	a	DT
37681	1205	22	center	center	NN
37681	1205	23	and	and	CC
37681	1205	24	any	any	DT
37681	1205	25	given	give	VBN
37681	1205	26	line	line	NN
37681	1205	27	as	as	IN
37681	1205	28	a	a	DT
37681	1205	29	radius	radius	NN
37681	1205	30	,	,	,
37681	1205	31	"	"	``
37681	1205	32	we	-PRON-	PRP
37681	1205	33	state	state	VBP
37681	1205	34	a	a	DT
37681	1205	35	special	special	JJ
37681	1205	36	assumption	assumption	NN
37681	1205	37	of	of	IN
37681	1205	38	geometry	geometry	NN
37681	1205	39	,	,	,
37681	1205	40	and	and	CC
37681	1205	41	this	this	DT
37681	1205	42	assumption	assumption	NN
37681	1205	43	is	be	VBZ
37681	1205	44	therefore	therefore	RB
37681	1205	45	a	a	DT
37681	1205	46	geometric	geometric	JJ
37681	1205	47	postulate	postulate	NN
37681	1205	48	.	.	.
37681	1206	1	Some	some	DT
37681	1206	2	few	few	JJ
37681	1206	3	writers	writer	NNS
37681	1206	4	have	have	VBP
37681	1206	5	sought	seek	VBN
37681	1206	6	to	to	TO
37681	1206	7	distinguish	distinguish	VB
37681	1206	8	between	between	IN
37681	1206	9	axiom	axiom	NN
37681	1206	10	and	and	CC
37681	1206	11	postulate	postulate	NN
37681	1206	12	by	by	IN
37681	1206	13	saying	say	VBG
37681	1206	14	that	that	IN
37681	1206	15	the	the	DT
37681	1206	16	former	former	JJ
37681	1206	17	was	be	VBD
37681	1206	18	an	an	DT
37681	1206	19	assumed	assumed	JJ
37681	1206	20	theorem	theorem	NN
37681	1206	21	and	and	CC
37681	1206	22	the	the	DT
37681	1206	23	latter	latter	JJ
37681	1206	24	an	an	DT
37681	1206	25	assumed	assumed	JJ
37681	1206	26	problem	problem	NN
37681	1206	27	,	,	,
37681	1206	28	but	but	CC
37681	1206	29	there	there	EX
37681	1206	30	is	be	VBZ
37681	1206	31	no	no	DT
37681	1206	32	standard	standard	JJ
37681	1206	33	authority	authority	NN
37681	1206	34	for	for	IN
37681	1206	35	such	such	PDT
37681	1206	36	a	a	DT
37681	1206	37	distinction	distinction	NN
37681	1206	38	,	,	,
37681	1206	39	and	and	CC
37681	1206	40	indeed	indeed	RB
37681	1206	41	the	the	DT
37681	1206	42	difference	difference	NN
37681	1206	43	between	between	IN
37681	1206	44	a	a	DT
37681	1206	45	theorem	theorem	NN
37681	1206	46	and	and	CC
37681	1206	47	a	a	DT
37681	1206	48	problem	problem	NN
37681	1206	49	is	be	VBZ
37681	1206	50	very	very	RB
37681	1206	51	slight	slight	JJ
37681	1206	52	.	.	.
37681	1207	1	If	if	IN
37681	1207	2	we	-PRON-	PRP
37681	1207	3	say	say	VBP
37681	1207	4	,	,	,
37681	1207	5	"	"	''
37681	1207	6	A	a	DT
37681	1207	7	circle	circle	NN
37681	1207	8	may	may	MD
37681	1207	9	be	be	VB
37681	1207	10	passed	pass	VBN
37681	1207	11	through	through	IN
37681	1207	12	three	three	CD
37681	1207	13	points	point	NNS
37681	1207	14	not	not	RB
37681	1207	15	in	in	IN
37681	1207	16	the	the	DT
37681	1207	17	same	same	JJ
37681	1207	18	straight	straight	JJ
37681	1207	19	line	line	NN
37681	1207	20	,	,	,
37681	1207	21	"	"	''
37681	1207	22	we	-PRON-	PRP
37681	1207	23	state	state	VBP
37681	1207	24	a	a	DT
37681	1207	25	theorem	theorem	NN
37681	1207	26	;	;	:
37681	1207	27	but	but	CC
37681	1207	28	if	if	IN
37681	1207	29	we	-PRON-	PRP
37681	1207	30	say	say	VBP
37681	1207	31	,	,	,
37681	1207	32	"	"	``
37681	1207	33	Required	require	VBN
37681	1207	34	to	to	TO
37681	1207	35	pass	pass	VB
37681	1207	36	a	a	DT
37681	1207	37	circle	circle	NN
37681	1207	38	through	through	IN
37681	1207	39	three	three	CD
37681	1207	40	points	point	NNS
37681	1207	41	,	,	,
37681	1207	42	"	"	''
37681	1207	43	we	-PRON-	PRP
37681	1207	44	state	state	VBP
37681	1207	45	a	a	DT
37681	1207	46	problem	problem	NN
37681	1207	47	.	.	.
37681	1208	1	The	the	DT
37681	1208	2	mental	mental	JJ
37681	1208	3	process	process	NN
37681	1208	4	of	of	IN
37681	1208	5	handling	handle	VBG
37681	1208	6	the	the	DT
37681	1208	7	two	two	CD
37681	1208	8	propositions	proposition	NNS
37681	1208	9	is	be	VBZ
37681	1208	10	,	,	,
37681	1208	11	however	however	RB
37681	1208	12	,	,	,
37681	1208	13	practically	practically	RB
37681	1208	14	the	the	DT
37681	1208	15	same	same	JJ
37681	1208	16	in	in	IN
37681	1208	17	spite	spite	NN
37681	1208	18	of	of	IN
37681	1208	19	the	the	DT
37681	1208	20	minor	minor	JJ
37681	1208	21	detail	detail	NN
37681	1208	22	of	of	IN
37681	1208	23	wording	wording	NN
37681	1208	24	.	.	.
37681	1209	1	So	so	RB
37681	1209	2	with	with	IN
37681	1209	3	the	the	DT
37681	1209	4	statement	statement	NN
37681	1209	5	,	,	,
37681	1209	6	"	"	``
37681	1209	7	A	a	DT
37681	1209	8	straight	straight	JJ
37681	1209	9	line	line	NN
37681	1209	10	may	may	MD
37681	1209	11	be	be	VB
37681	1209	12	produced	produce	VBN
37681	1209	13	to	to	IN
37681	1209	14	any	any	DT
37681	1209	15	required	require	VBN
37681	1209	16	length	length	NN
37681	1209	17	.	.	.
37681	1209	18	"	"	''
37681	1210	1	This	this	DT
37681	1210	2	is	be	VBZ
37681	1210	3	stated	state	VBN
37681	1210	4	in	in	IN
37681	1210	5	the	the	DT
37681	1210	6	form	form	NN
37681	1210	7	of	of	IN
37681	1210	8	a	a	DT
37681	1210	9	theorem	theorem	NN
37681	1210	10	,	,	,
37681	1210	11	but	but	CC
37681	1210	12	it	-PRON-	PRP
37681	1210	13	might	may	MD
37681	1210	14	equally	equally	RB
37681	1210	15	well	well	RB
37681	1210	16	be	be	VB
37681	1210	17	stated	state	VBN
37681	1210	18	thus	thus	RB
37681	1210	19	:	:	:
37681	1210	20	"	"	``
37681	1210	21	To	to	TO
37681	1210	22	produce	produce	VB
37681	1210	23	a	a	DT
37681	1210	24	straight	straight	JJ
37681	1210	25	line	line	NN
37681	1210	26	to	to	IN
37681	1210	27	any	any	DT
37681	1210	28	required	require	VBN
37681	1210	29	length	length	NN
37681	1210	30	.	.	.
37681	1210	31	"	"	''
37681	1211	1	It	-PRON-	PRP
37681	1211	2	is	be	VBZ
37681	1211	3	unreasonable	unreasonable	JJ
37681	1211	4	to	to	TO
37681	1211	5	call	call	VB
37681	1211	6	this	this	DT
37681	1211	7	an	an	DT
37681	1211	8	axiom	axiom	NN
37681	1211	9	in	in	IN
37681	1211	10	one	one	CD
37681	1211	11	case	case	NN
37681	1211	12	and	and	CC
37681	1211	13	a	a	DT
37681	1211	14	postulate	postulate	NN
37681	1211	15	in	in	IN
37681	1211	16	the	the	DT
37681	1211	17	other	other	JJ
37681	1211	18	.	.	.
37681	1212	1	However	however	RB
37681	1212	2	stated	state	VBN
37681	1212	3	,	,	,
37681	1212	4	it	-PRON-	PRP
37681	1212	5	is	be	VBZ
37681	1212	6	a	a	DT
37681	1212	7	geometric	geometric	JJ
37681	1212	8	postulate	postulate	NN
37681	1212	9	and	and	CC
37681	1212	10	should	should	MD
37681	1212	11	be	be	VB
37681	1212	12	so	so	RB
37681	1212	13	classed	classed	JJ
37681	1212	14	.	.	.
37681	1213	1	What	what	WP
37681	1213	2	,	,	,
37681	1213	3	now	now	RB
37681	1213	4	,	,	,
37681	1213	5	are	be	VBP
37681	1213	6	the	the	DT
37681	1213	7	axioms	axiom	NNS
37681	1213	8	and	and	CC
37681	1213	9	postulates	postulate	NNS
37681	1213	10	that	that	IN
37681	1213	11	we	-PRON-	PRP
37681	1213	12	are	be	VBP
37681	1213	13	justified	justify	VBN
37681	1213	14	in	in	IN
37681	1213	15	assuming	assume	VBG
37681	1213	16	,	,	,
37681	1213	17	and	and	CC
37681	1213	18	what	what	WP
37681	1213	19	determines	determine	VBZ
37681	1213	20	their	-PRON-	PRP$
37681	1213	21	number	number	NN
37681	1213	22	and	and	CC
37681	1213	23	character	character	NN
37681	1213	24	?	?	.
37681	1214	1	It	-PRON-	PRP
37681	1214	2	seems	seem	VBZ
37681	1214	3	reasonable	reasonable	JJ
37681	1214	4	to	to	TO
37681	1214	5	agree	agree	VB
37681	1214	6	that	that	IN
37681	1214	7	they	-PRON-	PRP
37681	1214	8	should	should	MD
37681	1214	9	be	be	VB
37681	1214	10	as	as	RB
37681	1214	11	few	few	JJ
37681	1214	12	as	as	IN
37681	1214	13	possible	possible	JJ
37681	1214	14	,	,	,
37681	1214	15	and	and	CC
37681	1214	16	that	that	IN
37681	1214	17	for	for	IN
37681	1214	18	educational	educational	JJ
37681	1214	19	purposes	purpose	NNS
37681	1214	20	they	-PRON-	PRP
37681	1214	21	should	should	MD
37681	1214	22	be	be	VB
37681	1214	23	so	so	RB
37681	1214	24	clear	clear	JJ
37681	1214	25	as	as	IN
37681	1214	26	to	to	TO
37681	1214	27	be	be	VB
37681	1214	28	intelligible	intelligible	JJ
37681	1214	29	to	to	IN
37681	1214	30	beginners	beginner	NNS
37681	1214	31	.	.	.
37681	1215	1	But	but	CC
37681	1215	2	here	here	RB
37681	1215	3	we	-PRON-	PRP
37681	1215	4	encounter	encounter	VBP
37681	1215	5	two	two	CD
37681	1215	6	conflicting	conflicting	JJ
37681	1215	7	ideas	idea	NNS
37681	1215	8	.	.	.
37681	1216	1	To	to	TO
37681	1216	2	get	get	VB
37681	1216	3	the	the	DT
37681	1216	4	"	"	``
37681	1216	5	irreducible	irreducible	JJ
37681	1216	6	minimum	minimum	NN
37681	1216	7	"	"	''
37681	1216	8	of	of	IN
37681	1216	9	assumptions	assumption	NNS
37681	1216	10	is	be	VBZ
37681	1216	11	to	to	TO
37681	1216	12	get	get	VB
37681	1216	13	a	a	DT
37681	1216	14	set	set	NN
37681	1216	15	of	of	IN
37681	1216	16	statements	statement	NNS
37681	1216	17	quite	quite	RB
37681	1216	18	unintelligible	unintelligible	JJ
37681	1216	19	to	to	IN
37681	1216	20	students	student	NNS
37681	1216	21	beginning	begin	VBG
37681	1216	22	geometry	geometry	NN
37681	1216	23	or	or	CC
37681	1216	24	any	any	DT
37681	1216	25	other	other	JJ
37681	1216	26	branch	branch	NN
37681	1216	27	of	of	IN
37681	1216	28	elementary	elementary	JJ
37681	1216	29	mathematics	mathematic	NNS
37681	1216	30	.	.	.
37681	1217	1	Such	such	PDT
37681	1217	2	an	an	DT
37681	1217	3	effort	effort	NN
37681	1217	4	is	be	VBZ
37681	1217	5	laudable	laudable	JJ
37681	1217	6	when	when	WRB
37681	1217	7	the	the	DT
37681	1217	8	results	result	NNS
37681	1217	9	are	be	VBP
37681	1217	10	intended	intend	VBN
37681	1217	11	for	for	IN
37681	1217	12	advanced	advanced	JJ
37681	1217	13	students	student	NNS
37681	1217	14	in	in	IN
37681	1217	15	the	the	DT
37681	1217	16	university	university	NN
37681	1217	17	,	,	,
37681	1217	18	but	but	CC
37681	1217	19	it	-PRON-	PRP
37681	1217	20	is	be	VBZ
37681	1217	21	merely	merely	RB
37681	1217	22	suggestive	suggestive	JJ
37681	1217	23	to	to	IN
37681	1217	24	teachers	teacher	NNS
37681	1217	25	rather	rather	RB
37681	1217	26	than	than	IN
37681	1217	27	usable	usable	JJ
37681	1217	28	with	with	IN
37681	1217	29	pupils	pupil	NNS
37681	1217	30	when	when	WRB
37681	1217	31	it	-PRON-	PRP
37681	1217	32	touches	touch	VBZ
37681	1217	33	upon	upon	IN
37681	1217	34	the	the	DT
37681	1217	35	primary	primary	JJ
37681	1217	36	steps	step	NNS
37681	1217	37	of	of	IN
37681	1217	38	any	any	DT
37681	1217	39	science	science	NN
37681	1217	40	.	.	.
37681	1218	1	In	in	IN
37681	1218	2	recent	recent	JJ
37681	1218	3	years	year	NNS
37681	1218	4	several	several	JJ
37681	1218	5	such	such	JJ
37681	1218	6	attempts	attempt	NNS
37681	1218	7	have	have	VBP
37681	1218	8	been	be	VBN
37681	1218	9	made	make	VBN
37681	1218	10	.	.	.
37681	1219	1	In	in	IN
37681	1219	2	particular	particular	JJ
37681	1219	3	,	,	,
37681	1219	4	Professor	Professor	NNP
37681	1219	5	Hilbert	Hilbert	NNP
37681	1219	6	has	have	VBZ
37681	1219	7	given	give	VBN
37681	1219	8	a	a	DT
37681	1219	9	system[45	system[45	NN
37681	1219	10	]	]	-RRB-
37681	1219	11	of	of	IN
37681	1219	12	congruence	congruence	NN
37681	1219	13	postulates	postulate	NNS
37681	1219	14	,	,	,
37681	1219	15	but	but	CC
37681	1219	16	they	-PRON-	PRP
37681	1219	17	are	be	VBP
37681	1219	18	rather	rather	RB
37681	1219	19	for	for	IN
37681	1219	20	the	the	DT
37681	1219	21	scientist	scientist	NN
37681	1219	22	than	than	IN
37681	1219	23	for	for	IN
37681	1219	24	the	the	DT
37681	1219	25	student	student	NN
37681	1219	26	of	of	IN
37681	1219	27	elementary	elementary	JJ
37681	1219	28	geometry	geometry	NN
37681	1219	29	.	.	.
37681	1220	1	In	in	IN
37681	1220	2	view	view	NN
37681	1220	3	of	of	IN
37681	1220	4	these	these	DT
37681	1220	5	efforts	effort	NNS
37681	1220	6	it	-PRON-	PRP
37681	1220	7	is	be	VBZ
37681	1220	8	well	well	JJ
37681	1220	9	to	to	TO
37681	1220	10	go	go	VB
37681	1220	11	back	back	RB
37681	1220	12	to	to	IN
37681	1220	13	Euclid	Euclid	NNP
37681	1220	14	and	and	CC
37681	1220	15	see	see	VB
37681	1220	16	what	what	WP
37681	1220	17	this	this	DT
37681	1220	18	great	great	JJ
37681	1220	19	teacher	teacher	NN
37681	1220	20	of	of	IN
37681	1220	21	university	university	NN
37681	1220	22	men[46	men[46	NN
37681	1220	23	]	]	-RRB-
37681	1220	24	had	have	VBD
37681	1220	25	to	to	TO
37681	1220	26	suggest	suggest	VB
37681	1220	27	.	.	.
37681	1221	1	The	the	DT
37681	1221	2	following	follow	VBG
37681	1221	3	are	be	VBP
37681	1221	4	the	the	DT
37681	1221	5	five	five	CD
37681	1221	6	"	"	``
37681	1221	7	common	common	JJ
37681	1221	8	notions	notion	NNS
37681	1221	9	"	"	''
37681	1221	10	that	that	IN
37681	1221	11	Euclid	Euclid	NNP
37681	1221	12	deemed	deem	VBD
37681	1221	13	sufficient	sufficient	JJ
37681	1221	14	for	for	IN
37681	1221	15	the	the	DT
37681	1221	16	purposes	purpose	NNS
37681	1221	17	of	of	IN
37681	1221	18	elementary	elementary	JJ
37681	1221	19	geometry	geometry	NN
37681	1221	20	.	.	.
37681	1222	1	1	1	LS
37681	1222	2	.	.	.
37681	1223	1	_	_	NNP
37681	1223	2	Things	thing	NNS
37681	1223	3	equal	equal	JJ
37681	1223	4	to	to	IN
37681	1223	5	the	the	DT
37681	1223	6	same	same	JJ
37681	1223	7	thing	thing	NN
37681	1223	8	are	be	VBP
37681	1223	9	also	also	RB
37681	1223	10	equal	equal	JJ
37681	1223	11	to	to	IN
37681	1223	12	each	each	DT
37681	1223	13	other	other	JJ
37681	1223	14	.	.	.
37681	1223	15	_	_	NNP
37681	1223	16	This	this	DT
37681	1223	17	axiom	axiom	NN
37681	1223	18	has	have	VBZ
37681	1223	19	persisted	persist	VBN
37681	1223	20	in	in	IN
37681	1223	21	all	all	DT
37681	1223	22	elementary	elementary	JJ
37681	1223	23	textbooks	textbook	NNS
37681	1223	24	.	.	.
37681	1224	1	Of	of	RB
37681	1224	2	course	course	RB
37681	1224	3	it	-PRON-	PRP
37681	1224	4	is	be	VBZ
37681	1224	5	a	a	DT
37681	1224	6	simple	simple	JJ
37681	1224	7	matter	matter	NN
37681	1224	8	to	to	TO
37681	1224	9	attempt	attempt	VB
37681	1224	10	criticism,--to	criticism,--to	NNP
37681	1224	11	say	say	VB
37681	1224	12	that	that	DT
37681	1224	13	-2	-2	NNP
37681	1224	14	is	be	VBZ
37681	1224	15	the	the	DT
37681	1224	16	square	square	JJ
37681	1224	17	root	root	NN
37681	1224	18	of	of	IN
37681	1224	19	4	4	CD
37681	1224	20	,	,	,
37681	1224	21	and	and	CC
37681	1224	22	+2	+2	NNP
37681	1224	23	is	be	VBZ
37681	1224	24	also	also	RB
37681	1224	25	the	the	DT
37681	1224	26	square	square	JJ
37681	1224	27	root	root	NN
37681	1224	28	of	of	IN
37681	1224	29	4	4	CD
37681	1224	30	,	,	,
37681	1224	31	whence	whence	NN
37681	1224	32	-2	-2	.
37681	1224	33	=	=	SYM
37681	1224	34	+2	+2	UH
37681	1224	35	;	;	:
37681	1224	36	but	but	CC
37681	1224	37	it	-PRON-	PRP
37681	1224	38	is	be	VBZ
37681	1224	39	evident	evident	JJ
37681	1224	40	that	that	IN
37681	1224	41	the	the	DT
37681	1224	42	argument	argument	NN
37681	1224	43	is	be	VBZ
37681	1224	44	not	not	RB
37681	1224	45	sound	sound	JJ
37681	1224	46	,	,	,
37681	1224	47	and	and	CC
37681	1224	48	that	that	IN
37681	1224	49	it	-PRON-	PRP
37681	1224	50	does	do	VBZ
37681	1224	51	not	not	RB
37681	1224	52	invalidate	invalidate	VB
37681	1224	53	the	the	DT
37681	1224	54	axiom	axiom	NN
37681	1224	55	.	.	.
37681	1225	1	Proclus	Proclus	NNP
37681	1225	2	tells	tell	VBZ
37681	1225	3	us	-PRON-	PRP
37681	1225	4	that	that	IN
37681	1225	5	Apollonius	Apollonius	NNP
37681	1225	6	attempted	attempt	VBD
37681	1225	7	to	to	TO
37681	1225	8	prove	prove	VB
37681	1225	9	the	the	DT
37681	1225	10	axiom	axiom	NN
37681	1225	11	by	by	IN
37681	1225	12	saying	say	VBG
37681	1225	13	,	,	,
37681	1225	14	"	"	``
37681	1225	15	Let	let	VB
37681	1225	16	_	_	NNP
37681	1225	17	a	a	DT
37681	1225	18	_	_	NNP
37681	1225	19	equal	equal	JJ
37681	1225	20	_	_	NNP
37681	1225	21	b	b	NNP
37681	1225	22	_	_	NNP
37681	1225	23	,	,	,
37681	1225	24	and	and	CC
37681	1225	25	_	_	NNP
37681	1225	26	b	b	NNP
37681	1225	27	_	_	NNP
37681	1225	28	equal	equal	JJ
37681	1225	29	_	_	NNP
37681	1225	30	c	c	NNP
37681	1225	31	_	_	NNP
37681	1225	32	.	.	.
37681	1226	1	I	-PRON-	PRP
37681	1226	2	say	say	VBP
37681	1226	3	that	that	IN
37681	1226	4	_	_	NNP
37681	1226	5	a	a	DT
37681	1226	6	_	_	NNP
37681	1226	7	equals	equal	VBZ
37681	1226	8	_	_	NNP
37681	1226	9	c	c	NNP
37681	1226	10	_	_	NNP
37681	1226	11	.	.	.
37681	1227	1	For	for	IN
37681	1227	2	,	,	,
37681	1227	3	since	since	IN
37681	1227	4	_	_	NNP
37681	1227	5	a	a	DT
37681	1227	6	_	_	NNP
37681	1227	7	equals	equal	VBZ
37681	1227	8	_	_	NNP
37681	1227	9	b	b	NNP
37681	1227	10	_	_	NNP
37681	1227	11	,	,	,
37681	1227	12	_	_	NNP
37681	1227	13	a	a	DT
37681	1227	14	_	_	NNP
37681	1227	15	occupies	occupy	VBZ
37681	1227	16	the	the	DT
37681	1227	17	same	same	JJ
37681	1227	18	space	space	NN
37681	1227	19	as	as	IN
37681	1227	20	_	_	NNP
37681	1227	21	b	b	NNP
37681	1227	22	_	_	NNP
37681	1227	23	.	.	.
37681	1228	1	Therefore	therefore	RB
37681	1228	2	_	_	NNP
37681	1228	3	a	a	DT
37681	1228	4	_	_	NNP
37681	1228	5	occupies	occupy	VBZ
37681	1228	6	the	the	DT
37681	1228	7	same	same	JJ
37681	1228	8	space	space	NN
37681	1228	9	as	as	IN
37681	1228	10	_	_	NNP
37681	1228	11	c	c	NNP
37681	1228	12	_	_	NNP
37681	1228	13	.	.	.
37681	1229	1	Therefore	therefore	RB
37681	1229	2	_	_	NNP
37681	1229	3	a	a	DT
37681	1229	4	_	_	NNP
37681	1229	5	equals	equal	VBZ
37681	1229	6	_	_	NNP
37681	1229	7	c	c	NNP
37681	1229	8	_	_	NNP
37681	1229	9	.	.	.
37681	1229	10	"	"	''
37681	1230	1	The	the	DT
37681	1230	2	proof	proof	NN
37681	1230	3	is	be	VBZ
37681	1230	4	of	of	IN
37681	1230	5	no	no	DT
37681	1230	6	value	value	NN
37681	1230	7	,	,	,
37681	1230	8	however	however	RB
37681	1230	9	,	,	,
37681	1230	10	save	save	IN
37681	1230	11	as	as	IN
37681	1230	12	a	a	DT
37681	1230	13	curiosity	curiosity	NN
37681	1230	14	.	.	.
37681	1231	1	2	2	LS
37681	1231	2	.	.	.
37681	1232	1	_	_	NNP
37681	1232	2	And	and	CC
37681	1232	3	if	if	IN
37681	1232	4	to	to	IN
37681	1232	5	equals	equal	NNS
37681	1232	6	equals	equal	NNS
37681	1232	7	are	be	VBP
37681	1232	8	added	add	VBN
37681	1232	9	,	,	,
37681	1232	10	the	the	DT
37681	1232	11	wholes	whole	NNS
37681	1232	12	are	be	VBP
37681	1232	13	equal	equal	JJ
37681	1232	14	.	.	.
37681	1232	15	_	_	NNP
37681	1232	16	3	3	CD
37681	1232	17	.	.	.
37681	1233	1	_	_	NNP
37681	1233	2	If	if	IN
37681	1233	3	equals	equal	NNS
37681	1233	4	are	be	VBP
37681	1233	5	subtracted	subtract	VBN
37681	1233	6	from	from	IN
37681	1233	7	equals	equal	NNS
37681	1233	8	,	,	,
37681	1233	9	the	the	DT
37681	1233	10	remainders	remainder	NNS
37681	1233	11	are	be	VBP
37681	1233	12	equal	equal	JJ
37681	1233	13	.	.	.
37681	1233	14	_	_	NNP
37681	1233	15	Axioms	Axioms	NNP
37681	1233	16	2	2	CD
37681	1233	17	and	and	CC
37681	1233	18	3	3	CD
37681	1233	19	are	be	VBP
37681	1233	20	older	old	JJR
37681	1233	21	than	than	IN
37681	1233	22	Euclid	Euclid	NNP
37681	1233	23	's	's	POS
37681	1233	24	time	time	NN
37681	1233	25	,	,	,
37681	1233	26	and	and	CC
37681	1233	27	are	be	VBP
37681	1233	28	the	the	DT
37681	1233	29	only	only	JJ
37681	1233	30	ones	one	NNS
37681	1233	31	given	give	VBN
37681	1233	32	by	by	IN
37681	1233	33	him	-PRON-	PRP
37681	1233	34	relating	relate	VBG
37681	1233	35	to	to	IN
37681	1233	36	the	the	DT
37681	1233	37	solution	solution	NN
37681	1233	38	of	of	IN
37681	1233	39	the	the	DT
37681	1233	40	equation	equation	NN
37681	1233	41	.	.	.
37681	1234	1	Certain	certain	JJ
37681	1234	2	other	other	JJ
37681	1234	3	axioms	axiom	NNS
37681	1234	4	were	be	VBD
37681	1234	5	added	add	VBN
37681	1234	6	by	by	IN
37681	1234	7	later	later	JJ
37681	1234	8	writers	writer	NNS
37681	1234	9	,	,	,
37681	1234	10	as	as	IN
37681	1234	11	,	,	,
37681	1234	12	"	"	``
37681	1234	13	Things	thing	NNS
37681	1234	14	which	which	WDT
37681	1234	15	are	be	VBP
37681	1234	16	double	double	JJ
37681	1234	17	of	of	IN
37681	1234	18	the	the	DT
37681	1234	19	same	same	JJ
37681	1234	20	thing	thing	NN
37681	1234	21	are	be	VBP
37681	1234	22	equal	equal	JJ
37681	1234	23	to	to	IN
37681	1234	24	one	one	CD
37681	1234	25	another	another	DT
37681	1234	26	,	,	,
37681	1234	27	"	"	''
37681	1234	28	and	and	CC
37681	1234	29	"	"	``
37681	1234	30	Things	thing	NNS
37681	1234	31	which	which	WDT
37681	1234	32	are	be	VBP
37681	1234	33	halves	half	NNS
37681	1234	34	of	of	IN
37681	1234	35	the	the	DT
37681	1234	36	same	same	JJ
37681	1234	37	thing	thing	NN
37681	1234	38	are	be	VBP
37681	1234	39	equal	equal	JJ
37681	1234	40	to	to	IN
37681	1234	41	one	one	CD
37681	1234	42	another	another	DT
37681	1234	43	.	.	.
37681	1234	44	"	"	''
37681	1235	1	These	these	DT
37681	1235	2	two	two	CD
37681	1235	3	illustrate	illustrate	VBP
37681	1235	4	the	the	DT
37681	1235	5	ancient	ancient	JJ
37681	1235	6	use	use	NN
37681	1235	7	of	of	IN
37681	1235	8	_	_	NNP
37681	1235	9	duplatio	duplatio	NN
37681	1235	10	_	_	NNP
37681	1235	11	(	(	-LRB-
37681	1235	12	doubling	double	VBG
37681	1235	13	)	)	-RRB-
37681	1235	14	and	and	CC
37681	1235	15	_	_	NNP
37681	1235	16	mediatio	mediatio	NN
37681	1235	17	_	_	NNP
37681	1235	18	(	(	-LRB-
37681	1235	19	halving	halving	NNP
37681	1235	20	)	)	-RRB-
37681	1235	21	,	,	,
37681	1235	22	the	the	DT
37681	1235	23	primitive	primitive	JJ
37681	1235	24	forms	form	NNS
37681	1235	25	of	of	IN
37681	1235	26	multiplication	multiplication	NN
37681	1235	27	and	and	CC
37681	1235	28	division	division	NN
37681	1235	29	.	.	.
37681	1236	1	Euclid	Euclid	NNP
37681	1236	2	would	would	MD
37681	1236	3	not	not	RB
37681	1236	4	admit	admit	VB
37681	1236	5	the	the	DT
37681	1236	6	multiplication	multiplication	NN
37681	1236	7	axiom	axiom	NN
37681	1236	8	,	,	,
37681	1236	9	since	since	IN
37681	1236	10	to	to	IN
37681	1236	11	him	-PRON-	PRP
37681	1236	12	this	this	DT
37681	1236	13	meant	mean	VBD
37681	1236	14	merely	merely	RB
37681	1236	15	repeated	repeat	VBN
37681	1236	16	addition	addition	NN
37681	1236	17	.	.	.
37681	1237	1	The	the	DT
37681	1237	2	partition	partition	NN
37681	1237	3	(	(	-LRB-
37681	1237	4	halving	halving	NN
37681	1237	5	)	)	-RRB-
37681	1237	6	axiom	axiom	RB
37681	1237	7	he	-PRON-	PRP
37681	1237	8	did	do	VBD
37681	1237	9	not	not	RB
37681	1237	10	need	need	VB
37681	1237	11	,	,	,
37681	1237	12	and	and	CC
37681	1237	13	if	if	IN
37681	1237	14	needed	need	VBN
37681	1237	15	,	,	,
37681	1237	16	he	-PRON-	PRP
37681	1237	17	would	would	MD
37681	1237	18	have	have	VB
37681	1237	19	inferred	infer	VBN
37681	1237	20	its	-PRON-	PRP$
37681	1237	21	truth	truth	NN
37681	1237	22	.	.	.
37681	1238	1	There	there	EX
37681	1238	2	are	be	VBP
37681	1238	3	also	also	RB
37681	1238	4	the	the	DT
37681	1238	5	axioms	axiom	NNS
37681	1238	6	,	,	,
37681	1238	7	"	"	``
37681	1238	8	If	if	IN
37681	1238	9	equals	equal	NNS
37681	1238	10	are	be	VBP
37681	1238	11	added	add	VBN
37681	1238	12	to	to	IN
37681	1238	13	unequals	unequal	NNS
37681	1238	14	,	,	,
37681	1238	15	the	the	DT
37681	1238	16	wholes	whole	NNS
37681	1238	17	are	be	VBP
37681	1238	18	unequal	unequal	JJ
37681	1238	19	,	,	,
37681	1238	20	"	"	''
37681	1238	21	and	and	CC
37681	1238	22	"	"	``
37681	1238	23	If	if	IN
37681	1238	24	equals	equal	NNS
37681	1238	25	are	be	VBP
37681	1238	26	subtracted	subtract	VBN
37681	1238	27	from	from	IN
37681	1238	28	unequals	unequal	NNS
37681	1238	29	,	,	,
37681	1238	30	the	the	DT
37681	1238	31	remainders	remainder	NNS
37681	1238	32	are	be	VBP
37681	1238	33	unequal	unequal	JJ
37681	1238	34	,	,	,
37681	1238	35	"	"	''
37681	1238	36	neither	neither	DT
37681	1238	37	of	of	IN
37681	1238	38	which	which	WDT
37681	1238	39	Euclid	Euclid	NNP
37681	1238	40	would	would	MD
37681	1238	41	have	have	VB
37681	1238	42	used	use	VBN
37681	1238	43	because	because	IN
37681	1238	44	he	-PRON-	PRP
37681	1238	45	did	do	VBD
37681	1238	46	not	not	RB
37681	1238	47	define	define	VB
37681	1238	48	"	"	``
37681	1238	49	unequals	unequal	NNS
37681	1238	50	.	.	.
37681	1238	51	"	"	''
37681	1239	1	The	the	DT
37681	1239	2	modern	modern	JJ
37681	1239	3	arrangement	arrangement	NN
37681	1239	4	of	of	IN
37681	1239	5	axioms	axiom	NNS
37681	1239	6	,	,	,
37681	1239	7	covering	cover	VBG
37681	1239	8	addition	addition	NN
37681	1239	9	,	,	,
37681	1239	10	subtraction	subtraction	NN
37681	1239	11	,	,	,
37681	1239	12	multiplication	multiplication	NN
37681	1239	13	,	,	,
37681	1239	14	division	division	NN
37681	1239	15	,	,	,
37681	1239	16	powers	power	NNS
37681	1239	17	,	,	,
37681	1239	18	and	and	CC
37681	1239	19	roots	root	NNS
37681	1239	20	,	,	,
37681	1239	21	sometimes	sometimes	RB
37681	1239	22	of	of	IN
37681	1239	23	unequals	unequal	NNS
37681	1239	24	as	as	RB
37681	1239	25	well	well	RB
37681	1239	26	as	as	IN
37681	1239	27	equals	equal	NNS
37681	1239	28	,	,	,
37681	1239	29	comes	come	VBZ
37681	1239	30	from	from	IN
37681	1239	31	the	the	DT
37681	1239	32	development	development	NN
37681	1239	33	of	of	IN
37681	1239	34	algebra	algebra	NN
37681	1239	35	.	.	.
37681	1240	1	They	-PRON-	PRP
37681	1240	2	are	be	VBP
37681	1240	3	not	not	RB
37681	1240	4	all	all	DT
37681	1240	5	needed	need	VBN
37681	1240	6	for	for	IN
37681	1240	7	geometry	geometry	NN
37681	1240	8	,	,	,
37681	1240	9	but	but	CC
37681	1240	10	in	in	IN
37681	1240	11	so	so	RB
37681	1240	12	far	far	RB
37681	1240	13	as	as	IN
37681	1240	14	they	-PRON-	PRP
37681	1240	15	show	show	VBP
37681	1240	16	the	the	DT
37681	1240	17	relation	relation	NN
37681	1240	18	of	of	IN
37681	1240	19	arithmetic	arithmetic	JJ
37681	1240	20	,	,	,
37681	1240	21	algebra	algebra	NN
37681	1240	22	,	,	,
37681	1240	23	and	and	CC
37681	1240	24	geometry	geometry	NN
37681	1240	25	,	,	,
37681	1240	26	they	-PRON-	PRP
37681	1240	27	serve	serve	VBP
37681	1240	28	a	a	DT
37681	1240	29	useful	useful	JJ
37681	1240	30	purpose	purpose	NN
37681	1240	31	.	.	.
37681	1241	1	There	there	EX
37681	1241	2	are	be	VBP
37681	1241	3	also	also	RB
37681	1241	4	other	other	JJ
37681	1241	5	axioms	axiom	NNS
37681	1241	6	concerning	concern	VBG
37681	1241	7	unequals	unequal	NNS
37681	1241	8	that	that	WDT
37681	1241	9	are	be	VBP
37681	1241	10	of	of	IN
37681	1241	11	advantage	advantage	NN
37681	1241	12	to	to	IN
37681	1241	13	beginners	beginner	NNS
37681	1241	14	,	,	,
37681	1241	15	even	even	RB
37681	1241	16	though	though	IN
37681	1241	17	unnecessary	unnecessary	JJ
37681	1241	18	from	from	IN
37681	1241	19	the	the	DT
37681	1241	20	standpoint	standpoint	NN
37681	1241	21	of	of	IN
37681	1241	22	strict	strict	JJ
37681	1241	23	logic	logic	NN
37681	1241	24	.	.	.
37681	1242	1	4	4	LS
37681	1242	2	.	.	.
37681	1243	1	_	_	NNP
37681	1243	2	Things	thing	NNS
37681	1243	3	that	that	WDT
37681	1243	4	coincide	coincide	VBP
37681	1243	5	with	with	IN
37681	1243	6	one	one	NN
37681	1243	7	another	another	DT
37681	1243	8	are	be	VBP
37681	1243	9	equal	equal	JJ
37681	1243	10	to	to	IN
37681	1243	11	one	one	CD
37681	1243	12	another	another	DT
37681	1243	13	.	.	.
37681	1243	14	_	_	NNP
37681	1243	15	This	this	DT
37681	1243	16	is	be	VBZ
37681	1243	17	no	no	RB
37681	1243	18	longer	long	RBR
37681	1243	19	included	include	VBN
37681	1243	20	in	in	IN
37681	1243	21	the	the	DT
37681	1243	22	list	list	NN
37681	1243	23	of	of	IN
37681	1243	24	axioms	axiom	NNS
37681	1243	25	.	.	.
37681	1244	1	It	-PRON-	PRP
37681	1244	2	is	be	VBZ
37681	1244	3	rather	rather	RB
37681	1244	4	a	a	DT
37681	1244	5	definition	definition	NN
37681	1244	6	of	of	IN
37681	1244	7	"	"	``
37681	1244	8	equal	equal	JJ
37681	1244	9	,	,	,
37681	1244	10	"	"	''
37681	1244	11	or	or	CC
37681	1244	12	of	of	IN
37681	1244	13	"	"	``
37681	1244	14	congruent	congruent	JJ
37681	1244	15	,	,	,
37681	1244	16	"	"	''
37681	1244	17	to	to	TO
37681	1244	18	take	take	VB
37681	1244	19	the	the	DT
37681	1244	20	modern	modern	JJ
37681	1244	21	term	term	NN
37681	1244	22	.	.	.
37681	1245	1	If	if	IN
37681	1245	2	not	not	RB
37681	1245	3	a	a	DT
37681	1245	4	definition	definition	NN
37681	1245	5	,	,	,
37681	1245	6	it	-PRON-	PRP
37681	1245	7	is	be	VBZ
37681	1245	8	certainly	certainly	RB
37681	1245	9	a	a	DT
37681	1245	10	postulate	postulate	NN
37681	1245	11	rather	rather	RB
37681	1245	12	than	than	IN
37681	1245	13	an	an	DT
37681	1245	14	axiom	axiom	NN
37681	1245	15	,	,	,
37681	1245	16	being	be	VBG
37681	1245	17	purely	purely	RB
37681	1245	18	geometric	geometric	JJ
37681	1245	19	in	in	IN
37681	1245	20	character	character	NN
37681	1245	21	.	.	.
37681	1246	1	It	-PRON-	PRP
37681	1246	2	is	be	VBZ
37681	1246	3	probable	probable	JJ
37681	1246	4	that	that	IN
37681	1246	5	Euclid	Euclid	NNP
37681	1246	6	included	include	VBD
37681	1246	7	it	-PRON-	PRP
37681	1246	8	to	to	TO
37681	1246	9	show	show	VB
37681	1246	10	that	that	DT
37681	1246	11	superposition	superposition	NN
37681	1246	12	is	be	VBZ
37681	1246	13	to	to	TO
37681	1246	14	be	be	VB
37681	1246	15	considered	consider	VBN
37681	1246	16	a	a	DT
37681	1246	17	legitimate	legitimate	JJ
37681	1246	18	form	form	NN
37681	1246	19	of	of	IN
37681	1246	20	proof	proof	NN
37681	1246	21	,	,	,
37681	1246	22	but	but	CC
37681	1246	23	why	why	WRB
37681	1246	24	it	-PRON-	PRP
37681	1246	25	was	be	VBD
37681	1246	26	not	not	RB
37681	1246	27	placed	place	VBN
37681	1246	28	among	among	IN
37681	1246	29	the	the	DT
37681	1246	30	postulates	postulate	NNS
37681	1246	31	is	be	VBZ
37681	1246	32	not	not	RB
37681	1246	33	easily	easily	RB
37681	1246	34	seen	see	VBN
37681	1246	35	.	.	.
37681	1247	1	At	at	IN
37681	1247	2	any	any	DT
37681	1247	3	rate	rate	NN
37681	1247	4	it	-PRON-	PRP
37681	1247	5	is	be	VBZ
37681	1247	6	unfortunately	unfortunately	RB
37681	1247	7	worded	word	VBN
37681	1247	8	,	,	,
37681	1247	9	and	and	CC
37681	1247	10	modern	modern	JJ
37681	1247	11	writers	writer	NNS
37681	1247	12	generally	generally	RB
37681	1247	13	insert	insert	VBP
37681	1247	14	the	the	DT
37681	1247	15	postulate	postulate	NN
37681	1247	16	of	of	IN
37681	1247	17	motion	motion	NN
37681	1247	18	instead,--that	instead,--that	.
37681	1247	19	a	a	DT
37681	1247	20	figure	figure	NN
37681	1247	21	may	may	MD
37681	1247	22	be	be	VB
37681	1247	23	moved	move	VBN
37681	1247	24	about	about	RB
37681	1247	25	in	in	IN
37681	1247	26	space	space	NN
37681	1247	27	without	without	IN
37681	1247	28	altering	alter	VBG
37681	1247	29	its	-PRON-	PRP$
37681	1247	30	size	size	NN
37681	1247	31	or	or	CC
37681	1247	32	shape	shape	NN
37681	1247	33	.	.	.
37681	1248	1	The	the	DT
37681	1248	2	German	german	JJ
37681	1248	3	philosopher	philosopher	NN
37681	1248	4	,	,	,
37681	1248	5	Schopenhauer	Schopenhauer	NNP
37681	1248	6	(	(	-LRB-
37681	1248	7	1844	1844	CD
37681	1248	8	)	)	-RRB-
37681	1248	9	,	,	,
37681	1248	10	criticized	criticize	VBD
37681	1248	11	Euclid	Euclid	NNP
37681	1248	12	's	's	POS
37681	1248	13	axiom	axiom	NN
37681	1248	14	as	as	IN
37681	1248	15	follows	follow	VBZ
37681	1248	16	:	:	:
37681	1248	17	"	"	``
37681	1248	18	Coincidence	coincidence	NN
37681	1248	19	is	be	VBZ
37681	1248	20	either	either	CC
37681	1248	21	mere	mere	JJ
37681	1248	22	tautology	tautology	NN
37681	1248	23	or	or	CC
37681	1248	24	something	something	NN
37681	1248	25	entirely	entirely	RB
37681	1248	26	empirical	empirical	JJ
37681	1248	27	,	,	,
37681	1248	28	which	which	WDT
37681	1248	29	belongs	belong	VBZ
37681	1248	30	not	not	RB
37681	1248	31	to	to	TO
37681	1248	32	pure	pure	JJ
37681	1248	33	intuition	intuition	NN
37681	1248	34	but	but	CC
37681	1248	35	to	to	IN
37681	1248	36	external	external	JJ
37681	1248	37	sensuous	sensuous	JJ
37681	1248	38	experience	experience	NN
37681	1248	39	.	.	.
37681	1249	1	It	-PRON-	PRP
37681	1249	2	presupposes	presuppose	VBZ
37681	1249	3	,	,	,
37681	1249	4	in	in	IN
37681	1249	5	fact	fact	NN
37681	1249	6	,	,	,
37681	1249	7	the	the	DT
37681	1249	8	mobility	mobility	NN
37681	1249	9	of	of	IN
37681	1249	10	figures	figure	NNS
37681	1249	11	.	.	.
37681	1249	12	"	"	''
37681	1250	1	5	5	CD
37681	1250	2	.	.	.
37681	1251	1	_	_	NNP
37681	1251	2	The	the	DT
37681	1251	3	whole	whole	NN
37681	1251	4	is	be	VBZ
37681	1251	5	greater	great	JJR
37681	1251	6	than	than	IN
37681	1251	7	the	the	DT
37681	1251	8	part	part	NN
37681	1251	9	.	.	.
37681	1251	10	_	_	IN
37681	1251	11	To	to	IN
37681	1251	12	this	this	DT
37681	1251	13	Clavius	Clavius	NNP
37681	1251	14	(	(	-LRB-
37681	1251	15	1574	1574	CD
37681	1251	16	)	)	-RRB-
37681	1251	17	added	add	VBD
37681	1251	18	,	,	,
37681	1251	19	"	"	``
37681	1251	20	The	the	DT
37681	1251	21	whole	whole	NN
37681	1251	22	is	be	VBZ
37681	1251	23	equal	equal	JJ
37681	1251	24	to	to	IN
37681	1251	25	the	the	DT
37681	1251	26	sum	sum	NN
37681	1251	27	of	of	IN
37681	1251	28	its	-PRON-	PRP$
37681	1251	29	parts	part	NNS
37681	1251	30	,	,	,
37681	1251	31	"	"	''
37681	1251	32	which	which	WDT
37681	1251	33	may	may	MD
37681	1251	34	be	be	VB
37681	1251	35	taken	take	VBN
37681	1251	36	to	to	TO
37681	1251	37	be	be	VB
37681	1251	38	a	a	DT
37681	1251	39	definition	definition	NN
37681	1251	40	of	of	IN
37681	1251	41	"	"	``
37681	1251	42	whole	whole	JJ
37681	1251	43	,	,	,
37681	1251	44	"	"	''
37681	1251	45	but	but	CC
37681	1251	46	which	which	WDT
37681	1251	47	is	be	VBZ
37681	1251	48	helpful	helpful	JJ
37681	1251	49	to	to	IN
37681	1251	50	beginners	beginner	NNS
37681	1251	51	,	,	,
37681	1251	52	even	even	RB
37681	1251	53	if	if	IN
37681	1251	54	not	not	RB
37681	1251	55	logically	logically	RB
37681	1251	56	necessary	necessary	JJ
37681	1251	57	.	.	.
37681	1252	1	Some	some	DT
37681	1252	2	writers	writer	NNS
37681	1252	3	doubt	doubt	VBP
37681	1252	4	the	the	DT
37681	1252	5	genuineness	genuineness	NN
37681	1252	6	of	of	IN
37681	1252	7	this	this	DT
37681	1252	8	axiom	axiom	NN
37681	1252	9	.	.	.
37681	1253	1	Having	have	VBG
37681	1253	2	considered	consider	VBN
37681	1253	3	the	the	DT
37681	1253	4	axioms	axiom	NNS
37681	1253	5	of	of	IN
37681	1253	6	Euclid	Euclid	NNP
37681	1253	7	,	,	,
37681	1253	8	we	-PRON-	PRP
37681	1253	9	shall	shall	MD
37681	1253	10	now	now	RB
37681	1253	11	consider	consider	VB
37681	1253	12	the	the	DT
37681	1253	13	axioms	axiom	NNS
37681	1253	14	that	that	WDT
37681	1253	15	are	be	VBP
37681	1253	16	needed	need	VBN
37681	1253	17	in	in	IN
37681	1253	18	the	the	DT
37681	1253	19	study	study	NN
37681	1253	20	of	of	IN
37681	1253	21	elementary	elementary	NNP
37681	1253	22	geometry	geometry	NN
37681	1253	23	.	.	.
37681	1254	1	The	the	DT
37681	1254	2	following	follow	VBG
37681	1254	3	are	be	VBP
37681	1254	4	suggested	suggest	VBN
37681	1254	5	,	,	,
37681	1254	6	not	not	RB
37681	1254	7	from	from	IN
37681	1254	8	the	the	DT
37681	1254	9	standpoint	standpoint	NN
37681	1254	10	of	of	IN
37681	1254	11	pure	pure	JJ
37681	1254	12	logic	logic	NN
37681	1254	13	,	,	,
37681	1254	14	but	but	CC
37681	1254	15	from	from	IN
37681	1254	16	that	that	DT
37681	1254	17	of	of	IN
37681	1254	18	the	the	DT
37681	1254	19	needs	need	NNS
37681	1254	20	of	of	IN
37681	1254	21	the	the	DT
37681	1254	22	teacher	teacher	NN
37681	1254	23	and	and	CC
37681	1254	24	pupil	pupil	NN
37681	1254	25	.	.	.
37681	1255	1	1	1	LS
37681	1255	2	.	.	.
37681	1256	1	_	_	NNP
37681	1256	2	If	if	IN
37681	1256	3	equals	equal	NNS
37681	1256	4	are	be	VBP
37681	1256	5	added	add	VBN
37681	1256	6	to	to	IN
37681	1256	7	equals	equal	NNS
37681	1256	8	,	,	,
37681	1256	9	the	the	DT
37681	1256	10	sums	sum	NNS
37681	1256	11	are	be	VBP
37681	1256	12	equal	equal	JJ
37681	1256	13	.	.	.
37681	1256	14	_	_	NNP
37681	1256	15	Instead	instead	RB
37681	1256	16	of	of	IN
37681	1256	17	this	this	DT
37681	1256	18	axiom	axiom	NN
37681	1256	19	,	,	,
37681	1256	20	the	the	DT
37681	1256	21	one	one	CD
37681	1256	22	numbered	number	VBD
37681	1256	23	8	8	CD
37681	1256	24	below	below	RB
37681	1256	25	is	be	VBZ
37681	1256	26	often	often	RB
37681	1256	27	given	give	VBN
37681	1256	28	first	first	RB
37681	1256	29	.	.	.
37681	1257	1	For	for	IN
37681	1257	2	convenience	convenience	NN
37681	1257	3	in	in	IN
37681	1257	4	memorizing	memorize	VBG
37681	1257	5	,	,	,
37681	1257	6	however	however	RB
37681	1257	7	,	,	,
37681	1257	8	it	-PRON-	PRP
37681	1257	9	is	be	VBZ
37681	1257	10	better	well	JJR
37681	1257	11	to	to	TO
37681	1257	12	give	give	VB
37681	1257	13	the	the	DT
37681	1257	14	axioms	axiom	NNS
37681	1257	15	in	in	IN
37681	1257	16	the	the	DT
37681	1257	17	following	follow	VBG
37681	1257	18	order	order	NN
37681	1257	19	:	:	:
37681	1257	20	(	(	-LRB-
37681	1257	21	1	1	LS
37681	1257	22	)	)	-RRB-
37681	1257	23	addition	addition	NN
37681	1257	24	,	,	,
37681	1257	25	(	(	-LRB-
37681	1257	26	2	2	LS
37681	1257	27	)	)	-RRB-
37681	1257	28	subtraction	subtraction	NN
37681	1257	29	,	,	,
37681	1257	30	(	(	-LRB-
37681	1257	31	3	3	LS
37681	1257	32	)	)	-RRB-
37681	1257	33	multiplication	multiplication	NN
37681	1257	34	,	,	,
37681	1257	35	(	(	-LRB-
37681	1257	36	4	4	LS
37681	1257	37	)	)	-RRB-
37681	1257	38	division	division	NN
37681	1257	39	,	,	,
37681	1257	40	(	(	-LRB-
37681	1257	41	5	5	LS
37681	1257	42	)	)	-RRB-
37681	1257	43	powers	power	NNS
37681	1257	44	and	and	CC
37681	1257	45	roots,--all	roots,--all	CD
37681	1257	46	of	of	IN
37681	1257	47	equal	equal	JJ
37681	1257	48	quantities	quantity	NNS
37681	1257	49	.	.	.
37681	1258	1	2	2	LS
37681	1258	2	.	.	.
37681	1259	1	_	_	NNP
37681	1259	2	If	if	IN
37681	1259	3	equals	equal	NNS
37681	1259	4	are	be	VBP
37681	1259	5	subtracted	subtract	VBN
37681	1259	6	from	from	IN
37681	1259	7	equals	equal	NNS
37681	1259	8	,	,	,
37681	1259	9	the	the	DT
37681	1259	10	remainders	remainder	NNS
37681	1259	11	are	be	VBP
37681	1259	12	equal	equal	JJ
37681	1259	13	.	.	.
37681	1259	14	_	_	NNP
37681	1259	15	3	3	CD
37681	1259	16	.	.	.
37681	1260	1	_	_	NNP
37681	1260	2	If	if	IN
37681	1260	3	equals	equal	NNS
37681	1260	4	are	be	VBP
37681	1260	5	multiplied	multiply	VBN
37681	1260	6	by	by	IN
37681	1260	7	equals	equal	NNS
37681	1260	8	,	,	,
37681	1260	9	the	the	DT
37681	1260	10	products	product	NNS
37681	1260	11	are	be	VBP
37681	1260	12	equal	equal	JJ
37681	1260	13	.	.	.
37681	1260	14	_	_	NNP
37681	1260	15	4	4	CD
37681	1260	16	.	.	.
37681	1261	1	_	_	NNP
37681	1261	2	If	if	IN
37681	1261	3	equals	equal	NNS
37681	1261	4	are	be	VBP
37681	1261	5	divided	divide	VBN
37681	1261	6	by	by	IN
37681	1261	7	equals	equal	NNS
37681	1261	8	,	,	,
37681	1261	9	the	the	DT
37681	1261	10	quotients	quotient	NNS
37681	1261	11	are	be	VBP
37681	1261	12	equal	equal	JJ
37681	1261	13	.	.	.
37681	1261	14	_	_	NNP
37681	1261	15	5	5	CD
37681	1261	16	.	.	.
37681	1262	1	_	_	NNP
37681	1262	2	Like	like	IN
37681	1262	3	powers	power	NNS
37681	1262	4	or	or	CC
37681	1262	5	like	like	IN
37681	1262	6	positive	positive	JJ
37681	1262	7	roots	root	NNS
37681	1262	8	of	of	IN
37681	1262	9	equals	equal	NNS
37681	1262	10	are	be	VBP
37681	1262	11	equal	equal	JJ
37681	1262	12	.	.	.
37681	1262	13	_	_	NNP
37681	1262	14	Formerly	Formerly	NNP
37681	1262	15	students	student	NNS
37681	1262	16	of	of	IN
37681	1262	17	geometry	geometry	NN
37681	1262	18	knew	know	VBD
37681	1262	19	nothing	nothing	NN
37681	1262	20	of	of	IN
37681	1262	21	algebra	algebra	NN
37681	1262	22	,	,	,
37681	1262	23	and	and	CC
37681	1262	24	in	in	IN
37681	1262	25	particular	particular	JJ
37681	1262	26	nothing	nothing	NN
37681	1262	27	of	of	IN
37681	1262	28	negative	negative	JJ
37681	1262	29	quantities	quantity	NNS
37681	1262	30	.	.	.
37681	1263	1	Now	now	RB
37681	1263	2	,	,	,
37681	1263	3	however	however	RB
37681	1263	4	,	,	,
37681	1263	5	in	in	IN
37681	1263	6	American	american	JJ
37681	1263	7	schools	school	NNS
37681	1263	8	a	a	DT
37681	1263	9	pupil	pupil	NN
37681	1263	10	usually	usually	RB
37681	1263	11	studies	study	NNS
37681	1263	12	algebra	algebra	VBP
37681	1263	13	a	a	DT
37681	1263	14	year	year	NN
37681	1263	15	before	before	IN
37681	1263	16	he	-PRON-	PRP
37681	1263	17	studies	study	VBZ
37681	1263	18	demonstrative	demonstrative	JJ
37681	1263	19	geometry	geometry	NN
37681	1263	20	.	.	.
37681	1264	1	It	-PRON-	PRP
37681	1264	2	is	be	VBZ
37681	1264	3	therefore	therefore	RB
37681	1264	4	better	well	JJR
37681	1264	5	,	,	,
37681	1264	6	in	in	IN
37681	1264	7	speaking	speaking	NN
37681	1264	8	of	of	IN
37681	1264	9	roots	root	NNS
37681	1264	10	,	,	,
37681	1264	11	to	to	TO
37681	1264	12	limit	limit	VB
37681	1264	13	them	-PRON-	PRP
37681	1264	14	to	to	IN
37681	1264	15	positive	positive	JJ
37681	1264	16	numbers	number	NNS
37681	1264	17	,	,	,
37681	1264	18	since	since	IN
37681	1264	19	the	the	DT
37681	1264	20	two	two	CD
37681	1264	21	square	square	JJ
37681	1264	22	roots	root	NNS
37681	1264	23	of	of	IN
37681	1264	24	4	4	CD
37681	1264	25	(	(	-LRB-
37681	1264	26	+2	+2	NNP
37681	1264	27	and	and	CC
37681	1264	28	-2	-2	NNP
37681	1264	29	)	)	-RRB-
37681	1264	30	,	,	,
37681	1264	31	for	for	IN
37681	1264	32	example	example	NN
37681	1264	33	,	,	,
37681	1264	34	are	be	VBP
37681	1264	35	not	not	RB
37681	1264	36	equal	equal	JJ
37681	1264	37	.	.	.
37681	1265	1	If	if	IN
37681	1265	2	the	the	DT
37681	1265	3	pupil	pupil	NN
37681	1265	4	had	have	VBD
37681	1265	5	studied	study	VBN
37681	1265	6	complex	complex	JJ
37681	1265	7	numbers	number	NNS
37681	1265	8	before	before	IN
37681	1265	9	he	-PRON-	PRP
37681	1265	10	began	begin	VBD
37681	1265	11	geometry	geometry	NN
37681	1265	12	,	,	,
37681	1265	13	it	-PRON-	PRP
37681	1265	14	would	would	MD
37681	1265	15	have	have	VB
37681	1265	16	been	be	VBN
37681	1265	17	advisable	advisable	JJ
37681	1265	18	to	to	TO
37681	1265	19	limit	limit	VB
37681	1265	20	the	the	DT
37681	1265	21	roots	root	NNS
37681	1265	22	still	still	RB
37681	1265	23	further	further	RB
37681	1265	24	to	to	IN
37681	1265	25	real	real	JJ
37681	1265	26	roots	root	NNS
37681	1265	27	,	,	,
37681	1265	28	since	since	IN
37681	1265	29	the	the	DT
37681	1265	30	four	four	CD
37681	1265	31	fourth	fourth	JJ
37681	1265	32	roots	root	NNS
37681	1265	33	of	of	IN
37681	1265	34	1	1	CD
37681	1265	35	(	(	-LRB-
37681	1265	36	+1	+1	NNS
37681	1265	37	,	,	,
37681	1265	38	-1	-1	.
37681	1265	39	,	,	,
37681	1265	40	+	+	CC
37681	1265	41	[	[	-LRB-
37681	1265	42	sqrt](-1	sqrt](-1	NNP
37681	1265	43	)	)	-RRB-
37681	1265	44	,	,	,
37681	1265	45	-[sqrt](-1	-[sqrt](-1	ADD
37681	1265	46	)	)	-RRB-
37681	1265	47	)	)	-RRB-
37681	1265	48	,	,	,
37681	1265	49	for	for	IN
37681	1265	50	example	example	NN
37681	1265	51	,	,	,
37681	1265	52	are	be	VBP
37681	1265	53	not	not	RB
37681	1265	54	equal	equal	JJ
37681	1265	55	save	save	RB
37681	1265	56	in	in	IN
37681	1265	57	absolute	absolute	JJ
37681	1265	58	value	value	NN
37681	1265	59	.	.	.
37681	1266	1	It	-PRON-	PRP
37681	1266	2	is	be	VBZ
37681	1266	3	well	well	RB
37681	1266	4	,	,	,
37681	1266	5	however	however	RB
37681	1266	6	,	,	,
37681	1266	7	to	to	TO
37681	1266	8	eliminate	eliminate	VB
37681	1266	9	these	these	DT
37681	1266	10	fine	fine	JJ
37681	1266	11	distinctions	distinction	NNS
37681	1266	12	as	as	RB
37681	1266	13	far	far	RB
37681	1266	14	as	as	IN
37681	1266	15	possible	possible	JJ
37681	1266	16	,	,	,
37681	1266	17	since	since	IN
37681	1266	18	their	-PRON-	PRP$
37681	1266	19	presence	presence	NN
37681	1266	20	only	only	RB
37681	1266	21	clouds	cloud	VBZ
37681	1266	22	the	the	DT
37681	1266	23	vision	vision	NN
37681	1266	24	of	of	IN
37681	1266	25	the	the	DT
37681	1266	26	beginner	beginner	NN
37681	1266	27	.	.	.
37681	1267	1	It	-PRON-	PRP
37681	1267	2	should	should	MD
37681	1267	3	also	also	RB
37681	1267	4	be	be	VB
37681	1267	5	noted	note	VBN
37681	1267	6	that	that	IN
37681	1267	7	these	these	DT
37681	1267	8	five	five	CD
37681	1267	9	axioms	axiom	NNS
37681	1267	10	might	may	MD
37681	1267	11	be	be	VB
37681	1267	12	combined	combine	VBN
37681	1267	13	in	in	IN
37681	1267	14	one	one	CD
37681	1267	15	,	,	,
37681	1267	16	namely	namely	RB
37681	1267	17	,	,	,
37681	1267	18	_	_	NNP
37681	1267	19	If	if	IN
37681	1267	20	equals	equal	NNS
37681	1267	21	are	be	VBP
37681	1267	22	operated	operate	VBN
37681	1267	23	on	on	RP
37681	1267	24	by	by	IN
37681	1267	25	equals	equal	NNS
37681	1267	26	in	in	IN
37681	1267	27	the	the	DT
37681	1267	28	same	same	JJ
37681	1267	29	way	way	NN
37681	1267	30	,	,	,
37681	1267	31	the	the	DT
37681	1267	32	results	result	NNS
37681	1267	33	are	be	VBP
37681	1267	34	equal	equal	JJ
37681	1267	35	_	_	NNP
37681	1267	36	.	.	.
37681	1268	1	In	in	IN
37681	1268	2	Axiom	Axiom	NNP
37681	1268	3	1	1	CD
37681	1268	4	this	this	DT
37681	1268	5	operation	operation	NN
37681	1268	6	is	be	VBZ
37681	1268	7	addition	addition	NN
37681	1268	8	,	,	,
37681	1268	9	in	in	IN
37681	1268	10	Axiom	Axiom	NNP
37681	1268	11	2	2	CD
37681	1268	12	it	-PRON-	PRP
37681	1268	13	is	be	VBZ
37681	1268	14	subtraction	subtraction	NN
37681	1268	15	,	,	,
37681	1268	16	and	and	CC
37681	1268	17	so	so	RB
37681	1268	18	on	on	RB
37681	1268	19	.	.	.
37681	1269	1	Indeed	indeed	RB
37681	1269	2	,	,	,
37681	1269	3	in	in	IN
37681	1269	4	order	order	NN
37681	1269	5	to	to	TO
37681	1269	6	reduce	reduce	VB
37681	1269	7	the	the	DT
37681	1269	8	number	number	NN
37681	1269	9	of	of	IN
37681	1269	10	axioms	axiom	NNS
37681	1269	11	two	two	CD
37681	1269	12	are	be	VBP
37681	1269	13	already	already	RB
37681	1269	14	combined	combine	VBN
37681	1269	15	in	in	IN
37681	1269	16	Axiom	Axiom	NNP
37681	1269	17	5	5	CD
37681	1269	18	.	.	.
37681	1270	1	But	but	CC
37681	1270	2	there	there	EX
37681	1270	3	is	be	VBZ
37681	1270	4	a	a	DT
37681	1270	5	good	good	JJ
37681	1270	6	reason	reason	NN
37681	1270	7	for	for	IN
37681	1270	8	not	not	RB
37681	1270	9	combining	combine	VBG
37681	1270	10	the	the	DT
37681	1270	11	first	first	JJ
37681	1270	12	four	four	CD
37681	1270	13	with	with	IN
37681	1270	14	the	the	DT
37681	1270	15	fifth	fifth	JJ
37681	1270	16	,	,	,
37681	1270	17	and	and	CC
37681	1270	18	there	there	EX
37681	1270	19	is	be	VBZ
37681	1270	20	also	also	RB
37681	1270	21	a	a	DT
37681	1270	22	good	good	JJ
37681	1270	23	reason	reason	NN
37681	1270	24	for	for	IN
37681	1270	25	combining	combine	VBG
37681	1270	26	two	two	CD
37681	1270	27	in	in	IN
37681	1270	28	Axiom	Axiom	NNP
37681	1270	29	5	5	CD
37681	1270	30	.	.	.
37681	1271	1	The	the	DT
37681	1271	2	reason	reason	NN
37681	1271	3	is	be	VBZ
37681	1271	4	that	that	IN
37681	1271	5	these	these	DT
37681	1271	6	are	be	VBP
37681	1271	7	the	the	DT
37681	1271	8	axioms	axiom	NNS
37681	1271	9	continually	continually	RB
37681	1271	10	used	use	VBN
37681	1271	11	in	in	IN
37681	1271	12	equations	equation	NNS
37681	1271	13	,	,	,
37681	1271	14	and	and	CC
37681	1271	15	to	to	TO
37681	1271	16	combine	combine	VB
37681	1271	17	them	-PRON-	PRP
37681	1271	18	all	all	DT
37681	1271	19	in	in	IN
37681	1271	20	one	one	PRP
37681	1271	21	would	would	MD
37681	1271	22	be	be	VB
37681	1271	23	to	to	TO
37681	1271	24	encourage	encourage	VB
37681	1271	25	laxness	laxness	NN
37681	1271	26	of	of	IN
37681	1271	27	thought	thought	NN
37681	1271	28	on	on	IN
37681	1271	29	the	the	DT
37681	1271	30	part	part	NN
37681	1271	31	of	of	IN
37681	1271	32	the	the	DT
37681	1271	33	pupil	pupil	NN
37681	1271	34	.	.	.
37681	1272	1	He	-PRON-	PRP
37681	1272	2	would	would	MD
37681	1272	3	always	always	RB
37681	1272	4	say	say	VB
37681	1272	5	"	"	''
37681	1272	6	by	by	IN
37681	1272	7	Axiom	Axiom	NNP
37681	1272	8	1	1	CD
37681	1272	9	"	"	''
37681	1272	10	whatever	whatever	WDT
37681	1272	11	he	-PRON-	PRP
37681	1272	12	did	do	VBD
37681	1272	13	to	to	IN
37681	1272	14	an	an	DT
37681	1272	15	equation	equation	NN
37681	1272	16	,	,	,
37681	1272	17	and	and	CC
37681	1272	18	the	the	DT
37681	1272	19	teacher	teacher	NN
37681	1272	20	would	would	MD
37681	1272	21	not	not	RB
37681	1272	22	be	be	VB
37681	1272	23	certain	certain	JJ
37681	1272	24	whether	whether	IN
37681	1272	25	the	the	DT
37681	1272	26	pupil	pupil	NN
37681	1272	27	was	be	VBD
37681	1272	28	thinking	think	VBG
37681	1272	29	definitely	definitely	RB
37681	1272	30	of	of	IN
37681	1272	31	dividing	divide	VBG
37681	1272	32	equals	equal	NNS
37681	1272	33	by	by	IN
37681	1272	34	equals	equal	NNS
37681	1272	35	,	,	,
37681	1272	36	or	or	CC
37681	1272	37	had	have	VBD
37681	1272	38	a	a	DT
37681	1272	39	hazy	hazy	JJ
37681	1272	40	idea	idea	NN
37681	1272	41	that	that	IN
37681	1272	42	he	-PRON-	PRP
37681	1272	43	was	be	VBD
37681	1272	44	manipulating	manipulate	VBG
37681	1272	45	an	an	DT
37681	1272	46	equation	equation	NN
37681	1272	47	in	in	IN
37681	1272	48	some	some	DT
37681	1272	49	other	other	JJ
37681	1272	50	way	way	NN
37681	1272	51	that	that	WDT
37681	1272	52	led	lead	VBD
37681	1272	53	to	to	IN
37681	1272	54	an	an	DT
37681	1272	55	answer	answer	NN
37681	1272	56	.	.	.
37681	1273	1	On	on	IN
37681	1273	2	the	the	DT
37681	1273	3	other	other	JJ
37681	1273	4	hand	hand	NN
37681	1273	5	,	,	,
37681	1273	6	Axiom	Axiom	NNP
37681	1273	7	5	5	CD
37681	1273	8	is	be	VBZ
37681	1273	9	not	not	RB
37681	1273	10	used	use	VBN
37681	1273	11	as	as	RB
37681	1273	12	often	often	RB
37681	1273	13	as	as	IN
37681	1273	14	the	the	DT
37681	1273	15	preceding	precede	VBG
37681	1273	16	four	four	CD
37681	1273	17	,	,	,
37681	1273	18	and	and	CC
37681	1273	19	the	the	DT
37681	1273	20	interchange	interchange	NN
37681	1273	21	of	of	IN
37681	1273	22	integral	integral	JJ
37681	1273	23	and	and	CC
37681	1273	24	fractional	fractional	JJ
37681	1273	25	exponents	exponent	NNS
37681	1273	26	is	be	VBZ
37681	1273	27	relatively	relatively	RB
37681	1273	28	common	common	JJ
37681	1273	29	,	,	,
37681	1273	30	so	so	IN
37681	1273	31	that	that	IN
37681	1273	32	the	the	DT
37681	1273	33	joining	joining	NN
37681	1273	34	of	of	IN
37681	1273	35	these	these	DT
37681	1273	36	two	two	CD
37681	1273	37	axioms	axiom	NNS
37681	1273	38	in	in	IN
37681	1273	39	one	one	CD
37681	1273	40	for	for	IN
37681	1273	41	the	the	DT
37681	1273	42	purpose	purpose	NN
37681	1273	43	of	of	IN
37681	1273	44	reducing	reduce	VBG
37681	1273	45	the	the	DT
37681	1273	46	total	total	JJ
37681	1273	47	number	number	NN
37681	1273	48	is	be	VBZ
37681	1273	49	justifiable	justifiable	JJ
37681	1273	50	.	.	.
37681	1274	1	6	6	CD
37681	1274	2	.	.	.
37681	1275	1	_	_	XX
37681	1275	2	If	if	IN
37681	1275	3	unequals	unequal	NNS
37681	1275	4	are	be	VBP
37681	1275	5	operated	operate	VBN
37681	1275	6	on	on	RP
37681	1275	7	by	by	IN
37681	1275	8	positive	positive	JJ
37681	1275	9	equals	equal	NNS
37681	1275	10	in	in	IN
37681	1275	11	the	the	DT
37681	1275	12	same	same	JJ
37681	1275	13	way	way	NN
37681	1275	14	,	,	,
37681	1275	15	the	the	DT
37681	1275	16	results	result	NNS
37681	1275	17	are	be	VBP
37681	1275	18	unequal	unequal	JJ
37681	1275	19	in	in	IN
37681	1275	20	the	the	DT
37681	1275	21	same	same	JJ
37681	1275	22	order	order	NN
37681	1275	23	.	.	.
37681	1275	24	_	_	NNP
37681	1275	25	This	this	DT
37681	1275	26	includes	include	VBZ
37681	1275	27	in	in	IN
37681	1275	28	a	a	DT
37681	1275	29	single	single	JJ
37681	1275	30	statement	statement	NN
37681	1275	31	the	the	DT
37681	1275	32	six	six	CD
37681	1275	33	operations	operation	NNS
37681	1275	34	mentioned	mention	VBN
37681	1275	35	in	in	IN
37681	1275	36	the	the	DT
37681	1275	37	preceding	precede	VBG
37681	1275	38	axioms	axiom	NNS
37681	1275	39	;	;	:
37681	1275	40	that	that	RB
37681	1275	41	is	is	RB
37681	1275	42	,	,	,
37681	1275	43	if	if	IN
37681	1275	44	_	_	NNP
37681	1275	45	a	a	DT
37681	1275	46	_	_	NNP
37681	1275	47	>	>	XX
37681	1275	48	_	_	NNP
37681	1275	49	b	b	NNP
37681	1275	50	_	_	NNP
37681	1275	51	and	and	CC
37681	1275	52	if	if	IN
37681	1275	53	_	_	NNP
37681	1275	54	x	x	NNP
37681	1275	55	_	_	NNP
37681	1275	56	=	=	SYM
37681	1275	57	_	_	NNP
37681	1275	58	y	y	NNP
37681	1275	59	_	_	NNP
37681	1275	60	,	,	,
37681	1275	61	then	then	RB
37681	1275	62	_	_	NNP
37681	1275	63	a	a	DT
37681	1275	64	_	_	NNP
37681	1275	65	+	+	NNP
37681	1275	66	_	_	NNP
37681	1275	67	x	x	NNP
37681	1275	68	_	_	NNP
37681	1275	69	>	>	XX
37681	1275	70	_	_	NNP
37681	1275	71	b	b	NNP
37681	1275	72	_	_	NNP
37681	1275	73	+	+	NNP
37681	1275	74	_	_	NNP
37681	1275	75	y	y	NNP
37681	1275	76	_	_	NNP
37681	1275	77	,	,	,
37681	1275	78	_	_	NNP
37681	1275	79	a	a	DT
37681	1275	80	_	_	NNP
37681	1275	81	-	-	HYPH
37681	1275	82	_	_	NNP
37681	1275	83	x	x	NNP
37681	1275	84	_	_	NNP
37681	1275	85	>	>	XX
37681	1275	86	_	_	NNP
37681	1275	87	b	b	NNP
37681	1275	88	_	_	NNP
37681	1275	89	-	-	HYPH
37681	1275	90	_	_	NNP
37681	1275	91	y	y	NNP
37681	1275	92	_	_	NNP
37681	1275	93	,	,	,
37681	1275	94	_	_	NNP
37681	1275	95	ax	ax	NN
37681	1275	96	_	_	NNP
37681	1275	97	>	>	XX
37681	1275	98	_	_	NNP
37681	1275	99	by	by	IN
37681	1275	100	_	_	NNP
37681	1275	101	,	,	,
37681	1275	102	etc	etc	FW
37681	1275	103	.	.	.
37681	1276	1	The	the	DT
37681	1276	2	reason	reason	NN
37681	1276	3	for	for	IN
37681	1276	4	thus	thus	RB
37681	1276	5	combining	combine	VBG
37681	1276	6	six	six	CD
37681	1276	7	axioms	axiom	NNS
37681	1276	8	in	in	IN
37681	1276	9	one	one	CD
37681	1276	10	in	in	IN
37681	1276	11	the	the	DT
37681	1276	12	case	case	NN
37681	1276	13	of	of	IN
37681	1276	14	inequalities	inequality	NNS
37681	1276	15	is	be	VBZ
37681	1276	16	apparent	apparent	JJ
37681	1276	17	.	.	.
37681	1277	1	They	-PRON-	PRP
37681	1277	2	are	be	VBP
37681	1277	3	rarely	rarely	RB
37681	1277	4	used	use	VBN
37681	1277	5	in	in	IN
37681	1277	6	geometry	geometry	NN
37681	1277	7	,	,	,
37681	1277	8	and	and	CC
37681	1277	9	if	if	IN
37681	1277	10	a	a	DT
37681	1277	11	teacher	teacher	NN
37681	1277	12	is	be	VBZ
37681	1277	13	in	in	IN
37681	1277	14	doubt	doubt	NN
37681	1277	15	as	as	IN
37681	1277	16	to	to	IN
37681	1277	17	the	the	DT
37681	1277	18	pupil	pupil	NN
37681	1277	19	's	's	POS
37681	1277	20	knowledge	knowledge	NN
37681	1277	21	,	,	,
37681	1277	22	he	-PRON-	PRP
37681	1277	23	can	can	MD
37681	1277	24	easily	easily	RB
37681	1277	25	inquire	inquire	VB
37681	1277	26	in	in	IN
37681	1277	27	the	the	DT
37681	1277	28	few	few	JJ
37681	1277	29	cases	case	NNS
37681	1277	30	that	that	WDT
37681	1277	31	arise	arise	VBP
37681	1277	32	,	,	,
37681	1277	33	whereas	whereas	IN
37681	1277	34	it	-PRON-	PRP
37681	1277	35	would	would	MD
37681	1277	36	consume	consume	VB
37681	1277	37	a	a	DT
37681	1277	38	great	great	JJ
37681	1277	39	deal	deal	NN
37681	1277	40	of	of	IN
37681	1277	41	time	time	NN
37681	1277	42	to	to	TO
37681	1277	43	do	do	VB
37681	1277	44	this	this	DT
37681	1277	45	for	for	IN
37681	1277	46	the	the	DT
37681	1277	47	many	many	JJ
37681	1277	48	equations	equation	NNS
37681	1277	49	that	that	WDT
37681	1277	50	are	be	VBP
37681	1277	51	met	meet	VBN
37681	1277	52	.	.	.
37681	1278	1	The	the	DT
37681	1278	2	axiom	axiom	NN
37681	1278	3	is	be	VBZ
37681	1278	4	stated	state	VBN
37681	1278	5	in	in	IN
37681	1278	6	such	such	PDT
37681	1278	7	a	a	DT
37681	1278	8	way	way	NN
37681	1278	9	as	as	IN
37681	1278	10	to	to	TO
37681	1278	11	exclude	exclude	VB
37681	1278	12	multiplying	multiply	VBG
37681	1278	13	or	or	CC
37681	1278	14	dividing	divide	VBG
37681	1278	15	by	by	IN
37681	1278	16	negative	negative	JJ
37681	1278	17	numbers	number	NNS
37681	1278	18	,	,	,
37681	1278	19	this	this	DT
37681	1278	20	case	case	NN
37681	1278	21	not	not	RB
37681	1278	22	being	be	VBG
37681	1278	23	needed	need	VBN
37681	1278	24	.	.	.
37681	1279	1	7	7	LS
37681	1279	2	.	.	.
37681	1280	1	_	_	XX
37681	1280	2	If	if	IN
37681	1280	3	unequals	unequal	NNS
37681	1280	4	are	be	VBP
37681	1280	5	added	add	VBN
37681	1280	6	to	to	IN
37681	1280	7	unequals	unequal	NNS
37681	1280	8	in	in	IN
37681	1280	9	the	the	DT
37681	1280	10	same	same	JJ
37681	1280	11	order	order	NN
37681	1280	12	,	,	,
37681	1280	13	the	the	DT
37681	1280	14	sums	sum	NNS
37681	1280	15	are	be	VBP
37681	1280	16	unequal	unequal	JJ
37681	1280	17	in	in	IN
37681	1280	18	the	the	DT
37681	1280	19	same	same	JJ
37681	1280	20	order	order	NN
37681	1280	21	;	;	:
37681	1280	22	if	if	IN
37681	1280	23	unequals	unequal	NNS
37681	1280	24	are	be	VBP
37681	1280	25	subtracted	subtract	VBN
37681	1280	26	from	from	IN
37681	1280	27	equals	equal	NNS
37681	1280	28	,	,	,
37681	1280	29	the	the	DT
37681	1280	30	remainders	remainder	NNS
37681	1280	31	are	be	VBP
37681	1280	32	unequal	unequal	JJ
37681	1280	33	in	in	IN
37681	1280	34	the	the	DT
37681	1280	35	reverse	reverse	JJ
37681	1280	36	order	order	NN
37681	1280	37	.	.	.
37681	1280	38	_	_	NNP
37681	1280	39	These	these	DT
37681	1280	40	are	be	VBP
37681	1280	41	the	the	DT
37681	1280	42	only	only	JJ
37681	1280	43	cases	case	NNS
37681	1280	44	in	in	IN
37681	1280	45	which	which	WDT
37681	1280	46	unequals	unequal	NNS
37681	1280	47	are	be	VBP
37681	1280	48	necessarily	necessarily	RB
37681	1280	49	combined	combine	VBN
37681	1280	50	with	with	IN
37681	1280	51	unequals	unequal	NNS
37681	1280	52	,	,	,
37681	1280	53	or	or	CC
37681	1280	54	operate	operate	VB
37681	1280	55	upon	upon	IN
37681	1280	56	equals	equal	NNS
37681	1280	57	in	in	IN
37681	1280	58	geometry	geometry	NN
37681	1280	59	,	,	,
37681	1280	60	and	and	CC
37681	1280	61	the	the	DT
37681	1280	62	axiom	axiom	NN
37681	1280	63	is	be	VBZ
37681	1280	64	easily	easily	RB
37681	1280	65	explained	explain	VBN
37681	1280	66	to	to	IN
37681	1280	67	the	the	DT
37681	1280	68	class	class	NN
37681	1280	69	by	by	IN
37681	1280	70	the	the	DT
37681	1280	71	use	use	NN
37681	1280	72	of	of	IN
37681	1280	73	numbers	number	NNS
37681	1280	74	.	.	.
37681	1281	1	8	8	LS
37681	1281	2	.	.	.
37681	1282	1	_	_	NNP
37681	1282	2	Quantities	Quantities	NNPS
37681	1282	3	that	that	WDT
37681	1282	4	are	be	VBP
37681	1282	5	equal	equal	JJ
37681	1282	6	to	to	IN
37681	1282	7	the	the	DT
37681	1282	8	same	same	JJ
37681	1282	9	quantity	quantity	NN
37681	1282	10	or	or	CC
37681	1282	11	to	to	TO
37681	1282	12	equal	equal	JJ
37681	1282	13	quantities	quantity	NNS
37681	1282	14	are	be	VBP
37681	1282	15	equal	equal	JJ
37681	1282	16	to	to	IN
37681	1282	17	each	each	DT
37681	1282	18	other	other	JJ
37681	1282	19	.	.	.
37681	1282	20	_	_	NNP
37681	1282	21	In	in	IN
37681	1282	22	this	this	DT
37681	1282	23	axiom	axiom	NN
37681	1282	24	the	the	DT
37681	1282	25	word	word	NN
37681	1282	26	"	"	``
37681	1282	27	quantity	quantity	NN
37681	1282	28	"	"	''
37681	1282	29	is	be	VBZ
37681	1282	30	used	use	VBN
37681	1282	31	,	,	,
37681	1282	32	in	in	IN
37681	1282	33	the	the	DT
37681	1282	34	common	common	JJ
37681	1282	35	manner	manner	NN
37681	1282	36	of	of	IN
37681	1282	37	the	the	DT
37681	1282	38	present	present	JJ
37681	1282	39	time	time	NN
37681	1282	40	,	,	,
37681	1282	41	to	to	TO
37681	1282	42	include	include	VB
37681	1282	43	number	number	NN
37681	1282	44	and	and	CC
37681	1282	45	all	all	DT
37681	1282	46	geometric	geometric	JJ
37681	1282	47	magnitudes	magnitude	NNS
37681	1282	48	(	(	-LRB-
37681	1282	49	length	length	NN
37681	1282	50	,	,	,
37681	1282	51	area	area	NN
37681	1282	52	,	,	,
37681	1282	53	volume	volume	NN
37681	1282	54	)	)	-RRB-
37681	1282	55	.	.	.
37681	1283	1	9	9	CD
37681	1283	2	.	.	.
37681	1284	1	_	_	NNP
37681	1284	2	A	a	DT
37681	1284	3	quantity	quantity	NN
37681	1284	4	may	may	MD
37681	1284	5	be	be	VB
37681	1284	6	substituted	substitute	VBN
37681	1284	7	for	for	IN
37681	1284	8	its	-PRON-	PRP$
37681	1284	9	equal	equal	JJ
37681	1284	10	in	in	IN
37681	1284	11	an	an	DT
37681	1284	12	equation	equation	NN
37681	1284	13	or	or	CC
37681	1284	14	in	in	IN
37681	1284	15	an	an	DT
37681	1284	16	inequality	inequality	NN
37681	1284	17	.	.	.
37681	1284	18	_	_	NNP
37681	1284	19	This	this	DT
37681	1284	20	axiom	axiom	NN
37681	1284	21	is	be	VBZ
37681	1284	22	tacitly	tacitly	RB
37681	1284	23	assumed	assume	VBN
37681	1284	24	by	by	IN
37681	1284	25	all	all	DT
37681	1284	26	writers	writer	NNS
37681	1284	27	,	,	,
37681	1284	28	and	and	CC
37681	1284	29	is	be	VBZ
37681	1284	30	very	very	RB
37681	1284	31	useful	useful	JJ
37681	1284	32	in	in	IN
37681	1284	33	the	the	DT
37681	1284	34	proofs	proof	NNS
37681	1284	35	of	of	IN
37681	1284	36	geometry	geometry	NN
37681	1284	37	.	.	.
37681	1285	1	It	-PRON-	PRP
37681	1285	2	is	be	VBZ
37681	1285	3	really	really	RB
37681	1285	4	the	the	DT
37681	1285	5	basis	basis	NN
37681	1285	6	of	of	IN
37681	1285	7	several	several	JJ
37681	1285	8	other	other	JJ
37681	1285	9	axioms	axiom	NNS
37681	1285	10	,	,	,
37681	1285	11	and	and	CC
37681	1285	12	if	if	IN
37681	1285	13	we	-PRON-	PRP
37681	1285	14	were	be	VBD
37681	1285	15	seeking	seek	VBG
37681	1285	16	the	the	DT
37681	1285	17	"	"	``
37681	1285	18	irreducible	irreducible	JJ
37681	1285	19	minimum	minimum	NN
37681	1285	20	,	,	,
37681	1285	21	"	"	''
37681	1285	22	it	-PRON-	PRP
37681	1285	23	would	would	MD
37681	1285	24	replace	replace	VB
37681	1285	25	them	-PRON-	PRP
37681	1285	26	.	.	.
37681	1286	1	Since	since	IN
37681	1286	2	,	,	,
37681	1286	3	however	however	RB
37681	1286	4	,	,	,
37681	1286	5	we	-PRON-	PRP
37681	1286	6	are	be	VBP
37681	1286	7	seeking	seek	VBG
37681	1286	8	only	only	RB
37681	1286	9	a	a	DT
37681	1286	10	reasonably	reasonably	RB
37681	1286	11	abridged	abridge	VBN
37681	1286	12	list	list	NN
37681	1286	13	of	of	IN
37681	1286	14	convenient	convenient	JJ
37681	1286	15	assumptions	assumption	NNS
37681	1286	16	that	that	IN
37681	1286	17	beginners	beginner	NNS
37681	1286	18	will	will	MD
37681	1286	19	understand	understand	VB
37681	1286	20	and	and	CC
37681	1286	21	use	use	VB
37681	1286	22	,	,	,
37681	1286	23	this	this	DT
37681	1286	24	axiom	axiom	NN
37681	1286	25	has	have	VBZ
37681	1286	26	much	much	JJ
37681	1286	27	to	to	TO
37681	1286	28	commend	commend	VB
37681	1286	29	it	-PRON-	PRP
37681	1286	30	.	.	.
37681	1287	1	If	if	IN
37681	1287	2	we	-PRON-	PRP
37681	1287	3	consider	consider	VBP
37681	1287	4	the	the	DT
37681	1287	5	equations	equation	NNS
37681	1287	6	(	(	-LRB-
37681	1287	7	1	1	LS
37681	1287	8	)	)	-RRB-
37681	1287	9	_	_	NNP
37681	1287	10	a	a	DT
37681	1287	11	_	_	NNP
37681	1287	12	=	=	SYM
37681	1287	13	_	_	NNP
37681	1287	14	x	x	NNP
37681	1287	15	_	_	NNP
37681	1287	16	and	and	CC
37681	1287	17	(	(	-LRB-
37681	1287	18	2	2	LS
37681	1287	19	)	)	-RRB-
37681	1287	20	_	_	NNP
37681	1287	21	b	b	NNP
37681	1287	22	_	_	NNP
37681	1287	23	=	=	SYM
37681	1287	24	_	_	NNP
37681	1287	25	x	x	NNP
37681	1287	26	_	_	NNP
37681	1287	27	,	,	,
37681	1287	28	we	-PRON-	PRP
37681	1287	29	see	see	VBP
37681	1287	30	that	that	IN
37681	1287	31	for	for	IN
37681	1287	32	_	_	NNP
37681	1287	33	x	x	NNP
37681	1287	34	_	_	NNP
37681	1287	35	in	in	IN
37681	1287	36	equation	equation	NN
37681	1287	37	(	(	-LRB-
37681	1287	38	1	1	LS
37681	1287	39	)	)	-RRB-
37681	1287	40	we	-PRON-	PRP
37681	1287	41	may	may	MD
37681	1287	42	substitute	substitute	VB
37681	1287	43	_	_	NNP
37681	1287	44	b	b	NNP
37681	1287	45	_	_	NNP
37681	1287	46	from	from	IN
37681	1287	47	equation	equation	NN
37681	1287	48	(	(	-LRB-
37681	1287	49	2	2	CD
37681	1287	50	)	)	-RRB-
37681	1287	51	and	and	CC
37681	1287	52	have	have	VB
37681	1287	53	_	_	NNP
37681	1287	54	a	a	DT
37681	1287	55	_	_	NNP
37681	1287	56	=	=	SYM
37681	1287	57	_	_	NNP
37681	1287	58	b	b	NNP
37681	1287	59	_	_	NNP
37681	1287	60	;	;	:
37681	1287	61	in	in	IN
37681	1287	62	other	other	JJ
37681	1287	63	words	word	NNS
37681	1287	64	,	,	,
37681	1287	65	that	that	IN
37681	1287	66	Axiom	Axiom	NNP
37681	1287	67	8	8	CD
37681	1287	68	is	be	VBZ
37681	1287	69	included	include	VBN
37681	1287	70	in	in	IN
37681	1287	71	Axiom	Axiom	NNP
37681	1287	72	9	9	CD
37681	1287	73	.	.	.
37681	1288	1	Furthermore	furthermore	RB
37681	1288	2	,	,	,
37681	1288	3	if	if	IN
37681	1288	4	(	(	-LRB-
37681	1288	5	1	1	CD
37681	1288	6	)	)	-RRB-
37681	1288	7	_	_	NNP
37681	1288	8	a	a	DT
37681	1288	9	_	_	NNP
37681	1288	10	=	=	SYM
37681	1288	11	_	_	NNP
37681	1288	12	b	b	NNP
37681	1288	13	_	_	NNP
37681	1288	14	and	and	CC
37681	1288	15	(	(	-LRB-
37681	1288	16	2	2	LS
37681	1288	17	)	)	-RRB-
37681	1288	18	_	_	NNP
37681	1288	19	x	x	NNP
37681	1288	20	_	_	NNP
37681	1288	21	=	=	SYM
37681	1288	22	_	_	NNP
37681	1288	23	y	y	NNP
37681	1288	24	_	_	NNP
37681	1288	25	,	,	,
37681	1288	26	then	then	RB
37681	1288	27	since	since	IN
37681	1288	28	_	_	NNP
37681	1288	29	a	a	DT
37681	1288	30	_	_	NNP
37681	1288	31	+	+	NNP
37681	1288	32	_	_	NNP
37681	1288	33	x	x	NNP
37681	1288	34	_	_	NNP
37681	1288	35	is	be	VBZ
37681	1288	36	the	the	DT
37681	1288	37	same	same	JJ
37681	1288	38	as	as	IN
37681	1288	39	_	_	NNP
37681	1288	40	a	a	DT
37681	1288	41	_	_	NNP
37681	1288	42	+	+	NNP
37681	1288	43	_	_	NNP
37681	1288	44	x	x	NNP
37681	1288	45	_	_	NNP
37681	1288	46	,	,	,
37681	1288	47	we	-PRON-	PRP
37681	1288	48	may	may	MD
37681	1288	49	,	,	,
37681	1288	50	by	by	IN
37681	1288	51	substituting	substitute	VBG
37681	1288	52	,	,	,
37681	1288	53	say	say	VBP
37681	1288	54	that	that	IN
37681	1288	55	_	_	NNP
37681	1288	56	a	a	DT
37681	1288	57	_	_	NNP
37681	1288	58	+	+	NNP
37681	1288	59	_	_	NNP
37681	1288	60	x	x	NNP
37681	1288	61	_	_	NNP
37681	1288	62	=	=	SYM
37681	1288	63	_	_	NNP
37681	1288	64	a	a	DT
37681	1288	65	_	_	NNP
37681	1288	66	+	+	NNP
37681	1288	67	_	_	NNP
37681	1288	68	x	x	NNP
37681	1288	69	_	_	NNP
37681	1288	70	=	=	SYM
37681	1288	71	_	_	NNP
37681	1288	72	b	b	NNP
37681	1288	73	_	_	NNP
37681	1288	74	+	+	NNP
37681	1288	75	_	_	NNP
37681	1288	76	x	x	NNP
37681	1288	77	_	_	NNP
37681	1288	78	=	=	SYM
37681	1288	79	_	_	NNP
37681	1288	80	b	b	NNP
37681	1288	81	_	_	NNP
37681	1288	82	+	+	NNP
37681	1288	83	_	_	NNP
37681	1288	84	y	y	NNP
37681	1288	85	_	_	NNP
37681	1288	86	.	.	.
37681	1289	1	In	in	IN
37681	1289	2	other	other	JJ
37681	1289	3	words	word	NNS
37681	1289	4	,	,	,
37681	1289	5	Axiom	Axiom	NNP
37681	1289	6	1	1	CD
37681	1289	7	is	be	VBZ
37681	1289	8	included	include	VBN
37681	1289	9	in	in	IN
37681	1289	10	Axiom	Axiom	NNP
37681	1289	11	9	9	CD
37681	1289	12	.	.	.
37681	1290	1	Thus	thus	RB
37681	1290	2	an	an	DT
37681	1290	3	axiom	axiom	NN
37681	1290	4	that	that	WDT
37681	1290	5	includes	include	VBZ
37681	1290	6	others	other	NNS
37681	1290	7	has	have	VBZ
37681	1290	8	a	a	DT
37681	1290	9	legitimate	legitimate	JJ
37681	1290	10	place	place	NN
37681	1290	11	,	,	,
37681	1290	12	because	because	IN
37681	1290	13	a	a	DT
37681	1290	14	beginner	beginner	NN
37681	1290	15	would	would	MD
37681	1290	16	be	be	VB
37681	1290	17	too	too	RB
37681	1290	18	much	much	RB
37681	1290	19	confused	confused	JJ
37681	1290	20	by	by	IN
37681	1290	21	seeing	see	VBG
37681	1290	22	its	-PRON-	PRP$
37681	1290	23	entire	entire	JJ
37681	1290	24	scope	scope	NN
37681	1290	25	,	,	,
37681	1290	26	and	and	CC
37681	1290	27	because	because	IN
37681	1290	28	he	-PRON-	PRP
37681	1290	29	will	will	MD
37681	1290	30	make	make	VB
37681	1290	31	frequent	frequent	JJ
37681	1290	32	use	use	NN
37681	1290	33	of	of	IN
37681	1290	34	it	-PRON-	PRP
37681	1290	35	in	in	IN
37681	1290	36	his	-PRON-	PRP$
37681	1290	37	mathematical	mathematical	JJ
37681	1290	38	work	work	NN
37681	1290	39	.	.	.
37681	1291	1	10	10	CD
37681	1291	2	.	.	.
37681	1292	1	_	_	XX
37681	1292	2	If	if	IN
37681	1292	3	the	the	DT
37681	1292	4	first	first	JJ
37681	1292	5	of	of	IN
37681	1292	6	three	three	CD
37681	1292	7	quantities	quantity	NNS
37681	1292	8	is	be	VBZ
37681	1292	9	greater	great	JJR
37681	1292	10	than	than	IN
37681	1292	11	the	the	DT
37681	1292	12	second	second	JJ
37681	1292	13	,	,	,
37681	1292	14	and	and	CC
37681	1292	15	the	the	DT
37681	1292	16	second	second	JJ
37681	1292	17	is	be	VBZ
37681	1292	18	greater	great	JJR
37681	1292	19	than	than	IN
37681	1292	20	the	the	DT
37681	1292	21	third	third	JJ
37681	1292	22	,	,	,
37681	1292	23	then	then	RB
37681	1292	24	the	the	DT
37681	1292	25	first	first	JJ
37681	1292	26	is	be	VBZ
37681	1292	27	greater	great	JJR
37681	1292	28	than	than	IN
37681	1292	29	the	the	DT
37681	1292	30	third	third	JJ
37681	1292	31	.	.	.
37681	1292	32	_	_	NNP
37681	1292	33	This	this	DT
37681	1292	34	axiom	axiom	NN
37681	1292	35	is	be	VBZ
37681	1292	36	needed	need	VBN
37681	1292	37	several	several	JJ
37681	1292	38	times	time	NNS
37681	1292	39	in	in	IN
37681	1292	40	geometry	geometry	NN
37681	1292	41	.	.	.
37681	1293	1	The	the	DT
37681	1293	2	case	case	NN
37681	1293	3	in	in	IN
37681	1293	4	which	which	WDT
37681	1293	5	_	_	NNP
37681	1293	6	a	a	DT
37681	1293	7	_	_	NNP
37681	1293	8	>	>	XX
37681	1293	9	_	_	NNP
37681	1293	10	b	b	NNP
37681	1293	11	_	_	NNP
37681	1293	12	and	and	CC
37681	1293	13	_	_	NNP
37681	1293	14	b	b	NNP
37681	1293	15	_	_	NNP
37681	1293	16	=	=	SYM
37681	1293	17	_	_	NNP
37681	1293	18	c	c	NNP
37681	1293	19	_	_	NNP
37681	1293	20	,	,	,
37681	1293	21	therefore	therefore	RB
37681	1293	22	_	_	NNP
37681	1293	23	a	a	DT
37681	1293	24	_	_	NNP
37681	1293	25	>	>	XX
37681	1293	26	_	_	NNP
37681	1293	27	c	c	NNP
37681	1293	28	_	_	NNP
37681	1293	29	,	,	,
37681	1293	30	is	be	VBZ
37681	1293	31	provided	provide	VBN
37681	1293	32	for	for	IN
37681	1293	33	in	in	IN
37681	1293	34	Axiom	Axiom	NNP
37681	1293	35	9	9	CD
37681	1293	36	.	.	.
37681	1294	1	11	11	CD
37681	1294	2	.	.	.
37681	1295	1	_	_	NNP
37681	1295	2	The	the	DT
37681	1295	3	whole	whole	NN
37681	1295	4	is	be	VBZ
37681	1295	5	greater	great	JJR
37681	1295	6	than	than	IN
37681	1295	7	any	any	DT
37681	1295	8	of	of	IN
37681	1295	9	its	-PRON-	PRP$
37681	1295	10	parts	part	NNS
37681	1295	11	and	and	CC
37681	1295	12	is	be	VBZ
37681	1295	13	equal	equal	JJ
37681	1295	14	to	to	IN
37681	1295	15	the	the	DT
37681	1295	16	sum	sum	NN
37681	1295	17	of	of	IN
37681	1295	18	all	all	DT
37681	1295	19	its	-PRON-	PRP$
37681	1295	20	parts	part	NNS
37681	1295	21	.	.	.
37681	1295	22	_	_	NNP
37681	1295	23	The	the	DT
37681	1295	24	latter	latter	JJ
37681	1295	25	part	part	NN
37681	1295	26	of	of	IN
37681	1295	27	this	this	DT
37681	1295	28	axiom	axiom	NN
37681	1295	29	is	be	VBZ
37681	1295	30	really	really	RB
37681	1295	31	only	only	RB
37681	1295	32	the	the	DT
37681	1295	33	definition	definition	NN
37681	1295	34	of	of	IN
37681	1295	35	"	"	``
37681	1295	36	whole	whole	JJ
37681	1295	37	,	,	,
37681	1295	38	"	"	''
37681	1295	39	and	and	CC
37681	1295	40	it	-PRON-	PRP
37681	1295	41	would	would	MD
37681	1295	42	be	be	VB
37681	1295	43	legitimate	legitimate	JJ
37681	1295	44	to	to	TO
37681	1295	45	state	state	VB
37681	1295	46	a	a	DT
37681	1295	47	definition	definition	NN
37681	1295	48	accordingly	accordingly	RB
37681	1295	49	and	and	CC
37681	1295	50	refer	refer	VB
37681	1295	51	to	to	IN
37681	1295	52	it	-PRON-	PRP
37681	1295	53	where	where	WRB
37681	1295	54	the	the	DT
37681	1295	55	word	word	NN
37681	1295	56	is	be	VBZ
37681	1295	57	employed	employ	VBN
37681	1295	58	.	.	.
37681	1296	1	Where	where	WRB
37681	1296	2	,	,	,
37681	1296	3	however	however	RB
37681	1296	4	,	,	,
37681	1296	5	we	-PRON-	PRP
37681	1296	6	wish	wish	VBP
37681	1296	7	to	to	TO
37681	1296	8	speak	speak	VB
37681	1296	9	of	of	IN
37681	1296	10	a	a	DT
37681	1296	11	polygon	polygon	NN
37681	1296	12	,	,	,
37681	1296	13	for	for	IN
37681	1296	14	example	example	NN
37681	1296	15	,	,	,
37681	1296	16	and	and	CC
37681	1296	17	wish	wish	VBP
37681	1296	18	to	to	TO
37681	1296	19	say	say	VB
37681	1296	20	that	that	IN
37681	1296	21	the	the	DT
37681	1296	22	area	area	NN
37681	1296	23	is	be	VBZ
37681	1296	24	equal	equal	JJ
37681	1296	25	to	to	IN
37681	1296	26	the	the	DT
37681	1296	27	combined	combine	VBN
37681	1296	28	areas	area	NNS
37681	1296	29	of	of	IN
37681	1296	30	the	the	DT
37681	1296	31	triangles	triangle	NNS
37681	1296	32	composing	compose	VBG
37681	1296	33	it	-PRON-	PRP
37681	1296	34	,	,	,
37681	1296	35	it	-PRON-	PRP
37681	1296	36	is	be	VBZ
37681	1296	37	more	more	RBR
37681	1296	38	satisfactory	satisfactory	JJ
37681	1296	39	to	to	TO
37681	1296	40	have	have	VB
37681	1296	41	this	this	DT
37681	1296	42	axiom	axiom	NN
37681	1296	43	to	to	TO
37681	1296	44	which	which	WDT
37681	1296	45	to	to	TO
37681	1296	46	refer	refer	VB
37681	1296	47	.	.	.
37681	1297	1	It	-PRON-	PRP
37681	1297	2	will	will	MD
37681	1297	3	be	be	VB
37681	1297	4	noticed	notice	VBN
37681	1297	5	that	that	IN
37681	1297	6	two	two	CD
37681	1297	7	related	related	JJ
37681	1297	8	axioms	axiom	NNS
37681	1297	9	are	be	VBP
37681	1297	10	here	here	RB
37681	1297	11	combined	combine	VBN
37681	1297	12	in	in	IN
37681	1297	13	one	one	CD
37681	1297	14	,	,	,
37681	1297	15	for	for	IN
37681	1297	16	a	a	DT
37681	1297	17	reason	reason	NN
37681	1297	18	similar	similar	JJ
37681	1297	19	to	to	IN
37681	1297	20	the	the	DT
37681	1297	21	one	one	NN
37681	1297	22	stated	state	VBN
37681	1297	23	under	under	IN
37681	1297	24	Axiom	Axiom	NNP
37681	1297	25	5	5	CD
37681	1297	26	.	.	.
37681	1298	1	In	in	IN
37681	1298	2	the	the	DT
37681	1298	3	case	case	NN
37681	1298	4	of	of	IN
37681	1298	5	the	the	DT
37681	1298	6	postulates	postulate	NNS
37681	1298	7	we	-PRON-	PRP
37681	1298	8	are	be	VBP
37681	1298	9	met	meet	VBN
37681	1298	10	by	by	IN
37681	1298	11	a	a	DT
37681	1298	12	problem	problem	NN
37681	1298	13	similar	similar	JJ
37681	1298	14	to	to	IN
37681	1298	15	the	the	DT
37681	1298	16	one	one	NN
37681	1298	17	confronting	confront	VBG
37681	1298	18	us	-PRON-	PRP
37681	1298	19	in	in	IN
37681	1298	20	connection	connection	NN
37681	1298	21	with	with	IN
37681	1298	22	the	the	DT
37681	1298	23	axioms,--the	axioms,--the	NNP
37681	1298	24	problem	problem	NN
37681	1298	25	of	of	IN
37681	1298	26	the	the	DT
37681	1298	27	"	"	``
37681	1298	28	irreducible	irreducible	JJ
37681	1298	29	minimum	minimum	NN
37681	1298	30	"	"	''
37681	1298	31	as	as	IN
37681	1298	32	related	relate	VBN
37681	1298	33	to	to	IN
37681	1298	34	the	the	DT
37681	1298	35	question	question	NN
37681	1298	36	of	of	IN
37681	1298	37	teaching	teaching	NN
37681	1298	38	.	.	.
37681	1299	1	Manifestly	manifestly	RB
37681	1299	2	Euclid	Euclid	NNP
37681	1299	3	used	use	VBD
37681	1299	4	postulates	postulate	NNS
37681	1299	5	that	that	IN
37681	1299	6	he	-PRON-	PRP
37681	1299	7	did	do	VBD
37681	1299	8	not	not	RB
37681	1299	9	state	state	VB
37681	1299	10	,	,	,
37681	1299	11	and	and	CC
37681	1299	12	proved	prove	VBD
37681	1299	13	some	some	DT
37681	1299	14	statements	statement	NNS
37681	1299	15	that	that	WDT
37681	1299	16	he	-PRON-	PRP
37681	1299	17	might	may	MD
37681	1299	18	have	have	VB
37681	1299	19	postulated	postulate	VBN
37681	1299	20	.	.	.
37681	1300	1	[	[	-LRB-
37681	1300	2	47	47	CD
37681	1300	3	]	]	-RRB-
37681	1300	4	The	the	DT
37681	1300	5	postulates	postulate	NNS
37681	1300	6	given	give	VBN
37681	1300	7	by	by	IN
37681	1300	8	Euclid	Euclid	NNP
37681	1300	9	under	under	IN
37681	1300	10	the	the	DT
37681	1300	11	name	name	NN
37681	1300	12	[	[	-LRB-
37681	1300	13	Greek	Greek	NNP
37681	1300	14	:	:	:
37681	1300	15	aitêmata](_aitemata	aitêmata](_aitemata	NNP
37681	1300	16	_	_	NNP
37681	1300	17	)	)	-RRB-
37681	1300	18	were	be	VBD
37681	1300	19	requests	request	NNS
37681	1300	20	made	make	VBN
37681	1300	21	by	by	IN
37681	1300	22	the	the	DT
37681	1300	23	teacher	teacher	NN
37681	1300	24	to	to	IN
37681	1300	25	his	-PRON-	PRP$
37681	1300	26	pupil	pupil	NN
37681	1300	27	that	that	IN
37681	1300	28	certain	certain	JJ
37681	1300	29	things	thing	NNS
37681	1300	30	be	be	VB
37681	1300	31	conceded	concede	VBN
37681	1300	32	.	.	.
37681	1301	1	They	-PRON-	PRP
37681	1301	2	were	be	VBD
37681	1301	3	five	five	CD
37681	1301	4	in	in	IN
37681	1301	5	number	number	NN
37681	1301	6	,	,	,
37681	1301	7	as	as	IN
37681	1301	8	follows	follow	VBZ
37681	1301	9	:	:	:
37681	1301	10	1	1	CD
37681	1301	11	.	.	.
37681	1302	1	_	_	NNP
37681	1302	2	Let	let	VB
37681	1302	3	the	the	DT
37681	1302	4	following	following	NN
37681	1302	5	be	be	VB
37681	1302	6	conceded	concede	VBN
37681	1302	7	:	:	:
37681	1302	8	to	to	TO
37681	1302	9	draw	draw	VB
37681	1302	10	a	a	DT
37681	1302	11	straight	straight	JJ
37681	1302	12	line	line	NN
37681	1302	13	from	from	IN
37681	1302	14	any	any	DT
37681	1302	15	point	point	NN
37681	1302	16	to	to	IN
37681	1302	17	any	any	DT
37681	1302	18	point	point	NN
37681	1302	19	.	.	.
37681	1302	20	_	_	NNP
37681	1302	21	Strictly	strictly	RB
37681	1302	22	speaking	speak	VBG
37681	1302	23	,	,	,
37681	1302	24	Euclid	Euclid	NNP
37681	1302	25	might	may	MD
37681	1302	26	have	have	VB
37681	1302	27	been	be	VBN
37681	1302	28	required	require	VBN
37681	1302	29	to	to	TO
37681	1302	30	postulate	postulate	VB
37681	1302	31	that	that	IN
37681	1302	32	points	point	NNS
37681	1302	33	and	and	CC
37681	1302	34	straight	straight	JJ
37681	1302	35	lines	line	NNS
37681	1302	36	exist	exist	VBP
37681	1302	37	,	,	,
37681	1302	38	but	but	CC
37681	1302	39	he	-PRON-	PRP
37681	1302	40	evidently	evidently	RB
37681	1302	41	considered	consider	VBD
37681	1302	42	this	this	DT
37681	1302	43	statement	statement	NN
37681	1302	44	sufficient	sufficient	JJ
37681	1302	45	.	.	.
37681	1303	1	Aristotle	Aristotle	NNP
37681	1303	2	had	have	VBD
37681	1303	3	,	,	,
37681	1303	4	however	however	RB
37681	1303	5	,	,	,
37681	1303	6	already	already	RB
37681	1303	7	called	call	VBD
37681	1303	8	attention	attention	NN
37681	1303	9	to	to	IN
37681	1303	10	the	the	DT
37681	1303	11	fact	fact	NN
37681	1303	12	that	that	IN
37681	1303	13	a	a	DT
37681	1303	14	mere	mere	JJ
37681	1303	15	definition	definition	NN
37681	1303	16	was	be	VBD
37681	1303	17	sufficient	sufficient	JJ
37681	1303	18	only	only	RB
37681	1303	19	to	to	TO
37681	1303	20	show	show	VB
37681	1303	21	what	what	WP
37681	1303	22	a	a	DT
37681	1303	23	concept	concept	NN
37681	1303	24	is	be	VBZ
37681	1303	25	,	,	,
37681	1303	26	and	and	CC
37681	1303	27	that	that	IN
37681	1303	28	this	this	DT
37681	1303	29	must	must	MD
37681	1303	30	be	be	VB
37681	1303	31	followed	follow	VBN
37681	1303	32	by	by	IN
37681	1303	33	a	a	DT
37681	1303	34	proof	proof	NN
37681	1303	35	that	that	IN
37681	1303	36	the	the	DT
37681	1303	37	thing	thing	NN
37681	1303	38	exists	exist	VBZ
37681	1303	39	.	.	.
37681	1304	1	We	-PRON-	PRP
37681	1304	2	might	may	MD
37681	1304	3	,	,	,
37681	1304	4	for	for	IN
37681	1304	5	example	example	NN
37681	1304	6	,	,	,
37681	1304	7	define	define	NNP
37681	1304	8	_	_	NNP
37681	1304	9	x	x	NNP
37681	1304	10	_	_	NNP
37681	1304	11	as	as	IN
37681	1304	12	a	a	DT
37681	1304	13	line	line	NN
37681	1304	14	that	that	WDT
37681	1304	15	bisects	bisect	VBZ
37681	1304	16	an	an	DT
37681	1304	17	angle	angle	NN
37681	1304	18	without	without	IN
37681	1304	19	meeting	meet	VBG
37681	1304	20	the	the	DT
37681	1304	21	vertex	vertex	NN
37681	1304	22	,	,	,
37681	1304	23	but	but	CC
37681	1304	24	this	this	DT
37681	1304	25	would	would	MD
37681	1304	26	not	not	RB
37681	1304	27	show	show	VB
37681	1304	28	that	that	IN
37681	1304	29	an	an	DT
37681	1304	30	_	_	NNP
37681	1304	31	x	x	NNP
37681	1304	32	_	_	NNP
37681	1304	33	exists	exist	VBZ
37681	1304	34	,	,	,
37681	1304	35	and	and	CC
37681	1304	36	indeed	indeed	RB
37681	1304	37	it	-PRON-	PRP
37681	1304	38	does	do	VBZ
37681	1304	39	not	not	RB
37681	1304	40	exist	exist	VB
37681	1304	41	.	.	.
37681	1305	1	Euclid	Euclid	NNP
37681	1305	2	evidently	evidently	RB
37681	1305	3	intended	intend	VBD
37681	1305	4	the	the	DT
37681	1305	5	postulate	postulate	NN
37681	1305	6	to	to	TO
37681	1305	7	assert	assert	VB
37681	1305	8	that	that	IN
37681	1305	9	this	this	DT
37681	1305	10	line	line	NN
37681	1305	11	joining	join	VBG
37681	1305	12	two	two	CD
37681	1305	13	points	point	NNS
37681	1305	14	is	be	VBZ
37681	1305	15	unique	unique	JJ
37681	1305	16	,	,	,
37681	1305	17	which	which	WDT
37681	1305	18	is	be	VBZ
37681	1305	19	only	only	RB
37681	1305	20	another	another	DT
37681	1305	21	way	way	NN
37681	1305	22	of	of	IN
37681	1305	23	saying	say	VBG
37681	1305	24	that	that	IN
37681	1305	25	two	two	CD
37681	1305	26	points	point	NNS
37681	1305	27	determine	determine	VBP
37681	1305	28	a	a	DT
37681	1305	29	straight	straight	JJ
37681	1305	30	line	line	NN
37681	1305	31	,	,	,
37681	1305	32	and	and	CC
37681	1305	33	really	really	RB
37681	1305	34	includes	include	VBZ
37681	1305	35	the	the	DT
37681	1305	36	idea	idea	NN
37681	1305	37	that	that	IN
37681	1305	38	two	two	CD
37681	1305	39	straight	straight	JJ
37681	1305	40	lines	line	NNS
37681	1305	41	can	can	MD
37681	1305	42	not	not	RB
37681	1305	43	inclose	inclose	VB
37681	1305	44	space	space	NN
37681	1305	45	.	.	.
37681	1306	1	For	for	IN
37681	1306	2	purposes	purpose	NNS
37681	1306	3	of	of	IN
37681	1306	4	instruction	instruction	NN
37681	1306	5	,	,	,
37681	1306	6	the	the	DT
37681	1306	7	postulate	postulate	NN
37681	1306	8	would	would	MD
37681	1306	9	be	be	VB
37681	1306	10	clearer	clear	JJR
37681	1306	11	if	if	IN
37681	1306	12	it	-PRON-	PRP
37681	1306	13	read	read	VBD
37681	1306	14	,	,	,
37681	1306	15	_	_	NNP
37681	1306	16	One	one	CD
37681	1306	17	straight	straight	JJ
37681	1306	18	line	line	NN
37681	1306	19	,	,	,
37681	1306	20	and	and	CC
37681	1306	21	only	only	RB
37681	1306	22	one	one	CD
37681	1306	23	,	,	,
37681	1306	24	can	can	MD
37681	1306	25	be	be	VB
37681	1306	26	drawn	draw	VBN
37681	1306	27	through	through	IN
37681	1306	28	two	two	CD
37681	1306	29	given	give	VBN
37681	1306	30	points	point	NNS
37681	1306	31	_	_	NNP
37681	1306	32	.	.	.
37681	1307	1	2	2	LS
37681	1307	2	.	.	.
37681	1308	1	_	_	NNP
37681	1308	2	To	to	TO
37681	1308	3	produce	produce	VB
37681	1308	4	a	a	DT
37681	1308	5	finite	finite	JJ
37681	1308	6	straight	straight	JJ
37681	1308	7	line	line	NN
37681	1308	8	continuously	continuously	RB
37681	1308	9	in	in	IN
37681	1308	10	a	a	DT
37681	1308	11	straight	straight	JJ
37681	1308	12	line	line	NN
37681	1308	13	.	.	.
37681	1308	14	_	_	NNP
37681	1308	15	In	in	IN
37681	1308	16	this	this	DT
37681	1308	17	postulate	postulate	NN
37681	1308	18	Euclid	Euclid	NNP
37681	1308	19	practically	practically	RB
37681	1308	20	assumes	assume	VBZ
37681	1308	21	that	that	IN
37681	1308	22	a	a	DT
37681	1308	23	straight	straight	JJ
37681	1308	24	line	line	NN
37681	1308	25	can	can	MD
37681	1308	26	be	be	VB
37681	1308	27	produced	produce	VBN
37681	1308	28	only	only	RB
37681	1308	29	in	in	IN
37681	1308	30	a	a	DT
37681	1308	31	straight	straight	JJ
37681	1308	32	line	line	NN
37681	1308	33	;	;	:
37681	1308	34	in	in	IN
37681	1308	35	other	other	JJ
37681	1308	36	words	word	NNS
37681	1308	37	,	,	,
37681	1308	38	that	that	IN
37681	1308	39	two	two	CD
37681	1308	40	different	different	JJ
37681	1308	41	straight	straight	JJ
37681	1308	42	lines	line	NNS
37681	1308	43	can	can	MD
37681	1308	44	not	not	RB
37681	1308	45	have	have	VB
37681	1308	46	a	a	DT
37681	1308	47	common	common	JJ
37681	1308	48	segment	segment	NN
37681	1308	49	.	.	.
37681	1309	1	Several	several	JJ
37681	1309	2	attempts	attempt	NNS
37681	1309	3	have	have	VBP
37681	1309	4	been	be	VBN
37681	1309	5	made	make	VBN
37681	1309	6	to	to	TO
37681	1309	7	prove	prove	VB
37681	1309	8	this	this	DT
37681	1309	9	fact	fact	NN
37681	1309	10	,	,	,
37681	1309	11	but	but	CC
37681	1309	12	without	without	IN
37681	1309	13	any	any	DT
37681	1309	14	marked	marked	JJ
37681	1309	15	success	success	NN
37681	1309	16	.	.	.
37681	1310	1	3	3	LS
37681	1310	2	.	.	.
37681	1311	1	_	_	NNP
37681	1311	2	To	to	TO
37681	1311	3	describe	describe	VB
37681	1311	4	a	a	DT
37681	1311	5	circle	circle	NN
37681	1311	6	with	with	IN
37681	1311	7	any	any	DT
37681	1311	8	center	center	NN
37681	1311	9	and	and	CC
37681	1311	10	radius	radius	NN
37681	1311	11	.	.	.
37681	1311	12	_	_	NNP
37681	1311	13	4	4	CD
37681	1311	14	.	.	.
37681	1312	1	_	_	NNP
37681	1312	2	That	that	IN
37681	1312	3	all	all	DT
37681	1312	4	right	right	JJ
37681	1312	5	angles	angle	NNS
37681	1312	6	are	be	VBP
37681	1312	7	equal	equal	JJ
37681	1312	8	to	to	IN
37681	1312	9	one	one	CD
37681	1312	10	another	another	DT
37681	1312	11	.	.	.
37681	1312	12	_	_	NNP
37681	1312	13	While	while	IN
37681	1312	14	this	this	DT
37681	1312	15	postulate	postulate	NN
37681	1312	16	asserts	assert	VBZ
37681	1312	17	the	the	DT
37681	1312	18	essential	essential	JJ
37681	1312	19	truth	truth	NN
37681	1312	20	that	that	WDT
37681	1312	21	a	a	DT
37681	1312	22	right	right	JJ
37681	1312	23	angle	angle	NN
37681	1312	24	is	be	VBZ
37681	1312	25	a	a	DT
37681	1312	26	_	_	NNP
37681	1312	27	determinate	determinate	NN
37681	1312	28	magnitude	magnitude	NN
37681	1312	29	_	_	NNP
37681	1312	30	so	so	IN
37681	1312	31	that	that	IN
37681	1312	32	it	-PRON-	PRP
37681	1312	33	really	really	RB
37681	1312	34	serves	serve	VBZ
37681	1312	35	as	as	IN
37681	1312	36	an	an	DT
37681	1312	37	invariable	invariable	JJ
37681	1312	38	standard	standard	NN
37681	1312	39	by	by	IN
37681	1312	40	which	which	WDT
37681	1312	41	other	other	JJ
37681	1312	42	(	(	-LRB-
37681	1312	43	acute	acute	JJ
37681	1312	44	and	and	CC
37681	1312	45	obtuse	obtuse	JJ
37681	1312	46	)	)	-RRB-
37681	1312	47	angles	angle	NNS
37681	1312	48	may	may	MD
37681	1312	49	be	be	VB
37681	1312	50	measured	measure	VBN
37681	1312	51	,	,	,
37681	1312	52	much	much	RB
37681	1312	53	more	more	JJR
37681	1312	54	than	than	IN
37681	1312	55	this	this	DT
37681	1312	56	is	be	VBZ
37681	1312	57	implied	imply	VBN
37681	1312	58	,	,	,
37681	1312	59	as	as	IN
37681	1312	60	will	will	MD
37681	1312	61	easily	easily	RB
37681	1312	62	be	be	VB
37681	1312	63	seen	see	VBN
37681	1312	64	from	from	IN
37681	1312	65	the	the	DT
37681	1312	66	following	follow	VBG
37681	1312	67	consideration	consideration	NN
37681	1312	68	.	.	.
37681	1313	1	If	if	IN
37681	1313	2	the	the	DT
37681	1313	3	statement	statement	NN
37681	1313	4	is	be	VBZ
37681	1313	5	to	to	TO
37681	1313	6	be	be	VB
37681	1313	7	_	_	NNP
37681	1313	8	proved	prove	VBD
37681	1313	9	_	_	NNP
37681	1313	10	,	,	,
37681	1313	11	it	-PRON-	PRP
37681	1313	12	can	can	MD
37681	1313	13	only	only	RB
37681	1313	14	be	be	VB
37681	1313	15	proved	prove	VBN
37681	1313	16	by	by	IN
37681	1313	17	the	the	DT
37681	1313	18	method	method	NN
37681	1313	19	of	of	IN
37681	1313	20	applying	apply	VBG
37681	1313	21	one	one	CD
37681	1313	22	pair	pair	NN
37681	1313	23	of	of	IN
37681	1313	24	right	right	JJ
37681	1313	25	angles	angle	NNS
37681	1313	26	to	to	IN
37681	1313	27	another	another	DT
37681	1313	28	and	and	CC
37681	1313	29	so	so	RB
37681	1313	30	arguing	argue	VBG
37681	1313	31	their	-PRON-	PRP$
37681	1313	32	equality	equality	NN
37681	1313	33	.	.	.
37681	1314	1	But	but	CC
37681	1314	2	this	this	DT
37681	1314	3	method	method	NN
37681	1314	4	would	would	MD
37681	1314	5	not	not	RB
37681	1314	6	be	be	VB
37681	1314	7	valid	valid	JJ
37681	1314	8	unless	unless	IN
37681	1314	9	on	on	IN
37681	1314	10	the	the	DT
37681	1314	11	assumption	assumption	NN
37681	1314	12	of	of	IN
37681	1314	13	the	the	DT
37681	1314	14	_	_	NNP
37681	1314	15	invariability	invariability	NN
37681	1314	16	of	of	IN
37681	1314	17	figures	figure	NNS
37681	1314	18	_	_	NNP
37681	1314	19	,	,	,
37681	1314	20	which	which	WDT
37681	1314	21	would	would	MD
37681	1314	22	have	have	VB
37681	1314	23	to	to	TO
37681	1314	24	be	be	VB
37681	1314	25	asserted	assert	VBN
37681	1314	26	as	as	IN
37681	1314	27	an	an	DT
37681	1314	28	antecedent	antecedent	NN
37681	1314	29	postulate	postulate	NN
37681	1314	30	.	.	.
37681	1315	1	Euclid	Euclid	NNP
37681	1315	2	preferred	prefer	VBD
37681	1315	3	to	to	TO
37681	1315	4	assert	assert	VB
37681	1315	5	as	as	IN
37681	1315	6	a	a	DT
37681	1315	7	postulate	postulate	NN
37681	1315	8	,	,	,
37681	1315	9	directly	directly	RB
37681	1315	10	,	,	,
37681	1315	11	the	the	DT
37681	1315	12	fact	fact	NN
37681	1315	13	that	that	IN
37681	1315	14	all	all	DT
37681	1315	15	right	right	JJ
37681	1315	16	angles	angle	NNS
37681	1315	17	are	be	VBP
37681	1315	18	equal	equal	JJ
37681	1315	19	;	;	:
37681	1315	20	and	and	CC
37681	1315	21	hence	hence	RB
37681	1315	22	his	-PRON-	PRP$
37681	1315	23	postulate	postulate	NN
37681	1315	24	must	must	MD
37681	1315	25	be	be	VB
37681	1315	26	taken	take	VBN
37681	1315	27	as	as	IN
37681	1315	28	equivalent	equivalent	JJ
37681	1315	29	to	to	IN
37681	1315	30	the	the	DT
37681	1315	31	principle	principle	NN
37681	1315	32	of	of	IN
37681	1315	33	_	_	NNP
37681	1315	34	invariability	invariability	NN
37681	1315	35	of	of	IN
37681	1315	36	figures	figure	NNS
37681	1315	37	_	_	NNP
37681	1315	38	,	,	,
37681	1315	39	or	or	CC
37681	1315	40	its	-PRON-	PRP$
37681	1315	41	equivalent	equivalent	NN
37681	1315	42	,	,	,
37681	1315	43	the	the	DT
37681	1315	44	_	_	NNP
37681	1315	45	homogeneity	homogeneity	NN
37681	1315	46	_	_	NNP
37681	1315	47	of	of	IN
37681	1315	48	space	space	NN
37681	1315	49	.	.	.
37681	1316	1	[	[	-LRB-
37681	1316	2	48	48	CD
37681	1316	3	]	]	-RRB-
37681	1316	4	It	-PRON-	PRP
37681	1316	5	is	be	VBZ
37681	1316	6	better	well	JJR
37681	1316	7	educational	educational	JJ
37681	1316	8	policy	policy	NN
37681	1316	9	,	,	,
37681	1316	10	however	however	RB
37681	1316	11	,	,	,
37681	1316	12	to	to	TO
37681	1316	13	assert	assert	VB
37681	1316	14	this	this	DT
37681	1316	15	fact	fact	NN
37681	1316	16	more	more	RBR
37681	1316	17	definitely	definitely	RB
37681	1316	18	,	,	,
37681	1316	19	and	and	CC
37681	1316	20	to	to	TO
37681	1316	21	state	state	VB
37681	1316	22	the	the	DT
37681	1316	23	additional	additional	JJ
37681	1316	24	assumption	assumption	NN
37681	1316	25	that	that	WDT
37681	1316	26	figures	figure	NNS
37681	1316	27	may	may	MD
37681	1316	28	be	be	VB
37681	1316	29	moved	move	VBN
37681	1316	30	about	about	RB
37681	1316	31	in	in	IN
37681	1316	32	space	space	NN
37681	1316	33	without	without	IN
37681	1316	34	deformation	deformation	NN
37681	1316	35	.	.	.
37681	1317	1	The	the	DT
37681	1317	2	fourth	fourth	JJ
37681	1317	3	of	of	IN
37681	1317	4	Euclid	Euclid	NNP
37681	1317	5	's	's	POS
37681	1317	6	postulates	postulate	NNS
37681	1317	7	is	be	VBZ
37681	1317	8	often	often	RB
37681	1317	9	given	give	VBN
37681	1317	10	as	as	IN
37681	1317	11	an	an	DT
37681	1317	12	axiom	axiom	NN
37681	1317	13	,	,	,
37681	1317	14	following	follow	VBG
37681	1317	15	the	the	DT
37681	1317	16	idea	idea	NN
37681	1317	17	of	of	IN
37681	1317	18	the	the	DT
37681	1317	19	Greek	greek	JJ
37681	1317	20	philosopher	philosopher	NN
37681	1317	21	Geminus	Geminus	NNP
37681	1317	22	(	(	-LRB-
37681	1317	23	who	who	WP
37681	1317	24	flourished	flourish	VBD
37681	1317	25	in	in	IN
37681	1317	26	the	the	DT
37681	1317	27	first	first	JJ
37681	1317	28	century	century	NN
37681	1317	29	B.C.	B.C.	NNP
37681	1318	1	)	)	-RRB-
37681	1318	2	,	,	,
37681	1318	3	but	but	CC
37681	1318	4	this	this	DT
37681	1318	5	is	be	VBZ
37681	1318	6	because	because	IN
37681	1318	7	Euclid	Euclid	NNP
37681	1318	8	's	's	POS
37681	1318	9	distinction	distinction	NN
37681	1318	10	between	between	IN
37681	1318	11	axiom	axiom	NN
37681	1318	12	and	and	CC
37681	1318	13	postulate	postulate	NN
37681	1318	14	is	be	VBZ
37681	1318	15	not	not	RB
37681	1318	16	always	always	RB
37681	1318	17	understood	understand	VBN
37681	1318	18	.	.	.
37681	1319	1	Proclus	Proclus	NNP
37681	1319	2	(	(	-LRB-
37681	1319	3	410	410	CD
37681	1319	4	-	-	SYM
37681	1319	5	485	485	CD
37681	1319	6	A.D.	A.D.	NNP
37681	1319	7	)	)	-RRB-
37681	1319	8	endeavored	endeavor	VBD
37681	1319	9	to	to	TO
37681	1319	10	prove	prove	VB
37681	1319	11	the	the	DT
37681	1319	12	postulate	postulate	NN
37681	1319	13	,	,	,
37681	1319	14	and	and	CC
37681	1319	15	a	a	DT
37681	1319	16	later	later	JJ
37681	1319	17	and	and	CC
37681	1319	18	more	more	RBR
37681	1319	19	scientific	scientific	JJ
37681	1319	20	effort	effort	NN
37681	1319	21	was	be	VBD
37681	1319	22	made	make	VBN
37681	1319	23	by	by	IN
37681	1319	24	the	the	DT
37681	1319	25	Italian	italian	JJ
37681	1319	26	geometrician	geometrician	NN
37681	1319	27	Saccheri	Saccheri	NNP
37681	1319	28	(	(	-LRB-
37681	1319	29	1667	1667	CD
37681	1319	30	-	-	SYM
37681	1319	31	1733	1733	CD
37681	1319	32	)	)	-RRB-
37681	1319	33	.	.	.
37681	1320	1	It	-PRON-	PRP
37681	1320	2	is	be	VBZ
37681	1320	3	very	very	RB
37681	1320	4	commonly	commonly	RB
37681	1320	5	taken	take	VBN
37681	1320	6	as	as	IN
37681	1320	7	a	a	DT
37681	1320	8	postulate	postulate	NN
37681	1320	9	that	that	WDT
37681	1320	10	all	all	DT
37681	1320	11	straight	straight	JJ
37681	1320	12	angles	angle	NNS
37681	1320	13	are	be	VBP
37681	1320	14	equal	equal	JJ
37681	1320	15	,	,	,
37681	1320	16	this	this	DT
37681	1320	17	being	be	VBG
37681	1320	18	more	more	RBR
37681	1320	19	evident	evident	JJ
37681	1320	20	to	to	IN
37681	1320	21	the	the	DT
37681	1320	22	senses	sense	NNS
37681	1320	23	,	,	,
37681	1320	24	and	and	CC
37681	1320	25	the	the	DT
37681	1320	26	equality	equality	NN
37681	1320	27	of	of	IN
37681	1320	28	right	right	JJ
37681	1320	29	angles	angle	NNS
37681	1320	30	is	be	VBZ
37681	1320	31	deduced	deduce	VBN
37681	1320	32	as	as	IN
37681	1320	33	a	a	DT
37681	1320	34	corollary	corollary	NN
37681	1320	35	.	.	.
37681	1321	1	This	this	DT
37681	1321	2	method	method	NN
37681	1321	3	of	of	IN
37681	1321	4	procedure	procedure	NN
37681	1321	5	has	have	VBZ
37681	1321	6	the	the	DT
37681	1321	7	sanction	sanction	NN
37681	1321	8	of	of	IN
37681	1321	9	many	many	JJ
37681	1321	10	of	of	IN
37681	1321	11	our	-PRON-	PRP$
37681	1321	12	best	good	JJS
37681	1321	13	modern	modern	JJ
37681	1321	14	scholars	scholar	NNS
37681	1321	15	.	.	.
37681	1322	1	5	5	CD
37681	1322	2	.	.	.
37681	1323	1	_	_	NNP
37681	1323	2	That	that	DT
37681	1323	3	,	,	,
37681	1323	4	if	if	IN
37681	1323	5	a	a	DT
37681	1323	6	straight	straight	JJ
37681	1323	7	line	line	NN
37681	1323	8	falling	fall	VBG
37681	1323	9	on	on	IN
37681	1323	10	two	two	CD
37681	1323	11	straight	straight	JJ
37681	1323	12	lines	line	NNS
37681	1323	13	make	make	VBP
37681	1323	14	the	the	DT
37681	1323	15	interior	interior	JJ
37681	1323	16	angle	angle	NN
37681	1323	17	on	on	IN
37681	1323	18	the	the	DT
37681	1323	19	same	same	JJ
37681	1323	20	side	side	NN
37681	1323	21	less	less	JJR
37681	1323	22	than	than	IN
37681	1323	23	two	two	CD
37681	1323	24	right	right	JJ
37681	1323	25	angles	angle	NNS
37681	1323	26	,	,	,
37681	1323	27	the	the	DT
37681	1323	28	two	two	CD
37681	1323	29	straight	straight	JJ
37681	1323	30	lines	line	NNS
37681	1323	31	,	,	,
37681	1323	32	if	if	IN
37681	1323	33	produced	produce	VBN
37681	1323	34	indefinitely	indefinitely	RB
37681	1323	35	,	,	,
37681	1323	36	meet	meet	VB
37681	1323	37	on	on	IN
37681	1323	38	that	that	DT
37681	1323	39	side	side	NN
37681	1323	40	on	on	IN
37681	1323	41	which	which	WDT
37681	1323	42	are	be	VBP
37681	1323	43	the	the	DT
37681	1323	44	angles	angle	NNS
37681	1323	45	less	less	JJR
37681	1323	46	than	than	IN
37681	1323	47	the	the	DT
37681	1323	48	two	two	CD
37681	1323	49	right	right	JJ
37681	1323	50	angles	angle	NNS
37681	1323	51	.	.	.
37681	1323	52	_	_	NNP
37681	1323	53	This	this	DT
37681	1323	54	famous	famous	JJ
37681	1323	55	postulate	postulate	NN
37681	1323	56	,	,	,
37681	1323	57	long	long	RB
37681	1323	58	since	since	IN
37681	1323	59	abandoned	abandon	VBN
37681	1323	60	in	in	IN
37681	1323	61	teaching	teach	VBG
37681	1323	62	the	the	DT
37681	1323	63	beginner	beginner	NN
37681	1323	64	in	in	IN
37681	1323	65	geometry	geometry	NN
37681	1323	66	,	,	,
37681	1323	67	is	be	VBZ
37681	1323	68	a	a	DT
37681	1323	69	remarkable	remarkable	JJ
37681	1323	70	evidence	evidence	NN
37681	1323	71	of	of	IN
37681	1323	72	the	the	DT
37681	1323	73	clear	clear	JJ
37681	1323	74	vision	vision	NN
37681	1323	75	of	of	IN
37681	1323	76	Euclid	Euclid	NNP
37681	1323	77	.	.	.
37681	1324	1	For	for	IN
37681	1324	2	two	two	CD
37681	1324	3	thousand	thousand	CD
37681	1324	4	years	year	NNS
37681	1324	5	mathematicians	mathematicians	NNPS
37681	1324	6	sought	seek	VBD
37681	1324	7	to	to	TO
37681	1324	8	prove	prove	VB
37681	1324	9	it	-PRON-	PRP
37681	1324	10	,	,	,
37681	1324	11	only	only	RB
37681	1324	12	to	to	TO
37681	1324	13	demonstrate	demonstrate	VB
37681	1324	14	the	the	DT
37681	1324	15	wisdom	wisdom	NN
37681	1324	16	of	of	IN
37681	1324	17	its	-PRON-	PRP$
37681	1324	18	author	author	NN
37681	1324	19	in	in	IN
37681	1324	20	placing	place	VBG
37681	1324	21	it	-PRON-	PRP
37681	1324	22	among	among	IN
37681	1324	23	the	the	DT
37681	1324	24	assumptions	assumption	NNS
37681	1324	25	.	.	.
37681	1325	1	[	[	-LRB-
37681	1325	2	49	49	CD
37681	1325	3	]	]	-RRB-
37681	1325	4	Every	every	DT
37681	1325	5	proof	proof	NN
37681	1325	6	adduced	adduce	VBD
37681	1325	7	contains	contain	VBZ
37681	1325	8	some	some	DT
37681	1325	9	assumption	assumption	NN
37681	1325	10	that	that	IN
37681	1325	11	practically	practically	RB
37681	1325	12	conceals	conceal	VBZ
37681	1325	13	the	the	DT
37681	1325	14	postulate	postulate	NN
37681	1325	15	itself	-PRON-	PRP
37681	1325	16	.	.	.
37681	1326	1	Thus	thus	RB
37681	1326	2	the	the	DT
37681	1326	3	great	great	JJ
37681	1326	4	English	english	JJ
37681	1326	5	mathematician	mathematician	NN
37681	1326	6	John	John	NNP
37681	1326	7	Wallis	Wallis	NNP
37681	1326	8	(	(	-LRB-
37681	1326	9	1616	1616	CD
37681	1326	10	-	-	SYM
37681	1326	11	1703	1703	CD
37681	1326	12	)	)	-RRB-
37681	1326	13	gave	give	VBD
37681	1326	14	a	a	DT
37681	1326	15	proof	proof	NN
37681	1326	16	based	base	VBN
37681	1326	17	upon	upon	IN
37681	1326	18	the	the	DT
37681	1326	19	assumption	assumption	NN
37681	1326	20	that	that	IN
37681	1326	21	"	"	``
37681	1326	22	given	give	VBN
37681	1326	23	a	a	DT
37681	1326	24	figure	figure	NN
37681	1326	25	,	,	,
37681	1326	26	another	another	DT
37681	1326	27	figure	figure	NN
37681	1326	28	is	be	VBZ
37681	1326	29	possible	possible	JJ
37681	1326	30	which	which	WDT
37681	1326	31	is	be	VBZ
37681	1326	32	similar	similar	JJ
37681	1326	33	to	to	IN
37681	1326	34	the	the	DT
37681	1326	35	given	give	VBN
37681	1326	36	one	one	CD
37681	1326	37	,	,	,
37681	1326	38	and	and	CC
37681	1326	39	of	of	IN
37681	1326	40	any	any	DT
37681	1326	41	size	size	NN
37681	1326	42	whatever	whatever	WDT
37681	1326	43	.	.	.
37681	1326	44	"	"	''
37681	1327	1	Legendre	Legendre	NNP
37681	1327	2	(	(	-LRB-
37681	1327	3	1752	1752	CD
37681	1327	4	-	-	SYM
37681	1327	5	1833	1833	CD
37681	1327	6	)	)	-RRB-
37681	1327	7	did	do	VBD
37681	1327	8	substantially	substantially	RB
37681	1327	9	the	the	DT
37681	1327	10	same	same	JJ
37681	1327	11	at	at	IN
37681	1327	12	one	one	CD
37681	1327	13	time	time	NN
37681	1327	14	,	,	,
37681	1327	15	and	and	CC
37681	1327	16	offered	offer	VBD
37681	1327	17	several	several	JJ
37681	1327	18	other	other	JJ
37681	1327	19	proofs	proof	NNS
37681	1327	20	,	,	,
37681	1327	21	each	each	DT
37681	1327	22	depending	depend	VBG
37681	1327	23	upon	upon	IN
37681	1327	24	some	some	DT
37681	1327	25	equally	equally	RB
37681	1327	26	unprovable	unprovable	JJ
37681	1327	27	assumption	assumption	NN
37681	1327	28	.	.	.
37681	1328	1	The	the	DT
37681	1328	2	definite	definite	JJ
37681	1328	3	proof	proof	NN
37681	1328	4	that	that	IN
37681	1328	5	the	the	DT
37681	1328	6	postulate	postulate	NN
37681	1328	7	can	can	MD
37681	1328	8	not	not	RB
37681	1328	9	be	be	VB
37681	1328	10	demonstrated	demonstrate	VBN
37681	1328	11	is	be	VBZ
37681	1328	12	due	due	JJ
37681	1328	13	to	to	IN
37681	1328	14	the	the	DT
37681	1328	15	Italian	Italian	NNP
37681	1328	16	Beltrami	Beltrami	NNP
37681	1328	17	(	(	-LRB-
37681	1328	18	1868	1868	CD
37681	1328	19	)	)	-RRB-
37681	1328	20	.	.	.
37681	1329	1	Of	of	IN
37681	1329	2	the	the	DT
37681	1329	3	alternative	alternative	JJ
37681	1329	4	forms	form	NNS
37681	1329	5	of	of	IN
37681	1329	6	the	the	DT
37681	1329	7	postulate	postulate	NN
37681	1329	8	,	,	,
37681	1329	9	that	that	DT
37681	1329	10	of	of	IN
37681	1329	11	Proclus	Proclus	NNP
37681	1329	12	is	be	VBZ
37681	1329	13	generally	generally	RB
37681	1329	14	considered	consider	VBN
37681	1329	15	the	the	DT
37681	1329	16	best	well	RBS
37681	1329	17	suited	suit	VBN
37681	1329	18	to	to	IN
37681	1329	19	beginners	beginner	NNS
37681	1329	20	.	.	.
37681	1330	1	As	as	IN
37681	1330	2	stated	state	VBN
37681	1330	3	by	by	IN
37681	1330	4	Playfair	Playfair	NNP
37681	1330	5	(	(	-LRB-
37681	1330	6	1795	1795	CD
37681	1330	7	)	)	-RRB-
37681	1330	8	,	,	,
37681	1330	9	this	this	DT
37681	1330	10	is	be	VBZ
37681	1330	11	,	,	,
37681	1330	12	"	"	``
37681	1330	13	Through	through	IN
37681	1330	14	a	a	DT
37681	1330	15	given	give	VBN
37681	1330	16	point	point	NN
37681	1330	17	only	only	RB
37681	1330	18	one	one	CD
37681	1330	19	parallel	parallel	NN
37681	1330	20	can	can	MD
37681	1330	21	be	be	VB
37681	1330	22	drawn	draw	VBN
37681	1330	23	to	to	IN
37681	1330	24	a	a	DT
37681	1330	25	given	give	VBN
37681	1330	26	straight	straight	JJ
37681	1330	27	line	line	NN
37681	1330	28	"	"	''
37681	1330	29	;	;	,
37681	1330	30	and	and	CC
37681	1330	31	as	as	IN
37681	1330	32	stated	state	VBN
37681	1330	33	by	by	IN
37681	1330	34	Proclus	Proclus	NNP
37681	1330	35	,	,	,
37681	1330	36	"	"	``
37681	1330	37	If	if	IN
37681	1330	38	a	a	DT
37681	1330	39	straight	straight	JJ
37681	1330	40	line	line	NN
37681	1330	41	intersect	intersect	VBP
37681	1330	42	one	one	CD
37681	1330	43	of	of	IN
37681	1330	44	two	two	CD
37681	1330	45	parallels	parallel	NNS
37681	1330	46	,	,	,
37681	1330	47	it	-PRON-	PRP
37681	1330	48	will	will	MD
37681	1330	49	intersect	intersect	VB
37681	1330	50	the	the	DT
37681	1330	51	other	other	JJ
37681	1330	52	also	also	RB
37681	1330	53	.	.	.
37681	1330	54	"	"	''
37681	1331	1	Playfair	Playfair	NNP
37681	1331	2	's	's	POS
37681	1331	3	form	form	NN
37681	1331	4	is	be	VBZ
37681	1331	5	now	now	RB
37681	1331	6	the	the	DT
37681	1331	7	common	common	JJ
37681	1331	8	"	"	``
37681	1331	9	postulate	postulate	NN
37681	1331	10	of	of	IN
37681	1331	11	parallels	parallel	NNS
37681	1331	12	,	,	,
37681	1331	13	"	"	''
37681	1331	14	and	and	CC
37681	1331	15	is	be	VBZ
37681	1331	16	the	the	DT
37681	1331	17	one	one	NN
37681	1331	18	that	that	WDT
37681	1331	19	seems	seem	VBZ
37681	1331	20	destined	destine	VBN
37681	1331	21	to	to	TO
37681	1331	22	endure	endure	VB
37681	1331	23	.	.	.
37681	1332	1	Posidonius	Posidonius	NNP
37681	1332	2	and	and	CC
37681	1332	3	Geminus	Geminus	NNP
37681	1332	4	,	,	,
37681	1332	5	both	both	DT
37681	1332	6	Stoics	Stoics	NNPS
37681	1332	7	of	of	IN
37681	1332	8	the	the	DT
37681	1332	9	first	first	JJ
37681	1332	10	century	century	NN
37681	1332	11	B.C.	B.C.	NNP
37681	1332	12	,	,	,
37681	1332	13	gave	give	VBD
37681	1332	14	as	as	IN
37681	1332	15	their	-PRON-	PRP$
37681	1332	16	alternative	alternative	NN
37681	1332	17	,	,	,
37681	1332	18	"	"	``
37681	1332	19	There	there	EX
37681	1332	20	exist	exist	VBP
37681	1332	21	straight	straight	JJ
37681	1332	22	lines	line	NNS
37681	1332	23	everywhere	everywhere	RB
37681	1332	24	equidistant	equidistant	JJ
37681	1332	25	from	from	IN
37681	1332	26	one	one	CD
37681	1332	27	another	another	DT
37681	1332	28	.	.	.
37681	1332	29	"	"	''
37681	1333	1	One	one	CD
37681	1333	2	of	of	IN
37681	1333	3	Legendre	Legendre	NNP
37681	1333	4	's	's	POS
37681	1333	5	alternatives	alternative	NNS
37681	1333	6	is	be	VBZ
37681	1333	7	,	,	,
37681	1333	8	"	"	``
37681	1333	9	There	there	EX
37681	1333	10	exists	exist	VBZ
37681	1333	11	a	a	DT
37681	1333	12	triangle	triangle	NN
37681	1333	13	in	in	IN
37681	1333	14	which	which	WDT
37681	1333	15	the	the	DT
37681	1333	16	sum	sum	NN
37681	1333	17	of	of	IN
37681	1333	18	the	the	DT
37681	1333	19	three	three	CD
37681	1333	20	angles	angle	NNS
37681	1333	21	is	be	VBZ
37681	1333	22	equal	equal	JJ
37681	1333	23	to	to	IN
37681	1333	24	two	two	CD
37681	1333	25	right	right	JJ
37681	1333	26	angles	angle	NNS
37681	1333	27	.	.	.
37681	1333	28	"	"	''
37681	1334	1	One	one	CD
37681	1334	2	of	of	IN
37681	1334	3	the	the	DT
37681	1334	4	latest	late	JJS
37681	1334	5	attempts	attempt	NNS
37681	1334	6	to	to	TO
37681	1334	7	suggest	suggest	VB
37681	1334	8	a	a	DT
37681	1334	9	substitute	substitute	NN
37681	1334	10	is	be	VBZ
37681	1334	11	that	that	DT
37681	1334	12	of	of	IN
37681	1334	13	the	the	DT
37681	1334	14	Italian	italian	JJ
37681	1334	15	Ingrami	Ingrami	NNP
37681	1334	16	(	(	-LRB-
37681	1334	17	1904	1904	CD
37681	1334	18	)	)	-RRB-
37681	1334	19	,	,	,
37681	1334	20	"	"	``
37681	1334	21	Two	two	CD
37681	1334	22	parallel	parallel	JJ
37681	1334	23	straight	straight	JJ
37681	1334	24	lines	line	NNS
37681	1334	25	intercept	intercept	VBP
37681	1334	26	,	,	,
37681	1334	27	on	on	IN
37681	1334	28	every	every	DT
37681	1334	29	transversal	transversal	NN
37681	1334	30	which	which	WDT
37681	1334	31	passes	pass	VBZ
37681	1334	32	through	through	IN
37681	1334	33	the	the	DT
37681	1334	34	mid	mid	NN
37681	1334	35	-	-	NN
37681	1334	36	point	point	NN
37681	1334	37	of	of	IN
37681	1334	38	a	a	DT
37681	1334	39	segment	segment	NN
37681	1334	40	included	include	VBN
37681	1334	41	between	between	IN
37681	1334	42	them	-PRON-	PRP
37681	1334	43	,	,	,
37681	1334	44	another	another	DT
37681	1334	45	segment	segment	NN
37681	1334	46	the	the	DT
37681	1334	47	mid	mid	NN
37681	1334	48	-	-	NN
37681	1334	49	point	point	NN
37681	1334	50	of	of	IN
37681	1334	51	which	which	WDT
37681	1334	52	is	be	VBZ
37681	1334	53	the	the	DT
37681	1334	54	mid	mid	NN
37681	1334	55	-	-	NN
37681	1334	56	point	point	NN
37681	1334	57	of	of	IN
37681	1334	58	the	the	DT
37681	1334	59	first	first	JJ
37681	1334	60	.	.	.
37681	1334	61	"	"	''
37681	1335	1	Of	of	RB
37681	1335	2	course	course	RB
37681	1335	3	it	-PRON-	PRP
37681	1335	4	is	be	VBZ
37681	1335	5	entirely	entirely	RB
37681	1335	6	possible	possible	JJ
37681	1335	7	to	to	TO
37681	1335	8	assume	assume	VB
37681	1335	9	that	that	IN
37681	1335	10	through	through	IN
37681	1335	11	a	a	DT
37681	1335	12	point	point	NN
37681	1335	13	more	more	JJR
37681	1335	14	than	than	IN
37681	1335	15	one	one	CD
37681	1335	16	line	line	NN
37681	1335	17	can	can	MD
37681	1335	18	be	be	VB
37681	1335	19	drawn	draw	VBN
37681	1335	20	parallel	parallel	JJ
37681	1335	21	to	to	IN
37681	1335	22	a	a	DT
37681	1335	23	given	give	VBN
37681	1335	24	straight	straight	JJ
37681	1335	25	line	line	NN
37681	1335	26	,	,	,
37681	1335	27	in	in	IN
37681	1335	28	which	which	WDT
37681	1335	29	case	case	NN
37681	1335	30	another	another	DT
37681	1335	31	type	type	NN
37681	1335	32	of	of	IN
37681	1335	33	geometry	geometry	NN
37681	1335	34	can	can	MD
37681	1335	35	be	be	VB
37681	1335	36	built	build	VBN
37681	1335	37	up	up	RP
37681	1335	38	,	,	,
37681	1335	39	equally	equally	RB
37681	1335	40	rigorous	rigorous	JJ
37681	1335	41	with	with	IN
37681	1335	42	Euclid	Euclid	NNP
37681	1335	43	's	's	POS
37681	1335	44	.	.	.
37681	1336	1	This	this	DT
37681	1336	2	was	be	VBD
37681	1336	3	done	do	VBN
37681	1336	4	at	at	IN
37681	1336	5	the	the	DT
37681	1336	6	close	close	NN
37681	1336	7	of	of	IN
37681	1336	8	the	the	DT
37681	1336	9	first	first	JJ
37681	1336	10	quarter	quarter	NN
37681	1336	11	of	of	IN
37681	1336	12	the	the	DT
37681	1336	13	nineteenth	nineteenth	JJ
37681	1336	14	century	century	NN
37681	1336	15	by	by	IN
37681	1336	16	Lobachevsky	Lobachevsky	NNP
37681	1336	17	(	(	-LRB-
37681	1336	18	1793	1793	CD
37681	1336	19	-	-	SYM
37681	1336	20	1856	1856	CD
37681	1336	21	)	)	-RRB-
37681	1336	22	and	and	CC
37681	1336	23	Bolyai	Bolyai	NNP
37681	1336	24	(	(	-LRB-
37681	1336	25	1802	1802	CD
37681	1336	26	-	-	SYM
37681	1336	27	1860	1860	CD
37681	1336	28	)	)	-RRB-
37681	1336	29	,	,	,
37681	1336	30	resulting	result	VBG
37681	1336	31	in	in	IN
37681	1336	32	the	the	DT
37681	1336	33	first	first	JJ
37681	1336	34	of	of	IN
37681	1336	35	several	several	JJ
37681	1336	36	"	"	``
37681	1336	37	non	non	JJ
37681	1336	38	-	-	JJ
37681	1336	39	Euclidean	euclidean	JJ
37681	1336	40	"	"	''
37681	1336	41	geometries	geometry	NNS
37681	1336	42	.	.	.
37681	1337	1	[	[	-LRB-
37681	1337	2	50	50	CD
37681	1337	3	]	]	-RRB-
37681	1337	4	Taking	take	VBG
37681	1337	5	the	the	DT
37681	1337	6	problem	problem	NN
37681	1337	7	to	to	TO
37681	1337	8	be	be	VB
37681	1337	9	that	that	DT
37681	1337	10	of	of	IN
37681	1337	11	stating	state	VBG
37681	1337	12	a	a	DT
37681	1337	13	reasonably	reasonably	RB
37681	1337	14	small	small	JJ
37681	1337	15	number	number	NN
37681	1337	16	of	of	IN
37681	1337	17	geometric	geometric	JJ
37681	1337	18	assumptions	assumption	NNS
37681	1337	19	that	that	WDT
37681	1337	20	may	may	MD
37681	1337	21	form	form	VB
37681	1337	22	a	a	DT
37681	1337	23	basis	basis	NN
37681	1337	24	to	to	TO
37681	1337	25	supplement	supplement	VB
37681	1337	26	the	the	DT
37681	1337	27	general	general	JJ
37681	1337	28	axioms	axiom	NNS
37681	1337	29	,	,	,
37681	1337	30	that	that	WDT
37681	1337	31	shall	shall	MD
37681	1337	32	cover	cover	VB
37681	1337	33	the	the	DT
37681	1337	34	most	most	RBS
37681	1337	35	important	important	JJ
37681	1337	36	matters	matter	NNS
37681	1337	37	to	to	TO
37681	1337	38	which	which	WDT
37681	1337	39	the	the	DT
37681	1337	40	student	student	NN
37681	1337	41	must	must	MD
37681	1337	42	refer	refer	VB
37681	1337	43	,	,	,
37681	1337	44	and	and	CC
37681	1337	45	that	that	DT
37681	1337	46	shall	shall	MD
37681	1337	47	be	be	VB
37681	1337	48	so	so	RB
37681	1337	49	simple	simple	JJ
37681	1337	50	as	as	RB
37681	1337	51	easily	easily	RB
37681	1337	52	to	to	TO
37681	1337	53	be	be	VB
37681	1337	54	understood	understand	VBN
37681	1337	55	by	by	IN
37681	1337	56	a	a	DT
37681	1337	57	beginner	beginner	NN
37681	1337	58	,	,	,
37681	1337	59	the	the	DT
37681	1337	60	following	follow	VBG
37681	1337	61	are	be	VBP
37681	1337	62	recommended	recommend	VBN
37681	1337	63	:	:	:
37681	1337	64	1	1	CD
37681	1337	65	.	.	.
37681	1338	1	_	_	NNP
37681	1338	2	One	one	CD
37681	1338	3	straight	straight	JJ
37681	1338	4	line	line	NN
37681	1338	5	,	,	,
37681	1338	6	and	and	CC
37681	1338	7	only	only	RB
37681	1338	8	one	one	CD
37681	1338	9	,	,	,
37681	1338	10	can	can	MD
37681	1338	11	be	be	VB
37681	1338	12	drawn	draw	VBN
37681	1338	13	through	through	IN
37681	1338	14	two	two	CD
37681	1338	15	given	give	VBN
37681	1338	16	points	point	NNS
37681	1338	17	.	.	.
37681	1338	18	_	_	NNP
37681	1338	19	This	this	DT
37681	1338	20	should	should	MD
37681	1338	21	also	also	RB
37681	1338	22	be	be	VB
37681	1338	23	stated	state	VBN
37681	1338	24	for	for	IN
37681	1338	25	convenience	convenience	NN
37681	1338	26	in	in	IN
37681	1338	27	the	the	DT
37681	1338	28	form	form	NN
37681	1338	29	,	,	,
37681	1338	30	_	_	NNP
37681	1338	31	Two	two	CD
37681	1338	32	points	point	NNS
37681	1338	33	determine	determine	VBP
37681	1338	34	a	a	DT
37681	1338	35	straight	straight	JJ
37681	1338	36	line	line	NN
37681	1338	37	_	_	NNP
37681	1338	38	.	.	.
37681	1339	1	From	from	IN
37681	1339	2	it	-PRON-	PRP
37681	1339	3	may	may	MD
37681	1339	4	also	also	RB
37681	1339	5	be	be	VB
37681	1339	6	drawn	draw	VBN
37681	1339	7	this	this	DT
37681	1339	8	corollary	corollary	NN
37681	1339	9	,	,	,
37681	1339	10	_	_	NNP
37681	1339	11	Two	two	CD
37681	1339	12	straight	straight	JJ
37681	1339	13	lines	line	NNS
37681	1339	14	can	can	MD
37681	1339	15	intersect	intersect	VB
37681	1339	16	in	in	IN
37681	1339	17	only	only	RB
37681	1339	18	one	one	CD
37681	1339	19	point	point	NN
37681	1339	20	_	_	NNP
37681	1339	21	,	,	,
37681	1339	22	since	since	IN
37681	1339	23	two	two	CD
37681	1339	24	points	point	NNS
37681	1339	25	would	would	MD
37681	1339	26	determine	determine	VB
37681	1339	27	a	a	DT
37681	1339	28	straight	straight	JJ
37681	1339	29	line	line	NN
37681	1339	30	.	.	.
37681	1340	1	Such	such	JJ
37681	1340	2	obvious	obvious	JJ
37681	1340	3	restatements	restatement	NNS
37681	1340	4	of	of	IN
37681	1340	5	or	or	CC
37681	1340	6	corollaries	corollary	NNS
37681	1340	7	to	to	IN
37681	1340	8	a	a	DT
37681	1340	9	postulate	postulate	NN
37681	1340	10	are	be	VBP
37681	1340	11	to	to	TO
37681	1340	12	be	be	VB
37681	1340	13	commended	commend	VBN
37681	1340	14	,	,	,
37681	1340	15	since	since	IN
37681	1340	16	a	a	DT
37681	1340	17	beginner	beginner	NN
37681	1340	18	is	be	VBZ
37681	1340	19	often	often	RB
37681	1340	20	discouraged	discourage	VBN
37681	1340	21	by	by	IN
37681	1340	22	having	have	VBG
37681	1340	23	to	to	TO
37681	1340	24	prove	prove	VB
37681	1340	25	what	what	WP
37681	1340	26	is	be	VBZ
37681	1340	27	so	so	RB
37681	1340	28	obvious	obvious	JJ
37681	1340	29	that	that	IN
37681	1340	30	a	a	DT
37681	1340	31	demonstration	demonstration	NN
37681	1340	32	fails	fail	VBZ
37681	1340	33	to	to	TO
37681	1340	34	commend	commend	VB
37681	1340	35	itself	-PRON-	PRP
37681	1340	36	to	to	IN
37681	1340	37	his	-PRON-	PRP$
37681	1340	38	mind	mind	NN
37681	1340	39	.	.	.
37681	1341	1	2	2	LS
37681	1341	2	.	.	.
37681	1342	1	_	_	NNP
37681	1342	2	A	a	DT
37681	1342	3	straight	straight	JJ
37681	1342	4	line	line	NN
37681	1342	5	may	may	MD
37681	1342	6	be	be	VB
37681	1342	7	produced	produce	VBN
37681	1342	8	to	to	IN
37681	1342	9	any	any	DT
37681	1342	10	required	require	VBN
37681	1342	11	length	length	NN
37681	1342	12	.	.	.
37681	1342	13	_	_	NNP
37681	1342	14	This	this	DT
37681	1342	15	,	,	,
37681	1342	16	like	like	IN
37681	1342	17	Postulate	Postulate	NNP
37681	1342	18	1	1	CD
37681	1342	19	,	,	,
37681	1342	20	requires	require	VBZ
37681	1342	21	the	the	DT
37681	1342	22	use	use	NN
37681	1342	23	of	of	IN
37681	1342	24	a	a	DT
37681	1342	25	straightedge	straightedge	NN
37681	1342	26	for	for	IN
37681	1342	27	drawing	draw	VBG
37681	1342	28	the	the	DT
37681	1342	29	physical	physical	JJ
37681	1342	30	figure	figure	NN
37681	1342	31	.	.	.
37681	1343	1	The	the	DT
37681	1343	2	required	require	VBN
37681	1343	3	length	length	NN
37681	1343	4	is	be	VBZ
37681	1343	5	attained	attain	VBN
37681	1343	6	by	by	IN
37681	1343	7	using	use	VBG
37681	1343	8	the	the	DT
37681	1343	9	compasses	compass	NNS
37681	1343	10	to	to	TO
37681	1343	11	measure	measure	VB
37681	1343	12	the	the	DT
37681	1343	13	distance	distance	NN
37681	1343	14	.	.	.
37681	1344	1	The	the	DT
37681	1344	2	straightedge	straightedge	NN
37681	1344	3	and	and	CC
37681	1344	4	the	the	DT
37681	1344	5	compasses	compass	NNS
37681	1344	6	are	be	VBP
37681	1344	7	the	the	DT
37681	1344	8	only	only	JJ
37681	1344	9	two	two	CD
37681	1344	10	drawing	draw	VBG
37681	1344	11	instruments	instrument	NNS
37681	1344	12	recognized	recognize	VBN
37681	1344	13	in	in	IN
37681	1344	14	elementary	elementary	JJ
37681	1344	15	geometry	geometry	NN
37681	1344	16	.	.	.
37681	1345	1	[	[	-LRB-
37681	1345	2	51	51	CD
37681	1345	3	]	]	-RRB-
37681	1345	4	While	while	IN
37681	1345	5	this	this	DT
37681	1345	6	involves	involve	VBZ
37681	1345	7	more	more	JJR
37681	1345	8	than	than	IN
37681	1345	9	Euclid	Euclid	NNP
37681	1345	10	's	's	POS
37681	1345	11	postulate	postulate	NN
37681	1345	12	,	,	,
37681	1345	13	it	-PRON-	PRP
37681	1345	14	is	be	VBZ
37681	1345	15	a	a	DT
37681	1345	16	better	well	JJR
37681	1345	17	working	working	NN
37681	1345	18	assumption	assumption	NN
37681	1345	19	for	for	IN
37681	1345	20	beginners	beginner	NNS
37681	1345	21	.	.	.
37681	1346	1	3	3	LS
37681	1346	2	.	.	.
37681	1347	1	_	_	NNP
37681	1347	2	A	a	DT
37681	1347	3	straight	straight	JJ
37681	1347	4	line	line	NN
37681	1347	5	is	be	VBZ
37681	1347	6	the	the	DT
37681	1347	7	shortest	short	JJS
37681	1347	8	path	path	NN
37681	1347	9	between	between	IN
37681	1347	10	two	two	CD
37681	1347	11	points	point	NNS
37681	1347	12	.	.	.
37681	1347	13	_	_	NNP
37681	1347	14	This	this	DT
37681	1347	15	is	be	VBZ
37681	1347	16	easily	easily	RB
37681	1347	17	proved	prove	VBN
37681	1347	18	by	by	IN
37681	1347	19	the	the	DT
37681	1347	20	method	method	NN
37681	1347	21	of	of	IN
37681	1347	22	Euclid[52	euclid[52	ADD
37681	1347	23	]	]	-RRB-
37681	1347	24	for	for	IN
37681	1347	25	the	the	DT
37681	1347	26	case	case	NN
37681	1347	27	where	where	WRB
37681	1347	28	the	the	DT
37681	1347	29	paths	path	NNS
37681	1347	30	are	be	VBP
37681	1347	31	broken	break	VBN
37681	1347	32	lines	line	NNS
37681	1347	33	,	,	,
37681	1347	34	but	but	CC
37681	1347	35	it	-PRON-	PRP
37681	1347	36	is	be	VBZ
37681	1347	37	needed	need	VBN
37681	1347	38	as	as	IN
37681	1347	39	a	a	DT
37681	1347	40	postulate	postulate	NN
37681	1347	41	for	for	IN
37681	1347	42	the	the	DT
37681	1347	43	case	case	NN
37681	1347	44	of	of	IN
37681	1347	45	curve	curve	NN
37681	1347	46	paths	path	NNS
37681	1347	47	.	.	.
37681	1348	1	It	-PRON-	PRP
37681	1348	2	is	be	VBZ
37681	1348	3	a	a	DT
37681	1348	4	better	well	JJR
37681	1348	5	statement	statement	NN
37681	1348	6	than	than	IN
37681	1348	7	the	the	DT
37681	1348	8	common	common	JJ
37681	1348	9	one	one	NN
37681	1348	10	that	that	WDT
37681	1348	11	a	a	DT
37681	1348	12	straight	straight	JJ
37681	1348	13	line	line	NN
37681	1348	14	is	be	VBZ
37681	1348	15	the	the	DT
37681	1348	16	shortest	short	JJS
37681	1348	17	_	_	NNP
37681	1348	18	distance	distance	NN
37681	1348	19	_	_	NNP
37681	1348	20	between	between	IN
37681	1348	21	two	two	CD
37681	1348	22	points	point	NNS
37681	1348	23	;	;	:
37681	1348	24	for	for	IN
37681	1348	25	distance	distance	NN
37681	1348	26	is	be	VBZ
37681	1348	27	measured	measure	VBN
37681	1348	28	on	on	IN
37681	1348	29	a	a	DT
37681	1348	30	line	line	NN
37681	1348	31	,	,	,
37681	1348	32	but	but	CC
37681	1348	33	it	-PRON-	PRP
37681	1348	34	is	be	VBZ
37681	1348	35	not	not	RB
37681	1348	36	itself	-PRON-	PRP
37681	1348	37	a	a	DT
37681	1348	38	line	line	NN
37681	1348	39	.	.	.
37681	1349	1	Furthermore	furthermore	RB
37681	1349	2	,	,	,
37681	1349	3	there	there	EX
37681	1349	4	are	be	VBP
37681	1349	5	scientific	scientific	JJ
37681	1349	6	objections	objection	NNS
37681	1349	7	to	to	IN
37681	1349	8	using	use	VBG
37681	1349	9	the	the	DT
37681	1349	10	word	word	NN
37681	1349	11	"	"	``
37681	1349	12	distance	distance	NN
37681	1349	13	"	"	''
37681	1349	14	any	any	DT
37681	1349	15	more	more	RBR
37681	1349	16	than	than	IN
37681	1349	17	is	be	VBZ
37681	1349	18	necessary	necessary	JJ
37681	1349	19	.	.	.
37681	1350	1	4	4	LS
37681	1350	2	.	.	.
37681	1351	1	_	_	NNP
37681	1351	2	A	a	DT
37681	1351	3	circle	circle	NN
37681	1351	4	may	may	MD
37681	1351	5	be	be	VB
37681	1351	6	described	describe	VBN
37681	1351	7	with	with	IN
37681	1351	8	any	any	DT
37681	1351	9	given	give	VBN
37681	1351	10	point	point	NN
37681	1351	11	as	as	IN
37681	1351	12	a	a	DT
37681	1351	13	center	center	NN
37681	1351	14	and	and	CC
37681	1351	15	any	any	DT
37681	1351	16	given	give	VBN
37681	1351	17	line	line	NN
37681	1351	18	as	as	IN
37681	1351	19	a	a	DT
37681	1351	20	radius	radius	NN
37681	1351	21	.	.	.
37681	1351	22	_	_	NNP
37681	1351	23	This	this	DT
37681	1351	24	involves	involve	VBZ
37681	1351	25	the	the	DT
37681	1351	26	use	use	NN
37681	1351	27	of	of	IN
37681	1351	28	the	the	DT
37681	1351	29	second	second	JJ
37681	1351	30	of	of	IN
37681	1351	31	the	the	DT
37681	1351	32	two	two	CD
37681	1351	33	geometric	geometric	JJ
37681	1351	34	instruments	instrument	NNS
37681	1351	35	,	,	,
37681	1351	36	the	the	DT
37681	1351	37	compasses	compass	NNS
37681	1351	38	.	.	.
37681	1352	1	5	5	CD
37681	1352	2	.	.	.
37681	1353	1	_	_	NNP
37681	1353	2	Any	any	DT
37681	1353	3	figure	figure	NN
37681	1353	4	may	may	MD
37681	1353	5	be	be	VB
37681	1353	6	moved	move	VBN
37681	1353	7	from	from	IN
37681	1353	8	one	one	CD
37681	1353	9	place	place	NN
37681	1353	10	to	to	IN
37681	1353	11	another	another	DT
37681	1353	12	without	without	IN
37681	1353	13	altering	alter	VBG
37681	1353	14	the	the	DT
37681	1353	15	size	size	NN
37681	1353	16	or	or	CC
37681	1353	17	shape	shape	NN
37681	1353	18	.	.	.
37681	1353	19	_	_	NNP
37681	1353	20	This	this	DT
37681	1353	21	is	be	VBZ
37681	1353	22	the	the	DT
37681	1353	23	postulate	postulate	NN
37681	1353	24	of	of	IN
37681	1353	25	the	the	DT
37681	1353	26	homogeneity	homogeneity	NN
37681	1353	27	of	of	IN
37681	1353	28	space	space	NN
37681	1353	29	,	,	,
37681	1353	30	and	and	CC
37681	1353	31	asserts	assert	VBZ
37681	1353	32	that	that	IN
37681	1353	33	space	space	NN
37681	1353	34	is	be	VBZ
37681	1353	35	such	such	JJ
37681	1353	36	that	that	IN
37681	1353	37	we	-PRON-	PRP
37681	1353	38	may	may	MD
37681	1353	39	move	move	VB
37681	1353	40	a	a	DT
37681	1353	41	figure	figure	NN
37681	1353	42	as	as	IN
37681	1353	43	we	-PRON-	PRP
37681	1353	44	please	please	VBP
37681	1353	45	without	without	IN
37681	1353	46	deformation	deformation	NN
37681	1353	47	of	of	IN
37681	1353	48	any	any	DT
37681	1353	49	kind	kind	NN
37681	1353	50	.	.	.
37681	1354	1	It	-PRON-	PRP
37681	1354	2	is	be	VBZ
37681	1354	3	the	the	DT
37681	1354	4	basis	basis	NN
37681	1354	5	of	of	IN
37681	1354	6	all	all	DT
37681	1354	7	cases	case	NNS
37681	1354	8	of	of	IN
37681	1354	9	superposition	superposition	NN
37681	1354	10	.	.	.
37681	1355	1	6	6	CD
37681	1355	2	.	.	.
37681	1356	1	_	_	NNP
37681	1356	2	All	all	DT
37681	1356	3	straight	straight	JJ
37681	1356	4	angles	angle	NNS
37681	1356	5	are	be	VBP
37681	1356	6	equal	equal	JJ
37681	1356	7	.	.	.
37681	1356	8	_	_	NNP
37681	1356	9	It	-PRON-	PRP
37681	1356	10	is	be	VBZ
37681	1356	11	possible	possible	JJ
37681	1356	12	to	to	TO
37681	1356	13	prove	prove	VB
37681	1356	14	this	this	DT
37681	1356	15	,	,	,
37681	1356	16	and	and	CC
37681	1356	17	therefore	therefore	RB
37681	1356	18	,	,	,
37681	1356	19	from	from	IN
37681	1356	20	the	the	DT
37681	1356	21	standpoint	standpoint	NN
37681	1356	22	of	of	IN
37681	1356	23	strict	strict	JJ
37681	1356	24	logic	logic	NN
37681	1356	25	,	,	,
37681	1356	26	it	-PRON-	PRP
37681	1356	27	is	be	VBZ
37681	1356	28	unnecessary	unnecessary	JJ
37681	1356	29	as	as	IN
37681	1356	30	a	a	DT
37681	1356	31	postulate	postulate	NN
37681	1356	32	.	.	.
37681	1357	1	On	on	IN
37681	1357	2	the	the	DT
37681	1357	3	other	other	JJ
37681	1357	4	hand	hand	NN
37681	1357	5	,	,	,
37681	1357	6	it	-PRON-	PRP
37681	1357	7	is	be	VBZ
37681	1357	8	poor	poor	JJ
37681	1357	9	educational	educational	JJ
37681	1357	10	policy	policy	NN
37681	1357	11	for	for	IN
37681	1357	12	a	a	DT
37681	1357	13	beginner	beginner	NN
37681	1357	14	to	to	TO
37681	1357	15	attempt	attempt	VB
37681	1357	16	to	to	TO
37681	1357	17	prove	prove	VB
37681	1357	18	a	a	DT
37681	1357	19	thing	thing	NN
37681	1357	20	that	that	WDT
37681	1357	21	is	be	VBZ
37681	1357	22	so	so	RB
37681	1357	23	obvious	obvious	JJ
37681	1357	24	.	.	.
37681	1358	1	The	the	DT
37681	1358	2	attempt	attempt	NN
37681	1358	3	leads	lead	VBZ
37681	1358	4	to	to	IN
37681	1358	5	a	a	DT
37681	1358	6	loss	loss	NN
37681	1358	7	of	of	IN
37681	1358	8	interest	interest	NN
37681	1358	9	in	in	IN
37681	1358	10	the	the	DT
37681	1358	11	subject	subject	NN
37681	1358	12	,	,	,
37681	1358	13	the	the	DT
37681	1358	14	proposition	proposition	NN
37681	1358	15	being	be	VBG
37681	1358	16	(	(	-LRB-
37681	1358	17	to	to	TO
37681	1358	18	state	state	VB
37681	1358	19	a	a	DT
37681	1358	20	paradox	paradox	NN
37681	1358	21	)	)	-RRB-
37681	1358	22	hard	hard	RB
37681	1358	23	because	because	IN
37681	1358	24	it	-PRON-	PRP
37681	1358	25	is	be	VBZ
37681	1358	26	so	so	RB
37681	1358	27	easy	easy	JJ
37681	1358	28	.	.	.
37681	1359	1	It	-PRON-	PRP
37681	1359	2	is	be	VBZ
37681	1359	3	,	,	,
37681	1359	4	of	of	IN
37681	1359	5	course	course	NN
37681	1359	6	,	,	,
37681	1359	7	possible	possible	JJ
37681	1359	8	to	to	TO
37681	1359	9	postulate	postulate	VB
37681	1359	10	that	that	DT
37681	1359	11	straight	straight	JJ
37681	1359	12	angles	angle	NNS
37681	1359	13	are	be	VBP
37681	1359	14	equal	equal	JJ
37681	1359	15	,	,	,
37681	1359	16	and	and	CC
37681	1359	17	to	to	TO
37681	1359	18	draw	draw	VB
37681	1359	19	the	the	DT
37681	1359	20	conclusion	conclusion	NN
37681	1359	21	that	that	IN
37681	1359	22	their	-PRON-	PRP$
37681	1359	23	halves	half	NNS
37681	1359	24	(	(	-LRB-
37681	1359	25	right	right	JJ
37681	1359	26	angles	angle	NNS
37681	1359	27	)	)	-RRB-
37681	1359	28	are	be	VBP
37681	1359	29	equal	equal	JJ
37681	1359	30	;	;	:
37681	1359	31	or	or	CC
37681	1359	32	to	to	TO
37681	1359	33	proceed	proceed	VB
37681	1359	34	in	in	IN
37681	1359	35	the	the	DT
37681	1359	36	opposite	opposite	JJ
37681	1359	37	direction	direction	NN
37681	1359	38	,	,	,
37681	1359	39	and	and	CC
37681	1359	40	postulate	postulate	VB
37681	1359	41	that	that	IN
37681	1359	42	all	all	DT
37681	1359	43	right	right	JJ
37681	1359	44	angles	angle	NNS
37681	1359	45	are	be	VBP
37681	1359	46	equal	equal	JJ
37681	1359	47	,	,	,
37681	1359	48	and	and	CC
37681	1359	49	draw	draw	VB
37681	1359	50	the	the	DT
37681	1359	51	conclusion	conclusion	NN
37681	1359	52	that	that	IN
37681	1359	53	their	-PRON-	PRP$
37681	1359	54	doubles	double	NNS
37681	1359	55	(	(	-LRB-
37681	1359	56	straight	straight	JJ
37681	1359	57	angles	angle	NNS
37681	1359	58	)	)	-RRB-
37681	1359	59	are	be	VBP
37681	1359	60	equal	equal	JJ
37681	1359	61	.	.	.
37681	1360	1	Of	of	IN
37681	1360	2	the	the	DT
37681	1360	3	two	two	CD
37681	1360	4	the	the	DT
37681	1360	5	former	former	JJ
37681	1360	6	has	have	VBZ
37681	1360	7	the	the	DT
37681	1360	8	advantage	advantage	NN
37681	1360	9	,	,	,
37681	1360	10	since	since	IN
37681	1360	11	it	-PRON-	PRP
37681	1360	12	is	be	VBZ
37681	1360	13	probably	probably	RB
37681	1360	14	more	more	RBR
37681	1360	15	obvious	obvious	JJ
37681	1360	16	that	that	IN
37681	1360	17	all	all	DT
37681	1360	18	straight	straight	JJ
37681	1360	19	angles	angle	NNS
37681	1360	20	are	be	VBP
37681	1360	21	equal	equal	JJ
37681	1360	22	.	.	.
37681	1361	1	It	-PRON-	PRP
37681	1361	2	is	be	VBZ
37681	1361	3	well	well	JJ
37681	1361	4	to	to	TO
37681	1361	5	state	state	VB
37681	1361	6	the	the	DT
37681	1361	7	following	follow	VBG
37681	1361	8	definite	definite	JJ
37681	1361	9	corollaries	corollary	NNS
37681	1361	10	to	to	IN
37681	1361	11	this	this	DT
37681	1361	12	postulate	postulate	NN
37681	1361	13	:	:	:
37681	1361	14	(	(	-LRB-
37681	1361	15	1	1	LS
37681	1361	16	)	)	-RRB-
37681	1361	17	_	_	NNP
37681	1361	18	All	All	NNP
37681	1361	19	right	right	JJ
37681	1361	20	angles	angle	NNS
37681	1361	21	are	be	VBP
37681	1361	22	equal	equal	JJ
37681	1361	23	_	_	NNP
37681	1361	24	;	;	:
37681	1361	25	(	(	-LRB-
37681	1361	26	2	2	LS
37681	1361	27	)	)	-RRB-
37681	1361	28	_	_	NNP
37681	1361	29	From	from	IN
37681	1361	30	a	a	DT
37681	1361	31	point	point	NN
37681	1361	32	in	in	IN
37681	1361	33	a	a	DT
37681	1361	34	line	line	NN
37681	1361	35	only	only	RB
37681	1361	36	one	one	CD
37681	1361	37	perpendicular	perpendicular	NN
37681	1361	38	can	can	MD
37681	1361	39	be	be	VB
37681	1361	40	drawn	draw	VBN
37681	1361	41	to	to	IN
37681	1361	42	the	the	DT
37681	1361	43	line	line	NN
37681	1361	44	_	_	NNP
37681	1361	45	,	,	,
37681	1361	46	since	since	IN
37681	1361	47	two	two	CD
37681	1361	48	perpendiculars	perpendicular	NNS
37681	1361	49	would	would	MD
37681	1361	50	make	make	VB
37681	1361	51	the	the	DT
37681	1361	52	whole	whole	JJ
37681	1361	53	(	(	-LRB-
37681	1361	54	right	right	JJ
37681	1361	55	angle	angle	NN
37681	1361	56	)	)	-RRB-
37681	1361	57	equal	equal	JJ
37681	1361	58	to	to	IN
37681	1361	59	its	-PRON-	PRP$
37681	1361	60	part	part	NN
37681	1361	61	;	;	,
37681	1361	62	(	(	-LRB-
37681	1361	63	3	3	LS
37681	1361	64	)	)	-RRB-
37681	1361	65	_	_	NNP
37681	1361	66	Equal	equal	JJ
37681	1361	67	angles	angle	NNS
37681	1361	68	have	have	VBP
37681	1361	69	equal	equal	JJ
37681	1361	70	complements	complement	NNS
37681	1361	71	,	,	,
37681	1361	72	equal	equal	JJ
37681	1361	73	supplements	supplement	NNS
37681	1361	74	,	,	,
37681	1361	75	and	and	CC
37681	1361	76	equal	equal	JJ
37681	1361	77	conjugates	conjugate	NNS
37681	1361	78	_	_	XX
37681	1361	79	;	;	:
37681	1361	80	(	(	-LRB-
37681	1361	81	4	4	LS
37681	1361	82	)	)	-RRB-
37681	1361	83	_	_	NNP
37681	1361	84	The	the	DT
37681	1361	85	greater	great	JJR
37681	1361	86	of	of	IN
37681	1361	87	two	two	CD
37681	1361	88	angles	angle	NNS
37681	1361	89	has	have	VBZ
37681	1361	90	the	the	DT
37681	1361	91	less	less	JJR
37681	1361	92	complement	complement	NN
37681	1361	93	,	,	,
37681	1361	94	the	the	DT
37681	1361	95	less	less	RBR
37681	1361	96	supplement	supplement	NN
37681	1361	97	,	,	,
37681	1361	98	and	and	CC
37681	1361	99	the	the	DT
37681	1361	100	less	less	RBR
37681	1361	101	conjugate	conjugate	NN
37681	1361	102	.	.	.
37681	1361	103	_	_	NNP
37681	1361	104	All	all	DT
37681	1361	105	of	of	IN
37681	1361	106	these	these	DT
37681	1361	107	four	four	CD
37681	1361	108	might	may	MD
37681	1361	109	appear	appear	VB
37681	1361	110	as	as	IN
37681	1361	111	propositions	proposition	NNS
37681	1361	112	,	,	,
37681	1361	113	but	but	CC
37681	1361	114	,	,	,
37681	1361	115	as	as	IN
37681	1361	116	already	already	RB
37681	1361	117	stated	state	VBN
37681	1361	118	,	,	,
37681	1361	119	they	-PRON-	PRP
37681	1361	120	are	be	VBP
37681	1361	121	so	so	RB
37681	1361	122	obvious	obvious	JJ
37681	1361	123	as	as	IN
37681	1361	124	to	to	TO
37681	1361	125	be	be	VB
37681	1361	126	more	more	RBR
37681	1361	127	harmful	harmful	JJ
37681	1361	128	than	than	IN
37681	1361	129	useful	useful	JJ
37681	1361	130	to	to	IN
37681	1361	131	beginners	beginner	NNS
37681	1361	132	when	when	WRB
37681	1361	133	given	give	VBN
37681	1361	134	in	in	IN
37681	1361	135	such	such	JJ
37681	1361	136	form	form	NN
37681	1361	137	.	.	.
37681	1362	1	The	the	DT
37681	1362	2	postulate	postulate	NN
37681	1362	3	of	of	IN
37681	1362	4	parallels	parallel	NNS
37681	1362	5	may	may	MD
37681	1362	6	properly	properly	RB
37681	1362	7	appear	appear	VB
37681	1362	8	in	in	IN
37681	1362	9	connection	connection	NN
37681	1362	10	with	with	IN
37681	1362	11	that	that	DT
37681	1362	12	topic	topic	NN
37681	1362	13	in	in	IN
37681	1362	14	Book	Book	NNP
37681	1362	15	I	I	NNP
37681	1362	16	,	,	,
37681	1362	17	and	and	CC
37681	1362	18	it	-PRON-	PRP
37681	1362	19	is	be	VBZ
37681	1362	20	accordingly	accordingly	RB
37681	1362	21	treated	treat	VBN
37681	1362	22	in	in	IN
37681	1362	23	Chapter	Chapter	NNP
37681	1362	24	XIV	XIV	NNP
37681	1362	25	.	.	.
37681	1363	1	There	there	EX
37681	1363	2	is	be	VBZ
37681	1363	3	also	also	RB
37681	1363	4	another	another	DT
37681	1363	5	assumption	assumption	NN
37681	1363	6	that	that	IN
37681	1363	7	some	some	DT
37681	1363	8	writers	writer	NNS
37681	1363	9	are	be	VBP
37681	1363	10	now	now	RB
37681	1363	11	trying	try	VBG
37681	1363	12	to	to	TO
37681	1363	13	formulate	formulate	VB
37681	1363	14	in	in	IN
37681	1363	15	a	a	DT
37681	1363	16	simple	simple	JJ
37681	1363	17	fashion	fashion	NN
37681	1363	18	.	.	.
37681	1364	1	We	-PRON-	PRP
37681	1364	2	take	take	VBP
37681	1364	3	,	,	,
37681	1364	4	for	for	IN
37681	1364	5	example	example	NN
37681	1364	6	,	,	,
37681	1364	7	a	a	DT
37681	1364	8	line	line	NN
37681	1364	9	segment	segment	NN
37681	1364	10	_	_	NNP
37681	1364	11	AB	AB	NNP
37681	1364	12	_	_	NNP
37681	1364	13	,	,	,
37681	1364	14	and	and	CC
37681	1364	15	describe	describe	VBP
37681	1364	16	circles	circle	NNS
37681	1364	17	with	with	IN
37681	1364	18	_	_	NNP
37681	1364	19	A	A	NNP
37681	1364	20	_	_	NNP
37681	1364	21	and	and	CC
37681	1364	22	_	_	NNP
37681	1364	23	B	B	NNP
37681	1364	24	_	_	NNP
37681	1364	25	respectively	respectively	RB
37681	1364	26	as	as	IN
37681	1364	27	centers	center	NNS
37681	1364	28	,	,	,
37681	1364	29	and	and	CC
37681	1364	30	with	with	IN
37681	1364	31	a	a	DT
37681	1364	32	radius	radius	NN
37681	1364	33	_	_	NNP
37681	1364	34	AB	AB	NNP
37681	1364	35	_	_	NNP
37681	1364	36	.	.	.
37681	1365	1	We	-PRON-	PRP
37681	1365	2	say	say	VBP
37681	1365	3	that	that	IN
37681	1365	4	the	the	DT
37681	1365	5	circles	circle	NNS
37681	1365	6	will	will	MD
37681	1365	7	intersect	intersect	VB
37681	1365	8	as	as	IN
37681	1365	9	at	at	IN
37681	1365	10	_	_	NNP
37681	1365	11	C	C	NNP
37681	1365	12	_	_	NNP
37681	1365	13	and	and	CC
37681	1365	14	_	_	NNP
37681	1365	15	D	D	NNP
37681	1365	16	_	_	NNP
37681	1365	17	.	.	.
37681	1366	1	But	but	CC
37681	1366	2	how	how	WRB
37681	1366	3	do	do	VBP
37681	1366	4	we	-PRON-	PRP
37681	1366	5	know	know	VB
37681	1366	6	that	that	IN
37681	1366	7	they	-PRON-	PRP
37681	1366	8	intersect	intersect	VBP
37681	1366	9	?	?	.
37681	1367	1	We	-PRON-	PRP
37681	1367	2	assume	assume	VBP
37681	1367	3	it	-PRON-	PRP
37681	1367	4	,	,	,
37681	1367	5	just	just	RB
37681	1367	6	as	as	IN
37681	1367	7	we	-PRON-	PRP
37681	1367	8	assume	assume	VBP
37681	1367	9	that	that	IN
37681	1367	10	an	an	DT
37681	1367	11	indefinite	indefinite	JJ
37681	1367	12	straight	straight	JJ
37681	1367	13	line	line	NN
37681	1367	14	drawn	draw	VBN
37681	1367	15	from	from	IN
37681	1367	16	a	a	DT
37681	1367	17	point	point	NN
37681	1367	18	inclosed	inclose	VBN
37681	1367	19	by	by	IN
37681	1367	20	a	a	DT
37681	1367	21	circle	circle	NN
37681	1367	22	will	will	MD
37681	1367	23	,	,	,
37681	1367	24	if	if	IN
37681	1367	25	produced	produce	VBN
37681	1367	26	far	far	RB
37681	1367	27	enough	enough	RB
37681	1367	28	,	,	,
37681	1367	29	cut	cut	VB
37681	1367	30	the	the	DT
37681	1367	31	circle	circle	NN
37681	1367	32	twice	twice	RB
37681	1367	33	.	.	.
37681	1368	1	Of	of	RB
37681	1368	2	course	course	RB
37681	1368	3	a	a	DT
37681	1368	4	pupil	pupil	NN
37681	1368	5	would	would	MD
37681	1368	6	not	not	RB
37681	1368	7	think	think	VB
37681	1368	8	of	of	IN
37681	1368	9	this	this	DT
37681	1368	10	if	if	IN
37681	1368	11	his	-PRON-	PRP$
37681	1368	12	attention	attention	NN
37681	1368	13	was	be	VBD
37681	1368	14	not	not	RB
37681	1368	15	called	call	VBN
37681	1368	16	to	to	IN
37681	1368	17	it	-PRON-	PRP
37681	1368	18	,	,	,
37681	1368	19	and	and	CC
37681	1368	20	the	the	DT
37681	1368	21	harm	harm	NN
37681	1368	22	outweighs	outweigh	VBZ
37681	1368	23	the	the	DT
37681	1368	24	good	good	NN
37681	1368	25	in	in	IN
37681	1368	26	doing	do	VBG
37681	1368	27	this	this	DT
37681	1368	28	with	with	IN
37681	1368	29	one	one	CD
37681	1368	30	who	who	WP
37681	1368	31	is	be	VBZ
37681	1368	32	beginning	begin	VBG
37681	1368	33	the	the	DT
37681	1368	34	study	study	NN
37681	1368	35	of	of	IN
37681	1368	36	geometry	geometry	NN
37681	1368	37	.	.	.
37681	1369	1	With	with	IN
37681	1369	2	axioms	axiom	NNS
37681	1369	3	and	and	CC
37681	1369	4	with	with	IN
37681	1369	5	postulates	postulate	NNS
37681	1369	6	,	,	,
37681	1369	7	therefore	therefore	RB
37681	1369	8	,	,	,
37681	1369	9	the	the	DT
37681	1369	10	conclusion	conclusion	NN
37681	1369	11	is	be	VBZ
37681	1369	12	the	the	DT
37681	1369	13	same	same	JJ
37681	1369	14	:	:	:
37681	1369	15	from	from	IN
37681	1369	16	the	the	DT
37681	1369	17	standpoint	standpoint	NN
37681	1369	18	of	of	IN
37681	1369	19	scientific	scientific	JJ
37681	1369	20	geometry	geometry	NN
37681	1369	21	there	there	EX
37681	1369	22	is	be	VBZ
37681	1369	23	an	an	DT
37681	1369	24	irreducible	irreducible	JJ
37681	1369	25	minimum	minimum	NN
37681	1369	26	of	of	IN
37681	1369	27	assumptions	assumption	NNS
37681	1369	28	,	,	,
37681	1369	29	but	but	CC
37681	1369	30	from	from	IN
37681	1369	31	the	the	DT
37681	1369	32	standpoint	standpoint	NN
37681	1369	33	of	of	IN
37681	1369	34	practical	practical	JJ
37681	1369	35	teaching	teaching	NN
37681	1369	36	this	this	DT
37681	1369	37	list	list	NN
37681	1369	38	should	should	MD
37681	1369	39	give	give	VB
37681	1369	40	place	place	NN
37681	1369	41	to	to	IN
37681	1369	42	a	a	DT
37681	1369	43	working	work	VBG
37681	1369	44	set	set	NN
37681	1369	45	of	of	IN
37681	1369	46	axioms	axiom	NNS
37681	1369	47	and	and	CC
37681	1369	48	postulates	postulate	NNS
37681	1369	49	that	that	WDT
37681	1369	50	meet	meet	VBP
37681	1369	51	the	the	DT
37681	1369	52	needs	need	NNS
37681	1369	53	of	of	IN
37681	1369	54	the	the	DT
37681	1369	55	beginner	beginner	NN
37681	1369	56	.	.	.
37681	1370	1	=	=	NFP
37681	1370	2	Bibliography.=	Bibliography.=	NNP
37681	1370	3	Smith	Smith	NNP
37681	1370	4	,	,	,
37681	1370	5	Teaching	Teaching	NNP
37681	1370	6	of	of	IN
37681	1370	7	Elementary	Elementary	NNP
37681	1370	8	Mathematics	Mathematics	NNPS
37681	1370	9	,	,	,
37681	1370	10	New	New	NNP
37681	1370	11	York	York	NNP
37681	1370	12	,	,	,
37681	1370	13	1900	1900	CD
37681	1370	14	;	;	:
37681	1370	15	Young	Young	NNP
37681	1370	16	,	,	,
37681	1370	17	The	the	DT
37681	1370	18	Teaching	Teaching	NNP
37681	1370	19	of	of	IN
37681	1370	20	Mathematics	Mathematics	NNP
37681	1370	21	,	,	,
37681	1370	22	New	New	NNP
37681	1370	23	York	York	NNP
37681	1370	24	,	,	,
37681	1370	25	1901	1901	CD
37681	1370	26	;	;	:
37681	1370	27	Moore	Moore	NNP
37681	1370	28	,	,	,
37681	1370	29	On	on	IN
37681	1370	30	the	the	DT
37681	1370	31	Foundations	Foundations	NNPS
37681	1370	32	of	of	IN
37681	1370	33	Mathematics	Mathematics	NNPS
37681	1370	34	,	,	,
37681	1370	35	_	_	NNP
37681	1370	36	Bulletin	Bulletin	NNP
37681	1370	37	of	of	IN
37681	1370	38	the	the	DT
37681	1370	39	American	American	NNP
37681	1370	40	Mathematical	Mathematical	NNP
37681	1370	41	Society	Society	NNP
37681	1370	42	_	_	NNP
37681	1370	43	,	,	,
37681	1370	44	1903	1903	CD
37681	1370	45	,	,	,
37681	1370	46	p.	p.	NN
37681	1370	47	402	402	CD
37681	1370	48	;	;	:
37681	1370	49	Betz	Betz	NNP
37681	1370	50	,	,	,
37681	1370	51	Intuition	Intuition	NNP
37681	1370	52	and	and	CC
37681	1370	53	Logic	Logic	NNP
37681	1370	54	in	in	IN
37681	1370	55	Geometry	Geometry	NNP
37681	1370	56	,	,	,
37681	1370	57	_	_	NNP
37681	1370	58	The	the	DT
37681	1370	59	Mathematics	Mathematics	NNP
37681	1370	60	Teacher	Teacher	NNP
37681	1370	61	_	_	NNP
37681	1370	62	,	,	,
37681	1370	63	Vol	Vol	NNP
37681	1370	64	.	.	.
37681	1371	1	II	II	NNP
37681	1371	2	,	,	,
37681	1371	3	p.	p.	NN
37681	1371	4	3	3	CD
37681	1371	5	;	;	:
37681	1371	6	Hilbert	Hilbert	NNP
37681	1371	7	,	,	,
37681	1371	8	The	the	DT
37681	1371	9	Foundations	Foundations	NNPS
37681	1371	10	of	of	IN
37681	1371	11	Geometry	Geometry	NNP
37681	1371	12	,	,	,
37681	1371	13	Chicago	Chicago	NNP
37681	1371	14	,	,	,
37681	1371	15	1902	1902	CD
37681	1371	16	;	;	:
37681	1371	17	Veblen	Veblen	NNP
37681	1371	18	,	,	,
37681	1371	19	A	a	DT
37681	1371	20	System	system	NN
37681	1371	21	of	of	IN
37681	1371	22	Axioms	Axioms	NNPS
37681	1371	23	for	for	IN
37681	1371	24	Geometry	Geometry	NNP
37681	1371	25	,	,	,
37681	1371	26	_	_	NNP
37681	1371	27	Transactions	Transactions	NNPS
37681	1371	28	of	of	IN
37681	1371	29	the	the	DT
37681	1371	30	American	American	NNP
37681	1371	31	Mathematical	Mathematical	NNP
37681	1371	32	Society	Society	NNP
37681	1371	33	_	_	NNP
37681	1371	34	,	,	,
37681	1371	35	1904	1904	CD
37681	1371	36	,	,	,
37681	1371	37	p.	p.	NN
37681	1371	38	343	343	CD
37681	1371	39	.	.	.
37681	1372	1	FOOTNOTES	footnote	NNS
37681	1372	2	:	:	:
37681	1372	3	[	[	-LRB-
37681	1372	4	42	42	CD
37681	1372	5	]	]	-RRB-
37681	1372	6	From	from	IN
37681	1372	7	the	the	DT
37681	1372	8	Greek	Greek	NNP
37681	1372	9	[	[	-LRB-
37681	1372	10	Greek	Greek	NNP
37681	1372	11	:	:	:
37681	1372	12	gê	gê	NNP
37681	1372	13	]	]	-RRB-
37681	1372	14	,	,	,
37681	1372	15	_	_	NNP
37681	1372	16	ge	ge	NNP
37681	1372	17	_	_	NNP
37681	1372	18	(	(	-LRB-
37681	1372	19	earth	earth	NN
37681	1372	20	)	)	-RRB-
37681	1372	21	,	,	,
37681	1372	22	+	+	CC
37681	1372	23	[	[	-LRB-
37681	1372	24	Greek	Greek	NNP
37681	1372	25	:	:	:
37681	1372	26	metrein	metrein	NN
37681	1372	27	]	]	-RRB-
37681	1372	28	,	,	,
37681	1372	29	_	_	NNP
37681	1372	30	metrein	metrein	NNP
37681	1372	31	_	_	NNP
37681	1372	32	(	(	-LRB-
37681	1372	33	to	to	TO
37681	1372	34	measure	measure	VB
37681	1372	35	)	)	-RRB-
37681	1372	36	,	,	,
37681	1372	37	although	although	IN
37681	1372	38	the	the	DT
37681	1372	39	science	science	NN
37681	1372	40	has	have	VBZ
37681	1372	41	not	not	RB
37681	1372	42	had	have	VBN
37681	1372	43	to	to	TO
37681	1372	44	do	do	VB
37681	1372	45	directly	directly	RB
37681	1372	46	with	with	IN
37681	1372	47	the	the	DT
37681	1372	48	measure	measure	NN
37681	1372	49	of	of	IN
37681	1372	50	the	the	DT
37681	1372	51	earth	earth	NN
37681	1372	52	for	for	IN
37681	1372	53	over	over	IN
37681	1372	54	two	two	CD
37681	1372	55	thousand	thousand	CD
37681	1372	56	years	year	NNS
37681	1372	57	.	.	.
37681	1373	1	[	[	-LRB-
37681	1373	2	43	43	CD
37681	1373	3	]	]	-RRB-
37681	1373	4	From	from	IN
37681	1373	5	the	the	DT
37681	1373	6	Arabic	Arabic	NNP
37681	1373	7	_	_	NNP
37681	1373	8	al	al	NNP
37681	1373	9	_	_	NNP
37681	1373	10	(	(	-LRB-
37681	1373	11	the	the	DT
37681	1373	12	)	)	-RRB-
37681	1373	13	+	+	CC
37681	1373	14	_	_	NNP
37681	1373	15	jabr	jabr	NN
37681	1373	16	_	_	NNP
37681	1373	17	(	(	-LRB-
37681	1373	18	restoration	restoration	NN
37681	1373	19	)	)	-RRB-
37681	1373	20	,	,	,
37681	1373	21	referring	refer	VBG
37681	1373	22	to	to	IN
37681	1373	23	taking	take	VBG
37681	1373	24	a	a	DT
37681	1373	25	quantity	quantity	NN
37681	1373	26	from	from	IN
37681	1373	27	one	one	CD
37681	1373	28	side	side	NN
37681	1373	29	of	of	IN
37681	1373	30	an	an	DT
37681	1373	31	equation	equation	NN
37681	1373	32	and	and	CC
37681	1373	33	then	then	RB
37681	1373	34	restoring	restore	VBG
37681	1373	35	the	the	DT
37681	1373	36	balance	balance	NN
37681	1373	37	by	by	IN
37681	1373	38	taking	take	VBG
37681	1373	39	it	-PRON-	PRP
37681	1373	40	from	from	IN
37681	1373	41	the	the	DT
37681	1373	42	other	other	JJ
37681	1373	43	side	side	NN
37681	1373	44	(	(	-LRB-
37681	1373	45	see	see	VB
37681	1373	46	page	page	NN
37681	1373	47	37	37	CD
37681	1373	48	)	)	-RRB-
37681	1373	49	.	.	.
37681	1374	1	[	[	-LRB-
37681	1374	2	44	44	CD
37681	1374	3	]	]	-RRB-
37681	1374	4	One	one	CD
37681	1374	5	of	of	IN
37681	1374	6	the	the	DT
37681	1374	7	clearest	clear	JJS
37681	1374	8	discussions	discussion	NNS
37681	1374	9	of	of	IN
37681	1374	10	the	the	DT
37681	1374	11	subject	subject	NN
37681	1374	12	is	be	VBZ
37681	1374	13	in	in	IN
37681	1374	14	W.	W.	NNP
37681	1374	15	B.	B.	NNP
37681	1374	16	Frankland	Frankland	NNP
37681	1374	17	,	,	,
37681	1374	18	"	"	``
37681	1374	19	The	the	DT
37681	1374	20	First	First	NNP
37681	1374	21	Book	Book	NNP
37681	1374	22	of	of	IN
37681	1374	23	Euclid	Euclid	NNP
37681	1374	24	's	's	POS
37681	1374	25	'	'	``
37681	1374	26	Elements	element	NNS
37681	1374	27	,	,	,
37681	1374	28	'	'	''
37681	1374	29	"	"	``
37681	1374	30	p.	p.	NN
37681	1374	31	26	26	CD
37681	1374	32	,	,	,
37681	1374	33	Cambridge	Cambridge	NNP
37681	1374	34	,	,	,
37681	1374	35	1905	1905	CD
37681	1374	36	.	.	.
37681	1375	1	[	[	-LRB-
37681	1375	2	45	45	CD
37681	1375	3	]	]	-RRB-
37681	1375	4	"	"	``
37681	1375	5	Grundlagen	Grundlagen	NNP
37681	1375	6	der	der	NN
37681	1375	7	Geometrie	Geometrie	NNP
37681	1375	8	,	,	,
37681	1375	9	"	"	''
37681	1375	10	Leipzig	Leipzig	NNP
37681	1375	11	,	,	,
37681	1375	12	1899	1899	CD
37681	1375	13	.	.	.
37681	1376	1	See	see	VB
37681	1376	2	Heath	Heath	NNP
37681	1376	3	's	's	POS
37681	1376	4	"	"	``
37681	1376	5	Euclid	Euclid	NNP
37681	1376	6	,	,	,
37681	1376	7	"	"	''
37681	1376	8	Vol	Vol	NNP
37681	1376	9	.	.	.
37681	1377	1	I	-PRON-	PRP
37681	1377	2	,	,	,
37681	1377	3	p.	p.	NN
37681	1377	4	229	229	CD
37681	1377	5	,	,	,
37681	1377	6	for	for	IN
37681	1377	7	an	an	DT
37681	1377	8	English	english	JJ
37681	1377	9	version	version	NN
37681	1377	10	;	;	:
37681	1377	11	also	also	RB
37681	1377	12	D.	D.	NNP
37681	1377	13	E.	E.	NNP
37681	1377	14	Smith	Smith	NNP
37681	1377	15	,	,	,
37681	1377	16	"	"	``
37681	1377	17	Teaching	Teaching	NNP
37681	1377	18	of	of	IN
37681	1377	19	Elementary	Elementary	NNP
37681	1377	20	Mathematics	Mathematics	NNPS
37681	1377	21	,	,	,
37681	1377	22	"	"	''
37681	1377	23	p.	p.	NN
37681	1377	24	266	266	CD
37681	1377	25	,	,	,
37681	1377	26	New	New	NNP
37681	1377	27	York	York	NNP
37681	1377	28	,	,	,
37681	1377	29	1900	1900	CD
37681	1377	30	.	.	.
37681	1378	1	[	[	-LRB-
37681	1378	2	46	46	CD
37681	1378	3	]	]	-RRB-
37681	1378	4	We	-PRON-	PRP
37681	1378	5	need	need	VBP
37681	1378	6	frequently	frequently	RB
37681	1378	7	to	to	TO
37681	1378	8	recall	recall	VB
37681	1378	9	the	the	DT
37681	1378	10	fact	fact	NN
37681	1378	11	that	that	IN
37681	1378	12	Euclid	Euclid	NNP
37681	1378	13	's	's	POS
37681	1378	14	"	"	``
37681	1378	15	Elements	Elements	NNPS
37681	1378	16	"	"	''
37681	1378	17	was	be	VBD
37681	1378	18	intended	intend	VBN
37681	1378	19	for	for	IN
37681	1378	20	advanced	advanced	JJ
37681	1378	21	students	student	NNS
37681	1378	22	who	who	WP
37681	1378	23	went	go	VBD
37681	1378	24	to	to	IN
37681	1378	25	Alexandria	Alexandria	NNP
37681	1378	26	as	as	IN
37681	1378	27	young	young	JJ
37681	1378	28	men	man	NNS
37681	1378	29	now	now	RB
37681	1378	30	go	go	VBP
37681	1378	31	to	to	IN
37681	1378	32	college	college	NN
37681	1378	33	,	,	,
37681	1378	34	and	and	CC
37681	1378	35	that	that	IN
37681	1378	36	the	the	DT
37681	1378	37	book	book	NN
37681	1378	38	was	be	VBD
37681	1378	39	used	use	VBN
37681	1378	40	only	only	RB
37681	1378	41	in	in	IN
37681	1378	42	university	university	NN
37681	1378	43	instruction	instruction	NN
37681	1378	44	in	in	IN
37681	1378	45	the	the	DT
37681	1378	46	Middle	Middle	NNP
37681	1378	47	Ages	Ages	NNPS
37681	1378	48	and	and	CC
37681	1378	49	indeed	indeed	RB
37681	1378	50	until	until	IN
37681	1378	51	recent	recent	JJ
37681	1378	52	times	time	NNS
37681	1378	53	.	.	.
37681	1379	1	[	[	-LRB-
37681	1379	2	47	47	CD
37681	1379	3	]	]	-RRB-
37681	1379	4	For	for	IN
37681	1379	5	example	example	NN
37681	1379	6	,	,	,
37681	1379	7	he	-PRON-	PRP
37681	1379	8	moves	move	VBZ
37681	1379	9	figures	figure	NNS
37681	1379	10	without	without	IN
37681	1379	11	deformation	deformation	NN
37681	1379	12	,	,	,
37681	1379	13	but	but	CC
37681	1379	14	states	state	VBZ
37681	1379	15	no	no	DT
37681	1379	16	postulate	postulate	NN
37681	1379	17	on	on	IN
37681	1379	18	the	the	DT
37681	1379	19	subject	subject	NN
37681	1379	20	;	;	:
37681	1379	21	and	and	CC
37681	1379	22	he	-PRON-	PRP
37681	1379	23	proves	prove	VBZ
37681	1379	24	that	that	IN
37681	1379	25	one	one	CD
37681	1379	26	side	side	NN
37681	1379	27	of	of	IN
37681	1379	28	a	a	DT
37681	1379	29	triangle	triangle	NN
37681	1379	30	is	be	VBZ
37681	1379	31	less	less	JJR
37681	1379	32	than	than	IN
37681	1379	33	the	the	DT
37681	1379	34	sum	sum	NN
37681	1379	35	of	of	IN
37681	1379	36	the	the	DT
37681	1379	37	other	other	JJ
37681	1379	38	two	two	CD
37681	1379	39	sides	side	NNS
37681	1379	40	,	,	,
37681	1379	41	when	when	WRB
37681	1379	42	he	-PRON-	PRP
37681	1379	43	might	may	MD
37681	1379	44	have	have	VB
37681	1379	45	postulated	postulate	VBN
37681	1379	46	that	that	IN
37681	1379	47	a	a	DT
37681	1379	48	straight	straight	JJ
37681	1379	49	line	line	NN
37681	1379	50	is	be	VBZ
37681	1379	51	the	the	DT
37681	1379	52	shortest	short	JJS
37681	1379	53	path	path	NN
37681	1379	54	between	between	IN
37681	1379	55	two	two	CD
37681	1379	56	points	point	NNS
37681	1379	57	.	.	.
37681	1380	1	Indeed	indeed	RB
37681	1380	2	,	,	,
37681	1380	3	his	-PRON-	PRP$
37681	1380	4	followers	follower	NNS
37681	1380	5	were	be	VBD
37681	1380	6	laughed	laugh	VBN
37681	1380	7	at	at	IN
37681	1380	8	for	for	IN
37681	1380	9	proving	prove	VBG
37681	1380	10	a	a	DT
37681	1380	11	fact	fact	NN
37681	1380	12	so	so	RB
37681	1380	13	obvious	obvious	JJ
37681	1380	14	as	as	IN
37681	1380	15	this	this	DT
37681	1380	16	one	one	NN
37681	1380	17	concerning	concern	VBG
37681	1380	18	the	the	DT
37681	1380	19	triangle	triangle	NN
37681	1380	20	.	.	.
37681	1381	1	[	[	-LRB-
37681	1381	2	48	48	CD
37681	1381	3	]	]	-RRB-
37681	1381	4	T.	T.	NNP
37681	1381	5	L.	L.	NNP
37681	1381	6	Heath	Heath	NNP
37681	1381	7	,	,	,
37681	1381	8	"	"	``
37681	1381	9	Euclid	euclid	JJ
37681	1381	10	,	,	,
37681	1381	11	"	"	''
37681	1381	12	Vol	Vol	NNP
37681	1381	13	.	.	.
37681	1382	1	I	-PRON-	PRP
37681	1382	2	,	,	,
37681	1382	3	p.	p.	NN
37681	1382	4	200	200	CD
37681	1382	5	.	.	.
37681	1383	1	[	[	-LRB-
37681	1383	2	49	49	CD
37681	1383	3	]	]	-RRB-
37681	1383	4	For	for	IN
37681	1383	5	a	a	DT
37681	1383	6	résumé	résumé	NN
37681	1383	7	of	of	IN
37681	1383	8	the	the	DT
37681	1383	9	best	well	RBS
37681	1383	10	known	know	VBN
37681	1383	11	attempts	attempt	NNS
37681	1383	12	to	to	TO
37681	1383	13	prove	prove	VB
37681	1383	14	this	this	DT
37681	1383	15	postulate	postulate	NN
37681	1383	16	,	,	,
37681	1383	17	see	see	VB
37681	1383	18	Heath	Heath	NNP
37681	1383	19	,	,	,
37681	1383	20	"	"	``
37681	1383	21	Euclid	euclid	JJ
37681	1383	22	,	,	,
37681	1383	23	"	"	''
37681	1383	24	Vol	Vol	NNP
37681	1383	25	.	.	.
37681	1384	1	I	-PRON-	PRP
37681	1384	2	,	,	,
37681	1384	3	p.	p.	NN
37681	1384	4	202	202	CD
37681	1384	5	;	;	:
37681	1384	6	W.	W.	NNP
37681	1384	7	B.	B.	NNP
37681	1384	8	Frankland	Frankland	NNP
37681	1384	9	,	,	,
37681	1384	10	"	"	``
37681	1384	11	Theories	theory	NNS
37681	1384	12	of	of	IN
37681	1384	13	Parallelism	parallelism	NN
37681	1384	14	,	,	,
37681	1384	15	"	"	''
37681	1384	16	Cambridge	Cambridge	NNP
37681	1384	17	,	,	,
37681	1384	18	1910	1910	CD
37681	1384	19	.	.	.
37681	1385	1	[	[	-LRB-
37681	1385	2	50	50	CD
37681	1385	3	]	]	-RRB-
37681	1385	4	For	for	IN
37681	1385	5	the	the	DT
37681	1385	6	early	early	JJ
37681	1385	7	history	history	NN
37681	1385	8	of	of	IN
37681	1385	9	this	this	DT
37681	1385	10	movement	movement	NN
37681	1385	11	see	see	VB
37681	1385	12	Engel	Engel	NNP
37681	1385	13	and	and	CC
37681	1385	14	Stäckel	Stäckel	NNP
37681	1385	15	,	,	,
37681	1385	16	"	"	``
37681	1385	17	Die	die	VB
37681	1385	18	Theorie	Theorie	NNP
37681	1385	19	der	der	NN
37681	1385	20	Parallellinien	Parallellinien	NNP
37681	1385	21	von	von	NNP
37681	1385	22	Euklid	Euklid	NNP
37681	1385	23	bis	bi	VBD
37681	1385	24	auf	auf	NNP
37681	1385	25	Gauss	Gauss	NNP
37681	1385	26	,	,	,
37681	1385	27	"	"	''
37681	1385	28	Leipzig	Leipzig	NNP
37681	1385	29	,	,	,
37681	1385	30	1895	1895	CD
37681	1385	31	;	;	:
37681	1385	32	Bonola	Bonola	NNP
37681	1385	33	,	,	,
37681	1385	34	Sulla	Sulla	NNP
37681	1385	35	teoria	teoria	NNP
37681	1385	36	delle	delle	NNP
37681	1385	37	parallele	parallele	NNP
37681	1385	38	e	e	NNP
37681	1385	39	sulle	sulle	NNP
37681	1385	40	geometrie	geometrie	NNP
37681	1385	41	non	non	JJ
37681	1385	42	-	-	JJ
37681	1385	43	euclidee	euclidee	JJ
37681	1385	44	,	,	,
37681	1385	45	in	in	IN
37681	1385	46	his	-PRON-	PRP$
37681	1385	47	"	"	``
37681	1385	48	Questioni	Questioni	NNP
37681	1385	49	riguardanti	riguardanti	NNP
37681	1385	50	la	la	NNP
37681	1385	51	geometria	geometria	NNP
37681	1385	52	elementare	elementare	NNP
37681	1385	53	,	,	,
37681	1385	54	"	"	''
37681	1385	55	1900	1900	CD
37681	1385	56	;	;	:
37681	1385	57	Karagiannides	Karagiannides	NNP
37681	1385	58	,	,	,
37681	1385	59	"	"	``
37681	1385	60	Die	die	VBP
37681	1385	61	nichteuklidische	nichteuklidische	NNP
37681	1385	62	Geometrie	Geometrie	NNP
37681	1385	63	vom	vom	VBZ
37681	1385	64	Alterthum	Alterthum	NNP
37681	1385	65	bis	bis	NN
37681	1385	66	zur	zur	NNP
37681	1385	67	Gegenwart	Gegenwart	NNP
37681	1385	68	,	,	,
37681	1385	69	"	"	``
37681	1385	70	Berlin	Berlin	NNP
37681	1385	71	,	,	,
37681	1385	72	1893	1893	CD
37681	1385	73	.	.	.
37681	1386	1	[	[	-LRB-
37681	1386	2	51	51	CD
37681	1386	3	]	]	-RRB-
37681	1386	4	This	this	DT
37681	1386	5	limitation	limitation	NN
37681	1386	6	upon	upon	IN
37681	1386	7	elementary	elementary	JJ
37681	1386	8	geometry	geometry	NN
37681	1386	9	was	be	VBD
37681	1386	10	placed	place	VBN
37681	1386	11	by	by	IN
37681	1386	12	Plato	Plato	NNP
37681	1386	13	(	(	-LRB-
37681	1386	14	died	die	VBN
37681	1386	15	347	347	CD
37681	1386	16	B.C.	B.C.	NNP
37681	1387	1	)	)	-RRB-
37681	1387	2	,	,	,
37681	1387	3	as	as	IN
37681	1387	4	already	already	RB
37681	1387	5	stated	state	VBN
37681	1387	6	.	.	.
37681	1388	1	[	[	-LRB-
37681	1388	2	52	52	CD
37681	1388	3	]	]	-RRB-
37681	1388	4	Book	Book	NNP
37681	1388	5	I	I	NNP
37681	1388	6	,	,	,
37681	1388	7	Proposition	Proposition	NNP
37681	1388	8	20	20	CD
37681	1388	9	.	.	.
37681	1389	1	CHAPTER	chapter	NN
37681	1389	2	XII	XII	NNP
37681	1389	3	THE	the	DT
37681	1389	4	DEFINITIONS	definition	NNS
37681	1389	5	OF	of	IN
37681	1389	6	GEOMETRY	GEOMETRY	NNP
37681	1389	7	When	when	WRB
37681	1389	8	we	-PRON-	PRP
37681	1389	9	consider	consider	VBP
37681	1389	10	the	the	DT
37681	1389	11	nature	nature	NN
37681	1389	12	of	of	IN
37681	1389	13	geometry	geometry	NN
37681	1389	14	it	-PRON-	PRP
37681	1389	15	is	be	VBZ
37681	1389	16	evident	evident	JJ
37681	1389	17	that	that	IN
37681	1389	18	more	more	JJR
37681	1389	19	attention	attention	NN
37681	1389	20	must	must	MD
37681	1389	21	be	be	VB
37681	1389	22	paid	pay	VBN
37681	1389	23	to	to	IN
37681	1389	24	accuracy	accuracy	NN
37681	1389	25	of	of	IN
37681	1389	26	definitions	definition	NNS
37681	1389	27	than	than	IN
37681	1389	28	is	be	VBZ
37681	1389	29	the	the	DT
37681	1389	30	case	case	NN
37681	1389	31	in	in	IN
37681	1389	32	most	most	JJS
37681	1389	33	of	of	IN
37681	1389	34	the	the	DT
37681	1389	35	other	other	JJ
37681	1389	36	sciences	science	NNS
37681	1389	37	.	.	.
37681	1390	1	The	the	DT
37681	1390	2	essence	essence	NN
37681	1390	3	of	of	IN
37681	1390	4	all	all	DT
37681	1390	5	geometry	geometry	NN
37681	1390	6	worthy	worthy	JJ
37681	1390	7	of	of	IN
37681	1390	8	serious	serious	JJ
37681	1390	9	study	study	NN
37681	1390	10	is	be	VBZ
37681	1390	11	not	not	RB
37681	1390	12	the	the	DT
37681	1390	13	knowledge	knowledge	NN
37681	1390	14	of	of	IN
37681	1390	15	some	some	DT
37681	1390	16	fact	fact	NN
37681	1390	17	,	,	,
37681	1390	18	but	but	CC
37681	1390	19	the	the	DT
37681	1390	20	proof	proof	NN
37681	1390	21	of	of	IN
37681	1390	22	that	that	DT
37681	1390	23	fact	fact	NN
37681	1390	24	;	;	:
37681	1390	25	and	and	CC
37681	1390	26	this	this	DT
37681	1390	27	proof	proof	NN
37681	1390	28	is	be	VBZ
37681	1390	29	always	always	RB
37681	1390	30	based	base	VBN
37681	1390	31	upon	upon	IN
37681	1390	32	preceding	precede	VBG
37681	1390	33	proofs	proof	NNS
37681	1390	34	,	,	,
37681	1390	35	assumptions	assumption	NNS
37681	1390	36	(	(	-LRB-
37681	1390	37	axioms	axiom	NNS
37681	1390	38	or	or	CC
37681	1390	39	postulates	postulate	NNS
37681	1390	40	)	)	-RRB-
37681	1390	41	,	,	,
37681	1390	42	or	or	CC
37681	1390	43	definitions	definition	NNS
37681	1390	44	.	.	.
37681	1391	1	If	if	IN
37681	1391	2	we	-PRON-	PRP
37681	1391	3	are	be	VBP
37681	1391	4	to	to	TO
37681	1391	5	prove	prove	VB
37681	1391	6	that	that	IN
37681	1391	7	one	one	CD
37681	1391	8	line	line	NN
37681	1391	9	is	be	VBZ
37681	1391	10	perpendicular	perpendicular	JJ
37681	1391	11	to	to	IN
37681	1391	12	another	another	DT
37681	1391	13	,	,	,
37681	1391	14	it	-PRON-	PRP
37681	1391	15	is	be	VBZ
37681	1391	16	essential	essential	JJ
37681	1391	17	that	that	IN
37681	1391	18	we	-PRON-	PRP
37681	1391	19	have	have	VBP
37681	1391	20	an	an	DT
37681	1391	21	exact	exact	JJ
37681	1391	22	definition	definition	NN
37681	1391	23	of	of	IN
37681	1391	24	"	"	``
37681	1391	25	perpendicular	perpendicular	JJ
37681	1391	26	,	,	,
37681	1391	27	"	"	''
37681	1391	28	else	else	RB
37681	1391	29	we	-PRON-	PRP
37681	1391	30	shall	shall	MD
37681	1391	31	not	not	RB
37681	1391	32	know	know	VB
37681	1391	33	when	when	WRB
37681	1391	34	we	-PRON-	PRP
37681	1391	35	have	have	VBP
37681	1391	36	reached	reach	VBN
37681	1391	37	the	the	DT
37681	1391	38	conclusion	conclusion	NN
37681	1391	39	of	of	IN
37681	1391	40	the	the	DT
37681	1391	41	proof	proof	NN
37681	1391	42	.	.	.
37681	1392	1	The	the	DT
37681	1392	2	essential	essential	JJ
37681	1392	3	features	feature	NNS
37681	1392	4	of	of	IN
37681	1392	5	a	a	DT
37681	1392	6	definition	definition	NN
37681	1392	7	are	be	VBP
37681	1392	8	that	that	IN
37681	1392	9	the	the	DT
37681	1392	10	term	term	NN
37681	1392	11	defined	define	VBN
37681	1392	12	shall	shall	MD
37681	1392	13	be	be	VB
37681	1392	14	described	describe	VBN
37681	1392	15	in	in	IN
37681	1392	16	terms	term	NNS
37681	1392	17	that	that	WDT
37681	1392	18	are	be	VBP
37681	1392	19	simpler	simple	JJR
37681	1392	20	than	than	IN
37681	1392	21	,	,	,
37681	1392	22	or	or	CC
37681	1392	23	at	at	IN
37681	1392	24	least	least	RBS
37681	1392	25	better	well	RBR
37681	1392	26	known	know	VBN
37681	1392	27	than	than	IN
37681	1392	28	,	,	,
37681	1392	29	the	the	DT
37681	1392	30	thing	thing	NN
37681	1392	31	itself	-PRON-	PRP
37681	1392	32	;	;	:
37681	1392	33	that	that	IN
37681	1392	34	this	this	DT
37681	1392	35	shall	shall	MD
37681	1392	36	be	be	VB
37681	1392	37	done	do	VBN
37681	1392	38	in	in	IN
37681	1392	39	such	such	PDT
37681	1392	40	a	a	DT
37681	1392	41	way	way	NN
37681	1392	42	as	as	IN
37681	1392	43	to	to	TO
37681	1392	44	limit	limit	VB
37681	1392	45	the	the	DT
37681	1392	46	term	term	NN
37681	1392	47	to	to	IN
37681	1392	48	the	the	DT
37681	1392	49	thing	thing	NN
37681	1392	50	defined	define	VBN
37681	1392	51	;	;	:
37681	1392	52	and	and	CC
37681	1392	53	that	that	IN
37681	1392	54	the	the	DT
37681	1392	55	description	description	NN
37681	1392	56	shall	shall	MD
37681	1392	57	not	not	RB
37681	1392	58	be	be	VB
37681	1392	59	redundant	redundant	JJ
37681	1392	60	.	.	.
37681	1393	1	It	-PRON-	PRP
37681	1393	2	would	would	MD
37681	1393	3	not	not	RB
37681	1393	4	be	be	VB
37681	1393	5	a	a	DT
37681	1393	6	good	good	JJ
37681	1393	7	definition	definition	NN
37681	1393	8	to	to	TO
37681	1393	9	say	say	VB
37681	1393	10	that	that	IN
37681	1393	11	a	a	DT
37681	1393	12	right	right	JJ
37681	1393	13	angle	angle	NN
37681	1393	14	is	be	VBZ
37681	1393	15	one	one	CD
37681	1393	16	fourth	fourth	JJ
37681	1393	17	of	of	IN
37681	1393	18	a	a	DT
37681	1393	19	perigon	perigon	NNP
37681	1393	20	and	and	CC
37681	1393	21	one	one	CD
37681	1393	22	half	half	NN
37681	1393	23	of	of	IN
37681	1393	24	a	a	DT
37681	1393	25	straight	straight	JJ
37681	1393	26	angle	angle	NN
37681	1393	27	,	,	,
37681	1393	28	because	because	IN
37681	1393	29	the	the	DT
37681	1393	30	concept	concept	NN
37681	1393	31	"	"	``
37681	1393	32	perigon	perigon	NNP
37681	1393	33	"	"	''
37681	1393	34	is	be	VBZ
37681	1393	35	not	not	RB
37681	1393	36	so	so	RB
37681	1393	37	simple	simple	JJ
37681	1393	38	,	,	,
37681	1393	39	and	and	CC
37681	1393	40	the	the	DT
37681	1393	41	term	term	NN
37681	1393	42	"	"	``
37681	1393	43	perigon	perigon	NNP
37681	1393	44	"	"	''
37681	1393	45	is	be	VBZ
37681	1393	46	not	not	RB
37681	1393	47	so	so	RB
37681	1393	48	well	well	RB
37681	1393	49	known	know	VBN
37681	1393	50	,	,	,
37681	1393	51	as	as	IN
37681	1393	52	the	the	DT
37681	1393	53	term	term	NN
37681	1393	54	and	and	CC
37681	1393	55	the	the	DT
37681	1393	56	concept	concept	NN
37681	1393	57	"	"	``
37681	1393	58	right	right	JJ
37681	1393	59	angle	angle	NN
37681	1393	60	,	,	,
37681	1393	61	"	"	''
37681	1393	62	and	and	CC
37681	1393	63	because	because	IN
37681	1393	64	the	the	DT
37681	1393	65	definition	definition	NN
37681	1393	66	is	be	VBZ
37681	1393	67	redundant	redundant	JJ
37681	1393	68	,	,	,
37681	1393	69	containing	contain	VBG
37681	1393	70	more	more	JJR
37681	1393	71	than	than	IN
37681	1393	72	is	be	VBZ
37681	1393	73	necessary	necessary	JJ
37681	1393	74	.	.	.
37681	1394	1	It	-PRON-	PRP
37681	1394	2	is	be	VBZ
37681	1394	3	evident	evident	JJ
37681	1394	4	that	that	IN
37681	1394	5	satisfactory	satisfactory	JJ
37681	1394	6	definitions	definition	NNS
37681	1394	7	are	be	VBP
37681	1394	8	not	not	RB
37681	1394	9	always	always	RB
37681	1394	10	possible	possible	JJ
37681	1394	11	;	;	:
37681	1394	12	for	for	IN
37681	1394	13	since	since	IN
37681	1394	14	the	the	DT
37681	1394	15	number	number	NN
37681	1394	16	of	of	IN
37681	1394	17	terms	term	NNS
37681	1394	18	is	be	VBZ
37681	1394	19	limited	limited	JJ
37681	1394	20	,	,	,
37681	1394	21	there	there	EX
37681	1394	22	must	must	MD
37681	1394	23	be	be	VB
37681	1394	24	at	at	RB
37681	1394	25	least	least	RBS
37681	1394	26	one	one	CD
37681	1394	27	that	that	WDT
37681	1394	28	is	be	VBZ
37681	1394	29	at	at	IN
37681	1394	30	least	least	JJS
37681	1394	31	as	as	RB
37681	1394	32	simple	simple	JJ
37681	1394	33	as	as	IN
37681	1394	34	any	any	DT
37681	1394	35	other	other	JJ
37681	1394	36	,	,	,
37681	1394	37	and	and	CC
37681	1394	38	this	this	DT
37681	1394	39	can	can	MD
37681	1394	40	not	not	RB
37681	1394	41	be	be	VB
37681	1394	42	described	describe	VBN
37681	1394	43	in	in	IN
37681	1394	44	terms	term	NNS
37681	1394	45	simpler	simple	JJR
37681	1394	46	than	than	IN
37681	1394	47	itself	-PRON-	PRP
37681	1394	48	.	.	.
37681	1395	1	Such	such	JJ
37681	1395	2	,	,	,
37681	1395	3	for	for	IN
37681	1395	4	example	example	NN
37681	1395	5	,	,	,
37681	1395	6	is	be	VBZ
37681	1395	7	the	the	DT
37681	1395	8	term	term	NN
37681	1395	9	"	"	``
37681	1395	10	angle	angle	NN
37681	1395	11	.	.	.
37681	1395	12	"	"	''
37681	1396	1	We	-PRON-	PRP
37681	1396	2	can	can	MD
37681	1396	3	easily	easily	RB
37681	1396	4	explain	explain	VB
37681	1396	5	the	the	DT
37681	1396	6	meaning	meaning	NN
37681	1396	7	of	of	IN
37681	1396	8	this	this	DT
37681	1396	9	word	word	NN
37681	1396	10	,	,	,
37681	1396	11	and	and	CC
37681	1396	12	we	-PRON-	PRP
37681	1396	13	can	can	MD
37681	1396	14	make	make	VB
37681	1396	15	the	the	DT
37681	1396	16	concept	concept	NN
37681	1396	17	clear	clear	JJ
37681	1396	18	,	,	,
37681	1396	19	but	but	CC
37681	1396	20	this	this	DT
37681	1396	21	must	must	MD
37681	1396	22	be	be	VB
37681	1396	23	done	do	VBN
37681	1396	24	by	by	IN
37681	1396	25	a	a	DT
37681	1396	26	certain	certain	JJ
37681	1396	27	amount	amount	NN
37681	1396	28	of	of	IN
37681	1396	29	circumlocution	circumlocution	NN
37681	1396	30	and	and	CC
37681	1396	31	explanation	explanation	NN
37681	1396	32	,	,	,
37681	1396	33	not	not	RB
37681	1396	34	by	by	IN
37681	1396	35	a	a	DT
37681	1396	36	concise	concise	NN
37681	1396	37	and	and	CC
37681	1396	38	perfect	perfect	JJ
37681	1396	39	definition	definition	NN
37681	1396	40	.	.	.
37681	1397	1	Unless	unless	IN
37681	1397	2	a	a	DT
37681	1397	3	beginner	beginner	NN
37681	1397	4	in	in	IN
37681	1397	5	geometry	geometry	NN
37681	1397	6	knows	know	VBZ
37681	1397	7	what	what	WP
37681	1397	8	an	an	DT
37681	1397	9	angle	angle	NN
37681	1397	10	is	be	VBZ
37681	1397	11	before	before	IN
37681	1397	12	he	-PRON-	PRP
37681	1397	13	reads	read	VBZ
37681	1397	14	the	the	DT
37681	1397	15	definition	definition	NN
37681	1397	16	in	in	IN
37681	1397	17	a	a	DT
37681	1397	18	textbook	textbook	NN
37681	1397	19	,	,	,
37681	1397	20	he	-PRON-	PRP
37681	1397	21	will	will	MD
37681	1397	22	not	not	RB
37681	1397	23	know	know	VB
37681	1397	24	from	from	IN
37681	1397	25	the	the	DT
37681	1397	26	definition	definition	NN
37681	1397	27	.	.	.
37681	1398	1	This	this	DT
37681	1398	2	fact	fact	NN
37681	1398	3	of	of	IN
37681	1398	4	the	the	DT
37681	1398	5	impossibility	impossibility	NN
37681	1398	6	of	of	IN
37681	1398	7	defining	define	VBG
37681	1398	8	some	some	DT
37681	1398	9	of	of	IN
37681	1398	10	the	the	DT
37681	1398	11	fundamental	fundamental	JJ
37681	1398	12	concepts	concept	NNS
37681	1398	13	will	will	MD
37681	1398	14	be	be	VB
37681	1398	15	evident	evident	JJ
37681	1398	16	when	when	WRB
37681	1398	17	we	-PRON-	PRP
37681	1398	18	come	come	VBP
37681	1398	19	to	to	TO
37681	1398	20	consider	consider	VB
37681	1398	21	certain	certain	JJ
37681	1398	22	attempts	attempt	NNS
37681	1398	23	that	that	WDT
37681	1398	24	have	have	VBP
37681	1398	25	been	be	VBN
37681	1398	26	made	make	VBN
37681	1398	27	in	in	IN
37681	1398	28	this	this	DT
37681	1398	29	direction	direction	NN
37681	1398	30	.	.	.
37681	1399	1	It	-PRON-	PRP
37681	1399	2	should	should	MD
37681	1399	3	also	also	RB
37681	1399	4	be	be	VB
37681	1399	5	understood	understand	VBN
37681	1399	6	in	in	IN
37681	1399	7	this	this	DT
37681	1399	8	connection	connection	NN
37681	1399	9	that	that	IN
37681	1399	10	a	a	DT
37681	1399	11	definition	definition	NN
37681	1399	12	makes	make	VBZ
37681	1399	13	no	no	DT
37681	1399	14	assertion	assertion	NN
37681	1399	15	as	as	IN
37681	1399	16	to	to	IN
37681	1399	17	the	the	DT
37681	1399	18	existence	existence	NN
37681	1399	19	of	of	IN
37681	1399	20	the	the	DT
37681	1399	21	thing	thing	NN
37681	1399	22	defined	define	VBN
37681	1399	23	.	.	.
37681	1400	1	If	if	IN
37681	1400	2	we	-PRON-	PRP
37681	1400	3	say	say	VBP
37681	1400	4	that	that	IN
37681	1400	5	a	a	DT
37681	1400	6	tangent	tangent	NN
37681	1400	7	to	to	IN
37681	1400	8	a	a	DT
37681	1400	9	circle	circle	NN
37681	1400	10	is	be	VBZ
37681	1400	11	an	an	DT
37681	1400	12	unlimited	unlimited	JJ
37681	1400	13	straight	straight	JJ
37681	1400	14	line	line	NN
37681	1400	15	that	that	WDT
37681	1400	16	touches	touch	VBZ
37681	1400	17	the	the	DT
37681	1400	18	circle	circle	NN
37681	1400	19	in	in	IN
37681	1400	20	one	one	CD
37681	1400	21	point	point	NN
37681	1400	22	,	,	,
37681	1400	23	and	and	CC
37681	1400	24	only	only	RB
37681	1400	25	one	one	CD
37681	1400	26	,	,	,
37681	1400	27	we	-PRON-	PRP
37681	1400	28	do	do	VBP
37681	1400	29	not	not	RB
37681	1400	30	assert	assert	VB
37681	1400	31	that	that	IN
37681	1400	32	it	-PRON-	PRP
37681	1400	33	is	be	VBZ
37681	1400	34	possible	possible	JJ
37681	1400	35	to	to	TO
37681	1400	36	have	have	VB
37681	1400	37	such	such	PDT
37681	1400	38	a	a	DT
37681	1400	39	line	line	NN
37681	1400	40	;	;	:
37681	1400	41	that	that	DT
37681	1400	42	is	be	VBZ
37681	1400	43	a	a	DT
37681	1400	44	matter	matter	NN
37681	1400	45	for	for	IN
37681	1400	46	proof	proof	NN
37681	1400	47	.	.	.
37681	1401	1	Not	not	RB
37681	1401	2	in	in	IN
37681	1401	3	all	all	DT
37681	1401	4	cases	case	NNS
37681	1401	5	,	,	,
37681	1401	6	however	however	RB
37681	1401	7	,	,	,
37681	1401	8	can	can	MD
37681	1401	9	this	this	DT
37681	1401	10	proof	proof	NN
37681	1401	11	be	be	VB
37681	1401	12	given	give	VBN
37681	1401	13	,	,	,
37681	1401	14	as	as	IN
37681	1401	15	in	in	IN
37681	1401	16	the	the	DT
37681	1401	17	existence	existence	NN
37681	1401	18	of	of	IN
37681	1401	19	the	the	DT
37681	1401	20	simplest	simple	JJS
37681	1401	21	concepts	concept	NNS
37681	1401	22	.	.	.
37681	1402	1	We	-PRON-	PRP
37681	1402	2	can	can	MD
37681	1402	3	not	not	RB
37681	1402	4	,	,	,
37681	1402	5	for	for	IN
37681	1402	6	example	example	NN
37681	1402	7	,	,	,
37681	1402	8	prove	prove	VBP
37681	1402	9	that	that	IN
37681	1402	10	a	a	DT
37681	1402	11	point	point	NN
37681	1402	12	or	or	CC
37681	1402	13	a	a	DT
37681	1402	14	straight	straight	JJ
37681	1402	15	line	line	NN
37681	1402	16	exists	exist	VBZ
37681	1402	17	after	after	IN
37681	1402	18	we	-PRON-	PRP
37681	1402	19	have	have	VBP
37681	1402	20	defined	define	VBN
37681	1402	21	these	these	DT
37681	1402	22	concepts	concept	NNS
37681	1402	23	.	.	.
37681	1403	1	We	-PRON-	PRP
37681	1403	2	therefore	therefore	RB
37681	1403	3	tacitly	tacitly	RB
37681	1403	4	or	or	CC
37681	1403	5	explicitly	explicitly	RB
37681	1403	6	assume	assume	VB
37681	1403	7	(	(	-LRB-
37681	1403	8	postulate	postulate	NN
37681	1403	9	)	)	-RRB-
37681	1403	10	the	the	DT
37681	1403	11	existence	existence	NN
37681	1403	12	of	of	IN
37681	1403	13	these	these	DT
37681	1403	14	fundamentals	fundamental	NNS
37681	1403	15	of	of	IN
37681	1403	16	geometry	geometry	NN
37681	1403	17	.	.	.
37681	1404	1	On	on	IN
37681	1404	2	the	the	DT
37681	1404	3	other	other	JJ
37681	1404	4	hand	hand	NN
37681	1404	5	,	,	,
37681	1404	6	we	-PRON-	PRP
37681	1404	7	can	can	MD
37681	1404	8	prove	prove	VB
37681	1404	9	that	that	IN
37681	1404	10	a	a	DT
37681	1404	11	tangent	tangent	NN
37681	1404	12	exists	exist	VBZ
37681	1404	13	,	,	,
37681	1404	14	and	and	CC
37681	1404	15	this	this	DT
37681	1404	16	may	may	MD
37681	1404	17	properly	properly	RB
37681	1404	18	be	be	VB
37681	1404	19	considered	consider	VBN
37681	1404	20	a	a	DT
37681	1404	21	legitimate	legitimate	JJ
37681	1404	22	proposition	proposition	NN
37681	1404	23	or	or	CC
37681	1404	24	corollary	corollary	JJ
37681	1404	25	of	of	IN
37681	1404	26	elementary	elementary	JJ
37681	1404	27	geometry	geometry	NNP
37681	1404	28	.	.	.
37681	1405	1	In	in	IN
37681	1405	2	relation	relation	NN
37681	1405	3	to	to	IN
37681	1405	4	geometric	geometric	JJ
37681	1405	5	proof	proof	NN
37681	1405	6	it	-PRON-	PRP
37681	1405	7	is	be	VBZ
37681	1405	8	necessary	necessary	JJ
37681	1405	9	to	to	TO
37681	1405	10	bear	bear	VB
37681	1405	11	in	in	IN
37681	1405	12	mind	mind	NN
37681	1405	13	,	,	,
37681	1405	14	therefore	therefore	RB
37681	1405	15	,	,	,
37681	1405	16	that	that	IN
37681	1405	17	we	-PRON-	PRP
37681	1405	18	are	be	VBP
37681	1405	19	permitted	permit	VBN
37681	1405	20	to	to	TO
37681	1405	21	define	define	VB
37681	1405	22	any	any	DT
37681	1405	23	term	term	NN
37681	1405	24	we	-PRON-	PRP
37681	1405	25	please	please	VBP
37681	1405	26	;	;	:
37681	1405	27	for	for	IN
37681	1405	28	example	example	NN
37681	1405	29	,	,	,
37681	1405	30	"	"	''
37681	1405	31	a	a	DT
37681	1405	32	seven	seven	CD
37681	1405	33	-	-	HYPH
37681	1405	34	edged	edge	VBN
37681	1405	35	polyhedron	polyhedron	NN
37681	1405	36	"	"	''
37681	1405	37	or	or	CC
37681	1405	38	Leibnitz	Leibnitz	NNP
37681	1405	39	's	's	POS
37681	1405	40	"	"	``
37681	1405	41	ten	ten	CD
37681	1405	42	-	-	HYPH
37681	1405	43	faced	faced	JJ
37681	1405	44	regular	regular	JJ
37681	1405	45	polyhedron	polyhedron	NN
37681	1405	46	,	,	,
37681	1405	47	"	"	''
37681	1405	48	neither	neither	DT
37681	1405	49	of	of	IN
37681	1405	50	which	which	WDT
37681	1405	51	exists	exist	VBZ
37681	1405	52	;	;	:
37681	1405	53	but	but	CC
37681	1405	54	,	,	,
37681	1405	55	strictly	strictly	RB
37681	1405	56	speaking	speak	VBG
37681	1405	57	,	,	,
37681	1405	58	we	-PRON-	PRP
37681	1405	59	have	have	VBP
37681	1405	60	no	no	DT
37681	1405	61	right	right	NN
37681	1405	62	to	to	TO
37681	1405	63	make	make	VB
37681	1405	64	use	use	NN
37681	1405	65	of	of	IN
37681	1405	66	a	a	DT
37681	1405	67	definition	definition	NN
37681	1405	68	in	in	IN
37681	1405	69	a	a	DT
37681	1405	70	proof	proof	NN
37681	1405	71	until	until	IN
37681	1405	72	we	-PRON-	PRP
37681	1405	73	have	have	VBP
37681	1405	74	shown	show	VBN
37681	1405	75	or	or	CC
37681	1405	76	postulated	postulate	VBN
37681	1405	77	that	that	IN
37681	1405	78	the	the	DT
37681	1405	79	thing	thing	NN
37681	1405	80	defined	define	VBN
37681	1405	81	has	have	VBZ
37681	1405	82	an	an	DT
37681	1405	83	existence	existence	NN
37681	1405	84	.	.	.
37681	1406	1	This	this	DT
37681	1406	2	is	be	VBZ
37681	1406	3	one	one	CD
37681	1406	4	of	of	IN
37681	1406	5	the	the	DT
37681	1406	6	strong	strong	JJ
37681	1406	7	features	feature	NNS
37681	1406	8	of	of	IN
37681	1406	9	Euclid	Euclid	NNP
37681	1406	10	's	's	POS
37681	1406	11	textbook	textbook	NN
37681	1406	12	.	.	.
37681	1407	1	Not	not	RB
37681	1407	2	being	be	VBG
37681	1407	3	able	able	JJ
37681	1407	4	to	to	TO
37681	1407	5	prove	prove	VB
37681	1407	6	that	that	IN
37681	1407	7	a	a	DT
37681	1407	8	point	point	NN
37681	1407	9	,	,	,
37681	1407	10	a	a	DT
37681	1407	11	straight	straight	JJ
37681	1407	12	line	line	NN
37681	1407	13	,	,	,
37681	1407	14	and	and	CC
37681	1407	15	a	a	DT
37681	1407	16	circle	circle	NN
37681	1407	17	exists	exist	VBZ
37681	1407	18	,	,	,
37681	1407	19	he	-PRON-	PRP
37681	1407	20	practically	practically	RB
37681	1407	21	postulates	postulate	VBZ
37681	1407	22	these	these	DT
37681	1407	23	facts	fact	NNS
37681	1407	24	;	;	:
37681	1407	25	but	but	CC
37681	1407	26	he	-PRON-	PRP
37681	1407	27	uses	use	VBZ
37681	1407	28	no	no	DT
37681	1407	29	other	other	JJ
37681	1407	30	definition	definition	NN
37681	1407	31	in	in	IN
37681	1407	32	a	a	DT
37681	1407	33	proof	proof	NN
37681	1407	34	without	without	IN
37681	1407	35	showing	show	VBG
37681	1407	36	that	that	IN
37681	1407	37	the	the	DT
37681	1407	38	thing	thing	NN
37681	1407	39	defined	define	VBN
37681	1407	40	exists	exist	VBZ
37681	1407	41	,	,	,
37681	1407	42	and	and	CC
37681	1407	43	this	this	DT
37681	1407	44	is	be	VBZ
37681	1407	45	his	-PRON-	PRP$
37681	1407	46	reason	reason	NN
37681	1407	47	for	for	IN
37681	1407	48	mingling	mingle	VBG
37681	1407	49	his	-PRON-	PRP$
37681	1407	50	problems	problem	NNS
37681	1407	51	with	with	IN
37681	1407	52	his	-PRON-	PRP$
37681	1407	53	theorems	theorem	NNS
37681	1407	54	.	.	.
37681	1408	1	At	at	IN
37681	1408	2	the	the	DT
37681	1408	3	present	present	JJ
37681	1408	4	time	time	NN
37681	1408	5	we	-PRON-	PRP
37681	1408	6	confessedly	confessedly	RB
37681	1408	7	sacrifice	sacrifice	VBP
37681	1408	8	his	-PRON-	PRP$
37681	1408	9	logic	logic	NN
37681	1408	10	in	in	IN
37681	1408	11	this	this	DT
37681	1408	12	respect	respect	NN
37681	1408	13	for	for	IN
37681	1408	14	the	the	DT
37681	1408	15	reason	reason	NN
37681	1408	16	that	that	WDT
37681	1408	17	we	-PRON-	PRP
37681	1408	18	teach	teach	VBP
37681	1408	19	geometry	geometry	NN
37681	1408	20	to	to	IN
37681	1408	21	pupils	pupil	NNS
37681	1408	22	who	who	WP
37681	1408	23	are	be	VBP
37681	1408	24	too	too	RB
37681	1408	25	young	young	JJ
37681	1408	26	to	to	TO
37681	1408	27	appreciate	appreciate	VB
37681	1408	28	that	that	DT
37681	1408	29	logic	logic	NN
37681	1408	30	.	.	.
37681	1409	1	It	-PRON-	PRP
37681	1409	2	was	be	VBD
37681	1409	3	pointed	point	VBN
37681	1409	4	out	out	RP
37681	1409	5	by	by	IN
37681	1409	6	Aristotle	Aristotle	NNP
37681	1409	7	,	,	,
37681	1409	8	long	long	RB
37681	1409	9	before	before	IN
37681	1409	10	Euclid	Euclid	NNP
37681	1409	11	,	,	,
37681	1409	12	that	that	IN
37681	1409	13	it	-PRON-	PRP
37681	1409	14	is	be	VBZ
37681	1409	15	not	not	RB
37681	1409	16	a	a	DT
37681	1409	17	satisfactory	satisfactory	JJ
37681	1409	18	procedure	procedure	NN
37681	1409	19	to	to	TO
37681	1409	20	define	define	VB
37681	1409	21	a	a	DT
37681	1409	22	thing	thing	NN
37681	1409	23	by	by	IN
37681	1409	24	means	mean	NNS
37681	1409	25	of	of	IN
37681	1409	26	terms	term	NNS
37681	1409	27	that	that	WDT
37681	1409	28	are	be	VBP
37681	1409	29	strictly	strictly	RB
37681	1409	30	not	not	RB
37681	1409	31	prior	prior	JJ
37681	1409	32	to	to	IN
37681	1409	33	it	-PRON-	PRP
37681	1409	34	,	,	,
37681	1409	35	as	as	IN
37681	1409	36	when	when	WRB
37681	1409	37	we	-PRON-	PRP
37681	1409	38	attempt	attempt	VBP
37681	1409	39	to	to	TO
37681	1409	40	define	define	VB
37681	1409	41	something	something	NN
37681	1409	42	by	by	IN
37681	1409	43	means	mean	NNS
37681	1409	44	of	of	IN
37681	1409	45	its	-PRON-	PRP$
37681	1409	46	opposite	opposite	NN
37681	1409	47	.	.	.
37681	1410	1	Thus	thus	RB
37681	1410	2	to	to	TO
37681	1410	3	define	define	VB
37681	1410	4	a	a	DT
37681	1410	5	curve	curve	NN
37681	1410	6	as	as	IN
37681	1410	7	"	"	``
37681	1410	8	a	a	DT
37681	1410	9	line	line	NN
37681	1410	10	,	,	,
37681	1410	11	no	no	DT
37681	1410	12	part	part	NN
37681	1410	13	of	of	IN
37681	1410	14	which	which	WDT
37681	1410	15	is	be	VBZ
37681	1410	16	straight	straight	JJ
37681	1410	17	,	,	,
37681	1410	18	"	"	``
37681	1410	19	would	would	MD
37681	1410	20	be	be	VB
37681	1410	21	a	a	DT
37681	1410	22	bad	bad	JJ
37681	1410	23	definition	definition	NN
37681	1410	24	unless	unless	IN
37681	1410	25	"	"	``
37681	1410	26	straight	straight	JJ
37681	1410	27	"	"	''
37681	1410	28	had	have	VBD
37681	1410	29	already	already	RB
37681	1410	30	been	be	VBN
37681	1410	31	explicitly	explicitly	RB
37681	1410	32	defined	define	VBN
37681	1410	33	;	;	:
37681	1410	34	and	and	CC
37681	1410	35	to	to	TO
37681	1410	36	define	define	VB
37681	1410	37	"	"	``
37681	1410	38	bad	bad	JJ
37681	1410	39	"	"	''
37681	1410	40	as	as	IN
37681	1410	41	"	"	``
37681	1410	42	not	not	RB
37681	1410	43	good	good	JJ
37681	1410	44	"	"	''
37681	1410	45	is	be	VBZ
37681	1410	46	unsatisfactory	unsatisfactory	JJ
37681	1410	47	for	for	IN
37681	1410	48	the	the	DT
37681	1410	49	reason	reason	NN
37681	1410	50	that	that	IN
37681	1410	51	"	"	``
37681	1410	52	bad	bad	JJ
37681	1410	53	"	"	''
37681	1410	54	and	and	CC
37681	1410	55	"	"	``
37681	1410	56	good	good	JJ
37681	1410	57	"	"	''
37681	1410	58	are	be	VBP
37681	1410	59	concepts	concept	NNS
37681	1410	60	that	that	WDT
37681	1410	61	are	be	VBP
37681	1410	62	evolved	evolve	VBN
37681	1410	63	simultaneously	simultaneously	RB
37681	1410	64	.	.	.
37681	1411	1	But	but	CC
37681	1411	2	all	all	PDT
37681	1411	3	this	this	DT
37681	1411	4	is	be	VBZ
37681	1411	5	only	only	RB
37681	1411	6	a	a	DT
37681	1411	7	detail	detail	NN
37681	1411	8	under	under	IN
37681	1411	9	the	the	DT
37681	1411	10	general	general	JJ
37681	1411	11	principle	principle	NN
37681	1411	12	that	that	IN
37681	1411	13	a	a	DT
37681	1411	14	definition	definition	NN
37681	1411	15	must	must	MD
37681	1411	16	employ	employ	VB
37681	1411	17	terms	term	NNS
37681	1411	18	that	that	WDT
37681	1411	19	are	be	VBP
37681	1411	20	better	well	RBR
37681	1411	21	understood	understand	VBN
37681	1411	22	than	than	IN
37681	1411	23	the	the	DT
37681	1411	24	one	one	CD
37681	1411	25	defined	define	VBN
37681	1411	26	.	.	.
37681	1412	1	It	-PRON-	PRP
37681	1412	2	should	should	MD
37681	1412	3	be	be	VB
37681	1412	4	understood	understand	VBN
37681	1412	5	that	that	IN
37681	1412	6	some	some	DT
37681	1412	7	definitions	definition	NNS
37681	1412	8	are	be	VBP
37681	1412	9	much	much	RB
37681	1412	10	more	more	RBR
37681	1412	11	important	important	JJ
37681	1412	12	than	than	IN
37681	1412	13	others	other	NNS
37681	1412	14	,	,	,
37681	1412	15	considered	consider	VBN
37681	1412	16	from	from	IN
37681	1412	17	the	the	DT
37681	1412	18	point	point	NN
37681	1412	19	of	of	IN
37681	1412	20	view	view	NN
37681	1412	21	of	of	IN
37681	1412	22	the	the	DT
37681	1412	23	logic	logic	NN
37681	1412	24	of	of	IN
37681	1412	25	geometry	geometry	NN
37681	1412	26	.	.	.
37681	1413	1	Those	those	DT
37681	1413	2	that	that	WDT
37681	1413	3	enter	enter	VBP
37681	1413	4	into	into	IN
37681	1413	5	geometric	geometric	JJ
37681	1413	6	proofs	proof	NNS
37681	1413	7	are	be	VBP
37681	1413	8	basal	basal	JJ
37681	1413	9	;	;	:
37681	1413	10	those	those	DT
37681	1413	11	that	that	WDT
37681	1413	12	form	form	VBP
37681	1413	13	part	part	NN
37681	1413	14	of	of	IN
37681	1413	15	the	the	DT
37681	1413	16	conversational	conversational	JJ
37681	1413	17	language	language	NN
37681	1413	18	of	of	IN
37681	1413	19	geometry	geometry	NN
37681	1413	20	are	be	VBP
37681	1413	21	not	not	RB
37681	1413	22	.	.	.
37681	1414	1	Euclid	Euclid	NNP
37681	1414	2	gave	give	VBD
37681	1414	3	twenty	twenty	CD
37681	1414	4	-	-	HYPH
37681	1414	5	three	three	CD
37681	1414	6	definitions	definition	NNS
37681	1414	7	in	in	IN
37681	1414	8	Book	Book	NNP
37681	1414	9	I	-PRON-	PRP
37681	1414	10	,	,	,
37681	1414	11	and	and	CC
37681	1414	12	did	do	VBD
37681	1414	13	not	not	RB
37681	1414	14	make	make	VB
37681	1414	15	use	use	NN
37681	1414	16	of	of	IN
37681	1414	17	even	even	RB
37681	1414	18	all	all	DT
37681	1414	19	of	of	IN
37681	1414	20	these	these	DT
37681	1414	21	terms	term	NNS
37681	1414	22	.	.	.
37681	1415	1	Other	other	JJ
37681	1415	2	terms	term	NNS
37681	1415	3	,	,	,
37681	1415	4	those	those	DT
37681	1415	5	not	not	RB
37681	1415	6	employed	employ	VBN
37681	1415	7	in	in	IN
37681	1415	8	his	-PRON-	PRP$
37681	1415	9	proofs	proof	NNS
37681	1415	10	,	,	,
37681	1415	11	he	-PRON-	PRP
37681	1415	12	assumed	assume	VBD
37681	1415	13	to	to	TO
37681	1415	14	be	be	VB
37681	1415	15	known	know	VBN
37681	1415	16	,	,	,
37681	1415	17	just	just	RB
37681	1415	18	as	as	IN
37681	1415	19	he	-PRON-	PRP
37681	1415	20	assumed	assume	VBD
37681	1415	21	a	a	DT
37681	1415	22	knowledge	knowledge	NN
37681	1415	23	of	of	IN
37681	1415	24	any	any	DT
37681	1415	25	other	other	JJ
37681	1415	26	words	word	NNS
37681	1415	27	in	in	IN
37681	1415	28	his	-PRON-	PRP$
37681	1415	29	language	language	NN
37681	1415	30	.	.	.
37681	1416	1	Such	such	JJ
37681	1416	2	procedure	procedure	NN
37681	1416	3	would	would	MD
37681	1416	4	not	not	RB
37681	1416	5	be	be	VB
37681	1416	6	satisfactory	satisfactory	JJ
37681	1416	7	under	under	IN
37681	1416	8	modern	modern	JJ
37681	1416	9	conditions	condition	NNS
37681	1416	10	,	,	,
37681	1416	11	but	but	CC
37681	1416	12	it	-PRON-	PRP
37681	1416	13	is	be	VBZ
37681	1416	14	of	of	IN
37681	1416	15	great	great	JJ
37681	1416	16	importance	importance	NN
37681	1416	17	that	that	IN
37681	1416	18	the	the	DT
37681	1416	19	teacher	teacher	NN
37681	1416	20	should	should	MD
37681	1416	21	recognize	recognize	VB
37681	1416	22	that	that	IN
37681	1416	23	certain	certain	JJ
37681	1416	24	definitions	definition	NNS
37681	1416	25	are	be	VBP
37681	1416	26	basal	basal	JJ
37681	1416	27	,	,	,
37681	1416	28	while	while	IN
37681	1416	29	others	other	NNS
37681	1416	30	are	be	VBP
37681	1416	31	merely	merely	RB
37681	1416	32	informational	informational	JJ
37681	1416	33	.	.	.
37681	1417	1	It	-PRON-	PRP
37681	1417	2	is	be	VBZ
37681	1417	3	now	now	RB
37681	1417	4	proposed	propose	VBN
37681	1417	5	to	to	TO
37681	1417	6	consider	consider	VB
37681	1417	7	the	the	DT
37681	1417	8	basal	basal	JJ
37681	1417	9	definitions	definition	NNS
37681	1417	10	of	of	IN
37681	1417	11	geometry	geometry	NN
37681	1417	12	,	,	,
37681	1417	13	first	first	RB
37681	1417	14	,	,	,
37681	1417	15	that	that	IN
37681	1417	16	the	the	DT
37681	1417	17	teacher	teacher	NN
37681	1417	18	may	may	MD
37681	1417	19	know	know	VB
37681	1417	20	what	what	WP
37681	1417	21	ones	one	NNS
37681	1417	22	are	be	VBP
37681	1417	23	to	to	TO
37681	1417	24	be	be	VB
37681	1417	25	emphasized	emphasize	VBN
37681	1417	26	and	and	CC
37681	1417	27	learned	learn	VBN
37681	1417	28	;	;	:
37681	1417	29	and	and	CC
37681	1417	30	second	second	RB
37681	1417	31	,	,	,
37681	1417	32	that	that	IN
37681	1417	33	he	-PRON-	PRP
37681	1417	34	may	may	MD
37681	1417	35	know	know	VB
37681	1417	36	that	that	IN
37681	1417	37	the	the	DT
37681	1417	38	idea	idea	NN
37681	1417	39	that	that	IN
37681	1417	40	the	the	DT
37681	1417	41	standard	standard	JJ
37681	1417	42	definitions	definition	NNS
37681	1417	43	can	can	MD
37681	1417	44	easily	easily	RB
37681	1417	45	be	be	VB
37681	1417	46	improved	improve	VBN
37681	1417	47	is	be	VBZ
37681	1417	48	incorrect	incorrect	JJ
37681	1417	49	.	.	.
37681	1418	1	It	-PRON-	PRP
37681	1418	2	is	be	VBZ
37681	1418	3	hoped	hope	VBN
37681	1418	4	that	that	IN
37681	1418	5	the	the	DT
37681	1418	6	result	result	NN
37681	1418	7	will	will	MD
37681	1418	8	be	be	VB
37681	1418	9	the	the	DT
37681	1418	10	bringing	bringing	NN
37681	1418	11	into	into	IN
37681	1418	12	prominence	prominence	NN
37681	1418	13	of	of	IN
37681	1418	14	the	the	DT
37681	1418	15	basal	basal	NN
37681	1418	16	concepts	concept	NNS
37681	1418	17	,	,	,
37681	1418	18	and	and	CC
37681	1418	19	the	the	DT
37681	1418	20	discouraging	discouraging	NN
37681	1418	21	of	of	IN
37681	1418	22	attempts	attempt	NNS
37681	1418	23	to	to	TO
37681	1418	24	change	change	VB
37681	1418	25	in	in	IN
37681	1418	26	unimportant	unimportant	JJ
37681	1418	27	respects	respect	VBZ
37681	1418	28	the	the	DT
37681	1418	29	definitions	definition	NNS
37681	1418	30	in	in	IN
37681	1418	31	the	the	DT
37681	1418	32	textbook	textbook	NN
37681	1418	33	used	use	VBN
37681	1418	34	by	by	IN
37681	1418	35	the	the	DT
37681	1418	36	pupil	pupil	NN
37681	1418	37	.	.	.
37681	1419	1	In	in	IN
37681	1419	2	order	order	NN
37681	1419	3	to	to	TO
37681	1419	4	have	have	VB
37681	1419	5	a	a	DT
37681	1419	6	systematic	systematic	JJ
37681	1419	7	basis	basis	NN
37681	1419	8	for	for	IN
37681	1419	9	work	work	NN
37681	1419	10	,	,	,
37681	1419	11	the	the	DT
37681	1419	12	definitions	definition	NNS
37681	1419	13	of	of	IN
37681	1419	14	two	two	CD
37681	1419	15	books	book	NNS
37681	1419	16	of	of	IN
37681	1419	17	Euclid	Euclid	NNP
37681	1419	18	will	will	MD
37681	1419	19	first	first	RB
37681	1419	20	be	be	VB
37681	1419	21	considered	consider	VBN
37681	1419	22	.	.	.
37681	1420	1	[	[	-LRB-
37681	1420	2	53	53	CD
37681	1420	3	]	]	-RRB-
37681	1420	4	1	1	CD
37681	1420	5	.	.	.
37681	1421	1	POINT	POINT	NNS
37681	1421	2	.	.	.
37681	1422	1	_	_	NNP
37681	1422	2	A	a	DT
37681	1422	3	point	point	NN
37681	1422	4	is	be	VBZ
37681	1422	5	that	that	DT
37681	1422	6	which	which	WDT
37681	1422	7	has	have	VBZ
37681	1422	8	no	no	DT
37681	1422	9	part	part	NN
37681	1422	10	.	.	.
37681	1422	11	_	_	NNP
37681	1422	12	This	this	DT
37681	1422	13	was	be	VBD
37681	1422	14	incorrectly	incorrectly	RB
37681	1422	15	translated	translate	VBN
37681	1422	16	by	by	IN
37681	1422	17	Capella	Capella	NNP
37681	1422	18	in	in	IN
37681	1422	19	the	the	DT
37681	1422	20	fifth	fifth	JJ
37681	1422	21	century	century	NN
37681	1422	22	,	,	,
37681	1422	23	"	"	''
37681	1422	24	Punctum	Punctum	NNP
37681	1422	25	est	est	NNP
37681	1422	26	cuius	cuius	NNP
37681	1422	27	pars	pars	NNP
37681	1422	28	nihil	nihil	NNP
37681	1422	29	est	est	NNP
37681	1422	30	"	"	``
37681	1422	31	(	(	-LRB-
37681	1422	32	a	a	DT
37681	1422	33	point	point	NN
37681	1422	34	is	be	VBZ
37681	1422	35	that	that	DT
37681	1422	36	of	of	IN
37681	1422	37	which	which	WDT
37681	1422	38	a	a	DT
37681	1422	39	part	part	NN
37681	1422	40	is	be	VBZ
37681	1422	41	nothing	nothing	NN
37681	1422	42	)	)	-RRB-
37681	1422	43	,	,	,
37681	1422	44	which	which	WDT
37681	1422	45	is	be	VBZ
37681	1422	46	as	as	RB
37681	1422	47	much	much	JJ
37681	1422	48	as	as	IN
37681	1422	49	to	to	TO
37681	1422	50	say	say	VB
37681	1422	51	that	that	IN
37681	1422	52	the	the	DT
37681	1422	53	point	point	NN
37681	1422	54	itself	-PRON-	PRP
37681	1422	55	is	be	VBZ
37681	1422	56	nothing	nothing	NN
37681	1422	57	.	.	.
37681	1423	1	It	-PRON-	PRP
37681	1423	2	generally	generally	RB
37681	1423	3	appears	appear	VBZ
37681	1423	4	,	,	,
37681	1423	5	however	however	RB
37681	1423	6	,	,	,
37681	1423	7	as	as	IN
37681	1423	8	in	in	IN
37681	1423	9	the	the	DT
37681	1423	10	Campanus	Campanus	NNP
37681	1423	11	edition,[54	edition,[54	CD
37681	1423	12	]	]	-RRB-
37681	1423	13	"	"	``
37681	1423	14	Punctus	Punctus	NNP
37681	1423	15	est	est	NN
37681	1423	16	cuius	cuius	NN
37681	1423	17	pars	par	NNS
37681	1423	18	non	non	AFX
37681	1423	19	est	est	NNP
37681	1423	20	,	,	,
37681	1423	21	"	"	''
37681	1423	22	which	which	WDT
37681	1423	23	is	be	VBZ
37681	1423	24	substantially	substantially	RB
37681	1423	25	Euclid	Euclid	NNP
37681	1423	26	's	's	POS
37681	1423	27	wording	wording	NN
37681	1423	28	.	.	.
37681	1424	1	Aristotle	Aristotle	NNP
37681	1424	2	tells	tell	VBZ
37681	1424	3	of	of	IN
37681	1424	4	the	the	DT
37681	1424	5	definitions	definition	NNS
37681	1424	6	of	of	IN
37681	1424	7	point	point	NN
37681	1424	8	,	,	,
37681	1424	9	line	line	NN
37681	1424	10	,	,	,
37681	1424	11	and	and	CC
37681	1424	12	surface	surface	NN
37681	1424	13	that	that	WDT
37681	1424	14	prevailed	prevail	VBD
37681	1424	15	in	in	IN
37681	1424	16	his	-PRON-	PRP$
37681	1424	17	time	time	NN
37681	1424	18	,	,	,
37681	1424	19	saying	say	VBG
37681	1424	20	that	that	IN
37681	1424	21	they	-PRON-	PRP
37681	1424	22	all	all	DT
37681	1424	23	defined	define	VBD
37681	1424	24	the	the	DT
37681	1424	25	prior	prior	NN
37681	1424	26	by	by	IN
37681	1424	27	means	mean	NNS
37681	1424	28	of	of	IN
37681	1424	29	the	the	DT
37681	1424	30	posterior	posterior	NN
37681	1424	31	.	.	.
37681	1425	1	[	[	-LRB-
37681	1425	2	55	55	CD
37681	1425	3	]	]	-RRB-
37681	1425	4	Thus	thus	RB
37681	1425	5	a	a	DT
37681	1425	6	point	point	NN
37681	1425	7	was	be	VBD
37681	1425	8	defined	define	VBN
37681	1425	9	as	as	IN
37681	1425	10	"	"	``
37681	1425	11	an	an	DT
37681	1425	12	extremity	extremity	NN
37681	1425	13	of	of	IN
37681	1425	14	a	a	DT
37681	1425	15	line	line	NN
37681	1425	16	,	,	,
37681	1425	17	"	"	''
37681	1425	18	a	a	DT
37681	1425	19	line	line	NN
37681	1425	20	as	as	IN
37681	1425	21	"	"	``
37681	1425	22	the	the	DT
37681	1425	23	extremity	extremity	NN
37681	1425	24	of	of	IN
37681	1425	25	a	a	DT
37681	1425	26	surface	surface	NN
37681	1425	27	,	,	,
37681	1425	28	"	"	''
37681	1425	29	and	and	CC
37681	1425	30	a	a	DT
37681	1425	31	surface	surface	NN
37681	1425	32	as	as	IN
37681	1425	33	"	"	``
37681	1425	34	the	the	DT
37681	1425	35	extremity	extremity	NN
37681	1425	36	of	of	IN
37681	1425	37	a	a	DT
37681	1425	38	solid,"--definitions	solid,"--definitions	NN
37681	1425	39	still	still	RB
37681	1425	40	in	in	IN
37681	1425	41	use	use	NN
37681	1425	42	and	and	CC
37681	1425	43	not	not	RB
37681	1425	44	without	without	IN
37681	1425	45	their	-PRON-	PRP$
37681	1425	46	value	value	NN
37681	1425	47	.	.	.
37681	1426	1	For	for	IN
37681	1426	2	it	-PRON-	PRP
37681	1426	3	must	must	MD
37681	1426	4	not	not	RB
37681	1426	5	be	be	VB
37681	1426	6	assumed	assume	VBN
37681	1426	7	that	that	IN
37681	1426	8	scientific	scientific	JJ
37681	1426	9	priority	priority	NN
37681	1426	10	is	be	VBZ
37681	1426	11	necessarily	necessarily	RB
37681	1426	12	priority	priority	NN
37681	1426	13	in	in	IN
37681	1426	14	fact	fact	NN
37681	1426	15	;	;	:
37681	1426	16	a	a	DT
37681	1426	17	child	child	NN
37681	1426	18	knows	know	VBZ
37681	1426	19	of	of	IN
37681	1426	20	"	"	``
37681	1426	21	solid	solid	JJ
37681	1426	22	"	"	''
37681	1426	23	before	before	IN
37681	1426	24	he	-PRON-	PRP
37681	1426	25	knows	know	VBZ
37681	1426	26	of	of	IN
37681	1426	27	"	"	``
37681	1426	28	point	point	NN
37681	1426	29	,	,	,
37681	1426	30	"	"	''
37681	1426	31	so	so	IN
37681	1426	32	that	that	IN
37681	1426	33	it	-PRON-	PRP
37681	1426	34	may	may	MD
37681	1426	35	be	be	VB
37681	1426	36	a	a	DT
37681	1426	37	very	very	RB
37681	1426	38	good	good	JJ
37681	1426	39	way	way	NN
37681	1426	40	to	to	TO
37681	1426	41	explain	explain	VB
37681	1426	42	,	,	,
37681	1426	43	if	if	IN
37681	1426	44	not	not	RB
37681	1426	45	to	to	TO
37681	1426	46	define	define	VB
37681	1426	47	,	,	,
37681	1426	48	by	by	IN
37681	1426	49	beginning	begin	VBG
37681	1426	50	with	with	IN
37681	1426	51	solid	solid	JJ
37681	1426	52	,	,	,
37681	1426	53	passing	pass	VBG
37681	1426	54	thence	thence	NN
37681	1426	55	to	to	IN
37681	1426	56	surface	surface	NN
37681	1426	57	,	,	,
37681	1426	58	thence	thence	NN
37681	1426	59	to	to	IN
37681	1426	60	line	line	NN
37681	1426	61	,	,	,
37681	1426	62	and	and	CC
37681	1426	63	thence	thence	NN
37681	1426	64	to	to	TO
37681	1426	65	point	point	VB
37681	1426	66	.	.	.
37681	1427	1	The	the	DT
37681	1427	2	first	first	JJ
37681	1427	3	definition	definition	NN
37681	1427	4	of	of	IN
37681	1427	5	point	point	NN
37681	1427	6	of	of	IN
37681	1427	7	which	which	WDT
37681	1427	8	Proclus	Proclus	NNP
37681	1427	9	could	could	MD
37681	1427	10	learn	learn	VB
37681	1427	11	is	be	VBZ
37681	1427	12	attributed	attribute	VBN
37681	1427	13	by	by	IN
37681	1427	14	him	-PRON-	PRP
37681	1427	15	to	to	IN
37681	1427	16	the	the	DT
37681	1427	17	Pythagoreans	Pythagoreans	NNPS
37681	1427	18	,	,	,
37681	1427	19	namely	namely	RB
37681	1427	20	,	,	,
37681	1427	21	"	"	''
37681	1427	22	a	a	DT
37681	1427	23	monad	monad	NN
37681	1427	24	having	have	VBG
37681	1427	25	position	position	NN
37681	1427	26	,	,	,
37681	1427	27	"	"	''
37681	1427	28	the	the	DT
37681	1427	29	early	early	JJ
37681	1427	30	form	form	NN
37681	1427	31	of	of	IN
37681	1427	32	our	-PRON-	PRP$
37681	1427	33	present	present	JJ
37681	1427	34	popular	popular	JJ
37681	1427	35	definition	definition	NN
37681	1427	36	of	of	IN
37681	1427	37	a	a	DT
37681	1427	38	point	point	NN
37681	1427	39	as	as	IN
37681	1427	40	"	"	``
37681	1427	41	position	position	NN
37681	1427	42	without	without	IN
37681	1427	43	magnitude	magnitude	NN
37681	1427	44	.	.	.
37681	1427	45	"	"	''
37681	1428	1	Plato	Plato	NNP
37681	1428	2	defined	define	VBD
37681	1428	3	it	-PRON-	PRP
37681	1428	4	as	as	IN
37681	1428	5	"	"	``
37681	1428	6	the	the	DT
37681	1428	7	beginning	beginning	NN
37681	1428	8	of	of	IN
37681	1428	9	a	a	DT
37681	1428	10	line	line	NN
37681	1428	11	,	,	,
37681	1428	12	"	"	''
37681	1428	13	thus	thus	RB
37681	1428	14	presupposing	presuppose	VBG
37681	1428	15	the	the	DT
37681	1428	16	definition	definition	NN
37681	1428	17	of	of	IN
37681	1428	18	"	"	``
37681	1428	19	line	line	NN
37681	1428	20	"	"	''
37681	1428	21	;	;	:
37681	1428	22	and	and	CC
37681	1428	23	,	,	,
37681	1428	24	strangely	strangely	RB
37681	1428	25	enough	enough	RB
37681	1428	26	,	,	,
37681	1428	27	he	-PRON-	PRP
37681	1428	28	anticipated	anticipate	VBD
37681	1428	29	by	by	IN
37681	1428	30	two	two	CD
37681	1428	31	thousand	thousand	CD
37681	1428	32	years	year	NNS
37681	1428	33	Cavalieri	Cavalieri	NNP
37681	1428	34	,	,	,
37681	1428	35	the	the	DT
37681	1428	36	Italian	italian	JJ
37681	1428	37	geometer	geometer	NN
37681	1428	38	,	,	,
37681	1428	39	by	by	IN
37681	1428	40	speaking	speak	VBG
37681	1428	41	of	of	IN
37681	1428	42	points	point	NNS
37681	1428	43	as	as	IN
37681	1428	44	"	"	``
37681	1428	45	indivisible	indivisible	JJ
37681	1428	46	lines	line	NNS
37681	1428	47	.	.	.
37681	1428	48	"	"	''
37681	1429	1	To	to	IN
37681	1429	2	Aristotle	Aristotle	NNP
37681	1429	3	,	,	,
37681	1429	4	who	who	WP
37681	1429	5	protested	protest	VBD
37681	1429	6	against	against	IN
37681	1429	7	Plato	Plato	NNP
37681	1429	8	's	's	POS
37681	1429	9	definitions	definition	NNS
37681	1429	10	,	,	,
37681	1429	11	is	be	VBZ
37681	1429	12	due	due	JJ
37681	1429	13	the	the	DT
37681	1429	14	definition	definition	NN
37681	1429	15	of	of	IN
37681	1429	16	a	a	DT
37681	1429	17	point	point	NN
37681	1429	18	as	as	IN
37681	1429	19	"	"	``
37681	1429	20	something	something	NN
37681	1429	21	indivisible	indivisible	JJ
37681	1429	22	but	but	CC
37681	1429	23	having	have	VBG
37681	1429	24	position	position	NN
37681	1429	25	.	.	.
37681	1429	26	"	"	''
37681	1430	1	Euclid	Euclid	NNP
37681	1430	2	's	's	POS
37681	1430	3	definition	definition	NN
37681	1430	4	is	be	VBZ
37681	1430	5	essentially	essentially	RB
37681	1430	6	that	that	DT
37681	1430	7	of	of	IN
37681	1430	8	Aristotle	Aristotle	NNP
37681	1430	9	,	,	,
37681	1430	10	and	and	CC
37681	1430	11	is	be	VBZ
37681	1430	12	followed	follow	VBN
37681	1430	13	by	by	IN
37681	1430	14	most	most	JJS
37681	1430	15	modern	modern	JJ
37681	1430	16	textbook	textbook	NN
37681	1430	17	writers	writer	NNS
37681	1430	18	,	,	,
37681	1430	19	except	except	IN
37681	1430	20	as	as	IN
37681	1430	21	to	to	IN
37681	1430	22	its	-PRON-	PRP$
37681	1430	23	omission	omission	NN
37681	1430	24	of	of	IN
37681	1430	25	the	the	DT
37681	1430	26	reference	reference	NN
37681	1430	27	to	to	IN
37681	1430	28	position	position	NN
37681	1430	29	.	.	.
37681	1431	1	It	-PRON-	PRP
37681	1431	2	has	have	VBZ
37681	1431	3	been	be	VBN
37681	1431	4	criticized	criticize	VBN
37681	1431	5	as	as	IN
37681	1431	6	being	be	VBG
37681	1431	7	negative	negative	JJ
37681	1431	8	,	,	,
37681	1431	9	"	"	''
37681	1431	10	which	which	WDT
37681	1431	11	has	have	VBZ
37681	1431	12	_	_	NNP
37681	1431	13	no	no	DT
37681	1431	14	_	_	NNP
37681	1431	15	part	part	NN
37681	1431	16	"	"	''
37681	1431	17	;	;	:
37681	1431	18	but	but	CC
37681	1431	19	it	-PRON-	PRP
37681	1431	20	is	be	VBZ
37681	1431	21	generally	generally	RB
37681	1431	22	admitted	admit	VBN
37681	1431	23	that	that	IN
37681	1431	24	a	a	DT
37681	1431	25	negative	negative	JJ
37681	1431	26	definition	definition	NN
37681	1431	27	is	be	VBZ
37681	1431	28	admissible	admissible	JJ
37681	1431	29	in	in	IN
37681	1431	30	the	the	DT
37681	1431	31	case	case	NN
37681	1431	32	of	of	IN
37681	1431	33	the	the	DT
37681	1431	34	most	most	RBS
37681	1431	35	elementary	elementary	JJ
37681	1431	36	concepts	concept	NNS
37681	1431	37	.	.	.
37681	1432	1	For	for	IN
37681	1432	2	example	example	NN
37681	1432	3	,	,	,
37681	1432	4	"	"	``
37681	1432	5	blind	blind	JJ
37681	1432	6	"	"	''
37681	1432	7	must	must	MD
37681	1432	8	be	be	VB
37681	1432	9	defined	define	VBN
37681	1432	10	in	in	IN
37681	1432	11	terms	term	NNS
37681	1432	12	of	of	IN
37681	1432	13	a	a	DT
37681	1432	14	negation	negation	NN
37681	1432	15	.	.	.
37681	1433	1	At	at	IN
37681	1433	2	present	present	JJ
37681	1433	3	not	not	RB
37681	1433	4	much	much	JJ
37681	1433	5	attention	attention	NN
37681	1433	6	is	be	VBZ
37681	1433	7	given	give	VBN
37681	1433	8	to	to	IN
37681	1433	9	the	the	DT
37681	1433	10	definition	definition	NN
37681	1433	11	of	of	IN
37681	1433	12	"	"	``
37681	1433	13	point	point	NN
37681	1433	14	,	,	,
37681	1433	15	"	"	''
37681	1433	16	since	since	IN
37681	1433	17	the	the	DT
37681	1433	18	term	term	NN
37681	1433	19	is	be	VBZ
37681	1433	20	not	not	RB
37681	1433	21	used	use	VBN
37681	1433	22	as	as	IN
37681	1433	23	the	the	DT
37681	1433	24	basis	basis	NN
37681	1433	25	of	of	IN
37681	1433	26	a	a	DT
37681	1433	27	proof	proof	NN
37681	1433	28	,	,	,
37681	1433	29	but	but	CC
37681	1433	30	every	every	DT
37681	1433	31	effort	effort	NN
37681	1433	32	is	be	VBZ
37681	1433	33	made	make	VBN
37681	1433	34	to	to	TO
37681	1433	35	have	have	VB
37681	1433	36	the	the	DT
37681	1433	37	concept	concept	NN
37681	1433	38	clear	clear	JJ
37681	1433	39	.	.	.
37681	1434	1	It	-PRON-	PRP
37681	1434	2	is	be	VBZ
37681	1434	3	the	the	DT
37681	1434	4	custom	custom	NN
37681	1434	5	to	to	TO
37681	1434	6	start	start	VB
37681	1434	7	from	from	IN
37681	1434	8	a	a	DT
37681	1434	9	small	small	JJ
37681	1434	10	solid	solid	JJ
37681	1434	11	,	,	,
37681	1434	12	conceive	conceive	VB
37681	1434	13	it	-PRON-	PRP
37681	1434	14	to	to	TO
37681	1434	15	decrease	decrease	VB
37681	1434	16	in	in	IN
37681	1434	17	size	size	NN
37681	1434	18	,	,	,
37681	1434	19	and	and	CC
37681	1434	20	think	think	VB
37681	1434	21	of	of	IN
37681	1434	22	the	the	DT
37681	1434	23	point	point	NN
37681	1434	24	as	as	IN
37681	1434	25	the	the	DT
37681	1434	26	limit	limit	NN
37681	1434	27	to	to	TO
37681	1434	28	which	which	WDT
37681	1434	29	it	-PRON-	PRP
37681	1434	30	is	be	VBZ
37681	1434	31	approaching	approach	VBG
37681	1434	32	,	,	,
37681	1434	33	using	use	VBG
37681	1434	34	these	these	DT
37681	1434	35	terms	term	NNS
37681	1434	36	in	in	IN
37681	1434	37	their	-PRON-	PRP$
37681	1434	38	usual	usual	JJ
37681	1434	39	sense	sense	NN
37681	1434	40	without	without	IN
37681	1434	41	further	further	JJ
37681	1434	42	explanation	explanation	NN
37681	1434	43	.	.	.
37681	1435	1	2	2	LS
37681	1435	2	.	.	.
37681	1436	1	LINE	LINE	NNP
37681	1436	2	.	.	.
37681	1437	1	_	_	NNP
37681	1437	2	A	a	DT
37681	1437	3	line	line	NN
37681	1437	4	is	be	VBZ
37681	1437	5	breadthless	breadthless	JJ
37681	1437	6	length	length	NN
37681	1437	7	.	.	.
37681	1437	8	_	_	NNP
37681	1437	9	This	this	DT
37681	1437	10	is	be	VBZ
37681	1437	11	usually	usually	RB
37681	1437	12	modified	modify	VBN
37681	1437	13	in	in	IN
37681	1437	14	modern	modern	JJ
37681	1437	15	textbooks	textbook	NNS
37681	1437	16	by	by	IN
37681	1437	17	saying	say	VBG
37681	1437	18	that	that	IN
37681	1437	19	"	"	``
37681	1437	20	a	a	DT
37681	1437	21	line	line	NN
37681	1437	22	is	be	VBZ
37681	1437	23	that	that	DT
37681	1437	24	which	which	WDT
37681	1437	25	has	have	VBZ
37681	1437	26	length	length	NN
37681	1437	27	without	without	IN
37681	1437	28	breadth	breadth	NN
37681	1437	29	or	or	CC
37681	1437	30	thickness	thickness	NN
37681	1437	31	,	,	,
37681	1437	32	"	"	''
37681	1437	33	a	a	DT
37681	1437	34	statement	statement	NN
37681	1437	35	that	that	WDT
37681	1437	36	is	be	VBZ
37681	1437	37	better	well	RBR
37681	1437	38	understood	understand	VBN
37681	1437	39	by	by	IN
37681	1437	40	beginners	beginner	NNS
37681	1437	41	.	.	.
37681	1438	1	Euclid	Euclid	NNP
37681	1438	2	's	's	POS
37681	1438	3	definition	definition	NN
37681	1438	4	is	be	VBZ
37681	1438	5	thought	think	VBN
37681	1438	6	to	to	TO
37681	1438	7	be	be	VB
37681	1438	8	due	due	IN
37681	1438	9	to	to	IN
37681	1438	10	Plato	Plato	NNP
37681	1438	11	,	,	,
37681	1438	12	and	and	CC
37681	1438	13	is	be	VBZ
37681	1438	14	only	only	RB
37681	1438	15	one	one	CD
37681	1438	16	of	of	IN
37681	1438	17	many	many	JJ
37681	1438	18	definitions	definition	NNS
37681	1438	19	that	that	WDT
37681	1438	20	have	have	VBP
37681	1438	21	been	be	VBN
37681	1438	22	suggested	suggest	VBN
37681	1438	23	.	.	.
37681	1439	1	The	the	DT
37681	1439	2	Pythagoreans	Pythagoreans	NNPS
37681	1439	3	having	have	VBG
37681	1439	4	spoken	speak	VBN
37681	1439	5	of	of	IN
37681	1439	6	the	the	DT
37681	1439	7	point	point	NN
37681	1439	8	as	as	IN
37681	1439	9	a	a	DT
37681	1439	10	monad	monad	NN
37681	1439	11	naturally	naturally	RB
37681	1439	12	were	be	VBD
37681	1439	13	led	lead	VBN
37681	1439	14	to	to	TO
37681	1439	15	speak	speak	VB
37681	1439	16	of	of	IN
37681	1439	17	the	the	DT
37681	1439	18	line	line	NN
37681	1439	19	as	as	IN
37681	1439	20	dyadic	dyadic	JJ
37681	1439	21	,	,	,
37681	1439	22	or	or	CC
37681	1439	23	related	relate	VBN
37681	1439	24	to	to	IN
37681	1439	25	two	two	CD
37681	1439	26	.	.	.
37681	1440	1	Proclus	Proclus	NNP
37681	1440	2	speaks	speak	VBZ
37681	1440	3	of	of	IN
37681	1440	4	another	another	DT
37681	1440	5	definition	definition	NN
37681	1440	6	,	,	,
37681	1440	7	"	"	``
37681	1440	8	magnitude	magnitude	NN
37681	1440	9	in	in	IN
37681	1440	10	one	one	CD
37681	1440	11	dimension	dimension	NN
37681	1440	12	,	,	,
37681	1440	13	"	"	''
37681	1440	14	and	and	CC
37681	1440	15	he	-PRON-	PRP
37681	1440	16	gives	give	VBZ
37681	1440	17	an	an	DT
37681	1440	18	excellent	excellent	JJ
37681	1440	19	illustration	illustration	NN
37681	1440	20	of	of	IN
37681	1440	21	line	line	NN
37681	1440	22	as	as	IN
37681	1440	23	"	"	``
37681	1440	24	the	the	DT
37681	1440	25	edge	edge	NN
37681	1440	26	of	of	IN
37681	1440	27	a	a	DT
37681	1440	28	shadow	shadow	NN
37681	1440	29	,	,	,
37681	1440	30	"	"	''
37681	1440	31	thus	thus	RB
37681	1440	32	making	make	VBG
37681	1440	33	it	-PRON-	PRP
37681	1440	34	real	real	JJ
37681	1440	35	but	but	CC
37681	1440	36	not	not	RB
37681	1440	37	material	material	JJ
37681	1440	38	.	.	.
37681	1441	1	Aristotle	Aristotle	NNP
37681	1441	2	speaks	speak	VBZ
37681	1441	3	of	of	IN
37681	1441	4	a	a	DT
37681	1441	5	line	line	NN
37681	1441	6	as	as	IN
37681	1441	7	a	a	DT
37681	1441	8	magnitude	magnitude	NN
37681	1441	9	"	"	``
37681	1441	10	divisible	divisible	JJ
37681	1441	11	in	in	IN
37681	1441	12	one	one	CD
37681	1441	13	way	way	NN
37681	1441	14	only	only	RB
37681	1441	15	,	,	,
37681	1441	16	"	"	''
37681	1441	17	as	as	IN
37681	1441	18	contrasted	contrast	VBN
37681	1441	19	with	with	IN
37681	1441	20	a	a	DT
37681	1441	21	surface	surface	NN
37681	1441	22	which	which	WDT
37681	1441	23	is	be	VBZ
37681	1441	24	divisible	divisible	JJ
37681	1441	25	in	in	IN
37681	1441	26	two	two	CD
37681	1441	27	ways	way	NNS
37681	1441	28	,	,	,
37681	1441	29	and	and	CC
37681	1441	30	with	with	IN
37681	1441	31	a	a	DT
37681	1441	32	solid	solid	JJ
37681	1441	33	which	which	WDT
37681	1441	34	is	be	VBZ
37681	1441	35	divisible	divisible	JJ
37681	1441	36	in	in	IN
37681	1441	37	three	three	CD
37681	1441	38	ways	way	NNS
37681	1441	39	.	.	.
37681	1442	1	Proclus	Proclus	NNP
37681	1442	2	also	also	RB
37681	1442	3	gives	give	VBZ
37681	1442	4	another	another	DT
37681	1442	5	definition	definition	NN
37681	1442	6	as	as	IN
37681	1442	7	the	the	DT
37681	1442	8	"	"	``
37681	1442	9	flux	flux	NN
37681	1442	10	of	of	IN
37681	1442	11	a	a	DT
37681	1442	12	point	point	NN
37681	1442	13	,	,	,
37681	1442	14	"	"	''
37681	1442	15	which	which	WDT
37681	1442	16	is	be	VBZ
37681	1442	17	sometimes	sometimes	RB
37681	1442	18	rendered	render	VBN
37681	1442	19	as	as	IN
37681	1442	20	the	the	DT
37681	1442	21	path	path	NN
37681	1442	22	of	of	IN
37681	1442	23	a	a	DT
37681	1442	24	moving	moving	NN
37681	1442	25	point	point	NN
37681	1442	26	.	.	.
37681	1443	1	Aristotle	Aristotle	NNP
37681	1443	2	had	have	VBD
37681	1443	3	suggested	suggest	VBN
37681	1443	4	the	the	DT
37681	1443	5	idea	idea	NN
37681	1443	6	when	when	WRB
37681	1443	7	he	-PRON-	PRP
37681	1443	8	wrote	write	VBD
37681	1443	9	,	,	,
37681	1443	10	"	"	``
37681	1443	11	They	-PRON-	PRP
37681	1443	12	say	say	VBP
37681	1443	13	that	that	IN
37681	1443	14	a	a	DT
37681	1443	15	line	line	NN
37681	1443	16	by	by	IN
37681	1443	17	its	-PRON-	PRP$
37681	1443	18	motion	motion	NN
37681	1443	19	produces	produce	VBZ
37681	1443	20	a	a	DT
37681	1443	21	surface	surface	NN
37681	1443	22	,	,	,
37681	1443	23	and	and	CC
37681	1443	24	a	a	DT
37681	1443	25	point	point	NN
37681	1443	26	by	by	IN
37681	1443	27	its	-PRON-	PRP$
37681	1443	28	motion	motion	NN
37681	1443	29	a	a	DT
37681	1443	30	line	line	NN
37681	1443	31	.	.	.
37681	1443	32	"	"	''
37681	1444	1	Euclid	Euclid	NNP
37681	1444	2	did	do	VBD
37681	1444	3	not	not	RB
37681	1444	4	deem	deem	VB
37681	1444	5	it	-PRON-	PRP
37681	1444	6	necessary	necessary	JJ
37681	1444	7	to	to	TO
37681	1444	8	attempt	attempt	VB
37681	1444	9	a	a	DT
37681	1444	10	classification	classification	NN
37681	1444	11	of	of	IN
37681	1444	12	lines	line	NNS
37681	1444	13	,	,	,
37681	1444	14	contenting	content	VBG
37681	1444	15	himself	-PRON-	PRP
37681	1444	16	with	with	IN
37681	1444	17	defining	define	VBG
37681	1444	18	only	only	RB
37681	1444	19	a	a	DT
37681	1444	20	straight	straight	JJ
37681	1444	21	line	line	NN
37681	1444	22	and	and	CC
37681	1444	23	a	a	DT
37681	1444	24	circle	circle	NN
37681	1444	25	,	,	,
37681	1444	26	and	and	CC
37681	1444	27	these	these	DT
37681	1444	28	are	be	VBP
37681	1444	29	really	really	RB
37681	1444	30	the	the	DT
37681	1444	31	only	only	JJ
37681	1444	32	lines	line	NNS
37681	1444	33	needed	need	VBN
37681	1444	34	in	in	IN
37681	1444	35	elementary	elementary	JJ
37681	1444	36	geometry	geometry	NN
37681	1444	37	.	.	.
37681	1445	1	His	-PRON-	PRP$
37681	1445	2	commentators	commentator	NNS
37681	1445	3	,	,	,
37681	1445	4	however	however	RB
37681	1445	5	,	,	,
37681	1445	6	made	make	VBD
37681	1445	7	the	the	DT
37681	1445	8	attempt	attempt	NN
37681	1445	9	.	.	.
37681	1446	1	For	for	IN
37681	1446	2	example	example	NN
37681	1446	3	.	.	.
37681	1447	1	Heron	Heron	NNP
37681	1447	2	(	(	-LRB-
37681	1447	3	first	first	JJ
37681	1447	4	century	century	NN
37681	1447	5	A.D.	A.D.	NNP
37681	1447	6	)	)	-RRB-
37681	1447	7	probably	probably	RB
37681	1447	8	followed	follow	VBD
37681	1447	9	his	-PRON-	PRP$
37681	1447	10	definition	definition	NN
37681	1447	11	of	of	IN
37681	1447	12	line	line	NN
37681	1447	13	by	by	IN
37681	1447	14	this	this	DT
37681	1447	15	classification	classification	NN
37681	1447	16	:	:	:
37681	1447	17	{	{	-LRB-
37681	1447	18	Straight	Straight	NNP
37681	1447	19	Lines	Lines	NNP
37681	1447	20	{	{	-LRB-
37681	1447	21	{	{	-LRB-
37681	1447	22	Circular	circular	JJ
37681	1447	23	circumferences	circumference	NNS
37681	1447	24	{	{	-LRB-
37681	1447	25	Not	not	RB
37681	1447	26	straight	straight	RB
37681	1447	27	{	{	-LRB-
37681	1447	28	Spiral	spiral	JJ
37681	1447	29	shaped	shape	VBN
37681	1447	30	{	{	-LRB-
37681	1447	31	Curved	Curved	NNP
37681	1447	32	(	(	-LRB-
37681	1447	33	generally	generally	RB
37681	1447	34	)	)	-RRB-
37681	1447	35	Proclus	Proclus	NNP
37681	1447	36	relates	relate	VBZ
37681	1447	37	that	that	IN
37681	1447	38	both	both	CC
37681	1447	39	Plato	Plato	NNP
37681	1447	40	and	and	CC
37681	1447	41	Aristotle	Aristotle	NNP
37681	1447	42	divided	divide	VBD
37681	1447	43	lines	line	NNS
37681	1447	44	into	into	IN
37681	1447	45	"	"	``
37681	1447	46	straight	straight	JJ
37681	1447	47	,	,	,
37681	1447	48	"	"	''
37681	1447	49	"	"	``
37681	1447	50	circular	circular	JJ
37681	1447	51	,	,	,
37681	1447	52	"	"	''
37681	1447	53	and	and	CC
37681	1447	54	"	"	``
37681	1447	55	a	a	DT
37681	1447	56	mixture	mixture	NN
37681	1447	57	of	of	IN
37681	1447	58	the	the	DT
37681	1447	59	two	two	CD
37681	1447	60	,	,	,
37681	1447	61	"	"	''
37681	1447	62	a	a	DT
37681	1447	63	statement	statement	NN
37681	1447	64	which	which	WDT
37681	1447	65	is	be	VBZ
37681	1447	66	not	not	RB
37681	1447	67	quite	quite	RB
37681	1447	68	exact	exact	JJ
37681	1447	69	,	,	,
37681	1447	70	but	but	CC
37681	1447	71	which	which	WDT
37681	1447	72	shows	show	VBZ
37681	1447	73	the	the	DT
37681	1447	74	origin	origin	NN
37681	1447	75	of	of	IN
37681	1447	76	a	a	DT
37681	1447	77	classification	classification	NN
37681	1447	78	not	not	RB
37681	1447	79	infrequently	infrequently	RB
37681	1447	80	found	find	VBN
37681	1447	81	in	in	IN
37681	1447	82	recent	recent	JJ
37681	1447	83	textbooks	textbook	NNS
37681	1447	84	.	.	.
37681	1448	1	Geminus	Geminus	NNP
37681	1448	2	(	(	-LRB-
37681	1448	3	_	_	NNP
37681	1448	4	ca	ca	NNP
37681	1448	5	.	.	.
37681	1448	6	_	_	NNP
37681	1448	7	50	50	CD
37681	1448	8	B.C.	B.C.	NNP
37681	1448	9	)	)	-RRB-
37681	1449	1	is	be	VBZ
37681	1449	2	said	say	VBN
37681	1449	3	by	by	IN
37681	1449	4	Proclus	Proclus	NNP
37681	1449	5	to	to	TO
37681	1449	6	have	have	VB
37681	1449	7	given	give	VBN
37681	1449	8	two	two	CD
37681	1449	9	classifications	classification	NNS
37681	1449	10	,	,	,
37681	1449	11	of	of	IN
37681	1449	12	which	which	WDT
37681	1449	13	one	one	PRP
37681	1449	14	will	will	MD
37681	1449	15	suffice	suffice	VB
37681	1449	16	for	for	IN
37681	1449	17	our	-PRON-	PRP$
37681	1449	18	purposes	purpose	NNS
37681	1449	19	:	:	:
37681	1449	20	{	{	-LRB-
37681	1449	21	Composite	composite	JJ
37681	1449	22	(	(	-LRB-
37681	1449	23	broken	break	VBN
37681	1449	24	line	line	NN
37681	1449	25	forming	form	VBG
37681	1449	26	an	an	DT
37681	1449	27	angle	angle	NN
37681	1449	28	)	)	-RRB-
37681	1449	29	{	{	-LRB-
37681	1449	30	Lines	line	NNS
37681	1449	31	{	{	-LRB-
37681	1449	32	{	{	-LRB-
37681	1449	33	Forming	form	VBG
37681	1449	34	a	a	DT
37681	1449	35	figure	figure	NN
37681	1449	36	,	,	,
37681	1449	37	or	or	CC
37681	1449	38	determinate	determinate	VB
37681	1449	39	.	.	.
37681	1450	1	(	(	-LRB-
37681	1450	2	Circle	Circle	NNP
37681	1450	3	,	,	,
37681	1450	4	{	{	-LRB-
37681	1450	5	{	{	-LRB-
37681	1450	6	ellipse	ellipse	NN
37681	1450	7	,	,	,
37681	1450	8	cissoid	cissoid	NN
37681	1450	9	.	.	.
37681	1450	10	)	)	-RRB-
37681	1451	1	{	{	-LRB-
37681	1451	2	Incomposite	Incomposite	NNP
37681	1451	3	{	{	-LRB-
37681	1451	4	Not	not	RB
37681	1451	5	forming	form	VBG
37681	1451	6	a	a	DT
37681	1451	7	figure	figure	NN
37681	1451	8	,	,	,
37681	1451	9	or	or	CC
37681	1451	10	indeterminate	indeterminate	JJ
37681	1451	11	and	and	CC
37681	1451	12	{	{	-LRB-
37681	1451	13	extending	extend	VBG
37681	1451	14	without	without	IN
37681	1451	15	a	a	DT
37681	1451	16	limit	limit	NN
37681	1451	17	.	.	.
37681	1452	1	(	(	-LRB-
37681	1452	2	Straight	straight	JJ
37681	1452	3	{	{	-LRB-
37681	1452	4	line	line	NN
37681	1452	5	,	,	,
37681	1452	6	parabola	parabola	NNP
37681	1452	7	,	,	,
37681	1452	8	hyperbola	hyperbola	NNP
37681	1452	9	,	,	,
37681	1452	10	conchoid	conchoid	NN
37681	1452	11	.	.	.
37681	1452	12	)	)	-RRB-
37681	1453	1	Of	of	RB
37681	1453	2	course	course	RB
37681	1453	3	his	-PRON-	PRP$
37681	1453	4	view	view	NN
37681	1453	5	of	of	IN
37681	1453	6	the	the	DT
37681	1453	7	cissoid	cissoid	NN
37681	1453	8	,	,	,
37681	1453	9	the	the	DT
37681	1453	10	curve	curve	NN
37681	1453	11	represented	represent	VBN
37681	1453	12	by	by	IN
37681	1453	13	the	the	DT
37681	1453	14	equation	equation	NN
37681	1453	15	_	_	NNP
37681	1453	16	y_^2(_a	y_^2(_a	NNP
37681	1453	17	_	_	NNP
37681	1453	18	+	+	NNP
37681	1453	19	_	_	NNP
37681	1453	20	x	x	NNP
37681	1453	21	_	_	NNP
37681	1453	22	)	)	-RRB-
37681	1453	23	=	=	NFP
37681	1453	24	(	(	-LRB-
37681	1453	25	_	_	NNP
37681	1453	26	a	a	DT
37681	1453	27	_	_	NNP
37681	1453	28	-	-	HYPH
37681	1453	29	_	_	NNP
37681	1453	30	x_)^3	x_)^3	NN
37681	1453	31	,	,	,
37681	1453	32	is	be	VBZ
37681	1453	33	not	not	RB
37681	1453	34	the	the	DT
37681	1453	35	modern	modern	JJ
37681	1453	36	view	view	NN
37681	1453	37	.	.	.
37681	1454	1	3	3	LS
37681	1454	2	.	.	.
37681	1455	1	_	_	NNP
37681	1455	2	The	the	DT
37681	1455	3	extremities	extremity	NNS
37681	1455	4	of	of	IN
37681	1455	5	a	a	DT
37681	1455	6	line	line	NN
37681	1455	7	are	be	VBP
37681	1455	8	points	point	NNS
37681	1455	9	.	.	.
37681	1455	10	_	_	NNP
37681	1455	11	This	this	DT
37681	1455	12	is	be	VBZ
37681	1455	13	not	not	RB
37681	1455	14	a	a	DT
37681	1455	15	definition	definition	NN
37681	1455	16	in	in	IN
37681	1455	17	the	the	DT
37681	1455	18	sense	sense	NN
37681	1455	19	of	of	IN
37681	1455	20	its	-PRON-	PRP$
37681	1455	21	two	two	CD
37681	1455	22	predecessors	predecessor	NNS
37681	1455	23	.	.	.
37681	1456	1	A	a	DT
37681	1456	2	modern	modern	JJ
37681	1456	3	writer	writer	NN
37681	1456	4	would	would	MD
37681	1456	5	put	put	VB
37681	1456	6	it	-PRON-	PRP
37681	1456	7	as	as	IN
37681	1456	8	a	a	DT
37681	1456	9	note	note	NN
37681	1456	10	under	under	IN
37681	1456	11	the	the	DT
37681	1456	12	definition	definition	NN
37681	1456	13	of	of	IN
37681	1456	14	line	line	NN
37681	1456	15	.	.	.
37681	1457	1	Euclid	Euclid	NNP
37681	1457	2	did	do	VBD
37681	1457	3	not	not	RB
37681	1457	4	wish	wish	VB
37681	1457	5	to	to	TO
37681	1457	6	define	define	VB
37681	1457	7	a	a	DT
37681	1457	8	point	point	NN
37681	1457	9	as	as	IN
37681	1457	10	the	the	DT
37681	1457	11	extremity	extremity	NN
37681	1457	12	of	of	IN
37681	1457	13	a	a	DT
37681	1457	14	line	line	NN
37681	1457	15	,	,	,
37681	1457	16	for	for	IN
37681	1457	17	Aristotle	Aristotle	NNP
37681	1457	18	had	have	VBD
37681	1457	19	asserted	assert	VBN
37681	1457	20	that	that	IN
37681	1457	21	this	this	DT
37681	1457	22	was	be	VBD
37681	1457	23	not	not	RB
37681	1457	24	scientific	scientific	JJ
37681	1457	25	;	;	:
37681	1457	26	so	so	CC
37681	1457	27	he	-PRON-	PRP
37681	1457	28	defined	define	VBD
37681	1457	29	point	point	NN
37681	1457	30	and	and	CC
37681	1457	31	line	line	NN
37681	1457	32	,	,	,
37681	1457	33	and	and	CC
37681	1457	34	then	then	RB
37681	1457	35	added	add	VBD
37681	1457	36	this	this	DT
37681	1457	37	statement	statement	NN
37681	1457	38	to	to	TO
37681	1457	39	show	show	VB
37681	1457	40	the	the	DT
37681	1457	41	relation	relation	NN
37681	1457	42	of	of	IN
37681	1457	43	one	one	CD
37681	1457	44	to	to	IN
37681	1457	45	the	the	DT
37681	1457	46	other	other	JJ
37681	1457	47	.	.	.
37681	1458	1	Aristotle	Aristotle	NNP
37681	1458	2	had	have	VBD
37681	1458	3	improved	improve	VBN
37681	1458	4	upon	upon	IN
37681	1458	5	this	this	DT
37681	1458	6	by	by	IN
37681	1458	7	stating	state	VBG
37681	1458	8	that	that	IN
37681	1458	9	the	the	DT
37681	1458	10	"	"	``
37681	1458	11	division	division	NN
37681	1458	12	"	"	''
37681	1458	13	of	of	IN
37681	1458	14	a	a	DT
37681	1458	15	line	line	NN
37681	1458	16	,	,	,
37681	1458	17	as	as	RB
37681	1458	18	well	well	RB
37681	1458	19	as	as	IN
37681	1458	20	an	an	DT
37681	1458	21	extremity	extremity	NN
37681	1458	22	,	,	,
37681	1458	23	is	be	VBZ
37681	1458	24	a	a	DT
37681	1458	25	point	point	NN
37681	1458	26	,	,	,
37681	1458	27	as	as	IN
37681	1458	28	is	be	VBZ
37681	1458	29	also	also	RB
37681	1458	30	the	the	DT
37681	1458	31	intersection	intersection	NN
37681	1458	32	of	of	IN
37681	1458	33	two	two	CD
37681	1458	34	lines	line	NNS
37681	1458	35	.	.	.
37681	1459	1	These	these	DT
37681	1459	2	statements	statement	NNS
37681	1459	3	,	,	,
37681	1459	4	if	if	IN
37681	1459	5	they	-PRON-	PRP
37681	1459	6	had	have	VBD
37681	1459	7	been	be	VBN
37681	1459	8	made	make	VBN
37681	1459	9	by	by	IN
37681	1459	10	Euclid	Euclid	NNP
37681	1459	11	,	,	,
37681	1459	12	would	would	MD
37681	1459	13	have	have	VB
37681	1459	14	avoided	avoid	VBN
37681	1459	15	the	the	DT
37681	1459	16	objection	objection	NN
37681	1459	17	made	make	VBN
37681	1459	18	by	by	IN
37681	1459	19	Proclus	Proclus	NNP
37681	1459	20	,	,	,
37681	1459	21	that	that	IN
37681	1459	22	some	some	DT
37681	1459	23	lines	line	NNS
37681	1459	24	have	have	VBP
37681	1459	25	no	no	DT
37681	1459	26	extremities	extremity	NNS
37681	1459	27	,	,	,
37681	1459	28	as	as	IN
37681	1459	29	,	,	,
37681	1459	30	for	for	IN
37681	1459	31	example	example	NN
37681	1459	32	,	,	,
37681	1459	33	a	a	DT
37681	1459	34	circle	circle	NN
37681	1459	35	,	,	,
37681	1459	36	and	and	CC
37681	1459	37	also	also	RB
37681	1459	38	a	a	DT
37681	1459	39	straight	straight	JJ
37681	1459	40	line	line	NN
37681	1459	41	extending	extend	VBG
37681	1459	42	infinitely	infinitely	RB
37681	1459	43	in	in	IN
37681	1459	44	both	both	DT
37681	1459	45	directions	direction	NNS
37681	1459	46	.	.	.
37681	1460	1	4	4	LS
37681	1460	2	.	.	.
37681	1461	1	STRAIGHT	STRAIGHT	NNP
37681	1461	2	LINE	LINE	NNP
37681	1461	3	.	.	.
37681	1462	1	_	_	NNP
37681	1462	2	A	a	DT
37681	1462	3	straight	straight	JJ
37681	1462	4	line	line	NN
37681	1462	5	is	be	VBZ
37681	1462	6	that	that	DT
37681	1462	7	which	which	WDT
37681	1462	8	lies	lie	VBZ
37681	1462	9	evenly	evenly	RB
37681	1462	10	with	with	IN
37681	1462	11	respect	respect	NN
37681	1462	12	to	to	IN
37681	1462	13	the	the	DT
37681	1462	14	points	point	NNS
37681	1462	15	on	on	IN
37681	1462	16	itself	-PRON-	PRP
37681	1462	17	.	.	.
37681	1462	18	_	_	NNP
37681	1462	19	This	this	DT
37681	1462	20	is	be	VBZ
37681	1462	21	the	the	DT
37681	1462	22	least	least	JJS
37681	1462	23	satisfactory	satisfactory	JJ
37681	1462	24	of	of	IN
37681	1462	25	all	all	DT
37681	1462	26	of	of	IN
37681	1462	27	the	the	DT
37681	1462	28	definitions	definition	NNS
37681	1462	29	of	of	IN
37681	1462	30	Euclid	Euclid	NNP
37681	1462	31	,	,	,
37681	1462	32	and	and	CC
37681	1462	33	emphasizes	emphasize	VBZ
37681	1462	34	the	the	DT
37681	1462	35	fact	fact	NN
37681	1462	36	that	that	IN
37681	1462	37	the	the	DT
37681	1462	38	straight	straight	JJ
37681	1462	39	line	line	NN
37681	1462	40	is	be	VBZ
37681	1462	41	the	the	DT
37681	1462	42	most	most	RBS
37681	1462	43	difficult	difficult	JJ
37681	1462	44	to	to	TO
37681	1462	45	define	define	VB
37681	1462	46	of	of	IN
37681	1462	47	the	the	DT
37681	1462	48	elementary	elementary	JJ
37681	1462	49	concepts	concept	NNS
37681	1462	50	of	of	IN
37681	1462	51	geometry	geometry	NN
37681	1462	52	.	.	.
37681	1463	1	What	what	WP
37681	1463	2	is	be	VBZ
37681	1463	3	meant	mean	VBN
37681	1463	4	by	by	IN
37681	1463	5	"	"	``
37681	1463	6	lies	lie	VBZ
37681	1463	7	evenly	evenly	RB
37681	1463	8	"	"	''
37681	1463	9	?	?	.
37681	1464	1	Who	who	WP
37681	1464	2	would	would	MD
37681	1464	3	know	know	VB
37681	1464	4	what	what	WP
37681	1464	5	a	a	DT
37681	1464	6	straight	straight	JJ
37681	1464	7	line	line	NN
37681	1464	8	is	be	VBZ
37681	1464	9	,	,	,
37681	1464	10	from	from	IN
37681	1464	11	this	this	DT
37681	1464	12	definition	definition	NN
37681	1464	13	,	,	,
37681	1464	14	if	if	IN
37681	1464	15	he	-PRON-	PRP
37681	1464	16	did	do	VBD
37681	1464	17	not	not	RB
37681	1464	18	know	know	VB
37681	1464	19	in	in	IN
37681	1464	20	advance	advance	NN
37681	1464	21	?	?	.
37681	1465	1	The	the	DT
37681	1465	2	ancients	ancient	NNS
37681	1465	3	suggested	suggest	VBD
37681	1465	4	many	many	JJ
37681	1465	5	definitions	definition	NNS
37681	1465	6	of	of	IN
37681	1465	7	straight	straight	JJ
37681	1465	8	line	line	NN
37681	1465	9	,	,	,
37681	1465	10	and	and	CC
37681	1465	11	it	-PRON-	PRP
37681	1465	12	is	be	VBZ
37681	1465	13	well	well	JJ
37681	1465	14	to	to	TO
37681	1465	15	consider	consider	VB
37681	1465	16	a	a	DT
37681	1465	17	few	few	JJ
37681	1465	18	in	in	IN
37681	1465	19	order	order	NN
37681	1465	20	to	to	TO
37681	1465	21	appreciate	appreciate	VB
37681	1465	22	the	the	DT
37681	1465	23	difficulties	difficulty	NNS
37681	1465	24	involved	involve	VBN
37681	1465	25	.	.	.
37681	1466	1	Plato	Plato	NNP
37681	1466	2	spoke	speak	VBD
37681	1466	3	of	of	IN
37681	1466	4	it	-PRON-	PRP
37681	1466	5	as	as	IN
37681	1466	6	"	"	``
37681	1466	7	that	that	DT
37681	1466	8	of	of	IN
37681	1466	9	which	which	WDT
37681	1466	10	the	the	DT
37681	1466	11	middle	middle	NN
37681	1466	12	covers	cover	VBZ
37681	1466	13	the	the	DT
37681	1466	14	ends	end	NNS
37681	1466	15	,	,	,
37681	1466	16	"	"	''
37681	1466	17	meaning	mean	VBG
37681	1466	18	that	that	IN
37681	1466	19	if	if	IN
37681	1466	20	looked	look	VBD
37681	1466	21	at	at	IN
37681	1466	22	endways	endway	NNS
37681	1466	23	,	,	,
37681	1466	24	the	the	DT
37681	1466	25	middle	middle	NN
37681	1466	26	would	would	MD
37681	1466	27	make	make	VB
37681	1466	28	it	-PRON-	PRP
37681	1466	29	impossible	impossible	JJ
37681	1466	30	to	to	TO
37681	1466	31	see	see	VB
37681	1466	32	the	the	DT
37681	1466	33	remote	remote	JJ
37681	1466	34	end	end	NN
37681	1466	35	.	.	.
37681	1467	1	This	this	DT
37681	1467	2	is	be	VBZ
37681	1467	3	often	often	RB
37681	1467	4	modified	modify	VBN
37681	1467	5	to	to	TO
37681	1467	6	read	read	VB
37681	1467	7	that	that	IN
37681	1467	8	"	"	``
37681	1467	9	a	a	DT
37681	1467	10	straight	straight	JJ
37681	1467	11	line	line	NN
37681	1467	12	when	when	WRB
37681	1467	13	looked	look	VBD
37681	1467	14	at	at	IN
37681	1467	15	endways	endway	NNS
37681	1467	16	appears	appear	VBZ
37681	1467	17	as	as	IN
37681	1467	18	a	a	DT
37681	1467	19	point,"--an	point,"--an	NNP
37681	1467	20	idea	idea	NN
37681	1467	21	that	that	WDT
37681	1467	22	involves	involve	VBZ
37681	1467	23	the	the	DT
37681	1467	24	postulate	postulate	NN
37681	1467	25	that	that	WDT
37681	1467	26	our	-PRON-	PRP$
37681	1467	27	line	line	NN
37681	1467	28	of	of	IN
37681	1467	29	sight	sight	NN
37681	1467	30	is	be	VBZ
37681	1467	31	straight	straight	JJ
37681	1467	32	.	.	.
37681	1468	1	Archimedes	archimede	NNS
37681	1468	2	made	make	VBD
37681	1468	3	the	the	DT
37681	1468	4	statement	statement	NN
37681	1468	5	that	that	IN
37681	1468	6	"	"	``
37681	1468	7	of	of	IN
37681	1468	8	all	all	PDT
37681	1468	9	the	the	DT
37681	1468	10	lines	line	NNS
37681	1468	11	which	which	WDT
37681	1468	12	have	have	VBP
37681	1468	13	the	the	DT
37681	1468	14	same	same	JJ
37681	1468	15	extremities	extremity	NNS
37681	1468	16	,	,	,
37681	1468	17	the	the	DT
37681	1468	18	straight	straight	JJ
37681	1468	19	line	line	NN
37681	1468	20	is	be	VBZ
37681	1468	21	the	the	DT
37681	1468	22	least	least	JJS
37681	1468	23	,	,	,
37681	1468	24	"	"	''
37681	1468	25	and	and	CC
37681	1468	26	this	this	DT
37681	1468	27	has	have	VBZ
37681	1468	28	been	be	VBN
37681	1468	29	modified	modify	VBN
37681	1468	30	by	by	IN
37681	1468	31	later	later	JJ
37681	1468	32	writers	writer	NNS
37681	1468	33	into	into	IN
37681	1468	34	the	the	DT
37681	1468	35	statement	statement	NN
37681	1468	36	that	that	IN
37681	1468	37	"	"	``
37681	1468	38	a	a	DT
37681	1468	39	straight	straight	JJ
37681	1468	40	line	line	NN
37681	1468	41	is	be	VBZ
37681	1468	42	the	the	DT
37681	1468	43	shortest	short	JJS
37681	1468	44	distance	distance	NN
37681	1468	45	between	between	IN
37681	1468	46	two	two	CD
37681	1468	47	points	point	NNS
37681	1468	48	.	.	.
37681	1468	49	"	"	''
37681	1469	1	This	this	DT
37681	1469	2	is	be	VBZ
37681	1469	3	open	open	JJ
37681	1469	4	to	to	IN
37681	1469	5	two	two	CD
37681	1469	6	objections	objection	NNS
37681	1469	7	as	as	IN
37681	1469	8	a	a	DT
37681	1469	9	definition	definition	NN
37681	1469	10	:	:	:
37681	1469	11	(	(	-LRB-
37681	1469	12	1	1	LS
37681	1469	13	)	)	-RRB-
37681	1469	14	a	a	DT
37681	1469	15	line	line	NN
37681	1469	16	is	be	VBZ
37681	1469	17	not	not	RB
37681	1469	18	distance	distance	NN
37681	1469	19	,	,	,
37681	1469	20	but	but	CC
37681	1469	21	distance	distance	NN
37681	1469	22	is	be	VBZ
37681	1469	23	the	the	DT
37681	1469	24	_	_	NNP
37681	1469	25	length	length	NN
37681	1469	26	_	_	NNP
37681	1469	27	of	of	IN
37681	1469	28	a	a	DT
37681	1469	29	line,--it	line,--it	NNP
37681	1469	30	is	be	VBZ
37681	1469	31	measured	measure	VBN
37681	1469	32	on	on	IN
37681	1469	33	a	a	DT
37681	1469	34	line	line	NN
37681	1469	35	;	;	,
37681	1469	36	(	(	-LRB-
37681	1469	37	2	2	LS
37681	1469	38	)	)	-RRB-
37681	1469	39	it	-PRON-	PRP
37681	1469	40	is	be	VBZ
37681	1469	41	merely	merely	RB
37681	1469	42	stating	state	VBG
37681	1469	43	a	a	DT
37681	1469	44	property	property	NN
37681	1469	45	of	of	IN
37681	1469	46	a	a	DT
37681	1469	47	straight	straight	JJ
37681	1469	48	line	line	NN
37681	1469	49	to	to	TO
37681	1469	50	say	say	VB
37681	1469	51	that	that	IN
37681	1469	52	"	"	``
37681	1469	53	a	a	DT
37681	1469	54	straight	straight	JJ
37681	1469	55	line	line	NN
37681	1469	56	is	be	VBZ
37681	1469	57	the	the	DT
37681	1469	58	shortest	short	JJS
37681	1469	59	path	path	NN
37681	1469	60	between	between	IN
37681	1469	61	two	two	CD
37681	1469	62	points,"--a	points,"--a	NNP
37681	1469	63	proper	proper	JJ
37681	1469	64	postulate	postulate	NN
37681	1469	65	but	but	CC
37681	1469	66	not	not	RB
37681	1469	67	a	a	DT
37681	1469	68	good	good	JJ
37681	1469	69	definition	definition	NN
37681	1469	70	.	.	.
37681	1470	1	Equally	equally	RB
37681	1470	2	objectionable	objectionable	JJ
37681	1470	3	is	be	VBZ
37681	1470	4	one	one	CD
37681	1470	5	of	of	IN
37681	1470	6	the	the	DT
37681	1470	7	definitions	definition	NNS
37681	1470	8	suggested	suggest	VBN
37681	1470	9	by	by	IN
37681	1470	10	both	both	CC
37681	1470	11	Heron	Heron	NNP
37681	1470	12	and	and	CC
37681	1470	13	Proclus	Proclus	NNP
37681	1470	14	,	,	,
37681	1470	15	that	that	IN
37681	1470	16	"	"	``
37681	1470	17	a	a	DT
37681	1470	18	straight	straight	JJ
37681	1470	19	line	line	NN
37681	1470	20	is	be	VBZ
37681	1470	21	a	a	DT
37681	1470	22	line	line	NN
37681	1470	23	that	that	WDT
37681	1470	24	is	be	VBZ
37681	1470	25	stretched	stretch	VBN
37681	1470	26	to	to	IN
37681	1470	27	its	-PRON-	PRP$
37681	1470	28	uttermost	uttermost	NN
37681	1470	29	"	"	''
37681	1470	30	;	;	:
37681	1470	31	for	for	IN
37681	1470	32	even	even	RB
37681	1470	33	then	then	RB
37681	1470	34	it	-PRON-	PRP
37681	1470	35	is	be	VBZ
37681	1470	36	reasonable	reasonable	JJ
37681	1470	37	to	to	TO
37681	1470	38	think	think	VB
37681	1470	39	of	of	IN
37681	1470	40	it	-PRON-	PRP
37681	1470	41	as	as	IN
37681	1470	42	a	a	DT
37681	1470	43	catenary	catenary	NN
37681	1470	44	,	,	,
37681	1470	45	although	although	IN
37681	1470	46	Proclus	Proclus	NNP
37681	1470	47	doubtless	doubtless	RB
37681	1470	48	had	have	VBD
37681	1470	49	in	in	IN
37681	1470	50	mind	mind	NN
37681	1470	51	the	the	DT
37681	1470	52	Archimedes	Archimedes	NNP
37681	1470	53	statement	statement	NN
37681	1470	54	.	.	.
37681	1471	1	He	-PRON-	PRP
37681	1471	2	also	also	RB
37681	1471	3	stated	state	VBD
37681	1471	4	that	that	IN
37681	1471	5	"	"	``
37681	1471	6	a	a	DT
37681	1471	7	straight	straight	JJ
37681	1471	8	line	line	NN
37681	1471	9	is	be	VBZ
37681	1471	10	a	a	DT
37681	1471	11	line	line	NN
37681	1471	12	such	such	JJ
37681	1471	13	that	that	IN
37681	1471	14	if	if	IN
37681	1471	15	any	any	DT
37681	1471	16	part	part	NN
37681	1471	17	of	of	IN
37681	1471	18	it	-PRON-	PRP
37681	1471	19	is	be	VBZ
37681	1471	20	in	in	IN
37681	1471	21	a	a	DT
37681	1471	22	plane	plane	NN
37681	1471	23	,	,	,
37681	1471	24	the	the	DT
37681	1471	25	whole	whole	NN
37681	1471	26	of	of	IN
37681	1471	27	it	-PRON-	PRP
37681	1471	28	is	be	VBZ
37681	1471	29	in	in	IN
37681	1471	30	the	the	DT
37681	1471	31	plane,"--a	plane,"--a	NNP
37681	1471	32	definition	definition	NN
37681	1471	33	that	that	WDT
37681	1471	34	runs	run	VBZ
37681	1471	35	in	in	IN
37681	1471	36	a	a	DT
37681	1471	37	circle	circle	NN
37681	1471	38	,	,	,
37681	1471	39	since	since	IN
37681	1471	40	plane	plane	NN
37681	1471	41	is	be	VBZ
37681	1471	42	defined	define	VBN
37681	1471	43	by	by	IN
37681	1471	44	means	mean	NNS
37681	1471	45	of	of	IN
37681	1471	46	straight	straight	JJ
37681	1471	47	line	line	NN
37681	1471	48	.	.	.
37681	1472	1	Proclus	Proclus	NNP
37681	1472	2	also	also	RB
37681	1472	3	defines	define	VBZ
37681	1472	4	it	-PRON-	PRP
37681	1472	5	as	as	IN
37681	1472	6	"	"	``
37681	1472	7	a	a	DT
37681	1472	8	uniform	uniform	JJ
37681	1472	9	line	line	NN
37681	1472	10	,	,	,
37681	1472	11	capable	capable	JJ
37681	1472	12	of	of	IN
37681	1472	13	sliding	slide	VBG
37681	1472	14	along	along	IN
37681	1472	15	itself	-PRON-	PRP
37681	1472	16	,	,	,
37681	1472	17	"	"	``
37681	1472	18	but	but	CC
37681	1472	19	this	this	DT
37681	1472	20	is	be	VBZ
37681	1472	21	also	also	RB
37681	1472	22	true	true	JJ
37681	1472	23	of	of	IN
37681	1472	24	a	a	DT
37681	1472	25	circle	circle	NN
37681	1472	26	.	.	.
37681	1473	1	Of	of	IN
37681	1473	2	the	the	DT
37681	1473	3	various	various	JJ
37681	1473	4	definitions	definition	NNS
37681	1473	5	two	two	CD
37681	1473	6	of	of	IN
37681	1473	7	the	the	DT
37681	1473	8	best	good	JJS
37681	1473	9	go	go	VBP
37681	1473	10	back	back	RB
37681	1473	11	to	to	IN
37681	1473	12	Heron	Heron	NNP
37681	1473	13	,	,	,
37681	1473	14	about	about	IN
37681	1473	15	the	the	DT
37681	1473	16	beginning	beginning	NN
37681	1473	17	of	of	IN
37681	1473	18	our	-PRON-	PRP$
37681	1473	19	era	era	NN
37681	1473	20	.	.	.
37681	1474	1	Proclus	Proclus	NNP
37681	1474	2	gives	give	VBZ
37681	1474	3	one	one	CD
37681	1474	4	of	of	IN
37681	1474	5	them	-PRON-	PRP
37681	1474	6	in	in	IN
37681	1474	7	this	this	DT
37681	1474	8	form	form	NN
37681	1474	9	,	,	,
37681	1474	10	"	"	''
37681	1474	11	That	that	DT
37681	1474	12	line	line	NN
37681	1474	13	which	which	WDT
37681	1474	14	,	,	,
37681	1474	15	when	when	WRB
37681	1474	16	its	-PRON-	PRP$
37681	1474	17	ends	end	NNS
37681	1474	18	remain	remain	VBP
37681	1474	19	fixed	fix	VBN
37681	1474	20	,	,	,
37681	1474	21	itself	-PRON-	PRP
37681	1474	22	remains	remain	VBZ
37681	1474	23	fixed	fix	VBN
37681	1474	24	.	.	.
37681	1474	25	"	"	''
37681	1475	1	Heron	Heron	NNP
37681	1475	2	proposed	propose	VBD
37681	1475	3	to	to	TO
37681	1475	4	add	add	VB
37681	1475	5	,	,	,
37681	1475	6	"	"	``
37681	1475	7	when	when	WRB
37681	1475	8	it	-PRON-	PRP
37681	1475	9	is	be	VBZ
37681	1475	10	,	,	,
37681	1475	11	as	as	IN
37681	1475	12	it	-PRON-	PRP
37681	1475	13	were	be	VBD
37681	1475	14	,	,	,
37681	1475	15	turned	turn	VBD
37681	1475	16	round	round	RB
37681	1475	17	in	in	IN
37681	1475	18	the	the	DT
37681	1475	19	same	same	JJ
37681	1475	20	plane	plane	NN
37681	1475	21	.	.	.
37681	1475	22	"	"	''
37681	1476	1	This	this	DT
37681	1476	2	has	have	VBZ
37681	1476	3	been	be	VBN
37681	1476	4	modified	modify	VBN
37681	1476	5	into	into	IN
37681	1476	6	"	"	``
37681	1476	7	that	that	IN
37681	1476	8	which	which	WDT
37681	1476	9	does	do	VBZ
37681	1476	10	not	not	RB
37681	1476	11	change	change	VB
37681	1476	12	its	-PRON-	PRP$
37681	1476	13	position	position	NN
37681	1476	14	when	when	WRB
37681	1476	15	it	-PRON-	PRP
37681	1476	16	is	be	VBZ
37681	1476	17	turned	turn	VBN
37681	1476	18	about	about	RP
37681	1476	19	its	-PRON-	PRP$
37681	1476	20	extremities	extremity	NNS
37681	1476	21	as	as	IN
37681	1476	22	poles	pole	NNS
37681	1476	23	,	,	,
37681	1476	24	"	"	''
37681	1476	25	and	and	CC
37681	1476	26	appears	appear	VBZ
37681	1476	27	in	in	IN
37681	1476	28	substantially	substantially	RB
37681	1476	29	this	this	DT
37681	1476	30	form	form	NN
37681	1476	31	in	in	IN
37681	1476	32	the	the	DT
37681	1476	33	works	work	NNS
37681	1476	34	of	of	IN
37681	1476	35	Leibnitz	Leibnitz	NNP
37681	1476	36	and	and	CC
37681	1476	37	Gauss	Gauss	NNP
37681	1476	38	.	.	.
37681	1477	1	The	the	DT
37681	1477	2	definition	definition	NN
37681	1477	3	of	of	IN
37681	1477	4	a	a	DT
37681	1477	5	straight	straight	JJ
37681	1477	6	line	line	NN
37681	1477	7	as	as	IN
37681	1477	8	"	"	``
37681	1477	9	such	such	PDT
37681	1477	10	a	a	DT
37681	1477	11	line	line	NN
37681	1477	12	as	as	IN
37681	1477	13	,	,	,
37681	1477	14	with	with	IN
37681	1477	15	another	another	DT
37681	1477	16	straight	straight	JJ
37681	1477	17	line	line	NN
37681	1477	18	,	,	,
37681	1477	19	does	do	VBZ
37681	1477	20	not	not	RB
37681	1477	21	inclose	inclose	VB
37681	1477	22	space	space	NN
37681	1477	23	,	,	,
37681	1477	24	"	"	''
37681	1477	25	is	be	VBZ
37681	1477	26	only	only	RB
37681	1477	27	a	a	DT
37681	1477	28	modification	modification	NN
37681	1477	29	of	of	IN
37681	1477	30	this	this	DT
37681	1477	31	one	one	NN
37681	1477	32	.	.	.
37681	1478	1	The	the	DT
37681	1478	2	other	other	JJ
37681	1478	3	definition	definition	NN
37681	1478	4	of	of	IN
37681	1478	5	Heron	Heron	NNP
37681	1478	6	states	state	VBZ
37681	1478	7	that	that	IN
37681	1478	8	in	in	IN
37681	1478	9	a	a	DT
37681	1478	10	straight	straight	JJ
37681	1478	11	line	line	NN
37681	1478	12	"	"	``
37681	1478	13	all	all	DT
37681	1478	14	its	-PRON-	PRP$
37681	1478	15	parts	part	NNS
37681	1478	16	fit	fit	VBP
37681	1478	17	on	on	IN
37681	1478	18	all	all	DT
37681	1478	19	in	in	IN
37681	1478	20	all	all	DT
37681	1478	21	ways	way	NNS
37681	1478	22	,	,	,
37681	1478	23	"	"	''
37681	1478	24	and	and	CC
37681	1478	25	this	this	DT
37681	1478	26	in	in	IN
37681	1478	27	its	-PRON-	PRP$
37681	1478	28	modern	modern	JJ
37681	1478	29	form	form	NN
37681	1478	30	is	be	VBZ
37681	1478	31	perhaps	perhaps	RB
37681	1478	32	the	the	DT
37681	1478	33	most	most	RBS
37681	1478	34	satisfactory	satisfactory	JJ
37681	1478	35	of	of	IN
37681	1478	36	all	all	DT
37681	1478	37	.	.	.
37681	1479	1	In	in	IN
37681	1479	2	this	this	DT
37681	1479	3	modern	modern	JJ
37681	1479	4	form	form	NN
37681	1479	5	it	-PRON-	PRP
37681	1479	6	may	may	MD
37681	1479	7	be	be	VB
37681	1479	8	stated	state	VBN
37681	1479	9	,	,	,
37681	1479	10	"	"	''
37681	1479	11	A	a	DT
37681	1479	12	line	line	NN
37681	1479	13	such	such	JJ
37681	1479	14	that	that	IN
37681	1479	15	any	any	DT
37681	1479	16	part	part	NN
37681	1479	17	,	,	,
37681	1479	18	placed	place	VBN
37681	1479	19	with	with	IN
37681	1479	20	its	-PRON-	PRP$
37681	1479	21	ends	end	NNS
37681	1479	22	on	on	IN
37681	1479	23	any	any	DT
37681	1479	24	other	other	JJ
37681	1479	25	part	part	NN
37681	1479	26	,	,	,
37681	1479	27	must	must	MD
37681	1479	28	lie	lie	VB
37681	1479	29	wholly	wholly	RB
37681	1479	30	in	in	IN
37681	1479	31	the	the	DT
37681	1479	32	line	line	NN
37681	1479	33	,	,	,
37681	1479	34	is	be	VBZ
37681	1479	35	called	call	VBN
37681	1479	36	a	a	DT
37681	1479	37	straight	straight	JJ
37681	1479	38	line	line	NN
37681	1479	39	,	,	,
37681	1479	40	"	"	''
37681	1479	41	in	in	IN
37681	1479	42	which	which	WDT
37681	1479	43	the	the	DT
37681	1479	44	force	force	NN
37681	1479	45	of	of	IN
37681	1479	46	the	the	DT
37681	1479	47	word	word	NN
37681	1479	48	"	"	``
37681	1479	49	must	must	MD
37681	1479	50	"	"	``
37681	1479	51	should	should	MD
37681	1479	52	be	be	VB
37681	1479	53	noted	note	VBN
37681	1479	54	.	.	.
37681	1480	1	This	this	DT
37681	1480	2	whole	whole	JJ
37681	1480	3	historical	historical	JJ
37681	1480	4	discussion	discussion	NN
37681	1480	5	goes	go	VBZ
37681	1480	6	to	to	TO
37681	1480	7	show	show	VB
37681	1480	8	how	how	WRB
37681	1480	9	futile	futile	JJ
37681	1480	10	it	-PRON-	PRP
37681	1480	11	is	be	VBZ
37681	1480	12	to	to	TO
37681	1480	13	attempt	attempt	VB
37681	1480	14	to	to	TO
37681	1480	15	define	define	VB
37681	1480	16	a	a	DT
37681	1480	17	straight	straight	JJ
37681	1480	18	line	line	NN
37681	1480	19	.	.	.
37681	1481	1	What	what	WP
37681	1481	2	is	be	VBZ
37681	1481	3	needed	need	VBN
37681	1481	4	is	be	VBZ
37681	1481	5	that	that	IN
37681	1481	6	we	-PRON-	PRP
37681	1481	7	should	should	MD
37681	1481	8	explain	explain	VB
37681	1481	9	what	what	WP
37681	1481	10	is	be	VBZ
37681	1481	11	meant	mean	VBN
37681	1481	12	by	by	IN
37681	1481	13	a	a	DT
37681	1481	14	straight	straight	JJ
37681	1481	15	line	line	NN
37681	1481	16	,	,	,
37681	1481	17	that	that	IN
37681	1481	18	we	-PRON-	PRP
37681	1481	19	should	should	MD
37681	1481	20	illustrate	illustrate	VB
37681	1481	21	it	-PRON-	PRP
37681	1481	22	,	,	,
37681	1481	23	and	and	CC
37681	1481	24	that	that	IN
37681	1481	25	pupils	pupil	NNS
37681	1481	26	should	should	MD
37681	1481	27	then	then	RB
37681	1481	28	read	read	VB
37681	1481	29	the	the	DT
37681	1481	30	definition	definition	NN
37681	1481	31	understandingly	understandingly	RB
37681	1481	32	.	.	.
37681	1482	1	5	5	CD
37681	1482	2	.	.	.
37681	1483	1	SURFACE	SURFACE	NNP
37681	1483	2	.	.	.
37681	1484	1	_	_	NNP
37681	1484	2	A	a	DT
37681	1484	3	surface	surface	NN
37681	1484	4	is	be	VBZ
37681	1484	5	that	that	DT
37681	1484	6	which	which	WDT
37681	1484	7	has	have	VBZ
37681	1484	8	length	length	NN
37681	1484	9	and	and	CC
37681	1484	10	breadth	breadth	NN
37681	1484	11	.	.	.
37681	1484	12	_	_	NNP
37681	1484	13	This	this	DT
37681	1484	14	is	be	VBZ
37681	1484	15	substantially	substantially	RB
37681	1484	16	the	the	DT
37681	1484	17	common	common	JJ
37681	1484	18	definition	definition	NN
37681	1484	19	of	of	IN
37681	1484	20	our	-PRON-	PRP$
37681	1484	21	modern	modern	JJ
37681	1484	22	textbooks	textbook	NNS
37681	1484	23	.	.	.
37681	1485	1	As	as	IN
37681	1485	2	with	with	IN
37681	1485	3	line	line	NN
37681	1485	4	,	,	,
37681	1485	5	so	so	CC
37681	1485	6	with	with	IN
37681	1485	7	surface	surface	NN
37681	1485	8	,	,	,
37681	1485	9	the	the	DT
37681	1485	10	definition	definition	NN
37681	1485	11	is	be	VBZ
37681	1485	12	not	not	RB
37681	1485	13	entirely	entirely	RB
37681	1485	14	satisfactory	satisfactory	JJ
37681	1485	15	,	,	,
37681	1485	16	and	and	CC
37681	1485	17	the	the	DT
37681	1485	18	chief	chief	JJ
37681	1485	19	consideration	consideration	NN
37681	1485	20	is	be	VBZ
37681	1485	21	that	that	IN
37681	1485	22	the	the	DT
37681	1485	23	meaning	meaning	NN
37681	1485	24	of	of	IN
37681	1485	25	the	the	DT
37681	1485	26	term	term	NN
37681	1485	27	should	should	MD
37681	1485	28	be	be	VB
37681	1485	29	made	make	VBN
37681	1485	30	clear	clear	JJ
37681	1485	31	by	by	IN
37681	1485	32	explanations	explanation	NNS
37681	1485	33	and	and	CC
37681	1485	34	illustrations	illustration	NNS
37681	1485	35	.	.	.
37681	1486	1	The	the	DT
37681	1486	2	shadow	shadow	NN
37681	1486	3	cast	cast	VBD
37681	1486	4	on	on	IN
37681	1486	5	a	a	DT
37681	1486	6	table	table	NN
37681	1486	7	top	top	NN
37681	1486	8	is	be	VBZ
37681	1486	9	a	a	DT
37681	1486	10	good	good	JJ
37681	1486	11	illustration	illustration	NN
37681	1486	12	,	,	,
37681	1486	13	since	since	IN
37681	1486	14	all	all	DT
37681	1486	15	idea	idea	NN
37681	1486	16	of	of	IN
37681	1486	17	thickness	thickness	NN
37681	1486	18	is	be	VBZ
37681	1486	19	wanting	want	VBG
37681	1486	20	.	.	.
37681	1487	1	It	-PRON-	PRP
37681	1487	2	adds	add	VBZ
37681	1487	3	to	to	IN
37681	1487	4	the	the	DT
37681	1487	5	understanding	understanding	NN
37681	1487	6	of	of	IN
37681	1487	7	the	the	DT
37681	1487	8	concept	concept	NN
37681	1487	9	to	to	TO
37681	1487	10	introduce	introduce	VB
37681	1487	11	Aristotle	Aristotle	NNP
37681	1487	12	's	's	POS
37681	1487	13	statement	statement	NN
37681	1487	14	that	that	IN
37681	1487	15	a	a	DT
37681	1487	16	surface	surface	NN
37681	1487	17	is	be	VBZ
37681	1487	18	generated	generate	VBN
37681	1487	19	by	by	IN
37681	1487	20	a	a	DT
37681	1487	21	moving	move	VBG
37681	1487	22	line	line	NN
37681	1487	23	,	,	,
37681	1487	24	modified	modify	VBN
37681	1487	25	by	by	IN
37681	1487	26	saying	say	VBG
37681	1487	27	that	that	IN
37681	1487	28	it	-PRON-	PRP
37681	1487	29	_	_	NNP
37681	1487	30	may	may	MD
37681	1487	31	_	_	NNP
37681	1487	32	be	be	VB
37681	1487	33	so	so	RB
37681	1487	34	generated	generate	VBN
37681	1487	35	,	,	,
37681	1487	36	since	since	IN
37681	1487	37	the	the	DT
37681	1487	38	line	line	NN
37681	1487	39	might	may	MD
37681	1487	40	slide	slide	VB
37681	1487	41	along	along	IN
37681	1487	42	its	-PRON-	PRP$
37681	1487	43	own	own	JJ
37681	1487	44	trace	trace	NN
37681	1487	45	,	,	,
37681	1487	46	or	or	CC
37681	1487	47	,	,	,
37681	1487	48	as	as	IN
37681	1487	49	is	be	VBZ
37681	1487	50	commonly	commonly	RB
37681	1487	51	said	say	VBN
37681	1487	52	in	in	IN
37681	1487	53	mathematics	mathematic	NNS
37681	1487	54	,	,	,
37681	1487	55	along	along	IN
37681	1487	56	itself	-PRON-	PRP
37681	1487	57	.	.	.
37681	1488	1	6	6	CD
37681	1488	2	.	.	.
37681	1489	1	_	_	NNP
37681	1489	2	The	the	DT
37681	1489	3	extremities	extremity	NNS
37681	1489	4	of	of	IN
37681	1489	5	a	a	DT
37681	1489	6	surface	surface	NN
37681	1489	7	are	be	VBP
37681	1489	8	lines	line	NNS
37681	1489	9	.	.	.
37681	1489	10	_	_	NNP
37681	1489	11	This	this	DT
37681	1489	12	is	be	VBZ
37681	1489	13	open	open	JJ
37681	1489	14	to	to	IN
37681	1489	15	the	the	DT
37681	1489	16	same	same	JJ
37681	1489	17	explanation	explanation	NN
37681	1489	18	and	and	CC
37681	1489	19	objection	objection	NN
37681	1489	20	as	as	IN
37681	1489	21	definition	definition	NN
37681	1489	22	3	3	CD
37681	1489	23	,	,	,
37681	1489	24	and	and	CC
37681	1489	25	is	be	VBZ
37681	1489	26	not	not	RB
37681	1489	27	usually	usually	RB
37681	1489	28	given	give	VBN
37681	1489	29	in	in	IN
37681	1489	30	modern	modern	JJ
37681	1489	31	textbooks	textbook	NNS
37681	1489	32	.	.	.
37681	1490	1	Proclus	proclus	NN
37681	1490	2	calls	call	VBZ
37681	1490	3	attention	attention	NN
37681	1490	4	to	to	IN
37681	1490	5	the	the	DT
37681	1490	6	fact	fact	NN
37681	1490	7	that	that	IN
37681	1490	8	the	the	DT
37681	1490	9	statement	statement	NN
37681	1490	10	is	be	VBZ
37681	1490	11	hardly	hardly	RB
37681	1490	12	true	true	JJ
37681	1490	13	for	for	IN
37681	1490	14	a	a	DT
37681	1490	15	complete	complete	JJ
37681	1490	16	spherical	spherical	JJ
37681	1490	17	surface	surface	NN
37681	1490	18	.	.	.
37681	1491	1	7	7	LS
37681	1491	2	.	.	.
37681	1492	1	PLANE	PLANE	NNP
37681	1492	2	.	.	.
37681	1493	1	_	_	NNP
37681	1493	2	A	a	DT
37681	1493	3	plane	plane	NN
37681	1493	4	surface	surface	NN
37681	1493	5	is	be	VBZ
37681	1493	6	a	a	DT
37681	1493	7	surface	surface	NN
37681	1493	8	which	which	WDT
37681	1493	9	lies	lie	VBZ
37681	1493	10	evenly	evenly	RB
37681	1493	11	with	with	IN
37681	1493	12	the	the	DT
37681	1493	13	straight	straight	JJ
37681	1493	14	lines	line	NNS
37681	1493	15	on	on	IN
37681	1493	16	itself	-PRON-	PRP
37681	1493	17	.	.	.
37681	1493	18	_	_	NNP
37681	1493	19	Euclid	Euclid	NNP
37681	1493	20	here	here	RB
37681	1493	21	follows	follow	VBZ
37681	1493	22	his	-PRON-	PRP$
37681	1493	23	definition	definition	NN
37681	1493	24	of	of	IN
37681	1493	25	straight	straight	JJ
37681	1493	26	line	line	NN
37681	1493	27	,	,	,
37681	1493	28	with	with	IN
37681	1493	29	a	a	DT
37681	1493	30	result	result	NN
37681	1493	31	that	that	WDT
37681	1493	32	is	be	VBZ
37681	1493	33	equally	equally	RB
37681	1493	34	unsatisfactory	unsatisfactory	JJ
37681	1493	35	.	.	.
37681	1494	1	For	for	IN
37681	1494	2	teaching	teaching	NN
37681	1494	3	purposes	purpose	NNS
37681	1494	4	the	the	DT
37681	1494	5	translation	translation	NN
37681	1494	6	from	from	IN
37681	1494	7	the	the	DT
37681	1494	8	Greek	Greek	NNP
37681	1494	9	is	be	VBZ
37681	1494	10	not	not	RB
37681	1494	11	clear	clear	JJ
37681	1494	12	to	to	IN
37681	1494	13	a	a	DT
37681	1494	14	beginner	beginner	NN
37681	1494	15	,	,	,
37681	1494	16	since	since	IN
37681	1494	17	"	"	``
37681	1494	18	lies	lie	VBZ
37681	1494	19	evenly	evenly	RB
37681	1494	20	"	"	''
37681	1494	21	is	be	VBZ
37681	1494	22	a	a	DT
37681	1494	23	term	term	NN
37681	1494	24	not	not	RB
37681	1494	25	simpler	simple	JJR
37681	1494	26	than	than	IN
37681	1494	27	the	the	DT
37681	1494	28	one	one	CD
37681	1494	29	defined	define	VBN
37681	1494	30	.	.	.
37681	1495	1	As	as	IN
37681	1495	2	with	with	IN
37681	1495	3	the	the	DT
37681	1495	4	definition	definition	NN
37681	1495	5	of	of	IN
37681	1495	6	a	a	DT
37681	1495	7	straight	straight	JJ
37681	1495	8	line	line	NN
37681	1495	9	,	,	,
37681	1495	10	so	so	CC
37681	1495	11	with	with	IN
37681	1495	12	that	that	DT
37681	1495	13	of	of	IN
37681	1495	14	a	a	DT
37681	1495	15	plane	plane	NN
37681	1495	16	,	,	,
37681	1495	17	numerous	numerous	JJ
37681	1495	18	efforts	effort	NNS
37681	1495	19	at	at	IN
37681	1495	20	improvement	improvement	NN
37681	1495	21	have	have	VBP
37681	1495	22	been	be	VBN
37681	1495	23	made	make	VBN
37681	1495	24	.	.	.
37681	1496	1	Proclus	Proclus	NNP
37681	1496	2	,	,	,
37681	1496	3	following	follow	VBG
37681	1496	4	a	a	DT
37681	1496	5	hint	hint	NN
37681	1496	6	of	of	IN
37681	1496	7	Heron	Heron	NNP
37681	1496	8	's	's	POS
37681	1496	9	,	,	,
37681	1496	10	defines	define	VBZ
37681	1496	11	it	-PRON-	PRP
37681	1496	12	as	as	IN
37681	1496	13	"	"	``
37681	1496	14	the	the	DT
37681	1496	15	surface	surface	NN
37681	1496	16	which	which	WDT
37681	1496	17	is	be	VBZ
37681	1496	18	stretched	stretch	VBN
37681	1496	19	to	to	IN
37681	1496	20	the	the	DT
37681	1496	21	utmost	utmost	NN
37681	1496	22	,	,	,
37681	1496	23	"	"	''
37681	1496	24	and	and	CC
37681	1496	25	also	also	RB
37681	1496	26	,	,	,
37681	1496	27	this	this	DT
37681	1496	28	time	time	NN
37681	1496	29	influenced	influence	VBN
37681	1496	30	by	by	IN
37681	1496	31	Archimedes	Archimedes	NNP
37681	1496	32	's	's	POS
37681	1496	33	assumption	assumption	NN
37681	1496	34	concerning	concern	VBG
37681	1496	35	a	a	DT
37681	1496	36	straight	straight	JJ
37681	1496	37	line	line	NN
37681	1496	38	,	,	,
37681	1496	39	as	as	IN
37681	1496	40	"	"	``
37681	1496	41	the	the	DT
37681	1496	42	least	least	JJS
37681	1496	43	surface	surface	NN
37681	1496	44	among	among	IN
37681	1496	45	all	all	PDT
37681	1496	46	those	those	DT
37681	1496	47	which	which	WDT
37681	1496	48	have	have	VBP
37681	1496	49	the	the	DT
37681	1496	50	same	same	JJ
37681	1496	51	extremities	extremity	NNS
37681	1496	52	.	.	.
37681	1496	53	"	"	''
37681	1497	1	Heron	Heron	NNP
37681	1497	2	gave	give	VBD
37681	1497	3	one	one	CD
37681	1497	4	of	of	IN
37681	1497	5	the	the	DT
37681	1497	6	best	good	JJS
37681	1497	7	definitions	definition	NNS
37681	1497	8	,	,	,
37681	1497	9	"	"	''
37681	1497	10	A	a	DT
37681	1497	11	surface	surface	NN
37681	1497	12	all	all	PDT
37681	1497	13	the	the	DT
37681	1497	14	parts	part	NNS
37681	1497	15	of	of	IN
37681	1497	16	which	which	WDT
37681	1497	17	have	have	VBP
37681	1497	18	the	the	DT
37681	1497	19	property	property	NN
37681	1497	20	of	of	IN
37681	1497	21	fitting	fit	VBG
37681	1497	22	on	on	IN
37681	1497	23	[	[	-LRB-
37681	1497	24	each	each	DT
37681	1497	25	other	other	JJ
37681	1497	26	]	]	-RRB-
37681	1497	27	.	.	.
37681	1497	28	"	"	''
37681	1498	1	The	the	DT
37681	1498	2	definition	definition	NN
37681	1498	3	that	that	WDT
37681	1498	4	has	have	VBZ
37681	1498	5	met	meet	VBN
37681	1498	6	with	with	IN
37681	1498	7	the	the	DT
37681	1498	8	widest	wide	JJS
37681	1498	9	acceptance	acceptance	NN
37681	1498	10	,	,	,
37681	1498	11	however	however	RB
37681	1498	12	,	,	,
37681	1498	13	is	be	VBZ
37681	1498	14	a	a	DT
37681	1498	15	modification	modification	NN
37681	1498	16	of	of	IN
37681	1498	17	one	one	CD
37681	1498	18	due	due	IN
37681	1498	19	to	to	IN
37681	1498	20	Proclus	Proclus	NNP
37681	1498	21	,	,	,
37681	1498	22	"	"	''
37681	1498	23	A	a	DT
37681	1498	24	surface	surface	NN
37681	1498	25	such	such	JJ
37681	1498	26	that	that	IN
37681	1498	27	a	a	DT
37681	1498	28	straight	straight	JJ
37681	1498	29	line	line	NN
37681	1498	30	fits	fit	VBZ
37681	1498	31	on	on	IN
37681	1498	32	all	all	DT
37681	1498	33	parts	part	NNS
37681	1498	34	of	of	IN
37681	1498	35	it	-PRON-	PRP
37681	1498	36	.	.	.
37681	1498	37	"	"	''
37681	1499	1	Proclus	Proclus	NNP
37681	1499	2	elsewhere	elsewhere	RB
37681	1499	3	says	say	VBZ
37681	1499	4	,	,	,
37681	1499	5	"	"	``
37681	1499	6	[	[	-LRB-
37681	1499	7	A	a	DT
37681	1499	8	plane	plane	NN
37681	1499	9	surface	surface	NN
37681	1499	10	is	be	VBZ
37681	1499	11	]	]	-RRB-
37681	1499	12	such	such	JJ
37681	1499	13	that	that	IN
37681	1499	14	the	the	DT
37681	1499	15	straight	straight	JJ
37681	1499	16	line	line	NN
37681	1499	17	fits	fit	VBZ
37681	1499	18	on	on	IN
37681	1499	19	it	-PRON-	PRP
37681	1499	20	all	all	DT
37681	1499	21	ways	way	NNS
37681	1499	22	,	,	,
37681	1499	23	"	"	''
37681	1499	24	and	and	CC
37681	1499	25	Heron	Heron	NNP
37681	1499	26	gives	give	VBZ
37681	1499	27	it	-PRON-	PRP
37681	1499	28	in	in	IN
37681	1499	29	this	this	DT
37681	1499	30	form	form	NN
37681	1499	31	,	,	,
37681	1499	32	"	"	''
37681	1499	33	[	[	-LRB-
37681	1499	34	A	a	DT
37681	1499	35	plane	plane	NN
37681	1499	36	surface	surface	NN
37681	1499	37	is	be	VBZ
37681	1499	38	]	]	-RRB-
37681	1499	39	such	such	JJ
37681	1499	40	that	that	IN
37681	1499	41	,	,	,
37681	1499	42	if	if	IN
37681	1499	43	a	a	DT
37681	1499	44	straight	straight	JJ
37681	1499	45	line	line	NN
37681	1499	46	pass	pass	VBP
37681	1499	47	through	through	IN
37681	1499	48	two	two	CD
37681	1499	49	points	point	NNS
37681	1499	50	on	on	IN
37681	1499	51	it	-PRON-	PRP
37681	1499	52	,	,	,
37681	1499	53	the	the	DT
37681	1499	54	line	line	NN
37681	1499	55	coincides	coincide	VBZ
37681	1499	56	with	with	IN
37681	1499	57	it	-PRON-	PRP
37681	1499	58	at	at	IN
37681	1499	59	every	every	DT
37681	1499	60	spot	spot	NN
37681	1499	61	,	,	,
37681	1499	62	all	all	DT
37681	1499	63	ways	way	NNS
37681	1499	64	.	.	.
37681	1499	65	"	"	''
37681	1500	1	In	in	IN
37681	1500	2	modern	modern	JJ
37681	1500	3	form	form	NN
37681	1500	4	this	this	DT
37681	1500	5	appears	appear	VBZ
37681	1500	6	as	as	IN
37681	1500	7	follows	follow	VBZ
37681	1500	8	:	:	:
37681	1500	9	"	"	``
37681	1500	10	A	a	DT
37681	1500	11	surface	surface	NN
37681	1500	12	such	such	JJ
37681	1500	13	that	that	IN
37681	1500	14	a	a	DT
37681	1500	15	straight	straight	JJ
37681	1500	16	line	line	NN
37681	1500	17	joining	join	VBG
37681	1500	18	any	any	DT
37681	1500	19	two	two	CD
37681	1500	20	of	of	IN
37681	1500	21	its	-PRON-	PRP$
37681	1500	22	points	point	NNS
37681	1500	23	lies	lie	VBZ
37681	1500	24	wholly	wholly	RB
37681	1500	25	in	in	IN
37681	1500	26	the	the	DT
37681	1500	27	surface	surface	NN
37681	1500	28	is	be	VBZ
37681	1500	29	called	call	VBN
37681	1500	30	a	a	DT
37681	1500	31	plane	plane	NN
37681	1500	32	,	,	,
37681	1500	33	"	"	''
37681	1500	34	and	and	CC
37681	1500	35	for	for	IN
37681	1500	36	teaching	teaching	NN
37681	1500	37	purposes	purpose	NNS
37681	1500	38	we	-PRON-	PRP
37681	1500	39	have	have	VBP
37681	1500	40	no	no	DT
37681	1500	41	better	well	JJR
37681	1500	42	definition	definition	NN
37681	1500	43	.	.	.
37681	1501	1	It	-PRON-	PRP
37681	1501	2	is	be	VBZ
37681	1501	3	often	often	RB
37681	1501	4	known	know	VBN
37681	1501	5	as	as	IN
37681	1501	6	Simson	Simson	NNP
37681	1501	7	's	's	POS
37681	1501	8	definition	definition	NN
37681	1501	9	,	,	,
37681	1501	10	having	have	VBG
37681	1501	11	been	be	VBN
37681	1501	12	given	give	VBN
37681	1501	13	by	by	IN
37681	1501	14	Robert	Robert	NNP
37681	1501	15	Simson	Simson	NNP
37681	1501	16	in	in	IN
37681	1501	17	1756	1756	CD
37681	1501	18	.	.	.
37681	1502	1	The	the	DT
37681	1502	2	French	french	JJ
37681	1502	3	mathematician	mathematician	NN
37681	1502	4	,	,	,
37681	1502	5	Fourier	Fourier	NNP
37681	1502	6	,	,	,
37681	1502	7	proposed	propose	VBD
37681	1502	8	to	to	TO
37681	1502	9	define	define	VB
37681	1502	10	a	a	DT
37681	1502	11	plane	plane	NN
37681	1502	12	as	as	IN
37681	1502	13	formed	form	VBN
37681	1502	14	by	by	IN
37681	1502	15	the	the	DT
37681	1502	16	aggregate	aggregate	NN
37681	1502	17	of	of	IN
37681	1502	18	all	all	PDT
37681	1502	19	the	the	DT
37681	1502	20	straight	straight	JJ
37681	1502	21	lines	line	NNS
37681	1502	22	which	which	WDT
37681	1502	23	,	,	,
37681	1502	24	passing	pass	VBG
37681	1502	25	through	through	IN
37681	1502	26	one	one	CD
37681	1502	27	point	point	NN
37681	1502	28	on	on	IN
37681	1502	29	a	a	DT
37681	1502	30	straight	straight	JJ
37681	1502	31	line	line	NN
37681	1502	32	in	in	IN
37681	1502	33	space	space	NN
37681	1502	34	,	,	,
37681	1502	35	are	be	VBP
37681	1502	36	perpendicular	perpendicular	JJ
37681	1502	37	to	to	IN
37681	1502	38	that	that	DT
37681	1502	39	line	line	NN
37681	1502	40	.	.	.
37681	1503	1	This	this	DT
37681	1503	2	is	be	VBZ
37681	1503	3	clear	clear	JJ
37681	1503	4	,	,	,
37681	1503	5	but	but	CC
37681	1503	6	it	-PRON-	PRP
37681	1503	7	is	be	VBZ
37681	1503	8	not	not	RB
37681	1503	9	so	so	RB
37681	1503	10	usable	usable	JJ
37681	1503	11	for	for	IN
37681	1503	12	beginners	beginner	NNS
37681	1503	13	as	as	IN
37681	1503	14	Simson	Simson	NNP
37681	1503	15	's	's	POS
37681	1503	16	definition	definition	NN
37681	1503	17	.	.	.
37681	1504	1	It	-PRON-	PRP
37681	1504	2	appears	appear	VBZ
37681	1504	3	as	as	IN
37681	1504	4	a	a	DT
37681	1504	5	theorem	theorem	NN
37681	1504	6	in	in	IN
37681	1504	7	many	many	JJ
37681	1504	8	recent	recent	JJ
37681	1504	9	geometries	geometry	NNS
37681	1504	10	.	.	.
37681	1505	1	The	the	DT
37681	1505	2	German	german	JJ
37681	1505	3	mathematician	mathematician	NN
37681	1505	4	,	,	,
37681	1505	5	Crelle	Crelle	NNP
37681	1505	6	,	,	,
37681	1505	7	defined	define	VBD
37681	1505	8	a	a	DT
37681	1505	9	plane	plane	NN
37681	1505	10	as	as	IN
37681	1505	11	a	a	DT
37681	1505	12	surface	surface	NN
37681	1505	13	containing	contain	VBG
37681	1505	14	all	all	PDT
37681	1505	15	the	the	DT
37681	1505	16	straight	straight	JJ
37681	1505	17	lines	line	NNS
37681	1505	18	(	(	-LRB-
37681	1505	19	throughout	throughout	IN
37681	1505	20	their	-PRON-	PRP$
37681	1505	21	whole	whole	JJ
37681	1505	22	length	length	NN
37681	1505	23	)	)	-RRB-
37681	1505	24	passing	pass	VBG
37681	1505	25	through	through	IN
37681	1505	26	a	a	DT
37681	1505	27	fixed	fix	VBN
37681	1505	28	point	point	NN
37681	1505	29	and	and	CC
37681	1505	30	also	also	RB
37681	1505	31	intersecting	intersect	VBG
37681	1505	32	a	a	DT
37681	1505	33	straight	straight	JJ
37681	1505	34	line	line	NN
37681	1505	35	in	in	IN
37681	1505	36	space	space	NN
37681	1505	37	,	,	,
37681	1505	38	but	but	CC
37681	1505	39	of	of	IN
37681	1505	40	course	course	NN
37681	1505	41	this	this	DT
37681	1505	42	intersected	intersect	VBN
37681	1505	43	straight	straight	JJ
37681	1505	44	line	line	NN
37681	1505	45	must	must	MD
37681	1505	46	not	not	RB
37681	1505	47	pass	pass	VB
37681	1505	48	through	through	IN
37681	1505	49	the	the	DT
37681	1505	50	fixed	fix	VBN
37681	1505	51	point	point	NN
37681	1505	52	.	.	.
37681	1506	1	Crelle	Crelle	NNP
37681	1506	2	's	's	POS
37681	1506	3	definition	definition	NN
37681	1506	4	is	be	VBZ
37681	1506	5	occasionally	occasionally	RB
37681	1506	6	seen	see	VBN
37681	1506	7	in	in	IN
37681	1506	8	modern	modern	JJ
37681	1506	9	textbooks	textbook	NNS
37681	1506	10	,	,	,
37681	1506	11	but	but	CC
37681	1506	12	it	-PRON-	PRP
37681	1506	13	is	be	VBZ
37681	1506	14	not	not	RB
37681	1506	15	so	so	RB
37681	1506	16	clear	clear	JJ
37681	1506	17	to	to	IN
37681	1506	18	the	the	DT
37681	1506	19	pupil	pupil	NN
37681	1506	20	as	as	IN
37681	1506	21	Simson	Simson	NNP
37681	1506	22	's	's	POS
37681	1506	23	.	.	.
37681	1507	1	Of	of	IN
37681	1507	2	the	the	DT
37681	1507	3	various	various	JJ
37681	1507	4	ultrascientific	ultrascientific	JJ
37681	1507	5	definitions	definition	NNS
37681	1507	6	of	of	IN
37681	1507	7	a	a	DT
37681	1507	8	plane	plane	NN
37681	1507	9	that	that	WDT
37681	1507	10	have	have	VBP
37681	1507	11	been	be	VBN
37681	1507	12	suggested	suggest	VBN
37681	1507	13	of	of	IN
37681	1507	14	late	late	JJ
37681	1507	15	it	-PRON-	PRP
37681	1507	16	is	be	VBZ
37681	1507	17	hardly	hardly	RB
37681	1507	18	of	of	IN
37681	1507	19	use	use	NN
37681	1507	20	to	to	TO
37681	1507	21	speak	speak	VB
37681	1507	22	in	in	IN
37681	1507	23	a	a	DT
37681	1507	24	book	book	NN
37681	1507	25	concerned	concern	VBN
37681	1507	26	primarily	primarily	RB
37681	1507	27	with	with	IN
37681	1507	28	practical	practical	JJ
37681	1507	29	teaching	teaching	NN
37681	1507	30	.	.	.
37681	1508	1	No	no	DT
37681	1508	2	one	one	NN
37681	1508	3	of	of	IN
37681	1508	4	them	-PRON-	PRP
37681	1508	5	is	be	VBZ
37681	1508	6	adapted	adapt	VBN
37681	1508	7	to	to	IN
37681	1508	8	the	the	DT
37681	1508	9	needs	need	NNS
37681	1508	10	and	and	CC
37681	1508	11	the	the	DT
37681	1508	12	comprehension	comprehension	NN
37681	1508	13	of	of	IN
37681	1508	14	the	the	DT
37681	1508	15	beginner	beginner	NN
37681	1508	16	,	,	,
37681	1508	17	and	and	CC
37681	1508	18	it	-PRON-	PRP
37681	1508	19	seems	seem	VBZ
37681	1508	20	that	that	IN
37681	1508	21	we	-PRON-	PRP
37681	1508	22	are	be	VBP
37681	1508	23	not	not	RB
37681	1508	24	likely	likely	JJ
37681	1508	25	to	to	TO
37681	1508	26	improve	improve	VB
37681	1508	27	upon	upon	IN
37681	1508	28	the	the	DT
37681	1508	29	so	so	RB
37681	1508	30	-	-	HYPH
37681	1508	31	called	call	VBN
37681	1508	32	Simson	Simson	NNP
37681	1508	33	form	form	NN
37681	1508	34	.	.	.
37681	1509	1	8	8	LS
37681	1509	2	.	.	.
37681	1510	1	PLANE	plane	NN
37681	1510	2	ANGLE	ANGLE	NNS
37681	1510	3	.	.	.
37681	1511	1	_	_	NNP
37681	1511	2	A	a	DT
37681	1511	3	plane	plane	NN
37681	1511	4	angle	angle	NN
37681	1511	5	is	be	VBZ
37681	1511	6	the	the	DT
37681	1511	7	inclination	inclination	NN
37681	1511	8	to	to	IN
37681	1511	9	each	each	DT
37681	1511	10	other	other	JJ
37681	1511	11	of	of	IN
37681	1511	12	two	two	CD
37681	1511	13	lines	line	NNS
37681	1511	14	in	in	IN
37681	1511	15	a	a	DT
37681	1511	16	plane	plane	NN
37681	1511	17	which	which	WDT
37681	1511	18	meet	meet	VBP
37681	1511	19	each	each	DT
37681	1511	20	other	other	JJ
37681	1511	21	and	and	CC
37681	1511	22	do	do	VBP
37681	1511	23	not	not	RB
37681	1511	24	lie	lie	VB
37681	1511	25	in	in	IN
37681	1511	26	a	a	DT
37681	1511	27	straight	straight	JJ
37681	1511	28	line	line	NN
37681	1511	29	.	.	.
37681	1511	30	_	_	NNP
37681	1511	31	This	this	DT
37681	1511	32	definition	definition	NN
37681	1511	33	,	,	,
37681	1511	34	it	-PRON-	PRP
37681	1511	35	will	will	MD
37681	1511	36	be	be	VB
37681	1511	37	noticed	notice	VBN
37681	1511	38	,	,	,
37681	1511	39	includes	include	VBZ
37681	1511	40	curvilinear	curvilinear	NN
37681	1511	41	angles	angle	NNS
37681	1511	42	,	,	,
37681	1511	43	and	and	CC
37681	1511	44	the	the	DT
37681	1511	45	expression	expression	NN
37681	1511	46	"	"	''
37681	1511	47	and	and	CC
37681	1511	48	do	do	VBP
37681	1511	49	not	not	RB
37681	1511	50	lie	lie	VB
37681	1511	51	in	in	IN
37681	1511	52	a	a	DT
37681	1511	53	straight	straight	JJ
37681	1511	54	line	line	NN
37681	1511	55	"	"	''
37681	1511	56	states	state	VBZ
37681	1511	57	that	that	IN
37681	1511	58	the	the	DT
37681	1511	59	lines	line	NNS
37681	1511	60	must	must	MD
37681	1511	61	not	not	RB
37681	1511	62	be	be	VB
37681	1511	63	continuous	continuous	JJ
37681	1511	64	one	one	CD
37681	1511	65	with	with	IN
37681	1511	66	the	the	DT
37681	1511	67	other	other	JJ
37681	1511	68	,	,	,
37681	1511	69	that	that	RB
37681	1511	70	is	is	RB
37681	1511	71	,	,	,
37681	1511	72	that	that	IN
37681	1511	73	zero	zero	CD
37681	1511	74	and	and	CC
37681	1511	75	straight	straight	JJ
37681	1511	76	angles	angle	NNS
37681	1511	77	are	be	VBP
37681	1511	78	excluded	exclude	VBN
37681	1511	79	.	.	.
37681	1512	1	Since	since	IN
37681	1512	2	Euclid	Euclid	NNP
37681	1512	3	does	do	VBZ
37681	1512	4	not	not	RB
37681	1512	5	use	use	VB
37681	1512	6	the	the	DT
37681	1512	7	curvilinear	curvilinear	NN
37681	1512	8	angle	angle	NN
37681	1512	9	,	,	,
37681	1512	10	and	and	CC
37681	1512	11	it	-PRON-	PRP
37681	1512	12	is	be	VBZ
37681	1512	13	only	only	RB
37681	1512	14	the	the	DT
37681	1512	15	rectilinear	rectilinear	JJ
37681	1512	16	angle	angle	NN
37681	1512	17	with	with	IN
37681	1512	18	which	which	WDT
37681	1512	19	we	-PRON-	PRP
37681	1512	20	are	be	VBP
37681	1512	21	concerned	concerned	JJ
37681	1512	22	,	,	,
37681	1512	23	we	-PRON-	PRP
37681	1512	24	will	will	MD
37681	1512	25	pass	pass	VB
37681	1512	26	to	to	IN
37681	1512	27	the	the	DT
37681	1512	28	next	next	JJ
37681	1512	29	definition	definition	NN
37681	1512	30	and	and	CC
37681	1512	31	consider	consider	VB
37681	1512	32	this	this	DT
37681	1512	33	one	one	NN
37681	1512	34	in	in	IN
37681	1512	35	connection	connection	NN
37681	1512	36	therewith	therewith	NN
37681	1512	37	.	.	.
37681	1513	1	9	9	CD
37681	1513	2	.	.	.
37681	1514	1	RECTILINEAR	RECTILINEAR	NNP
37681	1514	2	ANGLE	ANGLE	NNS
37681	1514	3	.	.	.
37681	1515	1	_	_	NNP
37681	1515	2	When	when	WRB
37681	1515	3	the	the	DT
37681	1515	4	lines	line	NNS
37681	1515	5	containing	contain	VBG
37681	1515	6	the	the	DT
37681	1515	7	angle	angle	NN
37681	1515	8	are	be	VBP
37681	1515	9	straight	straight	JJ
37681	1515	10	,	,	,
37681	1515	11	the	the	DT
37681	1515	12	angle	angle	NN
37681	1515	13	is	be	VBZ
37681	1515	14	called	call	VBN
37681	1515	15	rectilinear	rectilinear	JJ
37681	1515	16	.	.	.
37681	1515	17	_	_	NNP
37681	1515	18	This	this	DT
37681	1515	19	definition	definition	NN
37681	1515	20	,	,	,
37681	1515	21	taken	take	VBN
37681	1515	22	with	with	IN
37681	1515	23	the	the	DT
37681	1515	24	preceding	precede	VBG
37681	1515	25	one	one	CD
37681	1515	26	,	,	,
37681	1515	27	has	have	VBZ
37681	1515	28	always	always	RB
37681	1515	29	been	be	VBN
37681	1515	30	a	a	DT
37681	1515	31	subject	subject	NN
37681	1515	32	of	of	IN
37681	1515	33	criticism	criticism	NN
37681	1515	34	.	.	.
37681	1516	1	In	in	IN
37681	1516	2	the	the	DT
37681	1516	3	first	first	JJ
37681	1516	4	place	place	NN
37681	1516	5	it	-PRON-	PRP
37681	1516	6	expressly	expressly	RB
37681	1516	7	excludes	exclude	VBZ
37681	1516	8	the	the	DT
37681	1516	9	straight	straight	JJ
37681	1516	10	angle	angle	NN
37681	1516	11	,	,	,
37681	1516	12	and	and	CC
37681	1516	13	,	,	,
37681	1516	14	indeed	indeed	RB
37681	1516	15	,	,	,
37681	1516	16	the	the	DT
37681	1516	17	angles	angle	NNS
37681	1516	18	of	of	IN
37681	1516	19	Euclid	Euclid	NNP
37681	1516	20	are	be	VBP
37681	1516	21	always	always	RB
37681	1516	22	less	less	JJR
37681	1516	23	than	than	IN
37681	1516	24	180	180	CD
37681	1516	25	°	°	NNS
37681	1516	26	,	,	,
37681	1516	27	contrary	contrary	JJ
37681	1516	28	to	to	IN
37681	1516	29	our	-PRON-	PRP$
37681	1516	30	modern	modern	JJ
37681	1516	31	concept	concept	NN
37681	1516	32	.	.	.
37681	1517	1	In	in	IN
37681	1517	2	the	the	DT
37681	1517	3	second	second	JJ
37681	1517	4	place	place	NN
37681	1517	5	it	-PRON-	PRP
37681	1517	6	defines	define	VBZ
37681	1517	7	angle	angle	NN
37681	1517	8	by	by	IN
37681	1517	9	means	mean	NNS
37681	1517	10	of	of	IN
37681	1517	11	the	the	DT
37681	1517	12	word	word	NN
37681	1517	13	"	"	``
37681	1517	14	inclination	inclination	NN
37681	1517	15	,	,	,
37681	1517	16	"	"	''
37681	1517	17	which	which	WDT
37681	1517	18	is	be	VBZ
37681	1517	19	itself	-PRON-	PRP
37681	1517	20	as	as	RB
37681	1517	21	difficult	difficult	JJ
37681	1517	22	to	to	TO
37681	1517	23	define	define	VB
37681	1517	24	as	as	IN
37681	1517	25	angle	angle	NN
37681	1517	26	.	.	.
37681	1518	1	To	to	TO
37681	1518	2	remedy	remedy	VB
37681	1518	3	these	these	DT
37681	1518	4	defects	defect	NNS
37681	1518	5	many	many	JJ
37681	1518	6	substitutes	substitute	NNS
37681	1518	7	have	have	VBP
37681	1518	8	been	be	VBN
37681	1518	9	proposed	propose	VBN
37681	1518	10	.	.	.
37681	1519	1	Apollonius	Apollonius	NNP
37681	1519	2	defined	define	VBD
37681	1519	3	angle	angle	NN
37681	1519	4	as	as	IN
37681	1519	5	"	"	``
37681	1519	6	a	a	DT
37681	1519	7	contracting	contracting	NN
37681	1519	8	of	of	IN
37681	1519	9	a	a	DT
37681	1519	10	surface	surface	NN
37681	1519	11	or	or	CC
37681	1519	12	a	a	DT
37681	1519	13	solid	solid	JJ
37681	1519	14	at	at	IN
37681	1519	15	one	one	CD
37681	1519	16	point	point	NN
37681	1519	17	under	under	IN
37681	1519	18	a	a	DT
37681	1519	19	broken	broken	JJ
37681	1519	20	line	line	NN
37681	1519	21	or	or	CC
37681	1519	22	surface	surface	NN
37681	1519	23	.	.	.
37681	1519	24	"	"	''
37681	1520	1	Another	another	DT
37681	1520	2	of	of	IN
37681	1520	3	the	the	DT
37681	1520	4	Greeks	Greeks	NNPS
37681	1520	5	defined	define	VBD
37681	1520	6	it	-PRON-	PRP
37681	1520	7	as	as	IN
37681	1520	8	"	"	``
37681	1520	9	a	a	DT
37681	1520	10	quantity	quantity	NN
37681	1520	11	,	,	,
37681	1520	12	namely	namely	RB
37681	1520	13	,	,	,
37681	1520	14	a	a	DT
37681	1520	15	distance	distance	NN
37681	1520	16	between	between	IN
37681	1520	17	the	the	DT
37681	1520	18	lines	line	NNS
37681	1520	19	or	or	CC
37681	1520	20	surfaces	surface	NNS
37681	1520	21	containing	contain	VBG
37681	1520	22	it	-PRON-	PRP
37681	1520	23	.	.	.
37681	1520	24	"	"	''
37681	1521	1	Schotten[56	schotten[56	ADD
37681	1521	2	]	]	-RRB-
37681	1521	3	says	say	VBZ
37681	1521	4	that	that	IN
37681	1521	5	the	the	DT
37681	1521	6	definitions	definition	NNS
37681	1521	7	of	of	IN
37681	1521	8	angle	angle	NN
37681	1521	9	generally	generally	RB
37681	1521	10	fall	fall	VBP
37681	1521	11	into	into	IN
37681	1521	12	three	three	CD
37681	1521	13	groups	group	NNS
37681	1521	14	:	:	:
37681	1521	15	_	_	NNP
37681	1521	16	a.	a.	NN
37681	1521	17	_	_	NNP
37681	1521	18	An	an	DT
37681	1521	19	angle	angle	NN
37681	1521	20	is	be	VBZ
37681	1521	21	the	the	DT
37681	1521	22	difference	difference	NN
37681	1521	23	of	of	IN
37681	1521	24	direction	direction	NN
37681	1521	25	between	between	IN
37681	1521	26	two	two	CD
37681	1521	27	lines	line	NNS
37681	1521	28	that	that	WDT
37681	1521	29	meet	meet	VBP
37681	1521	30	.	.	.
37681	1522	1	This	this	DT
37681	1522	2	is	be	VBZ
37681	1522	3	no	no	RB
37681	1522	4	better	well	JJR
37681	1522	5	than	than	IN
37681	1522	6	Euclid	Euclid	NNP
37681	1522	7	's	's	POS
37681	1522	8	,	,	,
37681	1522	9	since	since	IN
37681	1522	10	"	"	``
37681	1522	11	difference	difference	NN
37681	1522	12	of	of	IN
37681	1522	13	direction	direction	NN
37681	1522	14	"	"	''
37681	1522	15	is	be	VBZ
37681	1522	16	as	as	RB
37681	1522	17	difficult	difficult	JJ
37681	1522	18	to	to	TO
37681	1522	19	define	define	VB
37681	1522	20	as	as	IN
37681	1522	21	"	"	``
37681	1522	22	inclination	inclination	NN
37681	1522	23	.	.	.
37681	1522	24	"	"	''
37681	1523	1	_	_	NNP
37681	1523	2	b.	b.	NN
37681	1523	3	_	_	NNP
37681	1523	4	An	an	DT
37681	1523	5	angle	angle	NN
37681	1523	6	is	be	VBZ
37681	1523	7	the	the	DT
37681	1523	8	amount	amount	NN
37681	1523	9	of	of	IN
37681	1523	10	turning	turn	VBG
37681	1523	11	necessary	necessary	JJ
37681	1523	12	to	to	TO
37681	1523	13	bring	bring	VB
37681	1523	14	one	one	CD
37681	1523	15	side	side	NN
37681	1523	16	to	to	IN
37681	1523	17	the	the	DT
37681	1523	18	position	position	NN
37681	1523	19	of	of	IN
37681	1523	20	the	the	DT
37681	1523	21	other	other	JJ
37681	1523	22	side	side	NN
37681	1523	23	.	.	.
37681	1524	1	_	_	NNP
37681	1524	2	c.	c.	NNP
37681	1524	3	_	_	NNP
37681	1524	4	An	an	DT
37681	1524	5	angle	angle	NN
37681	1524	6	is	be	VBZ
37681	1524	7	the	the	DT
37681	1524	8	portion	portion	NN
37681	1524	9	of	of	IN
37681	1524	10	the	the	DT
37681	1524	11	plane	plane	NN
37681	1524	12	included	include	VBN
37681	1524	13	between	between	IN
37681	1524	14	its	-PRON-	PRP$
37681	1524	15	sides	side	NNS
37681	1524	16	.	.	.
37681	1525	1	Of	of	IN
37681	1525	2	these	these	DT
37681	1525	3	,	,	,
37681	1525	4	_	_	NNP
37681	1525	5	b	b	NNP
37681	1525	6	_	_	NNP
37681	1525	7	is	be	VBZ
37681	1525	8	given	give	VBN
37681	1525	9	by	by	IN
37681	1525	10	way	way	NN
37681	1525	11	of	of	IN
37681	1525	12	explanation	explanation	NN
37681	1525	13	in	in	IN
37681	1525	14	most	most	JJS
37681	1525	15	modern	modern	JJ
37681	1525	16	textbooks	textbook	NNS
37681	1525	17	.	.	.
37681	1526	1	Indeed	indeed	RB
37681	1526	2	,	,	,
37681	1526	3	we	-PRON-	PRP
37681	1526	4	can	can	MD
37681	1526	5	not	not	RB
37681	1526	6	do	do	VB
37681	1526	7	better	well	RBR
37681	1526	8	than	than	IN
37681	1526	9	simply	simply	RB
37681	1526	10	to	to	TO
37681	1526	11	define	define	VB
37681	1526	12	an	an	DT
37681	1526	13	angle	angle	NN
37681	1526	14	as	as	IN
37681	1526	15	the	the	DT
37681	1526	16	opening	opening	NN
37681	1526	17	between	between	IN
37681	1526	18	two	two	CD
37681	1526	19	lines	line	NNS
37681	1526	20	which	which	WDT
37681	1526	21	meet	meet	VBP
37681	1526	22	,	,	,
37681	1526	23	and	and	CC
37681	1526	24	then	then	RB
37681	1526	25	explain	explain	VB
37681	1526	26	what	what	WP
37681	1526	27	is	be	VBZ
37681	1526	28	meant	mean	VBN
37681	1526	29	by	by	IN
37681	1526	30	size	size	NN
37681	1526	31	,	,	,
37681	1526	32	through	through	IN
37681	1526	33	the	the	DT
37681	1526	34	bringing	bringing	NN
37681	1526	35	in	in	RP
37681	1526	36	of	of	IN
37681	1526	37	the	the	DT
37681	1526	38	idea	idea	NN
37681	1526	39	of	of	IN
37681	1526	40	rotation	rotation	NN
37681	1526	41	.	.	.
37681	1527	1	This	this	DT
37681	1527	2	is	be	VBZ
37681	1527	3	a	a	DT
37681	1527	4	simple	simple	JJ
37681	1527	5	presentation	presentation	NN
37681	1527	6	,	,	,
37681	1527	7	it	-PRON-	PRP
37681	1527	8	is	be	VBZ
37681	1527	9	easily	easily	RB
37681	1527	10	understood	understand	VBN
37681	1527	11	,	,	,
37681	1527	12	and	and	CC
37681	1527	13	it	-PRON-	PRP
37681	1527	14	is	be	VBZ
37681	1527	15	sufficiently	sufficiently	RB
37681	1527	16	accurate	accurate	JJ
37681	1527	17	for	for	IN
37681	1527	18	the	the	DT
37681	1527	19	real	real	JJ
37681	1527	20	purpose	purpose	NN
37681	1527	21	in	in	IN
37681	1527	22	mind	mind	NN
37681	1527	23	,	,	,
37681	1527	24	namely	namely	RB
37681	1527	25	,	,	,
37681	1527	26	the	the	DT
37681	1527	27	grasping	grasping	NN
37681	1527	28	of	of	IN
37681	1527	29	the	the	DT
37681	1527	30	concept	concept	NN
37681	1527	31	.	.	.
37681	1528	1	We	-PRON-	PRP
37681	1528	2	should	should	MD
37681	1528	3	frankly	frankly	RB
37681	1528	4	acknowledge	acknowledge	VB
37681	1528	5	that	that	IN
37681	1528	6	the	the	DT
37681	1528	7	concept	concept	NN
37681	1528	8	of	of	IN
37681	1528	9	angle	angle	NN
37681	1528	10	is	be	VBZ
37681	1528	11	such	such	PDT
37681	1528	12	a	a	DT
37681	1528	13	simple	simple	JJ
37681	1528	14	one	one	NN
37681	1528	15	that	that	WDT
37681	1528	16	a	a	DT
37681	1528	17	satisfactory	satisfactory	JJ
37681	1528	18	definition	definition	NN
37681	1528	19	is	be	VBZ
37681	1528	20	impossible	impossible	JJ
37681	1528	21	,	,	,
37681	1528	22	and	and	CC
37681	1528	23	we	-PRON-	PRP
37681	1528	24	should	should	MD
37681	1528	25	therefore	therefore	RB
37681	1528	26	confine	confine	VB
37681	1528	27	our	-PRON-	PRP$
37681	1528	28	attention	attention	NN
37681	1528	29	to	to	IN
37681	1528	30	having	have	VBG
37681	1528	31	the	the	DT
37681	1528	32	concept	concept	NN
37681	1528	33	understood	understand	VBN
37681	1528	34	.	.	.
37681	1529	1	10	10	CD
37681	1529	2	.	.	.
37681	1530	1	_	_	NNP
37681	1530	2	When	when	WRB
37681	1530	3	a	a	DT
37681	1530	4	straight	straight	JJ
37681	1530	5	line	line	NN
37681	1530	6	set	set	VBN
37681	1530	7	up	up	RP
37681	1530	8	on	on	IN
37681	1530	9	a	a	DT
37681	1530	10	straight	straight	JJ
37681	1530	11	line	line	NN
37681	1530	12	makes	make	VBZ
37681	1530	13	the	the	DT
37681	1530	14	adjacent	adjacent	JJ
37681	1530	15	angles	angle	NNS
37681	1530	16	equal	equal	JJ
37681	1530	17	to	to	IN
37681	1530	18	one	one	CD
37681	1530	19	another	another	DT
37681	1530	20	,	,	,
37681	1530	21	each	each	DT
37681	1530	22	of	of	IN
37681	1530	23	the	the	DT
37681	1530	24	equal	equal	JJ
37681	1530	25	angles	angle	NNS
37681	1530	26	is	be	VBZ
37681	1530	27	right	right	JJ
37681	1530	28	,	,	,
37681	1530	29	and	and	CC
37681	1530	30	the	the	DT
37681	1530	31	straight	straight	JJ
37681	1530	32	line	line	NN
37681	1530	33	standing	stand	VBG
37681	1530	34	on	on	IN
37681	1530	35	the	the	DT
37681	1530	36	other	other	JJ
37681	1530	37	is	be	VBZ
37681	1530	38	called	call	VBN
37681	1530	39	a	a	DT
37681	1530	40	perpendicular	perpendicular	NN
37681	1530	41	to	to	IN
37681	1530	42	that	that	DT
37681	1530	43	on	on	IN
37681	1530	44	which	which	WDT
37681	1530	45	it	-PRON-	PRP
37681	1530	46	stands	stand	VBZ
37681	1530	47	.	.	.
37681	1530	48	_	_	IN
37681	1530	49	We	-PRON-	PRP
37681	1530	50	at	at	IN
37681	1530	51	present	present	JJ
37681	1530	52	separate	separate	JJ
37681	1530	53	these	these	DT
37681	1530	54	definitions	definition	NNS
37681	1530	55	and	and	CC
37681	1530	56	simplify	simplify	VB
37681	1530	57	the	the	DT
37681	1530	58	language	language	NN
37681	1530	59	.	.	.
37681	1531	1	11	11	CD
37681	1531	2	.	.	.
37681	1532	1	_	_	NNP
37681	1532	2	An	an	DT
37681	1532	3	obtuse	obtuse	JJ
37681	1532	4	angle	angle	NN
37681	1532	5	is	be	VBZ
37681	1532	6	an	an	DT
37681	1532	7	angle	angle	NN
37681	1532	8	greater	great	JJR
37681	1532	9	than	than	IN
37681	1532	10	a	a	DT
37681	1532	11	right	right	JJ
37681	1532	12	angle	angle	NN
37681	1532	13	.	.	.
37681	1532	14	_	_	NNP
37681	1532	15	12	12	CD
37681	1532	16	.	.	.
37681	1533	1	_	_	NNP
37681	1533	2	An	an	DT
37681	1533	3	acute	acute	JJ
37681	1533	4	angle	angle	NN
37681	1533	5	is	be	VBZ
37681	1533	6	an	an	DT
37681	1533	7	angle	angle	NN
37681	1533	8	less	less	JJR
37681	1533	9	than	than	IN
37681	1533	10	a	a	DT
37681	1533	11	right	right	JJ
37681	1533	12	angle	angle	NN
37681	1533	13	.	.	.
37681	1533	14	_	_	NNP
37681	1533	15	The	the	DT
37681	1533	16	question	question	NN
37681	1533	17	sometimes	sometimes	RB
37681	1533	18	asked	ask	VBD
37681	1533	19	as	as	IN
37681	1533	20	to	to	IN
37681	1533	21	whether	whether	IN
37681	1533	22	an	an	DT
37681	1533	23	angle	angle	NN
37681	1533	24	of	of	IN
37681	1533	25	200	200	CD
37681	1533	26	°	°	NNS
37681	1533	27	is	be	VBZ
37681	1533	28	obtuse	obtuse	JJ
37681	1533	29	,	,	,
37681	1533	30	and	and	CC
37681	1533	31	whether	whether	IN
37681	1533	32	a	a	DT
37681	1533	33	negative	negative	JJ
37681	1533	34	angle	angle	NN
37681	1533	35	,	,	,
37681	1533	36	say	say	VBP
37681	1533	37	-90	-90	NN
37681	1533	38	°	°	NNS
37681	1533	39	,	,	,
37681	1533	40	is	be	VBZ
37681	1533	41	acute	acute	JJ
37681	1533	42	,	,	,
37681	1533	43	is	be	VBZ
37681	1533	44	answered	answer	VBN
37681	1533	45	by	by	IN
37681	1533	46	saying	say	VBG
37681	1533	47	that	that	IN
37681	1533	48	Euclid	Euclid	NNP
37681	1533	49	did	do	VBD
37681	1533	50	not	not	RB
37681	1533	51	conceive	conceive	VB
37681	1533	52	of	of	IN
37681	1533	53	angles	angle	NNS
37681	1533	54	equal	equal	JJ
37681	1533	55	to	to	IN
37681	1533	56	or	or	CC
37681	1533	57	greater	great	JJR
37681	1533	58	than	than	IN
37681	1533	59	180	180	CD
37681	1533	60	°	°	NNS
37681	1533	61	and	and	CC
37681	1533	62	had	have	VBD
37681	1533	63	no	no	DT
37681	1533	64	notion	notion	NN
37681	1533	65	of	of	IN
37681	1533	66	negative	negative	JJ
37681	1533	67	quantities	quantity	NNS
37681	1533	68	.	.	.
37681	1534	1	Generally	generally	RB
37681	1534	2	to	to	IN
37681	1534	3	-	-	HYPH
37681	1534	4	day	day	NN
37681	1534	5	we	-PRON-	PRP
37681	1534	6	define	define	VBP
37681	1534	7	an	an	DT
37681	1534	8	obtuse	obtuse	JJ
37681	1534	9	angle	angle	NN
37681	1534	10	as	as	IN
37681	1534	11	"	"	``
37681	1534	12	greater	great	JJR
37681	1534	13	than	than	IN
37681	1534	14	one	one	CD
37681	1534	15	and	and	CC
37681	1534	16	less	less	JJR
37681	1534	17	than	than	IN
37681	1534	18	two	two	CD
37681	1534	19	right	right	JJ
37681	1534	20	angles	angle	NNS
37681	1534	21	.	.	.
37681	1534	22	"	"	''
37681	1535	1	An	an	DT
37681	1535	2	acute	acute	JJ
37681	1535	3	angle	angle	NN
37681	1535	4	is	be	VBZ
37681	1535	5	defined	define	VBN
37681	1535	6	as	as	IN
37681	1535	7	"	"	``
37681	1535	8	an	an	DT
37681	1535	9	angle	angle	NN
37681	1535	10	less	less	JJR
37681	1535	11	than	than	IN
37681	1535	12	a	a	DT
37681	1535	13	right	right	JJ
37681	1535	14	angle	angle	NN
37681	1535	15	,	,	,
37681	1535	16	"	"	''
37681	1535	17	and	and	CC
37681	1535	18	is	be	VBZ
37681	1535	19	considered	consider	VBN
37681	1535	20	as	as	RB
37681	1535	21	positive	positive	JJ
37681	1535	22	under	under	IN
37681	1535	23	the	the	DT
37681	1535	24	general	general	JJ
37681	1535	25	understanding	understanding	NN
37681	1535	26	that	that	WDT
37681	1535	27	all	all	DT
37681	1535	28	geometric	geometric	JJ
37681	1535	29	magnitudes	magnitude	NNS
37681	1535	30	are	be	VBP
37681	1535	31	positive	positive	JJ
37681	1535	32	unless	unless	IN
37681	1535	33	the	the	DT
37681	1535	34	contrary	contrary	NN
37681	1535	35	is	be	VBZ
37681	1535	36	stated	state	VBN
37681	1535	37	.	.	.
37681	1536	1	13	13	CD
37681	1536	2	.	.	.
37681	1537	1	_	_	NNP
37681	1537	2	A	a	DT
37681	1537	3	boundary	boundary	NN
37681	1537	4	is	be	VBZ
37681	1537	5	that	that	DT
37681	1537	6	which	which	WDT
37681	1537	7	is	be	VBZ
37681	1537	8	an	an	DT
37681	1537	9	extremity	extremity	NN
37681	1537	10	of	of	IN
37681	1537	11	anything	anything	NN
37681	1537	12	.	.	.
37681	1537	13	_	_	NNP
37681	1537	14	The	the	DT
37681	1537	15	definition	definition	NN
37681	1537	16	is	be	VBZ
37681	1537	17	not	not	RB
37681	1537	18	exactly	exactly	RB
37681	1537	19	satisfactory	satisfactory	JJ
37681	1537	20	,	,	,
37681	1537	21	for	for	IN
37681	1537	22	a	a	DT
37681	1537	23	circle	circle	NN
37681	1537	24	is	be	VBZ
37681	1537	25	the	the	DT
37681	1537	26	boundary	boundary	NN
37681	1537	27	of	of	IN
37681	1537	28	the	the	DT
37681	1537	29	space	space	NN
37681	1537	30	inclosed	inclose	VBN
37681	1537	31	,	,	,
37681	1537	32	but	but	CC
37681	1537	33	we	-PRON-	PRP
37681	1537	34	hardly	hardly	RB
37681	1537	35	consider	consider	VBP
37681	1537	36	it	-PRON-	PRP
37681	1537	37	as	as	IN
37681	1537	38	the	the	DT
37681	1537	39	extremity	extremity	NN
37681	1537	40	of	of	IN
37681	1537	41	that	that	DT
37681	1537	42	space	space	NN
37681	1537	43	.	.	.
37681	1538	1	Euclid	Euclid	NNP
37681	1538	2	wishes	wish	VBZ
37681	1538	3	the	the	DT
37681	1538	4	definition	definition	NN
37681	1538	5	before	before	IN
37681	1538	6	No	no	UH
37681	1538	7	.	.	.
37681	1539	1	14	14	CD
37681	1539	2	.	.	.
37681	1540	1	14	14	CD
37681	1540	2	.	.	.
37681	1541	1	_	_	NNP
37681	1541	2	A	a	DT
37681	1541	3	figure	figure	NN
37681	1541	4	is	be	VBZ
37681	1541	5	that	that	DT
37681	1541	6	which	which	WDT
37681	1541	7	is	be	VBZ
37681	1541	8	contained	contain	VBN
37681	1541	9	by	by	IN
37681	1541	10	any	any	DT
37681	1541	11	boundary	boundary	NN
37681	1541	12	or	or	CC
37681	1541	13	boundaries	boundary	NNS
37681	1541	14	.	.	.
37681	1541	15	_	_	NNP
37681	1541	16	The	the	DT
37681	1541	17	definition	definition	NN
37681	1541	18	is	be	VBZ
37681	1541	19	not	not	RB
37681	1541	20	satisfactory	satisfactory	JJ
37681	1541	21	,	,	,
37681	1541	22	since	since	IN
37681	1541	23	it	-PRON-	PRP
37681	1541	24	excludes	exclude	VBZ
37681	1541	25	the	the	DT
37681	1541	26	unlimited	unlimited	JJ
37681	1541	27	straight	straight	JJ
37681	1541	28	line	line	NN
37681	1541	29	,	,	,
37681	1541	30	the	the	DT
37681	1541	31	angle	angle	NN
37681	1541	32	,	,	,
37681	1541	33	an	an	DT
37681	1541	34	assemblage	assemblage	NN
37681	1541	35	of	of	IN
37681	1541	36	points	point	NNS
37681	1541	37	,	,	,
37681	1541	38	and	and	CC
37681	1541	39	other	other	JJ
37681	1541	40	combinations	combination	NNS
37681	1541	41	of	of	IN
37681	1541	42	lines	line	NNS
37681	1541	43	and	and	CC
37681	1541	44	points	point	NNS
37681	1541	45	which	which	WDT
37681	1541	46	we	-PRON-	PRP
37681	1541	47	should	should	MD
37681	1541	48	now	now	RB
37681	1541	49	consider	consider	VB
37681	1541	50	as	as	IN
37681	1541	51	figures	figure	NNS
37681	1541	52	.	.	.
37681	1542	1	15	15	CD
37681	1542	2	.	.	.
37681	1543	1	_	_	NNP
37681	1543	2	A	a	DT
37681	1543	3	circle	circle	NN
37681	1543	4	is	be	VBZ
37681	1543	5	a	a	DT
37681	1543	6	plane	plane	NN
37681	1543	7	figure	figure	NN
37681	1543	8	contained	contain	VBN
37681	1543	9	by	by	IN
37681	1543	10	one	one	CD
37681	1543	11	line	line	NN
37681	1543	12	such	such	JJ
37681	1543	13	that	that	IN
37681	1543	14	all	all	PDT
37681	1543	15	the	the	DT
37681	1543	16	straight	straight	JJ
37681	1543	17	lines	line	NNS
37681	1543	18	falling	fall	VBG
37681	1543	19	upon	upon	IN
37681	1543	20	it	-PRON-	PRP
37681	1543	21	from	from	IN
37681	1543	22	one	one	CD
37681	1543	23	point	point	NN
37681	1543	24	among	among	IN
37681	1543	25	those	those	DT
37681	1543	26	lying	lie	VBG
37681	1543	27	within	within	IN
37681	1543	28	the	the	DT
37681	1543	29	figure	figure	NN
37681	1543	30	are	be	VBP
37681	1543	31	equal	equal	JJ
37681	1543	32	to	to	IN
37681	1543	33	one	one	CD
37681	1543	34	another	another	DT
37681	1543	35	.	.	.
37681	1543	36	_	_	NNP
37681	1543	37	16	16	CD
37681	1543	38	.	.	.
37681	1544	1	_	_	NNP
37681	1544	2	And	and	CC
37681	1544	3	the	the	DT
37681	1544	4	point	point	NN
37681	1544	5	is	be	VBZ
37681	1544	6	called	call	VBN
37681	1544	7	the	the	DT
37681	1544	8	center	center	NN
37681	1544	9	of	of	IN
37681	1544	10	the	the	DT
37681	1544	11	circle	circle	NN
37681	1544	12	.	.	.
37681	1544	13	_	_	NNP
37681	1544	14	Some	some	DT
37681	1544	15	commentators	commentator	NNS
37681	1544	16	add	add	VBP
37681	1544	17	after	after	IN
37681	1544	18	"	"	``
37681	1544	19	one	one	CD
37681	1544	20	line	line	NN
37681	1544	21	,	,	,
37681	1544	22	"	"	''
37681	1544	23	definition	definition	NN
37681	1544	24	15	15	CD
37681	1544	25	,	,	,
37681	1544	26	the	the	DT
37681	1544	27	words	word	NNS
37681	1544	28	"	"	``
37681	1544	29	which	which	WDT
37681	1544	30	is	be	VBZ
37681	1544	31	called	call	VBN
37681	1544	32	the	the	DT
37681	1544	33	circumference	circumference	NN
37681	1544	34	,	,	,
37681	1544	35	"	"	``
37681	1544	36	but	but	CC
37681	1544	37	these	these	DT
37681	1544	38	are	be	VBP
37681	1544	39	not	not	RB
37681	1544	40	in	in	IN
37681	1544	41	the	the	DT
37681	1544	42	oldest	old	JJS
37681	1544	43	manuscripts	manuscript	NNS
37681	1544	44	.	.	.
37681	1545	1	The	the	DT
37681	1545	2	Greek	greek	JJ
37681	1545	3	idea	idea	NN
37681	1545	4	of	of	IN
37681	1545	5	a	a	DT
37681	1545	6	circle	circle	NN
37681	1545	7	was	be	VBD
37681	1545	8	usually	usually	RB
37681	1545	9	that	that	DT
37681	1545	10	of	of	IN
37681	1545	11	part	part	NN
37681	1545	12	of	of	IN
37681	1545	13	a	a	DT
37681	1545	14	plane	plane	NN
37681	1545	15	which	which	WDT
37681	1545	16	is	be	VBZ
37681	1545	17	bounded	bound	VBN
37681	1545	18	by	by	IN
37681	1545	19	a	a	DT
37681	1545	20	line	line	NN
37681	1545	21	called	call	VBN
37681	1545	22	in	in	IN
37681	1545	23	modern	modern	JJ
37681	1545	24	times	time	NNS
37681	1545	25	the	the	DT
37681	1545	26	circumference	circumference	NN
37681	1545	27	,	,	,
37681	1545	28	although	although	IN
37681	1545	29	Aristotle	Aristotle	NNP
37681	1545	30	used	use	VBD
37681	1545	31	"	"	``
37681	1545	32	circle	circle	NN
37681	1545	33	"	"	''
37681	1545	34	as	as	IN
37681	1545	35	synonymous	synonymous	JJ
37681	1545	36	with	with	IN
37681	1545	37	"	"	``
37681	1545	38	the	the	DT
37681	1545	39	bounding	bound	VBG
37681	1545	40	line	line	NN
37681	1545	41	.	.	.
37681	1545	42	"	"	''
37681	1546	1	With	with	IN
37681	1546	2	the	the	DT
37681	1546	3	growth	growth	NN
37681	1546	4	of	of	IN
37681	1546	5	modern	modern	JJ
37681	1546	6	mathematics	mathematic	NNS
37681	1546	7	,	,	,
37681	1546	8	however	however	RB
37681	1546	9	,	,	,
37681	1546	10	and	and	CC
37681	1546	11	particularly	particularly	RB
37681	1546	12	as	as	IN
37681	1546	13	a	a	DT
37681	1546	14	result	result	NN
37681	1546	15	of	of	IN
37681	1546	16	the	the	DT
37681	1546	17	development	development	NN
37681	1546	18	of	of	IN
37681	1546	19	analytic	analytic	JJ
37681	1546	20	geometry	geometry	NN
37681	1546	21	,	,	,
37681	1546	22	the	the	DT
37681	1546	23	word	word	NN
37681	1546	24	"	"	``
37681	1546	25	circle	circle	NN
37681	1546	26	"	"	''
37681	1546	27	has	have	VBZ
37681	1546	28	come	come	VBN
37681	1546	29	to	to	TO
37681	1546	30	mean	mean	VB
37681	1546	31	the	the	DT
37681	1546	32	bounding	bound	VBG
37681	1546	33	line	line	NN
37681	1546	34	,	,	,
37681	1546	35	as	as	IN
37681	1546	36	it	-PRON-	PRP
37681	1546	37	did	do	VBD
37681	1546	38	with	with	IN
37681	1546	39	Aristotle	Aristotle	NNP
37681	1546	40	,	,	,
37681	1546	41	a	a	DT
37681	1546	42	century	century	NN
37681	1546	43	before	before	IN
37681	1546	44	Euclid	Euclid	NNP
37681	1546	45	's	's	POS
37681	1546	46	time	time	NN
37681	1546	47	.	.	.
37681	1547	1	This	this	DT
37681	1547	2	has	have	VBZ
37681	1547	3	grown	grow	VBN
37681	1547	4	out	out	IN
37681	1547	5	of	of	IN
37681	1547	6	the	the	DT
37681	1547	7	equations	equation	NNS
37681	1547	8	of	of	IN
37681	1547	9	the	the	DT
37681	1547	10	various	various	JJ
37681	1547	11	curves	curve	NNS
37681	1547	12	,	,	,
37681	1547	13	_	_	NNP
37681	1547	14	x_^2	x_^2	NNP
37681	1547	15	+	+	SYM
37681	1547	16	_	_	NNP
37681	1547	17	y_^2	y_^2	NNP
37681	1547	18	=	=	SYM
37681	1547	19	_	_	NNP
37681	1547	20	r_^2	r_^2	NNP
37681	1547	21	representing	represent	VBG
37681	1547	22	the	the	DT
37681	1547	23	circle-_line	circle-_line	NN
37681	1547	24	_	_	NNP
37681	1547	25	,	,	,
37681	1547	26	_	_	NNP
37681	1547	27	a_^2_y_^2	a_^2_y_^2	CD
37681	1547	28	+	+	SYM
37681	1547	29	_	_	NNP
37681	1547	30	b_^2_x_^2	b_^2_x_^2	NNP
37681	1547	31	=	=	SYM
37681	1547	32	_	_	NNP
37681	1547	33	a_^2_b_^2	a_^2_b_^2	NNP
37681	1547	34	representing	represent	VBG
37681	1547	35	the	the	DT
37681	1547	36	ellipse-_line	ellipse-_line	NN
37681	1547	37	_	_	NNP
37681	1547	38	,	,	,
37681	1547	39	and	and	CC
37681	1547	40	so	so	RB
37681	1547	41	on	on	RB
37681	1547	42	.	.	.
37681	1548	1	It	-PRON-	PRP
37681	1548	2	is	be	VBZ
37681	1548	3	natural	natural	JJ
37681	1548	4	,	,	,
37681	1548	5	therefore	therefore	RB
37681	1548	6	,	,	,
37681	1548	7	that	that	DT
37681	1548	8	circle	circle	NN
37681	1548	9	,	,	,
37681	1548	10	ellipse	ellipse	VB
37681	1548	11	,	,	,
37681	1548	12	parabola	parabola	NNP
37681	1548	13	,	,	,
37681	1548	14	and	and	CC
37681	1548	15	hyperbola	hyperbola	NNP
37681	1548	16	should	should	MD
37681	1548	17	all	all	DT
37681	1548	18	be	be	VB
37681	1548	19	looked	look	VBN
37681	1548	20	upon	upon	IN
37681	1548	21	as	as	IN
37681	1548	22	lines	line	NNS
37681	1548	23	.	.	.
37681	1549	1	Since	since	IN
37681	1549	2	this	this	DT
37681	1549	3	is	be	VBZ
37681	1549	4	the	the	DT
37681	1549	5	modern	modern	JJ
37681	1549	6	use	use	NN
37681	1549	7	of	of	IN
37681	1549	8	"	"	``
37681	1549	9	circle	circle	NN
37681	1549	10	"	"	''
37681	1549	11	in	in	IN
37681	1549	12	English	English	NNP
37681	1549	13	,	,	,
37681	1549	14	it	-PRON-	PRP
37681	1549	15	has	have	VBZ
37681	1549	16	naturally	naturally	RB
37681	1549	17	found	find	VBN
37681	1549	18	its	-PRON-	PRP$
37681	1549	19	way	way	NN
37681	1549	20	into	into	IN
37681	1549	21	elementary	elementary	JJ
37681	1549	22	geometry	geometry	NN
37681	1549	23	,	,	,
37681	1549	24	in	in	IN
37681	1549	25	order	order	NN
37681	1549	26	that	that	IN
37681	1549	27	students	student	NNS
37681	1549	28	should	should	MD
37681	1549	29	not	not	RB
37681	1549	30	have	have	VB
37681	1549	31	to	to	TO
37681	1549	32	form	form	VB
37681	1549	33	an	an	DT
37681	1549	34	entirely	entirely	RB
37681	1549	35	different	different	JJ
37681	1549	36	idea	idea	NN
37681	1549	37	of	of	IN
37681	1549	38	circle	circle	NN
37681	1549	39	on	on	IN
37681	1549	40	beginning	begin	VBG
37681	1549	41	analytic	analytic	JJ
37681	1549	42	geometry	geometry	NN
37681	1549	43	.	.	.
37681	1550	1	The	the	DT
37681	1550	2	general	general	JJ
37681	1550	3	body	body	NN
37681	1550	4	of	of	IN
37681	1550	5	American	american	JJ
37681	1550	6	teachers	teacher	NNS
37681	1550	7	,	,	,
37681	1550	8	therefore	therefore	RB
37681	1550	9	,	,	,
37681	1550	10	at	at	IN
37681	1550	11	present	present	JJ
37681	1550	12	favors	favor	NNS
37681	1550	13	using	use	VBG
37681	1550	14	"	"	``
37681	1550	15	circle	circle	NN
37681	1550	16	"	"	''
37681	1550	17	to	to	TO
37681	1550	18	mean	mean	VB
37681	1550	19	the	the	DT
37681	1550	20	bounding	bound	VBG
37681	1550	21	line	line	NN
37681	1550	22	and	and	CC
37681	1550	23	"	"	``
37681	1550	24	circumference	circumference	NN
37681	1550	25	"	"	''
37681	1550	26	to	to	TO
37681	1550	27	mean	mean	VB
37681	1550	28	the	the	DT
37681	1550	29	length	length	NN
37681	1550	30	of	of	IN
37681	1550	31	that	that	DT
37681	1550	32	line	line	NN
37681	1550	33	.	.	.
37681	1551	1	This	this	DT
37681	1551	2	requires	require	VBZ
37681	1551	3	redefining	redefine	VBG
37681	1551	4	"	"	``
37681	1551	5	area	area	NN
37681	1551	6	of	of	IN
37681	1551	7	a	a	DT
37681	1551	8	circle	circle	NN
37681	1551	9	,	,	,
37681	1551	10	"	"	''
37681	1551	11	and	and	CC
37681	1551	12	this	this	DT
37681	1551	13	is	be	VBZ
37681	1551	14	done	do	VBN
37681	1551	15	by	by	IN
37681	1551	16	saying	say	VBG
37681	1551	17	that	that	IN
37681	1551	18	it	-PRON-	PRP
37681	1551	19	is	be	VBZ
37681	1551	20	the	the	DT
37681	1551	21	area	area	NN
37681	1551	22	of	of	IN
37681	1551	23	the	the	DT
37681	1551	24	plane	plane	NN
37681	1551	25	space	space	NN
37681	1551	26	inclosed	inclose	VBD
37681	1551	27	.	.	.
37681	1552	1	The	the	DT
37681	1552	2	matter	matter	NN
37681	1552	3	is	be	VBZ
37681	1552	4	not	not	RB
37681	1552	5	of	of	IN
37681	1552	6	greatest	great	JJS
37681	1552	7	consequence	consequence	NN
37681	1552	8	,	,	,
37681	1552	9	but	but	CC
37681	1552	10	teachers	teacher	NNS
37681	1552	11	will	will	MD
37681	1552	12	probably	probably	RB
37681	1552	13	prefer	prefer	VB
37681	1552	14	to	to	TO
37681	1552	15	join	join	VB
37681	1552	16	in	in	IN
37681	1552	17	the	the	DT
37681	1552	18	modern	modern	JJ
37681	1552	19	American	american	JJ
37681	1552	20	usage	usage	NN
37681	1552	21	of	of	IN
37681	1552	22	the	the	DT
37681	1552	23	term	term	NN
37681	1552	24	.	.	.
37681	1553	1	17	17	CD
37681	1553	2	.	.	.
37681	1554	1	DIAMETER	DIAMETER	NNP
37681	1554	2	.	.	.
37681	1555	1	_	_	NNP
37681	1555	2	A	a	DT
37681	1555	3	diameter	diameter	NN
37681	1555	4	of	of	IN
37681	1555	5	the	the	DT
37681	1555	6	circle	circle	NN
37681	1555	7	is	be	VBZ
37681	1555	8	any	any	DT
37681	1555	9	straight	straight	JJ
37681	1555	10	line	line	NN
37681	1555	11	drawn	draw	VBN
37681	1555	12	through	through	IN
37681	1555	13	the	the	DT
37681	1555	14	center	center	NN
37681	1555	15	and	and	CC
37681	1555	16	terminated	terminate	VBN
37681	1555	17	in	in	IN
37681	1555	18	both	both	DT
37681	1555	19	directions	direction	NNS
37681	1555	20	by	by	IN
37681	1555	21	the	the	DT
37681	1555	22	circumference	circumference	NN
37681	1555	23	of	of	IN
37681	1555	24	the	the	DT
37681	1555	25	circle	circle	NN
37681	1555	26	,	,	,
37681	1555	27	and	and	CC
37681	1555	28	such	such	PDT
37681	1555	29	a	a	DT
37681	1555	30	straight	straight	JJ
37681	1555	31	line	line	NN
37681	1555	32	also	also	RB
37681	1555	33	bisects	bisect	VBZ
37681	1555	34	the	the	DT
37681	1555	35	circle	circle	NN
37681	1555	36	.	.	.
37681	1555	37	_	_	NNP
37681	1555	38	The	the	DT
37681	1555	39	word	word	NN
37681	1555	40	"	"	``
37681	1555	41	diameter	diameter	NN
37681	1555	42	"	"	''
37681	1555	43	is	be	VBZ
37681	1555	44	from	from	IN
37681	1555	45	two	two	CD
37681	1555	46	Greek	greek	JJ
37681	1555	47	words	word	NNS
37681	1555	48	meaning	mean	VBG
37681	1555	49	a	a	DT
37681	1555	50	"	"	``
37681	1555	51	through	through	IN
37681	1555	52	measurer	measurer	NN
37681	1555	53	,	,	,
37681	1555	54	"	"	''
37681	1555	55	and	and	CC
37681	1555	56	it	-PRON-	PRP
37681	1555	57	was	be	VBD
37681	1555	58	also	also	RB
37681	1555	59	used	use	VBN
37681	1555	60	by	by	IN
37681	1555	61	Euclid	Euclid	NNP
37681	1555	62	for	for	IN
37681	1555	63	the	the	DT
37681	1555	64	diagonal	diagonal	NN
37681	1555	65	of	of	IN
37681	1555	66	a	a	DT
37681	1555	67	square	square	NN
37681	1555	68	,	,	,
37681	1555	69	and	and	CC
37681	1555	70	more	more	RBR
37681	1555	71	generally	generally	RB
37681	1555	72	for	for	IN
37681	1555	73	the	the	DT
37681	1555	74	diagonal	diagonal	JJ
37681	1555	75	of	of	IN
37681	1555	76	any	any	DT
37681	1555	77	parallelogram	parallelogram	NN
37681	1555	78	.	.	.
37681	1556	1	The	the	DT
37681	1556	2	word	word	NN
37681	1556	3	"	"	``
37681	1556	4	diagonal	diagonal	JJ
37681	1556	5	"	"	''
37681	1556	6	is	be	VBZ
37681	1556	7	a	a	DT
37681	1556	8	later	later	JJ
37681	1556	9	term	term	NN
37681	1556	10	and	and	CC
37681	1556	11	means	mean	VBZ
37681	1556	12	the	the	DT
37681	1556	13	"	"	``
37681	1556	14	through	through	IN
37681	1556	15	angle	angle	NN
37681	1556	16	.	.	.
37681	1556	17	"	"	''
37681	1557	1	It	-PRON-	PRP
37681	1557	2	will	will	MD
37681	1557	3	be	be	VB
37681	1557	4	noticed	notice	VBN
37681	1557	5	that	that	IN
37681	1557	6	Euclid	Euclid	NNP
37681	1557	7	adds	add	VBZ
37681	1557	8	to	to	IN
37681	1557	9	the	the	DT
37681	1557	10	usual	usual	JJ
37681	1557	11	definition	definition	NN
37681	1557	12	the	the	DT
37681	1557	13	statement	statement	NN
37681	1557	14	that	that	IN
37681	1557	15	a	a	DT
37681	1557	16	diameter	diameter	NN
37681	1557	17	bisects	bisect	VBZ
37681	1557	18	the	the	DT
37681	1557	19	circle	circle	NN
37681	1557	20	.	.	.
37681	1558	1	He	-PRON-	PRP
37681	1558	2	does	do	VBZ
37681	1558	3	this	this	DT
37681	1558	4	apparently	apparently	RB
37681	1558	5	to	to	TO
37681	1558	6	justify	justify	VB
37681	1558	7	his	-PRON-	PRP$
37681	1558	8	definition	definition	NN
37681	1558	9	(	(	-LRB-
37681	1558	10	18	18	CD
37681	1558	11	)	)	-RRB-
37681	1558	12	,	,	,
37681	1558	13	of	of	IN
37681	1558	14	a	a	DT
37681	1558	15	semicircle	semicircle	NN
37681	1558	16	(	(	-LRB-
37681	1558	17	a	a	DT
37681	1558	18	half	half	NN
37681	1558	19	circle	circle	NN
37681	1558	20	)	)	-RRB-
37681	1558	21	.	.	.
37681	1559	1	Thales	thale	NNS
37681	1559	2	is	be	VBZ
37681	1559	3	said	say	VBN
37681	1559	4	to	to	TO
37681	1559	5	have	have	VB
37681	1559	6	been	be	VBN
37681	1559	7	the	the	DT
37681	1559	8	first	first	JJ
37681	1559	9	to	to	TO
37681	1559	10	prove	prove	VB
37681	1559	11	that	that	IN
37681	1559	12	a	a	DT
37681	1559	13	diameter	diameter	NN
37681	1559	14	bisects	bisect	VBZ
37681	1559	15	the	the	DT
37681	1559	16	circle	circle	NN
37681	1559	17	,	,	,
37681	1559	18	this	this	DT
37681	1559	19	being	be	VBG
37681	1559	20	one	one	CD
37681	1559	21	of	of	IN
37681	1559	22	three	three	CD
37681	1559	23	or	or	CC
37681	1559	24	four	four	CD
37681	1559	25	propositions	proposition	NNS
37681	1559	26	definitely	definitely	RB
37681	1559	27	attributed	attribute	VBD
37681	1559	28	to	to	IN
37681	1559	29	him	-PRON-	PRP
37681	1559	30	,	,	,
37681	1559	31	and	and	CC
37681	1559	32	it	-PRON-	PRP
37681	1559	33	is	be	VBZ
37681	1559	34	sometimes	sometimes	RB
37681	1559	35	given	give	VBN
37681	1559	36	as	as	IN
37681	1559	37	a	a	DT
37681	1559	38	proposition	proposition	NN
37681	1559	39	to	to	TO
37681	1559	40	be	be	VB
37681	1559	41	proved	prove	VBN
37681	1559	42	.	.	.
37681	1560	1	As	as	IN
37681	1560	2	a	a	DT
37681	1560	3	proposition	proposition	NN
37681	1560	4	,	,	,
37681	1560	5	however	however	RB
37681	1560	6	,	,	,
37681	1560	7	it	-PRON-	PRP
37681	1560	8	is	be	VBZ
37681	1560	9	unsatisfactory	unsatisfactory	JJ
37681	1560	10	,	,	,
37681	1560	11	since	since	IN
37681	1560	12	the	the	DT
37681	1560	13	proof	proof	NN
37681	1560	14	of	of	IN
37681	1560	15	what	what	WP
37681	1560	16	is	be	VBZ
37681	1560	17	so	so	RB
37681	1560	18	evident	evident	JJ
37681	1560	19	usually	usually	RB
37681	1560	20	instills	instill	VBZ
37681	1560	21	more	more	JJR
37681	1560	22	doubt	doubt	NN
37681	1560	23	than	than	IN
37681	1560	24	certainty	certainty	NN
37681	1560	25	in	in	IN
37681	1560	26	the	the	DT
37681	1560	27	minds	mind	NNS
37681	1560	28	of	of	IN
37681	1560	29	beginners	beginner	NNS
37681	1560	30	.	.	.
37681	1561	1	18	18	CD
37681	1561	2	.	.	.
37681	1562	1	SEMICIRCLE	SEMICIRCLE	VBN
37681	1562	2	.	.	.
37681	1563	1	_	_	NNP
37681	1563	2	A	a	DT
37681	1563	3	semicircle	semicircle	NN
37681	1563	4	is	be	VBZ
37681	1563	5	the	the	DT
37681	1563	6	figure	figure	NN
37681	1563	7	contained	contain	VBN
37681	1563	8	by	by	IN
37681	1563	9	the	the	DT
37681	1563	10	diameter	diameter	NN
37681	1563	11	and	and	CC
37681	1563	12	the	the	DT
37681	1563	13	circumference	circumference	NN
37681	1563	14	cut	cut	VBD
37681	1563	15	off	off	RP
37681	1563	16	by	by	IN
37681	1563	17	it	-PRON-	PRP
37681	1563	18	.	.	.
37681	1564	1	And	and	CC
37681	1564	2	the	the	DT
37681	1564	3	center	center	NN
37681	1564	4	of	of	IN
37681	1564	5	the	the	DT
37681	1564	6	semicircle	semicircle	NN
37681	1564	7	is	be	VBZ
37681	1564	8	the	the	DT
37681	1564	9	same	same	JJ
37681	1564	10	as	as	IN
37681	1564	11	that	that	DT
37681	1564	12	of	of	IN
37681	1564	13	the	the	DT
37681	1564	14	circle	circle	NN
37681	1564	15	.	.	.
37681	1564	16	_	_	NNP
37681	1564	17	Proclus	Proclus	NNP
37681	1564	18	remarked	remark	VBD
37681	1564	19	that	that	IN
37681	1564	20	the	the	DT
37681	1564	21	semicircle	semicircle	NN
37681	1564	22	is	be	VBZ
37681	1564	23	the	the	DT
37681	1564	24	only	only	JJ
37681	1564	25	plane	plane	NN
37681	1564	26	figure	figure	NN
37681	1564	27	that	that	WDT
37681	1564	28	has	have	VBZ
37681	1564	29	its	-PRON-	PRP$
37681	1564	30	center	center	NN
37681	1564	31	on	on	IN
37681	1564	32	its	-PRON-	PRP$
37681	1564	33	perimeter	perimeter	NN
37681	1564	34	.	.	.
37681	1565	1	Some	some	DT
37681	1565	2	writers	writer	NNS
37681	1565	3	object	object	VBP
37681	1565	4	to	to	IN
37681	1565	5	defining	define	VBG
37681	1565	6	a	a	DT
37681	1565	7	circle	circle	NN
37681	1565	8	as	as	IN
37681	1565	9	a	a	DT
37681	1565	10	line	line	NN
37681	1565	11	and	and	CC
37681	1565	12	then	then	RB
37681	1565	13	speaking	speak	VBG
37681	1565	14	of	of	IN
37681	1565	15	the	the	DT
37681	1565	16	area	area	NN
37681	1565	17	of	of	IN
37681	1565	18	a	a	DT
37681	1565	19	circle	circle	NN
37681	1565	20	,	,	,
37681	1565	21	showing	show	VBG
37681	1565	22	minds	mind	NNS
37681	1565	23	that	that	WDT
37681	1565	24	have	have	VBP
37681	1565	25	at	at	RB
37681	1565	26	least	least	RBS
37681	1565	27	one	one	CD
37681	1565	28	characteristic	characteristic	NN
37681	1565	29	of	of	IN
37681	1565	30	that	that	DT
37681	1565	31	of	of	IN
37681	1565	32	Proclus	Proclus	NNP
37681	1565	33	.	.	.
37681	1566	1	The	the	DT
37681	1566	2	modern	modern	JJ
37681	1566	3	definition	definition	NN
37681	1566	4	of	of	IN
37681	1566	5	semicircle	semicircle	NN
37681	1566	6	is	be	VBZ
37681	1566	7	"	"	``
37681	1566	8	half	half	NN
37681	1566	9	of	of	IN
37681	1566	10	a	a	DT
37681	1566	11	circle	circle	NN
37681	1566	12	,	,	,
37681	1566	13	"	"	''
37681	1566	14	that	that	RB
37681	1566	15	is	is	RB
37681	1566	16	,	,	,
37681	1566	17	an	an	DT
37681	1566	18	arc	arc	NN
37681	1566	19	of	of	IN
37681	1566	20	180	180	CD
37681	1566	21	°	°	NNS
37681	1566	22	,	,	,
37681	1566	23	although	although	IN
37681	1566	24	the	the	DT
37681	1566	25	term	term	NN
37681	1566	26	is	be	VBZ
37681	1566	27	commonly	commonly	RB
37681	1566	28	used	use	VBN
37681	1566	29	to	to	TO
37681	1566	30	mean	mean	VB
37681	1566	31	both	both	DT
37681	1566	32	the	the	DT
37681	1566	33	arc	arc	NN
37681	1566	34	and	and	CC
37681	1566	35	the	the	DT
37681	1566	36	segment	segment	NN
37681	1566	37	.	.	.
37681	1567	1	19	19	CD
37681	1567	2	.	.	.
37681	1568	1	RECTILINEAR	RECTILINEAR	NNP
37681	1568	2	FIGURES	FIGURES	NNP
37681	1568	3	.	.	.
37681	1569	1	_	_	NNP
37681	1569	2	Rectilinear	Rectilinear	NNP
37681	1569	3	figures	figure	NNS
37681	1569	4	are	be	VBP
37681	1569	5	those	those	DT
37681	1569	6	which	which	WDT
37681	1569	7	are	be	VBP
37681	1569	8	contained	contain	VBN
37681	1569	9	by	by	IN
37681	1569	10	straight	straight	JJ
37681	1569	11	lines	line	NNS
37681	1569	12	,	,	,
37681	1569	13	trilateral	trilateral	JJ
37681	1569	14	figures	figure	NNS
37681	1569	15	being	be	VBG
37681	1569	16	those	those	DT
37681	1569	17	contained	contain	VBN
37681	1569	18	by	by	IN
37681	1569	19	three	three	CD
37681	1569	20	,	,	,
37681	1569	21	quadrilateral	quadrilateral	JJ
37681	1569	22	those	those	DT
37681	1569	23	contained	contain	VBN
37681	1569	24	by	by	IN
37681	1569	25	four	four	CD
37681	1569	26	,	,	,
37681	1569	27	and	and	CC
37681	1569	28	multilateral	multilateral	JJ
37681	1569	29	those	those	DT
37681	1569	30	contained	contain	VBN
37681	1569	31	by	by	IN
37681	1569	32	more	more	JJR
37681	1569	33	than	than	IN
37681	1569	34	four	four	CD
37681	1569	35	,	,	,
37681	1569	36	straight	straight	JJ
37681	1569	37	lines	line	NNS
37681	1569	38	.	.	.
37681	1569	39	_	_	NNP
37681	1569	40	20	20	CD
37681	1569	41	.	.	.
37681	1570	1	_	_	NNP
37681	1570	2	Of	of	IN
37681	1570	3	trilateral	trilateral	JJ
37681	1570	4	figures	figure	NNS
37681	1570	5	,	,	,
37681	1570	6	an	an	DT
37681	1570	7	equilateral	equilateral	JJ
37681	1570	8	triangle	triangle	NN
37681	1570	9	is	be	VBZ
37681	1570	10	that	that	DT
37681	1570	11	which	which	WDT
37681	1570	12	has	have	VBZ
37681	1570	13	its	-PRON-	PRP$
37681	1570	14	three	three	CD
37681	1570	15	sides	side	NNS
37681	1570	16	equal	equal	JJ
37681	1570	17	,	,	,
37681	1570	18	an	an	DT
37681	1570	19	isosceles	isoscele	NNS
37681	1570	20	triangle	triangle	VBP
37681	1570	21	that	that	IN
37681	1570	22	which	which	WDT
37681	1570	23	has	have	VBZ
37681	1570	24	two	two	CD
37681	1570	25	of	of	IN
37681	1570	26	its	-PRON-	PRP$
37681	1570	27	sides	side	NNS
37681	1570	28	alone	alone	RB
37681	1570	29	equal	equal	JJ
37681	1570	30	,	,	,
37681	1570	31	and	and	CC
37681	1570	32	a	a	DT
37681	1570	33	scalene	scalene	JJ
37681	1570	34	triangle	triangle	NN
37681	1570	35	that	that	IN
37681	1570	36	which	which	WDT
37681	1570	37	has	have	VBZ
37681	1570	38	its	-PRON-	PRP$
37681	1570	39	three	three	CD
37681	1570	40	sides	side	NNS
37681	1570	41	unequal	unequal	JJ
37681	1570	42	.	.	.
37681	1570	43	_	_	NNP
37681	1570	44	21	21	CD
37681	1570	45	.	.	.
37681	1571	1	_	_	NNP
37681	1571	2	Further	further	RB
37681	1571	3	,	,	,
37681	1571	4	of	of	IN
37681	1571	5	trilateral	trilateral	JJ
37681	1571	6	figures	figure	NNS
37681	1571	7	,	,	,
37681	1571	8	a	a	DT
37681	1571	9	right	right	RB
37681	1571	10	-	-	HYPH
37681	1571	11	angled	angle	VBN
37681	1571	12	triangle	triangle	NN
37681	1571	13	is	be	VBZ
37681	1571	14	that	that	DT
37681	1571	15	which	which	WDT
37681	1571	16	has	have	VBZ
37681	1571	17	a	a	DT
37681	1571	18	right	right	JJ
37681	1571	19	angle	angle	NN
37681	1571	20	,	,	,
37681	1571	21	an	an	DT
37681	1571	22	obtuse	obtuse	NN
37681	1571	23	-	-	HYPH
37681	1571	24	angled	angle	VBN
37681	1571	25	triangle	triangle	NN
37681	1571	26	that	that	IN
37681	1571	27	which	which	WDT
37681	1571	28	has	have	VBZ
37681	1571	29	an	an	DT
37681	1571	30	obtuse	obtuse	JJ
37681	1571	31	angle	angle	NN
37681	1571	32	,	,	,
37681	1571	33	and	and	CC
37681	1571	34	an	an	DT
37681	1571	35	acute	acute	RB
37681	1571	36	-	-	HYPH
37681	1571	37	angled	angled	JJ
37681	1571	38	triangle	triangle	NN
37681	1571	39	that	that	IN
37681	1571	40	which	which	WDT
37681	1571	41	has	have	VBZ
37681	1571	42	its	-PRON-	PRP$
37681	1571	43	three	three	CD
37681	1571	44	angles	angle	NNS
37681	1571	45	acute	acute	NN
37681	1571	46	.	.	.
37681	1571	47	_	_	NNP
37681	1571	48	These	these	DT
37681	1571	49	three	three	CD
37681	1571	50	definitions	definition	NNS
37681	1571	51	may	may	MD
37681	1571	52	properly	properly	RB
37681	1571	53	be	be	VB
37681	1571	54	considered	consider	VBN
37681	1571	55	together	together	RB
37681	1571	56	.	.	.
37681	1572	1	"	"	``
37681	1572	2	Rectilinear	Rectilinear	NNP
37681	1572	3	"	"	''
37681	1572	4	is	be	VBZ
37681	1572	5	from	from	IN
37681	1572	6	the	the	DT
37681	1572	7	Latin	latin	JJ
37681	1572	8	translation	translation	NN
37681	1572	9	of	of	IN
37681	1572	10	the	the	DT
37681	1572	11	Greek	Greek	NNP
37681	1572	12	_	_	NNP
37681	1572	13	euthygrammos	euthygrammos	NN
37681	1572	14	_	_	NNP
37681	1572	15	,	,	,
37681	1572	16	and	and	CC
37681	1572	17	means	mean	VBZ
37681	1572	18	"	"	``
37681	1572	19	right	right	RB
37681	1572	20	-	-	HYPH
37681	1572	21	lined	line	VBN
37681	1572	22	,	,	,
37681	1572	23	"	"	''
37681	1572	24	or	or	CC
37681	1572	25	"	"	``
37681	1572	26	straight	straight	RB
37681	1572	27	-	-	HYPH
37681	1572	28	lined	line	VBN
37681	1572	29	.	.	.
37681	1572	30	"	"	''
37681	1573	1	Euclid	Euclid	NNP
37681	1573	2	's	's	POS
37681	1573	3	idea	idea	NN
37681	1573	4	of	of	IN
37681	1573	5	such	such	PDT
37681	1573	6	a	a	DT
37681	1573	7	figure	figure	NN
37681	1573	8	is	be	VBZ
37681	1573	9	that	that	DT
37681	1573	10	of	of	IN
37681	1573	11	the	the	DT
37681	1573	12	space	space	NN
37681	1573	13	inclosed	inclose	VBN
37681	1573	14	,	,	,
37681	1573	15	while	while	IN
37681	1573	16	the	the	DT
37681	1573	17	modern	modern	JJ
37681	1573	18	idea	idea	NN
37681	1573	19	is	be	VBZ
37681	1573	20	tending	tend	VBG
37681	1573	21	to	to	TO
37681	1573	22	become	become	VB
37681	1573	23	that	that	DT
37681	1573	24	of	of	IN
37681	1573	25	the	the	DT
37681	1573	26	inclosing	inclose	VBG
37681	1573	27	lines	line	NNS
37681	1573	28	.	.	.
37681	1574	1	In	in	IN
37681	1574	2	elementary	elementary	JJ
37681	1574	3	geometry	geometry	NN
37681	1574	4	,	,	,
37681	1574	5	however	however	RB
37681	1574	6	,	,	,
37681	1574	7	the	the	DT
37681	1574	8	Euclidean	euclidean	JJ
37681	1574	9	idea	idea	NN
37681	1574	10	is	be	VBZ
37681	1574	11	still	still	RB
37681	1574	12	held	hold	VBN
37681	1574	13	.	.	.
37681	1575	1	"	"	``
37681	1575	2	Trilateral	trilateral	JJ
37681	1575	3	"	"	''
37681	1575	4	is	be	VBZ
37681	1575	5	from	from	IN
37681	1575	6	the	the	DT
37681	1575	7	Latin	latin	JJ
37681	1575	8	translation	translation	NN
37681	1575	9	of	of	IN
37681	1575	10	the	the	DT
37681	1575	11	Greek	Greek	NNP
37681	1575	12	_	_	NNP
37681	1575	13	tripleuros	tripleuro	NNS
37681	1575	14	_	_	NNP
37681	1575	15	(	(	-LRB-
37681	1575	16	three	three	CD
37681	1575	17	-	-	HYPH
37681	1575	18	sided	sided	JJ
37681	1575	19	)	)	-RRB-
37681	1575	20	.	.	.
37681	1576	1	In	in	IN
37681	1576	2	elementary	elementary	JJ
37681	1576	3	geometry	geometry	NN
37681	1576	4	the	the	DT
37681	1576	5	word	word	NN
37681	1576	6	"	"	``
37681	1576	7	triangle	triangle	NN
37681	1576	8	"	"	''
37681	1576	9	is	be	VBZ
37681	1576	10	more	more	RBR
37681	1576	11	commonly	commonly	RB
37681	1576	12	used	use	VBN
37681	1576	13	,	,	,
37681	1576	14	although	although	IN
37681	1576	15	"	"	``
37681	1576	16	quadrilateral	quadrilateral	JJ
37681	1576	17	"	"	''
37681	1576	18	is	be	VBZ
37681	1576	19	more	more	RBR
37681	1576	20	common	common	JJ
37681	1576	21	than	than	IN
37681	1576	22	"	"	``
37681	1576	23	quadrangle	quadrangle	JJ
37681	1576	24	.	.	.
37681	1576	25	"	"	''
37681	1577	1	The	the	DT
37681	1577	2	use	use	NN
37681	1577	3	of	of	IN
37681	1577	4	these	these	DT
37681	1577	5	two	two	CD
37681	1577	6	different	different	JJ
37681	1577	7	forms	form	NNS
37681	1577	8	is	be	VBZ
37681	1577	9	eccentric	eccentric	JJ
37681	1577	10	and	and	CC
37681	1577	11	is	be	VBZ
37681	1577	12	merely	merely	RB
37681	1577	13	a	a	DT
37681	1577	14	matter	matter	NN
37681	1577	15	of	of	IN
37681	1577	16	fashion	fashion	NN
37681	1577	17	.	.	.
37681	1578	1	Thus	thus	RB
37681	1578	2	we	-PRON-	PRP
37681	1578	3	speak	speak	VBP
37681	1578	4	of	of	IN
37681	1578	5	a	a	DT
37681	1578	6	pentagon	pentagon	NNP
37681	1578	7	but	but	CC
37681	1578	8	not	not	RB
37681	1578	9	of	of	IN
37681	1578	10	a	a	DT
37681	1578	11	tetragon	tetragon	NN
37681	1578	12	or	or	CC
37681	1578	13	a	a	DT
37681	1578	14	trigon	trigon	NN
37681	1578	15	,	,	,
37681	1578	16	although	although	IN
37681	1578	17	both	both	DT
37681	1578	18	words	word	NNS
37681	1578	19	are	be	VBP
37681	1578	20	correct	correct	JJ
37681	1578	21	in	in	IN
37681	1578	22	form	form	NN
37681	1578	23	.	.	.
37681	1579	1	The	the	DT
37681	1579	2	word	word	NN
37681	1579	3	"	"	``
37681	1579	4	multilateral	multilateral	NN
37681	1579	5	"	"	''
37681	1579	6	(	(	-LRB-
37681	1579	7	many	many	JJ
37681	1579	8	-	-	HYPH
37681	1579	9	sided	sided	JJ
37681	1579	10	)	)	-RRB-
37681	1579	11	is	be	VBZ
37681	1579	12	a	a	DT
37681	1579	13	translation	translation	NN
37681	1579	14	of	of	IN
37681	1579	15	the	the	DT
37681	1579	16	Greek	Greek	NNP
37681	1579	17	_	_	NNP
37681	1579	18	polypleuros	polypleuro	NNS
37681	1579	19	_	_	NNP
37681	1579	20	.	.	.
37681	1580	1	Fashion	fashion	NN
37681	1580	2	has	have	VBZ
37681	1580	3	changed	change	VBN
37681	1580	4	this	this	DT
37681	1580	5	to	to	IN
37681	1580	6	"	"	``
37681	1580	7	polygonal	polygonal	VB
37681	1580	8	"	"	''
37681	1580	9	(	(	-LRB-
37681	1580	10	many	many	RB
37681	1580	11	-	-	HYPH
37681	1580	12	angled	angle	VBN
37681	1580	13	)	)	-RRB-
37681	1580	14	,	,	,
37681	1580	15	the	the	DT
37681	1580	16	word	word	NN
37681	1580	17	"	"	``
37681	1580	18	multilateral	multilateral	JJ
37681	1580	19	"	"	''
37681	1580	20	rarely	rarely	RB
37681	1580	21	being	be	VBG
37681	1580	22	seen	see	VBN
37681	1580	23	.	.	.
37681	1581	1	Of	of	IN
37681	1581	2	the	the	DT
37681	1581	3	triangles	triangle	NNS
37681	1581	4	,	,	,
37681	1581	5	"	"	''
37681	1581	6	equilateral	equilateral	JJ
37681	1581	7	"	"	''
37681	1581	8	means	mean	VBZ
37681	1581	9	"	"	``
37681	1581	10	equal	equal	JJ
37681	1581	11	-	-	HYPH
37681	1581	12	sided	sided	JJ
37681	1581	13	"	"	''
37681	1581	14	;	;	:
37681	1581	15	"	"	``
37681	1581	16	isosceles	isoscele	NNS
37681	1581	17	"	"	''
37681	1581	18	is	be	VBZ
37681	1581	19	from	from	IN
37681	1581	20	the	the	DT
37681	1581	21	Greek	Greek	NNP
37681	1581	22	_	_	NNP
37681	1581	23	isoskeles	isoskele	NNS
37681	1581	24	_	_	NNP
37681	1581	25	,	,	,
37681	1581	26	meaning	mean	VBG
37681	1581	27	"	"	``
37681	1581	28	with	with	IN
37681	1581	29	equal	equal	JJ
37681	1581	30	legs	leg	NNS
37681	1581	31	,	,	,
37681	1581	32	"	"	''
37681	1581	33	and	and	CC
37681	1581	34	"	"	``
37681	1581	35	scalene	scalene	NN
37681	1581	36	"	"	''
37681	1581	37	from	from	IN
37681	1581	38	_	_	NNP
37681	1581	39	skalenos	skalenos	NNP
37681	1581	40	_	_	NNP
37681	1581	41	,	,	,
37681	1581	42	possibly	possibly	RB
37681	1581	43	from	from	IN
37681	1581	44	_	_	NNP
37681	1581	45	skazo	skazo	NN
37681	1581	46	_	_	NNP
37681	1581	47	(	(	-LRB-
37681	1581	48	to	to	TO
37681	1581	49	limp	limp	VB
37681	1581	50	)	)	-RRB-
37681	1581	51	,	,	,
37681	1581	52	or	or	CC
37681	1581	53	from	from	IN
37681	1581	54	_	_	NNP
37681	1581	55	skolios	skolio	NNS
37681	1581	56	_	_	NNP
37681	1581	57	(	(	-LRB-
37681	1581	58	crooked	crooked	NNP
37681	1581	59	)	)	-RRB-
37681	1581	60	.	.	.
37681	1582	1	Euclid	Euclid	NNP
37681	1582	2	's	's	POS
37681	1582	3	limitation	limitation	NN
37681	1582	4	of	of	IN
37681	1582	5	isosceles	isoscele	NNS
37681	1582	6	to	to	IN
37681	1582	7	a	a	DT
37681	1582	8	triangle	triangle	NN
37681	1582	9	with	with	IN
37681	1582	10	two	two	CD
37681	1582	11	,	,	,
37681	1582	12	and	and	CC
37681	1582	13	only	only	RB
37681	1582	14	two	two	CD
37681	1582	15	,	,	,
37681	1582	16	equal	equal	JJ
37681	1582	17	sides	side	NNS
37681	1582	18	would	would	MD
37681	1582	19	not	not	RB
37681	1582	20	now	now	RB
37681	1582	21	be	be	VB
37681	1582	22	accepted	accept	VBN
37681	1582	23	.	.	.
37681	1583	1	We	-PRON-	PRP
37681	1583	2	are	be	VBP
37681	1583	3	at	at	IN
37681	1583	4	present	present	JJ
37681	1583	5	more	more	JJR
37681	1583	6	given	give	VBN
37681	1583	7	to	to	IN
37681	1583	8	generalizing	generalize	VBG
37681	1583	9	than	than	IN
37681	1583	10	he	-PRON-	PRP
37681	1583	11	was	be	VBD
37681	1583	12	,	,	,
37681	1583	13	and	and	CC
37681	1583	14	when	when	WRB
37681	1583	15	we	-PRON-	PRP
37681	1583	16	have	have	VBP
37681	1583	17	proved	prove	VBN
37681	1583	18	a	a	DT
37681	1583	19	proposition	proposition	NN
37681	1583	20	relating	relate	VBG
37681	1583	21	to	to	IN
37681	1583	22	the	the	DT
37681	1583	23	isosceles	isoscele	NNS
37681	1583	24	triangle	triangle	VB
37681	1583	25	,	,	,
37681	1583	26	we	-PRON-	PRP
37681	1583	27	wish	wish	VBP
37681	1583	28	to	to	TO
37681	1583	29	say	say	VB
37681	1583	30	that	that	IN
37681	1583	31	we	-PRON-	PRP
37681	1583	32	have	have	VBP
37681	1583	33	thereby	thereby	RB
37681	1583	34	proved	prove	VBN
37681	1583	35	it	-PRON-	PRP
37681	1583	36	for	for	IN
37681	1583	37	the	the	DT
37681	1583	38	equilateral	equilateral	JJ
37681	1583	39	triangle	triangle	NN
37681	1583	40	.	.	.
37681	1584	1	We	-PRON-	PRP
37681	1584	2	therefore	therefore	RB
37681	1584	3	say	say	VBP
37681	1584	4	that	that	IN
37681	1584	5	an	an	DT
37681	1584	6	isosceles	isoscele	NNS
37681	1584	7	triangle	triangle	NN
37681	1584	8	has	have	VBZ
37681	1584	9	two	two	CD
37681	1584	10	sides	side	NNS
37681	1584	11	equal	equal	JJ
37681	1584	12	,	,	,
37681	1584	13	leaving	leave	VBG
37681	1584	14	it	-PRON-	PRP
37681	1584	15	possible	possible	JJ
37681	1584	16	that	that	IN
37681	1584	17	all	all	DT
37681	1584	18	three	three	CD
37681	1584	19	sides	side	NNS
37681	1584	20	should	should	MD
37681	1584	21	be	be	VB
37681	1584	22	equal	equal	JJ
37681	1584	23	.	.	.
37681	1585	1	The	the	DT
37681	1585	2	expression	expression	NN
37681	1585	3	"	"	``
37681	1585	4	equal	equal	JJ
37681	1585	5	legs	leg	NNS
37681	1585	6	"	"	''
37681	1585	7	is	be	VBZ
37681	1585	8	now	now	RB
37681	1585	9	being	be	VBG
37681	1585	10	discarded	discard	VBN
37681	1585	11	on	on	IN
37681	1585	12	the	the	DT
37681	1585	13	score	score	NN
37681	1585	14	of	of	IN
37681	1585	15	inelegance	inelegance	NN
37681	1585	16	.	.	.
37681	1586	1	In	in	IN
37681	1586	2	place	place	NN
37681	1586	3	of	of	IN
37681	1586	4	"	"	``
37681	1586	5	right	right	RB
37681	1586	6	-	-	HYPH
37681	1586	7	angled	angle	VBN
37681	1586	8	triangle	triangle	NN
37681	1586	9	"	"	''
37681	1586	10	modern	modern	JJ
37681	1586	11	writers	writer	NNS
37681	1586	12	speak	speak	VBP
37681	1586	13	of	of	IN
37681	1586	14	"	"	``
37681	1586	15	right	right	JJ
37681	1586	16	triangle	triangle	NN
37681	1586	17	,	,	,
37681	1586	18	"	"	''
37681	1586	19	and	and	CC
37681	1586	20	so	so	RB
37681	1586	21	for	for	IN
37681	1586	22	the	the	DT
37681	1586	23	obtuse	obtuse	NN
37681	1586	24	and	and	CC
37681	1586	25	acute	acute	JJ
37681	1586	26	triangles	triangle	NNS
37681	1586	27	.	.	.
37681	1587	1	The	the	DT
37681	1587	2	terms	term	NNS
37681	1587	3	are	be	VBP
37681	1587	4	briefer	briefer	JJ
37681	1587	5	and	and	CC
37681	1587	6	are	be	VBP
37681	1587	7	as	as	RB
37681	1587	8	readily	readily	RB
37681	1587	9	understood	understand	VBN
37681	1587	10	.	.	.
37681	1588	1	It	-PRON-	PRP
37681	1588	2	may	may	MD
37681	1588	3	add	add	VB
37681	1588	4	a	a	DT
37681	1588	5	little	little	JJ
37681	1588	6	interest	interest	NN
37681	1588	7	to	to	IN
37681	1588	8	the	the	DT
37681	1588	9	subject	subject	NN
37681	1588	10	to	to	TO
37681	1588	11	know	know	VB
37681	1588	12	that	that	IN
37681	1588	13	Plutarch	Plutarch	NNP
37681	1588	14	tells	tell	VBZ
37681	1588	15	us	-PRON-	PRP
37681	1588	16	that	that	IN
37681	1588	17	the	the	DT
37681	1588	18	ancients	ancient	NNS
37681	1588	19	thought	think	VBD
37681	1588	20	that	that	IN
37681	1588	21	"	"	``
37681	1588	22	the	the	DT
37681	1588	23	power	power	NN
37681	1588	24	of	of	IN
37681	1588	25	the	the	DT
37681	1588	26	triangle	triangle	NN
37681	1588	27	is	be	VBZ
37681	1588	28	expressive	expressive	JJ
37681	1588	29	of	of	IN
37681	1588	30	the	the	DT
37681	1588	31	nature	nature	NN
37681	1588	32	of	of	IN
37681	1588	33	Pluto	Pluto	NNP
37681	1588	34	,	,	,
37681	1588	35	Bacchus	Bacchus	NNP
37681	1588	36	,	,	,
37681	1588	37	and	and	CC
37681	1588	38	Mars	Mars	NNP
37681	1588	39	.	.	.
37681	1588	40	"	"	''
37681	1589	1	He	-PRON-	PRP
37681	1589	2	also	also	RB
37681	1589	3	states	state	VBZ
37681	1589	4	that	that	IN
37681	1589	5	the	the	DT
37681	1589	6	Pythagoreans	Pythagoreans	NNPS
37681	1589	7	called	call	VBD
37681	1589	8	"	"	``
37681	1589	9	the	the	DT
37681	1589	10	equilateral	equilateral	JJ
37681	1589	11	triangle	triangle	NN
37681	1589	12	the	the	DT
37681	1589	13	head	head	NN
37681	1589	14	-	-	HYPH
37681	1589	15	born	bear	VBN
37681	1589	16	Minerva	Minerva	NNP
37681	1589	17	and	and	CC
37681	1589	18	Tritogeneia	Tritogeneia	NNP
37681	1589	19	(	(	-LRB-
37681	1589	20	born	bear	VBN
37681	1589	21	of	of	IN
37681	1589	22	Triton	Triton	NNP
37681	1589	23	)	)	-RRB-
37681	1589	24	because	because	IN
37681	1589	25	it	-PRON-	PRP
37681	1589	26	may	may	MD
37681	1589	27	be	be	VB
37681	1589	28	equally	equally	RB
37681	1589	29	divided	divide	VBN
37681	1589	30	by	by	IN
37681	1589	31	the	the	DT
37681	1589	32	perpendicular	perpendicular	JJ
37681	1589	33	lines	line	NNS
37681	1589	34	drawn	draw	VBN
37681	1589	35	from	from	IN
37681	1589	36	each	each	DT
37681	1589	37	of	of	IN
37681	1589	38	its	-PRON-	PRP$
37681	1589	39	angles	angle	NNS
37681	1589	40	.	.	.
37681	1589	41	"	"	''
37681	1590	1	22	22	CD
37681	1590	2	.	.	.
37681	1591	1	_	_	NNP
37681	1591	2	Of	of	IN
37681	1591	3	quadrilateral	quadrilateral	JJ
37681	1591	4	figures	figure	NNS
37681	1591	5	a	a	DT
37681	1591	6	square	square	NN
37681	1591	7	is	be	VBZ
37681	1591	8	that	that	DT
37681	1591	9	which	which	WDT
37681	1591	10	is	be	VBZ
37681	1591	11	both	both	CC
37681	1591	12	equilateral	equilateral	JJ
37681	1591	13	and	and	CC
37681	1591	14	right	right	RB
37681	1591	15	-	-	HYPH
37681	1591	16	angled	angle	VBN
37681	1591	17	;	;	:
37681	1591	18	an	an	DT
37681	1591	19	oblong	oblong	NN
37681	1591	20	that	that	IN
37681	1591	21	which	which	WDT
37681	1591	22	is	be	VBZ
37681	1591	23	right	right	RB
37681	1591	24	-	-	HYPH
37681	1591	25	angled	angle	VBN
37681	1591	26	but	but	CC
37681	1591	27	not	not	RB
37681	1591	28	equilateral	equilateral	JJ
37681	1591	29	;	;	:
37681	1591	30	a	a	DT
37681	1591	31	rhombus	rhombus	NN
37681	1591	32	that	that	WDT
37681	1591	33	which	which	WDT
37681	1591	34	is	be	VBZ
37681	1591	35	equilateral	equilateral	JJ
37681	1591	36	and	and	CC
37681	1591	37	not	not	RB
37681	1591	38	right	right	RB
37681	1591	39	-	-	HYPH
37681	1591	40	angled	angle	VBN
37681	1591	41	;	;	:
37681	1591	42	and	and	CC
37681	1591	43	a	a	DT
37681	1591	44	rhomboid	rhomboid	NN
37681	1591	45	that	that	WDT
37681	1591	46	which	which	WDT
37681	1591	47	has	have	VBZ
37681	1591	48	its	-PRON-	PRP$
37681	1591	49	opposite	opposite	JJ
37681	1591	50	sides	side	NNS
37681	1591	51	and	and	CC
37681	1591	52	angles	angle	NNS
37681	1591	53	equal	equal	JJ
37681	1591	54	to	to	IN
37681	1591	55	one	one	CD
37681	1591	56	another	another	DT
37681	1591	57	,	,	,
37681	1591	58	but	but	CC
37681	1591	59	is	be	VBZ
37681	1591	60	neither	neither	CC
37681	1591	61	equilateral	equilateral	JJ
37681	1591	62	nor	nor	CC
37681	1591	63	right	right	RB
37681	1591	64	-	-	HYPH
37681	1591	65	angled	angle	VBN
37681	1591	66	.	.	.
37681	1592	1	And	and	CC
37681	1592	2	let	let	VB
37681	1592	3	all	all	DT
37681	1592	4	quadrilaterals	quadrilateral	NNS
37681	1592	5	other	other	JJ
37681	1592	6	than	than	IN
37681	1592	7	these	these	DT
37681	1592	8	be	be	VB
37681	1592	9	called	call	VBN
37681	1592	10	trapezia	trapezia	NN
37681	1592	11	.	.	.
37681	1592	12	_	_	NNP
37681	1592	13	In	in	IN
37681	1592	14	this	this	DT
37681	1592	15	definition	definition	NN
37681	1592	16	Euclid	Euclid	NNP
37681	1592	17	also	also	RB
37681	1592	18	specializes	specialize	VBZ
37681	1592	19	in	in	IN
37681	1592	20	a	a	DT
37681	1592	21	manner	manner	NN
37681	1592	22	not	not	RB
37681	1592	23	now	now	RB
37681	1592	24	generally	generally	RB
37681	1592	25	approved	approve	VBN
37681	1592	26	.	.	.
37681	1593	1	Thus	thus	RB
37681	1593	2	we	-PRON-	PRP
37681	1593	3	are	be	VBP
37681	1593	4	more	more	RBR
37681	1593	5	apt	apt	JJ
37681	1593	6	to	to	IN
37681	1593	7	-	-	HYPH
37681	1593	8	day	day	NN
37681	1593	9	to	to	TO
37681	1593	10	omit	omit	VB
37681	1593	11	the	the	DT
37681	1593	12	oblong	oblong	JJ
37681	1593	13	and	and	CC
37681	1593	14	rhomboid	rhomboid	VB
37681	1593	15	as	as	IN
37681	1593	16	unnecessary	unnecessary	JJ
37681	1593	17	,	,	,
37681	1593	18	and	and	CC
37681	1593	19	to	to	TO
37681	1593	20	define	define	VB
37681	1593	21	"	"	``
37681	1593	22	rhombus	rhombus	NN
37681	1593	23	"	"	''
37681	1593	24	in	in	IN
37681	1593	25	such	such	PDT
37681	1593	26	a	a	DT
37681	1593	27	manner	manner	NN
37681	1593	28	as	as	IN
37681	1593	29	to	to	TO
37681	1593	30	include	include	VB
37681	1593	31	a	a	DT
37681	1593	32	square	square	NN
37681	1593	33	.	.	.
37681	1594	1	We	-PRON-	PRP
37681	1594	2	use	use	VBP
37681	1594	3	"	"	``
37681	1594	4	parallelogram	parallelogram	NN
37681	1594	5	"	"	''
37681	1594	6	to	to	TO
37681	1594	7	cover	cover	VB
37681	1594	8	"	"	``
37681	1594	9	rhomboid	rhomboid	NN
37681	1594	10	,	,	,
37681	1594	11	"	"	''
37681	1594	12	"	"	``
37681	1594	13	rhombus	rhombus	NN
37681	1594	14	,	,	,
37681	1594	15	"	"	''
37681	1594	16	"	"	``
37681	1594	17	oblong	oblong	JJ
37681	1594	18	,	,	,
37681	1594	19	"	"	''
37681	1594	20	and	and	CC
37681	1594	21	"	"	``
37681	1594	22	square	square	JJ
37681	1594	23	.	.	.
37681	1594	24	"	"	''
37681	1595	1	For	for	IN
37681	1595	2	"	"	``
37681	1595	3	oblong	oblong	JJ
37681	1595	4	"	"	''
37681	1595	5	we	-PRON-	PRP
37681	1595	6	use	use	VBP
37681	1595	7	"	"	''
37681	1595	8	rectangle	rectangle	NN
37681	1595	9	,	,	,
37681	1595	10	"	"	''
37681	1595	11	letting	let	VBG
37681	1595	12	it	-PRON-	PRP
37681	1595	13	include	include	VB
37681	1595	14	square	square	NN
37681	1595	15	.	.	.
37681	1596	1	Euclid	Euclid	NNP
37681	1596	2	's	's	POS
37681	1596	3	definition	definition	NN
37681	1596	4	of	of	IN
37681	1596	5	"	"	``
37681	1596	6	square	square	JJ
37681	1596	7	"	"	''
37681	1596	8	illustrates	illustrate	VBZ
37681	1596	9	his	-PRON-	PRP$
37681	1596	10	freedom	freedom	NN
37681	1596	11	in	in	IN
37681	1596	12	stating	state	VBG
37681	1596	13	more	more	JJR
37681	1596	14	attributes	attribute	NNS
37681	1596	15	than	than	IN
37681	1596	16	are	be	VBP
37681	1596	17	necessary	necessary	JJ
37681	1596	18	,	,	,
37681	1596	19	in	in	IN
37681	1596	20	order	order	NN
37681	1596	21	to	to	TO
37681	1596	22	make	make	VB
37681	1596	23	sure	sure	JJ
37681	1596	24	that	that	IN
37681	1596	25	the	the	DT
37681	1596	26	concept	concept	NN
37681	1596	27	is	be	VBZ
37681	1596	28	clear	clear	JJ
37681	1596	29	;	;	:
37681	1596	30	for	for	IN
37681	1596	31	he	-PRON-	PRP
37681	1596	32	might	may	MD
37681	1596	33	have	have	VB
37681	1596	34	said	say	VBN
37681	1596	35	that	that	IN
37681	1596	36	it	-PRON-	PRP
37681	1596	37	"	"	``
37681	1596	38	is	be	VBZ
37681	1596	39	that	that	DT
37681	1596	40	which	which	WDT
37681	1596	41	is	be	VBZ
37681	1596	42	equilateral	equilateral	JJ
37681	1596	43	and	and	CC
37681	1596	44	has	have	VBZ
37681	1596	45	one	one	CD
37681	1596	46	right	right	JJ
37681	1596	47	angle	angle	NN
37681	1596	48	.	.	.
37681	1596	49	"	"	''
37681	1597	1	We	-PRON-	PRP
37681	1597	2	may	may	MD
37681	1597	3	profit	profit	VB
37681	1597	4	by	by	IN
37681	1597	5	his	-PRON-	PRP$
37681	1597	6	method	method	NN
37681	1597	7	,	,	,
37681	1597	8	sacrificing	sacrifice	VBG
37681	1597	9	logic	logic	NN
37681	1597	10	to	to	IN
37681	1597	11	educational	educational	JJ
37681	1597	12	necessity	necessity	NN
37681	1597	13	.	.	.
37681	1598	1	Euclid	euclid	NN
37681	1598	2	does	do	VBZ
37681	1598	3	not	not	RB
37681	1598	4	use	use	VB
37681	1598	5	"	"	``
37681	1598	6	oblong	oblong	JJ
37681	1598	7	,	,	,
37681	1598	8	"	"	''
37681	1598	9	"	"	``
37681	1598	10	rhombus	rhombus	NN
37681	1598	11	,	,	,
37681	1598	12	"	"	''
37681	1598	13	"	"	``
37681	1598	14	rhomboid	rhomboid	NN
37681	1598	15	,	,	,
37681	1598	16	"	"	''
37681	1598	17	and	and	CC
37681	1598	18	"	"	``
37681	1598	19	trapezium	trapezium	NN
37681	1598	20	"	"	''
37681	1598	21	(	(	-LRB-
37681	1598	22	_	_	NNP
37681	1598	23	plural	plural	JJ
37681	1598	24	_	_	NNP
37681	1598	25	,	,	,
37681	1598	26	"	"	''
37681	1598	27	trapezia	trapezia	NN
37681	1598	28	"	"	''
37681	1598	29	)	)	-RRB-
37681	1598	30	in	in	IN
37681	1598	31	his	-PRON-	PRP$
37681	1598	32	proofs	proof	NNS
37681	1598	33	,	,	,
37681	1598	34	so	so	IN
37681	1598	35	that	that	IN
37681	1598	36	he	-PRON-	PRP
37681	1598	37	might	may	MD
37681	1598	38	well	well	RB
37681	1598	39	have	have	VB
37681	1598	40	omitted	omit	VBN
37681	1598	41	the	the	DT
37681	1598	42	definitions	definition	NNS
37681	1598	43	,	,	,
37681	1598	44	as	as	IN
37681	1598	45	we	-PRON-	PRP
37681	1598	46	often	often	RB
37681	1598	47	do	do	VBP
37681	1598	48	.	.	.
37681	1599	1	23	23	CD
37681	1599	2	.	.	.
37681	1600	1	PARALLELS	PARALLELS	NNP
37681	1600	2	.	.	.
37681	1601	1	_	_	NNP
37681	1601	2	Parallel	parallel	JJ
37681	1601	3	straight	straight	JJ
37681	1601	4	lines	line	NNS
37681	1601	5	are	be	VBP
37681	1601	6	straight	straight	JJ
37681	1601	7	lines	line	NNS
37681	1601	8	which	which	WDT
37681	1601	9	,	,	,
37681	1601	10	being	be	VBG
37681	1601	11	in	in	IN
37681	1601	12	the	the	DT
37681	1601	13	same	same	JJ
37681	1601	14	plane	plane	NN
37681	1601	15	and	and	CC
37681	1601	16	being	be	VBG
37681	1601	17	produced	produce	VBN
37681	1601	18	indefinitely	indefinitely	RB
37681	1601	19	in	in	IN
37681	1601	20	both	both	DT
37681	1601	21	directions	direction	NNS
37681	1601	22	,	,	,
37681	1601	23	do	do	VBP
37681	1601	24	not	not	RB
37681	1601	25	meet	meet	VB
37681	1601	26	one	one	NN
37681	1601	27	another	another	DT
37681	1601	28	in	in	IN
37681	1601	29	either	either	DT
37681	1601	30	direction	direction	NN
37681	1601	31	.	.	.
37681	1601	32	_	_	NNP
37681	1601	33	This	this	DT
37681	1601	34	definition	definition	NN
37681	1601	35	of	of	IN
37681	1601	36	parallels	parallel	NNS
37681	1601	37	,	,	,
37681	1601	38	simplified	simplify	VBN
37681	1601	39	in	in	IN
37681	1601	40	its	-PRON-	PRP$
37681	1601	41	language	language	NN
37681	1601	42	,	,	,
37681	1601	43	is	be	VBZ
37681	1601	44	the	the	DT
37681	1601	45	one	one	CD
37681	1601	46	commonly	commonly	RB
37681	1601	47	used	use	VBN
37681	1601	48	to	to	IN
37681	1601	49	-	-	HYPH
37681	1601	50	day	day	NN
37681	1601	51	.	.	.
37681	1602	1	Other	other	JJ
37681	1602	2	definitions	definition	NNS
37681	1602	3	have	have	VBP
37681	1602	4	been	be	VBN
37681	1602	5	suggested	suggest	VBN
37681	1602	6	,	,	,
37681	1602	7	but	but	CC
37681	1602	8	none	none	NN
37681	1602	9	has	have	VBZ
37681	1602	10	been	be	VBN
37681	1602	11	so	so	RB
37681	1602	12	generally	generally	RB
37681	1602	13	used	use	VBN
37681	1602	14	.	.	.
37681	1603	1	Proclus	Proclus	NNP
37681	1603	2	states	state	VBZ
37681	1603	3	that	that	IN
37681	1603	4	Posidonius	Posidonius	NNP
37681	1603	5	gave	give	VBD
37681	1603	6	the	the	DT
37681	1603	7	definition	definition	NN
37681	1603	8	based	base	VBN
37681	1603	9	upon	upon	IN
37681	1603	10	the	the	DT
37681	1603	11	lines	line	NNS
37681	1603	12	always	always	RB
37681	1603	13	being	be	VBG
37681	1603	14	at	at	IN
37681	1603	15	the	the	DT
37681	1603	16	same	same	JJ
37681	1603	17	distance	distance	NN
37681	1603	18	apart	apart	RB
37681	1603	19	.	.	.
37681	1604	1	Geminus	Geminus	NNP
37681	1604	2	has	have	VBZ
37681	1604	3	the	the	DT
37681	1604	4	same	same	JJ
37681	1604	5	idea	idea	NN
37681	1604	6	in	in	IN
37681	1604	7	his	-PRON-	PRP$
37681	1604	8	definition	definition	NN
37681	1604	9	.	.	.
37681	1605	1	There	there	EX
37681	1605	2	are	be	VBP
37681	1605	3	,	,	,
37681	1605	4	as	as	IN
37681	1605	5	Schotten	Schotten	NNP
37681	1605	6	has	have	VBZ
37681	1605	7	pointed	point	VBN
37681	1605	8	out	out	RP
37681	1605	9	,	,	,
37681	1605	10	three	three	CD
37681	1605	11	general	general	JJ
37681	1605	12	types	type	NNS
37681	1605	13	of	of	IN
37681	1605	14	definitions	definition	NNS
37681	1605	15	of	of	IN
37681	1605	16	parallels	parallel	NNS
37681	1605	17	,	,	,
37681	1605	18	namely	namely	RB
37681	1605	19	:	:	:
37681	1605	20	_	_	NNP
37681	1605	21	a.	a.	NN
37681	1605	22	_	_	NNP
37681	1605	23	They	-PRON-	PRP
37681	1605	24	have	have	VBP
37681	1605	25	no	no	DT
37681	1605	26	point	point	NN
37681	1605	27	in	in	IN
37681	1605	28	common	common	JJ
37681	1605	29	.	.	.
37681	1606	1	This	this	DT
37681	1606	2	may	may	MD
37681	1606	3	be	be	VB
37681	1606	4	expressed	express	VBN
37681	1606	5	by	by	IN
37681	1606	6	saying	say	VBG
37681	1606	7	that	that	IN
37681	1606	8	(	(	-LRB-
37681	1606	9	1	1	LS
37681	1606	10	)	)	-RRB-
37681	1606	11	they	-PRON-	PRP
37681	1606	12	do	do	VBP
37681	1606	13	not	not	RB
37681	1606	14	intersect	intersect	VB
37681	1606	15	,	,	,
37681	1606	16	(	(	-LRB-
37681	1606	17	2	2	LS
37681	1606	18	)	)	-RRB-
37681	1606	19	they	-PRON-	PRP
37681	1606	20	meet	meet	VBP
37681	1606	21	at	at	IN
37681	1606	22	infinity	infinity	NN
37681	1606	23	.	.	.
37681	1607	1	_	_	NNP
37681	1607	2	b.	b.	NN
37681	1607	3	_	_	NNP
37681	1607	4	They	-PRON-	PRP
37681	1607	5	are	be	VBP
37681	1607	6	equidistant	equidistant	JJ
37681	1607	7	from	from	IN
37681	1607	8	one	one	CD
37681	1607	9	another	another	DT
37681	1607	10	.	.	.
37681	1608	1	_	_	NNP
37681	1608	2	c.	c.	NNP
37681	1608	3	_	_	NNP
37681	1608	4	They	-PRON-	PRP
37681	1608	5	have	have	VBP
37681	1608	6	the	the	DT
37681	1608	7	same	same	JJ
37681	1608	8	direction	direction	NN
37681	1608	9	.	.	.
37681	1609	1	Of	of	IN
37681	1609	2	these	these	DT
37681	1609	3	,	,	,
37681	1609	4	the	the	DT
37681	1609	5	first	first	JJ
37681	1609	6	is	be	VBZ
37681	1609	7	Euclid	Euclid	NNP
37681	1609	8	's	's	POS
37681	1609	9	,	,	,
37681	1609	10	the	the	DT
37681	1609	11	idea	idea	NN
37681	1609	12	of	of	IN
37681	1609	13	the	the	DT
37681	1609	14	point	point	NN
37681	1609	15	at	at	IN
37681	1609	16	infinity	infinity	NN
37681	1609	17	being	be	VBG
37681	1609	18	suggested	suggest	VBN
37681	1609	19	by	by	IN
37681	1609	20	Kepler	Kepler	NNP
37681	1609	21	(	(	-LRB-
37681	1609	22	1604	1604	CD
37681	1609	23	)	)	-RRB-
37681	1609	24	.	.	.
37681	1610	1	The	the	DT
37681	1610	2	second	second	JJ
37681	1610	3	part	part	NN
37681	1610	4	of	of	IN
37681	1610	5	this	this	DT
37681	1610	6	definition	definition	NN
37681	1610	7	is	be	VBZ
37681	1610	8	,	,	,
37681	1610	9	of	of	IN
37681	1610	10	course	course	NN
37681	1610	11	,	,	,
37681	1610	12	unusable	unusable	JJ
37681	1610	13	for	for	IN
37681	1610	14	beginners	beginner	NNS
37681	1610	15	.	.	.
37681	1611	1	Dr.	Dr.	NNP
37681	1611	2	(	(	-LRB-
37681	1611	3	now	now	RB
37681	1611	4	Sir	Sir	NNP
37681	1611	5	Thomas	Thomas	NNP
37681	1611	6	)	)	-RRB-
37681	1611	7	Heath	Heath	NNP
37681	1611	8	says	say	VBZ
37681	1611	9	,	,	,
37681	1611	10	"	"	``
37681	1611	11	It	-PRON-	PRP
37681	1611	12	seems	seem	VBZ
37681	1611	13	best	good	JJS
37681	1611	14	,	,	,
37681	1611	15	therefore	therefore	RB
37681	1611	16	,	,	,
37681	1611	17	to	to	TO
37681	1611	18	leave	leave	VB
37681	1611	19	to	to	IN
37681	1611	20	higher	high	JJR
37681	1611	21	geometry	geometry	VB
37681	1611	22	the	the	DT
37681	1611	23	conception	conception	NN
37681	1611	24	of	of	IN
37681	1611	25	infinitely	infinitely	RB
37681	1611	26	distant	distant	JJ
37681	1611	27	points	point	NNS
37681	1611	28	on	on	IN
37681	1611	29	a	a	DT
37681	1611	30	line	line	NN
37681	1611	31	and	and	CC
37681	1611	32	of	of	IN
37681	1611	33	two	two	CD
37681	1611	34	straight	straight	JJ
37681	1611	35	lines	line	NNS
37681	1611	36	meeting	meet	VBG
37681	1611	37	at	at	IN
37681	1611	38	infinity	infinity	NN
37681	1611	39	,	,	,
37681	1611	40	like	like	IN
37681	1611	41	imaginary	imaginary	JJ
37681	1611	42	points	point	NNS
37681	1611	43	of	of	IN
37681	1611	44	intersection	intersection	NN
37681	1611	45	,	,	,
37681	1611	46	and	and	CC
37681	1611	47	,	,	,
37681	1611	48	for	for	IN
37681	1611	49	the	the	DT
37681	1611	50	purposes	purpose	NNS
37681	1611	51	of	of	IN
37681	1611	52	elementary	elementary	JJ
37681	1611	53	geometry	geometry	NN
37681	1611	54	,	,	,
37681	1611	55	to	to	TO
37681	1611	56	rely	rely	VB
37681	1611	57	on	on	IN
37681	1611	58	the	the	DT
37681	1611	59	plain	plain	JJ
37681	1611	60	distinction	distinction	NN
37681	1611	61	between	between	IN
37681	1611	62	'	'	``
37681	1611	63	parallel	parallel	NN
37681	1611	64	'	'	''
37681	1611	65	and	and	CC
37681	1611	66	'	'	''
37681	1611	67	cutting	cutting	NN
37681	1611	68	,	,	,
37681	1611	69	'	'	''
37681	1611	70	which	which	WDT
37681	1611	71	average	average	JJ
37681	1611	72	human	human	JJ
37681	1611	73	intelligence	intelligence	NN
37681	1611	74	can	can	MD
37681	1611	75	readily	readily	RB
37681	1611	76	grasp	grasp	VB
37681	1611	77	.	.	.
37681	1611	78	"	"	''
37681	1612	1	The	the	DT
37681	1612	2	direction	direction	NN
37681	1612	3	definition	definition	NN
37681	1612	4	seems	seem	VBZ
37681	1612	5	to	to	TO
37681	1612	6	have	have	VB
37681	1612	7	originated	originate	VBN
37681	1612	8	with	with	IN
37681	1612	9	Leibnitz	Leibnitz	NNP
37681	1612	10	.	.	.
37681	1613	1	It	-PRON-	PRP
37681	1613	2	is	be	VBZ
37681	1613	3	open	open	JJ
37681	1613	4	to	to	IN
37681	1613	5	the	the	DT
37681	1613	6	serious	serious	JJ
37681	1613	7	objection	objection	NN
37681	1613	8	that	that	IN
37681	1613	9	"	"	``
37681	1613	10	direction	direction	NN
37681	1613	11	"	"	''
37681	1613	12	is	be	VBZ
37681	1613	13	not	not	RB
37681	1613	14	easy	easy	JJ
37681	1613	15	of	of	IN
37681	1613	16	definition	definition	NN
37681	1613	17	,	,	,
37681	1613	18	and	and	CC
37681	1613	19	that	that	IN
37681	1613	20	it	-PRON-	PRP
37681	1613	21	is	be	VBZ
37681	1613	22	used	use	VBN
37681	1613	23	very	very	RB
37681	1613	24	loosely	loosely	RB
37681	1613	25	.	.	.
37681	1614	1	If	if	IN
37681	1614	2	two	two	CD
37681	1614	3	people	people	NNS
37681	1614	4	on	on	IN
37681	1614	5	different	different	JJ
37681	1614	6	meridians	meridian	NNS
37681	1614	7	travel	travel	VBP
37681	1614	8	due	due	JJ
37681	1614	9	north	north	RB
37681	1614	10	,	,	,
37681	1614	11	do	do	VBP
37681	1614	12	they	-PRON-	PRP
37681	1614	13	travel	travel	VB
37681	1614	14	in	in	IN
37681	1614	15	the	the	DT
37681	1614	16	same	same	JJ
37681	1614	17	direction	direction	NN
37681	1614	18	?	?	.
37681	1615	1	on	on	IN
37681	1615	2	parallel	parallel	JJ
37681	1615	3	lines	line	NNS
37681	1615	4	?	?	.
37681	1616	1	The	the	DT
37681	1616	2	definition	definition	NN
37681	1616	3	is	be	VBZ
37681	1616	4	as	as	RB
37681	1616	5	objectionable	objectionable	JJ
37681	1616	6	as	as	IN
37681	1616	7	that	that	DT
37681	1616	8	of	of	IN
37681	1616	9	angle	angle	NN
37681	1616	10	as	as	IN
37681	1616	11	the	the	DT
37681	1616	12	"	"	``
37681	1616	13	difference	difference	NN
37681	1616	14	of	of	IN
37681	1616	15	direction	direction	NN
37681	1616	16	"	"	''
37681	1616	17	of	of	IN
37681	1616	18	two	two	CD
37681	1616	19	intersecting	intersect	VBG
37681	1616	20	lines	line	NNS
37681	1616	21	.	.	.
37681	1617	1	From	from	IN
37681	1617	2	these	these	DT
37681	1617	3	definitions	definition	NNS
37681	1617	4	of	of	IN
37681	1617	5	the	the	DT
37681	1617	6	first	first	JJ
37681	1617	7	book	book	NN
37681	1617	8	of	of	IN
37681	1617	9	Euclid	Euclid	NNP
37681	1617	10	we	-PRON-	PRP
37681	1617	11	see	see	VBP
37681	1617	12	(	(	-LRB-
37681	1617	13	1	1	CD
37681	1617	14	)	)	-RRB-
37681	1617	15	what	what	WDT
37681	1617	16	a	a	DT
37681	1617	17	small	small	JJ
37681	1617	18	number	number	NN
37681	1617	19	Euclid	Euclid	NNP
37681	1617	20	considered	consider	VBN
37681	1617	21	as	as	IN
37681	1617	22	basal	basal	NN
37681	1617	23	;	;	,
37681	1617	24	(	(	-LRB-
37681	1617	25	2	2	LS
37681	1617	26	)	)	-RRB-
37681	1617	27	what	what	WDT
37681	1617	28	a	a	DT
37681	1617	29	change	change	NN
37681	1617	30	has	have	VBZ
37681	1617	31	taken	take	VBN
37681	1617	32	place	place	NN
37681	1617	33	in	in	IN
37681	1617	34	the	the	DT
37681	1617	35	generalization	generalization	NN
37681	1617	36	of	of	IN
37681	1617	37	concepts	concept	NNS
37681	1617	38	;	;	:
37681	1617	39	(	(	-LRB-
37681	1617	40	3	3	LS
37681	1617	41	)	)	-RRB-
37681	1617	42	how	how	WRB
37681	1617	43	the	the	DT
37681	1617	44	language	language	NN
37681	1617	45	has	have	VBZ
37681	1617	46	varied	vary	VBN
37681	1617	47	.	.	.
37681	1618	1	Nevertheless	nevertheless	RB
37681	1618	2	we	-PRON-	PRP
37681	1618	3	are	be	VBP
37681	1618	4	not	not	RB
37681	1618	5	to	to	TO
37681	1618	6	be	be	VB
37681	1618	7	commended	commend	VBN
37681	1618	8	if	if	IN
37681	1618	9	we	-PRON-	PRP
37681	1618	10	adhere	adhere	VBP
37681	1618	11	to	to	IN
37681	1618	12	Euclid	Euclid	NNP
37681	1618	13	's	's	POS
37681	1618	14	small	small	JJ
37681	1618	15	number	number	NN
37681	1618	16	,	,	,
37681	1618	17	because	because	IN
37681	1618	18	geometry	geometry	NN
37681	1618	19	is	be	VBZ
37681	1618	20	now	now	RB
37681	1618	21	taught	teach	VBN
37681	1618	22	to	to	IN
37681	1618	23	pupils	pupil	NNS
37681	1618	24	whose	whose	WP$
37681	1618	25	vocabulary	vocabulary	NN
37681	1618	26	is	be	VBZ
37681	1618	27	limited	limited	JJ
37681	1618	28	.	.	.
37681	1619	1	It	-PRON-	PRP
37681	1619	2	is	be	VBZ
37681	1619	3	necessary	necessary	JJ
37681	1619	4	to	to	TO
37681	1619	5	define	define	VB
37681	1619	6	more	more	JJR
37681	1619	7	terms	term	NNS
37681	1619	8	,	,	,
37681	1619	9	and	and	CC
37681	1619	10	to	to	TO
37681	1619	11	scatter	scatter	VB
37681	1619	12	the	the	DT
37681	1619	13	definitions	definition	NNS
37681	1619	14	through	through	IN
37681	1619	15	the	the	DT
37681	1619	16	work	work	NN
37681	1619	17	for	for	IN
37681	1619	18	use	use	NN
37681	1619	19	as	as	IN
37681	1619	20	they	-PRON-	PRP
37681	1619	21	are	be	VBP
37681	1619	22	needed	need	VBN
37681	1619	23	,	,	,
37681	1619	24	instead	instead	RB
37681	1619	25	of	of	IN
37681	1619	26	massing	mass	VBG
37681	1619	27	them	-PRON-	PRP
37681	1619	28	at	at	IN
37681	1619	29	the	the	DT
37681	1619	30	beginning	beginning	NN
37681	1619	31	,	,	,
37681	1619	32	as	as	IN
37681	1619	33	in	in	IN
37681	1619	34	a	a	DT
37681	1619	35	dictionary	dictionary	NN
37681	1619	36	.	.	.
37681	1620	1	The	the	DT
37681	1620	2	most	most	RBS
37681	1620	3	important	important	JJ
37681	1620	4	lesson	lesson	NN
37681	1620	5	to	to	TO
37681	1620	6	be	be	VB
37681	1620	7	learned	learn	VBN
37681	1620	8	from	from	IN
37681	1620	9	Euclid	Euclid	NNP
37681	1620	10	's	's	POS
37681	1620	11	definitions	definition	NNS
37681	1620	12	is	be	VBZ
37681	1620	13	that	that	IN
37681	1620	14	only	only	RB
37681	1620	15	the	the	DT
37681	1620	16	basal	basal	NN
37681	1620	17	ones	one	NNS
37681	1620	18	,	,	,
37681	1620	19	relatively	relatively	RB
37681	1620	20	few	few	JJ
37681	1620	21	in	in	IN
37681	1620	22	number	number	NN
37681	1620	23	,	,	,
37681	1620	24	need	need	VBP
37681	1620	25	to	to	TO
37681	1620	26	be	be	VB
37681	1620	27	learned	learn	VBN
37681	1620	28	,	,	,
37681	1620	29	and	and	CC
37681	1620	30	these	these	DT
37681	1620	31	because	because	IN
37681	1620	32	they	-PRON-	PRP
37681	1620	33	are	be	VBP
37681	1620	34	used	use	VBN
37681	1620	35	as	as	IN
37681	1620	36	the	the	DT
37681	1620	37	foundations	foundation	NNS
37681	1620	38	upon	upon	IN
37681	1620	39	which	which	WDT
37681	1620	40	proofs	proof	NNS
37681	1620	41	are	be	VBP
37681	1620	42	built	build	VBN
37681	1620	43	.	.	.
37681	1621	1	It	-PRON-	PRP
37681	1621	2	should	should	MD
37681	1621	3	also	also	RB
37681	1621	4	be	be	VB
37681	1621	5	noticed	notice	VBN
37681	1621	6	that	that	IN
37681	1621	7	Euclid	Euclid	NNP
37681	1621	8	explains	explain	VBZ
37681	1621	9	nothing	nothing	NN
37681	1621	10	in	in	IN
37681	1621	11	these	these	DT
37681	1621	12	definitions	definition	NNS
37681	1621	13	;	;	:
37681	1621	14	they	-PRON-	PRP
37681	1621	15	are	be	VBP
37681	1621	16	hard	hard	JJ
37681	1621	17	statements	statement	NNS
37681	1621	18	of	of	IN
37681	1621	19	fact	fact	NN
37681	1621	20	,	,	,
37681	1621	21	massed	mass	VBN
37681	1621	22	at	at	IN
37681	1621	23	the	the	DT
37681	1621	24	beginning	beginning	NN
37681	1621	25	of	of	IN
37681	1621	26	his	-PRON-	PRP$
37681	1621	27	treatise	treatise	NN
37681	1621	28	.	.	.
37681	1622	1	Not	not	RB
37681	1622	2	always	always	RB
37681	1622	3	as	as	IN
37681	1622	4	statements	statement	NNS
37681	1622	5	,	,	,
37681	1622	6	and	and	CC
37681	1622	7	not	not	RB
37681	1622	8	at	at	RB
37681	1622	9	all	all	RB
37681	1622	10	in	in	IN
37681	1622	11	their	-PRON-	PRP$
37681	1622	12	arrangement	arrangement	NN
37681	1622	13	,	,	,
37681	1622	14	are	be	VBP
37681	1622	15	they	-PRON-	PRP
37681	1622	16	suited	suited	JJ
37681	1622	17	to	to	IN
37681	1622	18	the	the	DT
37681	1622	19	needs	need	NNS
37681	1622	20	of	of	IN
37681	1622	21	our	-PRON-	PRP$
37681	1622	22	boys	boy	NNS
37681	1622	23	and	and	CC
37681	1622	24	girls	girl	NNS
37681	1622	25	at	at	IN
37681	1622	26	present	present	NN
37681	1622	27	.	.	.
37681	1623	1	Having	have	VBG
37681	1623	2	considered	consider	VBN
37681	1623	3	Euclid	Euclid	NNP
37681	1623	4	's	's	POS
37681	1623	5	definitions	definition	NNS
37681	1623	6	of	of	IN
37681	1623	7	Book	Book	NNP
37681	1623	8	I	-PRON-	PRP
37681	1623	9	,	,	,
37681	1623	10	it	-PRON-	PRP
37681	1623	11	is	be	VBZ
37681	1623	12	proper	proper	JJ
37681	1623	13	to	to	TO
37681	1623	14	turn	turn	VB
37681	1623	15	to	to	IN
37681	1623	16	some	some	DT
37681	1623	17	of	of	IN
37681	1623	18	those	those	DT
37681	1623	19	terms	term	NNS
37681	1623	20	that	that	WDT
37681	1623	21	have	have	VBP
37681	1623	22	been	be	VBN
37681	1623	23	added	add	VBN
37681	1623	24	from	from	IN
37681	1623	25	time	time	NN
37681	1623	26	to	to	IN
37681	1623	27	time	time	NN
37681	1623	28	to	to	IN
37681	1623	29	his	-PRON-	PRP$
37681	1623	30	list	list	NN
37681	1623	31	,	,	,
37681	1623	32	and	and	CC
37681	1623	33	are	be	VBP
37681	1623	34	now	now	RB
37681	1623	35	usually	usually	RB
37681	1623	36	incorporated	incorporate	VBN
37681	1623	37	in	in	IN
37681	1623	38	American	american	JJ
37681	1623	39	textbooks	textbook	NNS
37681	1623	40	.	.	.
37681	1624	1	It	-PRON-	PRP
37681	1624	2	will	will	MD
37681	1624	3	be	be	VB
37681	1624	4	seen	see	VBN
37681	1624	5	that	that	IN
37681	1624	6	most	most	JJS
37681	1624	7	of	of	IN
37681	1624	8	these	these	DT
37681	1624	9	were	be	VBD
37681	1624	10	assumed	assume	VBN
37681	1624	11	by	by	IN
37681	1624	12	Euclid	Euclid	NNP
37681	1624	13	to	to	TO
37681	1624	14	be	be	VB
37681	1624	15	known	know	VBN
37681	1624	16	by	by	IN
37681	1624	17	his	-PRON-	PRP$
37681	1624	18	mature	mature	JJ
37681	1624	19	readers	reader	NNS
37681	1624	20	.	.	.
37681	1625	1	They	-PRON-	PRP
37681	1625	2	need	need	VBP
37681	1625	3	to	to	TO
37681	1625	4	be	be	VB
37681	1625	5	defined	define	VBN
37681	1625	6	for	for	IN
37681	1625	7	young	young	JJ
37681	1625	8	people	people	NNS
37681	1625	9	,	,	,
37681	1625	10	but	but	CC
37681	1625	11	most	most	JJS
37681	1625	12	of	of	IN
37681	1625	13	them	-PRON-	PRP
37681	1625	14	are	be	VBP
37681	1625	15	not	not	RB
37681	1625	16	basal	basal	JJ
37681	1625	17	,	,	,
37681	1625	18	that	that	RB
37681	1625	19	is	is	RB
37681	1625	20	,	,	,
37681	1625	21	they	-PRON-	PRP
37681	1625	22	are	be	VBP
37681	1625	23	not	not	RB
37681	1625	24	used	use	VBN
37681	1625	25	in	in	IN
37681	1625	26	the	the	DT
37681	1625	27	proofs	proof	NNS
37681	1625	28	of	of	IN
37681	1625	29	propositions	proposition	NNS
37681	1625	30	.	.	.
37681	1626	1	Some	some	DT
37681	1626	2	of	of	IN
37681	1626	3	these	these	DT
37681	1626	4	terms	term	NNS
37681	1626	5	,	,	,
37681	1626	6	such	such	JJ
37681	1626	7	as	as	IN
37681	1626	8	magnitudes	magnitude	NNS
37681	1626	9	,	,	,
37681	1626	10	curve	curve	NN
37681	1626	11	line	line	NN
37681	1626	12	,	,	,
37681	1626	13	broken	broken	JJ
37681	1626	14	line	line	NN
37681	1626	15	,	,	,
37681	1626	16	curvilinear	curvilinear	NN
37681	1626	17	figure	figure	NN
37681	1626	18	,	,	,
37681	1626	19	bisector	bisector	NN
37681	1626	20	,	,	,
37681	1626	21	adjacent	adjacent	JJ
37681	1626	22	angles	angle	NNS
37681	1626	23	,	,	,
37681	1626	24	reflex	reflex	NNP
37681	1626	25	angles	angle	NNS
37681	1626	26	,	,	,
37681	1626	27	oblique	oblique	JJ
37681	1626	28	angles	angle	NNS
37681	1626	29	and	and	CC
37681	1626	30	lines	line	NNS
37681	1626	31	,	,	,
37681	1626	32	and	and	CC
37681	1626	33	vertical	vertical	JJ
37681	1626	34	angles	angle	NNS
37681	1626	35	,	,	,
37681	1626	36	need	need	VBP
37681	1626	37	merely	merely	RB
37681	1626	38	a	a	DT
37681	1626	39	word	word	NN
37681	1626	40	of	of	IN
37681	1626	41	explanation	explanation	NN
37681	1626	42	so	so	IN
37681	1626	43	that	that	IN
37681	1626	44	they	-PRON-	PRP
37681	1626	45	may	may	MD
37681	1626	46	be	be	VB
37681	1626	47	used	use	VBN
37681	1626	48	intelligently	intelligently	RB
37681	1626	49	.	.	.
37681	1627	1	If	if	IN
37681	1627	2	they	-PRON-	PRP
37681	1627	3	were	be	VBD
37681	1627	4	numerous	numerous	JJ
37681	1627	5	enough	enough	RB
37681	1627	6	to	to	TO
37681	1627	7	make	make	VB
37681	1627	8	it	-PRON-	PRP
37681	1627	9	worth	worth	JJ
37681	1627	10	the	the	DT
37681	1627	11	while	while	NN
37681	1627	12	,	,	,
37681	1627	13	they	-PRON-	PRP
37681	1627	14	could	could	MD
37681	1627	15	be	be	VB
37681	1627	16	classified	classify	VBN
37681	1627	17	in	in	IN
37681	1627	18	our	-PRON-	PRP$
37681	1627	19	textbooks	textbook	NNS
37681	1627	20	as	as	IN
37681	1627	21	of	of	IN
37681	1627	22	minor	minor	JJ
37681	1627	23	importance	importance	NN
37681	1627	24	,	,	,
37681	1627	25	but	but	CC
37681	1627	26	such	such	PDT
37681	1627	27	a	a	DT
37681	1627	28	course	course	NN
37681	1627	29	would	would	MD
37681	1627	30	cause	cause	VB
37681	1627	31	more	more	JJR
37681	1627	32	trouble	trouble	NN
37681	1627	33	than	than	IN
37681	1627	34	it	-PRON-	PRP
37681	1627	35	is	be	VBZ
37681	1627	36	worth	worth	JJ
37681	1627	37	.	.	.
37681	1628	1	Other	other	JJ
37681	1628	2	terms	term	NNS
37681	1628	3	have	have	VBP
37681	1628	4	come	come	VBN
37681	1628	5	into	into	IN
37681	1628	6	use	use	NN
37681	1628	7	in	in	IN
37681	1628	8	modern	modern	JJ
37681	1628	9	times	time	NNS
37681	1628	10	that	that	WDT
37681	1628	11	are	be	VBP
37681	1628	12	not	not	RB
37681	1628	13	common	common	JJ
37681	1628	14	expressions	expression	NNS
37681	1628	15	with	with	IN
37681	1628	16	which	which	WDT
37681	1628	17	students	student	NNS
37681	1628	18	are	be	VBP
37681	1628	19	familiar	familiar	JJ
37681	1628	20	.	.	.
37681	1629	1	Such	such	PDT
37681	1629	2	a	a	DT
37681	1629	3	term	term	NN
37681	1629	4	is	be	VBZ
37681	1629	5	"	"	``
37681	1629	6	straight	straight	JJ
37681	1629	7	angle	angle	NN
37681	1629	8	,	,	,
37681	1629	9	"	"	''
37681	1629	10	a	a	DT
37681	1629	11	concept	concept	NN
37681	1629	12	not	not	RB
37681	1629	13	used	use	VBN
37681	1629	14	by	by	IN
37681	1629	15	Euclid	Euclid	NNP
37681	1629	16	,	,	,
37681	1629	17	but	but	CC
37681	1629	18	one	one	CD
37681	1629	19	that	that	WDT
37681	1629	20	adds	add	VBZ
37681	1629	21	so	so	RB
37681	1629	22	materially	materially	RB
37681	1629	23	to	to	IN
37681	1629	24	the	the	DT
37681	1629	25	interest	interest	NN
37681	1629	26	and	and	CC
37681	1629	27	value	value	NN
37681	1629	28	of	of	IN
37681	1629	29	geometry	geometry	NN
37681	1629	30	as	as	RB
37681	1629	31	now	now	RB
37681	1629	32	to	to	TO
37681	1629	33	be	be	VB
37681	1629	34	generally	generally	RB
37681	1629	35	recognized	recognize	VBN
37681	1629	36	.	.	.
37681	1630	1	There	there	EX
37681	1630	2	is	be	VBZ
37681	1630	3	also	also	RB
37681	1630	4	the	the	DT
37681	1630	5	word	word	NN
37681	1630	6	"	"	``
37681	1630	7	perigon	perigon	NNP
37681	1630	8	,	,	,
37681	1630	9	"	"	''
37681	1630	10	meaning	mean	VBG
37681	1630	11	the	the	DT
37681	1630	12	whole	whole	JJ
37681	1630	13	angular	angular	JJ
37681	1630	14	space	space	NN
37681	1630	15	about	about	IN
37681	1630	16	a	a	DT
37681	1630	17	point	point	NN
37681	1630	18	.	.	.
37681	1631	1	This	this	DT
37681	1631	2	was	be	VBD
37681	1631	3	excluded	exclude	VBN
37681	1631	4	by	by	IN
37681	1631	5	the	the	DT
37681	1631	6	Greeks	Greeks	NNPS
37681	1631	7	because	because	IN
37681	1631	8	their	-PRON-	PRP$
37681	1631	9	idea	idea	NN
37681	1631	10	of	of	IN
37681	1631	11	angle	angle	NN
37681	1631	12	required	require	VBD
37681	1631	13	it	-PRON-	PRP
37681	1631	14	to	to	TO
37681	1631	15	be	be	VB
37681	1631	16	less	less	JJR
37681	1631	17	than	than	IN
37681	1631	18	a	a	DT
37681	1631	19	straight	straight	JJ
37681	1631	20	angle	angle	NN
37681	1631	21	.	.	.
37681	1632	1	The	the	DT
37681	1632	2	word	word	NN
37681	1632	3	means	mean	VBZ
37681	1632	4	"	"	``
37681	1632	5	around	around	IN
37681	1632	6	angle	angle	NN
37681	1632	7	,	,	,
37681	1632	8	"	"	''
37681	1632	9	and	and	CC
37681	1632	10	is	be	VBZ
37681	1632	11	the	the	DT
37681	1632	12	best	good	JJS
37681	1632	13	one	one	NN
37681	1632	14	that	that	WDT
37681	1632	15	has	have	VBZ
37681	1632	16	been	be	VBN
37681	1632	17	coined	coin	VBN
37681	1632	18	for	for	IN
37681	1632	19	the	the	DT
37681	1632	20	purpose	purpose	NN
37681	1632	21	.	.	.
37681	1633	1	"	"	``
37681	1633	2	Flat	flat	JJ
37681	1633	3	angle	angle	NN
37681	1633	4	"	"	''
37681	1633	5	and	and	CC
37681	1633	6	"	"	``
37681	1633	7	whole	whole	JJ
37681	1633	8	angle	angle	NN
37681	1633	9	"	"	''
37681	1633	10	are	be	VBP
37681	1633	11	among	among	IN
37681	1633	12	the	the	DT
37681	1633	13	names	name	NNS
37681	1633	14	suggested	suggest	VBN
37681	1633	15	for	for	IN
37681	1633	16	these	these	DT
37681	1633	17	two	two	CD
37681	1633	18	modern	modern	JJ
37681	1633	19	concepts	concept	NNS
37681	1633	20	.	.	.
37681	1634	1	The	the	DT
37681	1634	2	terms	term	NNS
37681	1634	3	"	"	``
37681	1634	4	complement	complement	JJ
37681	1634	5	,	,	,
37681	1634	6	"	"	''
37681	1634	7	"	"	``
37681	1634	8	supplement	supplement	NN
37681	1634	9	,	,	,
37681	1634	10	"	"	''
37681	1634	11	and	and	CC
37681	1634	12	"	"	``
37681	1634	13	conjugate	conjugate	JJ
37681	1634	14	,	,	,
37681	1634	15	"	"	''
37681	1634	16	meaning	mean	VBG
37681	1634	17	the	the	DT
37681	1634	18	difference	difference	NN
37681	1634	19	between	between	IN
37681	1634	20	a	a	DT
37681	1634	21	given	give	VBN
37681	1634	22	angle	angle	NN
37681	1634	23	and	and	CC
37681	1634	24	a	a	DT
37681	1634	25	right	right	JJ
37681	1634	26	angle	angle	NN
37681	1634	27	,	,	,
37681	1634	28	straight	straight	JJ
37681	1634	29	angle	angle	NN
37681	1634	30	,	,	,
37681	1634	31	and	and	CC
37681	1634	32	perigon	perigon	NNP
37681	1634	33	respectively	respectively	RB
37681	1634	34	,	,	,
37681	1634	35	have	have	VBP
37681	1634	36	also	also	RB
37681	1634	37	entered	enter	VBN
37681	1634	38	our	-PRON-	PRP$
37681	1634	39	vocabulary	vocabulary	NN
37681	1634	40	and	and	CC
37681	1634	41	need	need	VBP
37681	1634	42	defining	define	VBG
37681	1634	43	.	.	.
37681	1635	1	There	there	EX
37681	1635	2	are	be	VBP
37681	1635	3	also	also	RB
37681	1635	4	certain	certain	JJ
37681	1635	5	terms	term	NNS
37681	1635	6	expressing	express	VBG
37681	1635	7	relationship	relationship	NN
37681	1635	8	which	which	WDT
37681	1635	9	Euclid	Euclid	NNP
37681	1635	10	does	do	VBZ
37681	1635	11	not	not	RB
37681	1635	12	define	define	VB
37681	1635	13	,	,	,
37681	1635	14	and	and	CC
37681	1635	15	which	which	WDT
37681	1635	16	have	have	VBP
37681	1635	17	been	be	VBN
37681	1635	18	so	so	RB
37681	1635	19	changed	change	VBN
37681	1635	20	in	in	IN
37681	1635	21	recent	recent	JJ
37681	1635	22	times	time	NNS
37681	1635	23	as	as	IN
37681	1635	24	to	to	TO
37681	1635	25	require	require	VB
37681	1635	26	careful	careful	JJ
37681	1635	27	definition	definition	NN
37681	1635	28	at	at	IN
37681	1635	29	present	present	NN
37681	1635	30	.	.	.
37681	1636	1	Chief	chief	NN
37681	1636	2	among	among	IN
37681	1636	3	these	these	DT
37681	1636	4	are	be	VBP
37681	1636	5	the	the	DT
37681	1636	6	words	word	NNS
37681	1636	7	"	"	``
37681	1636	8	equal	equal	JJ
37681	1636	9	,	,	,
37681	1636	10	"	"	''
37681	1636	11	"	"	``
37681	1636	12	congruent	congruent	JJ
37681	1636	13	,	,	,
37681	1636	14	"	"	''
37681	1636	15	and	and	CC
37681	1636	16	"	"	``
37681	1636	17	equivalent	equivalent	JJ
37681	1636	18	.	.	.
37681	1636	19	"	"	''
37681	1637	1	Euclid	Euclid	NNP
37681	1637	2	used	use	VBD
37681	1637	3	the	the	DT
37681	1637	4	single	single	JJ
37681	1637	5	word	word	NN
37681	1637	6	"	"	``
37681	1637	7	equal	equal	JJ
37681	1637	8	"	"	''
37681	1637	9	for	for	IN
37681	1637	10	all	all	DT
37681	1637	11	three	three	CD
37681	1637	12	concepts	concept	NNS
37681	1637	13	,	,	,
37681	1637	14	although	although	IN
37681	1637	15	some	some	DT
37681	1637	16	of	of	IN
37681	1637	17	his	-PRON-	PRP$
37681	1637	18	recent	recent	JJ
37681	1637	19	editors	editor	NNS
37681	1637	20	have	have	VBP
37681	1637	21	changed	change	VBN
37681	1637	22	it	-PRON-	PRP
37681	1637	23	to	to	IN
37681	1637	24	"	"	``
37681	1637	25	identically	identically	RB
37681	1637	26	equal	equal	JJ
37681	1637	27	"	"	''
37681	1637	28	in	in	IN
37681	1637	29	the	the	DT
37681	1637	30	case	case	NN
37681	1637	31	of	of	IN
37681	1637	32	congruence	congruence	NN
37681	1637	33	.	.	.
37681	1638	1	In	in	IN
37681	1638	2	modern	modern	JJ
37681	1638	3	speech	speech	NN
37681	1638	4	we	-PRON-	PRP
37681	1638	5	use	use	VBP
37681	1638	6	the	the	DT
37681	1638	7	word	word	NN
37681	1638	8	"	"	``
37681	1638	9	equal	equal	JJ
37681	1638	10	"	"	''
37681	1638	11	commonly	commonly	RB
37681	1638	12	to	to	TO
37681	1638	13	mean	mean	VB
37681	1638	14	"	"	``
37681	1638	15	like	like	RB
37681	1638	16	-	-	HYPH
37681	1638	17	valued	value	VBN
37681	1638	18	,	,	,
37681	1638	19	"	"	''
37681	1638	20	"	"	``
37681	1638	21	having	have	VBG
37681	1638	22	the	the	DT
37681	1638	23	same	same	JJ
37681	1638	24	measure	measure	NN
37681	1638	25	,	,	,
37681	1638	26	"	"	''
37681	1638	27	as	as	IN
37681	1638	28	when	when	WRB
37681	1638	29	we	-PRON-	PRP
37681	1638	30	say	say	VBP
37681	1638	31	the	the	DT
37681	1638	32	circumference	circumference	NN
37681	1638	33	of	of	IN
37681	1638	34	a	a	DT
37681	1638	35	circle	circle	NN
37681	1638	36	"	"	``
37681	1638	37	equals	equal	VBZ
37681	1638	38	"	"	''
37681	1638	39	a	a	DT
37681	1638	40	straight	straight	JJ
37681	1638	41	line	line	NN
37681	1638	42	whose	whose	WP$
37681	1638	43	length	length	NN
37681	1638	44	is	be	VBZ
37681	1638	45	2[pi]_r	2[pi]_r	CD
37681	1638	46	_	_	NNP
37681	1638	47	,	,	,
37681	1638	48	although	although	IN
37681	1638	49	it	-PRON-	PRP
37681	1638	50	could	could	MD
37681	1638	51	not	not	RB
37681	1638	52	coincide	coincide	VB
37681	1638	53	with	with	IN
37681	1638	54	it	-PRON-	PRP
37681	1638	55	.	.	.
37681	1639	1	Of	of	IN
37681	1639	2	late	late	RB
37681	1639	3	,	,	,
37681	1639	4	therefore	therefore	RB
37681	1639	5	,	,	,
37681	1639	6	in	in	IN
37681	1639	7	Europe	Europe	NNP
37681	1639	8	and	and	CC
37681	1639	9	America	America	NNP
37681	1639	10	,	,	,
37681	1639	11	and	and	CC
37681	1639	12	wherever	wherever	WRB
37681	1639	13	European	european	JJ
37681	1639	14	influence	influence	NN
37681	1639	15	reaches	reach	VBZ
37681	1639	16	,	,	,
37681	1639	17	the	the	DT
37681	1639	18	word	word	NN
37681	1639	19	"	"	``
37681	1639	20	congruent	congruent	JJ
37681	1639	21	"	"	''
37681	1639	22	is	be	VBZ
37681	1639	23	coming	come	VBG
37681	1639	24	into	into	IN
37681	1639	25	use	use	NN
37681	1639	26	to	to	TO
37681	1639	27	mean	mean	VB
37681	1639	28	"	"	``
37681	1639	29	identically	identically	RB
37681	1639	30	equal	equal	JJ
37681	1639	31	"	"	''
37681	1639	32	in	in	IN
37681	1639	33	the	the	DT
37681	1639	34	sense	sense	NN
37681	1639	35	of	of	IN
37681	1639	36	superposable	superposable	JJ
37681	1639	37	.	.	.
37681	1640	1	We	-PRON-	PRP
37681	1640	2	therefore	therefore	RB
37681	1640	3	speak	speak	VBP
37681	1640	4	of	of	IN
37681	1640	5	congruent	congruent	JJ
37681	1640	6	triangles	triangle	NNS
37681	1640	7	and	and	CC
37681	1640	8	congruent	congruent	JJ
37681	1640	9	parallelograms	parallelogram	NNS
37681	1640	10	as	as	IN
37681	1640	11	being	be	VBG
37681	1640	12	those	those	DT
37681	1640	13	that	that	WDT
37681	1640	14	are	be	VBP
37681	1640	15	superposable	superposable	JJ
37681	1640	16	.	.	.
37681	1641	1	It	-PRON-	PRP
37681	1641	2	is	be	VBZ
37681	1641	3	a	a	DT
37681	1641	4	little	little	JJ
37681	1641	5	unfortunate	unfortunate	JJ
37681	1641	6	that	that	IN
37681	1641	7	"	"	``
37681	1641	8	equal	equal	JJ
37681	1641	9	"	"	''
37681	1641	10	has	have	VBZ
37681	1641	11	come	come	VBN
37681	1641	12	to	to	TO
37681	1641	13	be	be	VB
37681	1641	14	so	so	RB
37681	1641	15	loosely	loosely	RB
37681	1641	16	used	use	VBN
37681	1641	17	in	in	IN
37681	1641	18	ordinary	ordinary	JJ
37681	1641	19	conversation	conversation	NN
37681	1641	20	that	that	IN
37681	1641	21	we	-PRON-	PRP
37681	1641	22	can	can	MD
37681	1641	23	not	not	RB
37681	1641	24	keep	keep	VB
37681	1641	25	it	-PRON-	PRP
37681	1641	26	to	to	TO
37681	1641	27	mean	mean	VB
37681	1641	28	"	"	``
37681	1641	29	congruent	congruent	JJ
37681	1641	30	"	"	''
37681	1641	31	;	;	:
37681	1641	32	but	but	CC
37681	1641	33	our	-PRON-	PRP$
37681	1641	34	language	language	NN
37681	1641	35	will	will	MD
37681	1641	36	not	not	RB
37681	1641	37	permit	permit	VB
37681	1641	38	it	-PRON-	PRP
37681	1641	39	,	,	,
37681	1641	40	and	and	CC
37681	1641	41	we	-PRON-	PRP
37681	1641	42	are	be	VBP
37681	1641	43	forced	force	VBN
37681	1641	44	to	to	TO
37681	1641	45	use	use	VB
37681	1641	46	the	the	DT
37681	1641	47	newer	new	JJR
37681	1641	48	word	word	NN
37681	1641	49	.	.	.
37681	1642	1	Whenever	whenever	WRB
37681	1642	2	it	-PRON-	PRP
37681	1642	3	can	can	MD
37681	1642	4	be	be	VB
37681	1642	5	used	use	VBN
37681	1642	6	without	without	IN
37681	1642	7	misunderstanding	misunderstanding	NN
37681	1642	8	,	,	,
37681	1642	9	however	however	RB
37681	1642	10	,	,	,
37681	1642	11	it	-PRON-	PRP
37681	1642	12	should	should	MD
37681	1642	13	be	be	VB
37681	1642	14	retained	retain	VBN
37681	1642	15	,	,	,
37681	1642	16	as	as	IN
37681	1642	17	in	in	IN
37681	1642	18	the	the	DT
37681	1642	19	case	case	NN
37681	1642	20	of	of	IN
37681	1642	21	"	"	``
37681	1642	22	equal	equal	JJ
37681	1642	23	straight	straight	JJ
37681	1642	24	lines	line	NNS
37681	1642	25	,	,	,
37681	1642	26	"	"	''
37681	1642	27	"	"	``
37681	1642	28	equal	equal	JJ
37681	1642	29	angles	angle	NNS
37681	1642	30	,	,	,
37681	1642	31	"	"	''
37681	1642	32	and	and	CC
37681	1642	33	"	"	``
37681	1642	34	equal	equal	JJ
37681	1642	35	arcs	arc	NNS
37681	1642	36	of	of	IN
37681	1642	37	the	the	DT
37681	1642	38	same	same	JJ
37681	1642	39	circle	circle	NN
37681	1642	40	.	.	.
37681	1642	41	"	"	''
37681	1643	1	The	the	DT
37681	1643	2	mathematical	mathematical	JJ
37681	1643	3	and	and	CC
37681	1643	4	educational	educational	JJ
37681	1643	5	world	world	NN
37681	1643	6	will	will	MD
37681	1643	7	never	never	RB
37681	1643	8	consent	consent	VB
37681	1643	9	to	to	TO
37681	1643	10	use	use	VB
37681	1643	11	"	"	``
37681	1643	12	congruent	congruent	JJ
37681	1643	13	straight	straight	JJ
37681	1643	14	lines	line	NNS
37681	1643	15	,	,	,
37681	1643	16	"	"	''
37681	1643	17	or	or	CC
37681	1643	18	"	"	``
37681	1643	19	congruent	congruent	JJ
37681	1643	20	angles	angle	NNS
37681	1643	21	,	,	,
37681	1643	22	"	"	''
37681	1643	23	for	for	IN
37681	1643	24	the	the	DT
37681	1643	25	reason	reason	NN
37681	1643	26	that	that	WDT
37681	1643	27	the	the	DT
37681	1643	28	terms	term	NNS
37681	1643	29	are	be	VBP
37681	1643	30	unnecessarily	unnecessarily	RB
37681	1643	31	long	long	JJ
37681	1643	32	,	,	,
37681	1643	33	no	no	DT
37681	1643	34	misunderstanding	misunderstanding	NN
37681	1643	35	being	be	VBG
37681	1643	36	possible	possible	JJ
37681	1643	37	when	when	WRB
37681	1643	38	"	"	``
37681	1643	39	equal	equal	JJ
37681	1643	40	"	"	''
37681	1643	41	is	be	VBZ
37681	1643	42	used	use	VBN
37681	1643	43	.	.	.
37681	1644	1	The	the	DT
37681	1644	2	word	word	NN
37681	1644	3	"	"	``
37681	1644	4	equivalent	equivalent	NN
37681	1644	5	"	"	''
37681	1644	6	was	be	VBD
37681	1644	7	introduced	introduce	VBN
37681	1644	8	by	by	IN
37681	1644	9	Legendre	Legendre	NNP
37681	1644	10	at	at	IN
37681	1644	11	the	the	DT
37681	1644	12	close	close	NN
37681	1644	13	of	of	IN
37681	1644	14	the	the	DT
37681	1644	15	eighteenth	eighteenth	JJ
37681	1644	16	century	century	NN
37681	1644	17	to	to	TO
37681	1644	18	indicate	indicate	VB
37681	1644	19	equality	equality	NN
37681	1644	20	of	of	IN
37681	1644	21	length	length	NN
37681	1644	22	,	,	,
37681	1644	23	or	or	CC
37681	1644	24	of	of	IN
37681	1644	25	area	area	NN
37681	1644	26	,	,	,
37681	1644	27	or	or	CC
37681	1644	28	of	of	IN
37681	1644	29	volume	volume	NN
37681	1644	30	.	.	.
37681	1645	1	Euclid	Euclid	NNP
37681	1645	2	had	have	VBD
37681	1645	3	said	say	VBN
37681	1645	4	,	,	,
37681	1645	5	"	"	``
37681	1645	6	Parallelograms	Parallelograms	NNP
37681	1645	7	which	which	WDT
37681	1645	8	are	be	VBP
37681	1645	9	on	on	IN
37681	1645	10	the	the	DT
37681	1645	11	same	same	JJ
37681	1645	12	base	base	NN
37681	1645	13	and	and	CC
37681	1645	14	in	in	IN
37681	1645	15	the	the	DT
37681	1645	16	same	same	JJ
37681	1645	17	parallels	parallel	NNS
37681	1645	18	are	be	VBP
37681	1645	19	equal	equal	JJ
37681	1645	20	to	to	IN
37681	1645	21	one	one	CD
37681	1645	22	another	another	DT
37681	1645	23	,	,	,
37681	1645	24	"	"	''
37681	1645	25	while	while	IN
37681	1645	26	Legendre	Legendre	NNP
37681	1645	27	and	and	CC
37681	1645	28	his	-PRON-	PRP$
37681	1645	29	followers	follower	NNS
37681	1645	30	would	would	MD
37681	1645	31	modify	modify	VB
37681	1645	32	the	the	DT
37681	1645	33	wording	wording	NN
37681	1645	34	somewhat	somewhat	RB
37681	1645	35	and	and	CC
37681	1645	36	introduce	introduce	VBP
37681	1645	37	"	"	``
37681	1645	38	equivalent	equivalent	JJ
37681	1645	39	"	"	''
37681	1645	40	for	for	IN
37681	1645	41	"	"	``
37681	1645	42	equal	equal	JJ
37681	1645	43	.	.	.
37681	1645	44	"	"	''
37681	1646	1	This	this	DT
37681	1646	2	usage	usage	NN
37681	1646	3	has	have	VBZ
37681	1646	4	been	be	VBN
37681	1646	5	retained	retain	VBN
37681	1646	6	.	.	.
37681	1647	1	Congruent	congruent	JJ
37681	1647	2	polygons	polygon	NNS
37681	1647	3	are	be	VBP
37681	1647	4	therefore	therefore	RB
37681	1647	5	necessarily	necessarily	RB
37681	1647	6	equivalent	equivalent	JJ
37681	1647	7	,	,	,
37681	1647	8	but	but	CC
37681	1647	9	equivalent	equivalent	JJ
37681	1647	10	polygons	polygon	NNS
37681	1647	11	are	be	VBP
37681	1647	12	not	not	RB
37681	1647	13	in	in	IN
37681	1647	14	general	general	JJ
37681	1647	15	congruent	congruent	NN
37681	1647	16	.	.	.
37681	1648	1	Congruent	congruent	JJ
37681	1648	2	polygons	polygon	NNS
37681	1648	3	have	have	VBP
37681	1648	4	mutually	mutually	RB
37681	1648	5	equal	equal	JJ
37681	1648	6	sides	side	NNS
37681	1648	7	and	and	CC
37681	1648	8	mutually	mutually	RB
37681	1648	9	equal	equal	JJ
37681	1648	10	angles	angle	NNS
37681	1648	11	,	,	,
37681	1648	12	while	while	IN
37681	1648	13	equivalent	equivalent	JJ
37681	1648	14	polygons	polygon	NNS
37681	1648	15	have	have	VBP
37681	1648	16	no	no	DT
37681	1648	17	equality	equality	NN
37681	1648	18	save	save	IN
37681	1648	19	that	that	DT
37681	1648	20	of	of	IN
37681	1648	21	area	area	NN
37681	1648	22	.	.	.
37681	1649	1	In	in	IN
37681	1649	2	general	general	JJ
37681	1649	3	,	,	,
37681	1649	4	as	as	RB
37681	1649	5	already	already	RB
37681	1649	6	stated	state	VBN
37681	1649	7	,	,	,
37681	1649	8	these	these	DT
37681	1649	9	and	and	CC
37681	1649	10	other	other	JJ
37681	1649	11	terms	term	NNS
37681	1649	12	should	should	MD
37681	1649	13	be	be	VB
37681	1649	14	defined	define	VBN
37681	1649	15	just	just	RB
37681	1649	16	before	before	IN
37681	1649	17	they	-PRON-	PRP
37681	1649	18	are	be	VBP
37681	1649	19	used	use	VBN
37681	1649	20	instead	instead	RB
37681	1649	21	of	of	IN
37681	1649	22	at	at	IN
37681	1649	23	the	the	DT
37681	1649	24	beginning	beginning	NN
37681	1649	25	of	of	IN
37681	1649	26	geometry	geometry	NN
37681	1649	27	.	.	.
37681	1650	1	The	the	DT
37681	1650	2	reason	reason	NN
37681	1650	3	for	for	IN
37681	1650	4	this	this	DT
37681	1650	5	,	,	,
37681	1650	6	from	from	IN
37681	1650	7	the	the	DT
37681	1650	8	educational	educational	JJ
37681	1650	9	standpoint	standpoint	NN
37681	1650	10	and	and	CC
37681	1650	11	considering	consider	VBG
37681	1650	12	the	the	DT
37681	1650	13	present	present	JJ
37681	1650	14	position	position	NN
37681	1650	15	of	of	IN
37681	1650	16	geometry	geometry	NN
37681	1650	17	in	in	IN
37681	1650	18	the	the	DT
37681	1650	19	curriculum	curriculum	NN
37681	1650	20	,	,	,
37681	1650	21	is	be	VBZ
37681	1650	22	apparent	apparent	JJ
37681	1650	23	.	.	.
37681	1651	1	We	-PRON-	PRP
37681	1651	2	shall	shall	MD
37681	1651	3	now	now	RB
37681	1651	4	consider	consider	VB
37681	1651	5	the	the	DT
37681	1651	6	definitions	definition	NNS
37681	1651	7	of	of	IN
37681	1651	8	Euclid	Euclid	NNP
37681	1651	9	's	's	POS
37681	1651	10	Book	Book	NNP
37681	1651	11	III	III	NNP
37681	1651	12	,	,	,
37681	1651	13	which	which	WDT
37681	1651	14	is	be	VBZ
37681	1651	15	usually	usually	RB
37681	1651	16	taken	take	VBN
37681	1651	17	as	as	IN
37681	1651	18	Book	Book	NNP
37681	1651	19	II	II	NNP
37681	1651	20	in	in	IN
37681	1651	21	America	America	NNP
37681	1651	22	.	.	.
37681	1652	1	1	1	LS
37681	1652	2	.	.	.
37681	1653	1	EQUAL	equal	NN
37681	1653	2	CIRCLES	circle	NNS
37681	1653	3	.	.	.
37681	1654	1	_	_	IN
37681	1654	2	Equal	equal	JJ
37681	1654	3	circles	circle	NNS
37681	1654	4	are	be	VBP
37681	1654	5	those	those	DT
37681	1654	6	the	the	DT
37681	1654	7	diameters	diameter	NNS
37681	1654	8	of	of	IN
37681	1654	9	which	which	WDT
37681	1654	10	are	be	VBP
37681	1654	11	equal	equal	JJ
37681	1654	12	,	,	,
37681	1654	13	or	or	CC
37681	1654	14	the	the	DT
37681	1654	15	radii	radii	NN
37681	1654	16	of	of	IN
37681	1654	17	which	which	WDT
37681	1654	18	are	be	VBP
37681	1654	19	equal	equal	JJ
37681	1654	20	.	.	.
37681	1654	21	_	_	NNP
37681	1654	22	Manifestly	manifestly	RB
37681	1654	23	this	this	DT
37681	1654	24	is	be	VBZ
37681	1654	25	a	a	DT
37681	1654	26	theorem	theorem	NN
37681	1654	27	,	,	,
37681	1654	28	for	for	IN
37681	1654	29	it	-PRON-	PRP
37681	1654	30	asserts	assert	VBZ
37681	1654	31	that	that	IN
37681	1654	32	if	if	IN
37681	1654	33	the	the	DT
37681	1654	34	radii	radii	NN
37681	1654	35	of	of	IN
37681	1654	36	two	two	CD
37681	1654	37	circles	circle	NNS
37681	1654	38	are	be	VBP
37681	1654	39	equal	equal	JJ
37681	1654	40	,	,	,
37681	1654	41	the	the	DT
37681	1654	42	circles	circle	NNS
37681	1654	43	may	may	MD
37681	1654	44	be	be	VB
37681	1654	45	made	make	VBN
37681	1654	46	to	to	TO
37681	1654	47	coincide	coincide	VB
37681	1654	48	.	.	.
37681	1655	1	In	in	IN
37681	1655	2	some	some	DT
37681	1655	3	textbooks	textbook	NNS
37681	1655	4	a	a	DT
37681	1655	5	proof	proof	NN
37681	1655	6	is	be	VBZ
37681	1655	7	given	give	VBN
37681	1655	8	by	by	IN
37681	1655	9	superposition	superposition	NN
37681	1655	10	,	,	,
37681	1655	11	and	and	CC
37681	1655	12	the	the	DT
37681	1655	13	proof	proof	NN
37681	1655	14	is	be	VBZ
37681	1655	15	legitimate	legitimate	JJ
37681	1655	16	,	,	,
37681	1655	17	but	but	CC
37681	1655	18	Euclid	Euclid	NNP
37681	1655	19	usually	usually	RB
37681	1655	20	avoided	avoid	VBD
37681	1655	21	superposition	superposition	NN
37681	1655	22	if	if	IN
37681	1655	23	possible	possible	JJ
37681	1655	24	.	.	.
37681	1656	1	Nevertheless	nevertheless	RB
37681	1656	2	he	-PRON-	PRP
37681	1656	3	might	may	MD
37681	1656	4	as	as	RB
37681	1656	5	well	well	RB
37681	1656	6	have	have	VB
37681	1656	7	proved	prove	VBN
37681	1656	8	this	this	DT
37681	1656	9	as	as	IN
37681	1656	10	that	that	DT
37681	1656	11	two	two	CD
37681	1656	12	triangles	triangle	NNS
37681	1656	13	are	be	VBP
37681	1656	14	congruent	congruent	JJ
37681	1656	15	if	if	IN
37681	1656	16	two	two	CD
37681	1656	17	sides	side	NNS
37681	1656	18	and	and	CC
37681	1656	19	the	the	DT
37681	1656	20	included	included	JJ
37681	1656	21	angle	angle	NN
37681	1656	22	of	of	IN
37681	1656	23	the	the	DT
37681	1656	24	one	one	CD
37681	1656	25	are	be	VBP
37681	1656	26	respectively	respectively	RB
37681	1656	27	equal	equal	JJ
37681	1656	28	to	to	IN
37681	1656	29	the	the	DT
37681	1656	30	corresponding	correspond	VBG
37681	1656	31	parts	part	NNS
37681	1656	32	of	of	IN
37681	1656	33	the	the	DT
37681	1656	34	other	other	JJ
37681	1656	35	,	,	,
37681	1656	36	and	and	CC
37681	1656	37	he	-PRON-	PRP
37681	1656	38	might	may	MD
37681	1656	39	as	as	RB
37681	1656	40	well	well	RB
37681	1656	41	have	have	VB
37681	1656	42	postulated	postulate	VBN
37681	1656	43	the	the	DT
37681	1656	44	latter	latter	JJ
37681	1656	45	as	as	IN
37681	1656	46	to	to	TO
37681	1656	47	have	have	VB
37681	1656	48	substantially	substantially	RB
37681	1656	49	postulated	postulate	VBN
37681	1656	50	this	this	DT
37681	1656	51	fact	fact	NN
37681	1656	52	.	.	.
37681	1657	1	For	for	IN
37681	1657	2	in	in	IN
37681	1657	3	reality	reality	NN
37681	1657	4	this	this	DT
37681	1657	5	definition	definition	NN
37681	1657	6	is	be	VBZ
37681	1657	7	a	a	DT
37681	1657	8	postulate	postulate	NN
37681	1657	9	,	,	,
37681	1657	10	and	and	CC
37681	1657	11	it	-PRON-	PRP
37681	1657	12	was	be	VBD
37681	1657	13	so	so	RB
37681	1657	14	considered	consider	VBN
37681	1657	15	by	by	IN
37681	1657	16	the	the	DT
37681	1657	17	great	great	JJ
37681	1657	18	Italian	italian	JJ
37681	1657	19	mathematician	mathematician	NN
37681	1657	20	Tartaglia	Tartaglia	NNP
37681	1657	21	(	(	-LRB-
37681	1657	22	_	_	NNP
37681	1657	23	ca	ca	NNP
37681	1657	24	.	.	.
37681	1657	25	_	_	NNP
37681	1657	26	1500-_ca	1500-_ca	CD
37681	1657	27	.	.	.
37681	1657	28	_	_	NNP
37681	1657	29	1557	1557	CD
37681	1657	30	)	)	-RRB-
37681	1657	31	.	.	.
37681	1658	1	The	the	DT
37681	1658	2	plan	plan	NN
37681	1658	3	usually	usually	RB
37681	1658	4	followed	follow	VBD
37681	1658	5	in	in	IN
37681	1658	6	America	America	NNP
37681	1658	7	to	to	IN
37681	1658	8	-	-	HYPH
37681	1658	9	day	day	NN
37681	1658	10	is	be	VBZ
37681	1658	11	to	to	TO
37681	1658	12	consider	consider	VB
37681	1658	13	this	this	DT
37681	1658	14	as	as	IN
37681	1658	15	one	one	CD
37681	1658	16	of	of	IN
37681	1658	17	many	many	JJ
37681	1658	18	unproved	unproved	JJ
37681	1658	19	propositions	proposition	NNS
37681	1658	20	,	,	,
37681	1658	21	too	too	RB
37681	1658	22	evident	evident	JJ
37681	1658	23	,	,	,
37681	1658	24	indeed	indeed	RB
37681	1658	25	,	,	,
37681	1658	26	for	for	IN
37681	1658	27	proof	proof	NN
37681	1658	28	,	,	,
37681	1658	29	accepted	accept	VBN
37681	1658	30	by	by	IN
37681	1658	31	intuition	intuition	NN
37681	1658	32	.	.	.
37681	1659	1	The	the	DT
37681	1659	2	result	result	NN
37681	1659	3	is	be	VBZ
37681	1659	4	a	a	DT
37681	1659	5	loss	loss	NN
37681	1659	6	in	in	IN
37681	1659	7	the	the	DT
37681	1659	8	logic	logic	NN
37681	1659	9	of	of	IN
37681	1659	10	Euclid	Euclid	NNP
37681	1659	11	,	,	,
37681	1659	12	but	but	CC
37681	1659	13	the	the	DT
37681	1659	14	method	method	NN
37681	1659	15	is	be	VBZ
37681	1659	16	thought	think	VBN
37681	1659	17	to	to	TO
37681	1659	18	be	be	VB
37681	1659	19	better	well	RBR
37681	1659	20	adapted	adapt	VBN
37681	1659	21	to	to	IN
37681	1659	22	the	the	DT
37681	1659	23	mind	mind	NN
37681	1659	24	of	of	IN
37681	1659	25	the	the	DT
37681	1659	26	youthful	youthful	JJ
37681	1659	27	learner	learner	NN
37681	1659	28	.	.	.
37681	1660	1	It	-PRON-	PRP
37681	1660	2	is	be	VBZ
37681	1660	3	interesting	interesting	JJ
37681	1660	4	to	to	TO
37681	1660	5	note	note	VB
37681	1660	6	in	in	IN
37681	1660	7	this	this	DT
37681	1660	8	connection	connection	NN
37681	1660	9	that	that	IN
37681	1660	10	the	the	DT
37681	1660	11	Greeks	Greeks	NNPS
37681	1660	12	had	have	VBD
37681	1660	13	no	no	DT
37681	1660	14	word	word	NN
37681	1660	15	for	for	IN
37681	1660	16	"	"	``
37681	1660	17	radius	radius	NN
37681	1660	18	,	,	,
37681	1660	19	"	"	''
37681	1660	20	and	and	CC
37681	1660	21	were	be	VBD
37681	1660	22	therefore	therefore	RB
37681	1660	23	compelled	compel	VBN
37681	1660	24	to	to	TO
37681	1660	25	use	use	VB
37681	1660	26	some	some	DT
37681	1660	27	such	such	JJ
37681	1660	28	phrase	phrase	NN
37681	1660	29	as	as	IN
37681	1660	30	"	"	``
37681	1660	31	the	the	DT
37681	1660	32	straight	straight	JJ
37681	1660	33	line	line	NN
37681	1660	34	from	from	IN
37681	1660	35	the	the	DT
37681	1660	36	center	center	NN
37681	1660	37	,	,	,
37681	1660	38	"	"	''
37681	1660	39	or	or	CC
37681	1660	40	,	,	,
37681	1660	41	briefly	briefly	RB
37681	1660	42	,	,	,
37681	1660	43	"	"	''
37681	1660	44	the	the	DT
37681	1660	45	from	from	IN
37681	1660	46	the	the	DT
37681	1660	47	center	center	NN
37681	1660	48	,	,	,
37681	1660	49	"	"	``
37681	1660	50	as	as	IN
37681	1660	51	if	if	IN
37681	1660	52	"	"	``
37681	1660	53	from	from	IN
37681	1660	54	the	the	DT
37681	1660	55	center	center	NN
37681	1660	56	"	"	''
37681	1660	57	were	be	VBD
37681	1660	58	one	one	CD
37681	1660	59	word	word	NN
37681	1660	60	.	.	.
37681	1661	1	2	2	LS
37681	1661	2	.	.	.
37681	1662	1	TANGENT	TANGENT	NNP
37681	1662	2	.	.	.
37681	1663	1	_	_	NNP
37681	1663	2	A	a	DT
37681	1663	3	straight	straight	JJ
37681	1663	4	line	line	NN
37681	1663	5	is	be	VBZ
37681	1663	6	said	say	VBN
37681	1663	7	to	to	TO
37681	1663	8	touch	touch	VB
37681	1663	9	a	a	DT
37681	1663	10	circle	circle	NN
37681	1663	11	which	which	WDT
37681	1663	12	,	,	,
37681	1663	13	meeting	meet	VBG
37681	1663	14	the	the	DT
37681	1663	15	circle	circle	NN
37681	1663	16	and	and	CC
37681	1663	17	being	be	VBG
37681	1663	18	produced	produce	VBN
37681	1663	19	,	,	,
37681	1663	20	does	do	VBZ
37681	1663	21	not	not	RB
37681	1663	22	cut	cut	VB
37681	1663	23	the	the	DT
37681	1663	24	circle	circle	NN
37681	1663	25	.	.	.
37681	1663	26	_	_	NNP
37681	1663	27	Teachers	Teachers	NNPS
37681	1663	28	who	who	WP
37681	1663	29	prefer	prefer	VBP
37681	1663	30	to	to	TO
37681	1663	31	use	use	VB
37681	1663	32	"	"	``
37681	1663	33	circumference	circumference	NN
37681	1663	34	"	"	''
37681	1663	35	instead	instead	RB
37681	1663	36	of	of	IN
37681	1663	37	"	"	``
37681	1663	38	circle	circle	NN
37681	1663	39	"	"	''
37681	1663	40	for	for	IN
37681	1663	41	the	the	DT
37681	1663	42	line	line	NN
37681	1663	43	should	should	MD
37681	1663	44	notice	notice	VB
37681	1663	45	how	how	WRB
37681	1663	46	often	often	RB
37681	1663	47	such	such	JJ
37681	1663	48	phrases	phrase	NNS
37681	1663	49	as	as	IN
37681	1663	50	"	"	``
37681	1663	51	cut	cut	VBD
37681	1663	52	the	the	DT
37681	1663	53	circle	circle	NN
37681	1663	54	"	"	''
37681	1663	55	and	and	CC
37681	1663	56	"	"	``
37681	1663	57	intersecting	intersect	VBG
37681	1663	58	circle	circle	NN
37681	1663	59	"	"	''
37681	1663	60	are	be	VBP
37681	1663	61	used,--phrases	used,--phrase	NNS
37681	1663	62	that	that	WDT
37681	1663	63	signify	signify	VBP
37681	1663	64	nothing	nothing	NN
37681	1663	65	unless	unless	IN
37681	1663	66	"	"	``
37681	1663	67	circle	circle	NN
37681	1663	68	"	"	''
37681	1663	69	is	be	VBZ
37681	1663	70	taken	take	VBN
37681	1663	71	to	to	TO
37681	1663	72	mean	mean	VB
37681	1663	73	the	the	DT
37681	1663	74	line	line	NN
37681	1663	75	.	.	.
37681	1664	1	So	so	CC
37681	1664	2	Aristotle	Aristotle	NNP
37681	1664	3	uses	use	VBZ
37681	1664	4	an	an	DT
37681	1664	5	expression	expression	NN
37681	1664	6	meaning	meaning	NN
37681	1664	7	that	that	IN
37681	1664	8	the	the	DT
37681	1664	9	locus	locus	NN
37681	1664	10	of	of	IN
37681	1664	11	a	a	DT
37681	1664	12	certain	certain	JJ
37681	1664	13	point	point	NN
37681	1664	14	is	be	VBZ
37681	1664	15	a	a	DT
37681	1664	16	circle	circle	NN
37681	1664	17	,	,	,
37681	1664	18	and	and	CC
37681	1664	19	he	-PRON-	PRP
37681	1664	20	speaks	speak	VBZ
37681	1664	21	of	of	IN
37681	1664	22	a	a	DT
37681	1664	23	circle	circle	NN
37681	1664	24	as	as	IN
37681	1664	25	passing	pass	VBG
37681	1664	26	through	through	RB
37681	1664	27	"	"	``
37681	1664	28	all	all	PDT
37681	1664	29	the	the	DT
37681	1664	30	angles	angle	NNS
37681	1664	31	.	.	.
37681	1664	32	"	"	''
37681	1665	1	Our	-PRON-	PRP$
37681	1665	2	word	word	NN
37681	1665	3	"	"	``
37681	1665	4	touch	touch	NN
37681	1665	5	"	"	''
37681	1665	6	is	be	VBZ
37681	1665	7	from	from	IN
37681	1665	8	the	the	DT
37681	1665	9	Latin	Latin	NNP
37681	1665	10	_	_	NNP
37681	1665	11	tangere	tangere	RB
37681	1665	12	_	_	NNP
37681	1665	13	,	,	,
37681	1665	14	from	from	IN
37681	1665	15	which	which	WDT
37681	1665	16	comes	come	VBZ
37681	1665	17	"	"	``
37681	1665	18	tangent	tangent	NN
37681	1665	19	,	,	,
37681	1665	20	"	"	''
37681	1665	21	and	and	CC
37681	1665	22	also	also	RB
37681	1665	23	"	"	``
37681	1665	24	tag	tag	NN
37681	1665	25	,	,	,
37681	1665	26	"	"	''
37681	1665	27	an	an	DT
37681	1665	28	old	old	JJ
37681	1665	29	touching	touching	JJ
37681	1665	30	game	game	NN
37681	1665	31	.	.	.
37681	1666	1	3	3	LS
37681	1666	2	.	.	.
37681	1667	1	TANGENT	tangent	JJ
37681	1667	2	CIRCLES	circle	NNS
37681	1667	3	.	.	.
37681	1668	1	_	_	NNP
37681	1668	2	Circles	Circles	NNP
37681	1668	3	are	be	VBP
37681	1668	4	said	say	VBN
37681	1668	5	to	to	TO
37681	1668	6	touch	touch	VB
37681	1668	7	one	one	NN
37681	1668	8	another	another	DT
37681	1668	9	which	which	WDT
37681	1668	10	,	,	,
37681	1668	11	meeting	meet	VBG
37681	1668	12	one	one	CD
37681	1668	13	another	another	DT
37681	1668	14	,	,	,
37681	1668	15	do	do	VBP
37681	1668	16	not	not	RB
37681	1668	17	cut	cut	VB
37681	1668	18	one	one	CD
37681	1668	19	another	another	DT
37681	1668	20	.	.	.
37681	1668	21	_	_	NNP
37681	1668	22	The	the	DT
37681	1668	23	definition	definition	NN
37681	1668	24	has	have	VBZ
37681	1668	25	not	not	RB
37681	1668	26	been	be	VBN
37681	1668	27	looked	look	VBN
37681	1668	28	upon	upon	IN
37681	1668	29	as	as	IN
37681	1668	30	entirely	entirely	RB
37681	1668	31	satisfactory	satisfactory	JJ
37681	1668	32	,	,	,
37681	1668	33	even	even	RB
37681	1668	34	aside	aside	RB
37681	1668	35	from	from	IN
37681	1668	36	its	-PRON-	PRP$
37681	1668	37	unfortunate	unfortunate	JJ
37681	1668	38	phraseology	phraseology	NN
37681	1668	39	.	.	.
37681	1669	1	It	-PRON-	PRP
37681	1669	2	is	be	VBZ
37681	1669	3	not	not	RB
37681	1669	4	certain	certain	JJ
37681	1669	5	,	,	,
37681	1669	6	for	for	IN
37681	1669	7	instance	instance	NN
37681	1669	8	,	,	,
37681	1669	9	whether	whether	IN
37681	1669	10	Euclid	Euclid	NNP
37681	1669	11	meant	mean	VBD
37681	1669	12	that	that	IN
37681	1669	13	the	the	DT
37681	1669	14	circles	circle	NNS
37681	1669	15	could	could	MD
37681	1669	16	not	not	RB
37681	1669	17	cut	cut	VB
37681	1669	18	at	at	IN
37681	1669	19	some	some	DT
37681	1669	20	other	other	JJ
37681	1669	21	point	point	NN
37681	1669	22	than	than	IN
37681	1669	23	that	that	DT
37681	1669	24	of	of	IN
37681	1669	25	tangency	tangency	NN
37681	1669	26	.	.	.
37681	1670	1	Furthermore	furthermore	RB
37681	1670	2	,	,	,
37681	1670	3	no	no	DT
37681	1670	4	distinction	distinction	NN
37681	1670	5	is	be	VBZ
37681	1670	6	made	make	VBN
37681	1670	7	between	between	IN
37681	1670	8	external	external	JJ
37681	1670	9	and	and	CC
37681	1670	10	internal	internal	JJ
37681	1670	11	contact	contact	NN
37681	1670	12	,	,	,
37681	1670	13	although	although	IN
37681	1670	14	both	both	DT
37681	1670	15	forms	form	NNS
37681	1670	16	are	be	VBP
37681	1670	17	used	use	VBN
37681	1670	18	in	in	IN
37681	1670	19	the	the	DT
37681	1670	20	propositions	proposition	NNS
37681	1670	21	.	.	.
37681	1671	1	Modern	modern	JJ
37681	1671	2	textbook	textbook	NN
37681	1671	3	makers	maker	NNS
37681	1671	4	find	find	VBP
37681	1671	5	it	-PRON-	PRP
37681	1671	6	convenient	convenient	JJ
37681	1671	7	to	to	TO
37681	1671	8	define	define	VB
37681	1671	9	tangent	tangent	NN
37681	1671	10	circles	circle	NNS
37681	1671	11	as	as	IN
37681	1671	12	those	those	DT
37681	1671	13	that	that	WDT
37681	1671	14	are	be	VBP
37681	1671	15	tangent	tangent	JJ
37681	1671	16	to	to	IN
37681	1671	17	the	the	DT
37681	1671	18	same	same	JJ
37681	1671	19	straight	straight	JJ
37681	1671	20	line	line	NN
37681	1671	21	at	at	IN
37681	1671	22	the	the	DT
37681	1671	23	same	same	JJ
37681	1671	24	point	point	NN
37681	1671	25	,	,	,
37681	1671	26	and	and	CC
37681	1671	27	to	to	TO
37681	1671	28	define	define	VB
37681	1671	29	external	external	JJ
37681	1671	30	and	and	CC
37681	1671	31	internal	internal	JJ
37681	1671	32	tangency	tangency	NN
37681	1671	33	by	by	IN
37681	1671	34	reference	reference	NN
37681	1671	35	to	to	IN
37681	1671	36	their	-PRON-	PRP$
37681	1671	37	position	position	NN
37681	1671	38	with	with	IN
37681	1671	39	respect	respect	NN
37681	1671	40	to	to	IN
37681	1671	41	the	the	DT
37681	1671	42	line	line	NN
37681	1671	43	,	,	,
37681	1671	44	although	although	IN
37681	1671	45	this	this	DT
37681	1671	46	may	may	MD
37681	1671	47	be	be	VB
37681	1671	48	characterized	characterize	VBN
37681	1671	49	as	as	IN
37681	1671	50	open	open	JJ
37681	1671	51	to	to	IN
37681	1671	52	about	about	IN
37681	1671	53	the	the	DT
37681	1671	54	same	same	JJ
37681	1671	55	objection	objection	NN
37681	1671	56	as	as	IN
37681	1671	57	Euclid	Euclid	NNP
37681	1671	58	's	's	POS
37681	1671	59	.	.	.
37681	1672	1	4	4	LS
37681	1672	2	.	.	.
37681	1673	1	DISTANCE	DISTANCE	NNP
37681	1673	2	.	.	.
37681	1674	1	_	_	NNP
37681	1674	2	In	in	IN
37681	1674	3	a	a	DT
37681	1674	4	circle	circle	NN
37681	1674	5	straight	straight	JJ
37681	1674	6	lines	line	NNS
37681	1674	7	are	be	VBP
37681	1674	8	said	say	VBN
37681	1674	9	to	to	TO
37681	1674	10	be	be	VB
37681	1674	11	equally	equally	RB
37681	1674	12	distant	distant	JJ
37681	1674	13	from	from	IN
37681	1674	14	the	the	DT
37681	1674	15	center	center	NN
37681	1674	16	,	,	,
37681	1674	17	when	when	WRB
37681	1674	18	the	the	DT
37681	1674	19	perpendiculars	perpendicular	NNS
37681	1674	20	drawn	draw	VBN
37681	1674	21	to	to	IN
37681	1674	22	them	-PRON-	PRP
37681	1674	23	from	from	IN
37681	1674	24	the	the	DT
37681	1674	25	center	center	NN
37681	1674	26	are	be	VBP
37681	1674	27	equal	equal	JJ
37681	1674	28	.	.	.
37681	1674	29	_	_	NNP
37681	1674	30	It	-PRON-	PRP
37681	1674	31	is	be	VBZ
37681	1674	32	now	now	RB
37681	1674	33	customary	customary	JJ
37681	1674	34	to	to	TO
37681	1674	35	define	define	VB
37681	1674	36	"	"	``
37681	1674	37	distance	distance	NN
37681	1674	38	"	"	''
37681	1674	39	from	from	IN
37681	1674	40	a	a	DT
37681	1674	41	point	point	NN
37681	1674	42	to	to	IN
37681	1674	43	a	a	DT
37681	1674	44	line	line	NN
37681	1674	45	as	as	IN
37681	1674	46	the	the	DT
37681	1674	47	length	length	NN
37681	1674	48	of	of	IN
37681	1674	49	the	the	DT
37681	1674	50	perpendicular	perpendicular	NN
37681	1674	51	from	from	IN
37681	1674	52	the	the	DT
37681	1674	53	point	point	NN
37681	1674	54	to	to	IN
37681	1674	55	the	the	DT
37681	1674	56	line	line	NN
37681	1674	57	,	,	,
37681	1674	58	and	and	CC
37681	1674	59	to	to	TO
37681	1674	60	do	do	VB
37681	1674	61	this	this	DT
37681	1674	62	in	in	IN
37681	1674	63	Book	Book	NNP
37681	1674	64	I.	i.	NN
37681	1675	1	In	in	IN
37681	1675	2	higher	high	JJR
37681	1675	3	mathematics	mathematic	NNS
37681	1675	4	it	-PRON-	PRP
37681	1675	5	is	be	VBZ
37681	1675	6	found	find	VBN
37681	1675	7	that	that	IN
37681	1675	8	distance	distance	NN
37681	1675	9	is	be	VBZ
37681	1675	10	not	not	RB
37681	1675	11	a	a	DT
37681	1675	12	satisfactory	satisfactory	JJ
37681	1675	13	term	term	NN
37681	1675	14	to	to	TO
37681	1675	15	use	use	VB
37681	1675	16	,	,	,
37681	1675	17	but	but	CC
37681	1675	18	the	the	DT
37681	1675	19	objections	objection	NNS
37681	1675	20	to	to	IN
37681	1675	21	it	-PRON-	PRP
37681	1675	22	have	have	VB
37681	1675	23	no	no	DT
37681	1675	24	particular	particular	JJ
37681	1675	25	significance	significance	NN
37681	1675	26	in	in	IN
37681	1675	27	elementary	elementary	JJ
37681	1675	28	geometry	geometry	NN
37681	1675	29	.	.	.
37681	1676	1	5	5	CD
37681	1676	2	.	.	.
37681	1677	1	GREATER	GREATER	NNP
37681	1677	2	DISTANCE	DISTANCE	NNP
37681	1677	3	.	.	.
37681	1678	1	_	_	NNP
37681	1678	2	And	and	CC
37681	1678	3	that	that	DT
37681	1678	4	straight	straight	JJ
37681	1678	5	line	line	NN
37681	1678	6	is	be	VBZ
37681	1678	7	said	say	VBN
37681	1678	8	to	to	TO
37681	1678	9	be	be	VB
37681	1678	10	at	at	IN
37681	1678	11	a	a	DT
37681	1678	12	greater	great	JJR
37681	1678	13	distance	distance	NN
37681	1678	14	on	on	IN
37681	1678	15	which	which	WDT
37681	1678	16	the	the	DT
37681	1678	17	greater	great	JJR
37681	1678	18	perpendicular	perpendicular	JJ
37681	1678	19	falls	fall	NNS
37681	1678	20	.	.	.
37681	1678	21	_	_	NNP
37681	1678	22	Such	such	PDT
37681	1678	23	a	a	DT
37681	1678	24	definition	definition	NN
37681	1678	25	is	be	VBZ
37681	1678	26	not	not	RB
37681	1678	27	thought	think	VBN
37681	1678	28	essential	essential	JJ
37681	1678	29	at	at	IN
37681	1678	30	the	the	DT
37681	1678	31	present	present	JJ
37681	1678	32	time	time	NN
37681	1678	33	.	.	.
37681	1679	1	6	6	CD
37681	1679	2	.	.	.
37681	1680	1	SEGMENT	SEGMENT	NNP
37681	1680	2	.	.	.
37681	1681	1	_	_	NNP
37681	1681	2	A	a	DT
37681	1681	3	segment	segment	NN
37681	1681	4	of	of	IN
37681	1681	5	a	a	DT
37681	1681	6	circle	circle	NN
37681	1681	7	is	be	VBZ
37681	1681	8	the	the	DT
37681	1681	9	figure	figure	NN
37681	1681	10	contained	contain	VBN
37681	1681	11	by	by	IN
37681	1681	12	a	a	DT
37681	1681	13	straight	straight	JJ
37681	1681	14	line	line	NN
37681	1681	15	and	and	CC
37681	1681	16	the	the	DT
37681	1681	17	circumference	circumference	NN
37681	1681	18	of	of	IN
37681	1681	19	a	a	DT
37681	1681	20	circle	circle	NN
37681	1681	21	.	.	.
37681	1681	22	_	_	NNP
37681	1681	23	The	the	DT
37681	1681	24	word	word	NN
37681	1681	25	"	"	``
37681	1681	26	segment	segment	NN
37681	1681	27	"	"	''
37681	1681	28	is	be	VBZ
37681	1681	29	from	from	IN
37681	1681	30	the	the	DT
37681	1681	31	Latin	Latin	NNP
37681	1681	32	root	root	NN
37681	1681	33	_	_	NNP
37681	1681	34	sect	sect	NN
37681	1681	35	_	_	NNP
37681	1681	36	,	,	,
37681	1681	37	meaning	mean	VBG
37681	1681	38	"	"	``
37681	1681	39	cut	cut	NN
37681	1681	40	.	.	.
37681	1681	41	"	"	''
37681	1682	1	So	so	RB
37681	1682	2	we	-PRON-	PRP
37681	1682	3	have	have	VBP
37681	1682	4	"	"	``
37681	1682	5	sector	sector	NN
37681	1682	6	"	"	''
37681	1682	7	(	(	-LRB-
37681	1682	8	a	a	DT
37681	1682	9	cutter	cutter	NN
37681	1682	10	)	)	-RRB-
37681	1682	11	,	,	,
37681	1682	12	"	"	``
37681	1682	13	section	section	NN
37681	1682	14	"	"	''
37681	1682	15	(	(	-LRB-
37681	1682	16	a	a	DT
37681	1682	17	cut	cut	NN
37681	1682	18	)	)	-RRB-
37681	1682	19	,	,	,
37681	1682	20	"	"	``
37681	1682	21	intersect	intersect	VB
37681	1682	22	,	,	,
37681	1682	23	"	"	''
37681	1682	24	and	and	CC
37681	1682	25	so	so	RB
37681	1682	26	on	on	RB
37681	1682	27	.	.	.
37681	1683	1	The	the	DT
37681	1683	2	word	word	NN
37681	1683	3	is	be	VBZ
37681	1683	4	not	not	RB
37681	1683	5	limited	limit	VBN
37681	1683	6	to	to	IN
37681	1683	7	a	a	DT
37681	1683	8	circle	circle	NN
37681	1683	9	;	;	:
37681	1683	10	we	-PRON-	PRP
37681	1683	11	have	have	VBP
37681	1683	12	long	long	RB
37681	1683	13	spoken	speak	VBN
37681	1683	14	of	of	IN
37681	1683	15	a	a	DT
37681	1683	16	spherical	spherical	JJ
37681	1683	17	segment	segment	NN
37681	1683	18	,	,	,
37681	1683	19	and	and	CC
37681	1683	20	it	-PRON-	PRP
37681	1683	21	is	be	VBZ
37681	1683	22	common	common	JJ
37681	1683	23	to	to	IN
37681	1683	24	-	-	HYPH
37681	1683	25	day	day	NN
37681	1683	26	to	to	TO
37681	1683	27	speak	speak	VB
37681	1683	28	of	of	IN
37681	1683	29	a	a	DT
37681	1683	30	line	line	NN
37681	1683	31	segment	segment	NN
37681	1683	32	,	,	,
37681	1683	33	to	to	TO
37681	1683	34	which	which	WDT
37681	1683	35	some	some	DT
37681	1683	36	would	would	MD
37681	1683	37	apply	apply	VB
37681	1683	38	a	a	DT
37681	1683	39	new	new	JJ
37681	1683	40	name	name	NN
37681	1683	41	"	"	``
37681	1683	42	sect	sect	JJ
37681	1683	43	.	.	.
37681	1683	44	"	"	''
37681	1684	1	There	there	EX
37681	1684	2	is	be	VBZ
37681	1684	3	little	little	JJ
37681	1684	4	confusion	confusion	NN
37681	1684	5	in	in	IN
37681	1684	6	the	the	DT
37681	1684	7	matter	matter	NN
37681	1684	8	,	,	,
37681	1684	9	however	however	RB
37681	1684	10	,	,	,
37681	1684	11	for	for	IN
37681	1684	12	the	the	DT
37681	1684	13	context	context	NN
37681	1684	14	shows	show	VBZ
37681	1684	15	what	what	WDT
37681	1684	16	kind	kind	NN
37681	1684	17	of	of	IN
37681	1684	18	a	a	DT
37681	1684	19	segment	segment	NN
37681	1684	20	is	be	VBZ
37681	1684	21	to	to	TO
37681	1684	22	be	be	VB
37681	1684	23	understood	understand	VBN
37681	1684	24	,	,	,
37681	1684	25	so	so	IN
37681	1684	26	that	that	IN
37681	1684	27	the	the	DT
37681	1684	28	word	word	NN
37681	1684	29	"	"	``
37681	1684	30	sect	sect	NN
37681	1684	31	"	"	''
37681	1684	32	is	be	VBZ
37681	1684	33	rather	rather	RB
37681	1684	34	pedantic	pedantic	JJ
37681	1684	35	than	than	IN
37681	1684	36	important	important	JJ
37681	1684	37	.	.	.
37681	1685	1	It	-PRON-	PRP
37681	1685	2	will	will	MD
37681	1685	3	be	be	VB
37681	1685	4	noticed	notice	VBN
37681	1685	5	that	that	IN
37681	1685	6	Euclid	Euclid	NNP
37681	1685	7	here	here	RB
37681	1685	8	uses	use	VBZ
37681	1685	9	"	"	``
37681	1685	10	circumference	circumference	NN
37681	1685	11	"	"	''
37681	1685	12	to	to	TO
37681	1685	13	mean	mean	VB
37681	1685	14	"	"	``
37681	1685	15	arc	arc	NN
37681	1685	16	.	.	.
37681	1685	17	"	"	''
37681	1686	1	7	7	LS
37681	1686	2	.	.	.
37681	1687	1	ANGLE	ANGLE	NNS
37681	1687	2	OF	of	IN
37681	1687	3	A	a	DT
37681	1687	4	SEGMENT	SEGMENT	NNP
37681	1687	5	.	.	.
37681	1688	1	_	_	NNP
37681	1688	2	An	an	DT
37681	1688	3	angle	angle	NN
37681	1688	4	of	of	IN
37681	1688	5	a	a	DT
37681	1688	6	segment	segment	NN
37681	1688	7	is	be	VBZ
37681	1688	8	that	that	DT
37681	1688	9	contained	contain	VBN
37681	1688	10	by	by	IN
37681	1688	11	a	a	DT
37681	1688	12	straight	straight	JJ
37681	1688	13	line	line	NN
37681	1688	14	and	and	CC
37681	1688	15	a	a	DT
37681	1688	16	circumference	circumference	NN
37681	1688	17	of	of	IN
37681	1688	18	a	a	DT
37681	1688	19	circle	circle	NN
37681	1688	20	.	.	.
37681	1688	21	_	_	NNP
37681	1688	22	This	this	DT
37681	1688	23	term	term	NN
37681	1688	24	has	have	VBZ
37681	1688	25	entirely	entirely	RB
37681	1688	26	dropped	drop	VBN
37681	1688	27	out	out	IN
37681	1688	28	of	of	IN
37681	1688	29	geometry	geometry	NN
37681	1688	30	,	,	,
37681	1688	31	and	and	CC
37681	1688	32	few	few	JJ
37681	1688	33	teachers	teacher	NNS
37681	1688	34	would	would	MD
37681	1688	35	know	know	VB
37681	1688	36	what	what	WP
37681	1688	37	it	-PRON-	PRP
37681	1688	38	meant	mean	VBD
37681	1688	39	if	if	IN
37681	1688	40	they	-PRON-	PRP
37681	1688	41	should	should	MD
37681	1688	42	hear	hear	VB
37681	1688	43	it	-PRON-	PRP
37681	1688	44	used	use	VBN
37681	1688	45	.	.	.
37681	1689	1	Proclus	Proclus	NNP
37681	1689	2	called	call	VBD
37681	1689	3	such	such	JJ
37681	1689	4	angles	angle	NNS
37681	1689	5	"	"	``
37681	1689	6	mixed	mixed	JJ
37681	1689	7	.	.	.
37681	1689	8	"	"	''
37681	1690	1	8	8	LS
37681	1690	2	.	.	.
37681	1691	1	ANGLE	ANGLE	NNPS
37681	1691	2	IN	in	IN
37681	1691	3	A	a	DT
37681	1691	4	SEGMENT	segment	NN
37681	1691	5	.	.	.
37681	1692	1	_	_	NNP
37681	1692	2	An	an	DT
37681	1692	3	angle	angle	NN
37681	1692	4	in	in	IN
37681	1692	5	a	a	DT
37681	1692	6	segment	segment	NN
37681	1692	7	is	be	VBZ
37681	1692	8	the	the	DT
37681	1692	9	angle	angle	NN
37681	1692	10	which	which	WDT
37681	1692	11	,	,	,
37681	1692	12	when	when	WRB
37681	1692	13	a	a	DT
37681	1692	14	point	point	NN
37681	1692	15	is	be	VBZ
37681	1692	16	taken	take	VBN
37681	1692	17	on	on	IN
37681	1692	18	the	the	DT
37681	1692	19	circumference	circumference	NN
37681	1692	20	of	of	IN
37681	1692	21	the	the	DT
37681	1692	22	segment	segment	NN
37681	1692	23	and	and	CC
37681	1692	24	straight	straight	JJ
37681	1692	25	lines	line	NNS
37681	1692	26	are	be	VBP
37681	1692	27	joined	join	VBN
37681	1692	28	from	from	IN
37681	1692	29	it	-PRON-	PRP
37681	1692	30	to	to	IN
37681	1692	31	the	the	DT
37681	1692	32	extremities	extremity	NNS
37681	1692	33	of	of	IN
37681	1692	34	the	the	DT
37681	1692	35	straight	straight	JJ
37681	1692	36	line	line	NN
37681	1692	37	which	which	WDT
37681	1692	38	is	be	VBZ
37681	1692	39	the	the	DT
37681	1692	40	base	base	NN
37681	1692	41	of	of	IN
37681	1692	42	the	the	DT
37681	1692	43	segment	segment	NN
37681	1692	44	,	,	,
37681	1692	45	is	be	VBZ
37681	1692	46	contained	contain	VBN
37681	1692	47	by	by	IN
37681	1692	48	the	the	DT
37681	1692	49	straight	straight	JJ
37681	1692	50	lines	line	NNS
37681	1692	51	so	so	RB
37681	1692	52	joined	join	VBD
37681	1692	53	.	.	.
37681	1692	54	_	_	NNP
37681	1692	55	Such	such	PDT
37681	1692	56	an	an	DT
37681	1692	57	involved	involved	JJ
37681	1692	58	definition	definition	NN
37681	1692	59	would	would	MD
37681	1692	60	not	not	RB
37681	1692	61	be	be	VB
37681	1692	62	usable	usable	JJ
37681	1692	63	to	to	IN
37681	1692	64	-	-	HYPH
37681	1692	65	day	day	NN
37681	1692	66	.	.	.
37681	1693	1	Moreover	moreover	RB
37681	1693	2	,	,	,
37681	1693	3	the	the	DT
37681	1693	4	words	word	NNS
37681	1693	5	"	"	``
37681	1693	6	circumference	circumference	NN
37681	1693	7	of	of	IN
37681	1693	8	the	the	DT
37681	1693	9	segment	segment	NN
37681	1693	10	"	"	``
37681	1693	11	would	would	MD
37681	1693	12	not	not	RB
37681	1693	13	be	be	VB
37681	1693	14	used	use	VBN
37681	1693	15	.	.	.
37681	1694	1	9	9	CD
37681	1694	2	.	.	.
37681	1695	1	_	_	NNP
37681	1695	2	And	and	CC
37681	1695	3	when	when	WRB
37681	1695	4	the	the	DT
37681	1695	5	straight	straight	JJ
37681	1695	6	lines	line	NNS
37681	1695	7	containing	contain	VBG
37681	1695	8	the	the	DT
37681	1695	9	angle	angle	NN
37681	1695	10	cut	cut	VBD
37681	1695	11	off	off	RP
37681	1695	12	a	a	DT
37681	1695	13	circumference	circumference	NN
37681	1695	14	,	,	,
37681	1695	15	the	the	DT
37681	1695	16	angle	angle	NN
37681	1695	17	is	be	VBZ
37681	1695	18	said	say	VBN
37681	1695	19	to	to	TO
37681	1695	20	stand	stand	VB
37681	1695	21	upon	upon	IN
37681	1695	22	that	that	DT
37681	1695	23	circumference	circumference	NN
37681	1695	24	.	.	.
37681	1695	25	_	_	NNP
37681	1695	26	10	10	CD
37681	1695	27	.	.	.
37681	1696	1	SECTOR	SECTOR	NNP
37681	1696	2	.	.	.
37681	1697	1	_	_	NNP
37681	1697	2	A	a	DT
37681	1697	3	sector	sector	NN
37681	1697	4	of	of	IN
37681	1697	5	a	a	DT
37681	1697	6	circle	circle	NN
37681	1697	7	is	be	VBZ
37681	1697	8	the	the	DT
37681	1697	9	figure	figure	NN
37681	1697	10	which	which	WDT
37681	1697	11	,	,	,
37681	1697	12	when	when	WRB
37681	1697	13	an	an	DT
37681	1697	14	angle	angle	NN
37681	1697	15	is	be	VBZ
37681	1697	16	constructed	construct	VBN
37681	1697	17	at	at	IN
37681	1697	18	the	the	DT
37681	1697	19	center	center	NN
37681	1697	20	of	of	IN
37681	1697	21	the	the	DT
37681	1697	22	circle	circle	NN
37681	1697	23	,	,	,
37681	1697	24	is	be	VBZ
37681	1697	25	contained	contain	VBN
37681	1697	26	by	by	IN
37681	1697	27	the	the	DT
37681	1697	28	straight	straight	JJ
37681	1697	29	lines	line	NNS
37681	1697	30	containing	contain	VBG
37681	1697	31	the	the	DT
37681	1697	32	angle	angle	NN
37681	1697	33	and	and	CC
37681	1697	34	the	the	DT
37681	1697	35	circumference	circumference	NN
37681	1697	36	cut	cut	VBD
37681	1697	37	off	off	RP
37681	1697	38	by	by	IN
37681	1697	39	them	-PRON-	PRP
37681	1697	40	.	.	.
37681	1697	41	_	_	NNP
37681	1697	42	There	there	EX
37681	1697	43	is	be	VBZ
37681	1697	44	no	no	DT
37681	1697	45	reason	reason	NN
37681	1697	46	for	for	IN
37681	1697	47	such	such	PDT
37681	1697	48	an	an	DT
37681	1697	49	extended	extended	JJ
37681	1697	50	definition	definition	NN
37681	1697	51	,	,	,
37681	1697	52	our	-PRON-	PRP$
37681	1697	53	modern	modern	JJ
37681	1697	54	phraseology	phraseology	NN
37681	1697	55	being	be	VBG
37681	1697	56	both	both	CC
37681	1697	57	more	more	RBR
37681	1697	58	exact	exact	JJ
37681	1697	59	(	(	-LRB-
37681	1697	60	as	as	IN
37681	1697	61	seen	see	VBN
37681	1697	62	in	in	IN
37681	1697	63	the	the	DT
37681	1697	64	above	above	JJ
37681	1697	65	use	use	NN
37681	1697	66	of	of	IN
37681	1697	67	"	"	``
37681	1697	68	circumference	circumference	NN
37681	1697	69	"	"	''
37681	1697	70	for	for	IN
37681	1697	71	"	"	``
37681	1697	72	arc	arc	NNP
37681	1697	73	"	"	''
37681	1697	74	)	)	-RRB-
37681	1697	75	and	and	CC
37681	1697	76	more	more	RBR
37681	1697	77	intelligible	intelligible	JJ
37681	1697	78	.	.	.
37681	1698	1	The	the	DT
37681	1698	2	Greek	greek	JJ
37681	1698	3	word	word	NN
37681	1698	4	for	for	IN
37681	1698	5	"	"	``
37681	1698	6	sector	sector	NN
37681	1698	7	"	"	''
37681	1698	8	is	be	VBZ
37681	1698	9	"	"	``
37681	1698	10	knife	knife	NN
37681	1698	11	"	"	''
37681	1698	12	(	(	-LRB-
37681	1698	13	_	_	NNP
37681	1698	14	tomeus	tomeus	NNP
37681	1698	15	_	_	NNP
37681	1698	16	)	)	-RRB-
37681	1698	17	,	,	,
37681	1698	18	"	"	``
37681	1698	19	sector	sector	NN
37681	1698	20	"	"	''
37681	1698	21	being	be	VBG
37681	1698	22	the	the	DT
37681	1698	23	Latin	latin	JJ
37681	1698	24	translation	translation	NN
37681	1698	25	.	.	.
37681	1699	1	A	a	DT
37681	1699	2	sector	sector	NN
37681	1699	3	is	be	VBZ
37681	1699	4	supposed	suppose	VBN
37681	1699	5	to	to	TO
37681	1699	6	resemble	resemble	VB
37681	1699	7	a	a	DT
37681	1699	8	shoemaker	shoemaker	NN
37681	1699	9	's	's	POS
37681	1699	10	knife	knife	NN
37681	1699	11	,	,	,
37681	1699	12	and	and	CC
37681	1699	13	hence	hence	RB
37681	1699	14	the	the	DT
37681	1699	15	significance	significance	NN
37681	1699	16	of	of	IN
37681	1699	17	the	the	DT
37681	1699	18	term	term	NN
37681	1699	19	.	.	.
37681	1700	1	Euclid	Euclid	NNP
37681	1700	2	followed	follow	VBD
37681	1700	3	this	this	DT
37681	1700	4	by	by	IN
37681	1700	5	a	a	DT
37681	1700	6	definition	definition	NN
37681	1700	7	of	of	IN
37681	1700	8	similar	similar	JJ
37681	1700	9	sectors	sector	NNS
37681	1700	10	,	,	,
37681	1700	11	a	a	DT
37681	1700	12	term	term	NN
37681	1700	13	now	now	RB
37681	1700	14	generally	generally	RB
37681	1700	15	abandoned	abandon	VBN
37681	1700	16	as	as	IN
37681	1700	17	unnecessary	unnecessary	JJ
37681	1700	18	.	.	.
37681	1701	1	It	-PRON-	PRP
37681	1701	2	will	will	MD
37681	1701	3	be	be	VB
37681	1701	4	noticed	notice	VBN
37681	1701	5	that	that	IN
37681	1701	6	Euclid	Euclid	NNP
37681	1701	7	did	do	VBD
37681	1701	8	not	not	RB
37681	1701	9	use	use	VB
37681	1701	10	or	or	CC
37681	1701	11	define	define	VB
37681	1701	12	the	the	DT
37681	1701	13	word	word	NN
37681	1701	14	"	"	``
37681	1701	15	polygon	polygon	NN
37681	1701	16	.	.	.
37681	1701	17	"	"	''
37681	1702	1	He	-PRON-	PRP
37681	1702	2	uses	use	VBZ
37681	1702	3	"	"	``
37681	1702	4	rectilinear	rectilinear	JJ
37681	1702	5	figure	figure	NN
37681	1702	6	"	"	''
37681	1702	7	instead	instead	RB
37681	1702	8	.	.	.
37681	1703	1	Polygon	polygon	NN
37681	1703	2	may	may	MD
37681	1703	3	be	be	VB
37681	1703	4	defined	define	VBN
37681	1703	5	to	to	TO
37681	1703	6	be	be	VB
37681	1703	7	a	a	DT
37681	1703	8	bounding	bound	VBG
37681	1703	9	line	line	NN
37681	1703	10	,	,	,
37681	1703	11	as	as	IN
37681	1703	12	a	a	DT
37681	1703	13	circle	circle	NN
37681	1703	14	is	be	VBZ
37681	1703	15	now	now	RB
37681	1703	16	defined	define	VBN
37681	1703	17	,	,	,
37681	1703	18	or	or	CC
37681	1703	19	as	as	IN
37681	1703	20	the	the	DT
37681	1703	21	space	space	NN
37681	1703	22	inclosed	inclose	VBN
37681	1703	23	by	by	IN
37681	1703	24	a	a	DT
37681	1703	25	broken	broken	JJ
37681	1703	26	line	line	NN
37681	1703	27	,	,	,
37681	1703	28	or	or	CC
37681	1703	29	as	as	IN
37681	1703	30	a	a	DT
37681	1703	31	figure	figure	NN
37681	1703	32	formed	form	VBN
37681	1703	33	by	by	IN
37681	1703	34	a	a	DT
37681	1703	35	broken	broken	JJ
37681	1703	36	line	line	NN
37681	1703	37	,	,	,
37681	1703	38	thus	thus	RB
37681	1703	39	including	include	VBG
37681	1703	40	both	both	CC
37681	1703	41	the	the	DT
37681	1703	42	limited	limited	JJ
37681	1703	43	plane	plane	NN
37681	1703	44	and	and	CC
37681	1703	45	its	-PRON-	PRP$
37681	1703	46	boundary	boundary	NN
37681	1703	47	.	.	.
37681	1704	1	It	-PRON-	PRP
37681	1704	2	is	be	VBZ
37681	1704	3	not	not	RB
37681	1704	4	of	of	IN
37681	1704	5	any	any	DT
37681	1704	6	great	great	JJ
37681	1704	7	consequence	consequence	NN
37681	1704	8	geometrically	geometrically	RB
37681	1704	9	which	which	WDT
37681	1704	10	of	of	IN
37681	1704	11	these	these	DT
37681	1704	12	ideas	idea	NNS
37681	1704	13	is	be	VBZ
37681	1704	14	adopted	adopt	VBN
37681	1704	15	,	,	,
37681	1704	16	so	so	IN
37681	1704	17	that	that	IN
37681	1704	18	the	the	DT
37681	1704	19	usual	usual	JJ
37681	1704	20	definition	definition	NN
37681	1704	21	of	of	IN
37681	1704	22	a	a	DT
37681	1704	23	portion	portion	NN
37681	1704	24	of	of	IN
37681	1704	25	a	a	DT
37681	1704	26	plane	plane	NN
37681	1704	27	bounded	bound	VBN
37681	1704	28	by	by	IN
37681	1704	29	a	a	DT
37681	1704	30	broken	broken	JJ
37681	1704	31	line	line	NN
37681	1704	32	may	may	MD
37681	1704	33	be	be	VB
37681	1704	34	taken	take	VBN
37681	1704	35	as	as	RB
37681	1704	36	sufficient	sufficient	JJ
37681	1704	37	for	for	IN
37681	1704	38	elementary	elementary	JJ
37681	1704	39	purposes	purpose	NNS
37681	1704	40	.	.	.
37681	1705	1	It	-PRON-	PRP
37681	1705	2	is	be	VBZ
37681	1705	3	proper	proper	JJ
37681	1705	4	to	to	TO
37681	1705	5	call	call	VB
37681	1705	6	attention	attention	NN
37681	1705	7	,	,	,
37681	1705	8	however	however	RB
37681	1705	9	,	,	,
37681	1705	10	to	to	IN
37681	1705	11	the	the	DT
37681	1705	12	fact	fact	NN
37681	1705	13	that	that	IN
37681	1705	14	we	-PRON-	PRP
37681	1705	15	may	may	MD
37681	1705	16	have	have	VB
37681	1705	17	cross	cross	JJ
37681	1705	18	polygons	polygon	NNS
37681	1705	19	of	of	IN
37681	1705	20	various	various	JJ
37681	1705	21	types	type	NNS
37681	1705	22	,	,	,
37681	1705	23	and	and	CC
37681	1705	24	that	that	IN
37681	1705	25	the	the	DT
37681	1705	26	line	line	NN
37681	1705	27	that	that	IN
37681	1705	28	"	"	``
37681	1705	29	bounds	bound	VBZ
37681	1705	30	"	"	''
37681	1705	31	the	the	DT
37681	1705	32	polygon	polygon	NN
37681	1705	33	must	must	MD
37681	1705	34	be	be	VB
37681	1705	35	continuous	continuous	JJ
37681	1705	36	,	,	,
37681	1705	37	as	as	IN
37681	1705	38	the	the	DT
37681	1705	39	definition	definition	NN
37681	1705	40	states	state	VBZ
37681	1705	41	.	.	.
37681	1706	1	That	that	RB
37681	1706	2	is	is	RB
37681	1706	3	,	,	,
37681	1706	4	in	in	IN
37681	1706	5	the	the	DT
37681	1706	6	second	second	JJ
37681	1706	7	of	of	IN
37681	1706	8	these	these	DT
37681	1706	9	figures	figure	NNS
37681	1706	10	the	the	DT
37681	1706	11	shaded	shaded	JJ
37681	1706	12	portion	portion	NN
37681	1706	13	is	be	VBZ
37681	1706	14	not	not	RB
37681	1706	15	considered	consider	VBN
37681	1706	16	a	a	DT
37681	1706	17	polygon	polygon	NN
37681	1706	18	.	.	.
37681	1707	1	Such	such	JJ
37681	1707	2	special	special	JJ
37681	1707	3	cases	case	NNS
37681	1707	4	are	be	VBP
37681	1707	5	not	not	RB
37681	1707	6	liable	liable	JJ
37681	1707	7	to	to	TO
37681	1707	8	arise	arise	VB
37681	1707	9	,	,	,
37681	1707	10	but	but	CC
37681	1707	11	if	if	IN
37681	1707	12	questions	question	NNS
37681	1707	13	relating	relate	VBG
37681	1707	14	to	to	IN
37681	1707	15	them	-PRON-	PRP
37681	1707	16	are	be	VBP
37681	1707	17	suggested	suggest	VBN
37681	1707	18	,	,	,
37681	1707	19	the	the	DT
37681	1707	20	teacher	teacher	NN
37681	1707	21	should	should	MD
37681	1707	22	be	be	VB
37681	1707	23	prepared	prepared	JJ
37681	1707	24	to	to	TO
37681	1707	25	answer	answer	VB
37681	1707	26	them	-PRON-	PRP
37681	1707	27	.	.	.
37681	1708	1	If	if	IN
37681	1708	2	suggested	suggest	VBN
37681	1708	3	to	to	IN
37681	1708	4	a	a	DT
37681	1708	5	class	class	NN
37681	1708	6	,	,	,
37681	1708	7	a	a	DT
37681	1708	8	note	note	NN
37681	1708	9	of	of	IN
37681	1708	10	this	this	DT
37681	1708	11	kind	kind	NN
37681	1708	12	should	should	MD
37681	1708	13	come	come	VB
37681	1708	14	out	out	RP
37681	1708	15	only	only	RB
37681	1708	16	incidentally	incidentally	RB
37681	1708	17	as	as	IN
37681	1708	18	a	a	DT
37681	1708	19	bit	bit	NN
37681	1708	20	of	of	IN
37681	1708	21	interest	interest	NN
37681	1708	22	,	,	,
37681	1708	23	and	and	CC
37681	1708	24	should	should	MD
37681	1708	25	not	not	RB
37681	1708	26	occupy	occupy	VB
37681	1708	27	much	much	JJ
37681	1708	28	time	time	NN
37681	1708	29	nor	nor	CC
37681	1708	30	be	be	VB
37681	1708	31	unduly	unduly	RB
37681	1708	32	emphasized	emphasize	VBN
37681	1708	33	.	.	.
37681	1709	1	[	[	-LRB-
37681	1709	2	Illustration	illustration	NN
37681	1709	3	]	]	-RRB-
37681	1709	4	It	-PRON-	PRP
37681	1709	5	may	may	MD
37681	1709	6	also	also	RB
37681	1709	7	be	be	VB
37681	1709	8	mentioned	mention	VBN
37681	1709	9	to	to	IN
37681	1709	10	a	a	DT
37681	1709	11	class	class	NN
37681	1709	12	at	at	IN
37681	1709	13	some	some	DT
37681	1709	14	convenient	convenient	JJ
37681	1709	15	time	time	NN
37681	1709	16	that	that	WDT
37681	1709	17	the	the	DT
37681	1709	18	old	old	JJ
37681	1709	19	idea	idea	NN
37681	1709	20	of	of	IN
37681	1709	21	a	a	DT
37681	1709	22	polygon	polygon	NN
37681	1709	23	was	be	VBD
37681	1709	24	that	that	DT
37681	1709	25	of	of	IN
37681	1709	26	a	a	DT
37681	1709	27	convex	convex	NNP
37681	1709	28	figure	figure	NN
37681	1709	29	,	,	,
37681	1709	30	and	and	CC
37681	1709	31	that	that	IN
37681	1709	32	the	the	DT
37681	1709	33	modern	modern	JJ
37681	1709	34	idea	idea	NN
37681	1709	35	,	,	,
37681	1709	36	which	which	WDT
37681	1709	37	is	be	VBZ
37681	1709	38	met	meet	VBN
37681	1709	39	in	in	IN
37681	1709	40	higher	high	JJR
37681	1709	41	mathematics	mathematic	NNS
37681	1709	42	,	,	,
37681	1709	43	leads	lead	VBZ
37681	1709	44	to	to	IN
37681	1709	45	a	a	DT
37681	1709	46	modification	modification	NN
37681	1709	47	of	of	IN
37681	1709	48	earlier	early	JJR
37681	1709	49	concepts	concept	NNS
37681	1709	50	.	.	.
37681	1710	1	For	for	IN
37681	1710	2	example	example	NN
37681	1710	3	,	,	,
37681	1710	4	here	here	RB
37681	1710	5	is	be	VBZ
37681	1710	6	a	a	DT
37681	1710	7	quadrilateral	quadrilateral	NN
37681	1710	8	with	with	IN
37681	1710	9	one	one	CD
37681	1710	10	of	of	IN
37681	1710	11	its	-PRON-	PRP$
37681	1710	12	diagonals	diagonal	NNS
37681	1710	13	,	,	,
37681	1710	14	_	_	NNP
37681	1710	15	BD	BD	NNP
37681	1710	16	_	_	NNP
37681	1710	17	,	,	,
37681	1710	18	_	_	NNP
37681	1710	19	outside	outside	IN
37681	1710	20	_	_	NNP
37681	1710	21	the	the	DT
37681	1710	22	figure	figure	NN
37681	1710	23	.	.	.
37681	1711	1	Furthermore	furthermore	RB
37681	1711	2	,	,	,
37681	1711	3	if	if	IN
37681	1711	4	we	-PRON-	PRP
37681	1711	5	consider	consider	VBP
37681	1711	6	a	a	DT
37681	1711	7	quadrilateral	quadrilateral	NN
37681	1711	8	as	as	IN
37681	1711	9	a	a	DT
37681	1711	10	figure	figure	NN
37681	1711	11	formed	form	VBN
37681	1711	12	by	by	IN
37681	1711	13	four	four	CD
37681	1711	14	intersecting	intersect	VBG
37681	1711	15	lines	line	NNS
37681	1711	16	,	,	,
37681	1711	17	_	_	NNP
37681	1711	18	AC	AC	NNP
37681	1711	19	_	_	NNP
37681	1711	20	,	,	,
37681	1711	21	_	_	NNP
37681	1711	22	CF	CF	NNP
37681	1711	23	_	_	NNP
37681	1711	24	,	,	,
37681	1711	25	_	_	NNP
37681	1711	26	BE	BE	NNP
37681	1711	27	_	_	NNP
37681	1711	28	,	,	,
37681	1711	29	and	and	CC
37681	1711	30	_	_	NNP
37681	1711	31	EA	EA	NNP
37681	1711	32	_	_	NNP
37681	1711	33	,	,	,
37681	1711	34	it	-PRON-	PRP
37681	1711	35	is	be	VBZ
37681	1711	36	apparent	apparent	JJ
37681	1711	37	that	that	IN
37681	1711	38	this	this	DT
37681	1711	39	_	_	NNP
37681	1711	40	general	general	JJ
37681	1711	41	quadrilateral	quadrilateral	NNP
37681	1711	42	_	_	NNP
37681	1711	43	has	have	VBZ
37681	1711	44	six	six	CD
37681	1711	45	vertices	vertex	NNS
37681	1711	46	,	,	,
37681	1711	47	_	_	NNP
37681	1711	48	A	A	NNP
37681	1711	49	_	_	NNP
37681	1711	50	,	,	,
37681	1711	51	_	_	NNP
37681	1711	52	B	B	NNP
37681	1711	53	_	_	NNP
37681	1711	54	,	,	,
37681	1711	55	_	_	NNP
37681	1711	56	C	C	NNP
37681	1711	57	_	_	NNP
37681	1711	58	,	,	,
37681	1711	59	_	_	NNP
37681	1711	60	D	D	NNP
37681	1711	61	_	_	NNP
37681	1711	62	,	,	,
37681	1711	63	_	_	NNP
37681	1711	64	E	E	NNP
37681	1711	65	_	_	NNP
37681	1711	66	,	,	,
37681	1711	67	_	_	NNP
37681	1711	68	F	F	NNP
37681	1711	69	_	_	NNP
37681	1711	70	,	,	,
37681	1711	71	and	and	CC
37681	1711	72	three	three	CD
37681	1711	73	diagonals	diagonal	NNS
37681	1711	74	,	,	,
37681	1711	75	_	_	NNP
37681	1711	76	AD	AD	NNP
37681	1711	77	_	_	NNP
37681	1711	78	,	,	,
37681	1711	79	_	_	NNP
37681	1711	80	BF	BF	NNP
37681	1711	81	_	_	NNP
37681	1711	82	,	,	,
37681	1711	83	and	and	CC
37681	1711	84	_	_	NNP
37681	1711	85	CE	CE	NNP
37681	1711	86	_	_	NNP
37681	1711	87	.	.	.
37681	1712	1	Such	such	JJ
37681	1712	2	broader	broad	JJR
37681	1712	3	ideas	idea	NNS
37681	1712	4	of	of	IN
37681	1712	5	geometry	geometry	NN
37681	1712	6	form	form	VBP
37681	1712	7	the	the	DT
37681	1712	8	basis	basis	NN
37681	1712	9	of	of	IN
37681	1712	10	what	what	WP
37681	1712	11	is	be	VBZ
37681	1712	12	called	call	VBN
37681	1712	13	modern	modern	JJ
37681	1712	14	elementary	elementary	JJ
37681	1712	15	geometry	geometry	NN
37681	1712	16	.	.	.
37681	1713	1	[	[	-LRB-
37681	1713	2	Illustration	illustration	NN
37681	1713	3	]	]	-RRB-
37681	1713	4	The	the	DT
37681	1713	5	other	other	JJ
37681	1713	6	definitions	definition	NNS
37681	1713	7	of	of	IN
37681	1713	8	plane	plane	NN
37681	1713	9	geometry	geometry	NN
37681	1713	10	need	nee	MD
37681	1713	11	not	not	RB
37681	1713	12	be	be	VB
37681	1713	13	discussed	discuss	VBN
37681	1713	14	,	,	,
37681	1713	15	since	since	IN
37681	1713	16	all	all	DT
37681	1713	17	that	that	WDT
37681	1713	18	have	have	VBP
37681	1713	19	any	any	DT
37681	1713	20	historical	historical	JJ
37681	1713	21	interest	interest	NN
37681	1713	22	have	have	VBP
37681	1713	23	been	be	VBN
37681	1713	24	considered	consider	VBN
37681	1713	25	.	.	.
37681	1714	1	On	on	IN
37681	1714	2	the	the	DT
37681	1714	3	whole	whole	NN
37681	1714	4	it	-PRON-	PRP
37681	1714	5	may	may	MD
37681	1714	6	be	be	VB
37681	1714	7	said	say	VBN
37681	1714	8	that	that	IN
37681	1714	9	our	-PRON-	PRP$
37681	1714	10	definitions	definition	NNS
37681	1714	11	to	to	IN
37681	1714	12	-	-	HYPH
37681	1714	13	day	day	NN
37681	1714	14	are	be	VBP
37681	1714	15	not	not	RB
37681	1714	16	in	in	IN
37681	1714	17	general	general	JJ
37681	1714	18	so	so	RB
37681	1714	19	carefully	carefully	RB
37681	1714	20	considered	consider	VBN
37681	1714	21	as	as	IN
37681	1714	22	those	those	DT
37681	1714	23	of	of	IN
37681	1714	24	Euclid	Euclid	NNP
37681	1714	25	,	,	,
37681	1714	26	who	who	WP
37681	1714	27	weighed	weigh	VBD
37681	1714	28	each	each	DT
37681	1714	29	word	word	NN
37681	1714	30	with	with	IN
37681	1714	31	greatest	great	JJS
37681	1714	32	skill	skill	NN
37681	1714	33	,	,	,
37681	1714	34	but	but	CC
37681	1714	35	they	-PRON-	PRP
37681	1714	36	are	be	VBP
37681	1714	37	more	more	RBR
37681	1714	38	teachable	teachable	JJ
37681	1714	39	to	to	IN
37681	1714	40	beginners	beginner	NNS
37681	1714	41	,	,	,
37681	1714	42	and	and	CC
37681	1714	43	are	be	VBP
37681	1714	44	,	,	,
37681	1714	45	on	on	IN
37681	1714	46	the	the	DT
37681	1714	47	whole	whole	NN
37681	1714	48	,	,	,
37681	1714	49	more	more	RBR
37681	1714	50	satisfactory	satisfactory	JJ
37681	1714	51	from	from	IN
37681	1714	52	the	the	DT
37681	1714	53	educational	educational	JJ
37681	1714	54	standpoint	standpoint	NN
37681	1714	55	.	.	.
37681	1715	1	The	the	DT
37681	1715	2	greatest	great	JJS
37681	1715	3	lesson	lesson	NN
37681	1715	4	to	to	TO
37681	1715	5	be	be	VB
37681	1715	6	learned	learn	VBN
37681	1715	7	from	from	IN
37681	1715	8	this	this	DT
37681	1715	9	discussion	discussion	NN
37681	1715	10	is	be	VBZ
37681	1715	11	that	that	IN
37681	1715	12	the	the	DT
37681	1715	13	number	number	NN
37681	1715	14	of	of	IN
37681	1715	15	basal	basal	NN
37681	1715	16	definitions	definition	NNS
37681	1715	17	to	to	TO
37681	1715	18	be	be	VB
37681	1715	19	learned	learn	VBN
37681	1715	20	for	for	IN
37681	1715	21	subsequent	subsequent	JJ
37681	1715	22	use	use	NN
37681	1715	23	is	be	VBZ
37681	1715	24	very	very	RB
37681	1715	25	small	small	JJ
37681	1715	26	.	.	.
37681	1716	1	Since	since	IN
37681	1716	2	teachers	teacher	NNS
37681	1716	3	are	be	VBP
37681	1716	4	occasionally	occasionally	RB
37681	1716	5	disturbed	disturb	VBN
37681	1716	6	over	over	IN
37681	1716	7	the	the	DT
37681	1716	8	form	form	NN
37681	1716	9	in	in	IN
37681	1716	10	which	which	WDT
37681	1716	11	definitions	definition	NNS
37681	1716	12	are	be	VBP
37681	1716	13	stated	state	VBN
37681	1716	14	,	,	,
37681	1716	15	it	-PRON-	PRP
37681	1716	16	is	be	VBZ
37681	1716	17	well	well	JJ
37681	1716	18	to	to	TO
37681	1716	19	say	say	VB
37681	1716	20	a	a	DT
37681	1716	21	few	few	JJ
37681	1716	22	words	word	NNS
37681	1716	23	upon	upon	IN
37681	1716	24	this	this	DT
37681	1716	25	subject	subject	NN
37681	1716	26	.	.	.
37681	1717	1	There	there	EX
37681	1717	2	are	be	VBP
37681	1717	3	several	several	JJ
37681	1717	4	standard	standard	JJ
37681	1717	5	types	type	NNS
37681	1717	6	that	that	WDT
37681	1717	7	may	may	MD
37681	1717	8	be	be	VB
37681	1717	9	used	use	VBN
37681	1717	10	.	.	.
37681	1718	1	(	(	-LRB-
37681	1718	2	1	1	LS
37681	1718	3	)	)	-RRB-
37681	1718	4	We	-PRON-	PRP
37681	1718	5	may	may	MD
37681	1718	6	use	use	VB
37681	1718	7	the	the	DT
37681	1718	8	dictionary	dictionary	JJ
37681	1718	9	form	form	NN
37681	1718	10	,	,	,
37681	1718	11	putting	put	VBG
37681	1718	12	the	the	DT
37681	1718	13	word	word	NN
37681	1718	14	defined	define	VBN
37681	1718	15	first	first	RB
37681	1718	16	,	,	,
37681	1718	17	thus	thus	RB
37681	1718	18	:	:	:
37681	1718	19	"	"	``
37681	1718	20	_	_	NNP
37681	1718	21	Right	Right	NNP
37681	1718	22	triangle	triangle	NN
37681	1718	23	_	_	NNP
37681	1718	24	.	.	.
37681	1719	1	A	a	DT
37681	1719	2	triangle	triangle	NN
37681	1719	3	that	that	WDT
37681	1719	4	has	have	VBZ
37681	1719	5	one	one	CD
37681	1719	6	of	of	IN
37681	1719	7	its	-PRON-	PRP$
37681	1719	8	angles	angle	NNS
37681	1719	9	a	a	DT
37681	1719	10	right	right	JJ
37681	1719	11	angle	angle	NN
37681	1719	12	.	.	.
37681	1719	13	"	"	''
37681	1720	1	This	this	DT
37681	1720	2	is	be	VBZ
37681	1720	3	scientifically	scientifically	RB
37681	1720	4	correct	correct	JJ
37681	1720	5	,	,	,
37681	1720	6	but	but	CC
37681	1720	7	it	-PRON-	PRP
37681	1720	8	is	be	VBZ
37681	1720	9	not	not	RB
37681	1720	10	a	a	DT
37681	1720	11	complete	complete	JJ
37681	1720	12	sentence	sentence	NN
37681	1720	13	,	,	,
37681	1720	14	and	and	CC
37681	1720	15	hence	hence	RB
37681	1720	16	it	-PRON-	PRP
37681	1720	17	is	be	VBZ
37681	1720	18	not	not	RB
37681	1720	19	easily	easily	RB
37681	1720	20	repeated	repeat	VBN
37681	1720	21	when	when	WRB
37681	1720	22	it	-PRON-	PRP
37681	1720	23	has	have	VBZ
37681	1720	24	to	to	TO
37681	1720	25	be	be	VB
37681	1720	26	quoted	quote	VBN
37681	1720	27	as	as	IN
37681	1720	28	an	an	DT
37681	1720	29	authority	authority	NN
37681	1720	30	.	.	.
37681	1721	1	(	(	-LRB-
37681	1721	2	2	2	LS
37681	1721	3	)	)	-RRB-
37681	1721	4	We	-PRON-	PRP
37681	1721	5	may	may	MD
37681	1721	6	put	put	VB
37681	1721	7	the	the	DT
37681	1721	8	word	word	NN
37681	1721	9	defined	define	VBN
37681	1721	10	at	at	IN
37681	1721	11	the	the	DT
37681	1721	12	end	end	NN
37681	1721	13	,	,	,
37681	1721	14	thus	thus	RB
37681	1721	15	:	:	:
37681	1721	16	"	"	``
37681	1721	17	A	a	DT
37681	1721	18	triangle	triangle	NN
37681	1721	19	that	that	WDT
37681	1721	20	has	have	VBZ
37681	1721	21	one	one	CD
37681	1721	22	of	of	IN
37681	1721	23	its	-PRON-	PRP$
37681	1721	24	angles	angle	NNS
37681	1721	25	a	a	DT
37681	1721	26	right	right	JJ
37681	1721	27	angle	angle	NN
37681	1721	28	is	be	VBZ
37681	1721	29	called	call	VBN
37681	1721	30	a	a	DT
37681	1721	31	right	right	JJ
37681	1721	32	triangle	triangle	NN
37681	1721	33	.	.	.
37681	1721	34	"	"	''
37681	1722	1	This	this	DT
37681	1722	2	is	be	VBZ
37681	1722	3	more	more	RBR
37681	1722	4	satisfactory	satisfactory	JJ
37681	1722	5	.	.	.
37681	1723	1	(	(	-LRB-
37681	1723	2	3	3	LS
37681	1723	3	)	)	-RRB-
37681	1723	4	We	-PRON-	PRP
37681	1723	5	may	may	MD
37681	1723	6	combine	combine	VB
37681	1723	7	(	(	-LRB-
37681	1723	8	1	1	CD
37681	1723	9	)	)	-RRB-
37681	1723	10	and	and	CC
37681	1723	11	(	(	-LRB-
37681	1723	12	2	2	CD
37681	1723	13	)	)	-RRB-
37681	1723	14	,	,	,
37681	1723	15	thus	thus	RB
37681	1723	16	:	:	:
37681	1723	17	"	"	``
37681	1723	18	_	_	NNP
37681	1723	19	Right	Right	NNP
37681	1723	20	triangle	triangle	NN
37681	1723	21	_	_	NNP
37681	1723	22	.	.	.
37681	1724	1	A	a	DT
37681	1724	2	triangle	triangle	NN
37681	1724	3	that	that	WDT
37681	1724	4	has	have	VBZ
37681	1724	5	one	one	CD
37681	1724	6	of	of	IN
37681	1724	7	its	-PRON-	PRP$
37681	1724	8	angles	angle	NNS
37681	1724	9	a	a	DT
37681	1724	10	right	right	JJ
37681	1724	11	angle	angle	NN
37681	1724	12	is	be	VBZ
37681	1724	13	called	call	VBN
37681	1724	14	a	a	DT
37681	1724	15	right	right	JJ
37681	1724	16	triangle	triangle	NN
37681	1724	17	.	.	.
37681	1724	18	"	"	''
37681	1725	1	This	this	DT
37681	1725	2	is	be	VBZ
37681	1725	3	still	still	RB
37681	1725	4	better	well	JJR
37681	1725	5	,	,	,
37681	1725	6	for	for	IN
37681	1725	7	it	-PRON-	PRP
37681	1725	8	has	have	VBZ
37681	1725	9	the	the	DT
37681	1725	10	catchword	catchword	NN
37681	1725	11	at	at	IN
37681	1725	12	the	the	DT
37681	1725	13	beginning	beginning	NN
37681	1725	14	of	of	IN
37681	1725	15	the	the	DT
37681	1725	16	paragraph	paragraph	NN
37681	1725	17	.	.	.
37681	1726	1	There	there	EX
37681	1726	2	is	be	VBZ
37681	1726	3	occasionally	occasionally	RB
37681	1726	4	some	some	DT
37681	1726	5	mental	mental	JJ
37681	1726	6	agitation	agitation	NN
37681	1726	7	over	over	IN
37681	1726	8	the	the	DT
37681	1726	9	trivial	trivial	JJ
37681	1726	10	things	thing	NNS
37681	1726	11	of	of	IN
37681	1726	12	a	a	DT
37681	1726	13	definition	definition	NN
37681	1726	14	,	,	,
37681	1726	15	such	such	JJ
37681	1726	16	as	as	IN
37681	1726	17	the	the	DT
37681	1726	18	use	use	NN
37681	1726	19	of	of	IN
37681	1726	20	the	the	DT
37681	1726	21	words	word	NNS
37681	1726	22	"	"	``
37681	1726	23	is	be	VBZ
37681	1726	24	called	call	VBN
37681	1726	25	.	.	.
37681	1726	26	"	"	''
37681	1727	1	It	-PRON-	PRP
37681	1727	2	would	would	MD
37681	1727	3	not	not	RB
37681	1727	4	be	be	VB
37681	1727	5	a	a	DT
37681	1727	6	very	very	RB
37681	1727	7	serious	serious	JJ
37681	1727	8	matter	matter	NN
37681	1727	9	if	if	IN
37681	1727	10	they	-PRON-	PRP
37681	1727	11	were	be	VBD
37681	1727	12	omitted	omit	VBN
37681	1727	13	,	,	,
37681	1727	14	but	but	CC
37681	1727	15	it	-PRON-	PRP
37681	1727	16	is	be	VBZ
37681	1727	17	better	well	JJR
37681	1727	18	to	to	TO
37681	1727	19	have	have	VB
37681	1727	20	them	-PRON-	PRP
37681	1727	21	there	there	RB
37681	1727	22	.	.	.
37681	1728	1	The	the	DT
37681	1728	2	reason	reason	NN
37681	1728	3	is	be	VBZ
37681	1728	4	that	that	IN
37681	1728	5	they	-PRON-	PRP
37681	1728	6	mark	mark	VBP
37681	1728	7	the	the	DT
37681	1728	8	statement	statement	NN
37681	1728	9	at	at	IN
37681	1728	10	once	once	RB
37681	1728	11	as	as	IN
37681	1728	12	a	a	DT
37681	1728	13	definition	definition	NN
37681	1728	14	.	.	.
37681	1729	1	For	for	IN
37681	1729	2	example	example	NN
37681	1729	3	,	,	,
37681	1729	4	suppose	suppose	VB
37681	1729	5	we	-PRON-	PRP
37681	1729	6	say	say	VBP
37681	1729	7	that	that	IN
37681	1729	8	"	"	``
37681	1729	9	a	a	DT
37681	1729	10	triangle	triangle	NN
37681	1729	11	that	that	WDT
37681	1729	12	has	have	VBZ
37681	1729	13	one	one	CD
37681	1729	14	of	of	IN
37681	1729	15	its	-PRON-	PRP$
37681	1729	16	angles	angle	NNS
37681	1729	17	a	a	DT
37681	1729	18	right	right	JJ
37681	1729	19	angle	angle	NN
37681	1729	20	is	be	VBZ
37681	1729	21	a	a	DT
37681	1729	22	right	right	JJ
37681	1729	23	triangle	triangle	NN
37681	1729	24	.	.	.
37681	1729	25	"	"	''
37681	1730	1	We	-PRON-	PRP
37681	1730	2	have	have	VBP
37681	1730	3	also	also	RB
37681	1730	4	the	the	DT
37681	1730	5	fact	fact	NN
37681	1730	6	that	that	IN
37681	1730	7	"	"	``
37681	1730	8	a	a	DT
37681	1730	9	triangle	triangle	NN
37681	1730	10	whose	whose	WP$
37681	1730	11	base	base	NN
37681	1730	12	is	be	VBZ
37681	1730	13	the	the	DT
37681	1730	14	diameter	diameter	NN
37681	1730	15	of	of	IN
37681	1730	16	a	a	DT
37681	1730	17	semicircle	semicircle	NN
37681	1730	18	and	and	CC
37681	1730	19	whose	whose	WP$
37681	1730	20	vertex	vertex	NN
37681	1730	21	lies	lie	VBZ
37681	1730	22	on	on	IN
37681	1730	23	the	the	DT
37681	1730	24	semicircle	semicircle	NN
37681	1730	25	is	be	VBZ
37681	1730	26	a	a	DT
37681	1730	27	right	right	JJ
37681	1730	28	triangle	triangle	NN
37681	1730	29	.	.	.
37681	1730	30	"	"	''
37681	1731	1	The	the	DT
37681	1731	2	style	style	NN
37681	1731	3	of	of	IN
37681	1731	4	statement	statement	NN
37681	1731	5	is	be	VBZ
37681	1731	6	the	the	DT
37681	1731	7	same	same	JJ
37681	1731	8	,	,	,
37681	1731	9	and	and	CC
37681	1731	10	we	-PRON-	PRP
37681	1731	11	have	have	VBP
37681	1731	12	nothing	nothing	NN
37681	1731	13	in	in	IN
37681	1731	14	the	the	DT
37681	1731	15	phraseology	phraseology	NN
37681	1731	16	to	to	TO
37681	1731	17	show	show	VB
37681	1731	18	that	that	IN
37681	1731	19	the	the	DT
37681	1731	20	first	first	JJ
37681	1731	21	is	be	VBZ
37681	1731	22	a	a	DT
37681	1731	23	definition	definition	NN
37681	1731	24	and	and	CC
37681	1731	25	the	the	DT
37681	1731	26	second	second	JJ
37681	1731	27	a	a	DT
37681	1731	28	theorem	theorem	NN
37681	1731	29	.	.	.
37681	1732	1	This	this	DT
37681	1732	2	may	may	MD
37681	1732	3	happen	happen	VB
37681	1732	4	with	with	IN
37681	1732	5	most	most	JJS
37681	1732	6	of	of	IN
37681	1732	7	the	the	DT
37681	1732	8	definitions	definition	NNS
37681	1732	9	,	,	,
37681	1732	10	and	and	CC
37681	1732	11	hence	hence	RB
37681	1732	12	the	the	DT
37681	1732	13	most	most	RBS
37681	1732	14	careful	careful	JJ
37681	1732	15	writers	writer	NNS
37681	1732	16	have	have	VBP
37681	1732	17	not	not	RB
37681	1732	18	consented	consent	VBN
37681	1732	19	to	to	TO
37681	1732	20	omit	omit	VB
37681	1732	21	the	the	DT
37681	1732	22	distinctive	distinctive	JJ
37681	1732	23	words	word	NNS
37681	1732	24	in	in	IN
37681	1732	25	question	question	NN
37681	1732	26	.	.	.
37681	1733	1	Apropos	Apropos	NNP
37681	1733	2	of	of	IN
37681	1733	3	the	the	DT
37681	1733	4	definitions	definition	NNS
37681	1733	5	of	of	IN
37681	1733	6	geometry	geometry	NN
37681	1733	7	,	,	,
37681	1733	8	the	the	DT
37681	1733	9	great	great	JJ
37681	1733	10	French	french	JJ
37681	1733	11	philosopher	philosopher	NN
37681	1733	12	and	and	CC
37681	1733	13	mathematician	mathematician	JJ
37681	1733	14	,	,	,
37681	1733	15	Pascal	Pascal	NNP
37681	1733	16	,	,	,
37681	1733	17	set	set	VBD
37681	1733	18	forth	forth	RP
37681	1733	19	certain	certain	JJ
37681	1733	20	rules	rule	NNS
37681	1733	21	relating	relate	VBG
37681	1733	22	to	to	IN
37681	1733	23	this	this	DT
37681	1733	24	subject	subject	NN
37681	1733	25	,	,	,
37681	1733	26	as	as	RB
37681	1733	27	also	also	RB
37681	1733	28	to	to	IN
37681	1733	29	the	the	DT
37681	1733	30	axioms	axiom	NNS
37681	1733	31	employed	employ	VBN
37681	1733	32	,	,	,
37681	1733	33	and	and	CC
37681	1733	34	these	these	DT
37681	1733	35	may	may	MD
37681	1733	36	properly	properly	RB
37681	1733	37	sum	sum	VB
37681	1733	38	up	up	RP
37681	1733	39	this	this	DT
37681	1733	40	chapter	chapter	NN
37681	1733	41	.	.	.
37681	1734	1	1	1	LS
37681	1734	2	.	.	.
37681	1735	1	Do	do	VB
37681	1735	2	not	not	RB
37681	1735	3	attempt	attempt	VB
37681	1735	4	to	to	TO
37681	1735	5	define	define	VB
37681	1735	6	terms	term	NNS
37681	1735	7	so	so	RB
37681	1735	8	well	well	RB
37681	1735	9	known	known	JJ
37681	1735	10	in	in	IN
37681	1735	11	themselves	-PRON-	PRP
37681	1735	12	that	that	IN
37681	1735	13	there	there	EX
37681	1735	14	are	be	VBP
37681	1735	15	no	no	DT
37681	1735	16	simpler	simple	JJR
37681	1735	17	terms	term	NNS
37681	1735	18	by	by	IN
37681	1735	19	which	which	WDT
37681	1735	20	to	to	TO
37681	1735	21	express	express	VB
37681	1735	22	them	-PRON-	PRP
37681	1735	23	.	.	.
37681	1736	1	2	2	LS
37681	1736	2	.	.	.
37681	1737	1	Admit	admit	VB
37681	1737	2	no	no	DT
37681	1737	3	obscure	obscure	JJ
37681	1737	4	or	or	CC
37681	1737	5	equivocal	equivocal	JJ
37681	1737	6	terms	term	NNS
37681	1737	7	without	without	IN
37681	1737	8	defining	define	VBG
37681	1737	9	them	-PRON-	PRP
37681	1737	10	.	.	.
37681	1738	1	3	3	LS
37681	1738	2	.	.	.
37681	1739	1	Use	use	VB
37681	1739	2	in	in	IN
37681	1739	3	the	the	DT
37681	1739	4	definitions	definition	NNS
37681	1739	5	only	only	RB
37681	1739	6	terms	term	NNS
37681	1739	7	that	that	WDT
37681	1739	8	are	be	VBP
37681	1739	9	perfectly	perfectly	RB
37681	1739	10	understood	understand	VBN
37681	1739	11	or	or	CC
37681	1739	12	are	be	VBP
37681	1739	13	there	there	EX
37681	1739	14	explained	explain	VBN
37681	1739	15	.	.	.
37681	1740	1	4	4	LS
37681	1740	2	.	.	.
37681	1741	1	Omit	omit	VB
37681	1741	2	no	no	DT
37681	1741	3	necessary	necessary	JJ
37681	1741	4	principles	principle	NNS
37681	1741	5	without	without	IN
37681	1741	6	general	general	JJ
37681	1741	7	agreement	agreement	NN
37681	1741	8	,	,	,
37681	1741	9	however	however	RB
37681	1741	10	clear	clear	JJ
37681	1741	11	and	and	CC
37681	1741	12	evident	evident	JJ
37681	1741	13	they	-PRON-	PRP
37681	1741	14	may	may	MD
37681	1741	15	be	be	VB
37681	1741	16	.	.	.
37681	1742	1	5	5	CD
37681	1742	2	.	.	.
37681	1743	1	Set	Set	VBN
37681	1743	2	forth	forth	RB
37681	1743	3	in	in	IN
37681	1743	4	the	the	DT
37681	1743	5	axioms	axiom	NNS
37681	1743	6	only	only	RB
37681	1743	7	those	those	DT
37681	1743	8	things	thing	NNS
37681	1743	9	that	that	WDT
37681	1743	10	are	be	VBP
37681	1743	11	in	in	IN
37681	1743	12	themselves	-PRON-	PRP
37681	1743	13	perfectly	perfectly	RB
37681	1743	14	evident	evident	JJ
37681	1743	15	.	.	.
37681	1744	1	6	6	CD
37681	1744	2	.	.	.
37681	1745	1	Do	do	VB
37681	1745	2	not	not	RB
37681	1745	3	attempt	attempt	VB
37681	1745	4	to	to	TO
37681	1745	5	demonstrate	demonstrate	VB
37681	1745	6	anything	anything	NN
37681	1745	7	that	that	WDT
37681	1745	8	is	be	VBZ
37681	1745	9	so	so	RB
37681	1745	10	evident	evident	JJ
37681	1745	11	in	in	IN
37681	1745	12	itself	-PRON-	PRP
37681	1745	13	that	that	IN
37681	1745	14	there	there	EX
37681	1745	15	is	be	VBZ
37681	1745	16	nothing	nothing	NN
37681	1745	17	more	more	JJR
37681	1745	18	simple	simple	JJ
37681	1745	19	by	by	IN
37681	1745	20	which	which	WDT
37681	1745	21	to	to	TO
37681	1745	22	prove	prove	VB
37681	1745	23	it	-PRON-	PRP
37681	1745	24	.	.	.
37681	1746	1	7	7	LS
37681	1746	2	.	.	.
37681	1747	1	Prove	prove	VB
37681	1747	2	whatever	whatever	WDT
37681	1747	3	is	be	VBZ
37681	1747	4	in	in	IN
37681	1747	5	the	the	DT
37681	1747	6	least	least	JJS
37681	1747	7	obscure	obscure	JJ
37681	1747	8	,	,	,
37681	1747	9	using	use	VBG
37681	1747	10	in	in	IN
37681	1747	11	the	the	DT
37681	1747	12	demonstration	demonstration	NN
37681	1747	13	only	only	RB
37681	1747	14	axioms	axiom	NNS
37681	1747	15	that	that	WDT
37681	1747	16	are	be	VBP
37681	1747	17	perfectly	perfectly	RB
37681	1747	18	evident	evident	JJ
37681	1747	19	in	in	IN
37681	1747	20	themselves	-PRON-	PRP
37681	1747	21	,	,	,
37681	1747	22	or	or	CC
37681	1747	23	propositions	proposition	NNS
37681	1747	24	already	already	RB
37681	1747	25	demonstrated	demonstrate	VBD
37681	1747	26	or	or	CC
37681	1747	27	allowed	allow	VBN
37681	1747	28	.	.	.
37681	1748	1	8	8	LS
37681	1748	2	.	.	.
37681	1749	1	In	in	IN
37681	1749	2	case	case	NN
37681	1749	3	of	of	IN
37681	1749	4	any	any	DT
37681	1749	5	uncertainty	uncertainty	NN
37681	1749	6	arising	arise	VBG
37681	1749	7	from	from	IN
37681	1749	8	a	a	DT
37681	1749	9	term	term	NN
37681	1749	10	employed	employ	VBN
37681	1749	11	,	,	,
37681	1749	12	always	always	RB
37681	1749	13	substitute	substitute	VB
37681	1749	14	mentally	mentally	RB
37681	1749	15	the	the	DT
37681	1749	16	definition	definition	NN
37681	1749	17	for	for	IN
37681	1749	18	the	the	DT
37681	1749	19	term	term	NN
37681	1749	20	itself	-PRON-	PRP
37681	1749	21	.	.	.
37681	1750	1	=	=	NFP
37681	1750	2	Bibliography.=	Bibliography.=	NNP
37681	1750	3	Heath	Heath	NNP
37681	1750	4	,	,	,
37681	1750	5	Euclid	Euclid	NNP
37681	1750	6	,	,	,
37681	1750	7	as	as	IN
37681	1750	8	cited	cite	VBN
37681	1750	9	;	;	:
37681	1750	10	Frankland	Frankland	NNP
37681	1750	11	,	,	,
37681	1750	12	The	the	DT
37681	1750	13	First	First	NNP
37681	1750	14	Book	Book	NNP
37681	1750	15	of	of	IN
37681	1750	16	Euclid	Euclid	NNP
37681	1750	17	,	,	,
37681	1750	18	as	as	IN
37681	1750	19	cited	cite	VBN
37681	1750	20	;	;	:
37681	1750	21	Smith	Smith	NNP
37681	1750	22	,	,	,
37681	1750	23	Teaching	Teaching	NNP
37681	1750	24	of	of	IN
37681	1750	25	Elementary	Elementary	NNP
37681	1750	26	Mathematics	Mathematics	NNP
37681	1750	27	,	,	,
37681	1750	28	p.	p.	NN
37681	1750	29	257	257	CD
37681	1750	30	,	,	,
37681	1750	31	New	New	NNP
37681	1750	32	York	York	NNP
37681	1750	33	,	,	,
37681	1750	34	1900	1900	CD
37681	1750	35	;	;	:
37681	1750	36	Young	Young	NNP
37681	1750	37	,	,	,
37681	1750	38	Teaching	Teaching	NNP
37681	1750	39	of	of	IN
37681	1750	40	Mathematics	Mathematics	NNP
37681	1750	41	,	,	,
37681	1750	42	p.	p.	NN
37681	1750	43	189	189	CD
37681	1750	44	,	,	,
37681	1750	45	New	New	NNP
37681	1750	46	York	York	NNP
37681	1750	47	,	,	,
37681	1750	48	1907	1907	CD
37681	1750	49	;	;	:
37681	1750	50	Veblen	Veblen	NNP
37681	1750	51	,	,	,
37681	1750	52	On	on	IN
37681	1750	53	Definitions	definition	NNS
37681	1750	54	,	,	,
37681	1750	55	in	in	IN
37681	1750	56	the	the	DT
37681	1750	57	_	_	NNP
37681	1750	58	Monist	Monist	NNP
37681	1750	59	_	_	NNP
37681	1750	60	,	,	,
37681	1750	61	1903	1903	CD
37681	1750	62	,	,	,
37681	1750	63	p.	p.	NN
37681	1750	64	303	303	CD
37681	1750	65	.	.	.
37681	1751	1	FOOTNOTES	footnote	NNS
37681	1751	2	:	:	:
37681	1751	3	[	[	-LRB-
37681	1751	4	53	53	CD
37681	1751	5	]	]	-RRB-
37681	1751	6	Free	free	JJ
37681	1751	7	use	use	NN
37681	1751	8	has	have	VBZ
37681	1751	9	been	be	VBN
37681	1751	10	made	make	VBN
37681	1751	11	of	of	IN
37681	1751	12	W.	W.	NNP
37681	1751	13	B.	B.	NNP
37681	1751	14	Frankland	Frankland	NNP
37681	1751	15	,	,	,
37681	1751	16	"	"	``
37681	1751	17	The	the	DT
37681	1751	18	First	First	NNP
37681	1751	19	Book	Book	NNP
37681	1751	20	of	of	IN
37681	1751	21	Euclid	Euclid	NNP
37681	1751	22	's	's	POS
37681	1751	23	'	'	``
37681	1751	24	Elements	element	NNS
37681	1751	25	,	,	,
37681	1751	26	'	'	''
37681	1751	27	"	"	''
37681	1751	28	Cambridge	Cambridge	NNP
37681	1751	29	,	,	,
37681	1751	30	1905	1905	CD
37681	1751	31	;	;	:
37681	1751	32	T.	T.	NNP
37681	1751	33	L.	L.	NNP
37681	1751	34	Heath	Heath	NNP
37681	1751	35	,	,	,
37681	1751	36	"	"	``
37681	1751	37	The	the	DT
37681	1751	38	Thirteen	Thirteen	NNP
37681	1751	39	Books	Books	NNPS
37681	1751	40	of	of	IN
37681	1751	41	Euclid	Euclid	NNP
37681	1751	42	's	's	POS
37681	1751	43	'	'	''
37681	1751	44	Elements	element	NNS
37681	1751	45	,	,	,
37681	1751	46	'	'	''
37681	1751	47	"	"	``
37681	1751	48	Cambridge	Cambridge	NNP
37681	1751	49	,	,	,
37681	1751	50	1908	1908	CD
37681	1751	51	;	;	:
37681	1751	52	H.	H.	NNP
37681	1751	53	Schotten	Schotten	NNP
37681	1751	54	,	,	,
37681	1751	55	"	"	``
37681	1751	56	Inhalt	Inhalt	NNP
37681	1751	57	und	und	JJ
37681	1751	58	Methode	Methode	NNP
37681	1751	59	des	des	FW
37681	1751	60	planimetrischen	planimetrischen	NN
37681	1751	61	Unterrichts	unterricht	NNS
37681	1751	62	,	,	,
37681	1751	63	"	"	''
37681	1751	64	Leipzig	Leipzig	NNP
37681	1751	65	,	,	,
37681	1751	66	1893	1893	CD
37681	1751	67	;	;	:
37681	1751	68	M.	M.	NNP
37681	1751	69	Simon	Simon	NNP
37681	1751	70	,	,	,
37681	1751	71	"	"	``
37681	1751	72	Euclid	euclid	JJ
37681	1751	73	und	und	NN
37681	1751	74	die	die	VBP
37681	1751	75	sechs	sechs	NN
37681	1751	76	planimetrischen	planimetrischen	NN
37681	1751	77	Bücher	Bücher	NNP
37681	1751	78	,	,	,
37681	1751	79	"	"	''
37681	1751	80	Leipzig	Leipzig	NNP
37681	1751	81	,	,	,
37681	1751	82	1901	1901	CD
37681	1751	83	.	.	.
37681	1752	1	[	[	-LRB-
37681	1752	2	54	54	CD
37681	1752	3	]	]	-RRB-
37681	1752	4	For	for	IN
37681	1752	5	a	a	DT
37681	1752	6	facsimile	facsimile	NN
37681	1752	7	of	of	IN
37681	1752	8	a	a	DT
37681	1752	9	thirteenth	thirteenth	JJ
37681	1752	10	-	-	HYPH
37681	1752	11	century	century	NN
37681	1752	12	MS	MS	NNP
37681	1752	13	.	.	.
37681	1752	14	containing	contain	VBG
37681	1752	15	this	this	DT
37681	1752	16	definition	definition	NN
37681	1752	17	,	,	,
37681	1752	18	see	see	VB
37681	1752	19	the	the	DT
37681	1752	20	author	author	NN
37681	1752	21	's	's	POS
37681	1752	22	"	"	``
37681	1752	23	Rara	Rara	NNP
37681	1752	24	Arithmetica	Arithmetica	NNP
37681	1752	25	,	,	,
37681	1752	26	"	"	''
37681	1752	27	Plate	Plate	NNP
37681	1752	28	IV	IV	NNP
37681	1752	29	,	,	,
37681	1752	30	Boston	Boston	NNP
37681	1752	31	,	,	,
37681	1752	32	1909	1909	CD
37681	1752	33	.	.	.
37681	1753	1	[	[	-LRB-
37681	1753	2	55	55	CD
37681	1753	3	]	]	-RRB-
37681	1753	4	Our	-PRON-	PRP$
37681	1753	5	slang	slang	NN
37681	1753	6	expression	expression	NN
37681	1753	7	"	"	``
37681	1753	8	The	the	DT
37681	1753	9	cart	cart	NN
37681	1753	10	before	before	IN
37681	1753	11	the	the	DT
37681	1753	12	horse	horse	NN
37681	1753	13	"	"	``
37681	1753	14	is	be	VBZ
37681	1753	15	suggestive	suggestive	JJ
37681	1753	16	of	of	IN
37681	1753	17	this	this	DT
37681	1753	18	procedure	procedure	NN
37681	1753	19	.	.	.
37681	1754	1	[	[	-LRB-
37681	1754	2	56	56	CD
37681	1754	3	]	]	-RRB-
37681	1754	4	Loc	Loc	NNP
37681	1754	5	.	.	.
37681	1755	1	cit	cit	NNP
37681	1755	2	.	.	.
37681	1755	3	,	,	,
37681	1755	4	Vol	Vol	NNP
37681	1755	5	.	.	.
37681	1756	1	II	II	NNP
37681	1756	2	,	,	,
37681	1756	3	p.	p.	NN
37681	1756	4	94	94	CD
37681	1756	5	.	.	.
37681	1757	1	CHAPTER	chapter	NN
37681	1757	2	XIII	xiii	NN
37681	1757	3	HOW	how	WRB
37681	1757	4	TO	to	IN
37681	1757	5	ATTACK	attack	VB
37681	1757	6	THE	the	DT
37681	1757	7	EXERCISES	exercise	NNS
37681	1757	8	The	the	DT
37681	1757	9	old	old	JJ
37681	1757	10	geometry	geometry	NN
37681	1757	11	,	,	,
37681	1757	12	say	say	VBP
37681	1757	13	of	of	IN
37681	1757	14	a	a	DT
37681	1757	15	century	century	NN
37681	1757	16	ago	ago	RB
37681	1757	17	,	,	,
37681	1757	18	usually	usually	RB
37681	1757	19	consisted	consist	VBN
37681	1757	20	,	,	,
37681	1757	21	as	as	IN
37681	1757	22	has	have	VBZ
37681	1757	23	been	be	VBN
37681	1757	24	stated	state	VBN
37681	1757	25	,	,	,
37681	1757	26	of	of	IN
37681	1757	27	a	a	DT
37681	1757	28	series	series	NN
37681	1757	29	of	of	IN
37681	1757	30	theorems	theorem	NNS
37681	1757	31	fully	fully	RB
37681	1757	32	proved	prove	VBN
37681	1757	33	and	and	CC
37681	1757	34	of	of	IN
37681	1757	35	problems	problem	NNS
37681	1757	36	fully	fully	RB
37681	1757	37	solved	solve	VBD
37681	1757	38	.	.	.
37681	1758	1	During	during	IN
37681	1758	2	the	the	DT
37681	1758	3	nineteenth	nineteenth	JJ
37681	1758	4	century	century	NN
37681	1758	5	exercises	exercise	NNS
37681	1758	6	were	be	VBD
37681	1758	7	gradually	gradually	RB
37681	1758	8	introduced	introduce	VBN
37681	1758	9	,	,	,
37681	1758	10	thus	thus	RB
37681	1758	11	developing	develop	VBG
37681	1758	12	geometry	geometry	NN
37681	1758	13	from	from	IN
37681	1758	14	a	a	DT
37681	1758	15	science	science	NN
37681	1758	16	in	in	IN
37681	1758	17	which	which	WDT
37681	1758	18	one	one	NN
37681	1758	19	learned	learn	VBD
37681	1758	20	by	by	IN
37681	1758	21	seeing	see	VBG
37681	1758	22	things	thing	NNS
37681	1758	23	done	do	VBN
37681	1758	24	,	,	,
37681	1758	25	into	into	IN
37681	1758	26	one	one	CD
37681	1758	27	in	in	IN
37681	1758	28	which	which	WDT
37681	1758	29	he	-PRON-	PRP
37681	1758	30	gained	gain	VBD
37681	1758	31	power	power	NN
37681	1758	32	by	by	IN
37681	1758	33	actually	actually	RB
37681	1758	34	doing	do	VBG
37681	1758	35	things	thing	NNS
37681	1758	36	.	.	.
37681	1759	1	Of	of	IN
37681	1759	2	the	the	DT
37681	1759	3	nature	nature	NN
37681	1759	4	of	of	IN
37681	1759	5	these	these	DT
37681	1759	6	exercises	exercise	NNS
37681	1759	7	(	(	-LRB-
37681	1759	8	"	"	``
37681	1759	9	originals	original	NNS
37681	1759	10	,	,	,
37681	1759	11	"	"	''
37681	1759	12	"	"	``
37681	1759	13	riders	rider	NNS
37681	1759	14	"	"	''
37681	1759	15	)	)	-RRB-
37681	1759	16	,	,	,
37681	1759	17	and	and	CC
37681	1759	18	of	of	IN
37681	1759	19	their	-PRON-	PRP$
37681	1759	20	gradual	gradual	JJ
37681	1759	21	change	change	NN
37681	1759	22	in	in	IN
37681	1759	23	the	the	DT
37681	1759	24	past	past	JJ
37681	1759	25	few	few	JJ
37681	1759	26	years	year	NNS
37681	1759	27	,	,	,
37681	1759	28	mention	mention	NN
37681	1759	29	has	have	VBZ
37681	1759	30	been	be	VBN
37681	1759	31	made	make	VBN
37681	1759	32	in	in	IN
37681	1759	33	Chapter	Chapter	NNP
37681	1759	34	VII	VII	NNP
37681	1759	35	.	.	.
37681	1760	1	It	-PRON-	PRP
37681	1760	2	now	now	RB
37681	1760	3	remains	remain	VBZ
37681	1760	4	to	to	TO
37681	1760	5	consider	consider	VB
37681	1760	6	the	the	DT
37681	1760	7	methods	method	NNS
37681	1760	8	of	of	IN
37681	1760	9	attacking	attack	VBG
37681	1760	10	these	these	DT
37681	1760	11	exercises	exercise	NNS
37681	1760	12	.	.	.
37681	1761	1	It	-PRON-	PRP
37681	1761	2	is	be	VBZ
37681	1761	3	evident	evident	JJ
37681	1761	4	that	that	IN
37681	1761	5	there	there	EX
37681	1761	6	is	be	VBZ
37681	1761	7	no	no	DT
37681	1761	8	single	single	JJ
37681	1761	9	method	method	NN
37681	1761	10	,	,	,
37681	1761	11	and	and	CC
37681	1761	12	this	this	DT
37681	1761	13	is	be	VBZ
37681	1761	14	a	a	DT
37681	1761	15	fortunate	fortunate	JJ
37681	1761	16	fact	fact	NN
37681	1761	17	,	,	,
37681	1761	18	since	since	IN
37681	1761	19	if	if	IN
37681	1761	20	it	-PRON-	PRP
37681	1761	21	were	be	VBD
37681	1761	22	not	not	RB
37681	1761	23	so	so	RB
37681	1761	24	,	,	,
37681	1761	25	the	the	DT
37681	1761	26	attack	attack	NN
37681	1761	27	would	would	MD
37681	1761	28	be	be	VB
37681	1761	29	too	too	RB
37681	1761	30	mechanical	mechanical	JJ
37681	1761	31	to	to	TO
37681	1761	32	be	be	VB
37681	1761	33	interesting	interesting	JJ
37681	1761	34	.	.	.
37681	1762	1	There	there	EX
37681	1762	2	is	be	VBZ
37681	1762	3	no	no	DT
37681	1762	4	one	one	NN
37681	1762	5	rule	rule	NN
37681	1762	6	for	for	IN
37681	1762	7	solving	solve	VBG
37681	1762	8	every	every	DT
37681	1762	9	problem	problem	NN
37681	1762	10	nor	nor	CC
37681	1762	11	even	even	RB
37681	1762	12	for	for	IN
37681	1762	13	seeing	see	VBG
37681	1762	14	how	how	WRB
37681	1762	15	to	to	TO
37681	1762	16	begin	begin	VB
37681	1762	17	.	.	.
37681	1763	1	On	on	IN
37681	1763	2	the	the	DT
37681	1763	3	other	other	JJ
37681	1763	4	hand	hand	NN
37681	1763	5	,	,	,
37681	1763	6	a	a	DT
37681	1763	7	pupil	pupil	NN
37681	1763	8	is	be	VBZ
37681	1763	9	saved	save	VBN
37681	1763	10	some	some	DT
37681	1763	11	time	time	NN
37681	1763	12	by	by	IN
37681	1763	13	having	have	VBG
37681	1763	14	his	-PRON-	PRP$
37681	1763	15	attention	attention	NN
37681	1763	16	called	call	VBN
37681	1763	17	to	to	IN
37681	1763	18	a	a	DT
37681	1763	19	few	few	JJ
37681	1763	20	rather	rather	RB
37681	1763	21	definite	definite	JJ
37681	1763	22	lines	line	NNS
37681	1763	23	of	of	IN
37681	1763	24	attack	attack	NN
37681	1763	25	,	,	,
37681	1763	26	and	and	CC
37681	1763	27	he	-PRON-	PRP
37681	1763	28	will	will	MD
37681	1763	29	undoubtedly	undoubtedly	RB
37681	1763	30	fare	fare	VB
37681	1763	31	the	the	DT
37681	1763	32	better	well	JJR
37681	1763	33	by	by	IN
37681	1763	34	not	not	RB
37681	1763	35	wasting	waste	VBG
37681	1763	36	his	-PRON-	PRP$
37681	1763	37	energies	energy	NNS
37681	1763	38	over	over	IN
37681	1763	39	attempts	attempt	NNS
37681	1763	40	that	that	WDT
37681	1763	41	are	be	VBP
37681	1763	42	in	in	IN
37681	1763	43	advance	advance	NN
37681	1763	44	doomed	doom	VBN
37681	1763	45	to	to	IN
37681	1763	46	failure	failure	NN
37681	1763	47	.	.	.
37681	1764	1	There	there	EX
37681	1764	2	are	be	VBP
37681	1764	3	two	two	CD
37681	1764	4	general	general	JJ
37681	1764	5	questions	question	NNS
37681	1764	6	to	to	TO
37681	1764	7	be	be	VB
37681	1764	8	considered	consider	VBN
37681	1764	9	:	:	:
37681	1764	10	first	first	RB
37681	1764	11	,	,	,
37681	1764	12	as	as	IN
37681	1764	13	to	to	IN
37681	1764	14	the	the	DT
37681	1764	15	discovery	discovery	NN
37681	1764	16	of	of	IN
37681	1764	17	new	new	JJ
37681	1764	18	truths	truth	NNS
37681	1764	19	,	,	,
37681	1764	20	and	and	CC
37681	1764	21	second	second	RB
37681	1764	22	,	,	,
37681	1764	23	as	as	IN
37681	1764	24	to	to	IN
37681	1764	25	the	the	DT
37681	1764	26	proof	proof	NN
37681	1764	27	.	.	.
37681	1765	1	With	with	IN
37681	1765	2	the	the	DT
37681	1765	3	first	first	JJ
37681	1765	4	the	the	DT
37681	1765	5	pupil	pupil	NN
37681	1765	6	will	will	MD
37681	1765	7	have	have	VB
37681	1765	8	little	little	JJ
37681	1765	9	to	to	TO
37681	1765	10	do	do	VB
37681	1765	11	,	,	,
37681	1765	12	not	not	RB
37681	1765	13	having	have	VBG
37681	1765	14	as	as	RB
37681	1765	15	yet	yet	RB
37681	1765	16	arrived	arrive	VBN
37681	1765	17	at	at	IN
37681	1765	18	this	this	DT
37681	1765	19	stage	stage	NN
37681	1765	20	in	in	IN
37681	1765	21	his	-PRON-	PRP$
37681	1765	22	progress	progress	NN
37681	1765	23	.	.	.
37681	1766	1	A	a	DT
37681	1766	2	bright	bright	JJ
37681	1766	3	student	student	NN
37681	1766	4	may	may	MD
37681	1766	5	take	take	VB
37681	1766	6	a	a	DT
37681	1766	7	little	little	JJ
37681	1766	8	interest	interest	NN
37681	1766	9	in	in	IN
37681	1766	10	seeing	see	VBG
37681	1766	11	what	what	WP
37681	1766	12	he	-PRON-	PRP
37681	1766	13	can	can	MD
37681	1766	14	find	find	VB
37681	1766	15	out	out	RP
37681	1766	16	that	that	WDT
37681	1766	17	is	be	VBZ
37681	1766	18	new	new	JJ
37681	1766	19	(	(	-LRB-
37681	1766	20	at	at	IN
37681	1766	21	least	least	JJS
37681	1766	22	to	to	IN
37681	1766	23	him	-PRON-	PRP
37681	1766	24	)	)	-RRB-
37681	1766	25	,	,	,
37681	1766	26	and	and	CC
37681	1766	27	if	if	IN
37681	1766	28	so	so	RB
37681	1766	29	,	,	,
37681	1766	30	he	-PRON-	PRP
37681	1766	31	may	may	MD
37681	1766	32	be	be	VB
37681	1766	33	told	tell	VBN
37681	1766	34	that	that	IN
37681	1766	35	many	many	JJ
37681	1766	36	new	new	JJ
37681	1766	37	propositions	proposition	NNS
37681	1766	38	have	have	VBP
37681	1766	39	been	be	VBN
37681	1766	40	discovered	discover	VBN
37681	1766	41	by	by	IN
37681	1766	42	the	the	DT
37681	1766	43	accurate	accurate	JJ
37681	1766	44	drawing	drawing	NN
37681	1766	45	of	of	IN
37681	1766	46	figures	figure	NNS
37681	1766	47	;	;	:
37681	1766	48	that	that	IN
37681	1766	49	some	some	DT
37681	1766	50	have	have	VBP
37681	1766	51	been	be	VBN
37681	1766	52	found	find	VBN
37681	1766	53	by	by	IN
37681	1766	54	actually	actually	RB
37681	1766	55	weighing	weigh	VBG
37681	1766	56	pieces	piece	NNS
37681	1766	57	of	of	IN
37681	1766	58	sheet	sheet	NN
37681	1766	59	metal	metal	NN
37681	1766	60	of	of	IN
37681	1766	61	certain	certain	JJ
37681	1766	62	sizes	size	NNS
37681	1766	63	;	;	:
37681	1766	64	and	and	CC
37681	1766	65	that	that	IN
37681	1766	66	still	still	RB
37681	1766	67	others	other	NNS
37681	1766	68	have	have	VBP
37681	1766	69	made	make	VBN
37681	1766	70	themselves	-PRON-	PRP
37681	1766	71	known	know	VBN
37681	1766	72	through	through	IN
37681	1766	73	paper	paper	NN
37681	1766	74	folding	folding	NN
37681	1766	75	.	.	.
37681	1767	1	In	in	IN
37681	1767	2	all	all	DT
37681	1767	3	of	of	IN
37681	1767	4	these	these	DT
37681	1767	5	cases	case	NNS
37681	1767	6	,	,	,
37681	1767	7	however	however	RB
37681	1767	8	,	,	,
37681	1767	9	the	the	DT
37681	1767	10	supposed	suppose	VBN
37681	1767	11	proposition	proposition	NN
37681	1767	12	must	must	MD
37681	1767	13	be	be	VB
37681	1767	14	proved	prove	VBN
37681	1767	15	before	before	IN
37681	1767	16	it	-PRON-	PRP
37681	1767	17	can	can	MD
37681	1767	18	be	be	VB
37681	1767	19	accepted	accept	VBN
37681	1767	20	.	.	.
37681	1768	1	As	as	IN
37681	1768	2	to	to	IN
37681	1768	3	the	the	DT
37681	1768	4	proof	proof	NN
37681	1768	5	,	,	,
37681	1768	6	the	the	DT
37681	1768	7	pupil	pupil	NN
37681	1768	8	usually	usually	RB
37681	1768	9	wanders	wander	VBZ
37681	1768	10	about	about	IN
37681	1768	11	more	more	RBR
37681	1768	12	or	or	CC
37681	1768	13	less	less	JJR
37681	1768	14	until	until	IN
37681	1768	15	he	-PRON-	PRP
37681	1768	16	strikes	strike	VBZ
37681	1768	17	the	the	DT
37681	1768	18	right	right	JJ
37681	1768	19	line	line	NN
37681	1768	20	,	,	,
37681	1768	21	and	and	CC
37681	1768	22	then	then	RB
37681	1768	23	he	-PRON-	PRP
37681	1768	24	follows	follow	VBZ
37681	1768	25	this	this	DT
37681	1768	26	to	to	IN
37681	1768	27	the	the	DT
37681	1768	28	conclusion	conclusion	NN
37681	1768	29	.	.	.
37681	1769	1	He	-PRON-	PRP
37681	1769	2	should	should	MD
37681	1769	3	not	not	RB
37681	1769	4	be	be	VB
37681	1769	5	blamed	blame	VBN
37681	1769	6	for	for	IN
37681	1769	7	doing	do	VBG
37681	1769	8	this	this	DT
37681	1769	9	,	,	,
37681	1769	10	for	for	IN
37681	1769	11	he	-PRON-	PRP
37681	1769	12	is	be	VBZ
37681	1769	13	pursuing	pursue	VBG
37681	1769	14	the	the	DT
37681	1769	15	method	method	NN
37681	1769	16	that	that	IN
37681	1769	17	the	the	DT
37681	1769	18	world	world	NN
37681	1769	19	followed	follow	VBD
37681	1769	20	in	in	IN
37681	1769	21	the	the	DT
37681	1769	22	earliest	early	JJS
37681	1769	23	times	time	NNS
37681	1769	24	,	,	,
37681	1769	25	and	and	CC
37681	1769	26	one	one	NN
37681	1769	27	that	that	WDT
37681	1769	28	has	have	VBZ
37681	1769	29	always	always	RB
37681	1769	30	been	be	VBN
37681	1769	31	common	common	JJ
37681	1769	32	and	and	CC
37681	1769	33	always	always	RB
37681	1769	34	will	will	MD
37681	1769	35	be	be	VB
37681	1769	36	.	.	.
37681	1770	1	This	this	DT
37681	1770	2	is	be	VBZ
37681	1770	3	the	the	DT
37681	1770	4	synthetic	synthetic	JJ
37681	1770	5	method	method	NN
37681	1770	6	,	,	,
37681	1770	7	the	the	DT
37681	1770	8	building	building	NN
37681	1770	9	up	up	RP
37681	1770	10	of	of	IN
37681	1770	11	the	the	DT
37681	1770	12	proof	proof	NN
37681	1770	13	from	from	IN
37681	1770	14	propositions	proposition	NNS
37681	1770	15	previously	previously	RB
37681	1770	16	proved	prove	VBN
37681	1770	17	.	.	.
37681	1771	1	If	if	IN
37681	1771	2	the	the	DT
37681	1771	3	proposition	proposition	NN
37681	1771	4	is	be	VBZ
37681	1771	5	a	a	DT
37681	1771	6	theorem	theorem	NN
37681	1771	7	,	,	,
37681	1771	8	it	-PRON-	PRP
37681	1771	9	is	be	VBZ
37681	1771	10	usually	usually	RB
37681	1771	11	not	not	RB
37681	1771	12	difficult	difficult	JJ
37681	1771	13	to	to	TO
37681	1771	14	recall	recall	VB
37681	1771	15	propositions	proposition	NNS
37681	1771	16	that	that	WDT
37681	1771	17	may	may	MD
37681	1771	18	lead	lead	VB
37681	1771	19	to	to	IN
37681	1771	20	the	the	DT
37681	1771	21	demonstration	demonstration	NN
37681	1771	22	,	,	,
37681	1771	23	and	and	CC
37681	1771	24	to	to	TO
37681	1771	25	select	select	VB
37681	1771	26	the	the	DT
37681	1771	27	ones	one	NNS
37681	1771	28	that	that	WDT
37681	1771	29	are	be	VBP
37681	1771	30	really	really	RB
37681	1771	31	needed	need	VBN
37681	1771	32	.	.	.
37681	1772	1	If	if	IN
37681	1772	2	it	-PRON-	PRP
37681	1772	3	is	be	VBZ
37681	1772	4	a	a	DT
37681	1772	5	problem	problem	NN
37681	1772	6	,	,	,
37681	1772	7	it	-PRON-	PRP
37681	1772	8	is	be	VBZ
37681	1772	9	usually	usually	RB
37681	1772	10	easy	easy	JJ
37681	1772	11	to	to	TO
37681	1772	12	look	look	VB
37681	1772	13	ahead	ahead	RB
37681	1772	14	and	and	CC
37681	1772	15	see	see	VB
37681	1772	16	what	what	WP
37681	1772	17	is	be	VBZ
37681	1772	18	necessary	necessary	JJ
37681	1772	19	for	for	IN
37681	1772	20	the	the	DT
37681	1772	21	solution	solution	NN
37681	1772	22	and	and	CC
37681	1772	23	to	to	TO
37681	1772	24	select	select	VB
37681	1772	25	the	the	DT
37681	1772	26	preceding	precede	VBG
37681	1772	27	propositions	proposition	NNS
37681	1772	28	accordingly	accordingly	RB
37681	1772	29	.	.	.
37681	1773	1	But	but	CC
37681	1773	2	pupils	pupil	NNS
37681	1773	3	should	should	MD
37681	1773	4	be	be	VB
37681	1773	5	told	tell	VBN
37681	1773	6	that	that	IN
37681	1773	7	if	if	IN
37681	1773	8	they	-PRON-	PRP
37681	1773	9	do	do	VBP
37681	1773	10	not	not	RB
37681	1773	11	rather	rather	RB
37681	1773	12	easily	easily	RB
37681	1773	13	find	find	VB
37681	1773	14	the	the	DT
37681	1773	15	necessary	necessary	JJ
37681	1773	16	propositions	proposition	NNS
37681	1773	17	for	for	IN
37681	1773	18	the	the	DT
37681	1773	19	construction	construction	NN
37681	1773	20	or	or	CC
37681	1773	21	the	the	DT
37681	1773	22	proof	proof	NN
37681	1773	23	,	,	,
37681	1773	24	they	-PRON-	PRP
37681	1773	25	should	should	MD
37681	1773	26	not	not	RB
37681	1773	27	delay	delay	VB
37681	1773	28	in	in	IN
37681	1773	29	resorting	resort	VBG
37681	1773	30	to	to	IN
37681	1773	31	another	another	DT
37681	1773	32	and	and	CC
37681	1773	33	more	more	JJR
37681	1773	34	systematic	systematic	JJ
37681	1773	35	method	method	NN
37681	1773	36	.	.	.
37681	1774	1	This	this	DT
37681	1774	2	is	be	VBZ
37681	1774	3	known	know	VBN
37681	1774	4	as	as	IN
37681	1774	5	the	the	DT
37681	1774	6	method	method	NN
37681	1774	7	of	of	IN
37681	1774	8	analysis	analysis	NN
37681	1774	9	,	,	,
37681	1774	10	and	and	CC
37681	1774	11	it	-PRON-	PRP
37681	1774	12	is	be	VBZ
37681	1774	13	applicable	applicable	JJ
37681	1774	14	both	both	DT
37681	1774	15	to	to	IN
37681	1774	16	theorems	theorem	NNS
37681	1774	17	and	and	CC
37681	1774	18	to	to	IN
37681	1774	19	problems	problem	NNS
37681	1774	20	.	.	.
37681	1775	1	It	-PRON-	PRP
37681	1775	2	has	have	VBZ
37681	1775	3	several	several	JJ
37681	1775	4	forms	form	NNS
37681	1775	5	,	,	,
37681	1775	6	but	but	CC
37681	1775	7	it	-PRON-	PRP
37681	1775	8	is	be	VBZ
37681	1775	9	of	of	IN
37681	1775	10	little	little	JJ
37681	1775	11	service	service	NN
37681	1775	12	to	to	IN
37681	1775	13	a	a	DT
37681	1775	14	pupil	pupil	NN
37681	1775	15	to	to	TO
37681	1775	16	have	have	VB
37681	1775	17	these	these	DT
37681	1775	18	differentiated	differentiate	VBN
37681	1775	19	,	,	,
37681	1775	20	and	and	CC
37681	1775	21	it	-PRON-	PRP
37681	1775	22	suffices	suffice	VBZ
37681	1775	23	that	that	IN
37681	1775	24	he	-PRON-	PRP
37681	1775	25	be	be	VB
37681	1775	26	given	give	VBN
37681	1775	27	the	the	DT
37681	1775	28	essential	essential	JJ
37681	1775	29	feature	feature	NN
37681	1775	30	of	of	IN
37681	1775	31	all	all	PDT
37681	1775	32	these	these	DT
37681	1775	33	forms	form	NNS
37681	1775	34	,	,	,
37681	1775	35	a	a	DT
37681	1775	36	feature	feature	NN
37681	1775	37	that	that	WDT
37681	1775	38	goes	go	VBZ
37681	1775	39	back	back	RB
37681	1775	40	to	to	IN
37681	1775	41	Plato	Plato	NNP
37681	1775	42	and	and	CC
37681	1775	43	his	-PRON-	PRP$
37681	1775	44	school	school	NN
37681	1775	45	in	in	IN
37681	1775	46	the	the	DT
37681	1775	47	fifth	fifth	JJ
37681	1775	48	century	century	NN
37681	1775	49	B.C.	B.C.	NNP
37681	1776	1	For	for	IN
37681	1776	2	a	a	DT
37681	1776	3	theorem	theorem	NN
37681	1776	4	,	,	,
37681	1776	5	the	the	DT
37681	1776	6	method	method	NN
37681	1776	7	of	of	IN
37681	1776	8	analysis	analysis	NN
37681	1776	9	consists	consist	VBZ
37681	1776	10	in	in	IN
37681	1776	11	reasoning	reasoning	NN
37681	1776	12	as	as	IN
37681	1776	13	follows	follow	VBZ
37681	1776	14	:	:	:
37681	1776	15	"	"	``
37681	1776	16	I	-PRON-	PRP
37681	1776	17	can	can	MD
37681	1776	18	prove	prove	VB
37681	1776	19	this	this	DT
37681	1776	20	proposition	proposition	NN
37681	1776	21	if	if	IN
37681	1776	22	I	-PRON-	PRP
37681	1776	23	can	can	MD
37681	1776	24	prove	prove	VB
37681	1776	25	this	this	DT
37681	1776	26	thing	thing	NN
37681	1776	27	;	;	:
37681	1776	28	I	-PRON-	PRP
37681	1776	29	can	can	MD
37681	1776	30	prove	prove	VB
37681	1776	31	this	this	DT
37681	1776	32	thing	thing	NN
37681	1776	33	if	if	IN
37681	1776	34	I	-PRON-	PRP
37681	1776	35	can	can	MD
37681	1776	36	prove	prove	VB
37681	1776	37	that	that	DT
37681	1776	38	;	;	:
37681	1776	39	I	-PRON-	PRP
37681	1776	40	can	can	MD
37681	1776	41	prove	prove	VB
37681	1776	42	that	that	IN
37681	1776	43	if	if	IN
37681	1776	44	I	-PRON-	PRP
37681	1776	45	can	can	MD
37681	1776	46	prove	prove	VB
37681	1776	47	a	a	DT
37681	1776	48	third	third	JJ
37681	1776	49	thing	thing	NN
37681	1776	50	,	,	,
37681	1776	51	"	"	''
37681	1776	52	and	and	CC
37681	1776	53	so	so	RB
37681	1776	54	the	the	DT
37681	1776	55	reasoning	reasoning	NN
37681	1776	56	runs	run	VBZ
37681	1776	57	until	until	IN
37681	1776	58	the	the	DT
37681	1776	59	pupil	pupil	NN
37681	1776	60	comes	come	VBZ
37681	1776	61	to	to	IN
37681	1776	62	the	the	DT
37681	1776	63	point	point	NN
37681	1776	64	where	where	WRB
37681	1776	65	he	-PRON-	PRP
37681	1776	66	is	be	VBZ
37681	1776	67	able	able	JJ
37681	1776	68	to	to	TO
37681	1776	69	add	add	VB
37681	1776	70	,	,	,
37681	1776	71	"	"	``
37681	1776	72	but	but	CC
37681	1776	73	I	-PRON-	PRP
37681	1776	74	_	_	NNP
37681	1776	75	can	can	MD
37681	1776	76	_	_	NNP
37681	1776	77	prove	prove	VB
37681	1776	78	that	that	DT
37681	1776	79	.	.	.
37681	1776	80	"	"	''
37681	1777	1	This	this	DT
37681	1777	2	does	do	VBZ
37681	1777	3	not	not	RB
37681	1777	4	prove	prove	VB
37681	1777	5	the	the	DT
37681	1777	6	proposition	proposition	NN
37681	1777	7	,	,	,
37681	1777	8	but	but	CC
37681	1777	9	it	-PRON-	PRP
37681	1777	10	enables	enable	VBZ
37681	1777	11	him	-PRON-	PRP
37681	1777	12	to	to	TO
37681	1777	13	reverse	reverse	VB
37681	1777	14	the	the	DT
37681	1777	15	process	process	NN
37681	1777	16	,	,	,
37681	1777	17	beginning	begin	VBG
37681	1777	18	with	with	IN
37681	1777	19	the	the	DT
37681	1777	20	thing	thing	NN
37681	1777	21	he	-PRON-	PRP
37681	1777	22	can	can	MD
37681	1777	23	prove	prove	VB
37681	1777	24	and	and	CC
37681	1777	25	going	go	VBG
37681	1777	26	back	back	RB
37681	1777	27	,	,	,
37681	1777	28	step	step	NN
37681	1777	29	by	by	IN
37681	1777	30	step	step	NN
37681	1777	31	,	,	,
37681	1777	32	to	to	IN
37681	1777	33	the	the	DT
37681	1777	34	thing	thing	NN
37681	1777	35	that	that	WDT
37681	1777	36	he	-PRON-	PRP
37681	1777	37	is	be	VBZ
37681	1777	38	to	to	TO
37681	1777	39	prove	prove	VB
37681	1777	40	.	.	.
37681	1778	1	Analysis	analysis	NN
37681	1778	2	is	be	VBZ
37681	1778	3	,	,	,
37681	1778	4	therefore	therefore	RB
37681	1778	5	,	,	,
37681	1778	6	his	-PRON-	PRP$
37681	1778	7	method	method	NN
37681	1778	8	of	of	IN
37681	1778	9	discovery	discovery	NN
37681	1778	10	of	of	IN
37681	1778	11	the	the	DT
37681	1778	12	way	way	NN
37681	1778	13	in	in	IN
37681	1778	14	which	which	WDT
37681	1778	15	he	-PRON-	PRP
37681	1778	16	may	may	MD
37681	1778	17	arrange	arrange	VB
37681	1778	18	his	-PRON-	PRP$
37681	1778	19	synthetic	synthetic	JJ
37681	1778	20	proof	proof	NN
37681	1778	21	.	.	.
37681	1779	1	Pupils	pupil	NNS
37681	1779	2	often	often	RB
37681	1779	3	wonder	wonder	VBP
37681	1779	4	how	how	WRB
37681	1779	5	any	any	DT
37681	1779	6	one	one	NN
37681	1779	7	ever	ever	RB
37681	1779	8	came	come	VBD
37681	1779	9	to	to	TO
37681	1779	10	know	know	VB
37681	1779	11	how	how	WRB
37681	1779	12	to	to	TO
37681	1779	13	arrange	arrange	VB
37681	1779	14	the	the	DT
37681	1779	15	proofs	proof	NNS
37681	1779	16	of	of	IN
37681	1779	17	geometry	geometry	NN
37681	1779	18	,	,	,
37681	1779	19	and	and	CC
37681	1779	20	this	this	DT
37681	1779	21	answers	answer	VBZ
37681	1779	22	the	the	DT
37681	1779	23	question	question	NN
37681	1779	24	.	.	.
37681	1780	1	Some	some	DT
37681	1780	2	one	one	NN
37681	1780	3	guessed	guess	VBD
37681	1780	4	that	that	IN
37681	1780	5	a	a	DT
37681	1780	6	statement	statement	NN
37681	1780	7	was	be	VBD
37681	1780	8	true	true	JJ
37681	1780	9	;	;	:
37681	1780	10	he	-PRON-	PRP
37681	1780	11	applied	apply	VBD
37681	1780	12	analysis	analysis	NN
37681	1780	13	and	and	CC
37681	1780	14	found	find	VBD
37681	1780	15	that	that	IN
37681	1780	16	he	-PRON-	PRP
37681	1780	17	_	_	NNP
37681	1780	18	could	could	MD
37681	1780	19	_	_	NNP
37681	1780	20	prove	prove	VB
37681	1780	21	it	-PRON-	PRP
37681	1780	22	;	;	:
37681	1780	23	he	-PRON-	PRP
37681	1780	24	then	then	RB
37681	1780	25	applied	apply	VBD
37681	1780	26	synthesis	synthesis	NN
37681	1780	27	and	and	CC
37681	1780	28	_	_	NNP
37681	1780	29	did	do	VBD
37681	1780	30	_	_	NNP
37681	1780	31	prove	prove	VB
37681	1780	32	it	-PRON-	PRP
37681	1780	33	.	.	.
37681	1781	1	For	for	IN
37681	1781	2	a	a	DT
37681	1781	3	problem	problem	NN
37681	1781	4	,	,	,
37681	1781	5	the	the	DT
37681	1781	6	method	method	NN
37681	1781	7	of	of	IN
37681	1781	8	analysis	analysis	NN
37681	1781	9	is	be	VBZ
37681	1781	10	much	much	RB
37681	1781	11	the	the	DT
37681	1781	12	same	same	JJ
37681	1781	13	as	as	IN
37681	1781	14	in	in	IN
37681	1781	15	the	the	DT
37681	1781	16	case	case	NN
37681	1781	17	of	of	IN
37681	1781	18	a	a	DT
37681	1781	19	theorem	theorem	NN
37681	1781	20	.	.	.
37681	1782	1	Two	two	CD
37681	1782	2	things	thing	NNS
37681	1782	3	are	be	VBP
37681	1782	4	involved	involve	VBN
37681	1782	5	,	,	,
37681	1782	6	however	however	RB
37681	1782	7	,	,	,
37681	1782	8	instead	instead	RB
37681	1782	9	of	of	IN
37681	1782	10	one	one	CD
37681	1782	11	,	,	,
37681	1782	12	for	for	IN
37681	1782	13	here	here	RB
37681	1782	14	we	-PRON-	PRP
37681	1782	15	must	must	MD
37681	1782	16	make	make	VB
37681	1782	17	the	the	DT
37681	1782	18	construction	construction	NN
37681	1782	19	and	and	CC
37681	1782	20	then	then	RB
37681	1782	21	prove	prove	VB
37681	1782	22	that	that	IN
37681	1782	23	this	this	DT
37681	1782	24	construction	construction	NN
37681	1782	25	is	be	VBZ
37681	1782	26	correct	correct	JJ
37681	1782	27	.	.	.
37681	1783	1	The	the	DT
37681	1783	2	pupil	pupil	NN
37681	1783	3	,	,	,
37681	1783	4	therefore	therefore	RB
37681	1783	5	,	,	,
37681	1783	6	first	first	RB
37681	1783	7	supposes	suppose	VBZ
37681	1783	8	the	the	DT
37681	1783	9	problem	problem	NN
37681	1783	10	solved	solve	VBN
37681	1783	11	,	,	,
37681	1783	12	and	and	CC
37681	1783	13	sees	see	VBZ
37681	1783	14	what	what	WDT
37681	1783	15	results	result	NNS
37681	1783	16	follow	follow	VBP
37681	1783	17	.	.	.
37681	1784	1	He	-PRON-	PRP
37681	1784	2	then	then	RB
37681	1784	3	reverses	reverse	VBZ
37681	1784	4	the	the	DT
37681	1784	5	process	process	NN
37681	1784	6	and	and	CC
37681	1784	7	sees	see	VBZ
37681	1784	8	if	if	IN
37681	1784	9	he	-PRON-	PRP
37681	1784	10	can	can	MD
37681	1784	11	attain	attain	VB
37681	1784	12	these	these	DT
37681	1784	13	results	result	NNS
37681	1784	14	and	and	CC
37681	1784	15	thus	thus	RB
37681	1784	16	effect	effect	VB
37681	1784	17	the	the	DT
37681	1784	18	required	required	JJ
37681	1784	19	construction	construction	NN
37681	1784	20	.	.	.
37681	1785	1	If	if	IN
37681	1785	2	so	so	RB
37681	1785	3	,	,	,
37681	1785	4	he	-PRON-	PRP
37681	1785	5	states	state	VBZ
37681	1785	6	the	the	DT
37681	1785	7	process	process	NN
37681	1785	8	and	and	CC
37681	1785	9	gives	give	VBZ
37681	1785	10	the	the	DT
37681	1785	11	resulting	result	VBG
37681	1785	12	proof	proof	NN
37681	1785	13	.	.	.
37681	1786	1	For	for	IN
37681	1786	2	example	example	NN
37681	1786	3	:	:	:
37681	1786	4	In	in	IN
37681	1786	5	a	a	DT
37681	1786	6	triangle	triangle	NN
37681	1786	7	_	_	NNP
37681	1786	8	ABC	ABC	NNP
37681	1786	9	_	_	NNP
37681	1786	10	,	,	,
37681	1786	11	to	to	TO
37681	1786	12	draw	draw	VB
37681	1786	13	_	_	NNP
37681	1786	14	PQ	PQ	NNP
37681	1786	15	_	_	NNP
37681	1786	16	parallel	parallel	NN
37681	1786	17	to	to	IN
37681	1786	18	the	the	DT
37681	1786	19	base	base	NN
37681	1786	20	_	_	NNP
37681	1786	21	AB	AB	NNP
37681	1786	22	_	_	NNP
37681	1786	23	,	,	,
37681	1786	24	cutting	cut	VBG
37681	1786	25	the	the	DT
37681	1786	26	sides	side	NNS
37681	1786	27	in	in	IN
37681	1786	28	_	_	NNP
37681	1786	29	P	P	NNP
37681	1786	30	_	_	NNP
37681	1786	31	and	and	CC
37681	1786	32	_	_	NNP
37681	1786	33	Q	Q	NNP
37681	1786	34	_	_	NNP
37681	1786	35	,	,	,
37681	1786	36	so	so	IN
37681	1786	37	that	that	IN
37681	1786	38	_	_	NNP
37681	1786	39	PQ	PQ	NNP
37681	1786	40	_	_	NNP
37681	1786	41	shall	shall	MD
37681	1786	42	equal	equal	VB
37681	1786	43	_	_	NNP
37681	1786	44	AP	AP	NNP
37681	1786	45	_	_	NNP
37681	1786	46	+	+	NNP
37681	1786	47	_	_	NNP
37681	1786	48	BQ	BQ	NNP
37681	1786	49	_	_	NNP
37681	1786	50	.	.	.
37681	1787	1	[	[	-LRB-
37681	1787	2	Illustration	illustration	NN
37681	1787	3	]	]	-RRB-
37681	1787	4	=	=	SYM
37681	1787	5	Analysis.=	analysis.=	NN
37681	1787	6	Assume	assume	VB
37681	1787	7	the	the	DT
37681	1787	8	problem	problem	NN
37681	1787	9	solved	solve	VBD
37681	1787	10	.	.	.
37681	1788	1	Then	then	RB
37681	1788	2	_	_	NNP
37681	1788	3	AP	AP	NNP
37681	1788	4	_	_	NNP
37681	1788	5	must	must	MD
37681	1788	6	equal	equal	VB
37681	1788	7	some	some	DT
37681	1788	8	part	part	NN
37681	1788	9	of	of	IN
37681	1788	10	_	_	NNP
37681	1788	11	PQ	PQ	NNP
37681	1788	12	_	_	NNP
37681	1788	13	as	as	IN
37681	1788	14	_	_	NNP
37681	1788	15	PX	PX	NNP
37681	1788	16	_	_	NNP
37681	1788	17	,	,	,
37681	1788	18	and	and	CC
37681	1788	19	_	_	NNP
37681	1788	20	BQ	BQ	NNP
37681	1788	21	_	_	NNP
37681	1788	22	must	must	MD
37681	1788	23	equal	equal	VB
37681	1788	24	_	_	NNP
37681	1788	25	QX	QX	NNP
37681	1788	26	_	_	NNP
37681	1788	27	.	.	.
37681	1789	1	But	but	CC
37681	1789	2	if	if	IN
37681	1789	3	_	_	NNP
37681	1789	4	AP	AP	NNP
37681	1789	5	_	_	NNP
37681	1789	6	=	=	SYM
37681	1789	7	_	_	NNP
37681	1789	8	PX	PX	NNP
37681	1789	9	_	_	NNP
37681	1789	10	,	,	,
37681	1789	11	what	what	WP
37681	1789	12	must	must	MD
37681	1789	13	[	[	-LRB-
37681	1789	14	L]_PXA	L]_PXA	NNP
37681	1789	15	_	_	NNP
37681	1789	16	equal	equal	JJ
37681	1789	17	?	?	.
37681	1790	1	[	[	-LRB-
37681	1790	2	because	because	IN
37681	1790	3	]	]	-RRB-
37681	1790	4	_	_	NNP
37681	1790	5	PQ	PQ	NNP
37681	1790	6	_	_	NNP
37681	1790	7	is	be	VBZ
37681	1790	8	||	||	NNP
37681	1790	9	_	_	NNP
37681	1790	10	AB	AB	NNP
37681	1790	11	_	_	NNP
37681	1790	12	,	,	,
37681	1790	13	what	what	WP
37681	1790	14	does	do	VBZ
37681	1790	15	[	[	-LRB-
37681	1790	16	L]_PXA	L]_PXA	NNP
37681	1790	17	_	_	NNP
37681	1790	18	equal	equal	JJ
37681	1790	19	?	?	.
37681	1791	1	Then	then	RB
37681	1791	2	why	why	WRB
37681	1791	3	must	must	MD
37681	1791	4	[	[	-LRB-
37681	1791	5	L]_BAX	l]_bax	NN
37681	1791	6	_	_	NNP
37681	1791	7	=	=	NFP
37681	1791	8	[	[	-LRB-
37681	1791	9	L]_XAP	L]_XAP	NNP
37681	1791	10	_	_	NNP
37681	1791	11	?	?	.
37681	1792	1	Similarly	similarly	RB
37681	1792	2	,	,	,
37681	1792	3	what	what	WP
37681	1792	4	about	about	IN
37681	1792	5	[	[	-LRB-
37681	1792	6	L]_QBX	L]_QBX	NNP
37681	1792	7	_	_	NNP
37681	1792	8	and	and	CC
37681	1792	9	[	[	-LRB-
37681	1792	10	L]_XBA	L]_XBA	NNP
37681	1792	11	_	_	NNP
37681	1792	12	?	?	.
37681	1793	1	=	=	NFP
37681	1793	2	Construction.=	Construction.=	NNP
37681	1793	3	Now	now	RB
37681	1793	4	reverse	reverse	VB
37681	1793	5	the	the	DT
37681	1793	6	process	process	NN
37681	1793	7	.	.	.
37681	1794	1	What	what	WP
37681	1794	2	may	may	MD
37681	1794	3	we	-PRON-	PRP
37681	1794	4	do	do	VB
37681	1794	5	to	to	IN
37681	1794	6	[	[	-LRB-
37681	1794	7	Ls	Ls	NNP
37681	1794	8	]	]	-RRB-
37681	1794	9	_	_	NNP
37681	1794	10	A	A	NNP
37681	1794	11	_	_	NNP
37681	1794	12	and	and	CC
37681	1794	13	_	_	NNP
37681	1794	14	B	B	NNP
37681	1794	15	_	_	NNP
37681	1794	16	in	in	IN
37681	1794	17	order	order	NN
37681	1794	18	to	to	TO
37681	1794	19	fix	fix	VB
37681	1794	20	_	_	NNP
37681	1794	21	X	X	NNP
37681	1794	22	_	_	NNP
37681	1794	23	?	?	.
37681	1795	1	Then	then	RB
37681	1795	2	how	how	WRB
37681	1795	3	shall	shall	MD
37681	1795	4	_	_	NNP
37681	1795	5	PQ	PQ	NNP
37681	1795	6	_	_	NNP
37681	1795	7	be	be	VB
37681	1795	8	drawn	draw	VBN
37681	1795	9	?	?	.
37681	1796	1	Now	now	RB
37681	1796	2	give	give	VB
37681	1796	3	the	the	DT
37681	1796	4	proof	proof	NN
37681	1796	5	.	.	.
37681	1797	1	[	[	-LRB-
37681	1797	2	Illustration	illustration	NN
37681	1797	3	]	]	-RRB-
37681	1797	4	[	[	-LRB-
37681	1797	5	Illustration	illustration	NN
37681	1797	6	]	]	-RRB-
37681	1797	7	The	the	DT
37681	1797	8	third	third	JJ
37681	1797	9	general	general	JJ
37681	1797	10	method	method	NN
37681	1797	11	of	of	IN
37681	1797	12	attack	attack	NN
37681	1797	13	applies	apply	VBZ
37681	1797	14	chiefly	chiefly	RB
37681	1797	15	to	to	IN
37681	1797	16	problems	problem	NNS
37681	1797	17	where	where	WRB
37681	1797	18	some	some	DT
37681	1797	19	point	point	NN
37681	1797	20	is	be	VBZ
37681	1797	21	to	to	TO
37681	1797	22	be	be	VB
37681	1797	23	determined	determine	VBN
37681	1797	24	.	.	.
37681	1798	1	This	this	DT
37681	1798	2	is	be	VBZ
37681	1798	3	the	the	DT
37681	1798	4	method	method	NN
37681	1798	5	of	of	IN
37681	1798	6	the	the	DT
37681	1798	7	intersection	intersection	NN
37681	1798	8	of	of	IN
37681	1798	9	loci	loci	NN
37681	1798	10	.	.	.
37681	1799	1	Thus	thus	RB
37681	1799	2	,	,	,
37681	1799	3	to	to	TO
37681	1799	4	locate	locate	VB
37681	1799	5	an	an	DT
37681	1799	6	electric	electric	JJ
37681	1799	7	light	light	NN
37681	1799	8	at	at	IN
37681	1799	9	a	a	DT
37681	1799	10	point	point	NN
37681	1799	11	eighteen	eighteen	CD
37681	1799	12	feet	foot	NNS
37681	1799	13	from	from	IN
37681	1799	14	the	the	DT
37681	1799	15	point	point	NN
37681	1799	16	of	of	IN
37681	1799	17	intersection	intersection	NN
37681	1799	18	of	of	IN
37681	1799	19	two	two	CD
37681	1799	20	streets	street	NNS
37681	1799	21	and	and	CC
37681	1799	22	equidistant	equidistant	NN
37681	1799	23	from	from	IN
37681	1799	24	them	-PRON-	PRP
37681	1799	25	,	,	,
37681	1799	26	evidently	evidently	RB
37681	1799	27	one	one	CD
37681	1799	28	locus	locus	NN
37681	1799	29	is	be	VBZ
37681	1799	30	a	a	DT
37681	1799	31	circle	circle	NN
37681	1799	32	with	with	IN
37681	1799	33	a	a	DT
37681	1799	34	radius	radius	NN
37681	1799	35	eighteen	eighteen	CD
37681	1799	36	feet	foot	NNS
37681	1799	37	and	and	CC
37681	1799	38	the	the	DT
37681	1799	39	center	center	NN
37681	1799	40	at	at	IN
37681	1799	41	the	the	DT
37681	1799	42	vertex	vertex	NNP
37681	1799	43	of	of	IN
37681	1799	44	the	the	DT
37681	1799	45	angle	angle	NN
37681	1799	46	made	make	VBN
37681	1799	47	by	by	IN
37681	1799	48	the	the	DT
37681	1799	49	streets	street	NNS
37681	1799	50	,	,	,
37681	1799	51	and	and	CC
37681	1799	52	the	the	DT
37681	1799	53	other	other	JJ
37681	1799	54	locus	locus	NN
37681	1799	55	is	be	VBZ
37681	1799	56	the	the	DT
37681	1799	57	bisector	bisector	NN
37681	1799	58	of	of	IN
37681	1799	59	the	the	DT
37681	1799	60	angle	angle	NN
37681	1799	61	.	.	.
37681	1800	1	The	the	DT
37681	1800	2	method	method	NN
37681	1800	3	is	be	VBZ
37681	1800	4	also	also	RB
37681	1800	5	occasionally	occasionally	RB
37681	1800	6	applicable	applicable	JJ
37681	1800	7	to	to	IN
37681	1800	8	theorems	theorem	NNS
37681	1800	9	.	.	.
37681	1801	1	For	for	IN
37681	1801	2	example	example	NN
37681	1801	3	,	,	,
37681	1801	4	to	to	TO
37681	1801	5	prove	prove	VB
37681	1801	6	that	that	IN
37681	1801	7	the	the	DT
37681	1801	8	perpendicular	perpendicular	JJ
37681	1801	9	bisectors	bisector	NNS
37681	1801	10	of	of	IN
37681	1801	11	the	the	DT
37681	1801	12	sides	side	NNS
37681	1801	13	of	of	IN
37681	1801	14	a	a	DT
37681	1801	15	triangle	triangle	NN
37681	1801	16	are	be	VBP
37681	1801	17	concurrent	concurrent	JJ
37681	1801	18	.	.	.
37681	1802	1	Here	here	RB
37681	1802	2	the	the	DT
37681	1802	3	locus	locus	NN
37681	1802	4	of	of	IN
37681	1802	5	points	point	NNS
37681	1802	6	equidistant	equidistant	NN
37681	1802	7	from	from	IN
37681	1802	8	_	_	NNP
37681	1802	9	A	A	NNP
37681	1802	10	_	_	NNP
37681	1802	11	and	and	CC
37681	1802	12	_	_	NNP
37681	1802	13	B	B	NNP
37681	1802	14	_	_	NNP
37681	1802	15	is	be	VBZ
37681	1802	16	_	_	NNP
37681	1802	17	PP	PP	NNP
37681	1802	18	'	'	''
37681	1802	19	_	_	NNP
37681	1802	20	,	,	,
37681	1802	21	and	and	CC
37681	1802	22	the	the	DT
37681	1802	23	locus	locus	NN
37681	1802	24	of	of	IN
37681	1802	25	points	point	NNS
37681	1802	26	equidistant	equidistant	NN
37681	1802	27	from	from	IN
37681	1802	28	_	_	NNP
37681	1802	29	B	B	NNP
37681	1802	30	_	_	NNP
37681	1802	31	and	and	CC
37681	1802	32	_	_	NNP
37681	1802	33	C	C	NNP
37681	1802	34	_	_	NNP
37681	1802	35	is	be	VBZ
37681	1802	36	_	_	NNP
37681	1802	37	QQ	QQ	NNP
37681	1802	38	'	'	''
37681	1802	39	_	_	NNP
37681	1802	40	.	.	.
37681	1803	1	These	these	DT
37681	1803	2	can	can	MD
37681	1803	3	easily	easily	RB
37681	1803	4	be	be	VB
37681	1803	5	shown	show	VBN
37681	1803	6	to	to	TO
37681	1803	7	intersect	intersect	VB
37681	1803	8	,	,	,
37681	1803	9	as	as	IN
37681	1803	10	at	at	IN
37681	1803	11	_	_	NNP
37681	1803	12	O	O	NNP
37681	1803	13	_	_	NNP
37681	1803	14	.	.	.
37681	1804	1	Then	then	RB
37681	1804	2	_	_	NNP
37681	1804	3	O	O	NNP
37681	1804	4	_	_	NNP
37681	1804	5	,	,	,
37681	1804	6	being	be	VBG
37681	1804	7	equidistant	equidistant	NN
37681	1804	8	from	from	IN
37681	1804	9	_	_	NNP
37681	1804	10	A	A	NNP
37681	1804	11	_	_	NNP
37681	1804	12	,	,	,
37681	1804	13	_	_	NNP
37681	1804	14	B	B	NNP
37681	1804	15	_	_	NNP
37681	1804	16	,	,	,
37681	1804	17	and	and	CC
37681	1804	18	_	_	NNP
37681	1804	19	C	C	NNP
37681	1804	20	_	_	NNP
37681	1804	21	,	,	,
37681	1804	22	is	be	VBZ
37681	1804	23	also	also	RB
37681	1804	24	on	on	IN
37681	1804	25	the	the	DT
37681	1804	26	perpendicular	perpendicular	JJ
37681	1804	27	bisector	bisector	NN
37681	1804	28	of	of	IN
37681	1804	29	_	_	NNP
37681	1804	30	AC	AC	NNP
37681	1804	31	_	_	NNP
37681	1804	32	.	.	.
37681	1805	1	Therefore	therefore	RB
37681	1805	2	these	these	DT
37681	1805	3	bisectors	bisector	NNS
37681	1805	4	are	be	VBP
37681	1805	5	concurrent	concurrent	JJ
37681	1805	6	in	in	IN
37681	1805	7	_	_	NNP
37681	1805	8	O	O	NNP
37681	1805	9	_	_	NNP
37681	1805	10	.	.	.
37681	1806	1	These	these	DT
37681	1806	2	are	be	VBP
37681	1806	3	the	the	DT
37681	1806	4	chief	chief	JJ
37681	1806	5	methods	method	NNS
37681	1806	6	of	of	IN
37681	1806	7	attack	attack	NN
37681	1806	8	,	,	,
37681	1806	9	and	and	CC
37681	1806	10	are	be	VBP
37681	1806	11	all	all	DT
37681	1806	12	that	that	WDT
37681	1806	13	should	should	MD
37681	1806	14	be	be	VB
37681	1806	15	given	give	VBN
37681	1806	16	to	to	IN
37681	1806	17	an	an	DT
37681	1806	18	average	average	JJ
37681	1806	19	class	class	NN
37681	1806	20	for	for	IN
37681	1806	21	practical	practical	JJ
37681	1806	22	use	use	NN
37681	1806	23	.	.	.
37681	1807	1	Besides	besides	IN
37681	1807	2	the	the	DT
37681	1807	3	methods	method	NNS
37681	1807	4	of	of	IN
37681	1807	5	attack	attack	NN
37681	1807	6	,	,	,
37681	1807	7	there	there	EX
37681	1807	8	are	be	VBP
37681	1807	9	a	a	DT
37681	1807	10	few	few	JJ
37681	1807	11	general	general	JJ
37681	1807	12	directions	direction	NNS
37681	1807	13	that	that	WDT
37681	1807	14	should	should	MD
37681	1807	15	be	be	VB
37681	1807	16	given	give	VBN
37681	1807	17	to	to	IN
37681	1807	18	pupils	pupil	NNS
37681	1807	19	.	.	.
37681	1808	1	1	1	LS
37681	1808	2	.	.	.
37681	1809	1	In	in	IN
37681	1809	2	attacking	attack	VBG
37681	1809	3	either	either	CC
37681	1809	4	a	a	DT
37681	1809	5	theorem	theorem	NN
37681	1809	6	or	or	CC
37681	1809	7	a	a	DT
37681	1809	8	problem	problem	NN
37681	1809	9	,	,	,
37681	1809	10	take	take	VB
37681	1809	11	the	the	DT
37681	1809	12	most	most	RBS
37681	1809	13	general	general	JJ
37681	1809	14	figure	figure	NN
37681	1809	15	possible	possible	JJ
37681	1809	16	.	.	.
37681	1810	1	Thus	thus	RB
37681	1810	2	,	,	,
37681	1810	3	if	if	IN
37681	1810	4	a	a	DT
37681	1810	5	proposition	proposition	NN
37681	1810	6	relates	relate	VBZ
37681	1810	7	to	to	IN
37681	1810	8	a	a	DT
37681	1810	9	quadrilateral	quadrilateral	NN
37681	1810	10	,	,	,
37681	1810	11	take	take	VB
37681	1810	12	one	one	CD
37681	1810	13	with	with	IN
37681	1810	14	unequal	unequal	JJ
37681	1810	15	sides	side	NNS
37681	1810	16	and	and	CC
37681	1810	17	unequal	unequal	JJ
37681	1810	18	angles	angle	NNS
37681	1810	19	rather	rather	RB
37681	1810	20	than	than	IN
37681	1810	21	a	a	DT
37681	1810	22	square	square	JJ
37681	1810	23	or	or	CC
37681	1810	24	even	even	RB
37681	1810	25	a	a	DT
37681	1810	26	rectangle	rectangle	NN
37681	1810	27	.	.	.
37681	1811	1	The	the	DT
37681	1811	2	simpler	simple	JJR
37681	1811	3	figures	figure	NNS
37681	1811	4	often	often	RB
37681	1811	5	deceive	deceive	VBP
37681	1811	6	a	a	DT
37681	1811	7	pupil	pupil	NN
37681	1811	8	into	into	IN
37681	1811	9	feeling	feeling	NN
37681	1811	10	that	that	IN
37681	1811	11	he	-PRON-	PRP
37681	1811	12	has	have	VBZ
37681	1811	13	a	a	DT
37681	1811	14	proof	proof	NN
37681	1811	15	,	,	,
37681	1811	16	when	when	WRB
37681	1811	17	in	in	IN
37681	1811	18	reality	reality	NN
37681	1811	19	he	-PRON-	PRP
37681	1811	20	has	have	VBZ
37681	1811	21	one	one	CD
37681	1811	22	only	only	RB
37681	1811	23	for	for	IN
37681	1811	24	a	a	DT
37681	1811	25	special	special	JJ
37681	1811	26	case	case	NN
37681	1811	27	.	.	.
37681	1812	1	2	2	LS
37681	1812	2	.	.	.
37681	1813	1	Set	Set	VBN
37681	1813	2	forth	forth	RB
37681	1813	3	very	very	RB
37681	1813	4	exactly	exactly	RB
37681	1813	5	the	the	DT
37681	1813	6	thing	thing	NN
37681	1813	7	that	that	WDT
37681	1813	8	is	be	VBZ
37681	1813	9	given	give	VBN
37681	1813	10	,	,	,
37681	1813	11	using	use	VBG
37681	1813	12	letters	letter	NNS
37681	1813	13	relating	relate	VBG
37681	1813	14	to	to	IN
37681	1813	15	the	the	DT
37681	1813	16	figure	figure	NN
37681	1813	17	that	that	WDT
37681	1813	18	has	have	VBZ
37681	1813	19	been	be	VBN
37681	1813	20	drawn	draw	VBN
37681	1813	21	.	.	.
37681	1814	1	Then	then	RB
37681	1814	2	set	set	VB
37681	1814	3	forth	forth	RP
37681	1814	4	with	with	IN
37681	1814	5	the	the	DT
37681	1814	6	same	same	JJ
37681	1814	7	exactness	exactness	NN
37681	1814	8	the	the	DT
37681	1814	9	thing	thing	NN
37681	1814	10	that	that	WDT
37681	1814	11	is	be	VBZ
37681	1814	12	to	to	TO
37681	1814	13	be	be	VB
37681	1814	14	proved	prove	VBN
37681	1814	15	.	.	.
37681	1815	1	The	the	DT
37681	1815	2	neglect	neglect	NN
37681	1815	3	to	to	TO
37681	1815	4	do	do	VB
37681	1815	5	this	this	DT
37681	1815	6	is	be	VBZ
37681	1815	7	the	the	DT
37681	1815	8	cause	cause	NN
37681	1815	9	of	of	IN
37681	1815	10	a	a	DT
37681	1815	11	large	large	JJ
37681	1815	12	per	per	IN
37681	1815	13	cent	cent	NN
37681	1815	14	of	of	IN
37681	1815	15	the	the	DT
37681	1815	16	failures	failure	NNS
37681	1815	17	.	.	.
37681	1816	1	The	the	DT
37681	1816	2	knowing	knowing	NN
37681	1816	3	of	of	IN
37681	1816	4	exactly	exactly	RB
37681	1816	5	what	what	WP
37681	1816	6	we	-PRON-	PRP
37681	1816	7	have	have	VBP
37681	1816	8	to	to	TO
37681	1816	9	do	do	VB
37681	1816	10	and	and	CC
37681	1816	11	exactly	exactly	RB
37681	1816	12	what	what	WP
37681	1816	13	we	-PRON-	PRP
37681	1816	14	have	have	VBP
37681	1816	15	with	with	IN
37681	1816	16	which	which	WDT
37681	1816	17	to	to	TO
37681	1816	18	do	do	VB
37681	1816	19	it	-PRON-	PRP
37681	1816	20	is	be	VBZ
37681	1816	21	half	half	PDT
37681	1816	22	the	the	DT
37681	1816	23	battle	battle	NN
37681	1816	24	.	.	.
37681	1817	1	3	3	LS
37681	1817	2	.	.	.
37681	1818	1	If	if	IN
37681	1818	2	the	the	DT
37681	1818	3	proposition	proposition	NN
37681	1818	4	seems	seem	VBZ
37681	1818	5	hazy	hazy	JJ
37681	1818	6	,	,	,
37681	1818	7	the	the	DT
37681	1818	8	difficulty	difficulty	NN
37681	1818	9	is	be	VBZ
37681	1818	10	probably	probably	RB
37681	1818	11	with	with	IN
37681	1818	12	the	the	DT
37681	1818	13	wording	wording	NN
37681	1818	14	.	.	.
37681	1819	1	In	in	IN
37681	1819	2	this	this	DT
37681	1819	3	case	case	NN
37681	1819	4	try	try	VB
37681	1819	5	substituting	substitute	VBG
37681	1819	6	the	the	DT
37681	1819	7	definition	definition	NN
37681	1819	8	for	for	IN
37681	1819	9	the	the	DT
37681	1819	10	name	name	NN
37681	1819	11	of	of	IN
37681	1819	12	the	the	DT
37681	1819	13	thing	thing	NN
37681	1819	14	defined	define	VBN
37681	1819	15	.	.	.
37681	1820	1	Thus	thus	RB
37681	1820	2	instead	instead	RB
37681	1820	3	of	of	IN
37681	1820	4	thinking	think	VBG
37681	1820	5	too	too	RB
37681	1820	6	long	long	RB
37681	1820	7	about	about	IN
37681	1820	8	proving	prove	VBG
37681	1820	9	that	that	IN
37681	1820	10	the	the	DT
37681	1820	11	median	median	NN
37681	1820	12	to	to	IN
37681	1820	13	the	the	DT
37681	1820	14	base	base	NN
37681	1820	15	of	of	IN
37681	1820	16	an	an	DT
37681	1820	17	isosceles	isoscele	NNS
37681	1820	18	triangle	triangle	NN
37681	1820	19	is	be	VBZ
37681	1820	20	perpendicular	perpendicular	JJ
37681	1820	21	to	to	IN
37681	1820	22	the	the	DT
37681	1820	23	base	base	NN
37681	1820	24	,	,	,
37681	1820	25	draw	draw	VB
37681	1820	26	the	the	DT
37681	1820	27	figure	figure	NN
37681	1820	28	and	and	CC
37681	1820	29	think	think	VB
37681	1820	30	that	that	IN
37681	1820	31	there	there	EX
37681	1820	32	is	be	VBZ
37681	1820	33	given	give	VBN
37681	1820	34	_	_	NNP
37681	1820	35	AC	AC	NNP
37681	1820	36	_	_	NNP
37681	1820	37	=	=	SYM
37681	1820	38	_	_	NNP
37681	1820	39	BC	BC	NNP
37681	1820	40	_	_	NNP
37681	1820	41	,	,	,
37681	1820	42	_	_	NNP
37681	1820	43	AD	AD	NNP
37681	1820	44	_	_	NNP
37681	1820	45	=	=	SYM
37681	1820	46	_	_	NNP
37681	1820	47	BD	BD	NNP
37681	1820	48	_	_	NNP
37681	1820	49	,	,	,
37681	1820	50	and	and	CC
37681	1820	51	that	that	IN
37681	1820	52	there	there	EX
37681	1820	53	is	be	VBZ
37681	1820	54	to	to	TO
37681	1820	55	be	be	VB
37681	1820	56	proved	prove	VBN
37681	1820	57	that	that	IN
37681	1820	58	[	[	-LRB-
37681	1820	59	L]_CDA	L]_CDA	NNP
37681	1820	60	_	_	NNP
37681	1820	61	=	=	NFP
37681	1820	62	[	[	-LRB-
37681	1820	63	L]_BDC	L]_BDC	NNP
37681	1820	64	_	_	NNP
37681	1820	65	.	.	.
37681	1821	1	[	[	-LRB-
37681	1821	2	Illustration	illustration	NN
37681	1821	3	]	]	-RRB-
37681	1821	4	Here	here	RB
37681	1821	5	we	-PRON-	PRP
37681	1821	6	have	have	VBP
37681	1821	7	replaced	replace	VBN
37681	1821	8	"	"	``
37681	1821	9	median	median	NNP
37681	1821	10	,	,	,
37681	1821	11	"	"	''
37681	1821	12	"	"	``
37681	1821	13	isosceles	isoscele	NNS
37681	1821	14	,	,	,
37681	1821	15	"	"	''
37681	1821	16	and	and	CC
37681	1821	17	"	"	``
37681	1821	18	perpendicular	perpendicular	JJ
37681	1821	19	"	"	''
37681	1821	20	by	by	IN
37681	1821	21	statements	statement	NNS
37681	1821	22	that	that	WDT
37681	1821	23	express	express	VBP
37681	1821	24	the	the	DT
37681	1821	25	same	same	JJ
37681	1821	26	idea	idea	NN
37681	1821	27	in	in	IN
37681	1821	28	simpler	simple	JJR
37681	1821	29	language	language	NN
37681	1821	30	.	.	.
37681	1822	1	=	=	NFP
37681	1822	2	Bibliography.=	Bibliography.=	NNP
37681	1822	3	Petersen	Petersen	NNP
37681	1822	4	,	,	,
37681	1822	5	Methods	Methods	NNPS
37681	1822	6	and	and	CC
37681	1822	7	Theories	Theories	NNPS
37681	1822	8	for	for	IN
37681	1822	9	the	the	DT
37681	1822	10	Solution	Solution	NNP
37681	1822	11	of	of	IN
37681	1822	12	Geometric	Geometric	NNP
37681	1822	13	Problems	Problems	NNPS
37681	1822	14	of	of	IN
37681	1822	15	Construction	Construction	NNP
37681	1822	16	,	,	,
37681	1822	17	Copenhagen	Copenhagen	NNP
37681	1822	18	,	,	,
37681	1822	19	1879	1879	CD
37681	1822	20	,	,	,
37681	1822	21	a	a	DT
37681	1822	22	curious	curious	JJ
37681	1822	23	piece	piece	NN
37681	1822	24	of	of	IN
37681	1822	25	English	English	NNP
37681	1822	26	and	and	CC
37681	1822	27	an	an	DT
37681	1822	28	extreme	extreme	JJ
37681	1822	29	view	view	NN
37681	1822	30	of	of	IN
37681	1822	31	the	the	DT
37681	1822	32	subject	subject	NN
37681	1822	33	,	,	,
37681	1822	34	but	but	CC
37681	1822	35	well	well	RB
37681	1822	36	worth	worth	JJ
37681	1822	37	consulting	consulting	NN
37681	1822	38	;	;	:
37681	1822	39	Alexandroff	Alexandroff	NNP
37681	1822	40	,	,	,
37681	1822	41	Problèmes	Problèmes	NNP
37681	1822	42	de	de	IN
37681	1822	43	géométrie	géométrie	NNP
37681	1822	44	élémentaire	élémentaire	NN
37681	1822	45	,	,	,
37681	1822	46	Paris	Paris	NNP
37681	1822	47	,	,	,
37681	1822	48	1899	1899	CD
37681	1822	49	,	,	,
37681	1822	50	with	with	IN
37681	1822	51	a	a	DT
37681	1822	52	German	german	JJ
37681	1822	53	translation	translation	NN
37681	1822	54	in	in	IN
37681	1822	55	1903	1903	CD
37681	1822	56	;	;	:
37681	1822	57	Loomis	Loomis	NNP
37681	1822	58	,	,	,
37681	1822	59	Original	Original	NNP
37681	1822	60	Investigation	Investigation	NNP
37681	1822	61	;	;	:
37681	1822	62	or	or	CC
37681	1822	63	,	,	,
37681	1822	64	How	how	WRB
37681	1822	65	to	to	TO
37681	1822	66	attack	attack	VB
37681	1822	67	an	an	DT
37681	1822	68	Exercise	Exercise	NNP
37681	1822	69	in	in	IN
37681	1822	70	Geometry	Geometry	NNP
37681	1822	71	,	,	,
37681	1822	72	Boston	Boston	NNP
37681	1822	73	,	,	,
37681	1822	74	1901	1901	CD
37681	1822	75	;	;	:
37681	1822	76	Sauvage	sauvage	NN
37681	1822	77	,	,	,
37681	1822	78	Les	Les	NNP
37681	1822	79	Lieux	Lieux	NNP
37681	1822	80	géométriques	géométrique	NNS
37681	1822	81	en	en	IN
37681	1822	82	géométrie	géométrie	NN
37681	1822	83	élémentaire	élémentaire	NN
37681	1822	84	,	,	,
37681	1822	85	Paris	Paris	NNP
37681	1822	86	,	,	,
37681	1822	87	1893	1893	CD
37681	1822	88	;	;	:
37681	1822	89	Hadamard	Hadamard	NNP
37681	1822	90	,	,	,
37681	1822	91	Leçons	Leçons	NNP
37681	1822	92	de	de	NNP
37681	1822	93	géométrie	géométrie	NNP
37681	1822	94	,	,	,
37681	1822	95	p.	p.	NN
37681	1822	96	261	261	CD
37681	1822	97	,	,	,
37681	1822	98	Paris	Paris	NNP
37681	1822	99	,	,	,
37681	1822	100	1898	1898	CD
37681	1822	101	;	;	:
37681	1822	102	Duhamel	Duhamel	NNP
37681	1822	103	,	,	,
37681	1822	104	Des	Des	NNP
37681	1822	105	Méthodes	Méthodes	NNP
37681	1822	106	dans	dan	VBZ
37681	1822	107	les	les	NNP
37681	1822	108	sciences	sciences	NNPS
37681	1822	109	de	de	NNP
37681	1822	110	raisonnement	raisonnement	NNP
37681	1822	111	,	,	,
37681	1822	112	3^e	3^e	NNP
37681	1822	113	éd	éd	NNP
37681	1822	114	.	.	NNP
37681	1822	115	,	,	,
37681	1822	116	Paris	Paris	NNP
37681	1822	117	,	,	,
37681	1822	118	1885	1885	CD
37681	1822	119	;	;	:
37681	1822	120	Henrici	Henrici	NNP
37681	1822	121	and	and	CC
37681	1822	122	Treutlein	Treutlein	NNP
37681	1822	123	,	,	,
37681	1822	124	Lehrbuch	Lehrbuch	NNP
37681	1822	125	der	der	IN
37681	1822	126	Elementar	Elementar	NNP
37681	1822	127	-	-	HYPH
37681	1822	128	Geometrie	Geometrie	NNP
37681	1822	129	,	,	,
37681	1822	130	Leipzig	Leipzig	NNP
37681	1822	131	,	,	,
37681	1822	132	3	3	CD
37681	1822	133	.	.	.
37681	1823	1	Aufl	Aufl	NNP
37681	1823	2	.	.	.
37681	1823	3	,	,	,
37681	1823	4	1897	1897	CD
37681	1823	5	;	;	:
37681	1823	6	Henrici	Henrici	NNP
37681	1823	7	,	,	,
37681	1823	8	Congruent	Congruent	NNP
37681	1823	9	Figures	Figures	NNPS
37681	1823	10	,	,	,
37681	1823	11	London	London	NNP
37681	1823	12	,	,	,
37681	1823	13	1879	1879	CD
37681	1823	14	.	.	.
37681	1824	1	CHAPTER	CHAPTER	NNP
37681	1824	2	XIV	XIV	NNP
37681	1824	3	BOOK	BOOK	NNP
37681	1824	4	I	-PRON-	PRP
37681	1824	5	AND	and	CC
37681	1824	6	ITS	its	PRP$
37681	1824	7	PROPOSITIONS	proposition	NNS
37681	1824	8	Having	have	VBG
37681	1824	9	considered	consider	VBN
37681	1824	10	the	the	DT
37681	1824	11	nature	nature	NN
37681	1824	12	of	of	IN
37681	1824	13	the	the	DT
37681	1824	14	geometry	geometry	NN
37681	1824	15	that	that	WDT
37681	1824	16	we	-PRON-	PRP
37681	1824	17	have	have	VBP
37681	1824	18	inherited	inherit	VBN
37681	1824	19	,	,	,
37681	1824	20	and	and	CC
37681	1824	21	some	some	DT
37681	1824	22	of	of	IN
37681	1824	23	the	the	DT
37681	1824	24	opportunities	opportunity	NNS
37681	1824	25	for	for	IN
37681	1824	26	improving	improve	VBG
37681	1824	27	upon	upon	IN
37681	1824	28	the	the	DT
37681	1824	29	methods	method	NNS
37681	1824	30	of	of	IN
37681	1824	31	presenting	present	VBG
37681	1824	32	it	-PRON-	PRP
37681	1824	33	,	,	,
37681	1824	34	the	the	DT
37681	1824	35	next	next	JJ
37681	1824	36	question	question	NN
37681	1824	37	that	that	WDT
37681	1824	38	arises	arise	VBZ
37681	1824	39	is	be	VBZ
37681	1824	40	the	the	DT
37681	1824	41	all	all	RB
37681	1824	42	-	-	HYPH
37681	1824	43	important	important	JJ
37681	1824	44	one	one	CD
37681	1824	45	of	of	IN
37681	1824	46	the	the	DT
37681	1824	47	subject	subject	JJ
37681	1824	48	matter	matter	NN
37681	1824	49	,	,	,
37681	1824	50	What	what	WP
37681	1824	51	shall	shall	MD
37681	1824	52	geometry	geometry	NN
37681	1824	53	be	be	VB
37681	1824	54	in	in	IN
37681	1824	55	detail	detail	NN
37681	1824	56	?	?	.
37681	1825	1	Shall	Shall	MD
37681	1825	2	it	-PRON-	PRP
37681	1825	3	be	be	VB
37681	1825	4	the	the	DT
37681	1825	5	text	text	NN
37681	1825	6	or	or	CC
37681	1825	7	the	the	DT
37681	1825	8	sequence	sequence	NN
37681	1825	9	of	of	IN
37681	1825	10	Euclid	Euclid	NNP
37681	1825	11	?	?	.
37681	1826	1	Few	few	JJ
37681	1826	2	teachers	teacher	NNS
37681	1826	3	have	have	VBP
37681	1826	4	any	any	DT
37681	1826	5	such	such	JJ
37681	1826	6	idea	idea	NN
37681	1826	7	at	at	IN
37681	1826	8	the	the	DT
37681	1826	9	present	present	JJ
37681	1826	10	time	time	NN
37681	1826	11	.	.	.
37681	1827	1	Shall	Shall	MD
37681	1827	2	it	-PRON-	PRP
37681	1827	3	be	be	VB
37681	1827	4	a	a	DT
37681	1827	5	mere	mere	JJ
37681	1827	6	dabbling	dabbling	NN
37681	1827	7	with	with	IN
37681	1827	8	forms	form	NNS
37681	1827	9	that	that	WDT
37681	1827	10	are	be	VBP
37681	1827	11	seen	see	VBN
37681	1827	12	in	in	IN
37681	1827	13	mechanics	mechanic	NNS
37681	1827	14	or	or	CC
37681	1827	15	architecture	architecture	NN
37681	1827	16	,	,	,
37681	1827	17	with	with	IN
37681	1827	18	no	no	DT
37681	1827	19	serious	serious	JJ
37681	1827	20	logical	logical	JJ
37681	1827	21	sequence	sequence	NN
37681	1827	22	?	?	.
37681	1828	1	This	this	DT
37681	1828	2	is	be	VBZ
37681	1828	3	an	an	DT
37681	1828	4	equally	equally	RB
37681	1828	5	dangerous	dangerous	JJ
37681	1828	6	extreme	extreme	NN
37681	1828	7	.	.	.
37681	1829	1	Shall	Shall	MD
37681	1829	2	it	-PRON-	PRP
37681	1829	3	be	be	VB
37681	1829	4	an	an	DT
37681	1829	5	entirely	entirely	RB
37681	1829	6	new	new	JJ
37681	1829	7	style	style	NN
37681	1829	8	of	of	IN
37681	1829	9	geometry	geometry	NN
37681	1829	10	based	base	VBN
37681	1829	11	upon	upon	IN
37681	1829	12	groups	group	NNS
37681	1829	13	of	of	IN
37681	1829	14	motions	motion	NNS
37681	1829	15	?	?	.
37681	1830	1	This	this	DT
37681	1830	2	may	may	MD
37681	1830	3	sometime	sometime	RB
37681	1830	4	be	be	VB
37681	1830	5	developed	develop	VBN
37681	1830	6	,	,	,
37681	1830	7	but	but	CC
37681	1830	8	as	as	IN
37681	1830	9	yet	yet	RB
37681	1830	10	it	-PRON-	PRP
37681	1830	11	exists	exist	VBZ
37681	1830	12	in	in	IN
37681	1830	13	the	the	DT
37681	1830	14	future	future	NN
37681	1830	15	if	if	IN
37681	1830	16	it	-PRON-	PRP
37681	1830	17	exists	exist	VBZ
37681	1830	18	at	at	RB
37681	1830	19	all	all	RB
37681	1830	20	,	,	,
37681	1830	21	since	since	IN
37681	1830	22	the	the	DT
37681	1830	23	recent	recent	JJ
37681	1830	24	efforts	effort	NNS
37681	1830	25	in	in	IN
37681	1830	26	this	this	DT
37681	1830	27	respect	respect	NN
37681	1830	28	are	be	VBP
37681	1830	29	generally	generally	RB
37681	1830	30	quite	quite	RB
37681	1830	31	as	as	IN
37681	1830	32	ill	ill	RB
37681	1830	33	suited	suit	VBN
37681	1830	34	to	to	IN
37681	1830	35	a	a	DT
37681	1830	36	young	young	JJ
37681	1830	37	pupil	pupil	NN
37681	1830	38	as	as	IN
37681	1830	39	is	be	VBZ
37681	1830	40	Euclid	Euclid	NNP
37681	1830	41	's	's	POS
37681	1830	42	"	"	``
37681	1830	43	Elements	Elements	NNPS
37681	1830	44	"	"	''
37681	1830	45	itself	-PRON-	PRP
37681	1830	46	.	.	.
37681	1831	1	No	no	DT
37681	1831	2	one	one	NN
37681	1831	3	can	can	MD
37681	1831	4	deny	deny	VB
37681	1831	5	the	the	DT
37681	1831	6	truth	truth	NN
37681	1831	7	of	of	IN
37681	1831	8	M.	M.	NNP
37681	1831	9	Bourlet	Bourlet	NNP
37681	1831	10	's	's	POS
37681	1831	11	recent	recent	JJ
37681	1831	12	assertion	assertion	NN
37681	1831	13	that	that	IN
37681	1831	14	"	"	``
37681	1831	15	Industry	industry	NN
37681	1831	16	,	,	,
37681	1831	17	daughter	daughter	NN
37681	1831	18	of	of	IN
37681	1831	19	the	the	DT
37681	1831	20	science	science	NN
37681	1831	21	of	of	IN
37681	1831	22	the	the	DT
37681	1831	23	nineteenth	nineteenth	JJ
37681	1831	24	century	century	NN
37681	1831	25	,	,	,
37681	1831	26	reigns	reign	VBZ
37681	1831	27	to	to	IN
37681	1831	28	-	-	HYPH
37681	1831	29	day	day	NN
37681	1831	30	the	the	DT
37681	1831	31	mistress	mistress	NN
37681	1831	32	of	of	IN
37681	1831	33	the	the	DT
37681	1831	34	world	world	NN
37681	1831	35	;	;	:
37681	1831	36	she	-PRON-	PRP
37681	1831	37	has	have	VBZ
37681	1831	38	transformed	transform	VBN
37681	1831	39	all	all	DT
37681	1831	40	ancient	ancient	JJ
37681	1831	41	methods	method	NNS
37681	1831	42	,	,	,
37681	1831	43	and	and	CC
37681	1831	44	she	-PRON-	PRP
37681	1831	45	has	have	VBZ
37681	1831	46	absorbed	absorb	VBN
37681	1831	47	in	in	IN
37681	1831	48	herself	-PRON-	PRP
37681	1831	49	almost	almost	RB
37681	1831	50	all	all	DT
37681	1831	51	human	human	JJ
37681	1831	52	activity	activity	NN
37681	1831	53	.	.	.
37681	1832	1	"	"	``
37681	1832	2	[	[	-LRB-
37681	1832	3	57	57	CD
37681	1832	4	]	]	-RRB-
37681	1832	5	Neither	neither	CC
37681	1832	6	can	can	MD
37681	1832	7	one	one	PRP
37681	1832	8	deny	deny	VB
37681	1832	9	the	the	DT
37681	1832	10	justice	justice	NN
37681	1832	11	of	of	IN
37681	1832	12	his	-PRON-	PRP$
37681	1832	13	comparison	comparison	NN
37681	1832	14	of	of	IN
37681	1832	15	Euclid	Euclid	NNP
37681	1832	16	with	with	IN
37681	1832	17	a	a	DT
37681	1832	18	noble	noble	JJ
37681	1832	19	piece	piece	NN
37681	1832	20	of	of	IN
37681	1832	21	Gothic	gothic	JJ
37681	1832	22	architecture	architecture	NN
37681	1832	23	and	and	CC
37681	1832	24	of	of	IN
37681	1832	25	his	-PRON-	PRP$
37681	1832	26	assertion	assertion	NN
37681	1832	27	that	that	IN
37681	1832	28	as	as	IN
37681	1832	29	modern	modern	JJ
37681	1832	30	life	life	NN
37681	1832	31	demands	demand	VBZ
37681	1832	32	another	another	DT
37681	1832	33	type	type	NN
37681	1832	34	of	of	IN
37681	1832	35	building	building	NN
37681	1832	36	,	,	,
37681	1832	37	so	so	CC
37681	1832	38	it	-PRON-	PRP
37681	1832	39	demands	demand	VBZ
37681	1832	40	another	another	DT
37681	1832	41	type	type	NN
37681	1832	42	of	of	IN
37681	1832	43	geometry	geometry	NN
37681	1832	44	.	.	.
37681	1833	1	But	but	CC
37681	1833	2	what	what	WP
37681	1833	3	does	do	VBZ
37681	1833	4	this	this	DT
37681	1833	5	mean	mean	VB
37681	1833	6	?	?	.
37681	1834	1	That	that	DT
37681	1834	2	geometry	geometry	NN
37681	1834	3	is	be	VBZ
37681	1834	4	to	to	TO
37681	1834	5	exist	exist	VB
37681	1834	6	merely	merely	RB
37681	1834	7	as	as	IN
37681	1834	8	it	-PRON-	PRP
37681	1834	9	touches	touch	VBZ
37681	1834	10	industry	industry	NN
37681	1834	11	,	,	,
37681	1834	12	or	or	CC
37681	1834	13	that	that	DT
37681	1834	14	bad	bad	JJ
37681	1834	15	architecture	architecture	NN
37681	1834	16	is	be	VBZ
37681	1834	17	to	to	TO
37681	1834	18	replace	replace	VB
37681	1834	19	the	the	DT
37681	1834	20	good	good	JJ
37681	1834	21	?	?	.
37681	1835	1	By	by	IN
37681	1835	2	no	no	DT
37681	1835	3	means	means	NN
37681	1835	4	.	.	.
37681	1836	1	A	a	DT
37681	1836	2	building	building	NN
37681	1836	3	should	should	MD
37681	1836	4	to	to	IN
37681	1836	5	-	-	HYPH
37681	1836	6	day	day	NN
37681	1836	7	have	have	VBP
37681	1836	8	steam	steam	NN
37681	1836	9	heat	heat	NN
37681	1836	10	and	and	CC
37681	1836	11	elevators	elevator	NNS
37681	1836	12	and	and	CC
37681	1836	13	electric	electric	JJ
37681	1836	14	lights	light	NNS
37681	1836	15	,	,	,
37681	1836	16	but	but	CC
37681	1836	17	it	-PRON-	PRP
37681	1836	18	should	should	MD
37681	1836	19	be	be	VB
37681	1836	20	constructed	construct	VBN
37681	1836	21	of	of	IN
37681	1836	22	just	just	RB
37681	1836	23	as	as	IN
37681	1836	24	enduring	endure	VBG
37681	1836	25	materials	material	NNS
37681	1836	26	as	as	IN
37681	1836	27	the	the	DT
37681	1836	28	Parthenon	Parthenon	NNP
37681	1836	29	,	,	,
37681	1836	30	and	and	CC
37681	1836	31	it	-PRON-	PRP
37681	1836	32	should	should	MD
37681	1836	33	have	have	VB
37681	1836	34	lines	line	NNS
37681	1836	35	as	as	RB
37681	1836	36	pleasing	pleasing	JJ
37681	1836	37	as	as	IN
37681	1836	38	those	those	DT
37681	1836	39	of	of	IN
37681	1836	40	a	a	DT
37681	1836	41	Gothic	Gothic	NNP
37681	1836	42	façade	façade	NN
37681	1836	43	.	.	.
37681	1837	1	Architecture	architecture	NN
37681	1837	2	should	should	MD
37681	1837	3	still	still	RB
37681	1837	4	be	be	VB
37681	1837	5	artistic	artistic	JJ
37681	1837	6	and	and	CC
37681	1837	7	construction	construction	NN
37681	1837	8	should	should	MD
37681	1837	9	still	still	RB
37681	1837	10	be	be	VB
37681	1837	11	substantial	substantial	JJ
37681	1837	12	,	,	,
37681	1837	13	else	else	RB
37681	1837	14	a	a	DT
37681	1837	15	building	building	NN
37681	1837	16	can	can	MD
37681	1837	17	never	never	RB
37681	1837	18	endure	endure	VB
37681	1837	19	.	.	.
37681	1838	1	So	so	RB
37681	1838	2	geometry	geometry	NN
37681	1838	3	must	must	MD
37681	1838	4	still	still	RB
37681	1838	5	exemplify	exemplify	VB
37681	1838	6	good	good	JJ
37681	1838	7	logic	logic	NN
37681	1838	8	and	and	CC
37681	1838	9	must	must	MD
37681	1838	10	still	still	RB
37681	1838	11	bring	bring	VB
37681	1838	12	to	to	IN
37681	1838	13	the	the	DT
37681	1838	14	pupil	pupil	NN
37681	1838	15	a	a	DT
37681	1838	16	feeling	feeling	NN
37681	1838	17	of	of	IN
37681	1838	18	exaltation	exaltation	NN
37681	1838	19	,	,	,
37681	1838	20	or	or	CC
37681	1838	21	it	-PRON-	PRP
37681	1838	22	will	will	MD
37681	1838	23	perish	perish	VB
37681	1838	24	and	and	CC
37681	1838	25	become	become	VB
37681	1838	26	a	a	DT
37681	1838	27	mere	mere	JJ
37681	1838	28	relic	relic	NN
37681	1838	29	in	in	IN
37681	1838	30	the	the	DT
37681	1838	31	museum	museum	NNP
37681	1838	32	of	of	IN
37681	1838	33	human	human	NNP
37681	1838	34	culture	culture	NN
37681	1838	35	.	.	.
37681	1839	1	What	what	WP
37681	1839	2	,	,	,
37681	1839	3	then	then	RB
37681	1839	4	,	,	,
37681	1839	5	shall	shall	MD
37681	1839	6	the	the	DT
37681	1839	7	propositions	proposition	NNS
37681	1839	8	of	of	IN
37681	1839	9	geometry	geometry	NN
37681	1839	10	be	be	VB
37681	1839	11	,	,	,
37681	1839	12	and	and	CC
37681	1839	13	in	in	IN
37681	1839	14	what	what	WDT
37681	1839	15	manner	manner	NN
37681	1839	16	shall	shall	MD
37681	1839	17	they	-PRON-	PRP
37681	1839	18	answer	answer	VB
37681	1839	19	to	to	IN
37681	1839	20	the	the	DT
37681	1839	21	challenge	challenge	NN
37681	1839	22	of	of	IN
37681	1839	23	the	the	DT
37681	1839	24	industrial	industrial	JJ
37681	1839	25	epoch	epoch	NN
37681	1839	26	in	in	IN
37681	1839	27	which	which	WDT
37681	1839	28	we	-PRON-	PRP
37681	1839	29	live	live	VBP
37681	1839	30	?	?	.
37681	1840	1	In	in	IN
37681	1840	2	reply	reply	NN
37681	1840	3	,	,	,
37681	1840	4	they	-PRON-	PRP
37681	1840	5	must	must	MD
37681	1840	6	be	be	VB
37681	1840	7	better	well	RBR
37681	1840	8	adapted	adapt	VBN
37681	1840	9	to	to	IN
37681	1840	10	young	young	JJ
37681	1840	11	minds	mind	NNS
37681	1840	12	and	and	CC
37681	1840	13	to	to	IN
37681	1840	14	all	all	DT
37681	1840	15	young	young	JJ
37681	1840	16	minds	mind	NNS
37681	1840	17	than	than	IN
37681	1840	18	Euclid	Euclid	NNP
37681	1840	19	ever	ever	RB
37681	1840	20	intended	intend	VBD
37681	1840	21	his	-PRON-	PRP$
37681	1840	22	own	own	JJ
37681	1840	23	propositions	proposition	NNS
37681	1840	24	to	to	TO
37681	1840	25	be	be	VB
37681	1840	26	.	.	.
37681	1841	1	Furthermore	furthermore	RB
37681	1841	2	,	,	,
37681	1841	3	they	-PRON-	PRP
37681	1841	4	must	must	MD
37681	1841	5	have	have	VB
37681	1841	6	a	a	DT
37681	1841	7	richness	richness	NN
37681	1841	8	of	of	IN
37681	1841	9	application	application	NN
37681	1841	10	to	to	IN
37681	1841	11	pure	pure	JJ
37681	1841	12	geometry	geometry	NN
37681	1841	13	,	,	,
37681	1841	14	in	in	IN
37681	1841	15	the	the	DT
37681	1841	16	way	way	NN
37681	1841	17	of	of	IN
37681	1841	18	carefully	carefully	RB
37681	1841	19	chosen	choose	VBN
37681	1841	20	exercises	exercise	NNS
37681	1841	21	,	,	,
37681	1841	22	that	that	IN
37681	1841	23	Euclid	Euclid	NNP
37681	1841	24	never	never	RB
37681	1841	25	attempted	attempt	VBD
37681	1841	26	.	.	.
37681	1842	1	And	and	CC
37681	1842	2	finally	finally	RB
37681	1842	3	,	,	,
37681	1842	4	they	-PRON-	PRP
37681	1842	5	must	must	MD
37681	1842	6	have	have	VB
37681	1842	7	application	application	NN
37681	1842	8	to	to	IN
37681	1842	9	this	this	DT
37681	1842	10	same	same	JJ
37681	1842	11	life	life	NN
37681	1842	12	of	of	IN
37681	1842	13	industry	industry	NN
37681	1842	14	of	of	IN
37681	1842	15	which	which	WDT
37681	1842	16	we	-PRON-	PRP
37681	1842	17	have	have	VBP
37681	1842	18	spoken	speak	VBN
37681	1842	19	,	,	,
37681	1842	20	whenever	whenever	WRB
37681	1842	21	this	this	DT
37681	1842	22	can	can	MD
37681	1842	23	really	really	RB
37681	1842	24	be	be	VB
37681	1842	25	found	find	VBN
37681	1842	26	,	,	,
37681	1842	27	but	but	CC
37681	1842	28	there	there	EX
37681	1842	29	must	must	MD
37681	1842	30	be	be	VB
37681	1842	31	no	no	DT
37681	1842	32	sham	sham	JJ
37681	1842	33	and	and	CC
37681	1842	34	pretense	pretense	VB
37681	1842	35	about	about	IN
37681	1842	36	it	-PRON-	PRP
37681	1842	37	,	,	,
37681	1842	38	else	else	RB
37681	1842	39	the	the	DT
37681	1842	40	very	very	JJ
37681	1842	41	honesty	honesty	NN
37681	1842	42	that	that	WDT
37681	1842	43	permeated	permeate	VBD
37681	1842	44	the	the	DT
37681	1842	45	ancient	ancient	JJ
37681	1842	46	geometry	geometry	NN
37681	1842	47	will	will	MD
37681	1842	48	seem	seem	VB
37681	1842	49	to	to	IN
37681	1842	50	the	the	DT
37681	1842	51	pupil	pupil	NN
37681	1842	52	to	to	TO
37681	1842	53	be	be	VB
37681	1842	54	wanting	want	VBG
37681	1842	55	in	in	IN
37681	1842	56	the	the	DT
37681	1842	57	whole	whole	JJ
37681	1842	58	subject	subject	NN
37681	1842	59	.	.	.
37681	1843	1	[	[	-LRB-
37681	1843	2	58	58	CD
37681	1843	3	]	]	-RRB-
37681	1843	4	Until	until	IN
37681	1843	5	some	some	DT
37681	1843	6	geometry	geometry	NN
37681	1843	7	on	on	IN
37681	1843	8	a	a	DT
37681	1843	9	radically	radically	RB
37681	1843	10	different	different	JJ
37681	1843	11	basis	basis	NN
37681	1843	12	shall	shall	MD
37681	1843	13	appear	appear	VB
37681	1843	14	,	,	,
37681	1843	15	and	and	CC
37681	1843	16	of	of	IN
37681	1843	17	this	this	DT
37681	1843	18	there	there	EX
37681	1843	19	is	be	VBZ
37681	1843	20	no	no	DT
37681	1843	21	very	very	RB
37681	1843	22	hopeful	hopeful	JJ
37681	1843	23	sign	sign	NN
37681	1843	24	at	at	IN
37681	1843	25	present	present	JJ
37681	1843	26	,	,	,
37681	1843	27	the	the	DT
37681	1843	28	propositions	proposition	NNS
37681	1843	29	will	will	MD
37681	1843	30	be	be	VB
37681	1843	31	the	the	DT
37681	1843	32	essential	essential	JJ
37681	1843	33	ones	one	NNS
37681	1843	34	of	of	IN
37681	1843	35	Euclid	Euclid	NNP
37681	1843	36	,	,	,
37681	1843	37	excluding	exclude	VBG
37681	1843	38	those	those	DT
37681	1843	39	that	that	WDT
37681	1843	40	may	may	MD
37681	1843	41	be	be	VB
37681	1843	42	considered	consider	VBN
37681	1843	43	merely	merely	RB
37681	1843	44	intuitive	intuitive	JJ
37681	1843	45	,	,	,
37681	1843	46	and	and	CC
37681	1843	47	excluding	exclude	VBG
37681	1843	48	all	all	DT
37681	1843	49	that	that	WDT
37681	1843	50	are	be	VBP
37681	1843	51	too	too	RB
37681	1843	52	difficult	difficult	JJ
37681	1843	53	for	for	IN
37681	1843	54	the	the	DT
37681	1843	55	pupil	pupil	NN
37681	1843	56	who	who	WP
37681	1843	57	to	to	IN
37681	1843	58	-	-	HYPH
37681	1843	59	day	day	NN
37681	1843	60	takes	take	VBZ
37681	1843	61	up	up	RP
37681	1843	62	their	-PRON-	PRP$
37681	1843	63	study	study	NN
37681	1843	64	.	.	.
37681	1844	1	The	the	DT
37681	1844	2	number	number	NN
37681	1844	3	will	will	MD
37681	1844	4	be	be	VB
37681	1844	5	limited	limit	VBN
37681	1844	6	in	in	IN
37681	1844	7	a	a	DT
37681	1844	8	reasonable	reasonable	JJ
37681	1844	9	way	way	NN
37681	1844	10	,	,	,
37681	1844	11	and	and	CC
37681	1844	12	every	every	DT
37681	1844	13	genuine	genuine	JJ
37681	1844	14	type	type	NN
37681	1844	15	of	of	IN
37681	1844	16	application	application	NN
37681	1844	17	will	will	MD
37681	1844	18	be	be	VB
37681	1844	19	placed	place	VBN
37681	1844	20	before	before	IN
37681	1844	21	the	the	DT
37681	1844	22	teacher	teacher	NN
37681	1844	23	to	to	TO
37681	1844	24	be	be	VB
37681	1844	25	used	use	VBN
37681	1844	26	as	as	IN
37681	1844	27	necessity	necessity	NN
37681	1844	28	requires	require	VBZ
37681	1844	29	.	.	.
37681	1845	1	But	but	CC
37681	1845	2	a	a	DT
37681	1845	3	fair	fair	JJ
37681	1845	4	amount	amount	NN
37681	1845	5	of	of	IN
37681	1845	6	logic	logic	NN
37681	1845	7	will	will	MD
37681	1845	8	be	be	VB
37681	1845	9	retained	retain	VBN
37681	1845	10	,	,	,
37681	1845	11	and	and	CC
37681	1845	12	the	the	DT
37681	1845	13	effort	effort	NN
37681	1845	14	to	to	TO
37681	1845	15	make	make	VB
37681	1845	16	of	of	IN
37681	1845	17	geometry	geometry	NN
37681	1845	18	an	an	DT
37681	1845	19	empty	empty	JJ
37681	1845	20	bauble	bauble	NN
37681	1845	21	of	of	IN
37681	1845	22	a	a	DT
37681	1845	23	listless	listless	JJ
37681	1845	24	mind	mind	NN
37681	1845	25	will	will	MD
37681	1845	26	be	be	VB
37681	1845	27	rejected	reject	VBN
37681	1845	28	by	by	IN
37681	1845	29	every	every	DT
37681	1845	30	worthy	worthy	JJ
37681	1845	31	teacher	teacher	NN
37681	1845	32	.	.	.
37681	1846	1	What	what	WP
37681	1846	2	the	the	DT
37681	1846	3	propositions	proposition	NNS
37681	1846	4	should	should	MD
37681	1846	5	be	be	VB
37681	1846	6	is	be	VBZ
37681	1846	7	a	a	DT
37681	1846	8	matter	matter	NN
37681	1846	9	upon	upon	IN
37681	1846	10	which	which	WDT
37681	1846	11	opinions	opinion	NNS
37681	1846	12	may	may	MD
37681	1846	13	justly	justly	RB
37681	1846	14	differ	differ	VB
37681	1846	15	;	;	:
37681	1846	16	but	but	CC
37681	1846	17	in	in	IN
37681	1846	18	this	this	DT
37681	1846	19	chapter	chapter	NN
37681	1846	20	there	there	EX
37681	1846	21	is	be	VBZ
37681	1846	22	set	set	VBN
37681	1846	23	forth	forth	RP
37681	1846	24	a	a	DT
37681	1846	25	reasonable	reasonable	JJ
37681	1846	26	list	list	NN
37681	1846	27	for	for	IN
37681	1846	28	Book	Book	NNP
37681	1846	29	I	-PRON-	PRP
37681	1846	30	,	,	,
37681	1846	31	arranged	arrange	VBN
37681	1846	32	in	in	IN
37681	1846	33	a	a	DT
37681	1846	34	workable	workable	JJ
37681	1846	35	sequence	sequence	NN
37681	1846	36	,	,	,
37681	1846	37	and	and	CC
37681	1846	38	this	this	DT
37681	1846	39	list	list	NN
37681	1846	40	may	may	MD
37681	1846	41	fairly	fairly	RB
37681	1846	42	be	be	VB
37681	1846	43	taken	take	VBN
37681	1846	44	as	as	IN
37681	1846	45	typical	typical	JJ
37681	1846	46	of	of	IN
37681	1846	47	what	what	WP
37681	1846	48	the	the	DT
37681	1846	49	American	american	JJ
37681	1846	50	school	school	NN
37681	1846	51	will	will	MD
37681	1846	52	probably	probably	RB
37681	1846	53	use	use	VB
37681	1846	54	for	for	IN
37681	1846	55	many	many	JJ
37681	1846	56	years	year	NNS
37681	1846	57	to	to	TO
37681	1846	58	come	come	VB
37681	1846	59	.	.	.
37681	1847	1	With	with	IN
37681	1847	2	the	the	DT
37681	1847	3	list	list	NN
37681	1847	4	is	be	VBZ
37681	1847	5	given	give	VBN
37681	1847	6	a	a	DT
37681	1847	7	set	set	NN
37681	1847	8	of	of	IN
37681	1847	9	typical	typical	JJ
37681	1847	10	applications	application	NNS
37681	1847	11	,	,	,
37681	1847	12	and	and	CC
37681	1847	13	some	some	DT
37681	1847	14	of	of	IN
37681	1847	15	the	the	DT
37681	1847	16	general	general	JJ
37681	1847	17	information	information	NN
37681	1847	18	that	that	WDT
37681	1847	19	will	will	MD
37681	1847	20	add	add	VB
37681	1847	21	to	to	IN
37681	1847	22	the	the	DT
37681	1847	23	interest	interest	NN
37681	1847	24	in	in	IN
37681	1847	25	the	the	DT
37681	1847	26	work	work	NN
37681	1847	27	and	and	CC
37681	1847	28	that	that	DT
37681	1847	29	should	should	MD
37681	1847	30	form	form	VB
37681	1847	31	part	part	NN
37681	1847	32	of	of	IN
37681	1847	33	the	the	DT
37681	1847	34	equipment	equipment	NN
37681	1847	35	of	of	IN
37681	1847	36	the	the	DT
37681	1847	37	teacher	teacher	NN
37681	1847	38	.	.	.
37681	1848	1	An	an	DT
37681	1848	2	ancient	ancient	JJ
37681	1848	3	treatise	treatise	NN
37681	1848	4	was	be	VBD
37681	1848	5	usually	usually	RB
37681	1848	6	written	write	VBN
37681	1848	7	on	on	IN
37681	1848	8	a	a	DT
37681	1848	9	kind	kind	NN
37681	1848	10	of	of	IN
37681	1848	11	paper	paper	NN
37681	1848	12	called	call	VBN
37681	1848	13	papyrus	papyrus	NNP
37681	1848	14	,	,	,
37681	1848	15	made	make	VBN
37681	1848	16	from	from	IN
37681	1848	17	the	the	DT
37681	1848	18	pith	pith	NN
37681	1848	19	of	of	IN
37681	1848	20	a	a	DT
37681	1848	21	large	large	JJ
37681	1848	22	reed	reed	NN
37681	1848	23	formerly	formerly	RB
37681	1848	24	common	common	JJ
37681	1848	25	in	in	IN
37681	1848	26	Egypt	Egypt	NNP
37681	1848	27	,	,	,
37681	1848	28	but	but	CC
37681	1848	29	now	now	RB
37681	1848	30	growing	grow	VBG
37681	1848	31	luxuriantly	luxuriantly	RB
37681	1848	32	only	only	RB
37681	1848	33	above	above	IN
37681	1848	34	Khartum	Khartum	NNP
37681	1848	35	in	in	IN
37681	1848	36	Upper	Upper	NNP
37681	1848	37	Egypt	Egypt	NNP
37681	1848	38	,	,	,
37681	1848	39	and	and	CC
37681	1848	40	near	near	IN
37681	1848	41	Syracuse	Syracuse	NNP
37681	1848	42	in	in	IN
37681	1848	43	Sicily	Sicily	NNP
37681	1848	44	;	;	,
37681	1848	45	or	or	CC
37681	1848	46	else	else	RB
37681	1848	47	it	-PRON-	PRP
37681	1848	48	was	be	VBD
37681	1848	49	written	write	VBN
37681	1848	50	on	on	IN
37681	1848	51	parchment	parchment	NN
37681	1848	52	,	,	,
37681	1848	53	so	so	RB
37681	1848	54	called	call	VBD
37681	1848	55	from	from	IN
37681	1848	56	Pergamos	Pergamos	NNP
37681	1848	57	in	in	IN
37681	1848	58	Asia	Asia	NNP
37681	1848	59	Minor	Minor	NNP
37681	1848	60	,	,	,
37681	1848	61	where	where	WRB
37681	1848	62	skins	skin	NNS
37681	1848	63	were	be	VBD
37681	1848	64	first	first	RB
37681	1848	65	prepared	prepare	VBN
37681	1848	66	in	in	IN
37681	1848	67	parchment	parchment	NN
37681	1848	68	form	form	NN
37681	1848	69	;	;	:
37681	1848	70	or	or	CC
37681	1848	71	occasionally	occasionally	RB
37681	1848	72	they	-PRON-	PRP
37681	1848	73	were	be	VBD
37681	1848	74	written	write	VBN
37681	1848	75	on	on	IN
37681	1848	76	ordinary	ordinary	JJ
37681	1848	77	leather	leather	NN
37681	1848	78	.	.	.
37681	1849	1	In	in	IN
37681	1849	2	any	any	DT
37681	1849	3	case	case	NN
37681	1849	4	they	-PRON-	PRP
37681	1849	5	were	be	VBD
37681	1849	6	generally	generally	RB
37681	1849	7	written	write	VBN
37681	1849	8	on	on	IN
37681	1849	9	long	long	JJ
37681	1849	10	strips	strip	NNS
37681	1849	11	of	of	IN
37681	1849	12	the	the	DT
37681	1849	13	material	material	NN
37681	1849	14	used	use	VBN
37681	1849	15	,	,	,
37681	1849	16	and	and	CC
37681	1849	17	these	these	DT
37681	1849	18	were	be	VBD
37681	1849	19	rolled	roll	VBN
37681	1849	20	up	up	RP
37681	1849	21	and	and	CC
37681	1849	22	tied	tie	VBN
37681	1849	23	.	.	.
37681	1850	1	Hence	hence	RB
37681	1850	2	we	-PRON-	PRP
37681	1850	3	have	have	VBP
37681	1850	4	such	such	PDT
37681	1850	5	an	an	DT
37681	1850	6	expression	expression	NN
37681	1850	7	as	as	IN
37681	1850	8	"	"	``
37681	1850	9	keeping	keep	VBG
37681	1850	10	the	the	DT
37681	1850	11	roll	roll	NN
37681	1850	12	"	"	''
37681	1850	13	in	in	IN
37681	1850	14	school	school	NN
37681	1850	15	,	,	,
37681	1850	16	and	and	CC
37681	1850	17	such	such	PDT
37681	1850	18	a	a	DT
37681	1850	19	word	word	NN
37681	1850	20	as	as	IN
37681	1850	21	"	"	``
37681	1850	22	volume	volume	NN
37681	1850	23	,	,	,
37681	1850	24	"	"	''
37681	1850	25	which	which	WDT
37681	1850	26	has	have	VBZ
37681	1850	27	in	in	IN
37681	1850	28	it	-PRON-	PRP
37681	1850	29	the	the	DT
37681	1850	30	same	same	JJ
37681	1850	31	root	root	NN
37681	1850	32	as	as	IN
37681	1850	33	"	"	``
37681	1850	34	involve	involve	VBP
37681	1850	35	"	"	''
37681	1850	36	(	(	-LRB-
37681	1850	37	to	to	TO
37681	1850	38	roll	roll	VB
37681	1850	39	in	in	RP
37681	1850	40	)	)	-RRB-
37681	1850	41	,	,	,
37681	1850	42	and	and	CC
37681	1850	43	"	"	``
37681	1850	44	evolve	evolve	VB
37681	1850	45	"	"	''
37681	1850	46	(	(	-LRB-
37681	1850	47	to	to	TO
37681	1850	48	roll	roll	VB
37681	1850	49	out	out	RP
37681	1850	50	)	)	-RRB-
37681	1850	51	.	.	.
37681	1851	1	Several	several	JJ
37681	1851	2	of	of	IN
37681	1851	3	these	these	DT
37681	1851	4	rolls	roll	NNS
37681	1851	5	were	be	VBD
37681	1851	6	often	often	RB
37681	1851	7	necessary	necessary	JJ
37681	1851	8	for	for	IN
37681	1851	9	a	a	DT
37681	1851	10	single	single	JJ
37681	1851	11	treatise	treatise	NN
37681	1851	12	,	,	,
37681	1851	13	in	in	IN
37681	1851	14	which	which	WDT
37681	1851	15	case	case	NN
37681	1851	16	each	each	DT
37681	1851	17	was	be	VBD
37681	1851	18	tied	tie	VBN
37681	1851	19	,	,	,
37681	1851	20	and	and	CC
37681	1851	21	all	all	DT
37681	1851	22	were	be	VBD
37681	1851	23	kept	keep	VBN
37681	1851	24	together	together	RB
37681	1851	25	in	in	IN
37681	1851	26	a	a	DT
37681	1851	27	receptacle	receptacle	NN
37681	1851	28	resembling	resemble	VBG
37681	1851	29	a	a	DT
37681	1851	30	pail	pail	NN
37681	1851	31	,	,	,
37681	1851	32	or	or	CC
37681	1851	33	in	in	IN
37681	1851	34	a	a	DT
37681	1851	35	compartment	compartment	NN
37681	1851	36	on	on	IN
37681	1851	37	a	a	DT
37681	1851	38	shelf	shelf	NN
37681	1851	39	.	.	.
37681	1852	1	The	the	DT
37681	1852	2	Greeks	Greeks	NNPS
37681	1852	3	called	call	VBD
37681	1852	4	each	each	DT
37681	1852	5	of	of	IN
37681	1852	6	the	the	DT
37681	1852	7	separate	separate	JJ
37681	1852	8	parts	part	NNS
37681	1852	9	of	of	IN
37681	1852	10	a	a	DT
37681	1852	11	treatise	treatise	NN
37681	1852	12	_	_	NNP
37681	1852	13	biblion	biblion	NN
37681	1852	14	_	_	NNP
37681	1852	15	(	(	-LRB-
37681	1852	16	[	[	-LRB-
37681	1852	17	Greek	Greek	NNP
37681	1852	18	:	:	:
37681	1852	19	biblion	biblion	NN
37681	1852	20	]	]	-RRB-
37681	1852	21	)	)	-RRB-
37681	1852	22	,	,	,
37681	1852	23	a	a	DT
37681	1852	24	word	word	NN
37681	1852	25	meaning	meaning	NN
37681	1852	26	"	"	``
37681	1852	27	book	book	NN
37681	1852	28	.	.	.
37681	1852	29	"	"	''
37681	1853	1	Hence	hence	RB
37681	1853	2	we	-PRON-	PRP
37681	1853	3	have	have	VBP
37681	1853	4	the	the	DT
37681	1853	5	books	book	NNS
37681	1853	6	of	of	IN
37681	1853	7	the	the	DT
37681	1853	8	Bible	Bible	NNP
37681	1853	9	,	,	,
37681	1853	10	the	the	DT
37681	1853	11	books	book	NNS
37681	1853	12	of	of	IN
37681	1853	13	Homer	Homer	NNP
37681	1853	14	,	,	,
37681	1853	15	and	and	CC
37681	1853	16	the	the	DT
37681	1853	17	books	book	NNS
37681	1853	18	of	of	IN
37681	1853	19	Euclid	Euclid	NNP
37681	1853	20	.	.	.
37681	1854	1	From	from	IN
37681	1854	2	the	the	DT
37681	1854	3	same	same	JJ
37681	1854	4	root	root	NN
37681	1854	5	,	,	,
37681	1854	6	indeed	indeed	RB
37681	1854	7	,	,	,
37681	1854	8	comes	come	VBZ
37681	1854	9	Bible	Bible	NNP
37681	1854	10	,	,	,
37681	1854	11	bibliophile	bibliophile	JJ
37681	1854	12	(	(	-LRB-
37681	1854	13	booklover	booklover	NNP
37681	1854	14	)	)	-RRB-
37681	1854	15	,	,	,
37681	1854	16	bibliography	bibliography	NNP
37681	1854	17	(	(	-LRB-
37681	1854	18	list	list	NN
37681	1854	19	of	of	IN
37681	1854	20	books	book	NNS
37681	1854	21	)	)	-RRB-
37681	1854	22	,	,	,
37681	1854	23	and	and	CC
37681	1854	24	kindred	kindred	JJ
37681	1854	25	words	word	NNS
37681	1854	26	.	.	.
37681	1855	1	Thus	thus	RB
37681	1855	2	the	the	DT
37681	1855	3	books	book	NNS
37681	1855	4	of	of	IN
37681	1855	5	geometry	geometry	NN
37681	1855	6	are	be	VBP
37681	1855	7	the	the	DT
37681	1855	8	large	large	JJ
37681	1855	9	chapters	chapter	NNS
37681	1855	10	of	of	IN
37681	1855	11	the	the	DT
37681	1855	12	subject	subject	NN
37681	1855	13	,	,	,
37681	1855	14	"	"	``
37681	1855	15	chapter	chapter	NN
37681	1855	16	"	"	''
37681	1855	17	being	be	VBG
37681	1855	18	from	from	IN
37681	1855	19	the	the	DT
37681	1855	20	Latin	Latin	NNP
37681	1855	21	_	_	NNP
37681	1855	22	caput	caput	NN
37681	1855	23	_	_	NNP
37681	1855	24	(	(	-LRB-
37681	1855	25	head	head	NN
37681	1855	26	)	)	-RRB-
37681	1855	27	,	,	,
37681	1855	28	a	a	DT
37681	1855	29	section	section	NN
37681	1855	30	under	under	IN
37681	1855	31	a	a	DT
37681	1855	32	new	new	JJ
37681	1855	33	heading	heading	NN
37681	1855	34	.	.	.
37681	1856	1	There	there	EX
37681	1856	2	have	have	VBP
37681	1856	3	been	be	VBN
37681	1856	4	efforts	effort	NNS
37681	1856	5	to	to	TO
37681	1856	6	change	change	VB
37681	1856	7	"	"	``
37681	1856	8	books	book	NNS
37681	1856	9	"	"	''
37681	1856	10	to	to	IN
37681	1856	11	"	"	``
37681	1856	12	chapters	chapter	NNS
37681	1856	13	,	,	,
37681	1856	14	"	"	''
37681	1856	15	but	but	CC
37681	1856	16	they	-PRON-	PRP
37681	1856	17	have	have	VBP
37681	1856	18	not	not	RB
37681	1856	19	succeeded	succeed	VBN
37681	1856	20	,	,	,
37681	1856	21	and	and	CC
37681	1856	22	there	there	EX
37681	1856	23	is	be	VBZ
37681	1856	24	no	no	DT
37681	1856	25	reason	reason	NN
37681	1856	26	why	why	WRB
37681	1856	27	they	-PRON-	PRP
37681	1856	28	should	should	MD
37681	1856	29	succeed	succeed	VB
37681	1856	30	,	,	,
37681	1856	31	for	for	IN
37681	1856	32	the	the	DT
37681	1856	33	term	term	NN
37681	1856	34	is	be	VBZ
37681	1856	35	clear	clear	JJ
37681	1856	36	and	and	CC
37681	1856	37	has	have	VBZ
37681	1856	38	the	the	DT
37681	1856	39	sanction	sanction	NN
37681	1856	40	of	of	IN
37681	1856	41	long	long	JJ
37681	1856	42	usage	usage	NN
37681	1856	43	.	.	.
37681	1857	1	THEOREM	THEOREM	NNP
37681	1857	2	.	.	.
37681	1858	1	_	_	XX
37681	1858	2	If	if	IN
37681	1858	3	two	two	CD
37681	1858	4	lines	line	NNS
37681	1858	5	intersect	intersect	VBP
37681	1858	6	,	,	,
37681	1858	7	the	the	DT
37681	1858	8	vertical	vertical	JJ
37681	1858	9	angles	angle	NNS
37681	1858	10	are	be	VBP
37681	1858	11	equal	equal	JJ
37681	1858	12	.	.	.
37681	1858	13	_	_	NNP
37681	1858	14	This	this	DT
37681	1858	15	was	be	VBD
37681	1858	16	Euclid	Euclid	NNP
37681	1858	17	's	's	POS
37681	1858	18	Proposition	Proposition	NNP
37681	1858	19	15	15	CD
37681	1858	20	,	,	,
37681	1858	21	being	be	VBG
37681	1858	22	put	put	VBN
37681	1858	23	so	so	RB
37681	1858	24	late	late	RB
37681	1858	25	because	because	IN
37681	1858	26	he	-PRON-	PRP
37681	1858	27	based	base	VBD
37681	1858	28	the	the	DT
37681	1858	29	proof	proof	NN
37681	1858	30	upon	upon	IN
37681	1858	31	his	-PRON-	PRP$
37681	1858	32	Proposition	Proposition	NNP
37681	1858	33	13	13	CD
37681	1858	34	,	,	,
37681	1858	35	now	now	RB
37681	1858	36	thought	think	VBN
37681	1858	37	to	to	TO
37681	1858	38	be	be	VB
37681	1858	39	best	good	JJS
37681	1858	40	taken	take	VBN
37681	1858	41	without	without	IN
37681	1858	42	proof	proof	NN
37681	1858	43	,	,	,
37681	1858	44	namely	namely	RB
37681	1858	45	,	,	,
37681	1858	46	"	"	``
37681	1858	47	If	if	IN
37681	1858	48	a	a	DT
37681	1858	49	straight	straight	JJ
37681	1858	50	line	line	NN
37681	1858	51	set	set	VBN
37681	1858	52	upon	upon	IN
37681	1858	53	a	a	DT
37681	1858	54	straight	straight	JJ
37681	1858	55	line	line	NN
37681	1858	56	makes	make	VBZ
37681	1858	57	angles	angle	NNS
37681	1858	58	,	,	,
37681	1858	59	it	-PRON-	PRP
37681	1858	60	will	will	MD
37681	1858	61	make	make	VB
37681	1858	62	either	either	CC
37681	1858	63	two	two	CD
37681	1858	64	right	right	JJ
37681	1858	65	angles	angle	NNS
37681	1858	66	or	or	CC
37681	1858	67	angles	angle	NNS
37681	1858	68	equal	equal	JJ
37681	1858	69	to	to	IN
37681	1858	70	two	two	CD
37681	1858	71	right	right	JJ
37681	1858	72	angles	angle	NNS
37681	1858	73	.	.	.
37681	1858	74	"	"	''
37681	1859	1	It	-PRON-	PRP
37681	1859	2	is	be	VBZ
37681	1859	3	found	find	VBN
37681	1859	4	to	to	TO
37681	1859	5	be	be	VB
37681	1859	6	better	well	JJR
37681	1859	7	pedagogy	pedagogy	NN
37681	1859	8	to	to	TO
37681	1859	9	assume	assume	VB
37681	1859	10	that	that	IN
37681	1859	11	this	this	DT
37681	1859	12	follows	follow	VBZ
37681	1859	13	from	from	IN
37681	1859	14	the	the	DT
37681	1859	15	definition	definition	NN
37681	1859	16	of	of	IN
37681	1859	17	straight	straight	JJ
37681	1859	18	angle	angle	NN
37681	1859	19	,	,	,
37681	1859	20	with	with	IN
37681	1859	21	reference	reference	NN
37681	1859	22	,	,	,
37681	1859	23	if	if	IN
37681	1859	24	necessary	necessary	JJ
37681	1859	25	,	,	,
37681	1859	26	to	to	IN
37681	1859	27	the	the	DT
37681	1859	28	meaning	meaning	NN
37681	1859	29	of	of	IN
37681	1859	30	the	the	DT
37681	1859	31	sum	sum	NN
37681	1859	32	of	of	IN
37681	1859	33	two	two	CD
37681	1859	34	angles	angle	NNS
37681	1859	35	.	.	.
37681	1860	1	This	this	DT
37681	1860	2	proposition	proposition	NN
37681	1860	3	on	on	IN
37681	1860	4	vertical	vertical	JJ
37681	1860	5	angles	angle	NNS
37681	1860	6	is	be	VBZ
37681	1860	7	probably	probably	RB
37681	1860	8	the	the	DT
37681	1860	9	best	good	JJS
37681	1860	10	one	one	NN
37681	1860	11	with	with	IN
37681	1860	12	which	which	WDT
37681	1860	13	to	to	TO
37681	1860	14	begin	begin	VB
37681	1860	15	geometry	geometry	NN
37681	1860	16	,	,	,
37681	1860	17	since	since	IN
37681	1860	18	it	-PRON-	PRP
37681	1860	19	is	be	VBZ
37681	1860	20	not	not	RB
37681	1860	21	so	so	RB
37681	1860	22	evident	evident	JJ
37681	1860	23	as	as	IN
37681	1860	24	to	to	TO
37681	1860	25	seem	seem	VB
37681	1860	26	to	to	TO
37681	1860	27	need	need	VB
37681	1860	28	no	no	DT
37681	1860	29	proof	proof	NN
37681	1860	30	,	,	,
37681	1860	31	although	although	IN
37681	1860	32	some	some	DT
37681	1860	33	prefer	prefer	VBP
37681	1860	34	to	to	TO
37681	1860	35	rank	rank	VB
37681	1860	36	it	-PRON-	PRP
37681	1860	37	as	as	IN
37681	1860	38	semiobvious	semiobvious	JJ
37681	1860	39	,	,	,
37681	1860	40	while	while	IN
37681	1860	41	the	the	DT
37681	1860	42	proof	proof	NN
37681	1860	43	is	be	VBZ
37681	1860	44	so	so	RB
37681	1860	45	simple	simple	JJ
37681	1860	46	as	as	RB
37681	1860	47	easily	easily	RB
37681	1860	48	to	to	TO
37681	1860	49	be	be	VB
37681	1860	50	understood	understand	VBN
37681	1860	51	.	.	.
37681	1861	1	Eudemus	Eudemus	NNP
37681	1861	2	,	,	,
37681	1861	3	a	a	DT
37681	1861	4	Greek	Greek	NNP
37681	1861	5	who	who	WP
37681	1861	6	wrote	write	VBD
37681	1861	7	not	not	RB
37681	1861	8	long	long	RB
37681	1861	9	before	before	RB
37681	1861	10	Euclid	Euclid	NNP
37681	1861	11	,	,	,
37681	1861	12	attributed	attribute	VBD
37681	1861	13	the	the	DT
37681	1861	14	discovery	discovery	NN
37681	1861	15	of	of	IN
37681	1861	16	this	this	DT
37681	1861	17	proposition	proposition	NN
37681	1861	18	to	to	IN
37681	1861	19	Thales	Thales	NNPS
37681	1861	20	of	of	IN
37681	1861	21	Miletus	Miletus	NNP
37681	1861	22	(	(	-LRB-
37681	1861	23	_	_	NNP
37681	1861	24	ca	ca	NNP
37681	1861	25	.	.	.
37681	1861	26	_	_	NNP
37681	1861	27	640	640	CD
37681	1861	28	-	-	HYPH
37681	1861	29	548	548	CD
37681	1861	30	B.C.	B.C.	NNP
37681	1862	1	)	)	-RRB-
37681	1862	2	,	,	,
37681	1862	3	one	one	CD
37681	1862	4	of	of	IN
37681	1862	5	the	the	DT
37681	1862	6	Seven	Seven	NNP
37681	1862	7	Wise	Wise	NNP
37681	1862	8	Men	Men	NNPS
37681	1862	9	of	of	IN
37681	1862	10	Greece	Greece	NNP
37681	1862	11	,	,	,
37681	1862	12	of	of	IN
37681	1862	13	whom	whom	WP
37681	1862	14	Proclus	Proclus	NNP
37681	1862	15	wrote	write	VBD
37681	1862	16	:	:	:
37681	1862	17	"	"	``
37681	1862	18	Thales	thale	NNS
37681	1862	19	it	-PRON-	PRP
37681	1862	20	was	be	VBD
37681	1862	21	who	who	WP
37681	1862	22	visited	visit	VBD
37681	1862	23	Egypt	Egypt	NNP
37681	1862	24	and	and	CC
37681	1862	25	first	first	RB
37681	1862	26	transferred	transfer	VBN
37681	1862	27	to	to	IN
37681	1862	28	Hellenic	Hellenic	NNP
37681	1862	29	soil	soil	NN
37681	1862	30	this	this	DT
37681	1862	31	theory	theory	NN
37681	1862	32	of	of	IN
37681	1862	33	geometry	geometry	NN
37681	1862	34	.	.	.
37681	1863	1	He	-PRON-	PRP
37681	1863	2	himself	-PRON-	PRP
37681	1863	3	,	,	,
37681	1863	4	indeed	indeed	RB
37681	1863	5	,	,	,
37681	1863	6	discovered	discover	VBN
37681	1863	7	much	much	RB
37681	1863	8	,	,	,
37681	1863	9	but	but	CC
37681	1863	10	still	still	RB
37681	1863	11	more	more	RBR
37681	1863	12	did	do	VBD
37681	1863	13	he	-PRON-	PRP
37681	1863	14	introduce	introduce	VB
37681	1863	15	to	to	IN
37681	1863	16	his	-PRON-	PRP$
37681	1863	17	successors	successor	NNS
37681	1863	18	the	the	DT
37681	1863	19	principles	principle	NNS
37681	1863	20	of	of	IN
37681	1863	21	the	the	DT
37681	1863	22	science	science	NN
37681	1863	23	.	.	.
37681	1863	24	"	"	''
37681	1864	1	The	the	DT
37681	1864	2	proposition	proposition	NN
37681	1864	3	is	be	VBZ
37681	1864	4	the	the	DT
37681	1864	5	only	only	JJ
37681	1864	6	basal	basal	NN
37681	1864	7	one	one	CD
37681	1864	8	relating	relate	VBG
37681	1864	9	to	to	IN
37681	1864	10	the	the	DT
37681	1864	11	intersection	intersection	NN
37681	1864	12	of	of	IN
37681	1864	13	two	two	CD
37681	1864	14	lines	line	NNS
37681	1864	15	,	,	,
37681	1864	16	and	and	CC
37681	1864	17	hence	hence	RB
37681	1864	18	there	there	EX
37681	1864	19	are	be	VBP
37681	1864	20	no	no	DT
37681	1864	21	others	other	NNS
37681	1864	22	with	with	IN
37681	1864	23	which	which	WDT
37681	1864	24	it	-PRON-	PRP
37681	1864	25	is	be	VBZ
37681	1864	26	necessarily	necessarily	RB
37681	1864	27	grouped	group	VBN
37681	1864	28	.	.	.
37681	1865	1	This	this	DT
37681	1865	2	is	be	VBZ
37681	1865	3	the	the	DT
37681	1865	4	reason	reason	NN
37681	1865	5	for	for	IN
37681	1865	6	placing	place	VBG
37681	1865	7	it	-PRON-	PRP
37681	1865	8	by	by	IN
37681	1865	9	itself	-PRON-	PRP
37681	1865	10	,	,	,
37681	1865	11	followed	follow	VBN
37681	1865	12	by	by	IN
37681	1865	13	the	the	DT
37681	1865	14	congruence	congruence	NN
37681	1865	15	theorems	theorem	NNS
37681	1865	16	.	.	.
37681	1866	1	There	there	EX
37681	1866	2	are	be	VBP
37681	1866	3	many	many	JJ
37681	1866	4	familiar	familiar	JJ
37681	1866	5	illustrations	illustration	NNS
37681	1866	6	of	of	IN
37681	1866	7	this	this	DT
37681	1866	8	theorem	theorem	NN
37681	1866	9	.	.	.
37681	1867	1	Indeed	indeed	RB
37681	1867	2	,	,	,
37681	1867	3	any	any	DT
37681	1867	4	two	two	CD
37681	1867	5	crossed	cross	VBN
37681	1867	6	lines	line	NNS
37681	1867	7	,	,	,
37681	1867	8	as	as	IN
37681	1867	9	in	in	IN
37681	1867	10	a	a	DT
37681	1867	11	pair	pair	NN
37681	1867	12	of	of	IN
37681	1867	13	shears	shear	NNS
37681	1867	14	or	or	CC
37681	1867	15	the	the	DT
37681	1867	16	legs	leg	NNS
37681	1867	17	of	of	IN
37681	1867	18	a	a	DT
37681	1867	19	camp	camp	NN
37681	1867	20	stool	stool	NN
37681	1867	21	,	,	,
37681	1867	22	bring	bring	VB
37681	1867	23	it	-PRON-	PRP
37681	1867	24	to	to	IN
37681	1867	25	mind	mind	NN
37681	1867	26	.	.	.
37681	1868	1	The	the	DT
37681	1868	2	word	word	NN
37681	1868	3	"	"	``
37681	1868	4	straight	straight	NN
37681	1868	5	"	"	''
37681	1868	6	is	be	VBZ
37681	1868	7	here	here	RB
37681	1868	8	omitted	omit	VBN
37681	1868	9	before	before	IN
37681	1868	10	"	"	``
37681	1868	11	lines	line	NNS
37681	1868	12	"	"	''
37681	1868	13	in	in	IN
37681	1868	14	accordance	accordance	NN
37681	1868	15	with	with	IN
37681	1868	16	the	the	DT
37681	1868	17	modern	modern	JJ
37681	1868	18	convention	convention	NN
37681	1868	19	that	that	IN
37681	1868	20	the	the	DT
37681	1868	21	word	word	NN
37681	1868	22	"	"	``
37681	1868	23	line	line	NN
37681	1868	24	"	"	''
37681	1868	25	unmodified	unmodified	JJ
37681	1868	26	means	mean	VBZ
37681	1868	27	a	a	DT
37681	1868	28	straight	straight	JJ
37681	1868	29	line	line	NN
37681	1868	30	.	.	.
37681	1869	1	Of	of	RB
37681	1869	2	course	course	RB
37681	1869	3	in	in	IN
37681	1869	4	cases	case	NNS
37681	1869	5	of	of	IN
37681	1869	6	special	special	JJ
37681	1869	7	emphasis	emphasis	NN
37681	1869	8	the	the	DT
37681	1869	9	adjective	adjective	NN
37681	1869	10	should	should	MD
37681	1869	11	be	be	VB
37681	1869	12	used	use	VBN
37681	1869	13	.	.	.
37681	1870	1	THEOREM	THEOREM	NNP
37681	1870	2	.	.	.
37681	1871	1	_	_	NNP
37681	1871	2	Two	two	CD
37681	1871	3	triangles	triangle	NNS
37681	1871	4	are	be	VBP
37681	1871	5	congruent	congruent	JJ
37681	1871	6	if	if	IN
37681	1871	7	two	two	CD
37681	1871	8	sides	side	NNS
37681	1871	9	and	and	CC
37681	1871	10	the	the	DT
37681	1871	11	included	included	JJ
37681	1871	12	angle	angle	NN
37681	1871	13	of	of	IN
37681	1871	14	the	the	DT
37681	1871	15	one	one	NN
37681	1871	16	are	be	VBP
37681	1871	17	equal	equal	JJ
37681	1871	18	respectively	respectively	RB
37681	1871	19	to	to	IN
37681	1871	20	two	two	CD
37681	1871	21	sides	side	NNS
37681	1871	22	and	and	CC
37681	1871	23	the	the	DT
37681	1871	24	included	included	JJ
37681	1871	25	angle	angle	NN
37681	1871	26	of	of	IN
37681	1871	27	the	the	DT
37681	1871	28	other	other	JJ
37681	1871	29	.	.	.
37681	1871	30	_	_	NNP
37681	1871	31	This	this	DT
37681	1871	32	is	be	VBZ
37681	1871	33	Euclid	Euclid	NNP
37681	1871	34	's	's	POS
37681	1871	35	Proposition	Proposition	NNP
37681	1871	36	4	4	CD
37681	1871	37	,	,	,
37681	1871	38	his	-PRON-	PRP$
37681	1871	39	first	first	JJ
37681	1871	40	three	three	CD
37681	1871	41	propositions	proposition	NNS
37681	1871	42	being	be	VBG
37681	1871	43	problems	problem	NNS
37681	1871	44	of	of	IN
37681	1871	45	construction	construction	NN
37681	1871	46	.	.	.
37681	1872	1	This	this	DT
37681	1872	2	would	would	MD
37681	1872	3	therefore	therefore	RB
37681	1872	4	have	have	VB
37681	1872	5	been	be	VBN
37681	1872	6	his	-PRON-	PRP$
37681	1872	7	first	first	JJ
37681	1872	8	proposition	proposition	NN
37681	1872	9	if	if	IN
37681	1872	10	he	-PRON-	PRP
37681	1872	11	had	have	VBD
37681	1872	12	placed	place	VBN
37681	1872	13	his	-PRON-	PRP$
37681	1872	14	problems	problem	NNS
37681	1872	15	later	later	RB
37681	1872	16	,	,	,
37681	1872	17	as	as	IN
37681	1872	18	we	-PRON-	PRP
37681	1872	19	do	do	VBP
37681	1872	20	to	to	IN
37681	1872	21	-	-	HYPH
37681	1872	22	day	day	NN
37681	1872	23	.	.	.
37681	1873	1	The	the	DT
37681	1873	2	words	word	NNS
37681	1873	3	"	"	``
37681	1873	4	congruent	congruent	JJ
37681	1873	5	"	"	''
37681	1873	6	and	and	CC
37681	1873	7	"	"	``
37681	1873	8	equal	equal	JJ
37681	1873	9	"	"	''
37681	1873	10	are	be	VBP
37681	1873	11	not	not	RB
37681	1873	12	used	use	VBN
37681	1873	13	as	as	IN
37681	1873	14	in	in	IN
37681	1873	15	Euclid	Euclid	NNP
37681	1873	16	,	,	,
37681	1873	17	for	for	IN
37681	1873	18	reasons	reason	NNS
37681	1873	19	already	already	RB
37681	1873	20	set	set	VBN
37681	1873	21	forth	forth	RP
37681	1873	22	on	on	IN
37681	1873	23	page	page	NN
37681	1873	24	151	151	CD
37681	1873	25	.	.	.
37681	1874	1	There	there	EX
37681	1874	2	have	have	VBP
37681	1874	3	been	be	VBN
37681	1874	4	many	many	JJ
37681	1874	5	attempts	attempt	NNS
37681	1874	6	to	to	TO
37681	1874	7	rearrange	rearrange	VB
37681	1874	8	the	the	DT
37681	1874	9	propositions	proposition	NNS
37681	1874	10	of	of	IN
37681	1874	11	Book	Book	NNP
37681	1874	12	I	-PRON-	PRP
37681	1874	13	,	,	,
37681	1874	14	putting	put	VBG
37681	1874	15	in	in	RP
37681	1874	16	separate	separate	JJ
37681	1874	17	groups	group	NNS
37681	1874	18	those	those	DT
37681	1874	19	concerning	concern	VBG
37681	1874	20	angles	angle	NNS
37681	1874	21	,	,	,
37681	1874	22	those	those	DT
37681	1874	23	concerning	concern	VBG
37681	1874	24	triangles	triangle	NNS
37681	1874	25	,	,	,
37681	1874	26	and	and	CC
37681	1874	27	those	those	DT
37681	1874	28	concerning	concern	VBG
37681	1874	29	parallels	parallel	NNS
37681	1874	30	,	,	,
37681	1874	31	but	but	CC
37681	1874	32	they	-PRON-	PRP
37681	1874	33	have	have	VBP
37681	1874	34	all	all	RB
37681	1874	35	failed	fail	VBN
37681	1874	36	,	,	,
37681	1874	37	and	and	CC
37681	1874	38	for	for	IN
37681	1874	39	the	the	DT
37681	1874	40	cogent	cogent	JJ
37681	1874	41	reason	reason	NN
37681	1874	42	that	that	IN
37681	1874	43	such	such	PDT
37681	1874	44	a	a	DT
37681	1874	45	scheme	scheme	NN
37681	1874	46	destroys	destroy	VBZ
37681	1874	47	the	the	DT
37681	1874	48	logical	logical	JJ
37681	1874	49	sequence	sequence	NN
37681	1874	50	.	.	.
37681	1875	1	This	this	DT
37681	1875	2	proposition	proposition	NN
37681	1875	3	may	may	MD
37681	1875	4	properly	properly	RB
37681	1875	5	follow	follow	VB
37681	1875	6	the	the	DT
37681	1875	7	one	one	CD
37681	1875	8	on	on	IN
37681	1875	9	vertical	vertical	JJ
37681	1875	10	angles	angle	NNS
37681	1875	11	simply	simply	RB
37681	1875	12	because	because	IN
37681	1875	13	the	the	DT
37681	1875	14	latter	latter	NN
37681	1875	15	is	be	VBZ
37681	1875	16	easier	easy	JJR
37681	1875	17	and	and	CC
37681	1875	18	does	do	VBZ
37681	1875	19	not	not	RB
37681	1875	20	involve	involve	VB
37681	1875	21	superposition	superposition	NN
37681	1875	22	.	.	.
37681	1876	1	As	as	RB
37681	1876	2	far	far	RB
37681	1876	3	as	as	IN
37681	1876	4	possible	possible	JJ
37681	1876	5	,	,	,
37681	1876	6	Euclid	euclid	JJ
37681	1876	7	and	and	CC
37681	1876	8	all	all	DT
37681	1876	9	other	other	JJ
37681	1876	10	good	good	JJ
37681	1876	11	geometers	geometer	NNS
37681	1876	12	avoid	avoid	VBP
37681	1876	13	the	the	DT
37681	1876	14	proof	proof	NN
37681	1876	15	by	by	IN
37681	1876	16	superposition	superposition	NN
37681	1876	17	.	.	.
37681	1877	1	As	as	IN
37681	1877	2	a	a	DT
37681	1877	3	practical	practical	JJ
37681	1877	4	test	test	NN
37681	1877	5	superposition	superposition	NN
37681	1877	6	is	be	VBZ
37681	1877	7	valuable	valuable	JJ
37681	1877	8	,	,	,
37681	1877	9	but	but	CC
37681	1877	10	as	as	IN
37681	1877	11	a	a	DT
37681	1877	12	theoretical	theoretical	JJ
37681	1877	13	one	one	NN
37681	1877	14	it	-PRON-	PRP
37681	1877	15	is	be	VBZ
37681	1877	16	open	open	JJ
37681	1877	17	to	to	IN
37681	1877	18	numerous	numerous	JJ
37681	1877	19	objections	objection	NNS
37681	1877	20	.	.	.
37681	1878	1	As	as	IN
37681	1878	2	Peletier	Peletier	NNP
37681	1878	3	pointed	point	VBD
37681	1878	4	out	out	RP
37681	1878	5	in	in	IN
37681	1878	6	his	-PRON-	PRP$
37681	1878	7	(	(	-LRB-
37681	1878	8	1557	1557	CD
37681	1878	9	)	)	-RRB-
37681	1878	10	edition	edition	NN
37681	1878	11	of	of	IN
37681	1878	12	Euclid	Euclid	NNP
37681	1878	13	,	,	,
37681	1878	14	if	if	IN
37681	1878	15	the	the	DT
37681	1878	16	superposition	superposition	NN
37681	1878	17	of	of	IN
37681	1878	18	lines	line	NNS
37681	1878	19	and	and	CC
37681	1878	20	figures	figure	NNS
37681	1878	21	could	could	MD
37681	1878	22	freely	freely	RB
37681	1878	23	be	be	VB
37681	1878	24	assumed	assume	VBN
37681	1878	25	as	as	IN
37681	1878	26	a	a	DT
37681	1878	27	method	method	NN
37681	1878	28	of	of	IN
37681	1878	29	demonstration	demonstration	NN
37681	1878	30	,	,	,
37681	1878	31	geometry	geometry	NN
37681	1878	32	would	would	MD
37681	1878	33	be	be	VB
37681	1878	34	full	full	JJ
37681	1878	35	of	of	IN
37681	1878	36	such	such	JJ
37681	1878	37	proofs	proof	NNS
37681	1878	38	.	.	.
37681	1879	1	There	there	EX
37681	1879	2	would	would	MD
37681	1879	3	be	be	VB
37681	1879	4	no	no	DT
37681	1879	5	reason	reason	NN
37681	1879	6	,	,	,
37681	1879	7	for	for	IN
37681	1879	8	example	example	NN
37681	1879	9	,	,	,
37681	1879	10	why	why	WRB
37681	1879	11	an	an	DT
37681	1879	12	angle	angle	NN
37681	1879	13	should	should	MD
37681	1879	14	not	not	RB
37681	1879	15	be	be	VB
37681	1879	16	constructed	construct	VBN
37681	1879	17	equal	equal	JJ
37681	1879	18	to	to	IN
37681	1879	19	a	a	DT
37681	1879	20	given	give	VBN
37681	1879	21	angle	angle	NN
37681	1879	22	by	by	IN
37681	1879	23	superposing	superpose	VBG
37681	1879	24	the	the	DT
37681	1879	25	given	give	VBN
37681	1879	26	angle	angle	NN
37681	1879	27	on	on	IN
37681	1879	28	another	another	DT
37681	1879	29	part	part	NN
37681	1879	30	of	of	IN
37681	1879	31	the	the	DT
37681	1879	32	plane	plane	NN
37681	1879	33	.	.	.
37681	1880	1	Indeed	indeed	RB
37681	1880	2	,	,	,
37681	1880	3	it	-PRON-	PRP
37681	1880	4	is	be	VBZ
37681	1880	5	possible	possible	JJ
37681	1880	6	that	that	IN
37681	1880	7	we	-PRON-	PRP
37681	1880	8	might	may	MD
37681	1880	9	then	then	RB
37681	1880	10	assume	assume	VB
37681	1880	11	to	to	TO
37681	1880	12	bisect	bisect	VB
37681	1880	13	an	an	DT
37681	1880	14	angle	angle	NN
37681	1880	15	by	by	IN
37681	1880	16	imagining	imagine	VBG
37681	1880	17	the	the	DT
37681	1880	18	plane	plane	NN
37681	1880	19	folded	fold	VBN
37681	1880	20	like	like	IN
37681	1880	21	a	a	DT
37681	1880	22	piece	piece	NN
37681	1880	23	of	of	IN
37681	1880	24	paper	paper	NN
37681	1880	25	.	.	.
37681	1881	1	Heath	Heath	NNP
37681	1881	2	(	(	-LRB-
37681	1881	3	1908	1908	CD
37681	1881	4	)	)	-RRB-
37681	1881	5	has	have	VBZ
37681	1881	6	pointed	point	VBN
37681	1881	7	out	out	RP
37681	1881	8	a	a	DT
37681	1881	9	subtle	subtle	JJ
37681	1881	10	defect	defect	NN
37681	1881	11	in	in	IN
37681	1881	12	Euclid	Euclid	NNP
37681	1881	13	's	's	POS
37681	1881	14	proof	proof	NN
37681	1881	15	,	,	,
37681	1881	16	in	in	IN
37681	1881	17	that	that	IN
37681	1881	18	it	-PRON-	PRP
37681	1881	19	is	be	VBZ
37681	1881	20	said	say	VBN
37681	1881	21	that	that	IN
37681	1881	22	because	because	IN
37681	1881	23	two	two	CD
37681	1881	24	lines	line	NNS
37681	1881	25	are	be	VBP
37681	1881	26	equal	equal	JJ
37681	1881	27	,	,	,
37681	1881	28	they	-PRON-	PRP
37681	1881	29	can	can	MD
37681	1881	30	be	be	VB
37681	1881	31	made	make	VBN
37681	1881	32	to	to	TO
37681	1881	33	coincide	coincide	VB
37681	1881	34	.	.	.
37681	1882	1	Euclid	Euclid	NNP
37681	1882	2	says	say	VBZ
37681	1882	3	,	,	,
37681	1882	4	practically	practically	RB
37681	1882	5	,	,	,
37681	1882	6	that	that	IN
37681	1882	7	if	if	IN
37681	1882	8	two	two	CD
37681	1882	9	lines	line	NNS
37681	1882	10	can	can	MD
37681	1882	11	be	be	VB
37681	1882	12	made	make	VBN
37681	1882	13	to	to	TO
37681	1882	14	coincide	coincide	VB
37681	1882	15	,	,	,
37681	1882	16	they	-PRON-	PRP
37681	1882	17	are	be	VBP
37681	1882	18	equal	equal	JJ
37681	1882	19	,	,	,
37681	1882	20	but	but	CC
37681	1882	21	he	-PRON-	PRP
37681	1882	22	does	do	VBZ
37681	1882	23	not	not	RB
37681	1882	24	say	say	VB
37681	1882	25	that	that	IN
37681	1882	26	if	if	IN
37681	1882	27	two	two	CD
37681	1882	28	straight	straight	JJ
37681	1882	29	lines	line	NNS
37681	1882	30	are	be	VBP
37681	1882	31	equal	equal	JJ
37681	1882	32	,	,	,
37681	1882	33	they	-PRON-	PRP
37681	1882	34	can	can	MD
37681	1882	35	be	be	VB
37681	1882	36	made	make	VBN
37681	1882	37	to	to	TO
37681	1882	38	coincide	coincide	VB
37681	1882	39	.	.	.
37681	1883	1	For	for	IN
37681	1883	2	the	the	DT
37681	1883	3	purposes	purpose	NNS
37681	1883	4	of	of	IN
37681	1883	5	elementary	elementary	JJ
37681	1883	6	geometry	geometry	NN
37681	1883	7	the	the	DT
37681	1883	8	matter	matter	NN
37681	1883	9	is	be	VBZ
37681	1883	10	hardly	hardly	RB
37681	1883	11	worth	worth	JJ
37681	1883	12	bringing	bring	VBG
37681	1883	13	to	to	IN
37681	1883	14	the	the	DT
37681	1883	15	attention	attention	NN
37681	1883	16	of	of	IN
37681	1883	17	a	a	DT
37681	1883	18	pupil	pupil	NN
37681	1883	19	,	,	,
37681	1883	20	but	but	CC
37681	1883	21	it	-PRON-	PRP
37681	1883	22	shows	show	VBZ
37681	1883	23	that	that	IN
37681	1883	24	even	even	RB
37681	1883	25	Euclid	Euclid	NNP
37681	1883	26	did	do	VBD
37681	1883	27	not	not	RB
37681	1883	28	cover	cover	VB
37681	1883	29	every	every	DT
37681	1883	30	point	point	NN
37681	1883	31	.	.	.
37681	1884	1	Applications	application	NNS
37681	1884	2	of	of	IN
37681	1884	3	this	this	DT
37681	1884	4	proposition	proposition	NN
37681	1884	5	are	be	VBP
37681	1884	6	easily	easily	RB
37681	1884	7	found	find	VBN
37681	1884	8	,	,	,
37681	1884	9	but	but	CC
37681	1884	10	they	-PRON-	PRP
37681	1884	11	are	be	VBP
37681	1884	12	all	all	RB
37681	1884	13	very	very	RB
37681	1884	14	much	much	RB
37681	1884	15	alike	alike	RB
37681	1884	16	.	.	.
37681	1885	1	There	there	EX
37681	1885	2	are	be	VBP
37681	1885	3	dozens	dozen	NNS
37681	1885	4	of	of	IN
37681	1885	5	measurements	measurement	NNS
37681	1885	6	that	that	WDT
37681	1885	7	can	can	MD
37681	1885	8	be	be	VB
37681	1885	9	made	make	VBN
37681	1885	10	by	by	IN
37681	1885	11	simply	simply	RB
37681	1885	12	constructing	construct	VBG
37681	1885	13	a	a	DT
37681	1885	14	triangle	triangle	NN
37681	1885	15	that	that	WDT
37681	1885	16	shall	shall	MD
37681	1885	17	be	be	VB
37681	1885	18	congruent	congruent	JJ
37681	1885	19	to	to	IN
37681	1885	20	another	another	DT
37681	1885	21	triangle	triangle	NN
37681	1885	22	.	.	.
37681	1886	1	It	-PRON-	PRP
37681	1886	2	seems	seem	VBZ
37681	1886	3	hardly	hardly	RB
37681	1886	4	worth	worth	JJ
37681	1886	5	the	the	DT
37681	1886	6	while	while	NN
37681	1886	7	at	at	IN
37681	1886	8	this	this	DT
37681	1886	9	time	time	NN
37681	1886	10	to	to	TO
37681	1886	11	do	do	VB
37681	1886	12	more	more	JJR
37681	1886	13	than	than	IN
37681	1886	14	mention	mention	VB
37681	1886	15	one	one	CD
37681	1886	16	typical	typical	JJ
37681	1886	17	case,[59	case,[59	NN
37681	1886	18	]	]	-RRB-
37681	1886	19	leaving	leave	VBG
37681	1886	20	it	-PRON-	PRP
37681	1886	21	to	to	IN
37681	1886	22	teachers	teacher	NNS
37681	1886	23	who	who	WP
37681	1886	24	may	may	MD
37681	1886	25	find	find	VB
37681	1886	26	it	-PRON-	PRP
37681	1886	27	desirable	desirable	JJ
37681	1886	28	to	to	TO
37681	1886	29	suggest	suggest	VB
37681	1886	30	others	other	NNS
37681	1886	31	to	to	IN
37681	1886	32	their	-PRON-	PRP$
37681	1886	33	pupils	pupil	NNS
37681	1886	34	.	.	.
37681	1887	1	[	[	-LRB-
37681	1887	2	Illustration	illustration	NN
37681	1887	3	]	]	-RRB-
37681	1887	4	Wishing	wish	VBG
37681	1887	5	to	to	TO
37681	1887	6	measure	measure	VB
37681	1887	7	the	the	DT
37681	1887	8	distance	distance	NN
37681	1887	9	across	across	IN
37681	1887	10	a	a	DT
37681	1887	11	river	river	NN
37681	1887	12	,	,	,
37681	1887	13	some	some	DT
37681	1887	14	boys	boy	NNS
37681	1887	15	sighted	sight	VBD
37681	1887	16	from	from	IN
37681	1887	17	_	_	NNP
37681	1887	18	A	A	NNP
37681	1887	19	_	_	NNP
37681	1887	20	to	to	IN
37681	1887	21	a	a	DT
37681	1887	22	point	point	NN
37681	1887	23	_	_	NNP
37681	1887	24	P	P	NNP
37681	1887	25	_	_	NNP
37681	1887	26	.	.	.
37681	1888	1	They	-PRON-	PRP
37681	1888	2	then	then	RB
37681	1888	3	turned	turn	VBD
37681	1888	4	and	and	CC
37681	1888	5	measured	measure	VBN
37681	1888	6	_	_	NNP
37681	1888	7	AB	AB	NNP
37681	1888	8	_	_	NNP
37681	1888	9	at	at	IN
37681	1888	10	right	right	JJ
37681	1888	11	angles	angle	NNS
37681	1888	12	to	to	IN
37681	1888	13	_	_	NNP
37681	1888	14	AP	AP	NNP
37681	1888	15	_	_	NNP
37681	1888	16	.	.	.
37681	1889	1	They	-PRON-	PRP
37681	1889	2	placed	place	VBD
37681	1889	3	a	a	DT
37681	1889	4	stake	stake	NN
37681	1889	5	at	at	IN
37681	1889	6	_	_	NNP
37681	1889	7	O	O	NNP
37681	1889	8	_	_	NNP
37681	1889	9	,	,	,
37681	1889	10	halfway	halfway	RB
37681	1889	11	from	from	IN
37681	1889	12	_	_	NNP
37681	1889	13	A	A	NNP
37681	1889	14	_	_	NNP
37681	1889	15	to	to	IN
37681	1889	16	_	_	NNP
37681	1889	17	B	B	NNP
37681	1889	18	_	_	NNP
37681	1889	19	,	,	,
37681	1889	20	and	and	CC
37681	1889	21	drew	draw	VBD
37681	1889	22	a	a	DT
37681	1889	23	perpendicular	perpendicular	NN
37681	1889	24	to	to	IN
37681	1889	25	_	_	NNP
37681	1889	26	AB	AB	NNP
37681	1889	27	_	_	NNP
37681	1889	28	at	at	IN
37681	1889	29	_	_	NNP
37681	1889	30	B	B	NNP
37681	1889	31	_	_	NNP
37681	1889	32	.	.	.
37681	1890	1	They	-PRON-	PRP
37681	1890	2	placed	place	VBD
37681	1890	3	a	a	DT
37681	1890	4	stake	stake	NN
37681	1890	5	at	at	IN
37681	1890	6	_	_	NNP
37681	1890	7	C	C	NNP
37681	1890	8	_	_	NNP
37681	1890	9	,	,	,
37681	1890	10	on	on	IN
37681	1890	11	this	this	DT
37681	1890	12	perpendicular	perpendicular	NN
37681	1890	13	,	,	,
37681	1890	14	and	and	CC
37681	1890	15	in	in	IN
37681	1890	16	line	line	NN
37681	1890	17	with	with	IN
37681	1890	18	_	_	NNP
37681	1890	19	O	O	NNP
37681	1890	20	_	_	NNP
37681	1890	21	and	and	CC
37681	1890	22	_	_	NNP
37681	1890	23	P	P	NNP
37681	1890	24	_	_	NNP
37681	1890	25	.	.	.
37681	1891	1	They	-PRON-	PRP
37681	1891	2	then	then	RB
37681	1891	3	found	find	VBD
37681	1891	4	the	the	DT
37681	1891	5	width	width	NN
37681	1891	6	by	by	IN
37681	1891	7	measuring	measure	VBG
37681	1891	8	_	_	NNP
37681	1891	9	BC	BC	NNP
37681	1891	10	_	_	NNP
37681	1891	11	.	.	.
37681	1892	1	Prove	prove	VB
37681	1892	2	that	that	IN
37681	1892	3	they	-PRON-	PRP
37681	1892	4	were	be	VBD
37681	1892	5	right	right	JJ
37681	1892	6	.	.	.
37681	1893	1	This	this	DT
37681	1893	2	involves	involve	VBZ
37681	1893	3	the	the	DT
37681	1893	4	ranging	ranging	NN
37681	1893	5	of	of	IN
37681	1893	6	a	a	DT
37681	1893	7	line	line	NN
37681	1893	8	,	,	,
37681	1893	9	and	and	CC
37681	1893	10	the	the	DT
37681	1893	11	running	running	NN
37681	1893	12	of	of	IN
37681	1893	13	a	a	DT
37681	1893	14	line	line	NN
37681	1893	15	at	at	IN
37681	1893	16	right	right	JJ
37681	1893	17	angles	angle	NNS
37681	1893	18	to	to	IN
37681	1893	19	a	a	DT
37681	1893	20	given	give	VBN
37681	1893	21	line	line	NN
37681	1893	22	,	,	,
37681	1893	23	both	both	DT
37681	1893	24	of	of	IN
37681	1893	25	which	which	WDT
37681	1893	26	have	have	VBP
37681	1893	27	been	be	VBN
37681	1893	28	described	describe	VBN
37681	1893	29	in	in	IN
37681	1893	30	Chapter	Chapter	NNP
37681	1893	31	IX	IX	NNP
37681	1893	32	.	.	.
37681	1894	1	It	-PRON-	PRP
37681	1894	2	is	be	VBZ
37681	1894	3	also	also	RB
37681	1894	4	fairly	fairly	RB
37681	1894	5	accurate	accurate	JJ
37681	1894	6	to	to	TO
37681	1894	7	run	run	VB
37681	1894	8	a	a	DT
37681	1894	9	line	line	NN
37681	1894	10	at	at	IN
37681	1894	11	any	any	DT
37681	1894	12	angle	angle	NN
37681	1894	13	to	to	IN
37681	1894	14	a	a	DT
37681	1894	15	given	give	VBN
37681	1894	16	line	line	NN
37681	1894	17	by	by	IN
37681	1894	18	sighting	sight	VBG
37681	1894	19	along	along	RB
37681	1894	20	two	two	CD
37681	1894	21	pins	pin	NNS
37681	1894	22	stuck	stick	VBN
37681	1894	23	in	in	IN
37681	1894	24	a	a	DT
37681	1894	25	protractor	protractor	NN
37681	1894	26	.	.	.
37681	1895	1	THEOREM	THEOREM	NNP
37681	1895	2	.	.	.
37681	1896	1	_	_	NNP
37681	1896	2	Two	two	CD
37681	1896	3	triangles	triangle	NNS
37681	1896	4	are	be	VBP
37681	1896	5	congruent	congruent	JJ
37681	1896	6	if	if	IN
37681	1896	7	two	two	CD
37681	1896	8	angles	angle	NNS
37681	1896	9	and	and	CC
37681	1896	10	the	the	DT
37681	1896	11	included	include	VBN
37681	1896	12	side	side	NN
37681	1896	13	of	of	IN
37681	1896	14	the	the	DT
37681	1896	15	one	one	NN
37681	1896	16	are	be	VBP
37681	1896	17	equal	equal	JJ
37681	1896	18	respectively	respectively	RB
37681	1896	19	to	to	IN
37681	1896	20	two	two	CD
37681	1896	21	angles	angle	NNS
37681	1896	22	and	and	CC
37681	1896	23	the	the	DT
37681	1896	24	included	include	VBN
37681	1896	25	side	side	NN
37681	1896	26	of	of	IN
37681	1896	27	the	the	DT
37681	1896	28	other	other	JJ
37681	1896	29	.	.	.
37681	1896	30	_	_	NNP
37681	1896	31	Euclid	Euclid	NNP
37681	1896	32	combines	combine	VBZ
37681	1896	33	this	this	DT
37681	1896	34	with	with	IN
37681	1896	35	his	-PRON-	PRP$
37681	1896	36	Proposition	Proposition	NNP
37681	1896	37	26	26	CD
37681	1896	38	:	:	:
37681	1896	39	If	if	IN
37681	1896	40	two	two	CD
37681	1896	41	triangles	triangle	NNS
37681	1896	42	have	have	VBP
37681	1896	43	the	the	DT
37681	1896	44	two	two	CD
37681	1896	45	angles	angle	NNS
37681	1896	46	equal	equal	JJ
37681	1896	47	to	to	IN
37681	1896	48	two	two	CD
37681	1896	49	angles	angle	NNS
37681	1896	50	respectively	respectively	RB
37681	1896	51	,	,	,
37681	1896	52	and	and	CC
37681	1896	53	one	one	CD
37681	1896	54	side	side	NN
37681	1896	55	equal	equal	JJ
37681	1896	56	to	to	IN
37681	1896	57	one	one	CD
37681	1896	58	side	side	NN
37681	1896	59	,	,	,
37681	1896	60	namely	namely	RB
37681	1896	61	,	,	,
37681	1896	62	either	either	CC
37681	1896	63	the	the	DT
37681	1896	64	side	side	NN
37681	1896	65	adjoining	adjoin	VBG
37681	1896	66	the	the	DT
37681	1896	67	equal	equal	JJ
37681	1896	68	angles	angle	NNS
37681	1896	69	,	,	,
37681	1896	70	or	or	CC
37681	1896	71	that	that	IN
37681	1896	72	subtending	subtend	VBG
37681	1896	73	one	one	CD
37681	1896	74	of	of	IN
37681	1896	75	the	the	DT
37681	1896	76	equal	equal	JJ
37681	1896	77	angles	angle	NNS
37681	1896	78	,	,	,
37681	1896	79	they	-PRON-	PRP
37681	1896	80	will	will	MD
37681	1896	81	also	also	RB
37681	1896	82	have	have	VB
37681	1896	83	the	the	DT
37681	1896	84	remaining	remain	VBG
37681	1896	85	sides	side	NNS
37681	1896	86	equal	equal	JJ
37681	1896	87	to	to	IN
37681	1896	88	the	the	DT
37681	1896	89	remaining	remain	VBG
37681	1896	90	sides	side	NNS
37681	1896	91	,	,	,
37681	1896	92	and	and	CC
37681	1896	93	the	the	DT
37681	1896	94	remaining	remain	VBG
37681	1896	95	angle	angle	NN
37681	1896	96	to	to	IN
37681	1896	97	the	the	DT
37681	1896	98	remaining	remain	VBG
37681	1896	99	angle	angle	NN
37681	1896	100	.	.	.
37681	1897	1	He	-PRON-	PRP
37681	1897	2	proves	prove	VBZ
37681	1897	3	this	this	DT
37681	1897	4	cumbersome	cumbersome	JJ
37681	1897	5	statement	statement	NN
37681	1897	6	without	without	IN
37681	1897	7	superposition	superposition	NN
37681	1897	8	,	,	,
37681	1897	9	desiring	desire	VBG
37681	1897	10	to	to	TO
37681	1897	11	avoid	avoid	VB
37681	1897	12	this	this	DT
37681	1897	13	method	method	NN
37681	1897	14	,	,	,
37681	1897	15	as	as	IN
37681	1897	16	already	already	RB
37681	1897	17	stated	state	VBN
37681	1897	18	,	,	,
37681	1897	19	whenever	whenever	WRB
37681	1897	20	possible	possible	JJ
37681	1897	21	.	.	.
37681	1898	1	The	the	DT
37681	1898	2	proof	proof	NN
37681	1898	3	by	by	IN
37681	1898	4	superposition	superposition	NN
37681	1898	5	is	be	VBZ
37681	1898	6	old	old	JJ
37681	1898	7	,	,	,
37681	1898	8	however	however	RB
37681	1898	9	,	,	,
37681	1898	10	for	for	IN
37681	1898	11	Al	Al	NNP
37681	1898	12	-	-	HYPH
37681	1898	13	Nair[=i]z[=i][60	Nair[=i]z[=i][60	NNP
37681	1898	14	]	]	-RRB-
37681	1898	15	gives	give	VBZ
37681	1898	16	it	-PRON-	PRP
37681	1898	17	and	and	CC
37681	1898	18	ascribes	ascribe	VBZ
37681	1898	19	it	-PRON-	PRP
37681	1898	20	to	to	IN
37681	1898	21	some	some	DT
37681	1898	22	earlier	early	JJR
37681	1898	23	author	author	NN
37681	1898	24	whose	whose	WP$
37681	1898	25	name	name	NN
37681	1898	26	he	-PRON-	PRP
37681	1898	27	did	do	VBD
37681	1898	28	not	not	RB
37681	1898	29	know	know	VB
37681	1898	30	.	.	.
37681	1899	1	Proclus	Proclus	NNP
37681	1899	2	tells	tell	VBZ
37681	1899	3	us	-PRON-	PRP
37681	1899	4	that	that	IN
37681	1899	5	"	"	``
37681	1899	6	Eudemus	Eudemus	NNP
37681	1899	7	in	in	IN
37681	1899	8	his	-PRON-	PRP$
37681	1899	9	geometrical	geometrical	JJ
37681	1899	10	history	history	NN
37681	1899	11	refers	refer	VBZ
37681	1899	12	this	this	DT
37681	1899	13	theorem	theorem	NN
37681	1899	14	to	to	IN
37681	1899	15	Thales	thale	NNS
37681	1899	16	.	.	.
37681	1900	1	For	for	IN
37681	1900	2	he	-PRON-	PRP
37681	1900	3	says	say	VBZ
37681	1900	4	that	that	IN
37681	1900	5	in	in	IN
37681	1900	6	the	the	DT
37681	1900	7	method	method	NN
37681	1900	8	by	by	IN
37681	1900	9	which	which	WDT
37681	1900	10	they	-PRON-	PRP
37681	1900	11	say	say	VBP
37681	1900	12	that	that	IN
37681	1900	13	Thales	thale	NNS
37681	1900	14	proved	prove	VBD
37681	1900	15	the	the	DT
37681	1900	16	distance	distance	NN
37681	1900	17	of	of	IN
37681	1900	18	ships	ship	NNS
37681	1900	19	in	in	IN
37681	1900	20	the	the	DT
37681	1900	21	sea	sea	NN
37681	1900	22	,	,	,
37681	1900	23	it	-PRON-	PRP
37681	1900	24	was	be	VBD
37681	1900	25	necessary	necessary	JJ
37681	1900	26	to	to	TO
37681	1900	27	make	make	VB
37681	1900	28	use	use	NN
37681	1900	29	of	of	IN
37681	1900	30	this	this	DT
37681	1900	31	theorem	theorem	NN
37681	1900	32	.	.	.
37681	1900	33	"	"	''
37681	1901	1	How	how	WRB
37681	1901	2	Thales	Thales	NNPS
37681	1901	3	did	do	VBD
37681	1901	4	this	this	DT
37681	1901	5	is	be	VBZ
37681	1901	6	purely	purely	RB
37681	1901	7	a	a	DT
37681	1901	8	matter	matter	NN
37681	1901	9	of	of	IN
37681	1901	10	conjecture	conjecture	NN
37681	1901	11	,	,	,
37681	1901	12	but	but	CC
37681	1901	13	he	-PRON-	PRP
37681	1901	14	might	may	MD
37681	1901	15	have	have	VB
37681	1901	16	stood	stand	VBN
37681	1901	17	on	on	IN
37681	1901	18	the	the	DT
37681	1901	19	top	top	NN
37681	1901	20	of	of	IN
37681	1901	21	a	a	DT
37681	1901	22	tower	tower	NN
37681	1901	23	rising	rise	VBG
37681	1901	24	from	from	IN
37681	1901	25	the	the	DT
37681	1901	26	level	level	NN
37681	1901	27	shore	shore	NN
37681	1901	28	,	,	,
37681	1901	29	or	or	CC
37681	1901	30	of	of	IN
37681	1901	31	such	such	JJ
37681	1901	32	headlands	headland	NNS
37681	1901	33	as	as	IN
37681	1901	34	abound	abound	NN
37681	1901	35	near	near	IN
37681	1901	36	Miletus	Miletus	NNP
37681	1901	37	,	,	,
37681	1901	38	and	and	CC
37681	1901	39	by	by	IN
37681	1901	40	some	some	DT
37681	1901	41	simple	simple	JJ
37681	1901	42	instrument	instrument	NN
37681	1901	43	sighted	sight	VBN
37681	1901	44	to	to	IN
37681	1901	45	the	the	DT
37681	1901	46	ship	ship	NN
37681	1901	47	.	.	.
37681	1902	1	Then	then	RB
37681	1902	2	,	,	,
37681	1902	3	turning	turn	VBG
37681	1902	4	,	,	,
37681	1902	5	he	-PRON-	PRP
37681	1902	6	might	may	MD
37681	1902	7	have	have	VB
37681	1902	8	sighted	sight	VBN
37681	1902	9	along	along	IN
37681	1902	10	the	the	DT
37681	1902	11	shore	shore	NN
37681	1902	12	to	to	IN
37681	1902	13	a	a	DT
37681	1902	14	point	point	NN
37681	1902	15	having	have	VBG
37681	1902	16	the	the	DT
37681	1902	17	same	same	JJ
37681	1902	18	angle	angle	NN
37681	1902	19	of	of	IN
37681	1902	20	declination	declination	NN
37681	1902	21	,	,	,
37681	1902	22	and	and	CC
37681	1902	23	then	then	RB
37681	1902	24	have	have	VBP
37681	1902	25	measured	measure	VBN
37681	1902	26	the	the	DT
37681	1902	27	distance	distance	NN
37681	1902	28	from	from	IN
37681	1902	29	the	the	DT
37681	1902	30	tower	tower	NN
37681	1902	31	to	to	IN
37681	1902	32	this	this	DT
37681	1902	33	point	point	NN
37681	1902	34	.	.	.
37681	1903	1	This	this	DT
37681	1903	2	seems	seem	VBZ
37681	1903	3	more	more	RBR
37681	1903	4	reasonable	reasonable	JJ
37681	1903	5	than	than	IN
37681	1903	6	any	any	DT
37681	1903	7	of	of	IN
37681	1903	8	the	the	DT
37681	1903	9	various	various	JJ
37681	1903	10	plans	plan	NNS
37681	1903	11	suggested	suggest	VBD
37681	1903	12	,	,	,
37681	1903	13	and	and	CC
37681	1903	14	it	-PRON-	PRP
37681	1903	15	is	be	VBZ
37681	1903	16	found	find	VBN
37681	1903	17	in	in	IN
37681	1903	18	so	so	RB
37681	1903	19	many	many	JJ
37681	1903	20	practical	practical	JJ
37681	1903	21	geometries	geometry	NNS
37681	1903	22	of	of	IN
37681	1903	23	the	the	DT
37681	1903	24	first	first	JJ
37681	1903	25	century	century	NN
37681	1903	26	of	of	IN
37681	1903	27	printing	print	VBG
37681	1903	28	that	that	IN
37681	1903	29	it	-PRON-	PRP
37681	1903	30	seems	seem	VBZ
37681	1903	31	to	to	TO
37681	1903	32	have	have	VB
37681	1903	33	long	long	RB
37681	1903	34	been	be	VBN
37681	1903	35	a	a	DT
37681	1903	36	common	common	JJ
37681	1903	37	expedient	expedient	NN
37681	1903	38	.	.	.
37681	1904	1	The	the	DT
37681	1904	2	stone	stone	NN
37681	1904	3	astrolabe	astrolabe	NN
37681	1904	4	from	from	IN
37681	1904	5	Mesopotamia	Mesopotamia	NNP
37681	1904	6	,	,	,
37681	1904	7	now	now	RB
37681	1904	8	preserved	preserve	VBN
37681	1904	9	in	in	IN
37681	1904	10	the	the	DT
37681	1904	11	British	British	NNP
37681	1904	12	Museum	Museum	NNP
37681	1904	13	,	,	,
37681	1904	14	shows	show	VBZ
37681	1904	15	that	that	IN
37681	1904	16	such	such	JJ
37681	1904	17	instruments	instrument	NNS
37681	1904	18	for	for	IN
37681	1904	19	the	the	DT
37681	1904	20	measuring	measuring	NN
37681	1904	21	of	of	IN
37681	1904	22	angles	angle	NNS
37681	1904	23	are	be	VBP
37681	1904	24	very	very	RB
37681	1904	25	old	old	JJ
37681	1904	26	,	,	,
37681	1904	27	and	and	CC
37681	1904	28	for	for	IN
37681	1904	29	the	the	DT
37681	1904	30	purposes	purpose	NNS
37681	1904	31	of	of	IN
37681	1904	32	Thales	Thales	NNPS
37681	1904	33	even	even	RB
37681	1904	34	a	a	DT
37681	1904	35	pair	pair	NN
37681	1904	36	of	of	IN
37681	1904	37	large	large	JJ
37681	1904	38	compasses	compass	NNS
37681	1904	39	would	would	MD
37681	1904	40	have	have	VB
37681	1904	41	answered	answer	VBN
37681	1904	42	very	very	RB
37681	1904	43	well	well	RB
37681	1904	44	.	.	.
37681	1905	1	An	an	DT
37681	1905	2	illustration	illustration	NN
37681	1905	3	of	of	IN
37681	1905	4	the	the	DT
37681	1905	5	method	method	NN
37681	1905	6	is	be	VBZ
37681	1905	7	seen	see	VBN
37681	1905	8	in	in	IN
37681	1905	9	Belli	Belli	NNP
37681	1905	10	's	's	POS
37681	1905	11	work	work	NN
37681	1905	12	of	of	IN
37681	1905	13	1569	1569	CD
37681	1905	14	,	,	,
37681	1905	15	as	as	IN
37681	1905	16	here	here	RB
37681	1905	17	shown	show	VBN
37681	1905	18	.	.	.
37681	1906	1	At	at	IN
37681	1906	2	the	the	DT
37681	1906	3	top	top	NN
37681	1906	4	of	of	IN
37681	1906	5	the	the	DT
37681	1906	6	picture	picture	NN
37681	1906	7	a	a	DT
37681	1906	8	man	man	NN
37681	1906	9	is	be	VBZ
37681	1906	10	getting	get	VBG
37681	1906	11	the	the	DT
37681	1906	12	angle	angle	NN
37681	1906	13	by	by	IN
37681	1906	14	means	mean	NNS
37681	1906	15	of	of	IN
37681	1906	16	the	the	DT
37681	1906	17	visor	visor	NN
37681	1906	18	of	of	IN
37681	1906	19	his	-PRON-	PRP$
37681	1906	20	cap	cap	NN
37681	1906	21	;	;	:
37681	1906	22	at	at	IN
37681	1906	23	the	the	DT
37681	1906	24	bottom	bottom	NN
37681	1906	25	of	of	IN
37681	1906	26	the	the	DT
37681	1906	27	picture	picture	NN
37681	1906	28	a	a	DT
37681	1906	29	man	man	NN
37681	1906	30	is	be	VBZ
37681	1906	31	using	use	VBG
37681	1906	32	a	a	DT
37681	1906	33	ruler	ruler	NN
37681	1906	34	screwed	screw	VBD
37681	1906	35	to	to	IN
37681	1906	36	a	a	DT
37681	1906	37	staff	staff	NN
37681	1906	38	.	.	.
37681	1907	1	[	[	-LRB-
37681	1907	2	61	61	CD
37681	1907	3	]	]	-RRB-
37681	1907	4	The	the	DT
37681	1907	5	story	story	NN
37681	1907	6	goes	go	VBZ
37681	1907	7	that	that	IN
37681	1907	8	one	one	CD
37681	1907	9	of	of	IN
37681	1907	10	Napoleon	Napoleon	NNP
37681	1907	11	's	's	POS
37681	1907	12	engineers	engineer	NNS
37681	1907	13	won	win	VBD
37681	1907	14	the	the	DT
37681	1907	15	imperial	imperial	JJ
37681	1907	16	favor	favor	NN
37681	1907	17	by	by	IN
37681	1907	18	quickly	quickly	RB
37681	1907	19	measuring	measure	VBG
37681	1907	20	the	the	DT
37681	1907	21	width	width	NN
37681	1907	22	of	of	IN
37681	1907	23	a	a	DT
37681	1907	24	stream	stream	NN
37681	1907	25	that	that	WDT
37681	1907	26	blocked	block	VBD
37681	1907	27	the	the	DT
37681	1907	28	progress	progress	NN
37681	1907	29	of	of	IN
37681	1907	30	the	the	DT
37681	1907	31	army	army	NN
37681	1907	32	,	,	,
37681	1907	33	using	use	VBG
37681	1907	34	this	this	DT
37681	1907	35	very	very	JJ
37681	1907	36	method	method	NN
37681	1907	37	.	.	.
37681	1908	1	[	[	-LRB-
37681	1908	2	Illustration	illustration	NN
37681	1908	3	:	:	:
37681	1908	4	SIXTEENTH	SIXTEENTH	NNP
37681	1908	5	-	-	HYPH
37681	1908	6	CENTURY	CENTURY	NNP
37681	1908	7	MENSURATION	MENSURATION	NNP
37681	1908	8	Belli	Belli	NNP
37681	1908	9	's	's	POS
37681	1908	10	"	"	``
37681	1908	11	Del	Del	NNP
37681	1908	12	Misurar	Misurar	NNP
37681	1908	13	con	con	NN
37681	1908	14	la	la	NNP
37681	1908	15	Vista	Vista	NNP
37681	1908	16	,	,	,
37681	1908	17	"	"	``
37681	1908	18	Venice	Venice	NNP
37681	1908	19	,	,	,
37681	1908	20	1569	1569	CD
37681	1908	21	]	]	-RRB-
37681	1908	22	This	this	DT
37681	1908	23	proposition	proposition	NN
37681	1908	24	is	be	VBZ
37681	1908	25	the	the	DT
37681	1908	26	reciprocal	reciprocal	JJ
37681	1908	27	or	or	CC
37681	1908	28	dual	dual	JJ
37681	1908	29	of	of	IN
37681	1908	30	the	the	DT
37681	1908	31	preceding	precede	VBG
37681	1908	32	one	one	CD
37681	1908	33	.	.	.
37681	1909	1	The	the	DT
37681	1909	2	relation	relation	NN
37681	1909	3	between	between	IN
37681	1909	4	the	the	DT
37681	1909	5	two	two	CD
37681	1909	6	may	may	MD
37681	1909	7	be	be	VB
37681	1909	8	seen	see	VBN
37681	1909	9	from	from	IN
37681	1909	10	the	the	DT
37681	1909	11	following	follow	VBG
37681	1909	12	arrangement	arrangement	NN
37681	1909	13	:	:	:
37681	1909	14	Two	two	CD
37681	1909	15	triangles	triangle	NNS
37681	1909	16	are	be	VBP
37681	1909	17	congruent	congruent	JJ
37681	1909	18	if	if	IN
37681	1909	19	two	two	CD
37681	1909	20	_	_	NNP
37681	1909	21	sides	side	NNS
37681	1909	22	_	_	NNP
37681	1909	23	and	and	CC
37681	1909	24	the	the	DT
37681	1909	25	included	include	VBN
37681	1909	26	_	_	NNP
37681	1909	27	angle	angle	NN
37681	1909	28	_	_	NNP
37681	1909	29	of	of	IN
37681	1909	30	the	the	DT
37681	1909	31	one	one	NN
37681	1909	32	are	be	VBP
37681	1909	33	equal	equal	JJ
37681	1909	34	respectively	respectively	RB
37681	1909	35	to	to	IN
37681	1909	36	two	two	CD
37681	1909	37	_	_	NNP
37681	1909	38	sides	side	NNS
37681	1909	39	_	_	NNP
37681	1909	40	and	and	CC
37681	1909	41	the	the	DT
37681	1909	42	included	include	VBN
37681	1909	43	_	_	NNP
37681	1909	44	angle	angle	NN
37681	1909	45	_	_	NNP
37681	1909	46	of	of	IN
37681	1909	47	the	the	DT
37681	1909	48	other	other	JJ
37681	1909	49	.	.	.
37681	1910	1	Two	two	CD
37681	1910	2	triangles	triangle	NNS
37681	1910	3	are	be	VBP
37681	1910	4	congruent	congruent	JJ
37681	1910	5	if	if	IN
37681	1910	6	two	two	CD
37681	1910	7	_	_	NNP
37681	1910	8	angles	angle	NNS
37681	1910	9	_	_	NNP
37681	1910	10	and	and	CC
37681	1910	11	the	the	DT
37681	1910	12	included	include	VBN
37681	1910	13	_	_	NNP
37681	1910	14	side	side	NN
37681	1910	15	_	_	NNP
37681	1910	16	of	of	IN
37681	1910	17	the	the	DT
37681	1910	18	one	one	NN
37681	1910	19	are	be	VBP
37681	1910	20	equal	equal	JJ
37681	1910	21	respectively	respectively	RB
37681	1910	22	to	to	IN
37681	1910	23	two	two	CD
37681	1910	24	_	_	NNP
37681	1910	25	angles	angle	NNS
37681	1910	26	_	_	NNP
37681	1910	27	and	and	CC
37681	1910	28	the	the	DT
37681	1910	29	included	include	VBN
37681	1910	30	_	_	NNP
37681	1910	31	side	side	NN
37681	1910	32	_	_	NNP
37681	1910	33	of	of	IN
37681	1910	34	the	the	DT
37681	1910	35	other	other	JJ
37681	1910	36	.	.	.
37681	1911	1	In	in	IN
37681	1911	2	general	general	JJ
37681	1911	3	,	,	,
37681	1911	4	to	to	IN
37681	1911	5	every	every	DT
37681	1911	6	proposition	proposition	NN
37681	1911	7	involving	involve	VBG
37681	1911	8	_	_	NNP
37681	1911	9	points	point	NNS
37681	1911	10	_	_	NNP
37681	1911	11	and	and	CC
37681	1911	12	_	_	NNP
37681	1911	13	lines	line	NNS
37681	1911	14	_	_	NNP
37681	1911	15	there	there	EX
37681	1911	16	is	be	VBZ
37681	1911	17	a	a	DT
37681	1911	18	reciprocal	reciprocal	JJ
37681	1911	19	proposition	proposition	NN
37681	1911	20	involving	involve	VBG
37681	1911	21	_	_	NNP
37681	1911	22	lines	line	NNS
37681	1911	23	_	_	NNP
37681	1911	24	and	and	CC
37681	1911	25	_	_	NNP
37681	1911	26	points	point	NNS
37681	1911	27	_	_	NNP
37681	1911	28	respectively	respectively	RB
37681	1911	29	that	that	WDT
37681	1911	30	is	be	VBZ
37681	1911	31	often	often	RB
37681	1911	32	true,--indeed	true,--indeed	NNP
37681	1911	33	,	,	,
37681	1911	34	that	that	DT
37681	1911	35	is	be	VBZ
37681	1911	36	always	always	RB
37681	1911	37	true	true	JJ
37681	1911	38	in	in	IN
37681	1911	39	a	a	DT
37681	1911	40	certain	certain	JJ
37681	1911	41	line	line	NN
37681	1911	42	of	of	IN
37681	1911	43	propositions	proposition	NNS
37681	1911	44	.	.	.
37681	1912	1	This	this	DT
37681	1912	2	relation	relation	NN
37681	1912	3	is	be	VBZ
37681	1912	4	known	know	VBN
37681	1912	5	as	as	IN
37681	1912	6	the	the	DT
37681	1912	7	Principle	Principle	NNP
37681	1912	8	of	of	IN
37681	1912	9	Reciprocity	Reciprocity	NNP
37681	1912	10	or	or	CC
37681	1912	11	of	of	IN
37681	1912	12	Duality	duality	NN
37681	1912	13	.	.	.
37681	1913	1	Instead	instead	RB
37681	1913	2	of	of	IN
37681	1913	3	points	point	NNS
37681	1913	4	and	and	CC
37681	1913	5	lines	line	NNS
37681	1913	6	we	-PRON-	PRP
37681	1913	7	have	have	VBP
37681	1913	8	here	here	RB
37681	1913	9	angles	angle	NNS
37681	1913	10	(	(	-LRB-
37681	1913	11	suggested	suggest	VBN
37681	1913	12	by	by	IN
37681	1913	13	the	the	DT
37681	1913	14	vertex	vertex	NNP
37681	1913	15	points	point	NNS
37681	1913	16	)	)	-RRB-
37681	1913	17	and	and	CC
37681	1913	18	lines	line	NNS
37681	1913	19	.	.	.
37681	1914	1	It	-PRON-	PRP
37681	1914	2	is	be	VBZ
37681	1914	3	interesting	interesting	JJ
37681	1914	4	to	to	IN
37681	1914	5	a	a	DT
37681	1914	6	class	class	NN
37681	1914	7	to	to	TO
37681	1914	8	have	have	VB
37681	1914	9	attention	attention	NN
37681	1914	10	called	call	VBN
37681	1914	11	to	to	IN
37681	1914	12	such	such	JJ
37681	1914	13	relations	relation	NNS
37681	1914	14	,	,	,
37681	1914	15	but	but	CC
37681	1914	16	it	-PRON-	PRP
37681	1914	17	is	be	VBZ
37681	1914	18	not	not	RB
37681	1914	19	of	of	IN
37681	1914	20	sufficient	sufficient	JJ
37681	1914	21	importance	importance	NN
37681	1914	22	in	in	IN
37681	1914	23	elementary	elementary	JJ
37681	1914	24	geometry	geometry	NN
37681	1914	25	to	to	TO
37681	1914	26	justify	justify	VB
37681	1914	27	more	more	JJR
37681	1914	28	than	than	IN
37681	1914	29	a	a	DT
37681	1914	30	reference	reference	NN
37681	1914	31	here	here	RB
37681	1914	32	and	and	CC
37681	1914	33	there	there	RB
37681	1914	34	.	.	.
37681	1915	1	There	there	EX
37681	1915	2	are	be	VBP
37681	1915	3	other	other	JJ
37681	1915	4	dual	dual	JJ
37681	1915	5	features	feature	NNS
37681	1915	6	that	that	WDT
37681	1915	7	are	be	VBP
37681	1915	8	seen	see	VBN
37681	1915	9	in	in	IN
37681	1915	10	geometry	geometry	NN
37681	1915	11	besides	besides	IN
37681	1915	12	those	those	DT
37681	1915	13	given	give	VBN
37681	1915	14	above	above	RB
37681	1915	15	.	.	.
37681	1916	1	THEOREM	THEOREM	NNP
37681	1916	2	.	.	.
37681	1917	1	_	_	NNP
37681	1917	2	In	in	IN
37681	1917	3	an	an	DT
37681	1917	4	isosceles	isoscele	NNS
37681	1917	5	triangle	triangle	VBP
37681	1917	6	the	the	DT
37681	1917	7	angles	angle	NNS
37681	1917	8	opposite	opposite	IN
37681	1917	9	the	the	DT
37681	1917	10	equal	equal	JJ
37681	1917	11	sides	side	NNS
37681	1917	12	are	be	VBP
37681	1917	13	equal	equal	JJ
37681	1917	14	.	.	.
37681	1917	15	_	_	NNP
37681	1917	16	This	this	DT
37681	1917	17	is	be	VBZ
37681	1917	18	Euclid	Euclid	NNP
37681	1917	19	's	's	POS
37681	1917	20	Proposition	Proposition	NNP
37681	1917	21	5	5	CD
37681	1917	22	,	,	,
37681	1917	23	the	the	DT
37681	1917	24	second	second	JJ
37681	1917	25	of	of	IN
37681	1917	26	his	-PRON-	PRP$
37681	1917	27	theorems	theorem	NNS
37681	1917	28	,	,	,
37681	1917	29	but	but	CC
37681	1917	30	he	-PRON-	PRP
37681	1917	31	adds	add	VBZ
37681	1917	32	,	,	,
37681	1917	33	"	"	``
37681	1917	34	and	and	CC
37681	1917	35	if	if	IN
37681	1917	36	the	the	DT
37681	1917	37	equal	equal	JJ
37681	1917	38	straight	straight	JJ
37681	1917	39	lines	line	NNS
37681	1917	40	be	be	VB
37681	1917	41	produced	produce	VBN
37681	1917	42	further	further	RB
37681	1917	43	,	,	,
37681	1917	44	the	the	DT
37681	1917	45	angles	angle	NNS
37681	1917	46	under	under	IN
37681	1917	47	the	the	DT
37681	1917	48	base	base	NN
37681	1917	49	will	will	MD
37681	1917	50	be	be	VB
37681	1917	51	equal	equal	JJ
37681	1917	52	to	to	IN
37681	1917	53	one	one	CD
37681	1917	54	another	another	DT
37681	1917	55	.	.	.
37681	1917	56	"	"	''
37681	1918	1	Since	since	IN
37681	1918	2	,	,	,
37681	1918	3	however	however	RB
37681	1918	4	,	,	,
37681	1918	5	he	-PRON-	PRP
37681	1918	6	does	do	VBZ
37681	1918	7	not	not	RB
37681	1918	8	use	use	VB
37681	1918	9	this	this	DT
37681	1918	10	second	second	JJ
37681	1918	11	part	part	NN
37681	1918	12	,	,	,
37681	1918	13	its	-PRON-	PRP$
37681	1918	14	genuineness	genuineness	NN
37681	1918	15	is	be	VBZ
37681	1918	16	doubted	doubt	VBN
37681	1918	17	.	.	.
37681	1919	1	He	-PRON-	PRP
37681	1919	2	would	would	MD
37681	1919	3	not	not	RB
37681	1919	4	admit	admit	VB
37681	1919	5	the	the	DT
37681	1919	6	common	common	JJ
37681	1919	7	proof	proof	NN
37681	1919	8	of	of	IN
37681	1919	9	to	to	IN
37681	1919	10	-	-	HYPH
37681	1919	11	day	day	NN
37681	1919	12	of	of	IN
37681	1919	13	supposing	suppose	VBG
37681	1919	14	the	the	DT
37681	1919	15	vertical	vertical	JJ
37681	1919	16	angle	angle	NN
37681	1919	17	bisected	bisect	VBD
37681	1919	18	,	,	,
37681	1919	19	because	because	IN
37681	1919	20	the	the	DT
37681	1919	21	problem	problem	NN
37681	1919	22	about	about	IN
37681	1919	23	bisecting	bisect	VBG
37681	1919	24	an	an	DT
37681	1919	25	angle	angle	NN
37681	1919	26	does	do	VBZ
37681	1919	27	not	not	RB
37681	1919	28	precede	precede	VB
37681	1919	29	this	this	DT
37681	1919	30	proposition	proposition	NN
37681	1919	31	,	,	,
37681	1919	32	and	and	CC
37681	1919	33	therefore	therefore	RB
37681	1919	34	his	-PRON-	PRP$
37681	1919	35	proof	proof	NN
37681	1919	36	is	be	VBZ
37681	1919	37	much	much	RB
37681	1919	38	more	more	RBR
37681	1919	39	involved	involved	JJ
37681	1919	40	than	than	IN
37681	1919	41	ours	ours	PRP$
37681	1919	42	.	.	.
37681	1920	1	He	-PRON-	PRP
37681	1920	2	makes	make	VBZ
37681	1920	3	_	_	NNP
37681	1920	4	CX	CX	NNP
37681	1920	5	_	_	NNP
37681	1920	6	=	=	SYM
37681	1920	7	_	_	NNP
37681	1920	8	CY	CY	NNP
37681	1920	9	_	_	NNP
37681	1920	10	,	,	,
37681	1920	11	and	and	CC
37681	1920	12	proves	prove	VBZ
37681	1920	13	[	[	-LRB-
37681	1920	14	triangles]_XBC	triangles]_XBC	NNP
37681	1920	15	_	_	NNP
37681	1920	16	and	and	CC
37681	1920	17	_	_	NNP
37681	1920	18	YAC	YAC	NNP
37681	1920	19	_	_	NNP
37681	1920	20	congruent,[62	congruent,[62	NNP
37681	1920	21	]	]	-RRB-
37681	1920	22	and	and	CC
37681	1920	23	also	also	RB
37681	1920	24	[	[	-LRB-
37681	1920	25	triangles]_XBA	triangles]_XBA	NNP
37681	1920	26	_	_	NNP
37681	1920	27	and	and	CC
37681	1920	28	_	_	NNP
37681	1920	29	YAB	YAB	NNP
37681	1920	30	_	_	NNP
37681	1920	31	congruent	congruent	NN
37681	1920	32	.	.	.
37681	1921	1	Then	then	RB
37681	1921	2	from	from	IN
37681	1921	3	[	[	-LRB-
37681	1921	4	L]_YAC	L]_YAC	NNP
37681	1921	5	_	_	NNP
37681	1921	6	he	-PRON-	PRP
37681	1921	7	takes	take	VBZ
37681	1921	8	[	[	-LRB-
37681	1921	9	L]_YAB	L]_YAB	NNP
37681	1921	10	_	_	NNP
37681	1921	11	,	,	,
37681	1921	12	leaving	leave	VBG
37681	1921	13	[	[	-LRB-
37681	1921	14	L]_BAC	L]_BAC	NNP
37681	1921	15	_	_	NNP
37681	1921	16	,	,	,
37681	1921	17	and	and	CC
37681	1921	18	so	so	RB
37681	1921	19	on	on	IN
37681	1921	20	the	the	DT
37681	1921	21	other	other	JJ
37681	1921	22	side	side	NN
37681	1921	23	,	,	,
37681	1921	24	leaving	leave	VBG
37681	1921	25	[	[	-LRB-
37681	1921	26	L]_CBA	L]_CBA	NNP
37681	1921	27	_	_	NNP
37681	1921	28	,	,	,
37681	1921	29	these	these	DT
37681	1921	30	therefore	therefore	RB
37681	1921	31	being	be	VBG
37681	1921	32	equal	equal	JJ
37681	1921	33	.	.	.
37681	1922	1	[	[	-LRB-
37681	1922	2	Illustration	illustration	NN
37681	1922	3	]	]	-RRB-
37681	1922	4	This	this	DT
37681	1922	5	proposition	proposition	NN
37681	1922	6	has	have	VBZ
37681	1922	7	long	long	RB
37681	1922	8	been	be	VBN
37681	1922	9	called	call	VBN
37681	1922	10	the	the	DT
37681	1922	11	_	_	NNP
37681	1922	12	pons	pons	NNP
37681	1922	13	asinorum	asinorum	NNP
37681	1922	14	_	_	NNP
37681	1922	15	,	,	,
37681	1922	16	or	or	CC
37681	1922	17	bridge	bridge	NN
37681	1922	18	of	of	IN
37681	1922	19	asses	ass	NNS
37681	1922	20	,	,	,
37681	1922	21	but	but	CC
37681	1922	22	no	no	DT
37681	1922	23	one	one	NN
37681	1922	24	knows	know	VBZ
37681	1922	25	where	where	WRB
37681	1922	26	or	or	CC
37681	1922	27	when	when	WRB
37681	1922	28	the	the	DT
37681	1922	29	name	name	NN
37681	1922	30	arose	arise	VBD
37681	1922	31	.	.	.
37681	1923	1	It	-PRON-	PRP
37681	1923	2	is	be	VBZ
37681	1923	3	usually	usually	RB
37681	1923	4	stated	state	VBN
37681	1923	5	that	that	IN
37681	1923	6	it	-PRON-	PRP
37681	1923	7	came	come	VBD
37681	1923	8	from	from	IN
37681	1923	9	the	the	DT
37681	1923	10	fact	fact	NN
37681	1923	11	that	that	IN
37681	1923	12	fools	fool	NNS
37681	1923	13	could	could	MD
37681	1923	14	not	not	RB
37681	1923	15	cross	cross	VB
37681	1923	16	this	this	DT
37681	1923	17	bridge	bridge	NN
37681	1923	18	,	,	,
37681	1923	19	and	and	CC
37681	1923	20	it	-PRON-	PRP
37681	1923	21	is	be	VBZ
37681	1923	22	a	a	DT
37681	1923	23	fact	fact	NN
37681	1923	24	that	that	IN
37681	1923	25	in	in	IN
37681	1923	26	the	the	DT
37681	1923	27	Middle	Middle	NNP
37681	1923	28	Ages	Ages	NNP
37681	1923	29	this	this	DT
37681	1923	30	was	be	VBD
37681	1923	31	often	often	RB
37681	1923	32	the	the	DT
37681	1923	33	limit	limit	NN
37681	1923	34	of	of	IN
37681	1923	35	the	the	DT
37681	1923	36	student	student	NN
37681	1923	37	's	's	POS
37681	1923	38	progress	progress	NN
37681	1923	39	in	in	IN
37681	1923	40	geometry	geometry	NN
37681	1923	41	.	.	.
37681	1924	1	It	-PRON-	PRP
37681	1924	2	has	have	VBZ
37681	1924	3	however	however	RB
37681	1924	4	been	be	VBN
37681	1924	5	suggested	suggest	VBN
37681	1924	6	that	that	IN
37681	1924	7	the	the	DT
37681	1924	8	name	name	NN
37681	1924	9	came	come	VBD
37681	1924	10	from	from	IN
37681	1924	11	Euclid	Euclid	NNP
37681	1924	12	's	's	POS
37681	1924	13	figure	figure	NN
37681	1924	14	,	,	,
37681	1924	15	which	which	WDT
37681	1924	16	resembles	resemble	VBZ
37681	1924	17	the	the	DT
37681	1924	18	simplest	simple	JJS
37681	1924	19	type	type	NN
37681	1924	20	of	of	IN
37681	1924	21	a	a	DT
37681	1924	22	wooden	wooden	JJ
37681	1924	23	truss	truss	NNP
37681	1924	24	bridge	bridge	NN
37681	1924	25	.	.	.
37681	1925	1	The	the	DT
37681	1925	2	name	name	NN
37681	1925	3	is	be	VBZ
37681	1925	4	applied	apply	VBN
37681	1925	5	by	by	IN
37681	1925	6	the	the	DT
37681	1925	7	French	French	NNP
37681	1925	8	to	to	IN
37681	1925	9	the	the	DT
37681	1925	10	Pythagorean	Pythagorean	NNP
37681	1925	11	Theorem	Theorem	NNP
37681	1925	12	.	.	.
37681	1926	1	Proclus	Proclus	NNP
37681	1926	2	attributes	attribute	VBZ
37681	1926	3	the	the	DT
37681	1926	4	discovery	discovery	NN
37681	1926	5	of	of	IN
37681	1926	6	this	this	DT
37681	1926	7	proposition	proposition	NN
37681	1926	8	to	to	IN
37681	1926	9	Thales	thale	NNS
37681	1926	10	.	.	.
37681	1927	1	He	-PRON-	PRP
37681	1927	2	also	also	RB
37681	1927	3	says	say	VBZ
37681	1927	4	that	that	IN
37681	1927	5	Pappus	Pappus	NNP
37681	1927	6	(	(	-LRB-
37681	1927	7	third	third	JJ
37681	1927	8	century	century	NN
37681	1927	9	A.D.	A.D.	NNP
37681	1927	10	)	)	-RRB-
37681	1927	11	,	,	,
37681	1927	12	a	a	DT
37681	1927	13	Greek	greek	JJ
37681	1927	14	commentator	commentator	NN
37681	1927	15	on	on	IN
37681	1927	16	Euclid	Euclid	NNP
37681	1927	17	,	,	,
37681	1927	18	proved	prove	VBD
37681	1927	19	the	the	DT
37681	1927	20	proposition	proposition	NN
37681	1927	21	as	as	IN
37681	1927	22	follows	follow	VBZ
37681	1927	23	:	:	:
37681	1927	24	Let	let	VB
37681	1927	25	_	_	NNP
37681	1927	26	ABC	ABC	NNP
37681	1927	27	_	_	NNP
37681	1927	28	be	be	VB
37681	1927	29	the	the	DT
37681	1927	30	triangle	triangle	NN
37681	1927	31	,	,	,
37681	1927	32	with	with	IN
37681	1927	33	_	_	NNP
37681	1927	34	AB	AB	NNP
37681	1927	35	_	_	NNP
37681	1927	36	=	=	SYM
37681	1927	37	_	_	NNP
37681	1927	38	AC	AC	NNP
37681	1927	39	_	_	NNP
37681	1927	40	.	.	.
37681	1928	1	Conceive	conceive	JJ
37681	1928	2	of	of	IN
37681	1928	3	this	this	DT
37681	1928	4	as	as	IN
37681	1928	5	two	two	CD
37681	1928	6	triangles	triangle	NNS
37681	1928	7	;	;	:
37681	1928	8	then	then	RB
37681	1928	9	_	_	NNP
37681	1928	10	AB	AB	NNP
37681	1928	11	_	_	NNP
37681	1928	12	=	=	SYM
37681	1928	13	_	_	NNP
37681	1928	14	AC	AC	NNP
37681	1928	15	_	_	NNP
37681	1928	16	,	,	,
37681	1928	17	_	_	NNP
37681	1928	18	AC	AC	NNP
37681	1928	19	_	_	NNP
37681	1928	20	=	=	SYM
37681	1928	21	_	_	NNP
37681	1928	22	AB	AB	NNP
37681	1928	23	_	_	NNP
37681	1928	24	,	,	,
37681	1928	25	and	and	CC
37681	1928	26	[	[	-LRB-
37681	1928	27	L]_A	L]_A	NNP
37681	1928	28	_	_	NNP
37681	1928	29	is	be	VBZ
37681	1928	30	common	common	JJ
37681	1928	31	;	;	:
37681	1928	32	hence	hence	RB
37681	1928	33	the	the	DT
37681	1928	34	[	[	-LRB-
37681	1928	35	triangles]_ABC	triangles]_ABC	NNP
37681	1928	36	_	_	NNP
37681	1928	37	and	and	CC
37681	1928	38	_	_	NNP
37681	1928	39	ACB	ACB	NNP
37681	1928	40	_	_	NNP
37681	1928	41	are	be	VBP
37681	1928	42	congruent	congruent	JJ
37681	1928	43	,	,	,
37681	1928	44	and	and	CC
37681	1928	45	[	[	-LRB-
37681	1928	46	L]_B	L]_B	NNP
37681	1928	47	_	_	NNP
37681	1928	48	of	of	IN
37681	1928	49	the	the	DT
37681	1928	50	one	one	NN
37681	1928	51	equals	equal	VBZ
37681	1928	52	[	[	-LRB-
37681	1928	53	L]_C	L]_C	NNP
37681	1928	54	_	_	NNP
37681	1928	55	of	of	IN
37681	1928	56	the	the	DT
37681	1928	57	other	other	JJ
37681	1928	58	.	.	.
37681	1929	1	This	this	DT
37681	1929	2	is	be	VBZ
37681	1929	3	a	a	DT
37681	1929	4	better	well	JJR
37681	1929	5	plan	plan	NN
37681	1929	6	than	than	IN
37681	1929	7	that	that	DT
37681	1929	8	followed	follow	VBN
37681	1929	9	by	by	IN
37681	1929	10	some	some	DT
37681	1929	11	textbook	textbook	NN
37681	1929	12	writers	writer	NNS
37681	1929	13	of	of	IN
37681	1929	14	imagining	imagine	VBG
37681	1929	15	[	[	-LRB-
37681	1929	16	triangle]_ABC	triangle]_abc	CD
37681	1929	17	_	_	NNP
37681	1929	18	taken	take	VBN
37681	1929	19	up	up	RP
37681	1929	20	and	and	CC
37681	1929	21	laid	lay	VBN
37681	1929	22	down	down	RP
37681	1929	23	on	on	IN
37681	1929	24	_	_	NNP
37681	1929	25	itself	-PRON-	PRP
37681	1929	26	_	_	XX
37681	1929	27	.	.	.
37681	1930	1	Even	even	RB
37681	1930	2	to	to	TO
37681	1930	3	lay	lay	VB
37681	1930	4	it	-PRON-	PRP
37681	1930	5	down	down	RP
37681	1930	6	on	on	IN
37681	1930	7	its	-PRON-	PRP$
37681	1930	8	"	"	``
37681	1930	9	trace	trace	NN
37681	1930	10	"	"	''
37681	1930	11	is	be	VBZ
37681	1930	12	more	more	RBR
37681	1930	13	objectionable	objectionable	JJ
37681	1930	14	than	than	IN
37681	1930	15	the	the	DT
37681	1930	16	plan	plan	NN
37681	1930	17	of	of	IN
37681	1930	18	Pappus	Pappus	NNP
37681	1930	19	.	.	.
37681	1931	1	THEOREM	THEOREM	NNP
37681	1931	2	.	.	.
37681	1932	1	_	_	XX
37681	1932	2	If	if	IN
37681	1932	3	two	two	CD
37681	1932	4	angles	angle	NNS
37681	1932	5	of	of	IN
37681	1932	6	a	a	DT
37681	1932	7	triangle	triangle	NN
37681	1932	8	are	be	VBP
37681	1932	9	equal	equal	JJ
37681	1932	10	,	,	,
37681	1932	11	the	the	DT
37681	1932	12	sides	side	NNS
37681	1932	13	opposite	opposite	IN
37681	1932	14	the	the	DT
37681	1932	15	equal	equal	JJ
37681	1932	16	angles	angle	NNS
37681	1932	17	are	be	VBP
37681	1932	18	equal	equal	JJ
37681	1932	19	,	,	,
37681	1932	20	and	and	CC
37681	1932	21	the	the	DT
37681	1932	22	triangle	triangle	NN
37681	1932	23	is	be	VBZ
37681	1932	24	isosceles	isoscele	NNS
37681	1932	25	.	.	.
37681	1932	26	_	_	NNP
37681	1932	27	The	the	DT
37681	1932	28	statement	statement	NN
37681	1932	29	is	be	VBZ
37681	1932	30	,	,	,
37681	1932	31	of	of	IN
37681	1932	32	course	course	NN
37681	1932	33	,	,	,
37681	1932	34	tautological	tautological	JJ
37681	1932	35	,	,	,
37681	1932	36	the	the	DT
37681	1932	37	last	last	JJ
37681	1932	38	five	five	CD
37681	1932	39	words	word	NNS
37681	1932	40	being	be	VBG
37681	1932	41	unnecessary	unnecessary	JJ
37681	1932	42	from	from	IN
37681	1932	43	the	the	DT
37681	1932	44	mathematical	mathematical	JJ
37681	1932	45	standpoint	standpoint	NN
37681	1932	46	,	,	,
37681	1932	47	but	but	CC
37681	1932	48	of	of	IN
37681	1932	49	value	value	NN
37681	1932	50	at	at	IN
37681	1932	51	this	this	DT
37681	1932	52	stage	stage	NN
37681	1932	53	of	of	IN
37681	1932	54	the	the	DT
37681	1932	55	student	student	NN
37681	1932	56	's	's	POS
37681	1932	57	progress	progress	NN
37681	1932	58	as	as	IN
37681	1932	59	emphasizing	emphasize	VBG
37681	1932	60	the	the	DT
37681	1932	61	nature	nature	NN
37681	1932	62	of	of	IN
37681	1932	63	the	the	DT
37681	1932	64	triangle	triangle	NN
37681	1932	65	.	.	.
37681	1933	1	Euclid	Euclid	NNP
37681	1933	2	stated	state	VBD
37681	1933	3	the	the	DT
37681	1933	4	proposition	proposition	NN
37681	1933	5	thus	thus	RB
37681	1933	6	,	,	,
37681	1933	7	"	"	``
37681	1933	8	If	if	IN
37681	1933	9	in	in	IN
37681	1933	10	a	a	DT
37681	1933	11	triangle	triangle	NN
37681	1933	12	two	two	CD
37681	1933	13	angles	angle	NNS
37681	1933	14	be	be	VB
37681	1933	15	equal	equal	JJ
37681	1933	16	to	to	IN
37681	1933	17	one	one	CD
37681	1933	18	another	another	DT
37681	1933	19	,	,	,
37681	1933	20	the	the	DT
37681	1933	21	sides	side	NNS
37681	1933	22	which	which	WDT
37681	1933	23	subtend	subtend	VBP
37681	1933	24	the	the	DT
37681	1933	25	equal	equal	JJ
37681	1933	26	angles	angle	NNS
37681	1933	27	will	will	MD
37681	1933	28	also	also	RB
37681	1933	29	be	be	VB
37681	1933	30	equal	equal	JJ
37681	1933	31	to	to	IN
37681	1933	32	one	one	CD
37681	1933	33	another	another	DT
37681	1933	34	.	.	.
37681	1933	35	"	"	''
37681	1934	1	He	-PRON-	PRP
37681	1934	2	did	do	VBD
37681	1934	3	not	not	RB
37681	1934	4	define	define	VB
37681	1934	5	"	"	``
37681	1934	6	subtend	subtend	VB
37681	1934	7	,	,	,
37681	1934	8	"	"	''
37681	1934	9	supposing	suppose	VBG
37681	1934	10	such	such	JJ
37681	1934	11	words	word	NNS
37681	1934	12	to	to	TO
37681	1934	13	be	be	VB
37681	1934	14	already	already	RB
37681	1934	15	understood	understand	VBN
37681	1934	16	.	.	.
37681	1935	1	This	this	DT
37681	1935	2	is	be	VBZ
37681	1935	3	the	the	DT
37681	1935	4	first	first	JJ
37681	1935	5	case	case	NN
37681	1935	6	of	of	IN
37681	1935	7	a	a	DT
37681	1935	8	converse	converse	NN
37681	1935	9	proposition	proposition	NN
37681	1935	10	in	in	IN
37681	1935	11	geometry	geometry	NN
37681	1935	12	.	.	.
37681	1936	1	Heath	Heath	NNP
37681	1936	2	distinguishes	distinguish	VBZ
37681	1936	3	the	the	DT
37681	1936	4	logical	logical	JJ
37681	1936	5	from	from	IN
37681	1936	6	the	the	DT
37681	1936	7	geometric	geometric	JJ
37681	1936	8	converse	converse	NN
37681	1936	9	.	.	.
37681	1937	1	The	the	DT
37681	1937	2	logical	logical	JJ
37681	1937	3	converse	converse	NN
37681	1937	4	of	of	IN
37681	1937	5	Euclid	Euclid	NNP
37681	1937	6	I	I	NNP
37681	1937	7	,	,	,
37681	1937	8	5	5	CD
37681	1937	9	,	,	,
37681	1937	10	would	would	MD
37681	1937	11	be	be	VB
37681	1937	12	that	that	IN
37681	1937	13	"	"	``
37681	1937	14	_	_	NNP
37681	1937	15	some	some	DT
37681	1937	16	_	_	NNP
37681	1937	17	triangles	triangle	NNS
37681	1937	18	with	with	IN
37681	1937	19	two	two	CD
37681	1937	20	angles	angle	NNS
37681	1937	21	equal	equal	JJ
37681	1937	22	are	be	VBP
37681	1937	23	isosceles	isoscele	NNS
37681	1937	24	,	,	,
37681	1937	25	"	"	``
37681	1937	26	while	while	IN
37681	1937	27	the	the	DT
37681	1937	28	geometric	geometric	JJ
37681	1937	29	converse	converse	NN
37681	1937	30	is	be	VBZ
37681	1937	31	the	the	DT
37681	1937	32	proposition	proposition	NN
37681	1937	33	as	as	IN
37681	1937	34	stated	state	VBN
37681	1937	35	.	.	.
37681	1938	1	Proclus	proclus	NN
37681	1938	2	called	call	VBD
37681	1938	3	attention	attention	NN
37681	1938	4	to	to	IN
37681	1938	5	two	two	CD
37681	1938	6	forms	form	NNS
37681	1938	7	of	of	IN
37681	1938	8	converse	converse	NN
37681	1938	9	(	(	-LRB-
37681	1938	10	and	and	CC
37681	1938	11	in	in	IN
37681	1938	12	the	the	DT
37681	1938	13	course	course	NN
37681	1938	14	of	of	IN
37681	1938	15	the	the	DT
37681	1938	16	work	work	NN
37681	1938	17	,	,	,
37681	1938	18	but	but	CC
37681	1938	19	not	not	RB
37681	1938	20	at	at	IN
37681	1938	21	this	this	DT
37681	1938	22	time	time	NN
37681	1938	23	,	,	,
37681	1938	24	the	the	DT
37681	1938	25	teacher	teacher	NN
37681	1938	26	may	may	MD
37681	1938	27	have	have	VB
37681	1938	28	to	to	TO
37681	1938	29	do	do	VB
37681	1938	30	the	the	DT
37681	1938	31	same	same	JJ
37681	1938	32	)	)	-RRB-
37681	1938	33	:	:	:
37681	1938	34	(	(	-LRB-
37681	1938	35	1	1	LS
37681	1938	36	)	)	-RRB-
37681	1938	37	the	the	DT
37681	1938	38	complete	complete	JJ
37681	1938	39	converse	converse	NN
37681	1938	40	,	,	,
37681	1938	41	in	in	IN
37681	1938	42	which	which	WDT
37681	1938	43	that	that	DT
37681	1938	44	which	which	WDT
37681	1938	45	is	be	VBZ
37681	1938	46	given	give	VBN
37681	1938	47	in	in	IN
37681	1938	48	one	one	CD
37681	1938	49	becomes	become	VBZ
37681	1938	50	that	that	DT
37681	1938	51	which	which	WDT
37681	1938	52	is	be	VBZ
37681	1938	53	to	to	TO
37681	1938	54	be	be	VB
37681	1938	55	proved	prove	VBN
37681	1938	56	in	in	IN
37681	1938	57	the	the	DT
37681	1938	58	other	other	JJ
37681	1938	59	,	,	,
37681	1938	60	and	and	CC
37681	1938	61	vice	vice	NN
37681	1938	62	versa	versa	RB
37681	1938	63	,	,	,
37681	1938	64	as	as	IN
37681	1938	65	in	in	IN
37681	1938	66	this	this	DT
37681	1938	67	and	and	CC
37681	1938	68	the	the	DT
37681	1938	69	preceding	precede	VBG
37681	1938	70	proposition	proposition	NN
37681	1938	71	;	;	,
37681	1938	72	(	(	-LRB-
37681	1938	73	2	2	LS
37681	1938	74	)	)	-RRB-
37681	1938	75	the	the	DT
37681	1938	76	partial	partial	JJ
37681	1938	77	converse	converse	NN
37681	1938	78	,	,	,
37681	1938	79	in	in	IN
37681	1938	80	which	which	WDT
37681	1938	81	two	two	CD
37681	1938	82	(	(	-LRB-
37681	1938	83	or	or	CC
37681	1938	84	even	even	RB
37681	1938	85	more	more	RBR
37681	1938	86	)	)	-RRB-
37681	1938	87	things	thing	NNS
37681	1938	88	may	may	MD
37681	1938	89	be	be	VB
37681	1938	90	given	give	VBN
37681	1938	91	,	,	,
37681	1938	92	and	and	CC
37681	1938	93	a	a	DT
37681	1938	94	certain	certain	JJ
37681	1938	95	thing	thing	NN
37681	1938	96	is	be	VBZ
37681	1938	97	to	to	TO
37681	1938	98	be	be	VB
37681	1938	99	proved	prove	VBN
37681	1938	100	,	,	,
37681	1938	101	the	the	DT
37681	1938	102	converse	converse	NN
37681	1938	103	being	be	VBG
37681	1938	104	that	that	IN
37681	1938	105	one	one	CD
37681	1938	106	(	(	-LRB-
37681	1938	107	or	or	CC
37681	1938	108	more	more	RBR
37681	1938	109	)	)	-RRB-
37681	1938	110	of	of	IN
37681	1938	111	the	the	DT
37681	1938	112	preceding	precede	VBG
37681	1938	113	things	thing	NNS
37681	1938	114	is	be	VBZ
37681	1938	115	now	now	RB
37681	1938	116	given	give	VBN
37681	1938	117	,	,	,
37681	1938	118	together	together	RB
37681	1938	119	with	with	IN
37681	1938	120	what	what	WP
37681	1938	121	was	be	VBD
37681	1938	122	to	to	TO
37681	1938	123	be	be	VB
37681	1938	124	proved	prove	VBN
37681	1938	125	,	,	,
37681	1938	126	and	and	CC
37681	1938	127	the	the	DT
37681	1938	128	other	other	JJ
37681	1938	129	given	give	VBN
37681	1938	130	thing	thing	NN
37681	1938	131	is	be	VBZ
37681	1938	132	now	now	RB
37681	1938	133	to	to	TO
37681	1938	134	be	be	VB
37681	1938	135	proved	prove	VBN
37681	1938	136	.	.	.
37681	1939	1	Symbolically	symbolically	RB
37681	1939	2	,	,	,
37681	1939	3	if	if	IN
37681	1939	4	it	-PRON-	PRP
37681	1939	5	is	be	VBZ
37681	1939	6	given	give	VBN
37681	1939	7	that	that	IN
37681	1939	8	_	_	NNP
37681	1939	9	a	a	DT
37681	1939	10	_	_	NNP
37681	1939	11	=	=	SYM
37681	1939	12	_	_	NNP
37681	1939	13	b	b	NNP
37681	1939	14	_	_	NNP
37681	1939	15	and	and	CC
37681	1939	16	_	_	NNP
37681	1939	17	c	c	NNP
37681	1939	18	_	_	NNP
37681	1939	19	=	=	SYM
37681	1939	20	_	_	NNP
37681	1939	21	d	d	NNP
37681	1939	22	_	_	NNP
37681	1939	23	,	,	,
37681	1939	24	to	to	TO
37681	1939	25	prove	prove	VB
37681	1939	26	that	that	IN
37681	1939	27	_	_	NNP
37681	1939	28	x	x	NNP
37681	1939	29	_	_	NNP
37681	1939	30	=	=	SYM
37681	1939	31	_	_	NNP
37681	1939	32	y	y	NNP
37681	1939	33	_	_	NNP
37681	1939	34	,	,	,
37681	1939	35	the	the	DT
37681	1939	36	partial	partial	JJ
37681	1939	37	converse	converse	NN
37681	1939	38	would	would	MD
37681	1939	39	have	have	VB
37681	1939	40	given	give	VBN
37681	1939	41	_	_	NNP
37681	1939	42	a	a	DT
37681	1939	43	_	_	NNP
37681	1939	44	=	=	SYM
37681	1939	45	_	_	NNP
37681	1939	46	b	b	NNP
37681	1939	47	_	_	NNP
37681	1939	48	and	and	CC
37681	1939	49	_	_	NNP
37681	1939	50	x	x	NNP
37681	1939	51	_	_	NNP
37681	1939	52	=	=	SYM
37681	1939	53	_	_	NNP
37681	1939	54	y	y	NNP
37681	1939	55	_	_	NNP
37681	1939	56	,	,	,
37681	1939	57	to	to	TO
37681	1939	58	prove	prove	VB
37681	1939	59	that	that	IN
37681	1939	60	_	_	NNP
37681	1939	61	c	c	NNP
37681	1939	62	_	_	NNP
37681	1939	63	=	=	SYM
37681	1939	64	_	_	NNP
37681	1939	65	d	d	NNP
37681	1939	66	_	_	NNP
37681	1939	67	.	.	.
37681	1940	1	Several	several	JJ
37681	1940	2	proofs	proof	NNS
37681	1940	3	for	for	IN
37681	1940	4	the	the	DT
37681	1940	5	proposition	proposition	NN
37681	1940	6	have	have	VBP
37681	1940	7	been	be	VBN
37681	1940	8	suggested	suggest	VBN
37681	1940	9	,	,	,
37681	1940	10	but	but	CC
37681	1940	11	a	a	DT
37681	1940	12	careful	careful	JJ
37681	1940	13	examination	examination	NN
37681	1940	14	of	of	IN
37681	1940	15	all	all	DT
37681	1940	16	of	of	IN
37681	1940	17	them	-PRON-	PRP
37681	1940	18	shows	show	VBZ
37681	1940	19	that	that	IN
37681	1940	20	the	the	DT
37681	1940	21	one	one	NN
37681	1940	22	given	give	VBN
37681	1940	23	below	below	RB
37681	1940	24	is	be	VBZ
37681	1940	25	,	,	,
37681	1940	26	all	all	DT
37681	1940	27	things	thing	NNS
37681	1940	28	considered	consider	VBN
37681	1940	29	,	,	,
37681	1940	30	the	the	DT
37681	1940	31	best	good	JJS
37681	1940	32	one	one	CD
37681	1940	33	for	for	IN
37681	1940	34	pupils	pupil	NNS
37681	1940	35	beginning	begin	VBG
37681	1940	36	geometry	geometry	NN
37681	1940	37	and	and	CC
37681	1940	38	following	follow	VBG
37681	1940	39	the	the	DT
37681	1940	40	sequence	sequence	NN
37681	1940	41	laid	lay	VBN
37681	1940	42	down	down	RP
37681	1940	43	in	in	IN
37681	1940	44	this	this	DT
37681	1940	45	chapter	chapter	NN
37681	1940	46	.	.	.
37681	1941	1	It	-PRON-	PRP
37681	1941	2	has	have	VBZ
37681	1941	3	the	the	DT
37681	1941	4	sanction	sanction	NN
37681	1941	5	of	of	IN
37681	1941	6	some	some	DT
37681	1941	7	of	of	IN
37681	1941	8	the	the	DT
37681	1941	9	most	most	RBS
37681	1941	10	eminent	eminent	JJ
37681	1941	11	mathematicians	mathematician	NNS
37681	1941	12	,	,	,
37681	1941	13	and	and	CC
37681	1941	14	while	while	IN
37681	1941	15	not	not	RB
37681	1941	16	as	as	RB
37681	1941	17	satisfactory	satisfactory	JJ
37681	1941	18	in	in	IN
37681	1941	19	some	some	DT
37681	1941	20	respects	respect	NNS
37681	1941	21	as	as	IN
37681	1941	22	the	the	DT
37681	1941	23	_	_	NNP
37681	1941	24	reductio	reductio	NN
37681	1941	25	ad	ad	NN
37681	1941	26	absurdum	absurdum	NN
37681	1941	27	_	_	NNP
37681	1941	28	,	,	,
37681	1941	29	mentioned	mention	VBN
37681	1941	30	below	below	RB
37681	1941	31	,	,	,
37681	1941	32	it	-PRON-	PRP
37681	1941	33	is	be	VBZ
37681	1941	34	more	more	RBR
37681	1941	35	satisfactory	satisfactory	JJ
37681	1941	36	in	in	IN
37681	1941	37	most	most	JJS
37681	1941	38	particulars	particular	NNS
37681	1941	39	.	.	.
37681	1942	1	The	the	DT
37681	1942	2	proof	proof	NN
37681	1942	3	is	be	VBZ
37681	1942	4	as	as	IN
37681	1942	5	follows	follow	VBZ
37681	1942	6	:	:	:
37681	1942	7	[	[	-LRB-
37681	1942	8	Illustration	illustration	NN
37681	1942	9	:	:	:
37681	1942	10	=	=	LS
37681	1942	11	Given	give	VBN
37681	1942	12	the	the	DT
37681	1942	13	triangle	triangle	NN
37681	1942	14	ABC	ABC	NNP
37681	1942	15	,	,	,
37681	1942	16	with	with	IN
37681	1942	17	the	the	DT
37681	1942	18	angle	angle	NN
37681	1942	19	A	a	DT
37681	1942	20	equal	equal	JJ
37681	1942	21	to	to	IN
37681	1942	22	the	the	DT
37681	1942	23	angle	angle	NN
37681	1942	24	B.=	B.=	NNP
37681	1942	25	]	]	-RRB-
37681	1942	26	_	_	NNP
37681	1942	27	To	to	TO
37681	1942	28	prove	prove	VB
37681	1942	29	that	that	IN
37681	1942	30	_	_	NNP
37681	1942	31	_	_	NNP
37681	1942	32	AC	AC	NNP
37681	1942	33	_	_	NNP
37681	1942	34	=	=	SYM
37681	1942	35	_	_	NNP
37681	1942	36	BC	BC	NNP
37681	1942	37	_	_	NNP
37681	1942	38	.	.	.
37681	1943	1	=	=	NFP
37681	1943	2	Proof.=	Proof.=	NNP
37681	1943	3	Suppose	suppose	VB
37681	1943	4	the	the	DT
37681	1943	5	second	second	JJ
37681	1943	6	triangle	triangle	NN
37681	1943	7	_	_	NNP
37681	1943	8	A'B'C	A'B'C	NNP
37681	1943	9	'	'	''
37681	1943	10	_	_	NNP
37681	1943	11	to	to	TO
37681	1943	12	be	be	VB
37681	1943	13	an	an	DT
37681	1943	14	exact	exact	JJ
37681	1943	15	reproduction	reproduction	NN
37681	1943	16	of	of	IN
37681	1943	17	the	the	DT
37681	1943	18	given	give	VBN
37681	1943	19	triangle	triangle	NN
37681	1943	20	_	_	NNP
37681	1943	21	ABC	ABC	NNP
37681	1943	22	_	_	NNP
37681	1943	23	.	.	.
37681	1944	1	Turn	turn	VB
37681	1944	2	the	the	DT
37681	1944	3	triangle	triangle	NN
37681	1944	4	_	_	NNP
37681	1944	5	A'B'C	A'B'C	NNP
37681	1944	6	'	'	''
37681	1944	7	_	_	NNP
37681	1944	8	over	over	IN
37681	1944	9	and	and	CC
37681	1944	10	place	place	VB
37681	1944	11	it	-PRON-	PRP
37681	1944	12	upon	upon	IN
37681	1944	13	_	_	NNP
37681	1944	14	ABC	ABC	NNP
37681	1944	15	_	_	NNP
37681	1944	16	so	so	IN
37681	1944	17	that	that	IN
37681	1944	18	_	_	NNP
37681	1944	19	B	B	NNP
37681	1944	20	'	'	''
37681	1944	21	_	_	NNP
37681	1944	22	shall	shall	MD
37681	1944	23	fall	fall	VB
37681	1944	24	on	on	IN
37681	1944	25	_	_	NNP
37681	1944	26	A	A	NNP
37681	1944	27	_	_	NNP
37681	1944	28	and	and	CC
37681	1944	29	_	_	NNP
37681	1944	30	A	A	NNP
37681	1944	31	'	'	''
37681	1944	32	_	_	NN
37681	1944	33	shall	shall	MD
37681	1944	34	fall	fall	VB
37681	1944	35	on	on	IN
37681	1944	36	_	_	NNP
37681	1944	37	B	B	NNP
37681	1944	38	_	_	NNP
37681	1944	39	.	.	.
37681	1945	1	Then	then	RB
37681	1945	2	_	_	NNP
37681	1945	3	B'A	B'A	NNP
37681	1945	4	'	'	''
37681	1945	5	_	_	NNP
37681	1945	6	will	will	MD
37681	1945	7	coincide	coincide	VB
37681	1945	8	with	with	IN
37681	1945	9	_	_	NNP
37681	1945	10	AB	AB	NNP
37681	1945	11	_	_	NNP
37681	1945	12	.	.	.
37681	1946	1	Since	since	IN
37681	1946	2	[	[	-LRB-
37681	1946	3	L]_A	L]_A	NNS
37681	1946	4	'	'	POS
37681	1946	5	_	_	NN
37681	1946	6	=	=	NFP
37681	1946	7	[	[	-LRB-
37681	1946	8	L]_B	L]_B	NNP
37681	1946	9	'	'	``
37681	1946	10	_	_	NNP
37681	1946	11	,	,	,
37681	1946	12	Given	give	VBN
37681	1946	13	and	and	CC
37681	1946	14	[	[	-LRB-
37681	1946	15	L]_A	L]_A	NNS
37681	1946	16	_	_	NNP
37681	1946	17	=	=	SYM
37681	1946	18	[	[	-LRB-
37681	1946	19	L]_A	L]_A	NNS
37681	1946	20	'	'	POS
37681	1946	21	_	_	NNP
37681	1946	22	,	,	,
37681	1946	23	Hyp	Hyp	NNP
37681	1946	24	.	.	.
37681	1947	1	[	[	-LRB-
37681	1947	2	therefore][L]_A	therefore][L]_A	NNP
37681	1947	3	_	_	NNP
37681	1947	4	=	=	SYM
37681	1947	5	[	[	-LRB-
37681	1947	6	L]_B	L]_B	NNP
37681	1947	7	'	'	``
37681	1947	8	_	_	NNP
37681	1947	9	.	.	.
37681	1948	1	[	[	-LRB-
37681	1948	2	therefore]_B'C	therefore]_b'c	IN
37681	1948	3	'	'	``
37681	1948	4	_	_	NNP
37681	1948	5	will	will	MD
37681	1948	6	lie	lie	VB
37681	1948	7	along	along	IN
37681	1948	8	_	_	NNP
37681	1948	9	AC	AC	NNP
37681	1948	10	_	_	NNP
37681	1948	11	.	.	.
37681	1949	1	Similarly	similarly	RB
37681	1949	2	,	,	,
37681	1949	3	_	_	NNP
37681	1949	4	A'C	a'c	RB
37681	1949	5	'	'	``
37681	1949	6	_	_	NNP
37681	1949	7	will	will	MD
37681	1949	8	lie	lie	VB
37681	1949	9	along	along	IN
37681	1949	10	_	_	NNP
37681	1949	11	BC	BC	NNP
37681	1949	12	_	_	NNP
37681	1949	13	.	.	.
37681	1950	1	Therefore	therefore	RB
37681	1950	2	_	_	NNP
37681	1950	3	C	C	NNP
37681	1950	4	'	'	''
37681	1950	5	_	_	NNP
37681	1950	6	will	will	MD
37681	1950	7	fall	fall	VB
37681	1950	8	on	on	IN
37681	1950	9	both	both	DT
37681	1950	10	_	_	NNP
37681	1950	11	AC	AC	NNP
37681	1950	12	_	_	NNP
37681	1950	13	and	and	CC
37681	1950	14	_	_	NNP
37681	1950	15	BC	BC	NNP
37681	1950	16	_	_	NNP
37681	1950	17	,	,	,
37681	1950	18	and	and	CC
37681	1950	19	hence	hence	RB
37681	1950	20	at	at	IN
37681	1950	21	their	-PRON-	PRP$
37681	1950	22	intersection	intersection	NN
37681	1950	23	.	.	.
37681	1951	1	[	[	-LRB-
37681	1951	2	therefore]_B'C	therefore]_b'c	IN
37681	1951	3	'	'	``
37681	1951	4	_	_	NNP
37681	1951	5	=	=	SYM
37681	1951	6	_	_	NNP
37681	1951	7	AC	AC	NNP
37681	1951	8	_	_	NNP
37681	1951	9	.	.	.
37681	1952	1	But	but	CC
37681	1952	2	_	_	NNP
37681	1952	3	B'C	B'C	NNP
37681	1952	4	'	'	``
37681	1952	5	_	_	NNP
37681	1952	6	was	be	VBD
37681	1952	7	made	make	VBN
37681	1952	8	equal	equal	JJ
37681	1952	9	to	to	IN
37681	1952	10	_	_	NNP
37681	1952	11	BC	BC	NNP
37681	1952	12	_	_	NNP
37681	1952	13	.	.	.
37681	1953	1	[	[	-LRB-
37681	1953	2	therefore]_AC	therefore]_AC	NNP
37681	1953	3	_	_	NNP
37681	1953	4	=	=	SYM
37681	1953	5	_	_	NNP
37681	1953	6	BC	BC	NNP
37681	1953	7	_	_	NNP
37681	1953	8	.	.	.
37681	1954	1	Q.E.D.	Q.E.D.	NNP
37681	1955	1	If	if	IN
37681	1955	2	the	the	DT
37681	1955	3	proposition	proposition	NN
37681	1955	4	should	should	MD
37681	1955	5	be	be	VB
37681	1955	6	postponed	postpone	VBN
37681	1955	7	until	until	IN
37681	1955	8	after	after	IN
37681	1955	9	the	the	DT
37681	1955	10	one	one	NN
37681	1955	11	on	on	IN
37681	1955	12	the	the	DT
37681	1955	13	sum	sum	NN
37681	1955	14	of	of	IN
37681	1955	15	the	the	DT
37681	1955	16	angles	angle	NNS
37681	1955	17	of	of	IN
37681	1955	18	a	a	DT
37681	1955	19	triangle	triangle	NN
37681	1955	20	,	,	,
37681	1955	21	the	the	DT
37681	1955	22	proof	proof	NN
37681	1955	23	would	would	MD
37681	1955	24	be	be	VB
37681	1955	25	simpler	simple	JJR
37681	1955	26	,	,	,
37681	1955	27	but	but	CC
37681	1955	28	it	-PRON-	PRP
37681	1955	29	is	be	VBZ
37681	1955	30	advantageous	advantageous	JJ
37681	1955	31	to	to	TO
37681	1955	32	couple	couple	VB
37681	1955	33	it	-PRON-	PRP
37681	1955	34	with	with	IN
37681	1955	35	its	-PRON-	PRP$
37681	1955	36	immediate	immediate	JJ
37681	1955	37	predecessor	predecessor	NN
37681	1955	38	.	.	.
37681	1956	1	This	this	DT
37681	1956	2	simpler	simple	JJR
37681	1956	3	proof	proof	NN
37681	1956	4	consists	consist	VBZ
37681	1956	5	in	in	IN
37681	1956	6	bisecting	bisect	VBG
37681	1956	7	the	the	DT
37681	1956	8	vertical	vertical	JJ
37681	1956	9	angle	angle	NN
37681	1956	10	,	,	,
37681	1956	11	and	and	CC
37681	1956	12	then	then	RB
37681	1956	13	proving	prove	VBG
37681	1956	14	the	the	DT
37681	1956	15	two	two	CD
37681	1956	16	triangles	triangle	NNS
37681	1956	17	congruent	congruent	JJ
37681	1956	18	.	.	.
37681	1957	1	Among	among	IN
37681	1957	2	the	the	DT
37681	1957	3	other	other	JJ
37681	1957	4	proofs	proof	NNS
37681	1957	5	is	be	VBZ
37681	1957	6	that	that	DT
37681	1957	7	of	of	IN
37681	1957	8	the	the	DT
37681	1957	9	_	_	NNP
37681	1957	10	reductio	reductio	NN
37681	1957	11	ad	ad	NN
37681	1957	12	absurdum	absurdum	NN
37681	1957	13	_	_	NNP
37681	1957	14	,	,	,
37681	1957	15	which	which	WDT
37681	1957	16	the	the	DT
37681	1957	17	student	student	NN
37681	1957	18	might	may	MD
37681	1957	19	now	now	RB
37681	1957	20	meet	meet	VB
37681	1957	21	,	,	,
37681	1957	22	but	but	CC
37681	1957	23	which	which	WDT
37681	1957	24	may	may	MD
37681	1957	25	better	better	RB
37681	1957	26	be	be	VB
37681	1957	27	postponed	postpone	VBN
37681	1957	28	.	.	.
37681	1958	1	The	the	DT
37681	1958	2	phrase	phrase	NN
37681	1958	3	_	_	NNP
37681	1958	4	reductio	reductio	NN
37681	1958	5	ad	ad	NN
37681	1958	6	absurdum	absurdum	NN
37681	1958	7	_	_	NNP
37681	1958	8	seems	seem	VBZ
37681	1958	9	likely	likely	JJ
37681	1958	10	to	to	TO
37681	1958	11	continue	continue	VB
37681	1958	12	in	in	IN
37681	1958	13	spite	spite	NN
37681	1958	14	of	of	IN
37681	1958	15	the	the	DT
37681	1958	16	efforts	effort	NNS
37681	1958	17	to	to	TO
37681	1958	18	find	find	VB
37681	1958	19	another	another	DT
37681	1958	20	one	one	NN
37681	1958	21	that	that	WDT
37681	1958	22	is	be	VBZ
37681	1958	23	simpler	simple	JJR
37681	1958	24	.	.	.
37681	1959	1	Such	such	PDT
37681	1959	2	a	a	DT
37681	1959	3	proof	proof	NN
37681	1959	4	is	be	VBZ
37681	1959	5	also	also	RB
37681	1959	6	called	call	VBN
37681	1959	7	an	an	DT
37681	1959	8	indirect	indirect	JJ
37681	1959	9	proof	proof	NN
37681	1959	10	,	,	,
37681	1959	11	but	but	CC
37681	1959	12	this	this	DT
37681	1959	13	term	term	NN
37681	1959	14	is	be	VBZ
37681	1959	15	not	not	RB
37681	1959	16	altogether	altogether	RB
37681	1959	17	satisfactory	satisfactory	JJ
37681	1959	18	.	.	.
37681	1960	1	Probably	probably	RB
37681	1960	2	both	both	DT
37681	1960	3	names	name	NNS
37681	1960	4	should	should	MD
37681	1960	5	be	be	VB
37681	1960	6	used	use	VBN
37681	1960	7	,	,	,
37681	1960	8	the	the	DT
37681	1960	9	Latin	Latin	NNP
37681	1960	10	to	to	TO
37681	1960	11	explain	explain	VB
37681	1960	12	the	the	DT
37681	1960	13	nature	nature	NN
37681	1960	14	of	of	IN
37681	1960	15	the	the	DT
37681	1960	16	English	English	NNP
37681	1960	17	.	.	.
37681	1961	1	The	the	DT
37681	1961	2	Latin	latin	JJ
37681	1961	3	name	name	NN
37681	1961	4	is	be	VBZ
37681	1961	5	merely	merely	RB
37681	1961	6	a	a	DT
37681	1961	7	translation	translation	NN
37681	1961	8	of	of	IN
37681	1961	9	one	one	CD
37681	1961	10	of	of	IN
37681	1961	11	several	several	JJ
37681	1961	12	Greek	greek	JJ
37681	1961	13	names	name	NNS
37681	1961	14	used	use	VBN
37681	1961	15	by	by	IN
37681	1961	16	Aristotle	Aristotle	NNP
37681	1961	17	,	,	,
37681	1961	18	a	a	DT
37681	1961	19	second	second	JJ
37681	1961	20	being	being	NN
37681	1961	21	in	in	IN
37681	1961	22	English	English	NNP
37681	1961	23	"	"	''
37681	1961	24	proof	proof	NN
37681	1961	25	by	by	IN
37681	1961	26	the	the	DT
37681	1961	27	impossible	impossible	JJ
37681	1961	28	,	,	,
37681	1961	29	"	"	''
37681	1961	30	and	and	CC
37681	1961	31	a	a	DT
37681	1961	32	third	third	JJ
37681	1961	33	being	be	VBG
37681	1961	34	"	"	``
37681	1961	35	proof	proof	NN
37681	1961	36	leading	lead	VBG
37681	1961	37	to	to	IN
37681	1961	38	the	the	DT
37681	1961	39	impossible	impossible	JJ
37681	1961	40	.	.	.
37681	1961	41	"	"	''
37681	1962	1	If	if	IN
37681	1962	2	teachers	teacher	NNS
37681	1962	3	desire	desire	VBP
37681	1962	4	to	to	TO
37681	1962	5	introduce	introduce	VB
37681	1962	6	this	this	DT
37681	1962	7	form	form	NN
37681	1962	8	of	of	IN
37681	1962	9	proof	proof	NN
37681	1962	10	here	here	RB
37681	1962	11	,	,	,
37681	1962	12	it	-PRON-	PRP
37681	1962	13	must	must	MD
37681	1962	14	be	be	VB
37681	1962	15	borne	bear	VBN
37681	1962	16	in	in	IN
37681	1962	17	mind	mind	NN
37681	1962	18	that	that	IN
37681	1962	19	only	only	RB
37681	1962	20	one	one	CD
37681	1962	21	supposition	supposition	NN
37681	1962	22	can	can	MD
37681	1962	23	be	be	VB
37681	1962	24	made	make	VBN
37681	1962	25	if	if	IN
37681	1962	26	such	such	PDT
37681	1962	27	a	a	DT
37681	1962	28	proof	proof	NN
37681	1962	29	is	be	VBZ
37681	1962	30	to	to	TO
37681	1962	31	be	be	VB
37681	1962	32	valid	valid	JJ
37681	1962	33	,	,	,
37681	1962	34	for	for	IN
37681	1962	35	if	if	IN
37681	1962	36	two	two	CD
37681	1962	37	are	be	VBP
37681	1962	38	made	make	VBN
37681	1962	39	,	,	,
37681	1962	40	then	then	RB
37681	1962	41	an	an	DT
37681	1962	42	absurd	absurd	JJ
37681	1962	43	conclusion	conclusion	NN
37681	1962	44	simply	simply	RB
37681	1962	45	shows	show	VBZ
37681	1962	46	that	that	IN
37681	1962	47	either	either	DT
37681	1962	48	or	or	CC
37681	1962	49	both	both	DT
37681	1962	50	must	must	MD
37681	1962	51	be	be	VB
37681	1962	52	false	false	JJ
37681	1962	53	,	,	,
37681	1962	54	but	but	CC
37681	1962	55	we	-PRON-	PRP
37681	1962	56	do	do	VBP
37681	1962	57	not	not	RB
37681	1962	58	know	know	VB
37681	1962	59	which	which	WDT
37681	1962	60	is	be	VBZ
37681	1962	61	false	false	JJ
37681	1962	62	,	,	,
37681	1962	63	or	or	CC
37681	1962	64	if	if	IN
37681	1962	65	only	only	RB
37681	1962	66	one	one	CD
37681	1962	67	is	be	VBZ
37681	1962	68	false	false	JJ
37681	1962	69	.	.	.
37681	1963	1	THEOREM	THEOREM	NNP
37681	1963	2	.	.	.
37681	1964	1	_	_	NNP
37681	1964	2	Two	two	CD
37681	1964	3	triangles	triangle	NNS
37681	1964	4	are	be	VBP
37681	1964	5	congruent	congruent	JJ
37681	1964	6	if	if	IN
37681	1964	7	the	the	DT
37681	1964	8	three	three	CD
37681	1964	9	sides	side	NNS
37681	1964	10	of	of	IN
37681	1964	11	the	the	DT
37681	1964	12	one	one	NN
37681	1964	13	are	be	VBP
37681	1964	14	equal	equal	JJ
37681	1964	15	respectively	respectively	RB
37681	1964	16	to	to	IN
37681	1964	17	the	the	DT
37681	1964	18	three	three	CD
37681	1964	19	sides	side	NNS
37681	1964	20	of	of	IN
37681	1964	21	the	the	DT
37681	1964	22	other	other	JJ
37681	1964	23	.	.	.
37681	1964	24	_	_	NNP
37681	1964	25	It	-PRON-	PRP
37681	1964	26	would	would	MD
37681	1964	27	be	be	VB
37681	1964	28	desirable	desirable	JJ
37681	1964	29	to	to	TO
37681	1964	30	place	place	VB
37681	1964	31	this	this	DT
37681	1964	32	after	after	IN
37681	1964	33	the	the	DT
37681	1964	34	fourth	fourth	JJ
37681	1964	35	proposition	proposition	NN
37681	1964	36	mentioned	mention	VBN
37681	1964	37	in	in	IN
37681	1964	38	this	this	DT
37681	1964	39	list	list	NN
37681	1964	40	if	if	IN
37681	1964	41	it	-PRON-	PRP
37681	1964	42	could	could	MD
37681	1964	43	be	be	VB
37681	1964	44	done	do	VBN
37681	1964	45	,	,	,
37681	1964	46	so	so	IN
37681	1964	47	as	as	IN
37681	1964	48	to	to	TO
37681	1964	49	get	get	VB
37681	1964	50	the	the	DT
37681	1964	51	triangles	triangle	NNS
37681	1964	52	in	in	IN
37681	1964	53	a	a	DT
37681	1964	54	group	group	NN
37681	1964	55	,	,	,
37681	1964	56	but	but	CC
37681	1964	57	we	-PRON-	PRP
37681	1964	58	need	need	VBP
37681	1964	59	the	the	DT
37681	1964	60	fourth	fourth	JJ
37681	1964	61	one	one	NN
37681	1964	62	for	for	IN
37681	1964	63	proving	prove	VBG
37681	1964	64	this	this	DT
37681	1964	65	,	,	,
37681	1964	66	so	so	IN
37681	1964	67	that	that	IN
37681	1964	68	the	the	DT
37681	1964	69	arrangement	arrangement	NN
37681	1964	70	can	can	MD
37681	1964	71	not	not	RB
37681	1964	72	be	be	VB
37681	1964	73	made	make	VBN
37681	1964	74	,	,	,
37681	1964	75	at	at	IN
37681	1964	76	least	least	JJS
37681	1964	77	with	with	IN
37681	1964	78	this	this	DT
37681	1964	79	method	method	NN
37681	1964	80	of	of	IN
37681	1964	81	proof	proof	NN
37681	1964	82	.	.	.
37681	1965	1	This	this	DT
37681	1965	2	proposition	proposition	NN
37681	1965	3	is	be	VBZ
37681	1965	4	a	a	DT
37681	1965	5	"	"	``
37681	1965	6	partial	partial	JJ
37681	1965	7	converse	converse	NN
37681	1965	8	"	"	''
37681	1965	9	of	of	IN
37681	1965	10	the	the	DT
37681	1965	11	second	second	JJ
37681	1965	12	proposition	proposition	NN
37681	1965	13	in	in	IN
37681	1965	14	this	this	DT
37681	1965	15	list	list	NN
37681	1965	16	;	;	:
37681	1965	17	for	for	IN
37681	1965	18	if	if	IN
37681	1965	19	the	the	DT
37681	1965	20	triangles	triangle	NNS
37681	1965	21	are	be	VBP
37681	1965	22	_	_	NNP
37681	1965	23	ABC	ABC	NNP
37681	1965	24	_	_	NNP
37681	1965	25	and	and	CC
37681	1965	26	_	_	NNP
37681	1965	27	A'B'C	A'B'C	NNP
37681	1965	28	'	'	''
37681	1965	29	_	_	NNP
37681	1965	30	,	,	,
37681	1965	31	with	with	IN
37681	1965	32	sides	side	NNS
37681	1965	33	_	_	NNP
37681	1965	34	a	a	DT
37681	1965	35	_	_	NNP
37681	1965	36	,	,	,
37681	1965	37	_	_	NNP
37681	1965	38	b	b	NNP
37681	1965	39	_	_	NNP
37681	1965	40	,	,	,
37681	1965	41	_	_	NNP
37681	1965	42	c	c	NNP
37681	1965	43	_	_	NNP
37681	1965	44	and	and	CC
37681	1965	45	_	_	NNP
37681	1965	46	a	a	DT
37681	1965	47	'	'	''
37681	1965	48	_	_	NNP
37681	1965	49	,	,	,
37681	1965	50	_	_	NNP
37681	1965	51	b	b	NNP
37681	1965	52	'	'	``
37681	1965	53	_	_	NNP
37681	1965	54	,	,	,
37681	1965	55	_	_	NNP
37681	1965	56	c	c	NNP
37681	1965	57	'	'	''
37681	1965	58	_	_	NNP
37681	1965	59	,	,	,
37681	1965	60	then	then	RB
37681	1965	61	the	the	DT
37681	1965	62	second	second	JJ
37681	1965	63	proposition	proposition	NN
37681	1965	64	asserts	assert	VBZ
37681	1965	65	that	that	IN
37681	1965	66	if	if	IN
37681	1965	67	_	_	NNP
37681	1965	68	b	b	NNP
37681	1965	69	_	_	NNP
37681	1965	70	=	=	SYM
37681	1965	71	_	_	NNP
37681	1965	72	b	b	NNP
37681	1965	73	'	'	''
37681	1965	74	_	_	NNP
37681	1965	75	,	,	,
37681	1965	76	_	_	NNP
37681	1965	77	c	c	NNP
37681	1965	78	_	_	NNP
37681	1965	79	=	=	SYM
37681	1965	80	_	_	NNP
37681	1965	81	c	c	NNP
37681	1965	82	'	'	''
37681	1965	83	_	_	NNP
37681	1965	84	,	,	,
37681	1965	85	and	and	CC
37681	1965	86	[	[	-LRB-
37681	1965	87	L]_A	L]_A	NNS
37681	1965	88	_	_	NNP
37681	1965	89	=	=	SYM
37681	1965	90	[	[	-LRB-
37681	1965	91	L]_A	L]_A	NNS
37681	1965	92	'	'	POS
37681	1965	93	_	_	NNP
37681	1965	94	,	,	,
37681	1965	95	then	then	RB
37681	1965	96	_	_	NNP
37681	1965	97	a	a	DT
37681	1965	98	_	_	NNP
37681	1965	99	=	=	SYM
37681	1965	100	_	_	NNP
37681	1965	101	a	a	DT
37681	1965	102	'	'	``
37681	1965	103	_	_	NN
37681	1965	104	and	and	CC
37681	1965	105	the	the	DT
37681	1965	106	triangles	triangle	NNS
37681	1965	107	are	be	VBP
37681	1965	108	congruent	congruent	JJ
37681	1965	109	,	,	,
37681	1965	110	while	while	IN
37681	1965	111	this	this	DT
37681	1965	112	proposition	proposition	NN
37681	1965	113	asserts	assert	VBZ
37681	1965	114	that	that	IN
37681	1965	115	if	if	IN
37681	1965	116	_	_	NNP
37681	1965	117	a	a	DT
37681	1965	118	_	_	NNP
37681	1965	119	=	=	SYM
37681	1965	120	_	_	NNP
37681	1965	121	a	a	DT
37681	1965	122	'	'	``
37681	1965	123	_	_	NNP
37681	1965	124	,	,	,
37681	1965	125	_	_	NNP
37681	1965	126	b	b	NNP
37681	1965	127	_	_	NNP
37681	1965	128	=	=	SYM
37681	1965	129	_	_	NNP
37681	1965	130	b	b	NNP
37681	1965	131	'	'	``
37681	1965	132	_	_	NNP
37681	1965	133	,	,	,
37681	1965	134	and	and	CC
37681	1965	135	_	_	NNP
37681	1965	136	c	c	NNP
37681	1965	137	_	_	NNP
37681	1965	138	=	=	SYM
37681	1965	139	_	_	NNP
37681	1965	140	c	c	NNP
37681	1965	141	'	'	''
37681	1965	142	_	_	NNP
37681	1965	143	,	,	,
37681	1965	144	then	then	RB
37681	1965	145	[	[	-LRB-
37681	1965	146	L]_A	L]_A	NNS
37681	1965	147	_	_	NNP
37681	1965	148	=	=	SYM
37681	1965	149	[	[	-LRB-
37681	1965	150	L]_A	L]_A	NNS
37681	1965	151	'	'	POS
37681	1965	152	_	_	NNP
37681	1965	153	and	and	CC
37681	1965	154	the	the	DT
37681	1965	155	triangles	triangle	NNS
37681	1965	156	are	be	VBP
37681	1965	157	congruent	congruent	JJ
37681	1965	158	.	.	.
37681	1966	1	The	the	DT
37681	1966	2	proposition	proposition	NN
37681	1966	3	was	be	VBD
37681	1966	4	known	know	VBN
37681	1966	5	at	at	IN
37681	1966	6	least	least	JJS
37681	1966	7	as	as	RB
37681	1966	8	early	early	RB
37681	1966	9	as	as	IN
37681	1966	10	Aristotle	Aristotle	NNP
37681	1966	11	's	's	POS
37681	1966	12	time	time	NN
37681	1966	13	.	.	.
37681	1967	1	Euclid	Euclid	NNP
37681	1967	2	proved	prove	VBD
37681	1967	3	it	-PRON-	PRP
37681	1967	4	by	by	IN
37681	1967	5	inserting	insert	VBG
37681	1967	6	a	a	DT
37681	1967	7	preliminary	preliminary	JJ
37681	1967	8	proposition	proposition	NN
37681	1967	9	to	to	IN
37681	1967	10	the	the	DT
37681	1967	11	effect	effect	NN
37681	1967	12	that	that	IN
37681	1967	13	it	-PRON-	PRP
37681	1967	14	is	be	VBZ
37681	1967	15	impossible	impossible	JJ
37681	1967	16	to	to	TO
37681	1967	17	have	have	VB
37681	1967	18	on	on	IN
37681	1967	19	the	the	DT
37681	1967	20	same	same	JJ
37681	1967	21	base	base	NN
37681	1967	22	_	_	NNP
37681	1967	23	AB	AB	NNP
37681	1967	24	_	_	NNP
37681	1967	25	and	and	CC
37681	1967	26	the	the	DT
37681	1967	27	same	same	JJ
37681	1967	28	side	side	NN
37681	1967	29	of	of	IN
37681	1967	30	it	-PRON-	PRP
37681	1967	31	two	two	CD
37681	1967	32	different	different	JJ
37681	1967	33	triangles	triangle	NNS
37681	1967	34	_	_	NNP
37681	1967	35	ABC	ABC	NNP
37681	1967	36	_	_	NNP
37681	1967	37	and	and	CC
37681	1967	38	_	_	NNP
37681	1967	39	ABC	ABC	NNP
37681	1967	40	'	'	POS
37681	1967	41	_	_	NNP
37681	1967	42	,	,	,
37681	1967	43	with	with	IN
37681	1967	44	_	_	NNP
37681	1967	45	AC	AC	NNP
37681	1967	46	_	_	NNP
37681	1967	47	=	=	SYM
37681	1967	48	_	_	NNP
37681	1967	49	AC	AC	NNP
37681	1967	50	'	'	''
37681	1967	51	_	_	NNP
37681	1967	52	,	,	,
37681	1967	53	and	and	CC
37681	1967	54	_	_	NNP
37681	1967	55	BC	BC	NNP
37681	1967	56	_	_	NNP
37681	1967	57	=	=	SYM
37681	1967	58	_	_	NNP
37681	1967	59	BC	BC	NNP
37681	1967	60	'	'	POS
37681	1967	61	_	_	NNP
37681	1967	62	.	.	.
37681	1968	1	The	the	DT
37681	1968	2	proof	proof	NN
37681	1968	3	ordinarily	ordinarily	RB
37681	1968	4	given	give	VBN
37681	1968	5	to	to	IN
37681	1968	6	-	-	HYPH
37681	1968	7	day	day	NN
37681	1968	8	,	,	,
37681	1968	9	wherein	wherein	WRB
37681	1968	10	the	the	DT
37681	1968	11	two	two	CD
37681	1968	12	triangles	triangle	NNS
37681	1968	13	are	be	VBP
37681	1968	14	constructed	construct	VBN
37681	1968	15	on	on	IN
37681	1968	16	opposite	opposite	JJ
37681	1968	17	sides	side	NNS
37681	1968	18	of	of	IN
37681	1968	19	the	the	DT
37681	1968	20	base	base	NN
37681	1968	21	,	,	,
37681	1968	22	is	be	VBZ
37681	1968	23	due	due	JJ
37681	1968	24	to	to	IN
37681	1968	25	Philo	Philo	NNP
37681	1968	26	of	of	IN
37681	1968	27	Byzantium	Byzantium	NNP
37681	1968	28	,	,	,
37681	1968	29	who	who	WP
37681	1968	30	lived	live	VBD
37681	1968	31	after	after	IN
37681	1968	32	Euclid	Euclid	NNP
37681	1968	33	's	's	POS
37681	1968	34	time	time	NN
37681	1968	35	but	but	CC
37681	1968	36	before	before	IN
37681	1968	37	the	the	DT
37681	1968	38	Christian	christian	JJ
37681	1968	39	era	era	NN
37681	1968	40	,	,	,
37681	1968	41	and	and	CC
37681	1968	42	it	-PRON-	PRP
37681	1968	43	is	be	VBZ
37681	1968	44	also	also	RB
37681	1968	45	given	give	VBN
37681	1968	46	by	by	IN
37681	1968	47	Proclus	Proclus	NNP
37681	1968	48	.	.	.
37681	1969	1	There	there	EX
37681	1969	2	are	be	VBP
37681	1969	3	really	really	RB
37681	1969	4	three	three	CD
37681	1969	5	cases	case	NNS
37681	1969	6	,	,	,
37681	1969	7	if	if	IN
37681	1969	8	one	one	CD
37681	1969	9	wishes	wish	VBZ
37681	1969	10	to	to	TO
37681	1969	11	be	be	VB
37681	1969	12	overparticular	overparticular	JJ
37681	1969	13	,	,	,
37681	1969	14	corresponding	correspond	VBG
37681	1969	15	to	to	IN
37681	1969	16	the	the	DT
37681	1969	17	three	three	CD
37681	1969	18	pairs	pair	NNS
37681	1969	19	of	of	IN
37681	1969	20	equal	equal	JJ
37681	1969	21	sides	side	NNS
37681	1969	22	.	.	.
37681	1970	1	But	but	CC
37681	1970	2	if	if	IN
37681	1970	3	we	-PRON-	PRP
37681	1970	4	are	be	VBP
37681	1970	5	allowed	allow	VBN
37681	1970	6	to	to	TO
37681	1970	7	take	take	VB
37681	1970	8	the	the	DT
37681	1970	9	longest	long	JJS
37681	1970	10	side	side	NN
37681	1970	11	for	for	IN
37681	1970	12	the	the	DT
37681	1970	13	common	common	JJ
37681	1970	14	base	base	NN
37681	1970	15	,	,	,
37681	1970	16	only	only	RB
37681	1970	17	one	one	CD
37681	1970	18	case	case	NN
37681	1970	19	need	nee	MD
37681	1970	20	be	be	VB
37681	1970	21	considered	consider	VBN
37681	1970	22	.	.	.
37681	1971	1	Of	of	IN
37681	1971	2	the	the	DT
37681	1971	3	applications	application	NNS
37681	1971	4	of	of	IN
37681	1971	5	the	the	DT
37681	1971	6	proposition	proposition	NN
37681	1971	7	one	one	CD
37681	1971	8	of	of	IN
37681	1971	9	the	the	DT
37681	1971	10	most	most	RBS
37681	1971	11	important	important	JJ
37681	1971	12	relates	relate	VBZ
37681	1971	13	to	to	IN
37681	1971	14	making	make	VBG
37681	1971	15	a	a	DT
37681	1971	16	figure	figure	NN
37681	1971	17	rigid	rigid	JJ
37681	1971	18	by	by	IN
37681	1971	19	means	mean	NNS
37681	1971	20	of	of	IN
37681	1971	21	diagonals	diagonal	NNS
37681	1971	22	.	.	.
37681	1972	1	For	for	IN
37681	1972	2	example	example	NN
37681	1972	3	,	,	,
37681	1972	4	how	how	WRB
37681	1972	5	many	many	JJ
37681	1972	6	diagonals	diagonal	NNS
37681	1972	7	must	must	MD
37681	1972	8	be	be	VB
37681	1972	9	drawn	draw	VBN
37681	1972	10	in	in	IN
37681	1972	11	order	order	NN
37681	1972	12	to	to	TO
37681	1972	13	make	make	VB
37681	1972	14	a	a	DT
37681	1972	15	quadrilateral	quadrilateral	JJ
37681	1972	16	rigid	rigid	JJ
37681	1972	17	?	?	.
37681	1973	1	to	to	TO
37681	1973	2	make	make	VB
37681	1973	3	a	a	DT
37681	1973	4	pentagon	pentagon	NNP
37681	1973	5	rigid	rigid	JJ
37681	1973	6	?	?	.
37681	1974	1	a	a	DT
37681	1974	2	hexagon	hexagon	NNP
37681	1974	3	?	?	.
37681	1975	1	a	a	DT
37681	1975	2	polygon	polygon	NN
37681	1975	3	of	of	IN
37681	1975	4	_	_	NNP
37681	1975	5	n	n	CC
37681	1975	6	_	_	NNP
37681	1975	7	sides	side	NNS
37681	1975	8	.	.	.
37681	1976	1	In	in	IN
37681	1976	2	particular	particular	JJ
37681	1976	3	,	,	,
37681	1976	4	the	the	DT
37681	1976	5	following	follow	VBG
37681	1976	6	questions	question	NNS
37681	1976	7	may	may	MD
37681	1976	8	be	be	VB
37681	1976	9	asked	ask	VBN
37681	1976	10	of	of	IN
37681	1976	11	a	a	DT
37681	1976	12	class	class	NN
37681	1976	13	:	:	:
37681	1976	14	[	[	-LRB-
37681	1976	15	Illustration	illustration	NN
37681	1976	16	]	]	-RRB-
37681	1976	17	1	1	CD
37681	1976	18	.	.	.
37681	1977	1	Three	three	CD
37681	1977	2	iron	iron	NN
37681	1977	3	rods	rod	NNS
37681	1977	4	are	be	VBP
37681	1977	5	hinged	hinge	VBN
37681	1977	6	at	at	IN
37681	1977	7	the	the	DT
37681	1977	8	extremities	extremity	NNS
37681	1977	9	,	,	,
37681	1977	10	as	as	IN
37681	1977	11	shown	show	VBN
37681	1977	12	in	in	IN
37681	1977	13	this	this	DT
37681	1977	14	figure	figure	NN
37681	1977	15	.	.	.
37681	1978	1	Is	be	VBZ
37681	1978	2	the	the	DT
37681	1978	3	figure	figure	NN
37681	1978	4	rigid	rigid	JJ
37681	1978	5	?	?	.
37681	1979	1	Why	why	WRB
37681	1979	2	?	?	.
37681	1980	1	2	2	LS
37681	1980	2	.	.	.
37681	1981	1	Four	four	CD
37681	1981	2	iron	iron	NN
37681	1981	3	rods	rod	NNS
37681	1981	4	are	be	VBP
37681	1981	5	hinged	hinge	VBN
37681	1981	6	,	,	,
37681	1981	7	as	as	IN
37681	1981	8	shown	show	VBN
37681	1981	9	in	in	IN
37681	1981	10	this	this	DT
37681	1981	11	figure	figure	NN
37681	1981	12	.	.	.
37681	1982	1	Is	be	VBZ
37681	1982	2	the	the	DT
37681	1982	3	figure	figure	NN
37681	1982	4	rigid	rigid	JJ
37681	1982	5	?	?	.
37681	1983	1	If	if	IN
37681	1983	2	not	not	RB
37681	1983	3	,	,	,
37681	1983	4	where	where	WRB
37681	1983	5	would	would	MD
37681	1983	6	you	-PRON-	PRP
37681	1983	7	put	put	VB
37681	1983	8	in	in	IN
37681	1983	9	the	the	DT
37681	1983	10	fifth	fifth	JJ
37681	1983	11	rod	rod	NN
37681	1983	12	to	to	TO
37681	1983	13	make	make	VB
37681	1983	14	it	-PRON-	PRP
37681	1983	15	rigid	rigid	JJ
37681	1983	16	?	?	.
37681	1984	1	Prove	prove	VB
37681	1984	2	that	that	IN
37681	1984	3	this	this	DT
37681	1984	4	would	would	MD
37681	1984	5	accomplish	accomplish	VB
37681	1984	6	the	the	DT
37681	1984	7	result	result	NN
37681	1984	8	.	.	.
37681	1985	1	[	[	-LRB-
37681	1985	2	Illustration	illustration	NN
37681	1985	3	]	]	-RRB-
37681	1985	4	Another	another	DT
37681	1985	5	interesting	interesting	JJ
37681	1985	6	application	application	NN
37681	1985	7	relates	relate	VBZ
37681	1985	8	to	to	IN
37681	1985	9	the	the	DT
37681	1985	10	most	most	RBS
37681	1985	11	ancient	ancient	JJ
37681	1985	12	form	form	NN
37681	1985	13	of	of	IN
37681	1985	14	leveling	level	VBG
37681	1985	15	instrument	instrument	NN
37681	1985	16	known	know	VBN
37681	1985	17	to	to	IN
37681	1985	18	us	-PRON-	PRP
37681	1985	19	.	.	.
37681	1986	1	This	this	DT
37681	1986	2	kind	kind	NN
37681	1986	3	of	of	IN
37681	1986	4	level	level	NN
37681	1986	5	is	be	VBZ
37681	1986	6	pictured	picture	VBN
37681	1986	7	on	on	IN
37681	1986	8	very	very	RB
37681	1986	9	ancient	ancient	JJ
37681	1986	10	monuments	monument	NNS
37681	1986	11	,	,	,
37681	1986	12	and	and	CC
37681	1986	13	it	-PRON-	PRP
37681	1986	14	is	be	VBZ
37681	1986	15	still	still	RB
37681	1986	16	used	use	VBN
37681	1986	17	in	in	IN
37681	1986	18	many	many	JJ
37681	1986	19	parts	part	NNS
37681	1986	20	of	of	IN
37681	1986	21	the	the	DT
37681	1986	22	world	world	NN
37681	1986	23	.	.	.
37681	1987	1	Pupils	pupil	NNS
37681	1987	2	in	in	IN
37681	1987	3	manual	manual	JJ
37681	1987	4	training	training	NN
37681	1987	5	may	may	MD
37681	1987	6	make	make	VB
37681	1987	7	such	such	PDT
37681	1987	8	an	an	DT
37681	1987	9	instrument	instrument	NN
37681	1987	10	,	,	,
37681	1987	11	and	and	CC
37681	1987	12	indeed	indeed	RB
37681	1987	13	one	one	CD
37681	1987	14	is	be	VBZ
37681	1987	15	easily	easily	RB
37681	1987	16	made	make	VBN
37681	1987	17	out	out	IN
37681	1987	18	of	of	IN
37681	1987	19	cardboard	cardboard	NN
37681	1987	20	.	.	.
37681	1988	1	If	if	IN
37681	1988	2	the	the	DT
37681	1988	3	plumb	plumb	JJ
37681	1988	4	line	line	NN
37681	1988	5	passes	pass	VBZ
37681	1988	6	through	through	IN
37681	1988	7	the	the	DT
37681	1988	8	mid	mid	NN
37681	1988	9	-	-	NN
37681	1988	10	point	point	NN
37681	1988	11	of	of	IN
37681	1988	12	the	the	DT
37681	1988	13	base	base	NN
37681	1988	14	,	,	,
37681	1988	15	the	the	DT
37681	1988	16	two	two	CD
37681	1988	17	triangles	triangle	NNS
37681	1988	18	are	be	VBP
37681	1988	19	congruent	congruent	JJ
37681	1988	20	and	and	CC
37681	1988	21	the	the	DT
37681	1988	22	plumb	plumb	JJ
37681	1988	23	line	line	NN
37681	1988	24	is	be	VBZ
37681	1988	25	then	then	RB
37681	1988	26	perpendicular	perpendicular	JJ
37681	1988	27	to	to	IN
37681	1988	28	the	the	DT
37681	1988	29	base	base	NN
37681	1988	30	.	.	.
37681	1989	1	In	in	IN
37681	1989	2	other	other	JJ
37681	1989	3	words	word	NNS
37681	1989	4	,	,	,
37681	1989	5	the	the	DT
37681	1989	6	base	base	NN
37681	1989	7	is	be	VBZ
37681	1989	8	level	level	NN
37681	1989	9	.	.	.
37681	1990	1	With	with	IN
37681	1990	2	such	such	JJ
37681	1990	3	simple	simple	JJ
37681	1990	4	primitive	primitive	JJ
37681	1990	5	instruments	instrument	NNS
37681	1990	6	,	,	,
37681	1990	7	easily	easily	RB
37681	1990	8	made	make	VBN
37681	1990	9	by	by	IN
37681	1990	10	pupils	pupil	NNS
37681	1990	11	,	,	,
37681	1990	12	a	a	DT
37681	1990	13	good	good	JJ
37681	1990	14	deal	deal	NN
37681	1990	15	of	of	IN
37681	1990	16	practical	practical	JJ
37681	1990	17	mathematical	mathematical	JJ
37681	1990	18	work	work	NN
37681	1990	19	can	can	MD
37681	1990	20	be	be	VB
37681	1990	21	performed	perform	VBN
37681	1990	22	.	.	.
37681	1991	1	The	the	DT
37681	1991	2	interesting	interesting	JJ
37681	1991	3	old	old	JJ
37681	1991	4	illustration	illustration	NN
37681	1991	5	here	here	RB
37681	1991	6	given	give	VBN
37681	1991	7	shows	show	VBZ
37681	1991	8	how	how	WRB
37681	1991	9	this	this	DT
37681	1991	10	form	form	NN
37681	1991	11	of	of	IN
37681	1991	12	level	level	NN
37681	1991	13	was	be	VBD
37681	1991	14	used	use	VBN
37681	1991	15	three	three	CD
37681	1991	16	hundred	hundred	CD
37681	1991	17	years	year	NNS
37681	1991	18	ago	ago	RB
37681	1991	19	.	.	.
37681	1992	1	[	[	-LRB-
37681	1992	2	Illustration	illustration	NN
37681	1992	3	:	:	:
37681	1992	4	EARLY	early	JJ
37681	1992	5	METHODS	methods	NN
37681	1992	6	OF	of	IN
37681	1992	7	LEVELING	LEVELING	NNP
37681	1992	8	Pomodoro	Pomodoro	NNP
37681	1992	9	's	's	POS
37681	1992	10	"	"	``
37681	1992	11	La	La	NNP
37681	1992	12	geometria	geometria	NNP
37681	1992	13	prattica	prattica	NNP
37681	1992	14	,	,	,
37681	1992	15	"	"	``
37681	1992	16	Rome	Rome	NNP
37681	1992	17	,	,	,
37681	1992	18	1624	1624	CD
37681	1992	19	]	]	-RRB-
37681	1992	20	[	[	-LRB-
37681	1992	21	Illustration	illustration	NN
37681	1992	22	]	]	-RRB-
37681	1992	23	Teachers	teacher	NNS
37681	1992	24	who	who	WP
37681	1992	25	seek	seek	VBP
37681	1992	26	for	for	IN
37681	1992	27	geometric	geometric	JJ
37681	1992	28	figures	figure	NNS
37681	1992	29	in	in	IN
37681	1992	30	practical	practical	JJ
37681	1992	31	mechanics	mechanic	NNS
37681	1992	32	will	will	MD
37681	1992	33	find	find	VB
37681	1992	34	this	this	DT
37681	1992	35	proposition	proposition	NN
37681	1992	36	illustrated	illustrate	VBN
37681	1992	37	in	in	IN
37681	1992	38	the	the	DT
37681	1992	39	ordinary	ordinary	JJ
37681	1992	40	hoisting	hoisting	NN
37681	1992	41	apparatus	apparatus	NN
37681	1992	42	of	of	IN
37681	1992	43	the	the	DT
37681	1992	44	kind	kind	NN
37681	1992	45	here	here	RB
37681	1992	46	shown	show	VBN
37681	1992	47	.	.	.
37681	1993	1	From	from	IN
37681	1993	2	the	the	DT
37681	1993	3	study	study	NN
37681	1993	4	of	of	IN
37681	1993	5	such	such	JJ
37681	1993	6	forms	form	NNS
37681	1993	7	and	and	CC
37681	1993	8	of	of	IN
37681	1993	9	simple	simple	JJ
37681	1993	10	roof	roof	NN
37681	1993	11	and	and	CC
37681	1993	12	bridge	bridge	NN
37681	1993	13	trusses	truss	NNS
37681	1993	14	,	,	,
37681	1993	15	a	a	DT
37681	1993	16	number	number	NN
37681	1993	17	of	of	IN
37681	1993	18	the	the	DT
37681	1993	19	usual	usual	JJ
37681	1993	20	properties	property	NNS
37681	1993	21	of	of	IN
37681	1993	22	the	the	DT
37681	1993	23	isosceles	isoscele	NNS
37681	1993	24	triangle	triangle	NN
37681	1993	25	may	may	MD
37681	1993	26	be	be	VB
37681	1993	27	derived	derive	VBN
37681	1993	28	.	.	.
37681	1994	1	THEOREM	THEOREM	NNP
37681	1994	2	.	.	.
37681	1995	1	_	_	NNP
37681	1995	2	The	the	DT
37681	1995	3	sum	sum	NN
37681	1995	4	of	of	IN
37681	1995	5	two	two	CD
37681	1995	6	lines	line	NNS
37681	1995	7	drawn	draw	VBN
37681	1995	8	from	from	IN
37681	1995	9	a	a	DT
37681	1995	10	given	give	VBN
37681	1995	11	point	point	NN
37681	1995	12	to	to	IN
37681	1995	13	the	the	DT
37681	1995	14	extremities	extremity	NNS
37681	1995	15	of	of	IN
37681	1995	16	a	a	DT
37681	1995	17	given	give	VBN
37681	1995	18	line	line	NN
37681	1995	19	is	be	VBZ
37681	1995	20	greater	great	JJR
37681	1995	21	than	than	IN
37681	1995	22	the	the	DT
37681	1995	23	sum	sum	NN
37681	1995	24	of	of	IN
37681	1995	25	two	two	CD
37681	1995	26	other	other	JJ
37681	1995	27	lines	line	NNS
37681	1995	28	similarly	similarly	RB
37681	1995	29	drawn	draw	VBN
37681	1995	30	,	,	,
37681	1995	31	but	but	CC
37681	1995	32	included	include	VBN
37681	1995	33	by	by	IN
37681	1995	34	them	-PRON-	PRP
37681	1995	35	.	.	.
37681	1995	36	_	_	NNP
37681	1995	37	It	-PRON-	PRP
37681	1995	38	should	should	MD
37681	1995	39	be	be	VB
37681	1995	40	noted	note	VBN
37681	1995	41	that	that	IN
37681	1995	42	the	the	DT
37681	1995	43	words	word	NNS
37681	1995	44	"	"	``
37681	1995	45	the	the	DT
37681	1995	46	extremities	extremity	NNS
37681	1995	47	of	of	IN
37681	1995	48	"	"	``
37681	1995	49	are	be	VBP
37681	1995	50	necessary	necessary	JJ
37681	1995	51	,	,	,
37681	1995	52	for	for	IN
37681	1995	53	it	-PRON-	PRP
37681	1995	54	is	be	VBZ
37681	1995	55	possible	possible	JJ
37681	1995	56	to	to	TO
37681	1995	57	draw	draw	VB
37681	1995	58	from	from	IN
37681	1995	59	a	a	DT
37681	1995	60	certain	certain	JJ
37681	1995	61	point	point	NN
37681	1995	62	within	within	IN
37681	1995	63	a	a	DT
37681	1995	64	certain	certain	JJ
37681	1995	65	triangle	triangle	NN
37681	1995	66	two	two	CD
37681	1995	67	lines	line	NNS
37681	1995	68	to	to	IN
37681	1995	69	the	the	DT
37681	1995	70	base	base	NN
37681	1995	71	such	such	JJ
37681	1995	72	that	that	IN
37681	1995	73	their	-PRON-	PRP$
37681	1995	74	sum	sum	NN
37681	1995	75	is	be	VBZ
37681	1995	76	greater	great	JJR
37681	1995	77	than	than	IN
37681	1995	78	the	the	DT
37681	1995	79	sum	sum	NN
37681	1995	80	of	of	IN
37681	1995	81	the	the	DT
37681	1995	82	other	other	JJ
37681	1995	83	two	two	CD
37681	1995	84	sides	side	NNS
37681	1995	85	.	.	.
37681	1996	1	[	[	-LRB-
37681	1996	2	Illustration	illustration	NN
37681	1996	3	]	]	-RRB-
37681	1996	4	Thus	thus	RB
37681	1996	5	,	,	,
37681	1996	6	in	in	IN
37681	1996	7	the	the	DT
37681	1996	8	right	right	JJ
37681	1996	9	triangle	triangle	NN
37681	1996	10	_	_	NNP
37681	1996	11	ABC	ABC	NNP
37681	1996	12	_	_	NNP
37681	1996	13	draw	draw	VBP
37681	1996	14	any	any	DT
37681	1996	15	line	line	NN
37681	1996	16	_	_	NNP
37681	1996	17	CX	CX	NNP
37681	1996	18	_	_	NNP
37681	1996	19	from	from	IN
37681	1996	20	_	_	NNP
37681	1996	21	C	C	NNP
37681	1996	22	_	_	NNP
37681	1996	23	to	to	IN
37681	1996	24	the	the	DT
37681	1996	25	base	base	NN
37681	1996	26	.	.	.
37681	1997	1	Make	make	VB
37681	1997	2	_	_	NNP
37681	1997	3	XY	XY	NNP
37681	1997	4	_	_	NNP
37681	1997	5	=	=	SYM
37681	1997	6	_	_	NNP
37681	1997	7	AC	AC	NNP
37681	1997	8	_	_	NNP
37681	1997	9	,	,	,
37681	1997	10	and	and	CC
37681	1997	11	_	_	NNP
37681	1997	12	CP	CP	NNP
37681	1997	13	_	_	NNP
37681	1997	14	=	=	SYM
37681	1997	15	_	_	NNP
37681	1997	16	PY	PY	NNP
37681	1997	17	_	_	NNP
37681	1997	18	.	.	.
37681	1998	1	Then	then	RB
37681	1998	2	it	-PRON-	PRP
37681	1998	3	is	be	VBZ
37681	1998	4	easily	easily	RB
37681	1998	5	shown	show	VBN
37681	1998	6	that	that	IN
37681	1998	7	_	_	NNP
37681	1998	8	PB	PB	NNP
37681	1998	9	_	_	NNP
37681	1998	10	+	+	CC
37681	1998	11	_	_	NNP
37681	1998	12	PX	PX	NNP
37681	1998	13	_	_	NNP
37681	1998	14	>	>	XX
37681	1998	15	_	_	NNP
37681	1998	16	CB	CB	NNP
37681	1998	17	_	_	NNP
37681	1998	18	+	+	CC
37681	1998	19	_	_	NNP
37681	1998	20	CA	CA	NNP
37681	1998	21	_	_	NNP
37681	1998	22	.	.	.
37681	1999	1	[	[	-LRB-
37681	1999	2	Illustration	illustration	NN
37681	1999	3	]	]	-RRB-
37681	1999	4	It	-PRON-	PRP
37681	1999	5	is	be	VBZ
37681	1999	6	interesting	interesting	JJ
37681	1999	7	to	to	IN
37681	1999	8	a	a	DT
37681	1999	9	class	class	NN
37681	1999	10	to	to	TO
37681	1999	11	have	have	VB
37681	1999	12	a	a	DT
37681	1999	13	teacher	teacher	NN
37681	1999	14	point	point	NN
37681	1999	15	out	out	RP
37681	1999	16	that	that	IN
37681	1999	17	,	,	,
37681	1999	18	in	in	IN
37681	1999	19	this	this	DT
37681	1999	20	figure	figure	NN
37681	1999	21	,	,	,
37681	1999	22	_	_	NNP
37681	1999	23	AP	AP	NNP
37681	1999	24	_	_	NNP
37681	1999	25	+	+	NNP
37681	1999	26	_	_	NNP
37681	1999	27	PB	PB	NNP
37681	1999	28	_	_	NNP
37681	1999	29	<	<	XX
37681	1999	30	_	_	NNP
37681	1999	31	AC	AC	NNP
37681	1999	32	_	_	NNP
37681	1999	33	+	+	SYM
37681	1999	34	_	_	NNP
37681	1999	35	CB	CB	NNP
37681	1999	36	_	_	NNP
37681	1999	37	,	,	,
37681	1999	38	and	and	CC
37681	1999	39	_	_	NNP
37681	1999	40	AP	AP	NNP
37681	1999	41	'	'	POS
37681	1999	42	_	_	NNP
37681	1999	43	+	+	SYM
37681	1999	44	_	_	NNP
37681	1999	45	P'B	P'B	NNP
37681	1999	46	_	_	NNP
37681	1999	47	<	<	XX
37681	1999	48	_	_	NNP
37681	1999	49	AP	AP	NNP
37681	1999	50	_	_	NNP
37681	1999	51	+	+	NNP
37681	1999	52	_	_	NNP
37681	1999	53	PB	PB	NNP
37681	1999	54	_	_	NNP
37681	1999	55	,	,	,
37681	1999	56	and	and	CC
37681	1999	57	that	that	IN
37681	1999	58	the	the	DT
37681	1999	59	nearer	nearer	NN
37681	1999	60	_	_	NNP
37681	1999	61	P	P	NNP
37681	1999	62	_	_	NNP
37681	1999	63	gets	get	VBZ
37681	1999	64	to	to	IN
37681	1999	65	_	_	NNP
37681	1999	66	AB	AB	NNP
37681	1999	67	_	_	NNP
37681	1999	68	,	,	,
37681	1999	69	the	the	DT
37681	1999	70	shorter	short	JJR
37681	1999	71	_	_	NNP
37681	1999	72	AP	AP	NNP
37681	1999	73	_	_	NNP
37681	1999	74	+	+	NNP
37681	1999	75	_	_	NNP
37681	1999	76	PB	PB	NNP
37681	1999	77	_	_	NNP
37681	1999	78	becomes	become	VBZ
37681	1999	79	,	,	,
37681	1999	80	the	the	DT
37681	1999	81	limit	limit	NN
37681	1999	82	being	be	VBG
37681	1999	83	the	the	DT
37681	1999	84	line	line	NN
37681	1999	85	_	_	NNP
37681	1999	86	AB	AB	NNP
37681	1999	87	_	_	NNP
37681	1999	88	.	.	.
37681	2000	1	From	from	IN
37681	2000	2	this	this	DT
37681	2000	3	we	-PRON-	PRP
37681	2000	4	may	may	MD
37681	2000	5	_	_	NNP
37681	2000	6	infer	infer	JJ
37681	2000	7	_	_	NNP
37681	2000	8	(	(	-LRB-
37681	2000	9	although	although	IN
37681	2000	10	we	-PRON-	PRP
37681	2000	11	have	have	VBP
37681	2000	12	not	not	RB
37681	2000	13	proved	prove	VBN
37681	2000	14	)	)	-RRB-
37681	2000	15	that	that	IN
37681	2000	16	"	"	``
37681	2000	17	a	a	DT
37681	2000	18	straight	straight	JJ
37681	2000	19	line	line	NN
37681	2000	20	(	(	-LRB-
37681	2000	21	_	_	NNP
37681	2000	22	AB	AB	NNP
37681	2000	23	_	_	NNP
37681	2000	24	)	)	-RRB-
37681	2000	25	is	be	VBZ
37681	2000	26	the	the	DT
37681	2000	27	shortest	short	JJS
37681	2000	28	path	path	NN
37681	2000	29	between	between	IN
37681	2000	30	two	two	CD
37681	2000	31	points	point	NNS
37681	2000	32	.	.	.
37681	2000	33	"	"	''
37681	2001	1	THEOREM	THEOREM	NNP
37681	2001	2	.	.	.
37681	2002	1	_	_	NNP
37681	2002	2	Only	Only	NNP
37681	2002	3	one	one	CD
37681	2002	4	perpendicular	perpendicular	NN
37681	2002	5	can	can	MD
37681	2002	6	be	be	VB
37681	2002	7	drawn	draw	VBN
37681	2002	8	to	to	IN
37681	2002	9	a	a	DT
37681	2002	10	given	give	VBN
37681	2002	11	line	line	NN
37681	2002	12	from	from	IN
37681	2002	13	a	a	DT
37681	2002	14	given	give	VBN
37681	2002	15	external	external	JJ
37681	2002	16	point	point	NN
37681	2002	17	.	.	.
37681	2002	18	_	_	NNP
37681	2002	19	THEOREM	THEOREM	NNP
37681	2002	20	.	.	.
37681	2003	1	_	_	NNP
37681	2003	2	Two	two	CD
37681	2003	3	lines	line	NNS
37681	2003	4	drawn	draw	VBN
37681	2003	5	from	from	IN
37681	2003	6	a	a	DT
37681	2003	7	point	point	NN
37681	2003	8	in	in	IN
37681	2003	9	a	a	DT
37681	2003	10	perpendicular	perpendicular	NN
37681	2003	11	to	to	IN
37681	2003	12	a	a	DT
37681	2003	13	given	give	VBN
37681	2003	14	line	line	NN
37681	2003	15	,	,	,
37681	2003	16	cutting	cut	VBG
37681	2003	17	off	off	RP
37681	2003	18	on	on	IN
37681	2003	19	the	the	DT
37681	2003	20	given	give	VBN
37681	2003	21	line	line	NN
37681	2003	22	equal	equal	JJ
37681	2003	23	segments	segment	NNS
37681	2003	24	from	from	IN
37681	2003	25	the	the	DT
37681	2003	26	foot	foot	NN
37681	2003	27	of	of	IN
37681	2003	28	the	the	DT
37681	2003	29	perpendicular	perpendicular	NN
37681	2003	30	,	,	,
37681	2003	31	are	be	VBP
37681	2003	32	equal	equal	JJ
37681	2003	33	and	and	CC
37681	2003	34	make	make	VB
37681	2003	35	equal	equal	JJ
37681	2003	36	angles	angle	NNS
37681	2003	37	with	with	IN
37681	2003	38	the	the	DT
37681	2003	39	perpendicular	perpendicular	NN
37681	2003	40	.	.	.
37681	2003	41	_	_	NNP
37681	2003	42	THEOREM	THEOREM	NNP
37681	2003	43	.	.	.
37681	2004	1	_	_	NNP
37681	2004	2	Of	of	IN
37681	2004	3	two	two	CD
37681	2004	4	lines	line	NNS
37681	2004	5	drawn	draw	VBN
37681	2004	6	from	from	IN
37681	2004	7	the	the	DT
37681	2004	8	same	same	JJ
37681	2004	9	point	point	NN
37681	2004	10	in	in	IN
37681	2004	11	a	a	DT
37681	2004	12	perpendicular	perpendicular	NN
37681	2004	13	to	to	IN
37681	2004	14	a	a	DT
37681	2004	15	given	give	VBN
37681	2004	16	line	line	NN
37681	2004	17	,	,	,
37681	2004	18	cutting	cut	VBG
37681	2004	19	off	off	RP
37681	2004	20	on	on	IN
37681	2004	21	the	the	DT
37681	2004	22	line	line	NN
37681	2004	23	unequal	unequal	JJ
37681	2004	24	segments	segment	NNS
37681	2004	25	from	from	IN
37681	2004	26	the	the	DT
37681	2004	27	foot	foot	NN
37681	2004	28	of	of	IN
37681	2004	29	the	the	DT
37681	2004	30	perpendicular	perpendicular	NN
37681	2004	31	,	,	,
37681	2004	32	the	the	DT
37681	2004	33	more	more	RBR
37681	2004	34	remote	remote	JJ
37681	2004	35	is	be	VBZ
37681	2004	36	the	the	DT
37681	2004	37	greater	great	JJR
37681	2004	38	.	.	.
37681	2004	39	_	_	NNP
37681	2004	40	THEOREM	THEOREM	NNP
37681	2004	41	.	.	.
37681	2005	1	_	_	NNP
37681	2005	2	The	the	DT
37681	2005	3	perpendicular	perpendicular	NN
37681	2005	4	is	be	VBZ
37681	2005	5	the	the	DT
37681	2005	6	shortest	short	JJS
37681	2005	7	line	line	NN
37681	2005	8	that	that	WDT
37681	2005	9	can	can	MD
37681	2005	10	be	be	VB
37681	2005	11	drawn	draw	VBN
37681	2005	12	to	to	IN
37681	2005	13	a	a	DT
37681	2005	14	straight	straight	JJ
37681	2005	15	line	line	NN
37681	2005	16	from	from	IN
37681	2005	17	a	a	DT
37681	2005	18	given	give	VBN
37681	2005	19	external	external	JJ
37681	2005	20	point	point	NN
37681	2005	21	.	.	.
37681	2005	22	_	_	NNP
37681	2005	23	These	these	DT
37681	2005	24	four	four	CD
37681	2005	25	propositions	proposition	NNS
37681	2005	26	,	,	,
37681	2005	27	while	while	IN
37681	2005	28	known	know	VBN
37681	2005	29	to	to	IN
37681	2005	30	the	the	DT
37681	2005	31	ancients	ancient	NNS
37681	2005	32	and	and	CC
37681	2005	33	incidentally	incidentally	RB
37681	2005	34	used	use	VBN
37681	2005	35	,	,	,
37681	2005	36	are	be	VBP
37681	2005	37	not	not	RB
37681	2005	38	explicitly	explicitly	RB
37681	2005	39	stated	state	VBN
37681	2005	40	by	by	IN
37681	2005	41	Euclid	Euclid	NNP
37681	2005	42	.	.	.
37681	2006	1	The	the	DT
37681	2006	2	reason	reason	NN
37681	2006	3	seems	seem	VBZ
37681	2006	4	to	to	TO
37681	2006	5	be	be	VB
37681	2006	6	that	that	IN
37681	2006	7	he	-PRON-	PRP
37681	2006	8	interspersed	intersperse	VBD
37681	2006	9	his	-PRON-	PRP$
37681	2006	10	problems	problem	NNS
37681	2006	11	with	with	IN
37681	2006	12	his	-PRON-	PRP$
37681	2006	13	theorems	theorem	NNS
37681	2006	14	,	,	,
37681	2006	15	and	and	CC
37681	2006	16	in	in	IN
37681	2006	17	his	-PRON-	PRP$
37681	2006	18	Propositions	proposition	NNS
37681	2006	19	11	11	CD
37681	2006	20	and	and	CC
37681	2006	21	12	12	CD
37681	2006	22	,	,	,
37681	2006	23	which	which	WDT
37681	2006	24	treat	treat	VBP
37681	2006	25	of	of	IN
37681	2006	26	drawing	draw	VBG
37681	2006	27	a	a	DT
37681	2006	28	perpendicular	perpendicular	NN
37681	2006	29	to	to	IN
37681	2006	30	a	a	DT
37681	2006	31	line	line	NN
37681	2006	32	,	,	,
37681	2006	33	the	the	DT
37681	2006	34	essential	essential	JJ
37681	2006	35	features	feature	NNS
37681	2006	36	of	of	IN
37681	2006	37	these	these	DT
37681	2006	38	theorems	theorem	NNS
37681	2006	39	are	be	VBP
37681	2006	40	proved	prove	VBN
37681	2006	41	.	.	.
37681	2007	1	Further	further	JJ
37681	2007	2	mention	mention	NN
37681	2007	3	will	will	MD
37681	2007	4	be	be	VB
37681	2007	5	made	make	VBN
37681	2007	6	of	of	IN
37681	2007	7	them	-PRON-	PRP
37681	2007	8	when	when	WRB
37681	2007	9	we	-PRON-	PRP
37681	2007	10	come	come	VBP
37681	2007	11	to	to	TO
37681	2007	12	consider	consider	VB
37681	2007	13	the	the	DT
37681	2007	14	problems	problem	NNS
37681	2007	15	in	in	IN
37681	2007	16	question	question	NN
37681	2007	17	.	.	.
37681	2008	1	Many	many	JJ
37681	2008	2	textbook	textbook	NN
37681	2008	3	writers	writer	NNS
37681	2008	4	put	put	VBD
37681	2008	5	the	the	DT
37681	2008	6	second	second	JJ
37681	2008	7	and	and	CC
37681	2008	8	third	third	JJ
37681	2008	9	of	of	IN
37681	2008	10	the	the	DT
37681	2008	11	four	four	CD
37681	2008	12	before	before	IN
37681	2008	13	the	the	DT
37681	2008	14	first	first	JJ
37681	2008	15	,	,	,
37681	2008	16	forgetting	forget	VBG
37681	2008	17	that	that	IN
37681	2008	18	the	the	DT
37681	2008	19	first	first	JJ
37681	2008	20	is	be	VBZ
37681	2008	21	assumed	assume	VBN
37681	2008	22	in	in	IN
37681	2008	23	the	the	DT
37681	2008	24	other	other	JJ
37681	2008	25	two	two	CD
37681	2008	26	,	,	,
37681	2008	27	and	and	CC
37681	2008	28	hence	hence	RB
37681	2008	29	should	should	MD
37681	2008	30	precede	precede	VB
37681	2008	31	them	-PRON-	PRP
37681	2008	32	.	.	.
37681	2009	1	THEOREM	THEOREM	NNP
37681	2009	2	.	.	.
37681	2010	1	_	_	NNP
37681	2010	2	Two	two	CD
37681	2010	3	right	right	JJ
37681	2010	4	triangles	triangle	NNS
37681	2010	5	are	be	VBP
37681	2010	6	congruent	congruent	JJ
37681	2010	7	if	if	IN
37681	2010	8	the	the	DT
37681	2010	9	hypotenuse	hypotenuse	NN
37681	2010	10	and	and	CC
37681	2010	11	a	a	DT
37681	2010	12	side	side	NN
37681	2010	13	of	of	IN
37681	2010	14	the	the	DT
37681	2010	15	one	one	NN
37681	2010	16	are	be	VBP
37681	2010	17	equal	equal	JJ
37681	2010	18	respectively	respectively	RB
37681	2010	19	to	to	IN
37681	2010	20	the	the	DT
37681	2010	21	hypotenuse	hypotenuse	NN
37681	2010	22	and	and	CC
37681	2010	23	a	a	DT
37681	2010	24	side	side	NN
37681	2010	25	of	of	IN
37681	2010	26	the	the	DT
37681	2010	27	other	other	JJ
37681	2010	28	.	.	.
37681	2010	29	_	_	NNP
37681	2010	30	THEOREM	THEOREM	NNP
37681	2010	31	.	.	.
37681	2011	1	_	_	NNP
37681	2011	2	Two	two	CD
37681	2011	3	right	right	JJ
37681	2011	4	triangles	triangle	NNS
37681	2011	5	are	be	VBP
37681	2011	6	congruent	congruent	JJ
37681	2011	7	if	if	IN
37681	2011	8	the	the	DT
37681	2011	9	hypotenuse	hypotenuse	NN
37681	2011	10	and	and	CC
37681	2011	11	an	an	DT
37681	2011	12	adjacent	adjacent	JJ
37681	2011	13	angle	angle	NN
37681	2011	14	of	of	IN
37681	2011	15	the	the	DT
37681	2011	16	one	one	NN
37681	2011	17	are	be	VBP
37681	2011	18	equal	equal	JJ
37681	2011	19	respectively	respectively	RB
37681	2011	20	to	to	IN
37681	2011	21	the	the	DT
37681	2011	22	hypotenuse	hypotenuse	NN
37681	2011	23	and	and	CC
37681	2011	24	an	an	DT
37681	2011	25	adjacent	adjacent	JJ
37681	2011	26	angle	angle	NN
37681	2011	27	of	of	IN
37681	2011	28	the	the	DT
37681	2011	29	other	other	JJ
37681	2011	30	.	.	.
37681	2011	31	_	_	NNP
37681	2011	32	As	as	IN
37681	2011	33	stated	state	VBN
37681	2011	34	in	in	IN
37681	2011	35	the	the	DT
37681	2011	36	notes	note	NNS
37681	2011	37	on	on	IN
37681	2011	38	the	the	DT
37681	2011	39	third	third	JJ
37681	2011	40	proposition	proposition	NN
37681	2011	41	in	in	IN
37681	2011	42	this	this	DT
37681	2011	43	sequence	sequence	NN
37681	2011	44	,	,	,
37681	2011	45	Euclid	Euclid	NNP
37681	2011	46	's	's	POS
37681	2011	47	cumbersome	cumbersome	JJ
37681	2011	48	Proposition	Proposition	NNP
37681	2011	49	26	26	CD
37681	2011	50	covers	cover	VBZ
37681	2011	51	several	several	JJ
37681	2011	52	cases	case	NNS
37681	2011	53	,	,	,
37681	2011	54	and	and	CC
37681	2011	55	these	these	DT
37681	2011	56	two	two	CD
37681	2011	57	among	among	IN
37681	2011	58	them	-PRON-	PRP
37681	2011	59	.	.	.
37681	2012	1	Of	of	RB
37681	2012	2	course	course	RB
37681	2012	3	this	this	DT
37681	2012	4	present	present	JJ
37681	2012	5	proposition	proposition	NN
37681	2012	6	could	could	MD
37681	2012	7	more	more	RBR
37681	2012	8	easily	easily	RB
37681	2012	9	be	be	VB
37681	2012	10	proved	prove	VBN
37681	2012	11	after	after	IN
37681	2012	12	the	the	DT
37681	2012	13	one	one	NN
37681	2012	14	concerning	concern	VBG
37681	2012	15	the	the	DT
37681	2012	16	sum	sum	NN
37681	2012	17	of	of	IN
37681	2012	18	the	the	DT
37681	2012	19	angles	angle	NNS
37681	2012	20	of	of	IN
37681	2012	21	a	a	DT
37681	2012	22	triangle	triangle	NN
37681	2012	23	,	,	,
37681	2012	24	but	but	CC
37681	2012	25	the	the	DT
37681	2012	26	proof	proof	NN
37681	2012	27	is	be	VBZ
37681	2012	28	so	so	RB
37681	2012	29	simple	simple	JJ
37681	2012	30	that	that	IN
37681	2012	31	it	-PRON-	PRP
37681	2012	32	is	be	VBZ
37681	2012	33	better	well	JJR
37681	2012	34	to	to	TO
37681	2012	35	leave	leave	VB
37681	2012	36	the	the	DT
37681	2012	37	proposition	proposition	NN
37681	2012	38	here	here	RB
37681	2012	39	in	in	IN
37681	2012	40	connection	connection	NN
37681	2012	41	with	with	IN
37681	2012	42	others	other	NNS
37681	2012	43	concerning	concern	VBG
37681	2012	44	triangles	triangle	NNS
37681	2012	45	.	.	.
37681	2013	1	THEOREM	THEOREM	NNP
37681	2013	2	.	.	.
37681	2014	1	_	_	NNP
37681	2014	2	Two	two	CD
37681	2014	3	lines	line	NNS
37681	2014	4	in	in	IN
37681	2014	5	the	the	DT
37681	2014	6	same	same	JJ
37681	2014	7	plane	plane	NN
37681	2014	8	perpendicular	perpendicular	JJ
37681	2014	9	to	to	IN
37681	2014	10	the	the	DT
37681	2014	11	same	same	JJ
37681	2014	12	line	line	NN
37681	2014	13	can	can	MD
37681	2014	14	not	not	RB
37681	2014	15	meet	meet	VB
37681	2014	16	,	,	,
37681	2014	17	however	however	RB
37681	2014	18	far	far	RB
37681	2014	19	they	-PRON-	PRP
37681	2014	20	are	be	VBP
37681	2014	21	produced	produce	VBN
37681	2014	22	.	.	.
37681	2014	23	_	_	NNP
37681	2014	24	This	this	DT
37681	2014	25	proposition	proposition	NN
37681	2014	26	is	be	VBZ
37681	2014	27	not	not	RB
37681	2014	28	in	in	IN
37681	2014	29	Euclid	Euclid	NNP
37681	2014	30	,	,	,
37681	2014	31	and	and	CC
37681	2014	32	it	-PRON-	PRP
37681	2014	33	is	be	VBZ
37681	2014	34	introduced	introduce	VBN
37681	2014	35	for	for	IN
37681	2014	36	educational	educational	JJ
37681	2014	37	rather	rather	RB
37681	2014	38	than	than	IN
37681	2014	39	for	for	IN
37681	2014	40	mathematical	mathematical	JJ
37681	2014	41	reasons	reason	NNS
37681	2014	42	.	.	.
37681	2015	1	Euclid	Euclid	NNP
37681	2015	2	introduced	introduce	VBD
37681	2015	3	the	the	DT
37681	2015	4	subject	subject	NN
37681	2015	5	by	by	IN
37681	2015	6	the	the	DT
37681	2015	7	proposition	proposition	NN
37681	2015	8	that	that	IN
37681	2015	9	,	,	,
37681	2015	10	if	if	IN
37681	2015	11	alternate	alternate	JJ
37681	2015	12	angles	angle	NNS
37681	2015	13	are	be	VBP
37681	2015	14	equal	equal	JJ
37681	2015	15	,	,	,
37681	2015	16	the	the	DT
37681	2015	17	lines	line	NNS
37681	2015	18	are	be	VBP
37681	2015	19	parallel	parallel	JJ
37681	2015	20	.	.	.
37681	2016	1	It	-PRON-	PRP
37681	2016	2	is	be	VBZ
37681	2016	3	,	,	,
37681	2016	4	however	however	RB
37681	2016	5	,	,	,
37681	2016	6	simpler	simple	JJR
37681	2016	7	to	to	TO
37681	2016	8	begin	begin	VB
37681	2016	9	with	with	IN
37681	2016	10	this	this	DT
37681	2016	11	proposition	proposition	NN
37681	2016	12	,	,	,
37681	2016	13	and	and	CC
37681	2016	14	there	there	EX
37681	2016	15	is	be	VBZ
37681	2016	16	some	some	DT
37681	2016	17	advantage	advantage	NN
37681	2016	18	in	in	IN
37681	2016	19	stating	state	VBG
37681	2016	20	it	-PRON-	PRP
37681	2016	21	in	in	IN
37681	2016	22	such	such	PDT
37681	2016	23	a	a	DT
37681	2016	24	way	way	NN
37681	2016	25	as	as	IN
37681	2016	26	to	to	TO
37681	2016	27	prove	prove	VB
37681	2016	28	that	that	IN
37681	2016	29	parallels	parallel	NNS
37681	2016	30	exist	exist	VBP
37681	2016	31	before	before	IN
37681	2016	32	they	-PRON-	PRP
37681	2016	33	are	be	VBP
37681	2016	34	defined	define	VBN
37681	2016	35	.	.	.
37681	2017	1	The	the	DT
37681	2017	2	proposition	proposition	NN
37681	2017	3	is	be	VBZ
37681	2017	4	properly	properly	RB
37681	2017	5	followed	follow	VBN
37681	2017	6	by	by	IN
37681	2017	7	the	the	DT
37681	2017	8	definition	definition	NN
37681	2017	9	of	of	IN
37681	2017	10	parallels	parallel	NNS
37681	2017	11	and	and	CC
37681	2017	12	by	by	IN
37681	2017	13	the	the	DT
37681	2017	14	postulate	postulate	NN
37681	2017	15	that	that	WDT
37681	2017	16	has	have	VBZ
37681	2017	17	been	be	VBN
37681	2017	18	discussed	discuss	VBN
37681	2017	19	on	on	IN
37681	2017	20	page	page	NN
37681	2017	21	127	127	CD
37681	2017	22	.	.	.
37681	2018	1	A	a	DT
37681	2018	2	good	good	JJ
37681	2018	3	application	application	NN
37681	2018	4	of	of	IN
37681	2018	5	this	this	DT
37681	2018	6	proposition	proposition	NN
37681	2018	7	is	be	VBZ
37681	2018	8	the	the	DT
37681	2018	9	one	one	NN
37681	2018	10	concerning	concern	VBG
37681	2018	11	a	a	DT
37681	2018	12	method	method	NN
37681	2018	13	of	of	IN
37681	2018	14	drawing	draw	VBG
37681	2018	15	parallel	parallel	JJ
37681	2018	16	lines	line	NNS
37681	2018	17	by	by	IN
37681	2018	18	the	the	DT
37681	2018	19	use	use	NN
37681	2018	20	of	of	IN
37681	2018	21	a	a	DT
37681	2018	22	carpenter	carpenter	NN
37681	2018	23	's	's	POS
37681	2018	24	square	square	NN
37681	2018	25	.	.	.
37681	2019	1	Here	here	RB
37681	2019	2	two	two	CD
37681	2019	3	lines	line	NNS
37681	2019	4	are	be	VBP
37681	2019	5	drawn	draw	VBN
37681	2019	6	perpendicular	perpendicular	JJ
37681	2019	7	to	to	IN
37681	2019	8	the	the	DT
37681	2019	9	edge	edge	NN
37681	2019	10	of	of	IN
37681	2019	11	a	a	DT
37681	2019	12	board	board	NN
37681	2019	13	or	or	CC
37681	2019	14	a	a	DT
37681	2019	15	ruler	ruler	NN
37681	2019	16	,	,	,
37681	2019	17	and	and	CC
37681	2019	18	these	these	DT
37681	2019	19	are	be	VBP
37681	2019	20	parallel	parallel	JJ
37681	2019	21	.	.	.
37681	2020	1	THEOREM	THEOREM	NNP
37681	2020	2	.	.	.
37681	2021	1	_	_	XX
37681	2021	2	If	if	IN
37681	2021	3	a	a	DT
37681	2021	4	line	line	NN
37681	2021	5	is	be	VBZ
37681	2021	6	perpendicular	perpendicular	JJ
37681	2021	7	to	to	IN
37681	2021	8	one	one	CD
37681	2021	9	of	of	IN
37681	2021	10	two	two	CD
37681	2021	11	parallel	parallel	JJ
37681	2021	12	lines	line	NNS
37681	2021	13	,	,	,
37681	2021	14	it	-PRON-	PRP
37681	2021	15	is	be	VBZ
37681	2021	16	perpendicular	perpendicular	JJ
37681	2021	17	to	to	IN
37681	2021	18	the	the	DT
37681	2021	19	other	other	JJ
37681	2021	20	also	also	RB
37681	2021	21	.	.	.
37681	2021	22	_	_	NNP
37681	2021	23	This	this	DT
37681	2021	24	,	,	,
37681	2021	25	like	like	IN
37681	2021	26	the	the	DT
37681	2021	27	preceding	precede	VBG
37681	2021	28	proposition	proposition	NN
37681	2021	29	,	,	,
37681	2021	30	is	be	VBZ
37681	2021	31	a	a	DT
37681	2021	32	special	special	JJ
37681	2021	33	case	case	NN
37681	2021	34	under	under	IN
37681	2021	35	a	a	DT
37681	2021	36	later	later	JJ
37681	2021	37	theorem	theorem	NN
37681	2021	38	.	.	.
37681	2022	1	It	-PRON-	PRP
37681	2022	2	simplifies	simplify	VBZ
37681	2022	3	the	the	DT
37681	2022	4	treatment	treatment	NN
37681	2022	5	of	of	IN
37681	2022	6	parallels	parallel	NNS
37681	2022	7	,	,	,
37681	2022	8	however	however	RB
37681	2022	9	,	,	,
37681	2022	10	and	and	CC
37681	2022	11	the	the	DT
37681	2022	12	beginner	beginner	NN
37681	2022	13	finds	find	VBZ
37681	2022	14	it	-PRON-	PRP
37681	2022	15	easier	easy	JJR
37681	2022	16	to	to	TO
37681	2022	17	approach	approach	VB
37681	2022	18	the	the	DT
37681	2022	19	difficulties	difficulty	NNS
37681	2022	20	gradually	gradually	RB
37681	2022	21	,	,	,
37681	2022	22	through	through	IN
37681	2022	23	these	these	DT
37681	2022	24	two	two	CD
37681	2022	25	cases	case	NNS
37681	2022	26	of	of	IN
37681	2022	27	perpendiculars	perpendicular	NNS
37681	2022	28	.	.	.
37681	2023	1	It	-PRON-	PRP
37681	2023	2	should	should	MD
37681	2023	3	be	be	VB
37681	2023	4	noticed	notice	VBN
37681	2023	5	that	that	IN
37681	2023	6	this	this	DT
37681	2023	7	is	be	VBZ
37681	2023	8	an	an	DT
37681	2023	9	example	example	NN
37681	2023	10	of	of	IN
37681	2023	11	a	a	DT
37681	2023	12	partial	partial	JJ
37681	2023	13	converse	converse	NN
37681	2023	14	,	,	,
37681	2023	15	as	as	IN
37681	2023	16	explained	explain	VBN
37681	2023	17	on	on	IN
37681	2023	18	page	page	NN
37681	2023	19	175	175	CD
37681	2023	20	.	.	.
37681	2024	1	The	the	DT
37681	2024	2	preceding	precede	VBG
37681	2024	3	proposition	proposition	NN
37681	2024	4	may	may	MD
37681	2024	5	be	be	VB
37681	2024	6	stated	state	VBN
37681	2024	7	thus	thus	RB
37681	2024	8	:	:	:
37681	2024	9	If	if	IN
37681	2024	10	_	_	NNP
37681	2024	11	a	a	DT
37681	2024	12	_	_	NNP
37681	2024	13	is	be	VBZ
37681	2024	14	[	[	-LRB-
37681	2024	15	perp	perp	FW
37681	2024	16	]	]	-RRB-
37681	2024	17	to	to	IN
37681	2024	18	_	_	NNP
37681	2024	19	x	x	NNP
37681	2024	20	_	_	NNP
37681	2024	21	and	and	CC
37681	2024	22	_	_	NNP
37681	2024	23	b	b	NNP
37681	2024	24	_	_	NNP
37681	2024	25	is	be	VBZ
37681	2024	26	[	[	-LRB-
37681	2024	27	perp	perp	FW
37681	2024	28	]	]	-RRB-
37681	2024	29	to	to	IN
37681	2024	30	_	_	NNP
37681	2024	31	x	x	NNP
37681	2024	32	_	_	NNP
37681	2024	33	,	,	,
37681	2024	34	then	then	RB
37681	2024	35	_	_	NNP
37681	2024	36	a	a	DT
37681	2024	37	_	_	NNP
37681	2024	38	is	be	VBZ
37681	2024	39	||	||	NNP
37681	2024	40	to	to	IN
37681	2024	41	_	_	NNP
37681	2024	42	b	b	NNP
37681	2024	43	_	_	NNP
37681	2024	44	.	.	.
37681	2025	1	This	this	DT
37681	2025	2	proposition	proposition	NN
37681	2025	3	may	may	MD
37681	2025	4	be	be	VB
37681	2025	5	stated	state	VBN
37681	2025	6	thus	thus	RB
37681	2025	7	:	:	:
37681	2025	8	If	if	IN
37681	2025	9	_	_	NNP
37681	2025	10	a	a	DT
37681	2025	11	_	_	NNP
37681	2025	12	is	be	VBZ
37681	2025	13	[	[	-LRB-
37681	2025	14	perp	perp	FW
37681	2025	15	]	]	-RRB-
37681	2025	16	to	to	IN
37681	2025	17	_	_	NNP
37681	2025	18	x	x	NNP
37681	2025	19	_	_	NNP
37681	2025	20	and	and	CC
37681	2025	21	_	_	NNP
37681	2025	22	a	a	DT
37681	2025	23	_	_	NNP
37681	2025	24	is	be	VBZ
37681	2025	25	||	||	NNP
37681	2025	26	to	to	IN
37681	2025	27	_	_	NNP
37681	2025	28	b	b	NNP
37681	2025	29	_	_	NNP
37681	2025	30	,	,	,
37681	2025	31	then	then	RB
37681	2025	32	_	_	NNP
37681	2025	33	b	b	NNP
37681	2025	34	_	_	NNP
37681	2025	35	is	be	VBZ
37681	2025	36	[	[	-LRB-
37681	2025	37	perp	perp	FW
37681	2025	38	]	]	-RRB-
37681	2025	39	to	to	IN
37681	2025	40	_	_	NNP
37681	2025	41	x	x	NNP
37681	2025	42	_	_	NNP
37681	2025	43	.	.	.
37681	2026	1	This	this	DT
37681	2026	2	is	be	VBZ
37681	2026	3	,	,	,
37681	2026	4	therefore	therefore	RB
37681	2026	5	,	,	,
37681	2026	6	a	a	DT
37681	2026	7	partial	partial	JJ
37681	2026	8	converse	converse	NN
37681	2026	9	.	.	.
37681	2027	1	These	these	DT
37681	2027	2	two	two	CD
37681	2027	3	propositions	proposition	NNS
37681	2027	4	having	have	VBG
37681	2027	5	been	be	VBN
37681	2027	6	proved	prove	VBN
37681	2027	7	,	,	,
37681	2027	8	the	the	DT
37681	2027	9	usual	usual	JJ
37681	2027	10	definitions	definition	NNS
37681	2027	11	of	of	IN
37681	2027	12	the	the	DT
37681	2027	13	angles	angle	NNS
37681	2027	14	made	make	VBN
37681	2027	15	by	by	IN
37681	2027	16	a	a	DT
37681	2027	17	transversal	transversal	NN
37681	2027	18	of	of	IN
37681	2027	19	two	two	CD
37681	2027	20	parallels	parallel	NNS
37681	2027	21	may	may	MD
37681	2027	22	be	be	VB
37681	2027	23	given	give	VBN
37681	2027	24	.	.	.
37681	2028	1	It	-PRON-	PRP
37681	2028	2	is	be	VBZ
37681	2028	3	unfortunate	unfortunate	JJ
37681	2028	4	that	that	IN
37681	2028	5	we	-PRON-	PRP
37681	2028	6	have	have	VBP
37681	2028	7	no	no	DT
37681	2028	8	name	name	NN
37681	2028	9	for	for	IN
37681	2028	10	each	each	DT
37681	2028	11	of	of	IN
37681	2028	12	the	the	DT
37681	2028	13	two	two	CD
37681	2028	14	groups	group	NNS
37681	2028	15	of	of	IN
37681	2028	16	four	four	CD
37681	2028	17	equal	equal	JJ
37681	2028	18	angles	angle	NNS
37681	2028	19	,	,	,
37681	2028	20	and	and	CC
37681	2028	21	the	the	DT
37681	2028	22	name	name	NN
37681	2028	23	of	of	IN
37681	2028	24	"	"	``
37681	2028	25	transverse	transverse	JJ
37681	2028	26	angles	angle	NNS
37681	2028	27	"	"	''
37681	2028	28	has	have	VBZ
37681	2028	29	been	be	VBN
37681	2028	30	suggested	suggest	VBN
37681	2028	31	.	.	.
37681	2029	1	This	this	DT
37681	2029	2	would	would	MD
37681	2029	3	simplify	simplify	VB
37681	2029	4	the	the	DT
37681	2029	5	statements	statement	NNS
37681	2029	6	of	of	IN
37681	2029	7	certain	certain	JJ
37681	2029	8	other	other	JJ
37681	2029	9	propositions	proposition	NNS
37681	2029	10	;	;	:
37681	2029	11	thus	thus	RB
37681	2029	12	:	:	:
37681	2029	13	"	"	``
37681	2029	14	If	if	IN
37681	2029	15	two	two	CD
37681	2029	16	parallel	parallel	JJ
37681	2029	17	lines	line	NNS
37681	2029	18	are	be	VBP
37681	2029	19	cut	cut	VBN
37681	2029	20	by	by	IN
37681	2029	21	a	a	DT
37681	2029	22	transversal	transversal	NN
37681	2029	23	,	,	,
37681	2029	24	the	the	DT
37681	2029	25	transverse	transverse	JJ
37681	2029	26	angles	angle	NNS
37681	2029	27	are	be	VBP
37681	2029	28	equal	equal	JJ
37681	2029	29	,	,	,
37681	2029	30	"	"	''
37681	2029	31	and	and	CC
37681	2029	32	this	this	DT
37681	2029	33	includes	include	VBZ
37681	2029	34	two	two	CD
37681	2029	35	propositions	proposition	NNS
37681	2029	36	as	as	IN
37681	2029	37	usually	usually	RB
37681	2029	38	given	give	VBN
37681	2029	39	.	.	.
37681	2030	1	There	there	EX
37681	2030	2	is	be	VBZ
37681	2030	3	not	not	RB
37681	2030	4	as	as	RB
37681	2030	5	yet	yet	RB
37681	2030	6	,	,	,
37681	2030	7	however	however	RB
37681	2030	8	,	,	,
37681	2030	9	any	any	DT
37681	2030	10	general	general	JJ
37681	2030	11	sanction	sanction	NN
37681	2030	12	for	for	IN
37681	2030	13	the	the	DT
37681	2030	14	term	term	NN
37681	2030	15	.	.	.
37681	2031	1	THEOREM	THEOREM	NNP
37681	2031	2	.	.	.
37681	2032	1	_	_	XX
37681	2032	2	If	if	IN
37681	2032	3	two	two	CD
37681	2032	4	parallel	parallel	JJ
37681	2032	5	lines	line	NNS
37681	2032	6	are	be	VBP
37681	2032	7	cut	cut	VBN
37681	2032	8	by	by	IN
37681	2032	9	a	a	DT
37681	2032	10	transversal	transversal	NN
37681	2032	11	,	,	,
37681	2032	12	the	the	DT
37681	2032	13	alternate	alternate	JJ
37681	2032	14	-	-	HYPH
37681	2032	15	interior	interior	JJ
37681	2032	16	angles	angle	NNS
37681	2032	17	are	be	VBP
37681	2032	18	equal	equal	JJ
37681	2032	19	.	.	.
37681	2032	20	_	_	NNP
37681	2032	21	Euclid	Euclid	NNP
37681	2032	22	gave	give	VBD
37681	2032	23	this	this	DT
37681	2032	24	as	as	IN
37681	2032	25	half	half	NN
37681	2032	26	of	of	IN
37681	2032	27	his	-PRON-	PRP$
37681	2032	28	Proposition	Proposition	NNP
37681	2032	29	29	29	CD
37681	2032	30	.	.	.
37681	2033	1	Indeed	indeed	RB
37681	2033	2	,	,	,
37681	2033	3	he	-PRON-	PRP
37681	2033	4	gives	give	VBZ
37681	2033	5	only	only	RB
37681	2033	6	four	four	CD
37681	2033	7	theorems	theorem	NNS
37681	2033	8	on	on	IN
37681	2033	9	parallels	parallel	NNS
37681	2033	10	,	,	,
37681	2033	11	as	as	IN
37681	2033	12	against	against	IN
37681	2033	13	five	five	CD
37681	2033	14	propositions	proposition	NNS
37681	2033	15	and	and	CC
37681	2033	16	several	several	JJ
37681	2033	17	corollaries	corollary	NNS
37681	2033	18	in	in	IN
37681	2033	19	most	most	JJS
37681	2033	20	of	of	IN
37681	2033	21	our	-PRON-	PRP$
37681	2033	22	American	american	JJ
37681	2033	23	textbooks	textbook	NNS
37681	2033	24	.	.	.
37681	2034	1	The	the	DT
37681	2034	2	reason	reason	NN
37681	2034	3	for	for	IN
37681	2034	4	increasing	increase	VBG
37681	2034	5	the	the	DT
37681	2034	6	number	number	NN
37681	2034	7	is	be	VBZ
37681	2034	8	that	that	IN
37681	2034	9	each	each	DT
37681	2034	10	proposition	proposition	NN
37681	2034	11	may	may	MD
37681	2034	12	be	be	VB
37681	2034	13	less	less	RBR
37681	2034	14	involved	involved	JJ
37681	2034	15	.	.	.
37681	2035	1	Thus	thus	RB
37681	2035	2	,	,	,
37681	2035	3	instead	instead	RB
37681	2035	4	of	of	IN
37681	2035	5	having	have	VBG
37681	2035	6	one	one	CD
37681	2035	7	proposition	proposition	NN
37681	2035	8	for	for	IN
37681	2035	9	both	both	CC
37681	2035	10	exterior	exterior	NNP
37681	2035	11	and	and	CC
37681	2035	12	interior	interior	JJ
37681	2035	13	angles	angle	NNS
37681	2035	14	,	,	,
37681	2035	15	modern	modern	JJ
37681	2035	16	authors	author	NNS
37681	2035	17	usually	usually	RB
37681	2035	18	have	have	VBP
37681	2035	19	one	one	CD
37681	2035	20	for	for	IN
37681	2035	21	the	the	DT
37681	2035	22	exterior	exterior	NN
37681	2035	23	and	and	CC
37681	2035	24	one	one	CD
37681	2035	25	for	for	IN
37681	2035	26	the	the	DT
37681	2035	27	interior	interior	NN
37681	2035	28	,	,	,
37681	2035	29	so	so	IN
37681	2035	30	as	as	IN
37681	2035	31	to	to	TO
37681	2035	32	make	make	VB
37681	2035	33	the	the	DT
37681	2035	34	difficult	difficult	JJ
37681	2035	35	subject	subject	NN
37681	2035	36	of	of	IN
37681	2035	37	parallels	parallel	NNS
37681	2035	38	easier	easy	JJR
37681	2035	39	for	for	IN
37681	2035	40	beginners	beginner	NNS
37681	2035	41	.	.	.
37681	2036	1	THEOREM	THEOREM	NNP
37681	2036	2	.	.	.
37681	2037	1	_	_	NNP
37681	2037	2	When	when	WRB
37681	2037	3	two	two	CD
37681	2037	4	straight	straight	JJ
37681	2037	5	lines	line	NNS
37681	2037	6	in	in	IN
37681	2037	7	the	the	DT
37681	2037	8	same	same	JJ
37681	2037	9	plane	plane	NN
37681	2037	10	are	be	VBP
37681	2037	11	cut	cut	VBN
37681	2037	12	by	by	IN
37681	2037	13	a	a	DT
37681	2037	14	transversal	transversal	NN
37681	2037	15	,	,	,
37681	2037	16	if	if	IN
37681	2037	17	the	the	DT
37681	2037	18	alternate	alternate	JJ
37681	2037	19	-	-	HYPH
37681	2037	20	interior	interior	JJ
37681	2037	21	angles	angle	NNS
37681	2037	22	are	be	VBP
37681	2037	23	equal	equal	JJ
37681	2037	24	,	,	,
37681	2037	25	the	the	DT
37681	2037	26	two	two	CD
37681	2037	27	straight	straight	JJ
37681	2037	28	lines	line	NNS
37681	2037	29	are	be	VBP
37681	2037	30	parallel	parallel	JJ
37681	2037	31	.	.	.
37681	2037	32	_	_	NNP
37681	2037	33	This	this	DT
37681	2037	34	is	be	VBZ
37681	2037	35	the	the	DT
37681	2037	36	converse	converse	NN
37681	2037	37	of	of	IN
37681	2037	38	the	the	DT
37681	2037	39	preceding	precede	VBG
37681	2037	40	theorem	theorem	NN
37681	2037	41	,	,	,
37681	2037	42	and	and	CC
37681	2037	43	is	be	VBZ
37681	2037	44	half	half	NN
37681	2037	45	of	of	IN
37681	2037	46	Euclid	Euclid	NNP
37681	2037	47	I	I	NNP
37681	2037	48	,	,	,
37681	2037	49	28	28	CD
37681	2037	50	,	,	,
37681	2037	51	his	-PRON-	PRP$
37681	2037	52	theorem	theorem	NN
37681	2037	53	being	be	VBG
37681	2037	54	divided	divide	VBN
37681	2037	55	for	for	IN
37681	2037	56	the	the	DT
37681	2037	57	reason	reason	NN
37681	2037	58	above	above	IN
37681	2037	59	stated	state	VBD
37681	2037	60	.	.	.
37681	2038	1	There	there	EX
37681	2038	2	are	be	VBP
37681	2038	3	several	several	JJ
37681	2038	4	typical	typical	JJ
37681	2038	5	pairs	pair	NNS
37681	2038	6	of	of	IN
37681	2038	7	equal	equal	JJ
37681	2038	8	or	or	CC
37681	2038	9	supplemental	supplemental	JJ
37681	2038	10	angles	angle	NNS
37681	2038	11	that	that	WDT
37681	2038	12	would	would	MD
37681	2038	13	lead	lead	VB
37681	2038	14	to	to	IN
37681	2038	15	parallel	parallel	JJ
37681	2038	16	lines	line	NNS
37681	2038	17	,	,	,
37681	2038	18	of	of	IN
37681	2038	19	which	which	WDT
37681	2038	20	Euclid	Euclid	NNP
37681	2038	21	uses	use	VBZ
37681	2038	22	only	only	JJ
37681	2038	23	part	part	NN
37681	2038	24	,	,	,
37681	2038	25	leaving	leave	VBG
37681	2038	26	the	the	DT
37681	2038	27	other	other	JJ
37681	2038	28	cases	case	NNS
37681	2038	29	to	to	TO
37681	2038	30	be	be	VB
37681	2038	31	inferred	infer	VBN
37681	2038	32	.	.	.
37681	2039	1	This	this	DT
37681	2039	2	accounts	account	VBZ
37681	2039	3	for	for	IN
37681	2039	4	the	the	DT
37681	2039	5	number	number	NN
37681	2039	6	of	of	IN
37681	2039	7	corollaries	corollary	NNS
37681	2039	8	in	in	IN
37681	2039	9	this	this	DT
37681	2039	10	connection	connection	NN
37681	2039	11	in	in	IN
37681	2039	12	later	later	JJ
37681	2039	13	textbooks	textbook	NNS
37681	2039	14	.	.	.
37681	2040	1	Surveyors	surveyor	NNS
37681	2040	2	make	make	VBP
37681	2040	3	use	use	NN
37681	2040	4	of	of	IN
37681	2040	5	this	this	DT
37681	2040	6	proposition	proposition	NN
37681	2040	7	when	when	WRB
37681	2040	8	they	-PRON-	PRP
37681	2040	9	wish	wish	VBP
37681	2040	10	,	,	,
37681	2040	11	without	without	IN
37681	2040	12	using	use	VBG
37681	2040	13	a	a	DT
37681	2040	14	transit	transit	NN
37681	2040	15	instrument	instrument	NN
37681	2040	16	,	,	,
37681	2040	17	to	to	TO
37681	2040	18	run	run	VB
37681	2040	19	one	one	CD
37681	2040	20	line	line	NN
37681	2040	21	parallel	parallel	JJ
37681	2040	22	to	to	IN
37681	2040	23	another	another	DT
37681	2040	24	.	.	.
37681	2041	1	[	[	-LRB-
37681	2041	2	Illustration	illustration	NN
37681	2041	3	]	]	-RRB-
37681	2041	4	For	for	IN
37681	2041	5	example	example	NN
37681	2041	6	,	,	,
37681	2041	7	suppose	suppose	VB
37681	2041	8	two	two	CD
37681	2041	9	boys	boy	NNS
37681	2041	10	are	be	VBP
37681	2041	11	laying	lay	VBG
37681	2041	12	out	out	RP
37681	2041	13	a	a	DT
37681	2041	14	tennis	tennis	NN
37681	2041	15	court	court	NN
37681	2041	16	and	and	CC
37681	2041	17	they	-PRON-	PRP
37681	2041	18	wish	wish	VBP
37681	2041	19	to	to	TO
37681	2041	20	run	run	VB
37681	2041	21	a	a	DT
37681	2041	22	line	line	NN
37681	2041	23	through	through	IN
37681	2041	24	_	_	NNP
37681	2041	25	P	P	NNP
37681	2041	26	_	_	NNP
37681	2041	27	parallel	parallel	NN
37681	2041	28	to	to	IN
37681	2041	29	_	_	NNP
37681	2041	30	AB	AB	NNP
37681	2041	31	_	_	NNP
37681	2041	32	.	.	.
37681	2042	1	Take	take	VB
37681	2042	2	a	a	DT
37681	2042	3	60-foot	60-foot	CD
37681	2042	4	tape	tape	NN
37681	2042	5	and	and	CC
37681	2042	6	swing	swing	VB
37681	2042	7	it	-PRON-	PRP
37681	2042	8	around	around	RB
37681	2042	9	_	_	NNP
37681	2042	10	P	P	NNP
37681	2042	11	_	_	NNP
37681	2042	12	until	until	IN
37681	2042	13	the	the	DT
37681	2042	14	other	other	JJ
37681	2042	15	end	end	NN
37681	2042	16	rests	rest	NNS
37681	2042	17	on	on	IN
37681	2042	18	_	_	NNP
37681	2042	19	AB	AB	NNP
37681	2042	20	_	_	NNP
37681	2042	21	,	,	,
37681	2042	22	as	as	IN
37681	2042	23	at	at	IN
37681	2042	24	_	_	NNP
37681	2042	25	M	M	NNP
37681	2042	26	_	_	NNP
37681	2042	27	.	.	.
37681	2043	1	Put	put	VB
37681	2043	2	a	a	DT
37681	2043	3	stake	stake	NN
37681	2043	4	at	at	IN
37681	2043	5	_	_	NNP
37681	2043	6	O	O	NNP
37681	2043	7	_	_	NNP
37681	2043	8	,	,	,
37681	2043	9	30	30	CD
37681	2043	10	feet	foot	NNS
37681	2043	11	from	from	IN
37681	2043	12	_	_	NNP
37681	2043	13	P	P	NNP
37681	2043	14	_	_	NNP
37681	2043	15	and	and	CC
37681	2043	16	_	_	NNP
37681	2043	17	M	M	NNP
37681	2043	18	_	_	NNP
37681	2043	19	.	.	.
37681	2044	1	Then	then	RB
37681	2044	2	take	take	VB
37681	2044	3	any	any	DT
37681	2044	4	convenient	convenient	JJ
37681	2044	5	point	point	NN
37681	2044	6	_	_	NNP
37681	2044	7	N	N	NNP
37681	2044	8	_	_	NNP
37681	2044	9	on	on	IN
37681	2044	10	_	_	NNP
37681	2044	11	AB	AB	NNP
37681	2044	12	_	_	NNP
37681	2044	13	,	,	,
37681	2044	14	and	and	CC
37681	2044	15	measure	measure	VB
37681	2044	16	_	_	NNP
37681	2044	17	ON	ON	NNP
37681	2044	18	_	_	NNP
37681	2044	19	.	.	.
37681	2045	1	Suppose	suppose	VB
37681	2045	2	it	-PRON-	PRP
37681	2045	3	equals	equal	VBZ
37681	2045	4	20	20	CD
37681	2045	5	feet	foot	NNS
37681	2045	6	.	.	.
37681	2046	1	Then	then	RB
37681	2046	2	sight	sight	NN
37681	2046	3	from	from	IN
37681	2046	4	_	_	NNP
37681	2046	5	N	N	NNP
37681	2046	6	_	_	NNP
37681	2046	7	through	through	IN
37681	2046	8	_	_	NNP
37681	2046	9	O	O	NNP
37681	2046	10	_	_	NNP
37681	2046	11	,	,	,
37681	2046	12	and	and	CC
37681	2046	13	put	put	VBD
37681	2046	14	a	a	DT
37681	2046	15	stake	stake	NN
37681	2046	16	at	at	IN
37681	2046	17	_	_	NNP
37681	2046	18	Q	Q	NNP
37681	2046	19	_	_	NNP
37681	2046	20	just	just	RB
37681	2046	21	20	20	CD
37681	2046	22	feet	foot	NNS
37681	2046	23	from	from	IN
37681	2046	24	_	_	NNP
37681	2046	25	O	O	NNP
37681	2046	26	_	_	NNP
37681	2046	27	.	.	.
37681	2047	1	Then	then	RB
37681	2047	2	_	_	NNP
37681	2047	3	P	P	NNP
37681	2047	4	_	_	NNP
37681	2047	5	and	and	CC
37681	2047	6	_	_	NNP
37681	2047	7	Q	Q	NNP
37681	2047	8	_	_	NNP
37681	2047	9	determine	determine	VBP
37681	2047	10	the	the	DT
37681	2047	11	parallel	parallel	NN
37681	2047	12	,	,	,
37681	2047	13	according	accord	VBG
37681	2047	14	to	to	IN
37681	2047	15	the	the	DT
37681	2047	16	proposition	proposition	NN
37681	2047	17	just	just	RB
37681	2047	18	mentioned	mention	VBN
37681	2047	19	.	.	.
37681	2048	1	THEOREM	THEOREM	NNP
37681	2048	2	.	.	.
37681	2049	1	_	_	XX
37681	2049	2	If	if	IN
37681	2049	3	two	two	CD
37681	2049	4	parallel	parallel	JJ
37681	2049	5	lines	line	NNS
37681	2049	6	are	be	VBP
37681	2049	7	cut	cut	VBN
37681	2049	8	by	by	IN
37681	2049	9	a	a	DT
37681	2049	10	transversal	transversal	NN
37681	2049	11	,	,	,
37681	2049	12	the	the	DT
37681	2049	13	exterior	exterior	JJ
37681	2049	14	-	-	HYPH
37681	2049	15	interior	interior	JJ
37681	2049	16	angles	angle	NNS
37681	2049	17	are	be	VBP
37681	2049	18	equal	equal	JJ
37681	2049	19	.	.	.
37681	2049	20	_	_	NNP
37681	2049	21	This	this	DT
37681	2049	22	is	be	VBZ
37681	2049	23	also	also	RB
37681	2049	24	a	a	DT
37681	2049	25	part	part	NN
37681	2049	26	of	of	IN
37681	2049	27	Euclid	Euclid	NNP
37681	2049	28	I	I	NNP
37681	2049	29	,	,	,
37681	2049	30	29	29	CD
37681	2049	31	.	.	.
37681	2050	1	It	-PRON-	PRP
37681	2050	2	is	be	VBZ
37681	2050	3	usually	usually	RB
37681	2050	4	followed	follow	VBN
37681	2050	5	by	by	IN
37681	2050	6	several	several	JJ
37681	2050	7	corollaries	corollary	NNS
37681	2050	8	,	,	,
37681	2050	9	covering	cover	VBG
37681	2050	10	the	the	DT
37681	2050	11	minor	minor	JJ
37681	2050	12	and	and	CC
37681	2050	13	obvious	obvious	JJ
37681	2050	14	cases	case	NNS
37681	2050	15	omitted	omit	VBN
37681	2050	16	by	by	IN
37681	2050	17	the	the	DT
37681	2050	18	older	old	JJR
37681	2050	19	writers	writer	NNS
37681	2050	20	.	.	.
37681	2051	1	While	while	IN
37681	2051	2	it	-PRON-	PRP
37681	2051	3	would	would	MD
37681	2051	4	be	be	VB
37681	2051	5	possible	possible	JJ
37681	2051	6	to	to	TO
37681	2051	7	dispense	dispense	VB
37681	2051	8	with	with	IN
37681	2051	9	these	these	DT
37681	2051	10	corollaries	corollary	NNS
37681	2051	11	,	,	,
37681	2051	12	they	-PRON-	PRP
37681	2051	13	are	be	VBP
37681	2051	14	helpful	helpful	JJ
37681	2051	15	for	for	IN
37681	2051	16	definite	definite	JJ
37681	2051	17	reference	reference	NN
37681	2051	18	in	in	IN
37681	2051	19	later	later	JJ
37681	2051	20	propositions	proposition	NNS
37681	2051	21	.	.	.
37681	2052	1	THEOREM	THEOREM	NNP
37681	2052	2	.	.	.
37681	2053	1	_	_	NNP
37681	2053	2	The	the	DT
37681	2053	3	sum	sum	NN
37681	2053	4	of	of	IN
37681	2053	5	the	the	DT
37681	2053	6	three	three	CD
37681	2053	7	angles	angle	NNS
37681	2053	8	of	of	IN
37681	2053	9	a	a	DT
37681	2053	10	triangle	triangle	NN
37681	2053	11	is	be	VBZ
37681	2053	12	equal	equal	JJ
37681	2053	13	to	to	IN
37681	2053	14	two	two	CD
37681	2053	15	right	right	JJ
37681	2053	16	angles	angle	NNS
37681	2053	17	.	.	.
37681	2053	18	_	_	NNP
37681	2053	19	Euclid	Euclid	NNP
37681	2053	20	stated	state	VBD
37681	2053	21	this	this	DT
37681	2053	22	as	as	IN
37681	2053	23	follows	follow	VBZ
37681	2053	24	:	:	:
37681	2053	25	"	"	``
37681	2053	26	In	in	IN
37681	2053	27	any	any	DT
37681	2053	28	triangle	triangle	NN
37681	2053	29	,	,	,
37681	2053	30	if	if	IN
37681	2053	31	one	one	CD
37681	2053	32	of	of	IN
37681	2053	33	the	the	DT
37681	2053	34	sides	side	NNS
37681	2053	35	be	be	VB
37681	2053	36	produced	produce	VBN
37681	2053	37	,	,	,
37681	2053	38	the	the	DT
37681	2053	39	exterior	exterior	NNP
37681	2053	40	angle	angle	NN
37681	2053	41	is	be	VBZ
37681	2053	42	equal	equal	JJ
37681	2053	43	to	to	IN
37681	2053	44	the	the	DT
37681	2053	45	two	two	CD
37681	2053	46	interior	interior	JJ
37681	2053	47	and	and	CC
37681	2053	48	opposite	opposite	JJ
37681	2053	49	angles	angle	NNS
37681	2053	50	,	,	,
37681	2053	51	and	and	CC
37681	2053	52	the	the	DT
37681	2053	53	three	three	CD
37681	2053	54	interior	interior	JJ
37681	2053	55	angles	angle	NNS
37681	2053	56	of	of	IN
37681	2053	57	the	the	DT
37681	2053	58	triangle	triangle	NN
37681	2053	59	are	be	VBP
37681	2053	60	equal	equal	JJ
37681	2053	61	to	to	IN
37681	2053	62	two	two	CD
37681	2053	63	right	right	JJ
37681	2053	64	angles	angle	NNS
37681	2053	65	.	.	.
37681	2053	66	"	"	''
37681	2054	1	This	this	DT
37681	2054	2	states	state	VBZ
37681	2054	3	more	more	RBR
37681	2054	4	than	than	IN
37681	2054	5	is	be	VBZ
37681	2054	6	necessary	necessary	JJ
37681	2054	7	for	for	IN
37681	2054	8	the	the	DT
37681	2054	9	basal	basal	JJ
37681	2054	10	fact	fact	NN
37681	2054	11	of	of	IN
37681	2054	12	the	the	DT
37681	2054	13	proposition	proposition	NN
37681	2054	14	,	,	,
37681	2054	15	which	which	WDT
37681	2054	16	is	be	VBZ
37681	2054	17	the	the	DT
37681	2054	18	constancy	constancy	NN
37681	2054	19	of	of	IN
37681	2054	20	the	the	DT
37681	2054	21	sum	sum	NN
37681	2054	22	of	of	IN
37681	2054	23	the	the	DT
37681	2054	24	angles	angle	NNS
37681	2054	25	.	.	.
37681	2055	1	The	the	DT
37681	2055	2	theorem	theorem	NN
37681	2055	3	is	be	VBZ
37681	2055	4	one	one	CD
37681	2055	5	of	of	IN
37681	2055	6	the	the	DT
37681	2055	7	three	three	CD
37681	2055	8	most	most	RBS
37681	2055	9	important	important	JJ
37681	2055	10	propositions	proposition	NNS
37681	2055	11	in	in	IN
37681	2055	12	plane	plane	NN
37681	2055	13	geometry	geometry	NN
37681	2055	14	,	,	,
37681	2055	15	the	the	DT
37681	2055	16	other	other	JJ
37681	2055	17	two	two	CD
37681	2055	18	being	be	VBG
37681	2055	19	the	the	DT
37681	2055	20	so	so	RB
37681	2055	21	-	-	HYPH
37681	2055	22	called	call	VBN
37681	2055	23	Pythagorean	Pythagorean	NNP
37681	2055	24	Theorem	Theorem	NNP
37681	2055	25	,	,	,
37681	2055	26	and	and	CC
37681	2055	27	a	a	DT
37681	2055	28	proposition	proposition	NN
37681	2055	29	relating	relate	VBG
37681	2055	30	to	to	IN
37681	2055	31	the	the	DT
37681	2055	32	proportionality	proportionality	NN
37681	2055	33	of	of	IN
37681	2055	34	the	the	DT
37681	2055	35	sides	side	NNS
37681	2055	36	of	of	IN
37681	2055	37	two	two	CD
37681	2055	38	triangles	triangle	NNS
37681	2055	39	.	.	.
37681	2056	1	These	these	DT
37681	2056	2	three	three	CD
37681	2056	3	form	form	NN
37681	2056	4	the	the	DT
37681	2056	5	foundation	foundation	NN
37681	2056	6	of	of	IN
37681	2056	7	trigonometry	trigonometry	NNP
37681	2056	8	and	and	CC
37681	2056	9	of	of	IN
37681	2056	10	the	the	DT
37681	2056	11	mensuration	mensuration	NN
37681	2056	12	of	of	IN
37681	2056	13	plane	plane	NN
37681	2056	14	figures	figure	NNS
37681	2056	15	.	.	.
37681	2057	1	The	the	DT
37681	2057	2	history	history	NN
37681	2057	3	of	of	IN
37681	2057	4	the	the	DT
37681	2057	5	proposition	proposition	NN
37681	2057	6	is	be	VBZ
37681	2057	7	extensive	extensive	JJ
37681	2057	8	.	.	.
37681	2058	1	Eutocius	Eutocius	NNP
37681	2058	2	(	(	-LRB-
37681	2058	3	_	_	NNP
37681	2058	4	ca	ca	NNP
37681	2058	5	.	.	.
37681	2058	6	_	_	NNP
37681	2058	7	510	510	CD
37681	2058	8	A.D.	A.D.	NNP
37681	2058	9	)	)	-RRB-
37681	2058	10	,	,	,
37681	2058	11	in	in	IN
37681	2058	12	his	-PRON-	PRP$
37681	2058	13	commentary	commentary	NN
37681	2058	14	on	on	IN
37681	2058	15	Apollonius	Apollonius	NNP
37681	2058	16	,	,	,
37681	2058	17	says	say	VBZ
37681	2058	18	that	that	IN
37681	2058	19	Geminus	Geminus	NNP
37681	2058	20	(	(	-LRB-
37681	2058	21	first	first	JJ
37681	2058	22	century	century	NN
37681	2058	23	B.C.	B.C.	NNP
37681	2058	24	)	)	-RRB-
37681	2059	1	testified	testify	VBD
37681	2059	2	that	that	IN
37681	2059	3	"	"	``
37681	2059	4	the	the	DT
37681	2059	5	ancients	ancient	NNS
37681	2059	6	investigated	investigate	VBD
37681	2059	7	the	the	DT
37681	2059	8	theorem	theorem	NN
37681	2059	9	of	of	IN
37681	2059	10	the	the	DT
37681	2059	11	two	two	CD
37681	2059	12	right	right	JJ
37681	2059	13	angles	angle	NNS
37681	2059	14	in	in	IN
37681	2059	15	each	each	DT
37681	2059	16	individual	individual	JJ
37681	2059	17	species	specie	NNS
37681	2059	18	of	of	IN
37681	2059	19	triangle	triangle	NNP
37681	2059	20	,	,	,
37681	2059	21	first	first	RB
37681	2059	22	in	in	IN
37681	2059	23	the	the	DT
37681	2059	24	equilateral	equilateral	JJ
37681	2059	25	,	,	,
37681	2059	26	again	again	RB
37681	2059	27	in	in	IN
37681	2059	28	the	the	DT
37681	2059	29	isosceles	isoscele	NNS
37681	2059	30	,	,	,
37681	2059	31	and	and	CC
37681	2059	32	afterwards	afterwards	RB
37681	2059	33	in	in	IN
37681	2059	34	the	the	DT
37681	2059	35	scalene	scalene	JJ
37681	2059	36	triangle	triangle	NN
37681	2059	37	.	.	.
37681	2059	38	"	"	''
37681	2060	1	This	this	DT
37681	2060	2	,	,	,
37681	2060	3	indeed	indeed	RB
37681	2060	4	,	,	,
37681	2060	5	was	be	VBD
37681	2060	6	the	the	DT
37681	2060	7	ancient	ancient	JJ
37681	2060	8	plan	plan	NN
37681	2060	9	,	,	,
37681	2060	10	to	to	TO
37681	2060	11	proceed	proceed	VB
37681	2060	12	from	from	IN
37681	2060	13	the	the	DT
37681	2060	14	particular	particular	JJ
37681	2060	15	to	to	IN
37681	2060	16	the	the	DT
37681	2060	17	general	general	NN
37681	2060	18	.	.	.
37681	2061	1	It	-PRON-	PRP
37681	2061	2	is	be	VBZ
37681	2061	3	the	the	DT
37681	2061	4	natural	natural	JJ
37681	2061	5	order	order	NN
37681	2061	6	,	,	,
37681	2061	7	it	-PRON-	PRP
37681	2061	8	is	be	VBZ
37681	2061	9	the	the	DT
37681	2061	10	world	world	NN
37681	2061	11	's	's	POS
37681	2061	12	order	order	NN
37681	2061	13	,	,	,
37681	2061	14	and	and	CC
37681	2061	15	it	-PRON-	PRP
37681	2061	16	is	be	VBZ
37681	2061	17	well	well	JJ
37681	2061	18	to	to	TO
37681	2061	19	follow	follow	VB
37681	2061	20	it	-PRON-	PRP
37681	2061	21	in	in	IN
37681	2061	22	all	all	DT
37681	2061	23	cases	case	NNS
37681	2061	24	of	of	IN
37681	2061	25	difficulty	difficulty	NN
37681	2061	26	in	in	IN
37681	2061	27	the	the	DT
37681	2061	28	classroom	classroom	NN
37681	2061	29	.	.	.
37681	2062	1	Proclus	Proclus	NNP
37681	2062	2	(	(	-LRB-
37681	2062	3	410	410	CD
37681	2062	4	-	-	SYM
37681	2062	5	485	485	CD
37681	2062	6	A.D.	A.D.	NNP
37681	2062	7	)	)	-RRB-
37681	2062	8	tells	tell	VBZ
37681	2062	9	us	-PRON-	PRP
37681	2062	10	that	that	IN
37681	2062	11	Eudemus	Eudemus	NNP
37681	2062	12	,	,	,
37681	2062	13	who	who	WP
37681	2062	14	lived	live	VBD
37681	2062	15	just	just	RB
37681	2062	16	before	before	RB
37681	2062	17	Euclid	Euclid	NNP
37681	2062	18	(	(	-LRB-
37681	2062	19	or	or	CC
37681	2062	20	probably	probably	RB
37681	2062	21	about	about	RB
37681	2062	22	325	325	CD
37681	2062	23	B.C.	B.C.	NNS
37681	2063	1	)	)	-RRB-
37681	2063	2	,	,	,
37681	2063	3	affirmed	affirm	VBD
37681	2063	4	that	that	IN
37681	2063	5	the	the	DT
37681	2063	6	theorem	theorem	NN
37681	2063	7	was	be	VBD
37681	2063	8	due	due	JJ
37681	2063	9	to	to	IN
37681	2063	10	the	the	DT
37681	2063	11	Pythagoreans	Pythagoreans	NNPS
37681	2063	12	,	,	,
37681	2063	13	although	although	IN
37681	2063	14	this	this	DT
37681	2063	15	does	do	VBZ
37681	2063	16	not	not	RB
37681	2063	17	necessarily	necessarily	RB
37681	2063	18	mean	mean	VB
37681	2063	19	to	to	IN
37681	2063	20	the	the	DT
37681	2063	21	actual	actual	JJ
37681	2063	22	pupils	pupil	NNS
37681	2063	23	of	of	IN
37681	2063	24	Pythagoras	Pythagoras	NNP
37681	2063	25	.	.	.
37681	2064	1	The	the	DT
37681	2064	2	proof	proof	NN
37681	2064	3	as	as	IN
37681	2064	4	he	-PRON-	PRP
37681	2064	5	gives	give	VBZ
37681	2064	6	it	-PRON-	PRP
37681	2064	7	consists	consist	VBZ
37681	2064	8	in	in	IN
37681	2064	9	showing	show	VBG
37681	2064	10	that	that	IN
37681	2064	11	_	_	NNP
37681	2064	12	a	a	DT
37681	2064	13	_	_	NNP
37681	2064	14	=	=	SYM
37681	2064	15	_	_	NNP
37681	2064	16	a	a	DT
37681	2064	17	_	_	NNP
37681	2064	18	´	´	NNP
37681	2064	19	,	,	,
37681	2064	20	_	_	NNP
37681	2064	21	b	b	NNP
37681	2064	22	_	_	NNP
37681	2064	23	=	=	SYM
37681	2064	24	_	_	NNP
37681	2064	25	b	b	NNP
37681	2064	26	_	_	NNP
37681	2064	27	´	´	CD
37681	2064	28	,	,	,
37681	2064	29	and	and	CC
37681	2064	30	_	_	NNP
37681	2064	31	a	a	DT
37681	2064	32	_	_	NNP
37681	2064	33	´	´	NNP
37681	2064	34	+	+	SYM
37681	2064	35	_	_	NNP
37681	2064	36	c	c	NNP
37681	2064	37	_	_	NNP
37681	2064	38	+	+	NNP
37681	2064	39	_	_	NNP
37681	2064	40	b	b	NNP
37681	2064	41	_	_	NNP
37681	2064	42	´	´	NNP
37681	2064	43	=	=	SYM
37681	2064	44	two	two	CD
37681	2064	45	right	right	JJ
37681	2064	46	angles	angle	NNS
37681	2064	47	.	.	.
37681	2065	1	Since	since	IN
37681	2065	2	the	the	DT
37681	2065	3	proposition	proposition	NN
37681	2065	4	about	about	IN
37681	2065	5	the	the	DT
37681	2065	6	exterior	exterior	JJ
37681	2065	7	angle	angle	NN
37681	2065	8	of	of	IN
37681	2065	9	a	a	DT
37681	2065	10	triangle	triangle	NN
37681	2065	11	is	be	VBZ
37681	2065	12	attributed	attribute	VBN
37681	2065	13	to	to	IN
37681	2065	14	Philippus	Philippus	NNP
37681	2065	15	of	of	IN
37681	2065	16	Mende	Mende	NNP
37681	2065	17	(	(	-LRB-
37681	2065	18	_	_	NNP
37681	2065	19	ca	ca	NNP
37681	2065	20	.	.	.
37681	2065	21	_	_	NNP
37681	2065	22	380	380	CD
37681	2065	23	B.C.	B.C.	NNP
37681	2066	1	)	)	-RRB-
37681	2066	2	,	,	,
37681	2066	3	the	the	DT
37681	2066	4	figure	figure	NN
37681	2066	5	given	give	VBN
37681	2066	6	by	by	IN
37681	2066	7	Eudemus	Eudemus	NNP
37681	2066	8	is	be	VBZ
37681	2066	9	probably	probably	RB
37681	2066	10	the	the	DT
37681	2066	11	one	one	NN
37681	2066	12	used	use	VBN
37681	2066	13	by	by	IN
37681	2066	14	the	the	DT
37681	2066	15	Pythagoreans	Pythagoreans	NNPS
37681	2066	16	.	.	.
37681	2067	1	[	[	-LRB-
37681	2067	2	Illustration	illustration	NN
37681	2067	3	]	]	-RRB-
37681	2067	4	There	there	EX
37681	2067	5	is	be	VBZ
37681	2067	6	also	also	RB
37681	2067	7	some	some	DT
37681	2067	8	reason	reason	NN
37681	2067	9	for	for	IN
37681	2067	10	believing	believe	VBG
37681	2067	11	that	that	IN
37681	2067	12	Thales	Thales	NNPS
37681	2067	13	(	(	-LRB-
37681	2067	14	_	_	NNP
37681	2067	15	ca	ca	NNP
37681	2067	16	.	.	.
37681	2067	17	_	_	NNP
37681	2067	18	600	600	CD
37681	2067	19	B.C.	B.C.	NNP
37681	2067	20	)	)	-RRB-
37681	2068	1	knew	know	VBD
37681	2068	2	the	the	DT
37681	2068	3	theorem	theorem	NN
37681	2068	4	,	,	,
37681	2068	5	for	for	IN
37681	2068	6	Diogenes	Diogenes	NNP
37681	2068	7	Laertius	Laertius	NNP
37681	2068	8	(	(	-LRB-
37681	2068	9	_	_	NNP
37681	2068	10	ca	ca	NNP
37681	2068	11	.	.	.
37681	2068	12	_	_	NNP
37681	2068	13	200	200	CD
37681	2068	14	A.D.	A.D.	NNP
37681	2068	15	)	)	-RRB-
37681	2068	16	quotes	quote	VBZ
37681	2068	17	Pamphilius	Pamphilius	NNP
37681	2068	18	(	(	-LRB-
37681	2068	19	first	first	JJ
37681	2068	20	century	century	NN
37681	2068	21	A.D.	A.D.	NNP
37681	2068	22	)	)	-RRB-
37681	2068	23	as	as	IN
37681	2068	24	saying	say	VBG
37681	2068	25	that	that	IN
37681	2068	26	"	"	``
37681	2068	27	he	-PRON-	PRP
37681	2068	28	,	,	,
37681	2068	29	having	have	VBG
37681	2068	30	learned	learn	VBN
37681	2068	31	geometry	geometry	NN
37681	2068	32	from	from	IN
37681	2068	33	the	the	DT
37681	2068	34	Egyptians	Egyptians	NNPS
37681	2068	35	,	,	,
37681	2068	36	was	be	VBD
37681	2068	37	the	the	DT
37681	2068	38	first	first	JJ
37681	2068	39	to	to	TO
37681	2068	40	inscribe	inscribe	VB
37681	2068	41	a	a	DT
37681	2068	42	right	right	JJ
37681	2068	43	triangle	triangle	NN
37681	2068	44	in	in	IN
37681	2068	45	a	a	DT
37681	2068	46	circle	circle	NN
37681	2068	47	,	,	,
37681	2068	48	and	and	CC
37681	2068	49	sacrificed	sacrifice	VBD
37681	2068	50	an	an	DT
37681	2068	51	ox	ox	NN
37681	2068	52	.	.	.
37681	2068	53	"	"	''
37681	2069	1	The	the	DT
37681	2069	2	proof	proof	NN
37681	2069	3	of	of	IN
37681	2069	4	this	this	DT
37681	2069	5	proposition	proposition	NN
37681	2069	6	requires	require	VBZ
37681	2069	7	the	the	DT
37681	2069	8	knowledge	knowledge	NN
37681	2069	9	that	that	IN
37681	2069	10	the	the	DT
37681	2069	11	sum	sum	NN
37681	2069	12	of	of	IN
37681	2069	13	the	the	DT
37681	2069	14	angles	angle	NNS
37681	2069	15	,	,	,
37681	2069	16	at	at	IN
37681	2069	17	least	least	JJS
37681	2069	18	in	in	IN
37681	2069	19	a	a	DT
37681	2069	20	right	right	JJ
37681	2069	21	triangle	triangle	NN
37681	2069	22	,	,	,
37681	2069	23	is	be	VBZ
37681	2069	24	two	two	CD
37681	2069	25	right	right	JJ
37681	2069	26	angles	angle	NNS
37681	2069	27	.	.	.
37681	2070	1	The	the	DT
37681	2070	2	proposition	proposition	NN
37681	2070	3	is	be	VBZ
37681	2070	4	frequently	frequently	RB
37681	2070	5	referred	refer	VBN
37681	2070	6	to	to	IN
37681	2070	7	by	by	IN
37681	2070	8	Aristotle	Aristotle	NNP
37681	2070	9	.	.	.
37681	2071	1	There	there	EX
37681	2071	2	have	have	VBP
37681	2071	3	been	be	VBN
37681	2071	4	numerous	numerous	JJ
37681	2071	5	attempts	attempt	NNS
37681	2071	6	to	to	TO
37681	2071	7	prove	prove	VB
37681	2071	8	the	the	DT
37681	2071	9	proposition	proposition	NN
37681	2071	10	without	without	IN
37681	2071	11	the	the	DT
37681	2071	12	use	use	NN
37681	2071	13	of	of	IN
37681	2071	14	parallel	parallel	JJ
37681	2071	15	lines	line	NNS
37681	2071	16	.	.	.
37681	2072	1	Of	of	IN
37681	2072	2	these	these	DT
37681	2072	3	a	a	DT
37681	2072	4	German	german	JJ
37681	2072	5	one	one	NN
37681	2072	6	,	,	,
37681	2072	7	first	first	RB
37681	2072	8	given	give	VBN
37681	2072	9	by	by	IN
37681	2072	10	Thibaut	Thibaut	NNP
37681	2072	11	in	in	IN
37681	2072	12	the	the	DT
37681	2072	13	early	early	JJ
37681	2072	14	part	part	NN
37681	2072	15	of	of	IN
37681	2072	16	the	the	DT
37681	2072	17	eighteenth	eighteenth	JJ
37681	2072	18	century	century	NN
37681	2072	19	,	,	,
37681	2072	20	is	be	VBZ
37681	2072	21	among	among	IN
37681	2072	22	the	the	DT
37681	2072	23	most	most	RBS
37681	2072	24	interesting	interesting	JJ
37681	2072	25	.	.	.
37681	2073	1	This	this	DT
37681	2073	2	,	,	,
37681	2073	3	in	in	IN
37681	2073	4	simplified	simplify	VBN
37681	2073	5	form	form	NN
37681	2073	6	,	,	,
37681	2073	7	is	be	VBZ
37681	2073	8	as	as	IN
37681	2073	9	follows	follow	VBZ
37681	2073	10	:	:	:
37681	2073	11	[	[	-LRB-
37681	2073	12	Illustration	illustration	NN
37681	2073	13	]	]	-RRB-
37681	2073	14	Suppose	suppose	VB
37681	2073	15	an	an	DT
37681	2073	16	indefinite	indefinite	JJ
37681	2073	17	line	line	NN
37681	2073	18	_	_	NNP
37681	2073	19	XY	XY	NNP
37681	2073	20	_	_	NNP
37681	2073	21	to	to	TO
37681	2073	22	lie	lie	VB
37681	2073	23	on	on	IN
37681	2073	24	_	_	NNP
37681	2073	25	AB	AB	NNP
37681	2073	26	_	_	NNP
37681	2073	27	.	.	.
37681	2074	1	Let	let	VB
37681	2074	2	it	-PRON-	PRP
37681	2074	3	swing	swing	VB
37681	2074	4	about	about	IN
37681	2074	5	_	_	NNP
37681	2074	6	A	A	NNP
37681	2074	7	_	_	NNP
37681	2074	8	,	,	,
37681	2074	9	counterclockwise	counterclockwise	NN
37681	2074	10	,	,	,
37681	2074	11	through	through	IN
37681	2074	12	[	[	-LRB-
37681	2074	13	L]_A	L]_A	NNS
37681	2074	14	_	_	NNP
37681	2074	15	,	,	,
37681	2074	16	so	so	IN
37681	2074	17	as	as	IN
37681	2074	18	to	to	TO
37681	2074	19	lie	lie	VB
37681	2074	20	on	on	IN
37681	2074	21	_	_	NNP
37681	2074	22	AC	AC	NNP
37681	2074	23	_	_	NNP
37681	2074	24	,	,	,
37681	2074	25	as	as	IN
37681	2074	26	_	_	NNP
37681	2074	27	X'Y	X'Y	NNP
37681	2074	28	'	'	``
37681	2074	29	_	_	NN
37681	2074	30	.	.	.
37681	2075	1	Then	then	RB
37681	2075	2	let	let	VB
37681	2075	3	it	-PRON-	PRP
37681	2075	4	swing	swing	VB
37681	2075	5	about	about	IN
37681	2075	6	_	_	NNP
37681	2075	7	C	C	NNP
37681	2075	8	_	_	NNP
37681	2075	9	,	,	,
37681	2075	10	through	through	IN
37681	2075	11	[	[	-LRB-
37681	2075	12	L]_C	L]_C	NNP
37681	2075	13	_	_	NNP
37681	2075	14	,	,	,
37681	2075	15	so	so	IN
37681	2075	16	as	as	IN
37681	2075	17	to	to	TO
37681	2075	18	lie	lie	VB
37681	2075	19	on	on	IN
37681	2075	20	_	_	NNP
37681	2075	21	CB	CB	NNP
37681	2075	22	_	_	NNP
37681	2075	23	,	,	,
37681	2075	24	as	as	IN
37681	2075	25	_	_	NNP
37681	2075	26	X''Y	x''y	NN
37681	2075	27	'	'	``
37681	2075	28	'	'	``
37681	2075	29	_	_	XX
37681	2075	30	.	.	.
37681	2076	1	Then	then	RB
37681	2076	2	let	let	VB
37681	2076	3	it	-PRON-	PRP
37681	2076	4	swing	swing	VB
37681	2076	5	about	about	IN
37681	2076	6	_	_	NNP
37681	2076	7	B	B	NNP
37681	2076	8	_	_	NNP
37681	2076	9	,	,	,
37681	2076	10	through	through	IN
37681	2076	11	[	[	-LRB-
37681	2076	12	L]_B	L]_B	NNP
37681	2076	13	_	_	NNP
37681	2076	14	,	,	,
37681	2076	15	so	so	IN
37681	2076	16	as	as	IN
37681	2076	17	to	to	TO
37681	2076	18	lie	lie	VB
37681	2076	19	on	on	IN
37681	2076	20	_	_	NNP
37681	2076	21	BA	BA	NNP
37681	2076	22	_	_	NNP
37681	2076	23	,	,	,
37681	2076	24	as	as	IN
37681	2076	25	_	_	NNP
37681	2076	26	X'''Y	X'''Y	NNP
37681	2076	27	'	'	POS
37681	2076	28	'	'	''
37681	2076	29	'	'	''
37681	2076	30	_	_	XX
37681	2076	31	.	.	.
37681	2077	1	It	-PRON-	PRP
37681	2077	2	now	now	RB
37681	2077	3	lies	lie	VBZ
37681	2077	4	on	on	IN
37681	2077	5	_	_	NNP
37681	2077	6	AB	AB	NNP
37681	2077	7	_	_	NNP
37681	2077	8	,	,	,
37681	2077	9	but	but	CC
37681	2077	10	it	-PRON-	PRP
37681	2077	11	is	be	VBZ
37681	2077	12	turned	turn	VBN
37681	2077	13	over	over	RP
37681	2077	14	,	,	,
37681	2077	15	_	_	NNP
37681	2077	16	X	X	NNP
37681	2077	17	'	'	NN
37681	2077	18	'	'	''
37681	2077	19	'	'	''
37681	2077	20	_	_	NNP
37681	2077	21	being	be	VBG
37681	2077	22	where	where	WRB
37681	2077	23	_	_	NNP
37681	2077	24	Y	Y	NNP
37681	2077	25	_	_	NNP
37681	2077	26	was	be	VBD
37681	2077	27	,	,	,
37681	2077	28	and	and	CC
37681	2077	29	_	_	NNP
37681	2077	30	Y	Y	NNP
37681	2077	31	'	'	''
37681	2077	32	'	'	''
37681	2077	33	'	'	''
37681	2077	34	_	_	NNP
37681	2077	35	where	where	WRB
37681	2077	36	_	_	NNP
37681	2077	37	X	X	NNP
37681	2077	38	_	_	NNP
37681	2077	39	was	be	VBD
37681	2077	40	.	.	.
37681	2078	1	In	in	IN
37681	2078	2	turning	turn	VBG
37681	2078	3	through	through	RP
37681	2078	4	[	[	-LRB-
37681	2078	5	Ls]_A	Ls]_A	NNP
37681	2078	6	_	_	NNP
37681	2078	7	,	,	,
37681	2078	8	_	_	NNP
37681	2078	9	B	B	NNP
37681	2078	10	_	_	NNP
37681	2078	11	,	,	,
37681	2078	12	and	and	CC
37681	2078	13	_	_	NNP
37681	2078	14	C	C	NNP
37681	2078	15	_	_	NNP
37681	2078	16	it	-PRON-	PRP
37681	2078	17	has	have	VBZ
37681	2078	18	therefore	therefore	RB
37681	2078	19	turned	turn	VBN
37681	2078	20	through	through	RP
37681	2078	21	two	two	CD
37681	2078	22	right	right	JJ
37681	2078	23	angles	angle	NNS
37681	2078	24	.	.	.
37681	2079	1	One	one	CD
37681	2079	2	trouble	trouble	NN
37681	2079	3	with	with	IN
37681	2079	4	the	the	DT
37681	2079	5	proof	proof	NN
37681	2079	6	is	be	VBZ
37681	2079	7	that	that	IN
37681	2079	8	the	the	DT
37681	2079	9	rotation	rotation	NN
37681	2079	10	has	have	VBZ
37681	2079	11	not	not	RB
37681	2079	12	been	be	VBN
37681	2079	13	about	about	IN
37681	2079	14	the	the	DT
37681	2079	15	same	same	JJ
37681	2079	16	point	point	NN
37681	2079	17	,	,	,
37681	2079	18	so	so	IN
37681	2079	19	that	that	IN
37681	2079	20	it	-PRON-	PRP
37681	2079	21	has	have	VBZ
37681	2079	22	never	never	RB
37681	2079	23	been	be	VBN
37681	2079	24	looked	look	VBN
37681	2079	25	upon	upon	IN
37681	2079	26	as	as	IN
37681	2079	27	other	other	JJ
37681	2079	28	than	than	IN
37681	2079	29	an	an	DT
37681	2079	30	interesting	interesting	JJ
37681	2079	31	illustration	illustration	NN
37681	2079	32	.	.	.
37681	2080	1	Proclus	Proclus	NNP
37681	2080	2	tried	try	VBD
37681	2080	3	to	to	TO
37681	2080	4	prove	prove	VB
37681	2080	5	the	the	DT
37681	2080	6	theorem	theorem	NN
37681	2080	7	by	by	IN
37681	2080	8	saying	say	VBG
37681	2080	9	that	that	IN
37681	2080	10	,	,	,
37681	2080	11	if	if	IN
37681	2080	12	we	-PRON-	PRP
37681	2080	13	have	have	VBP
37681	2080	14	two	two	CD
37681	2080	15	perpendiculars	perpendicular	NNS
37681	2080	16	to	to	IN
37681	2080	17	the	the	DT
37681	2080	18	same	same	JJ
37681	2080	19	line	line	NN
37681	2080	20	,	,	,
37681	2080	21	and	and	CC
37681	2080	22	suppose	suppose	VB
37681	2080	23	them	-PRON-	PRP
37681	2080	24	to	to	TO
37681	2080	25	revolve	revolve	VB
37681	2080	26	about	about	IN
37681	2080	27	their	-PRON-	PRP$
37681	2080	28	feet	foot	NNS
37681	2080	29	so	so	IN
37681	2080	30	as	as	IN
37681	2080	31	to	to	TO
37681	2080	32	make	make	VB
37681	2080	33	a	a	DT
37681	2080	34	triangle	triangle	NN
37681	2080	35	,	,	,
37681	2080	36	then	then	RB
37681	2080	37	the	the	DT
37681	2080	38	amount	amount	NN
37681	2080	39	taken	take	VBN
37681	2080	40	from	from	IN
37681	2080	41	the	the	DT
37681	2080	42	right	right	JJ
37681	2080	43	angles	angle	NNS
37681	2080	44	is	be	VBZ
37681	2080	45	added	add	VBN
37681	2080	46	to	to	IN
37681	2080	47	the	the	DT
37681	2080	48	vertical	vertical	JJ
37681	2080	49	angle	angle	NN
37681	2080	50	of	of	IN
37681	2080	51	the	the	DT
37681	2080	52	triangle	triangle	NN
37681	2080	53	,	,	,
37681	2080	54	and	and	CC
37681	2080	55	therefore	therefore	RB
37681	2080	56	the	the	DT
37681	2080	57	sum	sum	NN
37681	2080	58	of	of	IN
37681	2080	59	the	the	DT
37681	2080	60	angles	angle	NNS
37681	2080	61	continues	continue	VBZ
37681	2080	62	to	to	TO
37681	2080	63	be	be	VB
37681	2080	64	two	two	CD
37681	2080	65	right	right	JJ
37681	2080	66	angles	angle	NNS
37681	2080	67	.	.	.
37681	2081	1	But	but	CC
37681	2081	2	,	,	,
37681	2081	3	of	of	IN
37681	2081	4	course	course	NN
37681	2081	5	,	,	,
37681	2081	6	to	to	TO
37681	2081	7	prove	prove	VB
37681	2081	8	his	-PRON-	PRP$
37681	2081	9	statement	statement	NN
37681	2081	10	requires	require	VBZ
37681	2081	11	a	a	DT
37681	2081	12	perpendicular	perpendicular	NN
37681	2081	13	to	to	TO
37681	2081	14	be	be	VB
37681	2081	15	drawn	draw	VBN
37681	2081	16	from	from	IN
37681	2081	17	the	the	DT
37681	2081	18	vertex	vertex	NN
37681	2081	19	to	to	IN
37681	2081	20	the	the	DT
37681	2081	21	base	base	NN
37681	2081	22	,	,	,
37681	2081	23	and	and	CC
37681	2081	24	the	the	DT
37681	2081	25	theorem	theorem	NN
37681	2081	26	of	of	IN
37681	2081	27	parallels	parallel	NNS
37681	2081	28	to	to	TO
37681	2081	29	be	be	VB
37681	2081	30	applied	apply	VBN
37681	2081	31	.	.	.
37681	2082	1	Pupils	pupil	NNS
37681	2082	2	will	will	MD
37681	2082	3	find	find	VB
37681	2082	4	it	-PRON-	PRP
37681	2082	5	interesting	interesting	JJ
37681	2082	6	to	to	TO
37681	2082	7	cut	cut	VB
37681	2082	8	off	off	RP
37681	2082	9	the	the	DT
37681	2082	10	corners	corner	NNS
37681	2082	11	of	of	IN
37681	2082	12	a	a	DT
37681	2082	13	paper	paper	NN
37681	2082	14	triangle	triangle	NN
37681	2082	15	and	and	CC
37681	2082	16	fit	fit	VB
37681	2082	17	the	the	DT
37681	2082	18	angles	angle	NNS
37681	2082	19	together	together	RB
37681	2082	20	so	so	IN
37681	2082	21	as	as	IN
37681	2082	22	to	to	TO
37681	2082	23	make	make	VB
37681	2082	24	a	a	DT
37681	2082	25	straight	straight	JJ
37681	2082	26	angle	angle	NN
37681	2082	27	.	.	.
37681	2083	1	This	this	DT
37681	2083	2	theorem	theorem	NN
37681	2083	3	furnishes	furnish	VBZ
37681	2083	4	an	an	DT
37681	2083	5	opportunity	opportunity	NN
37681	2083	6	for	for	IN
37681	2083	7	many	many	JJ
37681	2083	8	interesting	interesting	JJ
37681	2083	9	exercises	exercise	NNS
37681	2083	10	,	,	,
37681	2083	11	and	and	CC
37681	2083	12	in	in	IN
37681	2083	13	particular	particular	JJ
37681	2083	14	for	for	IN
37681	2083	15	determining	determine	VBG
37681	2083	16	the	the	DT
37681	2083	17	third	third	JJ
37681	2083	18	angle	angle	NN
37681	2083	19	when	when	WRB
37681	2083	20	two	two	CD
37681	2083	21	angles	angle	NNS
37681	2083	22	of	of	IN
37681	2083	23	a	a	DT
37681	2083	24	triangle	triangle	NN
37681	2083	25	are	be	VBP
37681	2083	26	given	give	VBN
37681	2083	27	,	,	,
37681	2083	28	or	or	CC
37681	2083	29	the	the	DT
37681	2083	30	second	second	JJ
37681	2083	31	acute	acute	JJ
37681	2083	32	angle	angle	NN
37681	2083	33	of	of	IN
37681	2083	34	a	a	DT
37681	2083	35	right	right	JJ
37681	2083	36	triangle	triangle	NN
37681	2083	37	when	when	WRB
37681	2083	38	one	one	CD
37681	2083	39	acute	acute	JJ
37681	2083	40	angle	angle	NN
37681	2083	41	is	be	VBZ
37681	2083	42	given	give	VBN
37681	2083	43	.	.	.
37681	2084	1	Of	of	IN
37681	2084	2	the	the	DT
37681	2084	3	simple	simple	JJ
37681	2084	4	outdoor	outdoor	JJ
37681	2084	5	applications	application	NNS
37681	2084	6	of	of	IN
37681	2084	7	the	the	DT
37681	2084	8	proposition	proposition	NN
37681	2084	9	,	,	,
37681	2084	10	one	one	CD
37681	2084	11	of	of	IN
37681	2084	12	the	the	DT
37681	2084	13	best	good	JJS
37681	2084	14	is	be	VBZ
37681	2084	15	illustrated	illustrate	VBN
37681	2084	16	in	in	IN
37681	2084	17	this	this	DT
37681	2084	18	figure	figure	NN
37681	2084	19	.	.	.
37681	2085	1	[	[	-LRB-
37681	2085	2	Illustration	illustration	NN
37681	2085	3	]	]	-RRB-
37681	2085	4	To	to	TO
37681	2085	5	ascertain	ascertain	VB
37681	2085	6	the	the	DT
37681	2085	7	height	height	NN
37681	2085	8	of	of	IN
37681	2085	9	a	a	DT
37681	2085	10	tree	tree	NN
37681	2085	11	or	or	CC
37681	2085	12	of	of	IN
37681	2085	13	the	the	DT
37681	2085	14	school	school	NN
37681	2085	15	building	building	NN
37681	2085	16	,	,	,
37681	2085	17	fold	fold	VB
37681	2085	18	a	a	DT
37681	2085	19	piece	piece	NN
37681	2085	20	of	of	IN
37681	2085	21	paper	paper	NN
37681	2085	22	so	so	IN
37681	2085	23	as	as	IN
37681	2085	24	to	to	TO
37681	2085	25	make	make	VB
37681	2085	26	an	an	DT
37681	2085	27	angle	angle	NN
37681	2085	28	of	of	IN
37681	2085	29	45	45	CD
37681	2085	30	°	°	NNS
37681	2085	31	.	.	.
37681	2086	1	Then	then	RB
37681	2086	2	walk	walk	VB
37681	2086	3	back	back	RB
37681	2086	4	from	from	IN
37681	2086	5	the	the	DT
37681	2086	6	tree	tree	NN
37681	2086	7	until	until	IN
37681	2086	8	the	the	DT
37681	2086	9	top	top	NN
37681	2086	10	is	be	VBZ
37681	2086	11	seen	see	VBN
37681	2086	12	at	at	IN
37681	2086	13	an	an	DT
37681	2086	14	angle	angle	NN
37681	2086	15	of	of	IN
37681	2086	16	45	45	CD
37681	2086	17	°	°	NNS
37681	2086	18	with	with	IN
37681	2086	19	the	the	DT
37681	2086	20	ground	ground	NN
37681	2086	21	(	(	-LRB-
37681	2086	22	being	be	VBG
37681	2086	23	therefore	therefore	RB
37681	2086	24	careful	careful	JJ
37681	2086	25	to	to	TO
37681	2086	26	have	have	VB
37681	2086	27	the	the	DT
37681	2086	28	base	base	NN
37681	2086	29	of	of	IN
37681	2086	30	the	the	DT
37681	2086	31	triangle	triangle	NN
37681	2086	32	level	level	NN
37681	2086	33	)	)	-RRB-
37681	2086	34	.	.	.
37681	2087	1	Then	then	RB
37681	2087	2	the	the	DT
37681	2087	3	height	height	NN
37681	2087	4	_	_	NNP
37681	2087	5	AC	AC	NNP
37681	2087	6	_	_	NNP
37681	2087	7	will	will	MD
37681	2087	8	equal	equal	VB
37681	2087	9	the	the	DT
37681	2087	10	base	base	NN
37681	2087	11	_	_	NNP
37681	2087	12	AB	AB	NNP
37681	2087	13	_	_	NNP
37681	2087	14	,	,	,
37681	2087	15	since	since	IN
37681	2087	16	_	_	NNP
37681	2087	17	ABC	ABC	NNP
37681	2087	18	_	_	NNP
37681	2087	19	is	be	VBZ
37681	2087	20	isosceles	isoscele	NNS
37681	2087	21	.	.	.
37681	2088	1	A	a	DT
37681	2088	2	paper	paper	NN
37681	2088	3	protractor	protractor	NN
37681	2088	4	may	may	MD
37681	2088	5	be	be	VB
37681	2088	6	used	use	VBN
37681	2088	7	for	for	IN
37681	2088	8	the	the	DT
37681	2088	9	same	same	JJ
37681	2088	10	purpose	purpose	NN
37681	2088	11	.	.	.
37681	2089	1	Distances	distance	NNS
37681	2089	2	can	can	MD
37681	2089	3	easily	easily	RB
37681	2089	4	be	be	VB
37681	2089	5	measured	measure	VBN
37681	2089	6	by	by	IN
37681	2089	7	constructing	construct	VBG
37681	2089	8	a	a	DT
37681	2089	9	large	large	JJ
37681	2089	10	equilateral	equilateral	JJ
37681	2089	11	triangle	triangle	NN
37681	2089	12	of	of	IN
37681	2089	13	heavy	heavy	JJ
37681	2089	14	pasteboard	pasteboard	NN
37681	2089	15	,	,	,
37681	2089	16	and	and	CC
37681	2089	17	standing	stand	VBG
37681	2089	18	pins	pin	NNS
37681	2089	19	at	at	IN
37681	2089	20	the	the	DT
37681	2089	21	vertices	vertex	NNS
37681	2089	22	for	for	IN
37681	2089	23	the	the	DT
37681	2089	24	purpose	purpose	NN
37681	2089	25	of	of	IN
37681	2089	26	sighting	sight	VBG
37681	2089	27	.	.	.
37681	2090	1	[	[	-LRB-
37681	2090	2	Illustration	illustration	NN
37681	2090	3	]	]	-RRB-
37681	2090	4	To	to	TO
37681	2090	5	measure	measure	VB
37681	2090	6	_	_	NNP
37681	2090	7	PC	PC	NNP
37681	2090	8	_	_	NNP
37681	2090	9	,	,	,
37681	2090	10	stand	stand	VB
37681	2090	11	at	at	IN
37681	2090	12	some	some	DT
37681	2090	13	convenient	convenient	JJ
37681	2090	14	point	point	NN
37681	2090	15	_	_	NNP
37681	2090	16	A	A	NNP
37681	2090	17	_	_	NNP
37681	2090	18	and	and	CC
37681	2090	19	sight	sight	NN
37681	2090	20	along	along	IN
37681	2090	21	_	_	NNP
37681	2090	22	APC	APC	NNP
37681	2090	23	_	_	NNP
37681	2090	24	and	and	CC
37681	2090	25	also	also	RB
37681	2090	26	along	along	IN
37681	2090	27	_	_	NNP
37681	2090	28	AB	AB	NNP
37681	2090	29	_	_	NNP
37681	2090	30	.	.	.
37681	2091	1	Then	then	RB
37681	2091	2	walk	walk	VB
37681	2091	3	along	along	IN
37681	2091	4	_	_	NNP
37681	2091	5	AB	AB	NNP
37681	2091	6	_	_	NNP
37681	2091	7	until	until	IN
37681	2091	8	a	a	DT
37681	2091	9	point	point	NN
37681	2091	10	_	_	NNP
37681	2091	11	B	B	NNP
37681	2091	12	_	_	NNP
37681	2091	13	is	be	VBZ
37681	2091	14	reached	reach	VBN
37681	2091	15	from	from	IN
37681	2091	16	which	which	WDT
37681	2091	17	_	_	NNP
37681	2091	18	BC	BC	NNP
37681	2091	19	_	_	NNP
37681	2091	20	makes	make	VBZ
37681	2091	21	with	with	IN
37681	2091	22	_	_	NNP
37681	2091	23	BA	BA	NNP
37681	2091	24	_	_	NNP
37681	2091	25	an	an	DT
37681	2091	26	angle	angle	NN
37681	2091	27	of	of	IN
37681	2091	28	the	the	DT
37681	2091	29	triangle	triangle	NN
37681	2091	30	(	(	-LRB-
37681	2091	31	60	60	CD
37681	2091	32	°	°	NNS
37681	2091	33	)	)	-RRB-
37681	2091	34	.	.	.
37681	2092	1	Then	then	RB
37681	2092	2	_	_	NNP
37681	2092	3	AC	AC	NNP
37681	2092	4	_	_	NNP
37681	2092	5	=	=	SYM
37681	2092	6	_	_	NNP
37681	2092	7	AB	AB	NNP
37681	2092	8	_	_	NNP
37681	2092	9	,	,	,
37681	2092	10	and	and	CC
37681	2092	11	since	since	IN
37681	2092	12	_	_	NNP
37681	2092	13	AP	AP	NNP
37681	2092	14	_	_	NNP
37681	2092	15	can	can	MD
37681	2092	16	be	be	VB
37681	2092	17	measured	measure	VBN
37681	2092	18	,	,	,
37681	2092	19	we	-PRON-	PRP
37681	2092	20	can	can	MD
37681	2092	21	find	find	VB
37681	2092	22	_	_	NNP
37681	2092	23	PC	PC	NNP
37681	2092	24	_	_	NNP
37681	2092	25	.	.	.
37681	2093	1	Another	another	DT
37681	2093	2	simple	simple	JJ
37681	2093	3	method	method	NN
37681	2093	4	of	of	IN
37681	2093	5	measuring	measure	VBG
37681	2093	6	a	a	DT
37681	2093	7	distance	distance	NN
37681	2093	8	_	_	NNP
37681	2093	9	AC	AC	NNP
37681	2093	10	_	_	NNP
37681	2093	11	across	across	IN
37681	2093	12	a	a	DT
37681	2093	13	stream	stream	NN
37681	2093	14	is	be	VBZ
37681	2093	15	shown	show	VBN
37681	2093	16	in	in	IN
37681	2093	17	this	this	DT
37681	2093	18	figure	figure	NN
37681	2093	19	.	.	.
37681	2094	1	[	[	-LRB-
37681	2094	2	Illustration	illustration	NN
37681	2094	3	]	]	-RRB-
37681	2094	4	Measure	measure	VB
37681	2094	5	the	the	DT
37681	2094	6	angle	angle	NN
37681	2094	7	_	_	NNP
37681	2094	8	CAX	CAX	NNP
37681	2094	9	_	_	NNP
37681	2094	10	,	,	,
37681	2094	11	either	either	CC
37681	2094	12	in	in	IN
37681	2094	13	degrees	degree	NNS
37681	2094	14	,	,	,
37681	2094	15	with	with	IN
37681	2094	16	a	a	DT
37681	2094	17	protractor	protractor	NN
37681	2094	18	,	,	,
37681	2094	19	or	or	CC
37681	2094	20	by	by	IN
37681	2094	21	sighting	sight	VBG
37681	2094	22	along	along	IN
37681	2094	23	a	a	DT
37681	2094	24	piece	piece	NN
37681	2094	25	of	of	IN
37681	2094	26	paper	paper	NN
37681	2094	27	and	and	CC
37681	2094	28	marking	mark	VBG
37681	2094	29	down	down	RP
37681	2094	30	the	the	DT
37681	2094	31	angle	angle	NN
37681	2094	32	.	.	.
37681	2095	1	Then	then	RB
37681	2095	2	go	go	VB
37681	2095	3	along	along	IN
37681	2095	4	_	_	NNP
37681	2095	5	XA	XA	NNP
37681	2095	6	_	_	NNP
37681	2095	7	produced	produce	VBD
37681	2095	8	until	until	IN
37681	2095	9	a	a	DT
37681	2095	10	point	point	NN
37681	2095	11	_	_	NNP
37681	2095	12	B	B	NNP
37681	2095	13	_	_	NNP
37681	2095	14	is	be	VBZ
37681	2095	15	reached	reach	VBN
37681	2095	16	from	from	IN
37681	2095	17	which	which	WDT
37681	2095	18	_	_	NNP
37681	2095	19	BC	BC	NNP
37681	2095	20	_	_	NNP
37681	2095	21	makes	make	VBZ
37681	2095	22	with	with	IN
37681	2095	23	_	_	NNP
37681	2095	24	A	A	NNP
37681	2095	25	_	_	NNP
37681	2095	26	an	an	DT
37681	2095	27	angle	angle	NN
37681	2095	28	equal	equal	JJ
37681	2095	29	to	to	IN
37681	2095	30	half	half	NN
37681	2095	31	of	of	IN
37681	2095	32	angle	angle	NN
37681	2095	33	_	_	NNP
37681	2095	34	CAX	CAX	NNP
37681	2095	35	_	_	NNP
37681	2095	36	.	.	.
37681	2096	1	Then	then	RB
37681	2096	2	it	-PRON-	PRP
37681	2096	3	is	be	VBZ
37681	2096	4	easily	easily	RB
37681	2096	5	shown	show	VBN
37681	2096	6	that	that	IN
37681	2096	7	_	_	NNP
37681	2096	8	AB	AB	NNP
37681	2096	9	_	_	NNP
37681	2096	10	=	=	SYM
37681	2096	11	_	_	NNP
37681	2096	12	AC	AC	NNP
37681	2096	13	_	_	NNP
37681	2096	14	.	.	.
37681	2097	1	A	a	DT
37681	2097	2	navigator	navigator	NN
37681	2097	3	uses	use	VBZ
37681	2097	4	the	the	DT
37681	2097	5	same	same	JJ
37681	2097	6	principle	principle	NN
37681	2097	7	when	when	WRB
37681	2097	8	he	-PRON-	PRP
37681	2097	9	"	"	``
37681	2097	10	doubles	double	VBZ
37681	2097	11	the	the	DT
37681	2097	12	angle	angle	NN
37681	2097	13	on	on	IN
37681	2097	14	the	the	DT
37681	2097	15	bow	bow	NN
37681	2097	16	"	"	''
37681	2097	17	to	to	TO
37681	2097	18	find	find	VB
37681	2097	19	his	-PRON-	PRP$
37681	2097	20	distance	distance	NN
37681	2097	21	from	from	IN
37681	2097	22	a	a	DT
37681	2097	23	lighthouse	lighthouse	NN
37681	2097	24	or	or	CC
37681	2097	25	other	other	JJ
37681	2097	26	object	object	NN
37681	2097	27	.	.	.
37681	2098	1	[	[	-LRB-
37681	2098	2	Illustration	illustration	NN
37681	2098	3	]	]	-RRB-
37681	2098	4	If	if	IN
37681	2098	5	he	-PRON-	PRP
37681	2098	6	is	be	VBZ
37681	2098	7	sailing	sail	VBG
37681	2098	8	on	on	IN
37681	2098	9	the	the	DT
37681	2098	10	course	course	NN
37681	2098	11	_	_	NNP
37681	2098	12	ABC	ABC	NNP
37681	2098	13	_	_	NNP
37681	2098	14	and	and	CC
37681	2098	15	notes	note	VBZ
37681	2098	16	a	a	DT
37681	2098	17	lighthouse	lighthouse	NN
37681	2098	18	_	_	NNP
37681	2098	19	L	L	NNP
37681	2098	20	_	_	NNP
37681	2098	21	when	when	WRB
37681	2098	22	he	-PRON-	PRP
37681	2098	23	is	be	VBZ
37681	2098	24	at	at	IN
37681	2098	25	_	_	NNP
37681	2098	26	A	A	NNP
37681	2098	27	_	_	NNP
37681	2098	28	,	,	,
37681	2098	29	and	and	CC
37681	2098	30	takes	take	VBZ
37681	2098	31	the	the	DT
37681	2098	32	angle	angle	NN
37681	2098	33	_	_	NNP
37681	2098	34	A	A	NNP
37681	2098	35	_	_	NNP
37681	2098	36	,	,	,
37681	2098	37	and	and	CC
37681	2098	38	if	if	IN
37681	2098	39	he	-PRON-	PRP
37681	2098	40	notices	notice	VBZ
37681	2098	41	when	when	WRB
37681	2098	42	the	the	DT
37681	2098	43	angle	angle	NN
37681	2098	44	that	that	WDT
37681	2098	45	the	the	DT
37681	2098	46	lighthouse	lighthouse	NN
37681	2098	47	makes	make	VBZ
37681	2098	48	with	with	IN
37681	2098	49	his	-PRON-	PRP$
37681	2098	50	course	course	NN
37681	2098	51	is	be	VBZ
37681	2098	52	just	just	RB
37681	2098	53	twice	twice	RB
37681	2098	54	the	the	DT
37681	2098	55	angle	angle	NN
37681	2098	56	noted	note	VBN
37681	2098	57	at	at	IN
37681	2098	58	_	_	NNP
37681	2098	59	A	A	NNP
37681	2098	60	_	_	NNP
37681	2098	61	,	,	,
37681	2098	62	then	then	RB
37681	2098	63	_	_	NNP
37681	2098	64	BL	BL	NNP
37681	2098	65	_	_	NNP
37681	2098	66	=	=	SYM
37681	2098	67	_	_	NNP
37681	2098	68	AB	AB	NNP
37681	2098	69	_	_	NNP
37681	2098	70	.	.	.
37681	2099	1	He	-PRON-	PRP
37681	2099	2	has	have	VBZ
37681	2099	3	_	_	NNP
37681	2099	4	AB	AB	NNP
37681	2099	5	_	_	NNP
37681	2099	6	from	from	IN
37681	2099	7	his	-PRON-	PRP$
37681	2099	8	log	log	NN
37681	2099	9	(	(	-LRB-
37681	2099	10	an	an	DT
37681	2099	11	instrument	instrument	NN
37681	2099	12	that	that	WDT
37681	2099	13	tells	tell	VBZ
37681	2099	14	how	how	WRB
37681	2099	15	far	far	RB
37681	2099	16	a	a	DT
37681	2099	17	ship	ship	NN
37681	2099	18	goes	go	VBZ
37681	2099	19	in	in	IN
37681	2099	20	a	a	DT
37681	2099	21	given	give	VBN
37681	2099	22	time	time	NN
37681	2099	23	)	)	-RRB-
37681	2099	24	,	,	,
37681	2099	25	so	so	CC
37681	2099	26	he	-PRON-	PRP
37681	2099	27	knows	know	VBZ
37681	2099	28	_	_	NNP
37681	2099	29	BL	BL	NNP
37681	2099	30	_	_	NNP
37681	2099	31	.	.	.
37681	2100	1	He	-PRON-	PRP
37681	2100	2	has	have	VBZ
37681	2100	3	"	"	``
37681	2100	4	doubled	double	VBN
37681	2100	5	the	the	DT
37681	2100	6	angle	angle	NN
37681	2100	7	on	on	IN
37681	2100	8	the	the	DT
37681	2100	9	bow	bow	NN
37681	2100	10	"	"	''
37681	2100	11	to	to	TO
37681	2100	12	get	get	VB
37681	2100	13	this	this	DT
37681	2100	14	distance	distance	NN
37681	2100	15	.	.	.
37681	2101	1	It	-PRON-	PRP
37681	2101	2	would	would	MD
37681	2101	3	have	have	VB
37681	2101	4	been	be	VBN
37681	2101	5	possible	possible	JJ
37681	2101	6	for	for	IN
37681	2101	7	Thales	thale	NNS
37681	2101	8	,	,	,
37681	2101	9	if	if	IN
37681	2101	10	he	-PRON-	PRP
37681	2101	11	knew	know	VBD
37681	2101	12	this	this	DT
37681	2101	13	proposition	proposition	NN
37681	2101	14	,	,	,
37681	2101	15	to	to	TO
37681	2101	16	have	have	VB
37681	2101	17	measured	measure	VBN
37681	2101	18	the	the	DT
37681	2101	19	distance	distance	NN
37681	2101	20	of	of	IN
37681	2101	21	the	the	DT
37681	2101	22	ship	ship	NN
37681	2101	23	at	at	IN
37681	2101	24	sea	sea	NN
37681	2101	25	by	by	IN
37681	2101	26	some	some	DT
37681	2101	27	such	such	JJ
37681	2101	28	device	device	NN
37681	2101	29	as	as	IN
37681	2101	30	this	this	DT
37681	2101	31	:	:	:
37681	2101	32	[	[	-LRB-
37681	2101	33	Illustration	illustration	NN
37681	2101	34	]	]	-RRB-
37681	2101	35	Make	make	VB
37681	2101	36	a	a	DT
37681	2101	37	large	large	JJ
37681	2101	38	isosceles	isoscele	NNS
37681	2101	39	triangle	triangle	VB
37681	2101	40	out	out	IN
37681	2101	41	of	of	IN
37681	2101	42	wood	wood	NN
37681	2101	43	,	,	,
37681	2101	44	and	and	CC
37681	2101	45	,	,	,
37681	2101	46	standing	stand	VBG
37681	2101	47	at	at	IN
37681	2101	48	_	_	NNP
37681	2101	49	T	T	NNP
37681	2101	50	_	_	NNP
37681	2101	51	,	,	,
37681	2101	52	sight	sight	NN
37681	2101	53	to	to	IN
37681	2101	54	the	the	DT
37681	2101	55	ship	ship	NN
37681	2101	56	and	and	CC
37681	2101	57	along	along	IN
37681	2101	58	the	the	DT
37681	2101	59	shore	shore	NN
37681	2101	60	on	on	IN
37681	2101	61	a	a	DT
37681	2101	62	line	line	NN
37681	2101	63	_	_	NNP
37681	2101	64	TA	TA	NNP
37681	2101	65	_	_	NNP
37681	2101	66	,	,	,
37681	2101	67	using	use	VBG
37681	2101	68	the	the	DT
37681	2101	69	vertical	vertical	JJ
37681	2101	70	angle	angle	NN
37681	2101	71	of	of	IN
37681	2101	72	the	the	DT
37681	2101	73	triangle	triangle	NN
37681	2101	74	.	.	.
37681	2102	1	Then	then	RB
37681	2102	2	go	go	VB
37681	2102	3	along	along	RB
37681	2102	4	_	_	NNP
37681	2102	5	TA	TA	NNP
37681	2102	6	_	_	NNP
37681	2102	7	until	until	IN
37681	2102	8	a	a	DT
37681	2102	9	point	point	NN
37681	2102	10	_	_	NNP
37681	2102	11	P	P	NNP
37681	2102	12	_	_	NNP
37681	2102	13	is	be	VBZ
37681	2102	14	reached	reach	VBN
37681	2102	15	,	,	,
37681	2102	16	from	from	IN
37681	2102	17	which	which	WDT
37681	2102	18	_	_	NNP
37681	2102	19	T	T	NNP
37681	2102	20	_	_	NNP
37681	2102	21	and	and	CC
37681	2102	22	_	_	NNP
37681	2102	23	S	S	NNP
37681	2102	24	_	_	NNP
37681	2102	25	can	can	MD
37681	2102	26	be	be	VB
37681	2102	27	seen	see	VBN
37681	2102	28	along	along	IN
37681	2102	29	the	the	DT
37681	2102	30	sides	side	NNS
37681	2102	31	of	of	IN
37681	2102	32	a	a	DT
37681	2102	33	base	base	JJ
37681	2102	34	angle	angle	NN
37681	2102	35	of	of	IN
37681	2102	36	the	the	DT
37681	2102	37	triangle	triangle	NN
37681	2102	38	.	.	.
37681	2103	1	Then	then	RB
37681	2103	2	_	_	NNP
37681	2103	3	TP	TP	NNP
37681	2103	4	_	_	NNP
37681	2103	5	=	=	SYM
37681	2103	6	_	_	NNP
37681	2103	7	TS	TS	NNP
37681	2103	8	_	_	NNP
37681	2103	9	.	.	.
37681	2104	1	By	by	IN
37681	2104	2	measuring	measure	VBG
37681	2104	3	_	_	NNP
37681	2104	4	TB	TB	NNP
37681	2104	5	_	_	NNP
37681	2104	6	,	,	,
37681	2104	7	_	_	NNP
37681	2104	8	BS	BS	NNP
37681	2104	9	_	_	NNP
37681	2104	10	can	can	MD
37681	2104	11	then	then	RB
37681	2104	12	be	be	VB
37681	2104	13	found	find	VBN
37681	2104	14	.	.	.
37681	2105	1	THEOREM	THEOREM	NNP
37681	2105	2	.	.	.
37681	2106	1	_	_	NNP
37681	2106	2	The	the	DT
37681	2106	3	sum	sum	NN
37681	2106	4	of	of	IN
37681	2106	5	two	two	CD
37681	2106	6	sides	side	NNS
37681	2106	7	of	of	IN
37681	2106	8	a	a	DT
37681	2106	9	triangle	triangle	NN
37681	2106	10	is	be	VBZ
37681	2106	11	greater	great	JJR
37681	2106	12	than	than	IN
37681	2106	13	the	the	DT
37681	2106	14	third	third	JJ
37681	2106	15	side	side	NN
37681	2106	16	,	,	,
37681	2106	17	and	and	CC
37681	2106	18	their	-PRON-	PRP$
37681	2106	19	difference	difference	NN
37681	2106	20	is	be	VBZ
37681	2106	21	less	less	JJR
37681	2106	22	than	than	IN
37681	2106	23	the	the	DT
37681	2106	24	third	third	JJ
37681	2106	25	side	side	NN
37681	2106	26	_	_	NNP
37681	2106	27	.	.	.
37681	2107	1	If	if	IN
37681	2107	2	the	the	DT
37681	2107	3	postulate	postulate	NN
37681	2107	4	is	be	VBZ
37681	2107	5	assumed	assume	VBN
37681	2107	6	that	that	IN
37681	2107	7	a	a	DT
37681	2107	8	straight	straight	JJ
37681	2107	9	line	line	NN
37681	2107	10	is	be	VBZ
37681	2107	11	the	the	DT
37681	2107	12	shortest	short	JJS
37681	2107	13	path	path	NN
37681	2107	14	between	between	IN
37681	2107	15	two	two	CD
37681	2107	16	points	point	NNS
37681	2107	17	,	,	,
37681	2107	18	then	then	RB
37681	2107	19	the	the	DT
37681	2107	20	first	first	JJ
37681	2107	21	part	part	NN
37681	2107	22	of	of	IN
37681	2107	23	this	this	DT
37681	2107	24	theorem	theorem	NN
37681	2107	25	requires	require	VBZ
37681	2107	26	no	no	DT
37681	2107	27	further	further	JJ
37681	2107	28	proof	proof	NN
37681	2107	29	,	,	,
37681	2107	30	and	and	CC
37681	2107	31	the	the	DT
37681	2107	32	second	second	JJ
37681	2107	33	part	part	NN
37681	2107	34	follows	follow	VBZ
37681	2107	35	at	at	IN
37681	2107	36	once	once	RB
37681	2107	37	from	from	IN
37681	2107	38	the	the	DT
37681	2107	39	axiom	axiom	NN
37681	2107	40	of	of	IN
37681	2107	41	inequalities	inequality	NNS
37681	2107	42	.	.	.
37681	2108	1	This	this	DT
37681	2108	2	seems	seem	VBZ
37681	2108	3	the	the	DT
37681	2108	4	better	well	JJR
37681	2108	5	plan	plan	NN
37681	2108	6	for	for	IN
37681	2108	7	beginners	beginner	NNS
37681	2108	8	,	,	,
37681	2108	9	and	and	CC
37681	2108	10	the	the	DT
37681	2108	11	proposition	proposition	NN
37681	2108	12	may	may	MD
37681	2108	13	be	be	VB
37681	2108	14	considered	consider	VBN
37681	2108	15	as	as	RB
37681	2108	16	semiobvious	semiobvious	JJ
37681	2108	17	.	.	.
37681	2109	1	Euclid	Euclid	NNP
37681	2109	2	proved	prove	VBD
37681	2109	3	the	the	DT
37681	2109	4	first	first	JJ
37681	2109	5	part	part	NN
37681	2109	6	,	,	,
37681	2109	7	not	not	RB
37681	2109	8	having	have	VBG
37681	2109	9	assumed	assume	VBN
37681	2109	10	the	the	DT
37681	2109	11	postulate	postulate	NN
37681	2109	12	.	.	.
37681	2110	1	Proclus	Proclus	NNP
37681	2110	2	tells	tell	VBZ
37681	2110	3	us	-PRON-	PRP
37681	2110	4	that	that	IN
37681	2110	5	the	the	DT
37681	2110	6	Epicureans	Epicureans	NNPS
37681	2110	7	(	(	-LRB-
37681	2110	8	the	the	DT
37681	2110	9	followers	follower	NNS
37681	2110	10	of	of	IN
37681	2110	11	Epicurus	Epicurus	NNP
37681	2110	12	,	,	,
37681	2110	13	the	the	DT
37681	2110	14	Greek	greek	JJ
37681	2110	15	philosopher	philosopher	NN
37681	2110	16	,	,	,
37681	2110	17	342	342	CD
37681	2110	18	-	-	SYM
37681	2110	19	270	270	CD
37681	2110	20	B.C.	B.C.	NNP
37681	2110	21	)	)	-RRB-
37681	2111	1	used	use	VBN
37681	2111	2	to	to	TO
37681	2111	3	ridicule	ridicule	VB
37681	2111	4	this	this	DT
37681	2111	5	theorem	theorem	NN
37681	2111	6	,	,	,
37681	2111	7	saying	say	VBG
37681	2111	8	that	that	IN
37681	2111	9	even	even	RB
37681	2111	10	an	an	DT
37681	2111	11	ass	ass	NN
37681	2111	12	knew	know	VBD
37681	2111	13	it	-PRON-	PRP
37681	2111	14	,	,	,
37681	2111	15	for	for	IN
37681	2111	16	if	if	IN
37681	2111	17	he	-PRON-	PRP
37681	2111	18	wished	wish	VBD
37681	2111	19	to	to	TO
37681	2111	20	get	get	VB
37681	2111	21	food	food	NN
37681	2111	22	,	,	,
37681	2111	23	he	-PRON-	PRP
37681	2111	24	walked	walk	VBD
37681	2111	25	in	in	IN
37681	2111	26	a	a	DT
37681	2111	27	straight	straight	JJ
37681	2111	28	line	line	NN
37681	2111	29	and	and	CC
37681	2111	30	not	not	RB
37681	2111	31	along	along	IN
37681	2111	32	two	two	CD
37681	2111	33	sides	side	NNS
37681	2111	34	of	of	IN
37681	2111	35	a	a	DT
37681	2111	36	triangle	triangle	NN
37681	2111	37	.	.	.
37681	2112	1	Proclus	Proclus	NNP
37681	2112	2	replied	reply	VBD
37681	2112	3	that	that	IN
37681	2112	4	it	-PRON-	PRP
37681	2112	5	was	be	VBD
37681	2112	6	one	one	CD
37681	2112	7	thing	thing	NN
37681	2112	8	to	to	TO
37681	2112	9	know	know	VB
37681	2112	10	the	the	DT
37681	2112	11	truth	truth	NN
37681	2112	12	and	and	CC
37681	2112	13	another	another	DT
37681	2112	14	thing	thing	NN
37681	2112	15	to	to	TO
37681	2112	16	prove	prove	VB
37681	2112	17	it	-PRON-	PRP
37681	2112	18	,	,	,
37681	2112	19	meaning	mean	VBG
37681	2112	20	that	that	IN
37681	2112	21	the	the	DT
37681	2112	22	value	value	NN
37681	2112	23	of	of	IN
37681	2112	24	geometry	geometry	NN
37681	2112	25	lay	lie	VBD
37681	2112	26	in	in	IN
37681	2112	27	the	the	DT
37681	2112	28	proof	proof	NN
37681	2112	29	rather	rather	RB
37681	2112	30	than	than	IN
37681	2112	31	in	in	IN
37681	2112	32	the	the	DT
37681	2112	33	mere	mere	JJ
37681	2112	34	facts	fact	NNS
37681	2112	35	,	,	,
37681	2112	36	a	a	DT
37681	2112	37	thing	thing	NN
37681	2112	38	that	that	WDT
37681	2112	39	all	all	DT
37681	2112	40	who	who	WP
37681	2112	41	seek	seek	VBP
37681	2112	42	to	to	TO
37681	2112	43	reform	reform	VB
37681	2112	44	the	the	DT
37681	2112	45	teaching	teaching	NN
37681	2112	46	of	of	IN
37681	2112	47	geometry	geometry	NN
37681	2112	48	would	would	MD
37681	2112	49	do	do	VB
37681	2112	50	well	well	RB
37681	2112	51	to	to	TO
37681	2112	52	keep	keep	VB
37681	2112	53	in	in	IN
37681	2112	54	mind	mind	NN
37681	2112	55	.	.	.
37681	2113	1	The	the	DT
37681	2113	2	theorem	theorem	NN
37681	2113	3	might	may	MD
37681	2113	4	simply	simply	RB
37681	2113	5	appear	appear	VB
37681	2113	6	as	as	IN
37681	2113	7	a	a	DT
37681	2113	8	corollary	corollary	NN
37681	2113	9	under	under	IN
37681	2113	10	the	the	DT
37681	2113	11	postulate	postulate	NN
37681	2113	12	if	if	IN
37681	2113	13	it	-PRON-	PRP
37681	2113	14	were	be	VBD
37681	2113	15	of	of	IN
37681	2113	16	any	any	DT
37681	2113	17	importance	importance	NN
37681	2113	18	to	to	TO
37681	2113	19	reduce	reduce	VB
37681	2113	20	the	the	DT
37681	2113	21	number	number	NN
37681	2113	22	of	of	IN
37681	2113	23	propositions	proposition	NNS
37681	2113	24	one	one	CD
37681	2113	25	more	more	JJR
37681	2113	26	.	.	.
37681	2114	1	If	if	IN
37681	2114	2	the	the	DT
37681	2114	3	proposition	proposition	NN
37681	2114	4	is	be	VBZ
37681	2114	5	postponed	postpone	VBN
37681	2114	6	until	until	IN
37681	2114	7	after	after	IN
37681	2114	8	those	those	DT
37681	2114	9	concerning	concern	VBG
37681	2114	10	the	the	DT
37681	2114	11	inequalities	inequality	NNS
37681	2114	12	of	of	IN
37681	2114	13	angles	angle	NNS
37681	2114	14	and	and	CC
37681	2114	15	sides	side	NNS
37681	2114	16	of	of	IN
37681	2114	17	a	a	DT
37681	2114	18	triangle	triangle	NN
37681	2114	19	,	,	,
37681	2114	20	there	there	EX
37681	2114	21	are	be	VBP
37681	2114	22	several	several	JJ
37681	2114	23	good	good	JJ
37681	2114	24	proofs	proof	NNS
37681	2114	25	.	.	.
37681	2115	1	[	[	-LRB-
37681	2115	2	Illustration	illustration	NN
37681	2115	3	]	]	-RRB-
37681	2115	4	For	for	IN
37681	2115	5	example	example	NN
37681	2115	6	,	,	,
37681	2115	7	produce	produce	VBP
37681	2115	8	_	_	NNP
37681	2115	9	AC	AC	NNP
37681	2115	10	_	_	NNP
37681	2115	11	to	to	IN
37681	2115	12	_	_	NNP
37681	2115	13	X	X	NNP
37681	2115	14	_	_	NNP
37681	2115	15	,	,	,
37681	2115	16	making	make	VBG
37681	2115	17	_	_	NNP
37681	2115	18	CX	CX	NNP
37681	2115	19	_	_	NNP
37681	2115	20	=	=	SYM
37681	2115	21	_	_	NNP
37681	2115	22	CB	CB	NNP
37681	2115	23	_	_	NNP
37681	2115	24	.	.	.
37681	2116	1	Then	then	RB
37681	2116	2	[	[	-LRB-
37681	2116	3	L]_X	L]_X	NNP
37681	2116	4	_	_	NNP
37681	2116	5	=	=	NFP
37681	2116	6	[	[	-LRB-
37681	2116	7	L]_XBC	L]_XBC	NNP
37681	2116	8	_	_	NNP
37681	2116	9	.	.	.
37681	2117	1	[	[	-LRB-
37681	2117	2	therefore	therefore	RB
37681	2117	3	]	]	-RRB-
37681	2117	4	[	[	-LRB-
37681	2117	5	L]_XBA	L]_XBA	NNP
37681	2117	6	_	_	NNP
37681	2117	7	>	>	XX
37681	2117	8	[	[	-LRB-
37681	2117	9	L]_X	L]_X	NNP
37681	2117	10	_	_	NNP
37681	2117	11	.	.	.
37681	2118	1	[	[	-LRB-
37681	2118	2	therefore	therefore	RB
37681	2118	3	]	]	-RRB-
37681	2118	4	_	_	NNP
37681	2118	5	AX	AX	NNP
37681	2118	6	_	_	NNP
37681	2118	7	>	>	XX
37681	2118	8	_	_	NNP
37681	2118	9	AB	AB	NNP
37681	2118	10	_	_	NNP
37681	2118	11	.	.	.
37681	2119	1	[	[	-LRB-
37681	2119	2	therefore	therefore	RB
37681	2119	3	]	]	-RRB-
37681	2119	4	_	_	NNP
37681	2119	5	AC	AC	NNP
37681	2119	6	_	_	NNP
37681	2119	7	+	+	SYM
37681	2119	8	_	_	NNP
37681	2119	9	CB	CB	NNP
37681	2119	10	_	_	NNP
37681	2119	11	>	>	XX
37681	2119	12	_	_	NNP
37681	2119	13	AB	AB	NNP
37681	2119	14	_	_	NNP
37681	2119	15	.	.	.
37681	2120	1	The	the	DT
37681	2120	2	above	above	JJ
37681	2120	3	proof	proof	NN
37681	2120	4	is	be	VBZ
37681	2120	5	due	due	JJ
37681	2120	6	to	to	IN
37681	2120	7	Euclid	Euclid	NNP
37681	2120	8	.	.	.
37681	2121	1	Heron	Heron	NNP
37681	2121	2	of	of	IN
37681	2121	3	Alexandria	Alexandria	NNP
37681	2121	4	(	(	-LRB-
37681	2121	5	first	first	JJ
37681	2121	6	century	century	NN
37681	2121	7	A.D.	A.D.	NNP
37681	2121	8	)	)	-RRB-
37681	2121	9	is	be	VBZ
37681	2121	10	said	say	VBN
37681	2121	11	by	by	IN
37681	2121	12	Proclus	Proclus	NNP
37681	2121	13	to	to	TO
37681	2121	14	have	have	VB
37681	2121	15	given	give	VBN
37681	2121	16	the	the	DT
37681	2121	17	following	follow	VBG
37681	2121	18	:	:	:
37681	2121	19	[	[	-LRB-
37681	2121	20	Illustration	illustration	NN
37681	2121	21	]	]	-RRB-
37681	2121	22	Let	let	VB
37681	2121	23	_	_	NNP
37681	2121	24	CX	CX	NNP
37681	2121	25	_	_	NNP
37681	2121	26	bisect	bisect	NN
37681	2121	27	[	[	-LRB-
37681	2121	28	L]_C	L]_C	NNP
37681	2121	29	_	_	NNP
37681	2121	30	.	.	.
37681	2122	1	Then	then	RB
37681	2122	2	[	[	-LRB-
37681	2122	3	L]_BXC	L]_BXC	NNP
37681	2122	4	_	_	NNP
37681	2122	5	>	>	XX
37681	2122	6	[	[	-LRB-
37681	2122	7	L]_ACX	L]_ACX	NNP
37681	2122	8	_	_	NNP
37681	2122	9	.	.	.
37681	2123	1	[	[	-LRB-
37681	2123	2	therefore	therefore	RB
37681	2123	3	]	]	-RRB-
37681	2123	4	[	[	-LRB-
37681	2123	5	L]_BXC	L]_BXC	NNP
37681	2123	6	_	_	NNP
37681	2123	7	>	>	XX
37681	2123	8	[	[	-LRB-
37681	2123	9	L]_XCB	L]_XCB	NNP
37681	2123	10	_	_	NNP
37681	2123	11	.	.	.
37681	2124	1	[	[	-LRB-
37681	2124	2	therefore	therefore	RB
37681	2124	3	]	]	-RRB-
37681	2124	4	_	_	NNP
37681	2124	5	CB	CB	NNP
37681	2124	6	_	_	NNP
37681	2124	7	>	>	XX
37681	2124	8	_	_	NNP
37681	2124	9	XB	XB	NNP
37681	2124	10	_	_	NNP
37681	2124	11	.	.	.
37681	2125	1	Similarly	similarly	RB
37681	2125	2	,	,	,
37681	2125	3	_	_	NNP
37681	2125	4	AC	AC	NNP
37681	2125	5	_	_	NNP
37681	2125	6	>	>	XX
37681	2125	7	_	_	NNP
37681	2125	8	AX	AX	NNP
37681	2125	9	_	_	NNP
37681	2125	10	.	.	.
37681	2126	1	Adding	add	VBG
37681	2126	2	,	,	,
37681	2126	3	_	_	NNP
37681	2126	4	AC	AC	NNP
37681	2126	5	_	_	NNP
37681	2126	6	+	+	SYM
37681	2126	7	_	_	NNP
37681	2126	8	CB	CB	NNP
37681	2126	9	_	_	NNP
37681	2126	10	>	>	XX
37681	2126	11	_	_	NNP
37681	2126	12	AB	AB	NNP
37681	2126	13	_	_	NNP
37681	2126	14	.	.	.
37681	2127	1	THEOREM	THEOREM	NNP
37681	2127	2	.	.	.
37681	2128	1	_	_	XX
37681	2128	2	If	if	IN
37681	2128	3	two	two	CD
37681	2128	4	sides	side	NNS
37681	2128	5	of	of	IN
37681	2128	6	a	a	DT
37681	2128	7	triangle	triangle	NN
37681	2128	8	are	be	VBP
37681	2128	9	unequal	unequal	JJ
37681	2128	10	,	,	,
37681	2128	11	the	the	DT
37681	2128	12	angles	angle	NNS
37681	2128	13	opposite	opposite	IN
37681	2128	14	these	these	DT
37681	2128	15	sides	side	NNS
37681	2128	16	are	be	VBP
37681	2128	17	unequal	unequal	JJ
37681	2128	18	,	,	,
37681	2128	19	and	and	CC
37681	2128	20	the	the	DT
37681	2128	21	angle	angle	NN
37681	2128	22	opposite	opposite	IN
37681	2128	23	the	the	DT
37681	2128	24	greater	great	JJR
37681	2128	25	side	side	NN
37681	2128	26	is	be	VBZ
37681	2128	27	the	the	DT
37681	2128	28	greater	great	JJR
37681	2128	29	.	.	.
37681	2128	30	_	_	NNP
37681	2128	31	Euclid	Euclid	NNP
37681	2128	32	stated	state	VBD
37681	2128	33	this	this	DT
37681	2128	34	more	more	JJR
37681	2128	35	briefly	briefly	NN
37681	2128	36	by	by	IN
37681	2128	37	saying	say	VBG
37681	2128	38	,	,	,
37681	2128	39	"	"	``
37681	2128	40	In	in	IN
37681	2128	41	any	any	DT
37681	2128	42	triangle	triangle	NN
37681	2128	43	the	the	DT
37681	2128	44	greater	great	JJR
37681	2128	45	side	side	NN
37681	2128	46	subtends	subtend	VBZ
37681	2128	47	the	the	DT
37681	2128	48	greater	great	JJR
37681	2128	49	angle	angle	NN
37681	2128	50	.	.	.
37681	2128	51	"	"	''
37681	2129	1	This	this	DT
37681	2129	2	is	be	VBZ
37681	2129	3	not	not	RB
37681	2129	4	so	so	RB
37681	2129	5	satisfactory	satisfactory	JJ
37681	2129	6	,	,	,
37681	2129	7	for	for	IN
37681	2129	8	there	there	EX
37681	2129	9	may	may	MD
37681	2129	10	be	be	VB
37681	2129	11	no	no	DT
37681	2129	12	greater	great	JJR
37681	2129	13	side	side	NN
37681	2129	14	.	.	.
37681	2130	1	THEOREM	THEOREM	NNP
37681	2130	2	.	.	.
37681	2131	1	_	_	XX
37681	2131	2	If	if	IN
37681	2131	3	two	two	CD
37681	2131	4	angles	angle	NNS
37681	2131	5	of	of	IN
37681	2131	6	a	a	DT
37681	2131	7	triangle	triangle	NN
37681	2131	8	are	be	VBP
37681	2131	9	unequal	unequal	JJ
37681	2131	10	,	,	,
37681	2131	11	the	the	DT
37681	2131	12	sides	side	NNS
37681	2131	13	opposite	opposite	IN
37681	2131	14	these	these	DT
37681	2131	15	angles	angle	NNS
37681	2131	16	are	be	VBP
37681	2131	17	unequal	unequal	JJ
37681	2131	18	,	,	,
37681	2131	19	and	and	CC
37681	2131	20	the	the	DT
37681	2131	21	side	side	NN
37681	2131	22	opposite	opposite	IN
37681	2131	23	the	the	DT
37681	2131	24	greater	great	JJR
37681	2131	25	angle	angle	NN
37681	2131	26	is	be	VBZ
37681	2131	27	the	the	DT
37681	2131	28	greater	great	JJR
37681	2131	29	.	.	.
37681	2131	30	_	_	NNP
37681	2131	31	Euclid	Euclid	NNP
37681	2131	32	also	also	RB
37681	2131	33	stated	state	VBD
37681	2131	34	this	this	DT
37681	2131	35	more	more	JJR
37681	2131	36	briefly	briefly	RB
37681	2131	37	,	,	,
37681	2131	38	but	but	CC
37681	2131	39	less	less	RBR
37681	2131	40	satisfactorily	satisfactorily	RB
37681	2131	41	,	,	,
37681	2131	42	thus	thus	RB
37681	2131	43	,	,	,
37681	2131	44	"	"	``
37681	2131	45	In	in	IN
37681	2131	46	any	any	DT
37681	2131	47	triangle	triangle	NN
37681	2131	48	the	the	DT
37681	2131	49	greater	great	JJR
37681	2131	50	angle	angle	NN
37681	2131	51	is	be	VBZ
37681	2131	52	subtended	subtend	VBN
37681	2131	53	by	by	IN
37681	2131	54	the	the	DT
37681	2131	55	greater	great	JJR
37681	2131	56	side	side	NN
37681	2131	57	.	.	.
37681	2131	58	"	"	''
37681	2132	1	Students	student	NNS
37681	2132	2	should	should	MD
37681	2132	3	have	have	VB
37681	2132	4	their	-PRON-	PRP$
37681	2132	5	attention	attention	NN
37681	2132	6	called	call	VBN
37681	2132	7	to	to	IN
37681	2132	8	the	the	DT
37681	2132	9	fact	fact	NN
37681	2132	10	that	that	IN
37681	2132	11	these	these	DT
37681	2132	12	two	two	CD
37681	2132	13	theorems	theorem	NNS
37681	2132	14	are	be	VBP
37681	2132	15	reciprocal	reciprocal	JJ
37681	2132	16	or	or	CC
37681	2132	17	dual	dual	JJ
37681	2132	18	theorems	theorem	NNS
37681	2132	19	,	,	,
37681	2132	20	the	the	DT
37681	2132	21	words	word	NNS
37681	2132	22	"	"	``
37681	2132	23	sides	side	NNS
37681	2132	24	"	"	''
37681	2132	25	and	and	CC
37681	2132	26	"	"	``
37681	2132	27	angles	angle	NNS
37681	2132	28	"	"	''
37681	2132	29	of	of	IN
37681	2132	30	the	the	DT
37681	2132	31	one	one	NN
37681	2132	32	corresponding	correspond	VBG
37681	2132	33	to	to	IN
37681	2132	34	the	the	DT
37681	2132	35	words	word	NNS
37681	2132	36	"	"	``
37681	2132	37	angles	angle	NNS
37681	2132	38	"	"	''
37681	2132	39	and	and	CC
37681	2132	40	"	"	``
37681	2132	41	sides	side	NNS
37681	2132	42	"	"	''
37681	2132	43	respectively	respectively	RB
37681	2132	44	of	of	IN
37681	2132	45	the	the	DT
37681	2132	46	other	other	JJ
37681	2132	47	.	.	.
37681	2133	1	It	-PRON-	PRP
37681	2133	2	may	may	MD
37681	2133	3	also	also	RB
37681	2133	4	be	be	VB
37681	2133	5	noticed	notice	VBN
37681	2133	6	that	that	IN
37681	2133	7	the	the	DT
37681	2133	8	proof	proof	NN
37681	2133	9	of	of	IN
37681	2133	10	this	this	DT
37681	2133	11	proposition	proposition	NN
37681	2133	12	involves	involve	VBZ
37681	2133	13	what	what	WP
37681	2133	14	is	be	VBZ
37681	2133	15	known	know	VBN
37681	2133	16	as	as	IN
37681	2133	17	the	the	DT
37681	2133	18	Law	Law	NNP
37681	2133	19	of	of	IN
37681	2133	20	Converse	Converse	NNP
37681	2133	21	;	;	:
37681	2133	22	for	for	IN
37681	2133	23	(	(	-LRB-
37681	2133	24	1	1	LS
37681	2133	25	)	)	-RRB-
37681	2133	26	if	if	IN
37681	2133	27	_	_	NNP
37681	2133	28	b	b	NNP
37681	2133	29	_	_	NNP
37681	2133	30	=	=	SYM
37681	2133	31	_	_	NNP
37681	2133	32	c	c	NNP
37681	2133	33	_	_	NNP
37681	2133	34	,	,	,
37681	2133	35	then	then	RB
37681	2133	36	[	[	-LRB-
37681	2133	37	L]_B	L]_B	NNP
37681	2133	38	_	_	NNP
37681	2133	39	=	=	NFP
37681	2133	40	[	[	-LRB-
37681	2133	41	L]_C	L]_C	NNP
37681	2133	42	_	_	NNP
37681	2133	43	;	;	:
37681	2133	44	(	(	-LRB-
37681	2133	45	2	2	LS
37681	2133	46	)	)	-RRB-
37681	2133	47	if	if	IN
37681	2133	48	_	_	NNP
37681	2133	49	b	b	NNP
37681	2133	50	_	_	NNP
37681	2133	51	>	>	XX
37681	2133	52	_	_	NNP
37681	2133	53	c	c	NNP
37681	2133	54	_	_	NNP
37681	2133	55	,	,	,
37681	2133	56	then	then	RB
37681	2133	57	[	[	-LRB-
37681	2133	58	L]_B	L]_B	NNP
37681	2133	59	_	_	NNP
37681	2133	60	>	>	XX
37681	2133	61	[	[	-LRB-
37681	2133	62	L]_C	L]_C	NNP
37681	2133	63	_	_	NNP
37681	2133	64	;	;	:
37681	2133	65	(	(	-LRB-
37681	2133	66	3	3	LS
37681	2133	67	)	)	-RRB-
37681	2133	68	if	if	IN
37681	2133	69	_	_	NNP
37681	2133	70	b	b	NNP
37681	2133	71	_	_	NNP
37681	2133	72	<	<	XX
37681	2133	73	_	_	NNP
37681	2133	74	c	c	NNP
37681	2133	75	_	_	NNP
37681	2133	76	,	,	,
37681	2133	77	then	then	RB
37681	2133	78	[	[	-LRB-
37681	2133	79	L]_B	L]_B	NNP
37681	2133	80	_	_	NNP
37681	2133	81	<	<	XX
37681	2133	82	[	[	-LRB-
37681	2133	83	L]_C	L]_C	NNP
37681	2133	84	_	_	NNP
37681	2133	85	;	;	:
37681	2133	86	therefore	therefore	RB
37681	2133	87	the	the	DT
37681	2133	88	converses	converse	NNS
37681	2133	89	must	must	MD
37681	2133	90	necessarily	necessarily	RB
37681	2133	91	be	be	VB
37681	2133	92	true	true	JJ
37681	2133	93	as	as	IN
37681	2133	94	a	a	DT
37681	2133	95	matter	matter	NN
37681	2133	96	of	of	IN
37681	2133	97	logic	logic	NN
37681	2133	98	;	;	:
37681	2133	99	for	for	IN
37681	2133	100	if	if	IN
37681	2133	101	[	[	-LRB-
37681	2133	102	L]_B	L]_B	NNP
37681	2133	103	_	_	NNP
37681	2133	104	=	=	NFP
37681	2133	105	[	[	-LRB-
37681	2133	106	L]_C	L]_C	NNP
37681	2133	107	_	_	NNP
37681	2133	108	,	,	,
37681	2133	109	then	then	RB
37681	2133	110	_	_	NNP
37681	2133	111	b	b	NNP
37681	2133	112	_	_	NNP
37681	2133	113	can	can	MD
37681	2133	114	not	not	RB
37681	2133	115	be	be	VB
37681	2133	116	greater	great	JJR
37681	2133	117	than	than	IN
37681	2133	118	_	_	NNP
37681	2133	119	c	c	NNP
37681	2133	120	_	_	NNP
37681	2133	121	without	without	IN
37681	2133	122	violating	violate	VBG
37681	2133	123	(	(	-LRB-
37681	2133	124	2	2	CD
37681	2133	125	)	)	-RRB-
37681	2133	126	,	,	,
37681	2133	127	and	and	CC
37681	2133	128	_	_	NNP
37681	2133	129	b	b	NNP
37681	2133	130	_	_	NNP
37681	2133	131	can	can	MD
37681	2133	132	not	not	RB
37681	2133	133	be	be	VB
37681	2133	134	less	less	JJR
37681	2133	135	than	than	IN
37681	2133	136	_	_	NNP
37681	2133	137	c	c	NNP
37681	2133	138	_	_	NNP
37681	2133	139	without	without	IN
37681	2133	140	violating	violate	VBG
37681	2133	141	(	(	-LRB-
37681	2133	142	3	3	CD
37681	2133	143	)	)	-RRB-
37681	2133	144	,	,	,
37681	2133	145	therefore	therefore	RB
37681	2133	146	_	_	NNP
37681	2133	147	b	b	NNP
37681	2133	148	_	_	NNP
37681	2133	149	=	=	SYM
37681	2133	150	_	_	NNP
37681	2133	151	c	c	NNP
37681	2133	152	_	_	NNP
37681	2133	153	;	;	:
37681	2133	154	and	and	CC
37681	2133	155	if	if	IN
37681	2133	156	[	[	-LRB-
37681	2133	157	L]_B	L]_B	NNP
37681	2133	158	_	_	NNP
37681	2133	159	>	>	XX
37681	2133	160	[	[	-LRB-
37681	2133	161	L]_C	L]_C	NNP
37681	2133	162	_	_	NNP
37681	2133	163	,	,	,
37681	2133	164	then	then	RB
37681	2133	165	_	_	NNP
37681	2133	166	b	b	NNP
37681	2133	167	_	_	NNP
37681	2133	168	can	can	MD
37681	2133	169	not	not	RB
37681	2133	170	equal	equal	VB
37681	2133	171	_	_	NNP
37681	2133	172	c	c	NNP
37681	2133	173	_	_	NNP
37681	2133	174	without	without	IN
37681	2133	175	violating	violate	VBG
37681	2133	176	(	(	-LRB-
37681	2133	177	1	1	CD
37681	2133	178	)	)	-RRB-
37681	2133	179	,	,	,
37681	2133	180	and	and	CC
37681	2133	181	_	_	NNP
37681	2133	182	b	b	NNP
37681	2133	183	_	_	NNP
37681	2133	184	can	can	MD
37681	2133	185	not	not	RB
37681	2133	186	be	be	VB
37681	2133	187	less	less	JJR
37681	2133	188	than	than	IN
37681	2133	189	_	_	NNP
37681	2133	190	c	c	NNP
37681	2133	191	_	_	NNP
37681	2133	192	without	without	IN
37681	2133	193	violating	violate	VBG
37681	2133	194	(	(	-LRB-
37681	2133	195	3	3	CD
37681	2133	196	)	)	-RRB-
37681	2133	197	,	,	,
37681	2133	198	therefore	therefore	RB
37681	2133	199	_	_	NNP
37681	2133	200	b	b	NNP
37681	2133	201	_	_	NNP
37681	2133	202	>	>	XX
37681	2133	203	_	_	NNP
37681	2133	204	c	c	NNP
37681	2133	205	_	_	NNP
37681	2133	206	;	;	:
37681	2133	207	similarly	similarly	RB
37681	2133	208	,	,	,
37681	2133	209	if	if	IN
37681	2133	210	[	[	-LRB-
37681	2133	211	L]_B	L]_B	NNP
37681	2133	212	_	_	NNP
37681	2133	213	<	<	XX
37681	2133	214	[	[	-LRB-
37681	2133	215	L]_C	L]_C	NNP
37681	2133	216	_	_	NNP
37681	2133	217	,	,	,
37681	2133	218	then	then	RB
37681	2133	219	_	_	NNP
37681	2133	220	b	b	NNP
37681	2133	221	_	_	NNP
37681	2133	222	<	<	XX
37681	2133	223	_	_	NNP
37681	2133	224	c	c	NNP
37681	2133	225	_	_	NNP
37681	2133	226	.	.	.
37681	2134	1	This	this	DT
37681	2134	2	Law	Law	NNP
37681	2134	3	of	of	IN
37681	2134	4	Converse	Converse	NNP
37681	2134	5	may	may	MD
37681	2134	6	readily	readily	RB
37681	2134	7	be	be	VB
37681	2134	8	taught	teach	VBN
37681	2134	9	to	to	IN
37681	2134	10	pupils	pupil	NNS
37681	2134	11	,	,	,
37681	2134	12	and	and	CC
37681	2134	13	it	-PRON-	PRP
37681	2134	14	has	have	VBZ
37681	2134	15	several	several	JJ
37681	2134	16	applications	application	NNS
37681	2134	17	in	in	IN
37681	2134	18	geometry	geometry	NN
37681	2134	19	.	.	.
37681	2135	1	THEOREM	THEOREM	NNP
37681	2135	2	.	.	.
37681	2136	1	_	_	XX
37681	2136	2	If	if	IN
37681	2136	3	two	two	CD
37681	2136	4	triangles	triangle	NNS
37681	2136	5	have	have	VBP
37681	2136	6	two	two	CD
37681	2136	7	sides	side	NNS
37681	2136	8	of	of	IN
37681	2136	9	the	the	DT
37681	2136	10	one	one	NN
37681	2136	11	equal	equal	JJ
37681	2136	12	respectively	respectively	RB
37681	2136	13	to	to	IN
37681	2136	14	two	two	CD
37681	2136	15	sides	side	NNS
37681	2136	16	of	of	IN
37681	2136	17	the	the	DT
37681	2136	18	other	other	JJ
37681	2136	19	,	,	,
37681	2136	20	but	but	CC
37681	2136	21	the	the	DT
37681	2136	22	included	included	JJ
37681	2136	23	angle	angle	NN
37681	2136	24	of	of	IN
37681	2136	25	the	the	DT
37681	2136	26	first	first	JJ
37681	2136	27	triangle	triangle	NN
37681	2136	28	greater	great	JJR
37681	2136	29	than	than	IN
37681	2136	30	the	the	DT
37681	2136	31	included	included	JJ
37681	2136	32	angle	angle	NN
37681	2136	33	of	of	IN
37681	2136	34	the	the	DT
37681	2136	35	second	second	JJ
37681	2136	36	,	,	,
37681	2136	37	then	then	RB
37681	2136	38	the	the	DT
37681	2136	39	third	third	JJ
37681	2136	40	side	side	NN
37681	2136	41	of	of	IN
37681	2136	42	the	the	DT
37681	2136	43	first	first	JJ
37681	2136	44	is	be	VBZ
37681	2136	45	greater	great	JJR
37681	2136	46	than	than	IN
37681	2136	47	the	the	DT
37681	2136	48	third	third	JJ
37681	2136	49	side	side	NN
37681	2136	50	of	of	IN
37681	2136	51	the	the	DT
37681	2136	52	second	second	JJ
37681	2136	53	,	,	,
37681	2136	54	and	and	CC
37681	2136	55	conversely	conversely	RB
37681	2136	56	.	.	.
37681	2136	57	_	_	NNP
37681	2136	58	[	[	-LRB-
37681	2136	59	Illustration	illustration	NN
37681	2136	60	]	]	-RRB-
37681	2136	61	In	in	IN
37681	2136	62	this	this	DT
37681	2136	63	proposition	proposition	NN
37681	2136	64	there	there	EX
37681	2136	65	are	be	VBP
37681	2136	66	three	three	CD
37681	2136	67	possible	possible	JJ
37681	2136	68	cases	case	NNS
37681	2136	69	:	:	:
37681	2136	70	the	the	DT
37681	2136	71	point	point	NN
37681	2136	72	_	_	NNP
37681	2136	73	Y	Y	NNP
37681	2136	74	_	_	NNP
37681	2136	75	may	may	MD
37681	2136	76	fall	fall	VB
37681	2136	77	below	below	IN
37681	2136	78	_	_	NNP
37681	2136	79	AB	AB	NNP
37681	2136	80	_	_	NNP
37681	2136	81	,	,	,
37681	2136	82	as	as	IN
37681	2136	83	here	here	RB
37681	2136	84	shown	show	VBN
37681	2136	85	,	,	,
37681	2136	86	or	or	CC
37681	2136	87	on	on	IN
37681	2136	88	_	_	NNP
37681	2136	89	AB	AB	NNP
37681	2136	90	_	_	NNP
37681	2136	91	,	,	,
37681	2136	92	or	or	CC
37681	2136	93	above	above	IN
37681	2136	94	_	_	NNP
37681	2136	95	AB	AB	NNP
37681	2136	96	_	_	NNP
37681	2136	97	.	.	.
37681	2137	1	As	as	IN
37681	2137	2	an	an	DT
37681	2137	3	exercise	exercise	NN
37681	2137	4	for	for	IN
37681	2137	5	pupils	pupil	NNS
37681	2137	6	all	all	DT
37681	2137	7	three	three	CD
37681	2137	8	may	may	MD
37681	2137	9	be	be	VB
37681	2137	10	considered	consider	VBN
37681	2137	11	if	if	IN
37681	2137	12	desired	desire	VBN
37681	2137	13	.	.	.
37681	2138	1	Following	follow	VBG
37681	2138	2	Euclid	euclid	JJ
37681	2138	3	and	and	CC
37681	2138	4	most	most	RBS
37681	2138	5	early	early	JJ
37681	2138	6	writers	writer	NNS
37681	2138	7	,	,	,
37681	2138	8	however	however	RB
37681	2138	9	,	,	,
37681	2138	10	only	only	RB
37681	2138	11	one	one	CD
37681	2138	12	case	case	NN
37681	2138	13	really	really	RB
37681	2138	14	need	nee	MD
37681	2138	15	be	be	VB
37681	2138	16	proved	prove	VBN
37681	2138	17	,	,	,
37681	2138	18	provided	provide	VBN
37681	2138	19	that	that	DT
37681	2138	20	is	be	VBZ
37681	2138	21	the	the	DT
37681	2138	22	most	most	RBS
37681	2138	23	difficult	difficult	JJ
37681	2138	24	one	one	NN
37681	2138	25	,	,	,
37681	2138	26	and	and	CC
37681	2138	27	is	be	VBZ
37681	2138	28	typical	typical	JJ
37681	2138	29	.	.	.
37681	2139	1	Proclus	Proclus	NNP
37681	2139	2	gave	give	VBD
37681	2139	3	the	the	DT
37681	2139	4	proofs	proof	NNS
37681	2139	5	of	of	IN
37681	2139	6	the	the	DT
37681	2139	7	other	other	JJ
37681	2139	8	two	two	CD
37681	2139	9	cases	case	NNS
37681	2139	10	,	,	,
37681	2139	11	and	and	CC
37681	2139	12	it	-PRON-	PRP
37681	2139	13	is	be	VBZ
37681	2139	14	interesting	interesting	JJ
37681	2139	15	to	to	IN
37681	2139	16	pupils	pupil	NNS
37681	2139	17	to	to	TO
37681	2139	18	work	work	VB
37681	2139	19	them	-PRON-	PRP
37681	2139	20	out	out	RP
37681	2139	21	for	for	IN
37681	2139	22	themselves	-PRON-	PRP
37681	2139	23	.	.	.
37681	2140	1	In	in	IN
37681	2140	2	such	such	JJ
37681	2140	3	work	work	NN
37681	2140	4	it	-PRON-	PRP
37681	2140	5	constantly	constantly	RB
37681	2140	6	appears	appear	VBZ
37681	2140	7	that	that	IN
37681	2140	8	every	every	DT
37681	2140	9	proposition	proposition	NN
37681	2140	10	suggests	suggest	VBZ
37681	2140	11	abundant	abundant	JJ
37681	2140	12	opportunity	opportunity	NN
37681	2140	13	for	for	IN
37681	2140	14	originality	originality	NN
37681	2140	15	,	,	,
37681	2140	16	and	and	CC
37681	2140	17	that	that	IN
37681	2140	18	the	the	DT
37681	2140	19	complete	complete	JJ
37681	2140	20	form	form	NN
37681	2140	21	of	of	IN
37681	2140	22	proof	proof	NN
37681	2140	23	in	in	IN
37681	2140	24	a	a	DT
37681	2140	25	textbook	textbook	NN
37681	2140	26	is	be	VBZ
37681	2140	27	not	not	RB
37681	2140	28	a	a	DT
37681	2140	29	bar	bar	NN
37681	2140	30	to	to	IN
37681	2140	31	independent	independent	JJ
37681	2140	32	thought	thought	NN
37681	2140	33	.	.	.
37681	2141	1	The	the	DT
37681	2141	2	Law	Law	NNP
37681	2141	3	of	of	IN
37681	2141	4	Converse	Converse	NNP
37681	2141	5	,	,	,
37681	2141	6	mentioned	mention	VBN
37681	2141	7	on	on	IN
37681	2141	8	page	page	NN
37681	2141	9	190	190	CD
37681	2141	10	,	,	,
37681	2141	11	may	may	MD
37681	2141	12	be	be	VB
37681	2141	13	applied	apply	VBN
37681	2141	14	to	to	IN
37681	2141	15	the	the	DT
37681	2141	16	converse	converse	NN
37681	2141	17	case	case	NN
37681	2141	18	if	if	IN
37681	2141	19	desired	desire	VBN
37681	2141	20	.	.	.
37681	2142	1	THEOREM	THEOREM	NNP
37681	2142	2	.	.	.
37681	2143	1	_	_	NNP
37681	2143	2	Two	two	CD
37681	2143	3	angles	angle	NNS
37681	2143	4	whose	whose	WP$
37681	2143	5	sides	side	NNS
37681	2143	6	are	be	VBP
37681	2143	7	parallel	parallel	JJ
37681	2143	8	,	,	,
37681	2143	9	each	each	DT
37681	2143	10	to	to	IN
37681	2143	11	each	each	DT
37681	2143	12	,	,	,
37681	2143	13	are	be	VBP
37681	2143	14	either	either	CC
37681	2143	15	equal	equal	JJ
37681	2143	16	or	or	CC
37681	2143	17	supplementary	supplementary	JJ
37681	2143	18	.	.	.
37681	2143	19	_	_	NNP
37681	2143	20	This	this	DT
37681	2143	21	is	be	VBZ
37681	2143	22	not	not	RB
37681	2143	23	an	an	DT
37681	2143	24	ancient	ancient	JJ
37681	2143	25	proposition	proposition	NN
37681	2143	26	,	,	,
37681	2143	27	although	although	IN
37681	2143	28	the	the	DT
37681	2143	29	Greeks	Greeks	NNPS
37681	2143	30	were	be	VBD
37681	2143	31	well	well	RB
37681	2143	32	aware	aware	JJ
37681	2143	33	of	of	IN
37681	2143	34	the	the	DT
37681	2143	35	principle	principle	NN
37681	2143	36	.	.	.
37681	2144	1	It	-PRON-	PRP
37681	2144	2	may	may	MD
37681	2144	3	be	be	VB
37681	2144	4	stated	state	VBN
37681	2144	5	so	so	IN
37681	2144	6	as	as	IN
37681	2144	7	to	to	TO
37681	2144	8	include	include	VB
37681	2144	9	the	the	DT
37681	2144	10	case	case	NN
37681	2144	11	of	of	IN
37681	2144	12	the	the	DT
37681	2144	13	sides	side	NNS
37681	2144	14	being	be	VBG
37681	2144	15	perpendicular	perpendicular	JJ
37681	2144	16	,	,	,
37681	2144	17	each	each	DT
37681	2144	18	to	to	IN
37681	2144	19	each	each	DT
37681	2144	20	,	,	,
37681	2144	21	but	but	CC
37681	2144	22	this	this	DT
37681	2144	23	is	be	VBZ
37681	2144	24	better	well	RBR
37681	2144	25	left	leave	VBN
37681	2144	26	as	as	IN
37681	2144	27	an	an	DT
37681	2144	28	exercise	exercise	NN
37681	2144	29	.	.	.
37681	2145	1	It	-PRON-	PRP
37681	2145	2	is	be	VBZ
37681	2145	3	possible	possible	JJ
37681	2145	4	,	,	,
37681	2145	5	by	by	IN
37681	2145	6	some	some	DT
37681	2145	7	circumlocution	circumlocution	NN
37681	2145	8	,	,	,
37681	2145	9	to	to	IN
37681	2145	10	so	so	RB
37681	2145	11	state	state	VB
37681	2145	12	the	the	DT
37681	2145	13	theorem	theorem	NN
37681	2145	14	as	as	IN
37681	2145	15	to	to	TO
37681	2145	16	tell	tell	VB
37681	2145	17	in	in	IN
37681	2145	18	what	what	WP
37681	2145	19	cases	case	NNS
37681	2145	20	the	the	DT
37681	2145	21	angles	angle	NNS
37681	2145	22	are	be	VBP
37681	2145	23	equal	equal	JJ
37681	2145	24	and	and	CC
37681	2145	25	in	in	IN
37681	2145	26	what	what	WP
37681	2145	27	cases	case	NNS
37681	2145	28	supplementary	supplementary	JJ
37681	2145	29	.	.	.
37681	2146	1	It	-PRON-	PRP
37681	2146	2	can	can	MD
37681	2146	3	not	not	RB
37681	2146	4	be	be	VB
37681	2146	5	tersely	tersely	RB
37681	2146	6	stated	state	VBN
37681	2146	7	,	,	,
37681	2146	8	however	however	RB
37681	2146	9	,	,	,
37681	2146	10	and	and	CC
37681	2146	11	it	-PRON-	PRP
37681	2146	12	seems	seem	VBZ
37681	2146	13	better	well	JJR
37681	2146	14	to	to	TO
37681	2146	15	leave	leave	VB
37681	2146	16	this	this	DT
37681	2146	17	point	point	NN
37681	2146	18	as	as	IN
37681	2146	19	a	a	DT
37681	2146	20	subject	subject	NN
37681	2146	21	for	for	IN
37681	2146	22	questioning	questioning	NN
37681	2146	23	by	by	IN
37681	2146	24	the	the	DT
37681	2146	25	teacher	teacher	NN
37681	2146	26	.	.	.
37681	2147	1	THEOREM	THEOREM	NNP
37681	2147	2	.	.	.
37681	2148	1	_	_	NNP
37681	2148	2	The	the	DT
37681	2148	3	opposite	opposite	JJ
37681	2148	4	sides	side	NNS
37681	2148	5	of	of	IN
37681	2148	6	a	a	DT
37681	2148	7	parallelogram	parallelogram	NN
37681	2148	8	are	be	VBP
37681	2148	9	equal	equal	JJ
37681	2148	10	.	.	.
37681	2148	11	_	_	NNP
37681	2148	12	THEOREM	THEOREM	NNP
37681	2148	13	.	.	.
37681	2149	1	_	_	XX
37681	2149	2	If	if	IN
37681	2149	3	the	the	DT
37681	2149	4	opposite	opposite	JJ
37681	2149	5	sides	side	NNS
37681	2149	6	of	of	IN
37681	2149	7	a	a	DT
37681	2149	8	quadrilateral	quadrilateral	NN
37681	2149	9	are	be	VBP
37681	2149	10	equal	equal	JJ
37681	2149	11	,	,	,
37681	2149	12	the	the	DT
37681	2149	13	figure	figure	NN
37681	2149	14	is	be	VBZ
37681	2149	15	a	a	DT
37681	2149	16	parallelogram	parallelogram	NN
37681	2149	17	.	.	.
37681	2149	18	_	_	NNP
37681	2149	19	[	[	-LRB-
37681	2149	20	Illustration	illustration	NN
37681	2149	21	]	]	-RRB-
37681	2149	22	This	this	DT
37681	2149	23	proposition	proposition	NN
37681	2149	24	is	be	VBZ
37681	2149	25	a	a	DT
37681	2149	26	very	very	RB
37681	2149	27	simple	simple	JJ
37681	2149	28	test	test	NN
37681	2149	29	for	for	IN
37681	2149	30	a	a	DT
37681	2149	31	parallelogram	parallelogram	NN
37681	2149	32	.	.	.
37681	2150	1	It	-PRON-	PRP
37681	2150	2	is	be	VBZ
37681	2150	3	the	the	DT
37681	2150	4	principle	principle	NN
37681	2150	5	involved	involve	VBN
37681	2150	6	in	in	IN
37681	2150	7	the	the	DT
37681	2150	8	case	case	NN
37681	2150	9	of	of	IN
37681	2150	10	the	the	DT
37681	2150	11	common	common	JJ
37681	2150	12	folding	fold	VBG
37681	2150	13	parallel	parallel	JJ
37681	2150	14	ruler	ruler	NN
37681	2150	15	,	,	,
37681	2150	16	an	an	DT
37681	2150	17	instrument	instrument	NN
37681	2150	18	that	that	WDT
37681	2150	19	has	have	VBZ
37681	2150	20	long	long	RB
37681	2150	21	been	be	VBN
37681	2150	22	recognized	recognize	VBN
37681	2150	23	as	as	IN
37681	2150	24	one	one	CD
37681	2150	25	of	of	IN
37681	2150	26	the	the	DT
37681	2150	27	valuable	valuable	JJ
37681	2150	28	tools	tool	NNS
37681	2150	29	of	of	IN
37681	2150	30	practical	practical	JJ
37681	2150	31	geometry	geometry	NN
37681	2150	32	.	.	.
37681	2151	1	It	-PRON-	PRP
37681	2151	2	will	will	MD
37681	2151	3	be	be	VB
37681	2151	4	of	of	IN
37681	2151	5	some	some	DT
37681	2151	6	interest	interest	NN
37681	2151	7	to	to	IN
37681	2151	8	teachers	teacher	NNS
37681	2151	9	to	to	TO
37681	2151	10	see	see	VB
37681	2151	11	one	one	CD
37681	2151	12	of	of	IN
37681	2151	13	the	the	DT
37681	2151	14	early	early	JJ
37681	2151	15	forms	form	NNS
37681	2151	16	of	of	IN
37681	2151	17	this	this	DT
37681	2151	18	parallel	parallel	JJ
37681	2151	19	ruler	ruler	NN
37681	2151	20	,	,	,
37681	2151	21	as	as	IN
37681	2151	22	shown	show	VBN
37681	2151	23	in	in	IN
37681	2151	24	the	the	DT
37681	2151	25	illustration	illustration	NN
37681	2151	26	.	.	.
37681	2152	1	[	[	-LRB-
37681	2152	2	63	63	CD
37681	2152	3	]	]	-RRB-
37681	2152	4	If	if	IN
37681	2152	5	such	such	PDT
37681	2152	6	an	an	DT
37681	2152	7	instrument	instrument	NN
37681	2152	8	is	be	VBZ
37681	2152	9	not	not	RB
37681	2152	10	available	available	JJ
37681	2152	11	in	in	IN
37681	2152	12	the	the	DT
37681	2152	13	school	school	NN
37681	2152	14	,	,	,
37681	2152	15	one	one	CD
37681	2152	16	suitable	suitable	JJ
37681	2152	17	for	for	IN
37681	2152	18	illustrative	illustrative	JJ
37681	2152	19	purposes	purpose	NNS
37681	2152	20	can	can	MD
37681	2152	21	easily	easily	RB
37681	2152	22	be	be	VB
37681	2152	23	made	make	VBN
37681	2152	24	from	from	IN
37681	2152	25	cardboard	cardboard	NN
37681	2152	26	.	.	.
37681	2153	1	[	[	-LRB-
37681	2153	2	Illustration	illustration	NN
37681	2153	3	:	:	:
37681	2153	4	PARALLEL	parallel	NN
37681	2153	5	RULER	RULER	NNS
37681	2153	6	OF	of	IN
37681	2153	7	THE	the	DT
37681	2153	8	SEVENTEENTH	SEVENTEENTH	NNP
37681	2153	9	CENTURY	CENTURY	NNP
37681	2153	10	San	San	NNP
37681	2153	11	Giovanni	Giovanni	NNP
37681	2153	12	's	's	POS
37681	2153	13	"	"	``
37681	2153	14	Seconda	Seconda	NNP
37681	2153	15	squara	squara	NNP
37681	2153	16	mobile	mobile	NN
37681	2153	17	,	,	,
37681	2153	18	"	"	''
37681	2153	19	Vicenza	Vicenza	NNP
37681	2153	20	,	,	,
37681	2153	21	1686	1686	CD
37681	2153	22	]	]	-RRB-
37681	2153	23	A	a	DT
37681	2153	24	somewhat	somewhat	RB
37681	2153	25	more	more	RBR
37681	2153	26	complicated	complicated	JJ
37681	2153	27	form	form	NN
37681	2153	28	of	of	IN
37681	2153	29	this	this	DT
37681	2153	30	instrument	instrument	NN
37681	2153	31	may	may	MD
37681	2153	32	also	also	RB
37681	2153	33	be	be	VB
37681	2153	34	made	make	VBN
37681	2153	35	by	by	IN
37681	2153	36	pupils	pupil	NNS
37681	2153	37	in	in	IN
37681	2153	38	manual	manual	JJ
37681	2153	39	training	training	NN
37681	2153	40	,	,	,
37681	2153	41	as	as	IN
37681	2153	42	is	be	VBZ
37681	2153	43	shown	show	VBN
37681	2153	44	in	in	IN
37681	2153	45	this	this	DT
37681	2153	46	illustration	illustration	NN
37681	2153	47	from	from	IN
37681	2153	48	Bion	Bion	NNP
37681	2153	49	's	's	POS
37681	2153	50	great	great	JJ
37681	2153	51	treatise	treatise	NN
37681	2153	52	.	.	.
37681	2154	1	The	the	DT
37681	2154	2	principle	principle	NN
37681	2154	3	involved	involved	JJ
37681	2154	4	may	may	MD
37681	2154	5	be	be	VB
37681	2154	6	taken	take	VBN
37681	2154	7	up	up	RP
37681	2154	8	in	in	IN
37681	2154	9	class	class	NN
37681	2154	10	,	,	,
37681	2154	11	even	even	RB
37681	2154	12	if	if	IN
37681	2154	13	the	the	DT
37681	2154	14	instrument	instrument	NN
37681	2154	15	is	be	VBZ
37681	2154	16	not	not	RB
37681	2154	17	used	use	VBN
37681	2154	18	.	.	.
37681	2155	1	It	-PRON-	PRP
37681	2155	2	is	be	VBZ
37681	2155	3	evident	evident	JJ
37681	2155	4	that	that	IN
37681	2155	5	,	,	,
37681	2155	6	unless	unless	IN
37681	2155	7	the	the	DT
37681	2155	8	workmanship	workmanship	NN
37681	2155	9	is	be	VBZ
37681	2155	10	unusually	unusually	RB
37681	2155	11	good	good	JJ
37681	2155	12	,	,	,
37681	2155	13	this	this	DT
37681	2155	14	form	form	NN
37681	2155	15	of	of	IN
37681	2155	16	parallel	parallel	JJ
37681	2155	17	ruler	ruler	NN
37681	2155	18	is	be	VBZ
37681	2155	19	not	not	RB
37681	2155	20	as	as	RB
37681	2155	21	accurate	accurate	JJ
37681	2155	22	as	as	IN
37681	2155	23	the	the	DT
37681	2155	24	common	common	JJ
37681	2155	25	one	one	NN
37681	2155	26	illustrated	illustrate	VBN
37681	2155	27	above	above	RB
37681	2155	28	.	.	.
37681	2156	1	The	the	DT
37681	2156	2	principle	principle	NN
37681	2156	3	is	be	VBZ
37681	2156	4	sometimes	sometimes	RB
37681	2156	5	used	use	VBN
37681	2156	6	in	in	IN
37681	2156	7	iron	iron	NN
37681	2156	8	gates	gate	NNS
37681	2156	9	.	.	.
37681	2157	1	[	[	-LRB-
37681	2157	2	Illustration	illustration	NN
37681	2157	3	:	:	:
37681	2157	4	PARALLEL	parallel	NN
37681	2157	5	RULER	RULER	NNS
37681	2157	6	OF	of	IN
37681	2157	7	THE	the	DT
37681	2157	8	EIGHTEENTH	EIGHTEENTH	NNP
37681	2157	9	CENTURY	CENTURY	NNP
37681	2157	10	N.	N.	NNP
37681	2157	11	Bion	Bion	NNP
37681	2157	12	's	's	POS
37681	2157	13	"	"	``
37681	2157	14	Traité	Traité	NNP
37681	2157	15	de	de	FW
37681	2157	16	la	la	JJ
37681	2157	17	construction	construction	NN
37681	2157	18	...	...	:
37681	2157	19	des	des	NNP
37681	2157	20	instrumens	instrumen	NNS
37681	2157	21	de	de	IN
37681	2157	22	mathématique	mathématique	NN
37681	2157	23	,	,	,
37681	2157	24	"	"	''
37681	2157	25	The	the	DT
37681	2157	26	Hague	Hague	NNP
37681	2157	27	,	,	,
37681	2157	28	1723	1723	CD
37681	2157	29	]	]	-RRB-
37681	2157	30	THEOREM	theorem	NN
37681	2157	31	.	.	.
37681	2158	1	_	_	NNP
37681	2158	2	Two	two	CD
37681	2158	3	parallelograms	parallelogram	NNS
37681	2158	4	are	be	VBP
37681	2158	5	congruent	congruent	JJ
37681	2158	6	if	if	IN
37681	2158	7	two	two	CD
37681	2158	8	sides	side	NNS
37681	2158	9	and	and	CC
37681	2158	10	the	the	DT
37681	2158	11	included	included	JJ
37681	2158	12	angle	angle	NN
37681	2158	13	of	of	IN
37681	2158	14	the	the	DT
37681	2158	15	one	one	NN
37681	2158	16	are	be	VBP
37681	2158	17	equal	equal	JJ
37681	2158	18	respectively	respectively	RB
37681	2158	19	to	to	IN
37681	2158	20	two	two	CD
37681	2158	21	sides	side	NNS
37681	2158	22	and	and	CC
37681	2158	23	the	the	DT
37681	2158	24	included	included	JJ
37681	2158	25	angle	angle	NN
37681	2158	26	of	of	IN
37681	2158	27	the	the	DT
37681	2158	28	other	other	JJ
37681	2158	29	.	.	.
37681	2158	30	_	_	NNP
37681	2158	31	This	this	DT
37681	2158	32	proposition	proposition	NN
37681	2158	33	is	be	VBZ
37681	2158	34	discussed	discuss	VBN
37681	2158	35	in	in	IN
37681	2158	36	connection	connection	NN
37681	2158	37	with	with	IN
37681	2158	38	the	the	DT
37681	2158	39	one	one	NN
37681	2158	40	that	that	WDT
37681	2158	41	follows	follow	VBZ
37681	2158	42	.	.	.
37681	2159	1	THEOREM	THEOREM	NNP
37681	2159	2	.	.	.
37681	2160	1	_	_	XX
37681	2160	2	If	if	IN
37681	2160	3	three	three	CD
37681	2160	4	or	or	CC
37681	2160	5	more	more	JJR
37681	2160	6	parallels	parallel	NNS
37681	2160	7	intercept	intercept	VBP
37681	2160	8	equal	equal	JJ
37681	2160	9	segments	segment	NNS
37681	2160	10	on	on	IN
37681	2160	11	one	one	CD
37681	2160	12	transversal	transversal	NN
37681	2160	13	,	,	,
37681	2160	14	they	-PRON-	PRP
37681	2160	15	intercept	intercept	VBP
37681	2160	16	equal	equal	JJ
37681	2160	17	segments	segment	NNS
37681	2160	18	on	on	IN
37681	2160	19	every	every	DT
37681	2160	20	transversal	transversal	NN
37681	2160	21	.	.	.
37681	2160	22	_	_	NNP
37681	2160	23	These	these	DT
37681	2160	24	two	two	CD
37681	2160	25	propositions	proposition	NNS
37681	2160	26	are	be	VBP
37681	2160	27	not	not	RB
37681	2160	28	given	give	VBN
37681	2160	29	in	in	IN
37681	2160	30	Euclid	Euclid	NNP
37681	2160	31	,	,	,
37681	2160	32	although	although	IN
37681	2160	33	generally	generally	RB
37681	2160	34	required	require	VBN
37681	2160	35	by	by	IN
37681	2160	36	American	american	JJ
37681	2160	37	syllabi	syllabi	NN
37681	2160	38	of	of	IN
37681	2160	39	the	the	DT
37681	2160	40	present	present	JJ
37681	2160	41	time	time	NN
37681	2160	42	.	.	.
37681	2161	1	The	the	DT
37681	2161	2	last	last	JJ
37681	2161	3	one	one	NN
37681	2161	4	is	be	VBZ
37681	2161	5	particularly	particularly	RB
37681	2161	6	useful	useful	JJ
37681	2161	7	in	in	IN
37681	2161	8	subsequent	subsequent	JJ
37681	2161	9	work	work	NN
37681	2161	10	.	.	.
37681	2162	1	Neither	neither	DT
37681	2162	2	one	one	NN
37681	2162	3	offers	offer	VBZ
37681	2162	4	any	any	DT
37681	2162	5	difficulty	difficulty	NN
37681	2162	6	,	,	,
37681	2162	7	and	and	CC
37681	2162	8	neither	neither	DT
37681	2162	9	has	have	VBZ
37681	2162	10	any	any	DT
37681	2162	11	interesting	interesting	JJ
37681	2162	12	history	history	NN
37681	2162	13	.	.	.
37681	2163	1	There	there	EX
37681	2163	2	are	be	VBP
37681	2163	3	,	,	,
37681	2163	4	however	however	RB
37681	2163	5	,	,	,
37681	2163	6	numerous	numerous	JJ
37681	2163	7	interesting	interesting	JJ
37681	2163	8	applications	application	NNS
37681	2163	9	to	to	IN
37681	2163	10	the	the	DT
37681	2163	11	last	last	JJ
37681	2163	12	one	one	NN
37681	2163	13	.	.	.
37681	2164	1	One	one	NN
37681	2164	2	that	that	WDT
37681	2164	3	is	be	VBZ
37681	2164	4	used	use	VBN
37681	2164	5	in	in	IN
37681	2164	6	mechanical	mechanical	JJ
37681	2164	7	drawing	drawing	NN
37681	2164	8	is	be	VBZ
37681	2164	9	here	here	RB
37681	2164	10	illustrated	illustrate	VBN
37681	2164	11	.	.	.
37681	2165	1	[	[	-LRB-
37681	2165	2	Illustration	illustration	NN
37681	2165	3	]	]	-RRB-
37681	2165	4	If	if	IN
37681	2165	5	it	-PRON-	PRP
37681	2165	6	is	be	VBZ
37681	2165	7	desired	desire	VBN
37681	2165	8	to	to	TO
37681	2165	9	divide	divide	VB
37681	2165	10	a	a	DT
37681	2165	11	line	line	NN
37681	2165	12	_	_	NNP
37681	2165	13	AB	AB	NNP
37681	2165	14	_	_	NNP
37681	2165	15	into	into	IN
37681	2165	16	five	five	CD
37681	2165	17	equal	equal	JJ
37681	2165	18	parts	part	NNS
37681	2165	19	,	,	,
37681	2165	20	we	-PRON-	PRP
37681	2165	21	may	may	MD
37681	2165	22	take	take	VB
37681	2165	23	a	a	DT
37681	2165	24	piece	piece	NN
37681	2165	25	of	of	IN
37681	2165	26	ruled	rule	VBN
37681	2165	27	tracing	trace	VBG
37681	2165	28	paper	paper	NN
37681	2165	29	and	and	CC
37681	2165	30	lay	lie	VBD
37681	2165	31	it	-PRON-	PRP
37681	2165	32	over	over	IN
37681	2165	33	the	the	DT
37681	2165	34	given	give	VBN
37681	2165	35	line	line	NN
37681	2165	36	so	so	IN
37681	2165	37	that	that	DT
37681	2165	38	line	line	NN
37681	2165	39	0	0	CD
37681	2165	40	passes	pass	VBZ
37681	2165	41	through	through	IN
37681	2165	42	_	_	NNP
37681	2165	43	A	A	NNP
37681	2165	44	_	_	NNP
37681	2165	45	,	,	,
37681	2165	46	and	and	CC
37681	2165	47	line	line	NN
37681	2165	48	5	5	CD
37681	2165	49	through	through	IN
37681	2165	50	_	_	NNP
37681	2165	51	B	B	NNP
37681	2165	52	_	_	NNP
37681	2165	53	.	.	.
37681	2166	1	We	-PRON-	PRP
37681	2166	2	may	may	MD
37681	2166	3	then	then	RB
37681	2166	4	prick	prick	VB
37681	2166	5	through	through	IN
37681	2166	6	the	the	DT
37681	2166	7	paper	paper	NN
37681	2166	8	and	and	CC
37681	2166	9	thus	thus	RB
37681	2166	10	determine	determine	VB
37681	2166	11	the	the	DT
37681	2166	12	points	point	NNS
37681	2166	13	on	on	IN
37681	2166	14	_	_	NNP
37681	2166	15	AB	AB	NNP
37681	2166	16	_	_	NNP
37681	2166	17	.	.	.
37681	2167	1	Similarly	similarly	RB
37681	2167	2	,	,	,
37681	2167	3	we	-PRON-	PRP
37681	2167	4	may	may	MD
37681	2167	5	divide	divide	VB
37681	2167	6	_	_	NNP
37681	2167	7	AB	AB	NNP
37681	2167	8	_	_	NNP
37681	2167	9	into	into	IN
37681	2167	10	any	any	DT
37681	2167	11	other	other	JJ
37681	2167	12	number	number	NN
37681	2167	13	of	of	IN
37681	2167	14	equal	equal	JJ
37681	2167	15	parts	part	NNS
37681	2167	16	.	.	.
37681	2168	1	Among	among	IN
37681	2168	2	the	the	DT
37681	2168	3	applications	application	NNS
37681	2168	4	of	of	IN
37681	2168	5	these	these	DT
37681	2168	6	propositions	proposition	NNS
37681	2168	7	is	be	VBZ
37681	2168	8	an	an	DT
37681	2168	9	interesting	interesting	JJ
37681	2168	10	one	one	NN
37681	2168	11	due	due	IN
37681	2168	12	to	to	IN
37681	2168	13	the	the	DT
37681	2168	14	Arab	Arab	NNP
37681	2168	15	Al	Al	NNP
37681	2168	16	-	-	HYPH
37681	2168	17	Nair[=i]z[=i	Nair[=i]z[=i	NNP
37681	2168	18	]	]	-RRB-
37681	2168	19	(	(	-LRB-
37681	2168	20	_	_	NNP
37681	2168	21	ca	ca	NNP
37681	2168	22	.	.	.
37681	2168	23	_	_	NNP
37681	2168	24	900	900	CD
37681	2168	25	A.D.	A.D.	NNP
37681	2168	26	)	)	-RRB-
37681	2168	27	.	.	.
37681	2169	1	The	the	DT
37681	2169	2	problem	problem	NN
37681	2169	3	is	be	VBZ
37681	2169	4	to	to	TO
37681	2169	5	divide	divide	VB
37681	2169	6	a	a	DT
37681	2169	7	line	line	NN
37681	2169	8	into	into	IN
37681	2169	9	any	any	DT
37681	2169	10	number	number	NN
37681	2169	11	of	of	IN
37681	2169	12	equal	equal	JJ
37681	2169	13	parts	part	NNS
37681	2169	14	,	,	,
37681	2169	15	and	and	CC
37681	2169	16	he	-PRON-	PRP
37681	2169	17	begins	begin	VBZ
37681	2169	18	with	with	IN
37681	2169	19	the	the	DT
37681	2169	20	case	case	NN
37681	2169	21	of	of	IN
37681	2169	22	trisecting	trisect	VBG
37681	2169	23	_	_	NNP
37681	2169	24	AB	AB	NNP
37681	2169	25	_	_	NNP
37681	2169	26	.	.	.
37681	2170	1	It	-PRON-	PRP
37681	2170	2	may	may	MD
37681	2170	3	be	be	VB
37681	2170	4	given	give	VBN
37681	2170	5	as	as	IN
37681	2170	6	a	a	DT
37681	2170	7	case	case	NN
37681	2170	8	of	of	IN
37681	2170	9	practical	practical	JJ
37681	2170	10	drawing	drawing	NN
37681	2170	11	even	even	RB
37681	2170	12	before	before	IN
37681	2170	13	the	the	DT
37681	2170	14	problems	problem	NNS
37681	2170	15	are	be	VBP
37681	2170	16	reached	reach	VBN
37681	2170	17	,	,	,
37681	2170	18	particularly	particularly	RB
37681	2170	19	if	if	IN
37681	2170	20	some	some	DT
37681	2170	21	preliminary	preliminary	JJ
37681	2170	22	work	work	NN
37681	2170	23	with	with	IN
37681	2170	24	the	the	DT
37681	2170	25	compasses	compass	NNS
37681	2170	26	and	and	CC
37681	2170	27	straightedge	straightedge	NN
37681	2170	28	has	have	VBZ
37681	2170	29	been	be	VBN
37681	2170	30	given	give	VBN
37681	2170	31	.	.	.
37681	2171	1	Make	make	VB
37681	2171	2	_	_	NNP
37681	2171	3	BQ	BQ	NNP
37681	2171	4	_	_	NNP
37681	2171	5	and	and	CC
37681	2171	6	_	_	NNP
37681	2171	7	AQ	AQ	NNP
37681	2171	8	'	'	''
37681	2171	9	_	_	NNP
37681	2171	10	perpendicular	perpendicular	NN
37681	2171	11	to	to	IN
37681	2171	12	_	_	NNP
37681	2171	13	AB	AB	NNP
37681	2171	14	_	_	NNP
37681	2171	15	,	,	,
37681	2171	16	and	and	CC
37681	2171	17	make	make	VB
37681	2171	18	_	_	NNP
37681	2171	19	BP	BP	NNP
37681	2171	20	_	_	NNP
37681	2171	21	=	=	SYM
37681	2171	22	_	_	NNP
37681	2171	23	PQ	PQ	NNP
37681	2171	24	_	_	NNP
37681	2171	25	=	=	SYM
37681	2171	26	_	_	NNP
37681	2171	27	AP	AP	NNP
37681	2171	28	'	'	POS
37681	2171	29	_	_	NNP
37681	2171	30	=	=	SYM
37681	2171	31	_	_	NNP
37681	2171	32	P'Q	P'Q	NNP
37681	2171	33	'	'	POS
37681	2171	34	_	_	NNP
37681	2171	35	.	.	.
37681	2172	1	Then	then	RB
37681	2172	2	[	[	-LRB-
37681	2172	3	triangle]_XYZ	triangle]_XYZ	NNP
37681	2172	4	_	_	NNP
37681	2172	5	is	be	VBZ
37681	2172	6	congruent	congruent	JJ
37681	2172	7	to	to	IN
37681	2172	8	[	[	-LRB-
37681	2172	9	triangle]_YBP	triangle]_YBP	NNP
37681	2172	10	_	_	NNP
37681	2172	11	,	,	,
37681	2172	12	and	and	CC
37681	2172	13	also	also	RB
37681	2172	14	to	to	IN
37681	2172	15	[	[	-LRB-
37681	2172	16	triangle]_XAP	triangle]_XAP	NNP
37681	2172	17	'	'	''
37681	2172	18	_	_	NNP
37681	2172	19	.	.	.
37681	2173	1	Therefore	therefore	RB
37681	2173	2	_	_	NNP
37681	2173	3	AX	AX	NNP
37681	2173	4	_	_	NNP
37681	2173	5	=	=	SYM
37681	2173	6	_	_	NNP
37681	2173	7	XY	XY	NNP
37681	2173	8	_	_	NNP
37681	2173	9	=	=	SYM
37681	2173	10	_	_	NNP
37681	2173	11	YB	YB	NNP
37681	2173	12	_	_	NNP
37681	2173	13	.	.	.
37681	2174	1	In	in	IN
37681	2174	2	the	the	DT
37681	2174	3	same	same	JJ
37681	2174	4	way	way	NN
37681	2174	5	we	-PRON-	PRP
37681	2174	6	might	may	MD
37681	2174	7	continue	continue	VB
37681	2174	8	to	to	TO
37681	2174	9	produce	produce	VB
37681	2174	10	_	_	NNP
37681	2174	11	BQ	BQ	NNP
37681	2174	12	_	_	NNP
37681	2174	13	until	until	IN
37681	2174	14	it	-PRON-	PRP
37681	2174	15	is	be	VBZ
37681	2174	16	made	make	VBN
37681	2174	17	up	up	RP
37681	2174	18	of	of	IN
37681	2174	19	_	_	NNP
37681	2174	20	n	n	CC
37681	2174	21	_	_	NNP
37681	2174	22	-	-	HYPH
37681	2174	23	1	1	CD
37681	2174	24	lengths	length	NNS
37681	2174	25	_	_	NNP
37681	2174	26	BP	BP	NNP
37681	2174	27	_	_	NNP
37681	2174	28	,	,	,
37681	2174	29	and	and	CC
37681	2174	30	so	so	RB
37681	2174	31	for	for	IN
37681	2174	32	_	_	NNP
37681	2174	33	AQ	AQ	NNP
37681	2174	34	'	'	''
37681	2174	35	_	_	NNP
37681	2174	36	,	,	,
37681	2174	37	and	and	CC
37681	2174	38	by	by	IN
37681	2174	39	properly	properly	RB
37681	2174	40	joining	join	VBG
37681	2174	41	points	point	NNS
37681	2174	42	we	-PRON-	PRP
37681	2174	43	could	could	MD
37681	2174	44	divide	divide	VB
37681	2174	45	_	_	NNP
37681	2174	46	AB	AB	NNP
37681	2174	47	_	_	NNP
37681	2174	48	into	into	IN
37681	2174	49	_	_	NNP
37681	2174	50	n	n	CC
37681	2174	51	_	_	NNP
37681	2174	52	equal	equal	JJ
37681	2174	53	parts	part	NNS
37681	2174	54	.	.	.
37681	2175	1	In	in	IN
37681	2175	2	particular	particular	JJ
37681	2175	3	,	,	,
37681	2175	4	if	if	IN
37681	2175	5	we	-PRON-	PRP
37681	2175	6	join	join	VBP
37681	2175	7	_	_	NNP
37681	2175	8	P	P	NNP
37681	2175	9	_	_	NNP
37681	2175	10	and	and	CC
37681	2175	11	_	_	NNP
37681	2175	12	P	P	NNP
37681	2175	13	'	'	''
37681	2175	14	_	_	NNP
37681	2175	15	,	,	,
37681	2175	16	we	-PRON-	PRP
37681	2175	17	bisect	bisect	VBP
37681	2175	18	the	the	DT
37681	2175	19	line	line	NN
37681	2175	20	_	_	NNP
37681	2175	21	AB	AB	NNP
37681	2175	22	_	_	NNP
37681	2175	23	.	.	.
37681	2176	1	[	[	-LRB-
37681	2176	2	Illustration	illustration	NN
37681	2176	3	]	]	-RRB-
37681	2176	4	THEOREM	THEOREM	NNP
37681	2176	5	.	.	.
37681	2177	1	_	_	XX
37681	2177	2	If	if	IN
37681	2177	3	two	two	CD
37681	2177	4	sides	side	NNS
37681	2177	5	of	of	IN
37681	2177	6	a	a	DT
37681	2177	7	quadrilateral	quadrilateral	NN
37681	2177	8	are	be	VBP
37681	2177	9	equal	equal	JJ
37681	2177	10	and	and	CC
37681	2177	11	parallel	parallel	JJ
37681	2177	12	,	,	,
37681	2177	13	then	then	RB
37681	2177	14	the	the	DT
37681	2177	15	other	other	JJ
37681	2177	16	two	two	CD
37681	2177	17	sides	side	NNS
37681	2177	18	are	be	VBP
37681	2177	19	equal	equal	JJ
37681	2177	20	and	and	CC
37681	2177	21	parallel	parallel	JJ
37681	2177	22	,	,	,
37681	2177	23	and	and	CC
37681	2177	24	the	the	DT
37681	2177	25	figure	figure	NN
37681	2177	26	is	be	VBZ
37681	2177	27	a	a	DT
37681	2177	28	parallelogram	parallelogram	NN
37681	2177	29	.	.	.
37681	2177	30	_	_	NNP
37681	2177	31	This	this	DT
37681	2177	32	was	be	VBD
37681	2177	33	Euclid	Euclid	NNP
37681	2177	34	's	's	POS
37681	2177	35	first	first	JJ
37681	2177	36	proposition	proposition	NN
37681	2177	37	on	on	IN
37681	2177	38	parallelograms	parallelogram	NNS
37681	2177	39	,	,	,
37681	2177	40	and	and	CC
37681	2177	41	Proclus	Proclus	NNP
37681	2177	42	speaks	speak	VBZ
37681	2177	43	of	of	IN
37681	2177	44	it	-PRON-	PRP
37681	2177	45	as	as	IN
37681	2177	46	the	the	DT
37681	2177	47	connecting	connect	VBG
37681	2177	48	link	link	NN
37681	2177	49	between	between	IN
37681	2177	50	the	the	DT
37681	2177	51	theory	theory	NN
37681	2177	52	of	of	IN
37681	2177	53	parallels	parallel	NNS
37681	2177	54	and	and	CC
37681	2177	55	that	that	DT
37681	2177	56	of	of	IN
37681	2177	57	parallelograms	parallelogram	NNS
37681	2177	58	.	.	.
37681	2178	1	The	the	DT
37681	2178	2	ancients	ancient	NNS
37681	2178	3	,	,	,
37681	2178	4	writing	write	VBG
37681	2178	5	for	for	IN
37681	2178	6	mature	mature	JJ
37681	2178	7	students	student	NNS
37681	2178	8	,	,	,
37681	2178	9	did	do	VBD
37681	2178	10	not	not	RB
37681	2178	11	add	add	VB
37681	2178	12	the	the	DT
37681	2178	13	words	word	NNS
37681	2178	14	"	"	''
37681	2178	15	and	and	CC
37681	2178	16	the	the	DT
37681	2178	17	figure	figure	NN
37681	2178	18	is	be	VBZ
37681	2178	19	a	a	DT
37681	2178	20	parallelogram	parallelogram	NN
37681	2178	21	,	,	,
37681	2178	22	"	"	''
37681	2178	23	because	because	IN
37681	2178	24	that	that	DT
37681	2178	25	follows	follow	VBZ
37681	2178	26	at	at	IN
37681	2178	27	once	once	RB
37681	2178	28	from	from	IN
37681	2178	29	the	the	DT
37681	2178	30	first	first	JJ
37681	2178	31	part	part	NN
37681	2178	32	and	and	CC
37681	2178	33	from	from	IN
37681	2178	34	the	the	DT
37681	2178	35	definition	definition	NN
37681	2178	36	of	of	IN
37681	2178	37	"	"	``
37681	2178	38	parallelogram	parallelogram	NN
37681	2178	39	,	,	,
37681	2178	40	"	"	''
37681	2178	41	but	but	CC
37681	2178	42	it	-PRON-	PRP
37681	2178	43	is	be	VBZ
37681	2178	44	helpful	helpful	JJ
37681	2178	45	to	to	IN
37681	2178	46	younger	young	JJR
37681	2178	47	students	student	NNS
37681	2178	48	because	because	IN
37681	2178	49	it	-PRON-	PRP
37681	2178	50	emphasizes	emphasize	VBZ
37681	2178	51	the	the	DT
37681	2178	52	fact	fact	NN
37681	2178	53	that	that	IN
37681	2178	54	here	here	RB
37681	2178	55	is	be	VBZ
37681	2178	56	a	a	DT
37681	2178	57	test	test	NN
37681	2178	58	for	for	IN
37681	2178	59	this	this	DT
37681	2178	60	kind	kind	NN
37681	2178	61	of	of	IN
37681	2178	62	figure	figure	NN
37681	2178	63	.	.	.
37681	2179	1	THEOREM	THEOREM	NNP
37681	2179	2	.	.	.
37681	2180	1	_	_	NNP
37681	2180	2	The	the	DT
37681	2180	3	diagonals	diagonal	NNS
37681	2180	4	of	of	IN
37681	2180	5	a	a	DT
37681	2180	6	parallelogram	parallelogram	JJ
37681	2180	7	bisect	bisect	NN
37681	2180	8	each	each	DT
37681	2180	9	other	other	JJ
37681	2180	10	.	.	.
37681	2180	11	_	_	NNP
37681	2180	12	This	this	DT
37681	2180	13	proposition	proposition	NN
37681	2180	14	was	be	VBD
37681	2180	15	not	not	RB
37681	2180	16	given	give	VBN
37681	2180	17	in	in	IN
37681	2180	18	Euclid	Euclid	NNP
37681	2180	19	,	,	,
37681	2180	20	but	but	CC
37681	2180	21	it	-PRON-	PRP
37681	2180	22	is	be	VBZ
37681	2180	23	usually	usually	RB
37681	2180	24	required	require	VBN
37681	2180	25	in	in	IN
37681	2180	26	American	american	JJ
37681	2180	27	syllabi	syllabi	NN
37681	2180	28	.	.	.
37681	2181	1	There	there	EX
37681	2181	2	is	be	VBZ
37681	2181	3	often	often	RB
37681	2181	4	given	give	VBN
37681	2181	5	in	in	IN
37681	2181	6	connection	connection	NN
37681	2181	7	with	with	IN
37681	2181	8	it	-PRON-	PRP
37681	2181	9	the	the	DT
37681	2181	10	exercise	exercise	NN
37681	2181	11	in	in	IN
37681	2181	12	which	which	WDT
37681	2181	13	it	-PRON-	PRP
37681	2181	14	is	be	VBZ
37681	2181	15	proved	prove	VBN
37681	2181	16	that	that	IN
37681	2181	17	the	the	DT
37681	2181	18	diagonals	diagonal	NNS
37681	2181	19	of	of	IN
37681	2181	20	a	a	DT
37681	2181	21	rectangle	rectangle	NN
37681	2181	22	are	be	VBP
37681	2181	23	equal	equal	JJ
37681	2181	24	.	.	.
37681	2182	1	When	when	WRB
37681	2182	2	this	this	DT
37681	2182	3	is	be	VBZ
37681	2182	4	taken	take	VBN
37681	2182	5	,	,	,
37681	2182	6	it	-PRON-	PRP
37681	2182	7	is	be	VBZ
37681	2182	8	well	well	JJ
37681	2182	9	to	to	TO
37681	2182	10	state	state	VB
37681	2182	11	to	to	IN
37681	2182	12	the	the	DT
37681	2182	13	class	class	NN
37681	2182	14	that	that	WDT
37681	2182	15	carpenters	carpenter	VBZ
37681	2182	16	and	and	CC
37681	2182	17	builders	builder	NNS
37681	2182	18	find	find	VBP
37681	2182	19	this	this	DT
37681	2182	20	one	one	CD
37681	2182	21	of	of	IN
37681	2182	22	the	the	DT
37681	2182	23	best	good	JJS
37681	2182	24	checks	check	NNS
37681	2182	25	in	in	IN
37681	2182	26	laying	lay	VBG
37681	2182	27	out	out	RP
37681	2182	28	floors	floor	NNS
37681	2182	29	and	and	CC
37681	2182	30	other	other	JJ
37681	2182	31	rectangles	rectangle	NNS
37681	2182	32	.	.	.
37681	2183	1	It	-PRON-	PRP
37681	2183	2	is	be	VBZ
37681	2183	3	frequently	frequently	RB
37681	2183	4	applied	apply	VBN
37681	2183	5	also	also	RB
37681	2183	6	in	in	IN
37681	2183	7	laying	lay	VBG
37681	2183	8	out	out	RP
37681	2183	9	tennis	tennis	NN
37681	2183	10	courts	court	NNS
37681	2183	11	.	.	.
37681	2184	1	If	if	IN
37681	2184	2	the	the	DT
37681	2184	3	class	class	NN
37681	2184	4	is	be	VBZ
37681	2184	5	doing	do	VBG
37681	2184	6	any	any	DT
37681	2184	7	work	work	NN
37681	2184	8	in	in	IN
37681	2184	9	mensuration	mensuration	NN
37681	2184	10	,	,	,
37681	2184	11	such	such	JJ
37681	2184	12	as	as	IN
37681	2184	13	finding	find	VBG
37681	2184	14	the	the	DT
37681	2184	15	area	area	NN
37681	2184	16	of	of	IN
37681	2184	17	the	the	DT
37681	2184	18	school	school	NN
37681	2184	19	grounds	ground	NNS
37681	2184	20	,	,	,
37681	2184	21	it	-PRON-	PRP
37681	2184	22	is	be	VBZ
37681	2184	23	a	a	DT
37681	2184	24	good	good	JJ
37681	2184	25	plan	plan	NN
37681	2184	26	to	to	TO
37681	2184	27	check	check	VB
37681	2184	28	a	a	DT
37681	2184	29	few	few	JJ
37681	2184	30	rectangles	rectangle	NNS
37681	2184	31	by	by	IN
37681	2184	32	this	this	DT
37681	2184	33	method	method	NN
37681	2184	34	.	.	.
37681	2185	1	An	an	DT
37681	2185	2	interesting	interesting	JJ
37681	2185	3	outdoor	outdoor	JJ
37681	2185	4	application	application	NN
37681	2185	5	of	of	IN
37681	2185	6	the	the	DT
37681	2185	7	theory	theory	NN
37681	2185	8	of	of	IN
37681	2185	9	parallelograms	parallelogram	NNS
37681	2185	10	is	be	VBZ
37681	2185	11	the	the	DT
37681	2185	12	following	follow	VBG
37681	2185	13	:	:	:
37681	2185	14	[	[	-LRB-
37681	2185	15	Illustration	illustration	NN
37681	2185	16	]	]	-RRB-
37681	2185	17	Suppose	suppose	VBP
37681	2185	18	you	-PRON-	PRP
37681	2185	19	are	be	VBP
37681	2185	20	on	on	IN
37681	2185	21	the	the	DT
37681	2185	22	side	side	NN
37681	2185	23	of	of	IN
37681	2185	24	this	this	DT
37681	2185	25	stream	stream	NN
37681	2185	26	opposite	opposite	RB
37681	2185	27	to	to	IN
37681	2185	28	_	_	NNP
37681	2185	29	XY	XY	NNP
37681	2185	30	_	_	NNP
37681	2185	31	,	,	,
37681	2185	32	and	and	CC
37681	2185	33	wish	wish	VBP
37681	2185	34	to	to	TO
37681	2185	35	measure	measure	VB
37681	2185	36	the	the	DT
37681	2185	37	length	length	NN
37681	2185	38	of	of	IN
37681	2185	39	_	_	NNP
37681	2185	40	XY	XY	NNP
37681	2185	41	_	_	NNP
37681	2185	42	.	.	.
37681	2186	1	Run	run	VB
37681	2186	2	a	a	DT
37681	2186	3	line	line	NN
37681	2186	4	_	_	NNP
37681	2186	5	AB	AB	NNP
37681	2186	6	_	_	NNP
37681	2186	7	along	along	IN
37681	2186	8	the	the	DT
37681	2186	9	bank	bank	NN
37681	2186	10	.	.	.
37681	2187	1	Then	then	RB
37681	2187	2	take	take	VB
37681	2187	3	a	a	DT
37681	2187	4	carpenter	carpenter	NN
37681	2187	5	's	's	POS
37681	2187	6	square	square	NN
37681	2187	7	,	,	,
37681	2187	8	or	or	CC
37681	2187	9	even	even	RB
37681	2187	10	a	a	DT
37681	2187	11	large	large	JJ
37681	2187	12	book	book	NN
37681	2187	13	,	,	,
37681	2187	14	and	and	CC
37681	2187	15	walk	walk	VB
37681	2187	16	along	along	IN
37681	2187	17	_	_	NNP
37681	2187	18	AB	AB	NNP
37681	2187	19	_	_	NNP
37681	2187	20	until	until	IN
37681	2187	21	you	-PRON-	PRP
37681	2187	22	reach	reach	VBP
37681	2187	23	_	_	NNP
37681	2187	24	P	P	NNP
37681	2187	25	_	_	NNP
37681	2187	26	,	,	,
37681	2187	27	a	a	DT
37681	2187	28	point	point	NN
37681	2187	29	from	from	IN
37681	2187	30	which	which	WDT
37681	2187	31	you	-PRON-	PRP
37681	2187	32	can	can	MD
37681	2187	33	just	just	RB
37681	2187	34	see	see	VB
37681	2187	35	_	_	NNP
37681	2187	36	X	X	NNP
37681	2187	37	_	_	NNP
37681	2187	38	and	and	CC
37681	2187	39	_	_	NNP
37681	2187	40	B	B	NNP
37681	2187	41	_	_	NNP
37681	2187	42	along	along	IN
37681	2187	43	two	two	CD
37681	2187	44	sides	side	NNS
37681	2187	45	of	of	IN
37681	2187	46	the	the	DT
37681	2187	47	square	square	NN
37681	2187	48	.	.	.
37681	2188	1	Do	do	VB
37681	2188	2	the	the	DT
37681	2188	3	same	same	JJ
37681	2188	4	for	for	IN
37681	2188	5	_	_	NNP
37681	2188	6	Y	Y	NNP
37681	2188	7	_	_	NNP
37681	2188	8	,	,	,
37681	2188	9	thus	thus	RB
37681	2188	10	fixing	fix	VBG
37681	2188	11	_	_	NNP
37681	2188	12	P	P	NNP
37681	2188	13	_	_	NNP
37681	2188	14	and	and	CC
37681	2188	15	_	_	NNP
37681	2188	16	Q	Q	NNP
37681	2188	17	_	_	NNP
37681	2188	18	.	.	.
37681	2189	1	Using	use	VBG
37681	2189	2	the	the	DT
37681	2189	3	tape	tape	NN
37681	2189	4	,	,	,
37681	2189	5	bisect	bisect	NNP
37681	2189	6	_	_	NNP
37681	2189	7	PQ	PQ	NNP
37681	2189	8	_	_	NNP
37681	2189	9	at	at	IN
37681	2189	10	_	_	NNP
37681	2189	11	M	M	NNP
37681	2189	12	_	_	NNP
37681	2189	13	.	.	.
37681	2190	1	Then	then	RB
37681	2190	2	walk	walk	VB
37681	2190	3	along	along	IN
37681	2190	4	_	_	NNP
37681	2190	5	YM	YM	NNP
37681	2190	6	_	_	NNP
37681	2190	7	produced	produce	VBD
37681	2190	8	until	until	IN
37681	2190	9	you	-PRON-	PRP
37681	2190	10	reach	reach	VBP
37681	2190	11	a	a	DT
37681	2190	12	point	point	NN
37681	2190	13	_	_	NNP
37681	2190	14	Y	Y	NNP
37681	2190	15	'	'	''
37681	2190	16	_	_	NN
37681	2190	17	that	that	WDT
37681	2190	18	is	be	VBZ
37681	2190	19	exactly	exactly	RB
37681	2190	20	in	in	IN
37681	2190	21	line	line	NN
37681	2190	22	with	with	IN
37681	2190	23	_	_	NNP
37681	2190	24	M	M	NNP
37681	2190	25	_	_	NNP
37681	2190	26	and	and	CC
37681	2190	27	_	_	NNP
37681	2190	28	Y	Y	NNP
37681	2190	29	_	_	NNP
37681	2190	30	,	,	,
37681	2190	31	and	and	CC
37681	2190	32	also	also	RB
37681	2190	33	with	with	IN
37681	2190	34	_	_	NNP
37681	2190	35	P	P	NNP
37681	2190	36	_	_	NNP
37681	2190	37	and	and	CC
37681	2190	38	_	_	NNP
37681	2190	39	X	X	NNP
37681	2190	40	_	_	NNP
37681	2190	41	.	.	.
37681	2191	1	Then	then	RB
37681	2191	2	walk	walk	VB
37681	2191	3	along	along	IN
37681	2191	4	_	_	NNP
37681	2191	5	XM	XM	NNP
37681	2191	6	_	_	NNP
37681	2191	7	produced	produce	VBD
37681	2191	8	until	until	IN
37681	2191	9	you	-PRON-	PRP
37681	2191	10	reach	reach	VBP
37681	2191	11	a	a	DT
37681	2191	12	point	point	NN
37681	2191	13	_	_	NNP
37681	2191	14	X	X	NNP
37681	2191	15	'	'	''
37681	2191	16	_	_	NN
37681	2191	17	that	that	WDT
37681	2191	18	is	be	VBZ
37681	2191	19	exactly	exactly	RB
37681	2191	20	in	in	IN
37681	2191	21	line	line	NN
37681	2191	22	with	with	IN
37681	2191	23	_	_	NNP
37681	2191	24	M	M	NNP
37681	2191	25	_	_	NNP
37681	2191	26	and	and	CC
37681	2191	27	_	_	NNP
37681	2191	28	X	X	NNP
37681	2191	29	_	_	NNP
37681	2191	30	,	,	,
37681	2191	31	and	and	CC
37681	2191	32	also	also	RB
37681	2191	33	with	with	IN
37681	2191	34	_	_	NNP
37681	2191	35	Q	Q	NNP
37681	2191	36	_	_	NNP
37681	2191	37	and	and	CC
37681	2191	38	_	_	NNP
37681	2191	39	Y	Y	NNP
37681	2191	40	_	_	NNP
37681	2191	41	.	.	.
37681	2192	1	Then	then	RB
37681	2192	2	measure	measure	VB
37681	2192	3	_	_	NNP
37681	2192	4	Y'X	Y'X	NNP
37681	2192	5	'	'	''
37681	2192	6	_	_	NNP
37681	2192	7	and	and	CC
37681	2192	8	you	-PRON-	PRP
37681	2192	9	have	have	VBP
37681	2192	10	the	the	DT
37681	2192	11	length	length	NN
37681	2192	12	of	of	IN
37681	2192	13	_	_	NNP
37681	2192	14	XY	XY	NNP
37681	2192	15	_	_	NNP
37681	2192	16	.	.	.
37681	2193	1	For	for	IN
37681	2193	2	since	since	IN
37681	2193	3	_	_	NNP
37681	2193	4	YX	YX	NNP
37681	2193	5	'	'	''
37681	2193	6	_	_	NNP
37681	2193	7	is	be	VBZ
37681	2193	8	[	[	-LRB-
37681	2193	9	perp	perp	FW
37681	2193	10	]	]	-RRB-
37681	2193	11	to	to	IN
37681	2193	12	_	_	NNP
37681	2193	13	PQ	PQ	NNP
37681	2193	14	_	_	NNP
37681	2193	15	,	,	,
37681	2193	16	and	and	CC
37681	2193	17	_	_	NNP
37681	2193	18	XY	XY	NNP
37681	2193	19	'	'	POS
37681	2193	20	_	_	NNP
37681	2193	21	is	be	VBZ
37681	2193	22	also	also	RB
37681	2193	23	[	[	-LRB-
37681	2193	24	perp	perp	NN
37681	2193	25	]	]	-RRB-
37681	2193	26	to	to	IN
37681	2193	27	_	_	NNP
37681	2193	28	PQ	PQ	NNP
37681	2193	29	_	_	NNP
37681	2193	30	,	,	,
37681	2193	31	_	_	NNP
37681	2193	32	YX	YX	NNP
37681	2193	33	'	'	``
37681	2193	34	_	_	NNP
37681	2193	35	is	be	VBZ
37681	2193	36	||	||	NNP
37681	2193	37	to	to	TO
37681	2193	38	_	_	NNP
37681	2193	39	XY	XY	NNP
37681	2193	40	'	'	POS
37681	2193	41	_	_	NNP
37681	2193	42	.	.	.
37681	2194	1	And	and	CC
37681	2194	2	since	since	IN
37681	2194	3	_	_	NNP
37681	2194	4	PM	PM	NNP
37681	2194	5	_	_	NNP
37681	2194	6	=	=	SYM
37681	2194	7	_	_	NNP
37681	2194	8	MQ	MQ	NNP
37681	2194	9	_	_	NNP
37681	2194	10	,	,	,
37681	2194	11	therefore	therefore	RB
37681	2194	12	_	_	NNP
37681	2194	13	XM	XM	NNP
37681	2194	14	_	_	NNP
37681	2194	15	=	=	SYM
37681	2194	16	_	_	NNP
37681	2194	17	MX	MX	NNP
37681	2194	18	'	'	``
37681	2194	19	_	_	NNP
37681	2194	20	and	and	CC
37681	2194	21	_	_	NNP
37681	2194	22	Y'M	Y'M	NNP
37681	2194	23	_	_	NNP
37681	2194	24	=	=	SYM
37681	2194	25	_	_	NNP
37681	2194	26	MY	MY	NNP
37681	2194	27	_	_	NNP
37681	2194	28	.	.	.
37681	2195	1	Therefore	therefore	RB
37681	2195	2	_	_	NNP
37681	2195	3	Y'X'YX	Y'X'YX	NNP
37681	2195	4	_	_	NNP
37681	2195	5	is	be	VBZ
37681	2195	6	a	a	DT
37681	2195	7	parallelogram	parallelogram	NN
37681	2195	8	.	.	.
37681	2196	1	The	the	DT
37681	2196	2	properties	property	NNS
37681	2196	3	of	of	IN
37681	2196	4	the	the	DT
37681	2196	5	parallelogram	parallelogram	NN
37681	2196	6	are	be	VBP
37681	2196	7	often	often	RB
37681	2196	8	applied	apply	VBN
37681	2196	9	to	to	IN
37681	2196	10	proving	prove	VBG
37681	2196	11	figures	figure	NNS
37681	2196	12	of	of	IN
37681	2196	13	various	various	JJ
37681	2196	14	kinds	kind	NNS
37681	2196	15	congruent	congruent	JJ
37681	2196	16	,	,	,
37681	2196	17	or	or	CC
37681	2196	18	to	to	IN
37681	2196	19	constructing	construct	VBG
37681	2196	20	them	-PRON-	PRP
37681	2196	21	so	so	IN
37681	2196	22	that	that	IN
37681	2196	23	they	-PRON-	PRP
37681	2196	24	will	will	MD
37681	2196	25	be	be	VB
37681	2196	26	congruent	congruent	JJ
37681	2196	27	.	.	.
37681	2197	1	[	[	-LRB-
37681	2197	2	Illustration	illustration	NN
37681	2197	3	]	]	-RRB-
37681	2197	4	For	for	IN
37681	2197	5	example	example	NN
37681	2197	6	,	,	,
37681	2197	7	if	if	IN
37681	2197	8	we	-PRON-	PRP
37681	2197	9	draw	draw	VBP
37681	2197	10	_	_	NNP
37681	2197	11	A'B	A'B	NNP
37681	2197	12	'	'	''
37681	2197	13	_	_	NNP
37681	2197	14	equal	equal	JJ
37681	2197	15	and	and	CC
37681	2197	16	parallel	parallel	JJ
37681	2197	17	to	to	IN
37681	2197	18	_	_	NNP
37681	2197	19	AB	AB	NNP
37681	2197	20	_	_	NNP
37681	2197	21	,	,	,
37681	2197	22	_	_	NNP
37681	2197	23	B'C	b'c	IN
37681	2197	24	'	'	``
37681	2197	25	_	_	NNP
37681	2197	26	equal	equal	JJ
37681	2197	27	and	and	CC
37681	2197	28	parallel	parallel	JJ
37681	2197	29	to	to	IN
37681	2197	30	_	_	NNP
37681	2197	31	BC	BC	NNP
37681	2197	32	_	_	NNP
37681	2197	33	,	,	,
37681	2197	34	and	and	CC
37681	2197	35	so	so	RB
37681	2197	36	on	on	RB
37681	2197	37	,	,	,
37681	2197	38	it	-PRON-	PRP
37681	2197	39	is	be	VBZ
37681	2197	40	easily	easily	RB
37681	2197	41	proved	prove	VBN
37681	2197	42	that	that	IN
37681	2197	43	_	_	NNP
37681	2197	44	ABCD	ABCD	NNP
37681	2197	45	_	_	NNP
37681	2197	46	and	and	CC
37681	2197	47	_	_	NNP
37681	2197	48	A'B'C'D	A'B'C'D	NNP
37681	2197	49	'	'	POS
37681	2197	50	_	_	NNP
37681	2197	51	are	be	VBP
37681	2197	52	congruent	congruent	JJ
37681	2197	53	.	.	.
37681	2198	1	This	this	DT
37681	2198	2	may	may	MD
37681	2198	3	be	be	VB
37681	2198	4	done	do	VBN
37681	2198	5	by	by	IN
37681	2198	6	ordinary	ordinary	JJ
37681	2198	7	superposition	superposition	NN
37681	2198	8	,	,	,
37681	2198	9	or	or	CC
37681	2198	10	by	by	IN
37681	2198	11	sliding	slide	VBG
37681	2198	12	_	_	NNP
37681	2198	13	ABCD	ABCD	NNP
37681	2198	14	_	_	NNP
37681	2198	15	along	along	IN
37681	2198	16	the	the	DT
37681	2198	17	dotted	dotted	JJ
37681	2198	18	parallels	parallel	NNS
37681	2198	19	.	.	.
37681	2199	1	There	there	EX
37681	2199	2	are	be	VBP
37681	2199	3	many	many	JJ
37681	2199	4	applications	application	NNS
37681	2199	5	of	of	IN
37681	2199	6	this	this	DT
37681	2199	7	principle	principle	NN
37681	2199	8	of	of	IN
37681	2199	9	parallel	parallel	JJ
37681	2199	10	translation	translation	NN
37681	2199	11	in	in	IN
37681	2199	12	practical	practical	JJ
37681	2199	13	construction	construction	NN
37681	2199	14	work	work	NN
37681	2199	15	.	.	.
37681	2200	1	The	the	DT
37681	2200	2	principle	principle	NN
37681	2200	3	is	be	VBZ
37681	2200	4	more	more	RBR
37681	2200	5	far	far	RB
37681	2200	6	-	-	HYPH
37681	2200	7	reaching	reach	VBG
37681	2200	8	than	than	IN
37681	2200	9	here	here	RB
37681	2200	10	intimated	intimate	VBN
37681	2200	11	,	,	,
37681	2200	12	however	however	RB
37681	2200	13	,	,	,
37681	2200	14	and	and	CC
37681	2200	15	a	a	DT
37681	2200	16	few	few	JJ
37681	2200	17	words	word	NNS
37681	2200	18	as	as	IN
37681	2200	19	to	to	IN
37681	2200	20	its	-PRON-	PRP$
37681	2200	21	significance	significance	NN
37681	2200	22	will	will	MD
37681	2200	23	now	now	RB
37681	2200	24	be	be	VB
37681	2200	25	in	in	IN
37681	2200	26	place	place	NN
37681	2200	27	.	.	.
37681	2201	1	The	the	DT
37681	2201	2	efforts	effort	NNS
37681	2201	3	usually	usually	RB
37681	2201	4	made	make	VBN
37681	2201	5	to	to	TO
37681	2201	6	improve	improve	VB
37681	2201	7	the	the	DT
37681	2201	8	spirit	spirit	NN
37681	2201	9	of	of	IN
37681	2201	10	Euclid	Euclid	NNP
37681	2201	11	are	be	VBP
37681	2201	12	trivial	trivial	JJ
37681	2201	13	.	.	.
37681	2202	1	They	-PRON-	PRP
37681	2202	2	ordinarily	ordinarily	RB
37681	2202	3	relate	relate	VBP
37681	2202	4	to	to	IN
37681	2202	5	some	some	DT
37681	2202	6	commonplace	commonplace	JJ
37681	2202	7	change	change	NN
37681	2202	8	of	of	IN
37681	2202	9	sequence	sequence	NN
37681	2202	10	,	,	,
37681	2202	11	to	to	IN
37681	2202	12	some	some	DT
37681	2202	13	slight	slight	JJ
37681	2202	14	change	change	NN
37681	2202	15	in	in	IN
37681	2202	16	language	language	NN
37681	2202	17	,	,	,
37681	2202	18	or	or	CC
37681	2202	19	to	to	IN
37681	2202	20	some	some	DT
37681	2202	21	narrow	narrow	JJ
37681	2202	22	line	line	NN
37681	2202	23	of	of	IN
37681	2202	24	applications	application	NNS
37681	2202	25	.	.	.
37681	2203	1	Such	such	JJ
37681	2203	2	attempts	attempt	NNS
37681	2203	3	require	require	VBP
37681	2203	4	no	no	DT
37681	2203	5	particular	particular	JJ
37681	2203	6	thought	thought	NN
37681	2203	7	and	and	CC
37681	2203	8	yield	yield	VB
37681	2203	9	no	no	DT
37681	2203	10	very	very	RB
37681	2203	11	noticeable	noticeable	JJ
37681	2203	12	result	result	NN
37681	2203	13	.	.	.
37681	2204	1	But	but	CC
37681	2204	2	there	there	EX
37681	2204	3	is	be	VBZ
37681	2204	4	a	a	DT
37681	2204	5	possibility	possibility	NN
37681	2204	6	,	,	,
37681	2204	7	remote	remote	JJ
37681	2204	8	though	though	IN
37681	2204	9	it	-PRON-	PRP
37681	2204	10	may	may	MD
37681	2204	11	be	be	VB
37681	2204	12	at	at	IN
37681	2204	13	present	present	JJ
37681	2204	14	,	,	,
37681	2204	15	that	that	IN
37681	2204	16	a	a	DT
37681	2204	17	geometry	geometry	NN
37681	2204	18	will	will	MD
37681	2204	19	be	be	VB
37681	2204	20	developed	develop	VBN
37681	2204	21	that	that	WDT
37681	2204	22	will	will	MD
37681	2204	23	be	be	VB
37681	2204	24	as	as	RB
37681	2204	25	serious	serious	JJ
37681	2204	26	as	as	IN
37681	2204	27	Euclid	Euclid	NNP
37681	2204	28	's	's	POS
37681	2204	29	and	and	CC
37681	2204	30	as	as	IN
37681	2204	31	effective	effective	JJ
37681	2204	32	in	in	IN
37681	2204	33	the	the	DT
37681	2204	34	education	education	NN
37681	2204	35	of	of	IN
37681	2204	36	the	the	DT
37681	2204	37	thinking	think	VBG
37681	2204	38	individual	individual	NN
37681	2204	39	.	.	.
37681	2205	1	If	if	IN
37681	2205	2	so	so	RB
37681	2205	3	,	,	,
37681	2205	4	it	-PRON-	PRP
37681	2205	5	seems	seem	VBZ
37681	2205	6	probable	probable	JJ
37681	2205	7	that	that	IN
37681	2205	8	it	-PRON-	PRP
37681	2205	9	will	will	MD
37681	2205	10	not	not	RB
37681	2205	11	be	be	VB
37681	2205	12	based	base	VBN
37681	2205	13	upon	upon	IN
37681	2205	14	the	the	DT
37681	2205	15	congruence	congruence	NN
37681	2205	16	of	of	IN
37681	2205	17	triangles	triangle	NNS
37681	2205	18	,	,	,
37681	2205	19	by	by	IN
37681	2205	20	which	which	WDT
37681	2205	21	so	so	RB
37681	2205	22	many	many	JJ
37681	2205	23	propositions	proposition	NNS
37681	2205	24	of	of	IN
37681	2205	25	Euclid	Euclid	NNP
37681	2205	26	are	be	VBP
37681	2205	27	proved	prove	VBN
37681	2205	28	,	,	,
37681	2205	29	but	but	CC
37681	2205	30	upon	upon	IN
37681	2205	31	certain	certain	JJ
37681	2205	32	postulates	postulate	NNS
37681	2205	33	of	of	IN
37681	2205	34	motion	motion	NN
37681	2205	35	,	,	,
37681	2205	36	of	of	IN
37681	2205	37	which	which	WDT
37681	2205	38	one	one	NN
37681	2205	39	is	be	VBZ
37681	2205	40	involved	involve	VBN
37681	2205	41	in	in	IN
37681	2205	42	the	the	DT
37681	2205	43	above	above	IN
37681	2205	44	illustration,--the	illustration,--the	PRP$
37681	2205	45	postulate	postulate	NN
37681	2205	46	of	of	IN
37681	2205	47	parallel	parallel	JJ
37681	2205	48	translation	translation	NN
37681	2205	49	.	.	.
37681	2206	1	If	if	IN
37681	2206	2	to	to	IN
37681	2206	3	this	this	DT
37681	2206	4	we	-PRON-	PRP
37681	2206	5	join	join	VBP
37681	2206	6	the	the	DT
37681	2206	7	two	two	CD
37681	2206	8	postulates	postulate	NNS
37681	2206	9	of	of	IN
37681	2206	10	rotation	rotation	NN
37681	2206	11	about	about	IN
37681	2206	12	an	an	DT
37681	2206	13	axis,[64	axis,[64	NN
37681	2206	14	]	]	-RRB-
37681	2206	15	leading	lead	VBG
37681	2206	16	to	to	IN
37681	2206	17	axial	axial	JJ
37681	2206	18	symmetry	symmetry	NN
37681	2206	19	;	;	:
37681	2206	20	and	and	CC
37681	2206	21	rotation	rotation	NN
37681	2206	22	about	about	IN
37681	2206	23	a	a	DT
37681	2206	24	point,[65	point,[65	XX
37681	2206	25	]	]	-RRB-
37681	2206	26	leading	lead	VBG
37681	2206	27	to	to	TO
37681	2206	28	symmetry	symmetry	VB
37681	2206	29	with	with	IN
37681	2206	30	respect	respect	NN
37681	2206	31	to	to	IN
37681	2206	32	a	a	DT
37681	2206	33	center	center	NN
37681	2206	34	,	,	,
37681	2206	35	we	-PRON-	PRP
37681	2206	36	have	have	VBP
37681	2206	37	a	a	DT
37681	2206	38	group	group	NN
37681	2206	39	of	of	IN
37681	2206	40	three	three	CD
37681	2206	41	motions	motion	NNS
37681	2206	42	upon	upon	IN
37681	2206	43	which	which	WDT
37681	2206	44	it	-PRON-	PRP
37681	2206	45	is	be	VBZ
37681	2206	46	possible	possible	JJ
37681	2206	47	to	to	TO
37681	2206	48	base	base	VB
37681	2206	49	an	an	DT
37681	2206	50	extensive	extensive	JJ
37681	2206	51	and	and	CC
37681	2206	52	rigid	rigid	JJ
37681	2206	53	geometry	geometry	NN
37681	2206	54	.	.	.
37681	2207	1	[	[	-LRB-
37681	2207	2	66	66	CD
37681	2207	3	]	]	-RRB-
37681	2207	4	It	-PRON-	PRP
37681	2207	5	will	will	MD
37681	2207	6	be	be	VB
37681	2207	7	through	through	IN
37681	2207	8	some	some	DT
37681	2207	9	such	such	JJ
37681	2207	10	effort	effort	NN
37681	2207	11	as	as	IN
37681	2207	12	this	this	DT
37681	2207	13	,	,	,
37681	2207	14	rather	rather	RB
37681	2207	15	than	than	IN
37681	2207	16	through	through	IN
37681	2207	17	the	the	DT
37681	2207	18	weakening	weakening	NN
37681	2207	19	of	of	IN
37681	2207	20	the	the	DT
37681	2207	21	Euclid	Euclid	NNP
37681	2207	22	-	-	HYPH
37681	2207	23	Legendre	Legendre	NNP
37681	2207	24	style	style	NN
37681	2207	25	of	of	IN
37681	2207	26	geometry	geometry	NN
37681	2207	27	,	,	,
37681	2207	28	that	that	IN
37681	2207	29	any	any	DT
37681	2207	30	improvement	improvement	NN
37681	2207	31	is	be	VBZ
37681	2207	32	likely	likely	JJ
37681	2207	33	to	to	TO
37681	2207	34	come	come	VB
37681	2207	35	.	.	.
37681	2208	1	At	at	IN
37681	2208	2	present	present	NN
37681	2208	3	,	,	,
37681	2208	4	in	in	IN
37681	2208	5	America	America	NNP
37681	2208	6	,	,	,
37681	2208	7	the	the	DT
37681	2208	8	important	important	JJ
37681	2208	9	work	work	NN
37681	2208	10	for	for	IN
37681	2208	11	teachers	teacher	NNS
37681	2208	12	is	be	VBZ
37681	2208	13	to	to	TO
37681	2208	14	vitalize	vitalize	VB
37681	2208	15	the	the	DT
37681	2208	16	geometry	geometry	NN
37681	2208	17	they	-PRON-	PRP
37681	2208	18	have,--an	have,--an	VBP
37681	2208	19	effort	effort	NN
37681	2208	20	in	in	IN
37681	2208	21	which	which	WDT
37681	2208	22	there	there	EX
37681	2208	23	are	be	VBP
37681	2208	24	great	great	JJ
37681	2208	25	possibilities,--seeing	possibilities,--seee	VBG
37681	2208	26	to	to	IN
37681	2208	27	it	-PRON-	PRP
37681	2208	28	that	that	DT
37681	2208	29	geometry	geometry	NN
37681	2208	30	is	be	VBZ
37681	2208	31	not	not	RB
37681	2208	32	reduced	reduce	VBN
37681	2208	33	to	to	IN
37681	2208	34	mere	mere	JJ
37681	2208	35	froth	froth	NN
37681	2208	36	,	,	,
37681	2208	37	and	and	CC
37681	2208	38	recognizing	recognize	VBG
37681	2208	39	the	the	DT
37681	2208	40	possibility	possibility	NN
37681	2208	41	of	of	IN
37681	2208	42	another	another	DT
37681	2208	43	geometry	geometry	NN
37681	2208	44	that	that	WDT
37681	2208	45	may	may	MD
37681	2208	46	sometime	sometime	RB
37681	2208	47	replace	replace	VB
37681	2208	48	it,--a	it,--a	CD
37681	2208	49	geometry	geometry	NN
37681	2208	50	as	as	RB
37681	2208	51	rigid	rigid	JJ
37681	2208	52	,	,	,
37681	2208	53	as	as	IN
37681	2208	54	thought	thought	NN
37681	2208	55	-	-	HYPH
37681	2208	56	compelling	compel	VBG
37681	2208	57	,	,	,
37681	2208	58	as	as	IN
37681	2208	59	logical	logical	JJ
37681	2208	60	,	,	,
37681	2208	61	and	and	CC
37681	2208	62	as	as	IN
37681	2208	63	truly	truly	RB
37681	2208	64	educational	educational	JJ
37681	2208	65	.	.	.
37681	2209	1	THEOREM	THEOREM	NNP
37681	2209	2	.	.	.
37681	2210	1	_	_	NNP
37681	2210	2	The	the	DT
37681	2210	3	sum	sum	NN
37681	2210	4	of	of	IN
37681	2210	5	the	the	DT
37681	2210	6	interior	interior	JJ
37681	2210	7	angles	angle	NNS
37681	2210	8	of	of	IN
37681	2210	9	a	a	DT
37681	2210	10	polygon	polygon	NN
37681	2210	11	is	be	VBZ
37681	2210	12	equal	equal	JJ
37681	2210	13	to	to	IN
37681	2210	14	two	two	CD
37681	2210	15	right	right	JJ
37681	2210	16	angles	angle	NNS
37681	2210	17	,	,	,
37681	2210	18	taken	take	VBN
37681	2210	19	as	as	IN
37681	2210	20	many	many	JJ
37681	2210	21	times	time	NNS
37681	2210	22	less	less	RBR
37681	2210	23	two	two	CD
37681	2210	24	as	as	IN
37681	2210	25	the	the	DT
37681	2210	26	figure	figure	NN
37681	2210	27	has	have	VBZ
37681	2210	28	sides	side	NNS
37681	2210	29	.	.	.
37681	2210	30	_	_	IN
37681	2210	31	This	this	DT
37681	2210	32	interesting	interesting	JJ
37681	2210	33	generalization	generalization	NN
37681	2210	34	of	of	IN
37681	2210	35	the	the	DT
37681	2210	36	proposition	proposition	NN
37681	2210	37	about	about	IN
37681	2210	38	the	the	DT
37681	2210	39	sum	sum	NN
37681	2210	40	of	of	IN
37681	2210	41	the	the	DT
37681	2210	42	angles	angle	NNS
37681	2210	43	of	of	IN
37681	2210	44	a	a	DT
37681	2210	45	triangle	triangle	NN
37681	2210	46	is	be	VBZ
37681	2210	47	given	give	VBN
37681	2210	48	by	by	IN
37681	2210	49	Proclus	Proclus	NNP
37681	2210	50	.	.	.
37681	2211	1	There	there	EX
37681	2211	2	are	be	VBP
37681	2211	3	several	several	JJ
37681	2211	4	proofs	proof	NNS
37681	2211	5	,	,	,
37681	2211	6	but	but	CC
37681	2211	7	all	all	DT
37681	2211	8	are	be	VBP
37681	2211	9	based	base	VBN
37681	2211	10	upon	upon	IN
37681	2211	11	the	the	DT
37681	2211	12	possibility	possibility	NN
37681	2211	13	of	of	IN
37681	2211	14	dissecting	dissect	VBG
37681	2211	15	the	the	DT
37681	2211	16	polygon	polygon	NN
37681	2211	17	into	into	IN
37681	2211	18	triangles	triangle	NNS
37681	2211	19	.	.	.
37681	2212	1	The	the	DT
37681	2212	2	point	point	NN
37681	2212	3	from	from	IN
37681	2212	4	which	which	WDT
37681	2212	5	lines	line	NNS
37681	2212	6	are	be	VBP
37681	2212	7	drawn	draw	VBN
37681	2212	8	to	to	IN
37681	2212	9	the	the	DT
37681	2212	10	vertices	vertex	NNS
37681	2212	11	is	be	VBZ
37681	2212	12	usually	usually	RB
37681	2212	13	taken	take	VBN
37681	2212	14	at	at	IN
37681	2212	15	a	a	DT
37681	2212	16	vertex	vertex	NN
37681	2212	17	,	,	,
37681	2212	18	so	so	IN
37681	2212	19	that	that	IN
37681	2212	20	there	there	EX
37681	2212	21	are	be	VBP
37681	2212	22	_	_	NNP
37681	2212	23	n	n	CC
37681	2212	24	_	_	NNP
37681	2212	25	-	-	HYPH
37681	2212	26	2	2	CD
37681	2212	27	triangles	triangle	NNS
37681	2212	28	.	.	.
37681	2213	1	It	-PRON-	PRP
37681	2213	2	may	may	MD
37681	2213	3	however	however	RB
37681	2213	4	be	be	VB
37681	2213	5	taken	take	VBN
37681	2213	6	within	within	IN
37681	2213	7	the	the	DT
37681	2213	8	figure	figure	NN
37681	2213	9	,	,	,
37681	2213	10	making	make	VBG
37681	2213	11	_	_	NNP
37681	2213	12	n	n	CC
37681	2213	13	_	_	NNP
37681	2213	14	triangles	triangle	NNS
37681	2213	15	,	,	,
37681	2213	16	from	from	IN
37681	2213	17	the	the	DT
37681	2213	18	sum	sum	NN
37681	2213	19	of	of	IN
37681	2213	20	the	the	DT
37681	2213	21	angles	angle	NNS
37681	2213	22	of	of	IN
37681	2213	23	which	which	WDT
37681	2213	24	the	the	DT
37681	2213	25	four	four	CD
37681	2213	26	right	right	JJ
37681	2213	27	angles	angle	NNS
37681	2213	28	about	about	IN
37681	2213	29	the	the	DT
37681	2213	30	point	point	NN
37681	2213	31	must	must	MD
37681	2213	32	be	be	VB
37681	2213	33	subtracted	subtract	VBN
37681	2213	34	.	.	.
37681	2214	1	The	the	DT
37681	2214	2	point	point	NN
37681	2214	3	may	may	MD
37681	2214	4	even	even	RB
37681	2214	5	be	be	VB
37681	2214	6	taken	take	VBN
37681	2214	7	on	on	IN
37681	2214	8	one	one	CD
37681	2214	9	side	side	NN
37681	2214	10	,	,	,
37681	2214	11	or	or	CC
37681	2214	12	outside	outside	IN
37681	2214	13	the	the	DT
37681	2214	14	polygon	polygon	NN
37681	2214	15	,	,	,
37681	2214	16	but	but	CC
37681	2214	17	the	the	DT
37681	2214	18	proof	proof	NN
37681	2214	19	is	be	VBZ
37681	2214	20	not	not	RB
37681	2214	21	so	so	RB
37681	2214	22	simple	simple	JJ
37681	2214	23	.	.	.
37681	2215	1	Teachers	teacher	NNS
37681	2215	2	who	who	WP
37681	2215	3	desire	desire	VBP
37681	2215	4	to	to	TO
37681	2215	5	do	do	VB
37681	2215	6	so	so	RB
37681	2215	7	may	may	MD
37681	2215	8	suggest	suggest	VB
37681	2215	9	to	to	TO
37681	2215	10	particularly	particularly	RB
37681	2215	11	good	good	JJ
37681	2215	12	students	student	NNS
37681	2215	13	the	the	DT
37681	2215	14	proving	proving	NN
37681	2215	15	of	of	IN
37681	2215	16	the	the	DT
37681	2215	17	theorem	theorem	NN
37681	2215	18	for	for	IN
37681	2215	19	a	a	DT
37681	2215	20	concave	concave	NNP
37681	2215	21	polygon	polygon	NN
37681	2215	22	,	,	,
37681	2215	23	or	or	CC
37681	2215	24	even	even	RB
37681	2215	25	for	for	IN
37681	2215	26	a	a	DT
37681	2215	27	cross	cross	NN
37681	2215	28	polygon	polygon	NN
37681	2215	29	,	,	,
37681	2215	30	although	although	IN
37681	2215	31	the	the	DT
37681	2215	32	latter	latter	JJ
37681	2215	33	requires	require	VBZ
37681	2215	34	negative	negative	JJ
37681	2215	35	angles	angle	NNS
37681	2215	36	.	.	.
37681	2216	1	Some	some	DT
37681	2216	2	schools	school	NNS
37681	2216	3	have	have	VBP
37681	2216	4	transit	transit	NN
37681	2216	5	instruments	instrument	NNS
37681	2216	6	for	for	IN
37681	2216	7	the	the	DT
37681	2216	8	use	use	NN
37681	2216	9	of	of	IN
37681	2216	10	their	-PRON-	PRP$
37681	2216	11	classes	class	NNS
37681	2216	12	in	in	IN
37681	2216	13	trigonometry	trigonometry	NNP
37681	2216	14	.	.	.
37681	2217	1	In	in	IN
37681	2217	2	such	such	PDT
37681	2217	3	a	a	DT
37681	2217	4	case	case	NN
37681	2217	5	it	-PRON-	PRP
37681	2217	6	is	be	VBZ
37681	2217	7	a	a	DT
37681	2217	8	good	good	JJ
37681	2217	9	plan	plan	NN
37681	2217	10	to	to	TO
37681	2217	11	measure	measure	VB
37681	2217	12	the	the	DT
37681	2217	13	angles	angle	NNS
37681	2217	14	in	in	IN
37681	2217	15	some	some	DT
37681	2217	16	piece	piece	NN
37681	2217	17	of	of	IN
37681	2217	18	land	land	NN
37681	2217	19	so	so	IN
37681	2217	20	as	as	IN
37681	2217	21	to	to	TO
37681	2217	22	verify	verify	VB
37681	2217	23	the	the	DT
37681	2217	24	proposition	proposition	NN
37681	2217	25	,	,	,
37681	2217	26	as	as	RB
37681	2217	27	well	well	RB
37681	2217	28	as	as	IN
37681	2217	29	show	show	VB
37681	2217	30	the	the	DT
37681	2217	31	care	care	NN
37681	2217	32	that	that	WDT
37681	2217	33	must	must	MD
37681	2217	34	be	be	VB
37681	2217	35	taken	take	VBN
37681	2217	36	in	in	IN
37681	2217	37	reading	read	VBG
37681	2217	38	angles	angle	NNS
37681	2217	39	.	.	.
37681	2218	1	In	in	IN
37681	2218	2	the	the	DT
37681	2218	3	absence	absence	NN
37681	2218	4	of	of	IN
37681	2218	5	this	this	DT
37681	2218	6	exercise	exercise	NN
37681	2218	7	it	-PRON-	PRP
37681	2218	8	is	be	VBZ
37681	2218	9	well	well	JJ
37681	2218	10	to	to	TO
37681	2218	11	take	take	VB
37681	2218	12	any	any	DT
37681	2218	13	irregular	irregular	JJ
37681	2218	14	polygon	polygon	NN
37681	2218	15	and	and	CC
37681	2218	16	measure	measure	VB
37681	2218	17	the	the	DT
37681	2218	18	angles	angle	NNS
37681	2218	19	by	by	IN
37681	2218	20	the	the	DT
37681	2218	21	help	help	NN
37681	2218	22	of	of	IN
37681	2218	23	a	a	DT
37681	2218	24	protractor	protractor	NN
37681	2218	25	,	,	,
37681	2218	26	and	and	CC
37681	2218	27	thus	thus	RB
37681	2218	28	accomplish	accomplish	VB
37681	2218	29	the	the	DT
37681	2218	30	same	same	JJ
37681	2218	31	results	result	NNS
37681	2218	32	.	.	.
37681	2219	1	THEOREM	THEOREM	NNP
37681	2219	2	.	.	.
37681	2220	1	_	_	NNP
37681	2220	2	The	the	DT
37681	2220	3	sum	sum	NN
37681	2220	4	of	of	IN
37681	2220	5	the	the	DT
37681	2220	6	exterior	exterior	JJ
37681	2220	7	angles	angle	NNS
37681	2220	8	of	of	IN
37681	2220	9	a	a	DT
37681	2220	10	polygon	polygon	NN
37681	2220	11	,	,	,
37681	2220	12	made	make	VBN
37681	2220	13	by	by	IN
37681	2220	14	producing	produce	VBG
37681	2220	15	each	each	DT
37681	2220	16	of	of	IN
37681	2220	17	its	-PRON-	PRP$
37681	2220	18	sides	side	NNS
37681	2220	19	in	in	IN
37681	2220	20	succession	succession	NN
37681	2220	21	,	,	,
37681	2220	22	is	be	VBZ
37681	2220	23	equal	equal	JJ
37681	2220	24	to	to	IN
37681	2220	25	four	four	CD
37681	2220	26	right	right	JJ
37681	2220	27	angles	angle	NNS
37681	2220	28	.	.	.
37681	2220	29	_	_	NNP
37681	2220	30	This	this	DT
37681	2220	31	is	be	VBZ
37681	2220	32	also	also	RB
37681	2220	33	a	a	DT
37681	2220	34	proposition	proposition	NN
37681	2220	35	not	not	RB
37681	2220	36	given	give	VBN
37681	2220	37	by	by	IN
37681	2220	38	the	the	DT
37681	2220	39	ancient	ancient	JJ
37681	2220	40	writers	writer	NNS
37681	2220	41	.	.	.
37681	2221	1	We	-PRON-	PRP
37681	2221	2	have	have	VBP
37681	2221	3	,	,	,
37681	2221	4	however	however	RB
37681	2221	5	,	,	,
37681	2221	6	no	no	DT
37681	2221	7	more	more	RBR
37681	2221	8	valuable	valuable	JJ
37681	2221	9	theorem	theorem	NN
37681	2221	10	for	for	IN
37681	2221	11	the	the	DT
37681	2221	12	purpose	purpose	NN
37681	2221	13	of	of	IN
37681	2221	14	showing	show	VBG
37681	2221	15	the	the	DT
37681	2221	16	nature	nature	NN
37681	2221	17	and	and	CC
37681	2221	18	significance	significance	NN
37681	2221	19	of	of	IN
37681	2221	20	the	the	DT
37681	2221	21	negative	negative	JJ
37681	2221	22	angle	angle	NN
37681	2221	23	;	;	:
37681	2221	24	and	and	CC
37681	2221	25	teachers	teacher	NNS
37681	2221	26	may	may	MD
37681	2221	27	arouse	arouse	VB
37681	2221	28	a	a	DT
37681	2221	29	great	great	JJ
37681	2221	30	deal	deal	NN
37681	2221	31	of	of	IN
37681	2221	32	interest	interest	NN
37681	2221	33	in	in	IN
37681	2221	34	the	the	DT
37681	2221	35	negative	negative	JJ
37681	2221	36	quantity	quantity	NN
37681	2221	37	by	by	IN
37681	2221	38	showing	show	VBG
37681	2221	39	to	to	IN
37681	2221	40	a	a	DT
37681	2221	41	class	class	NN
37681	2221	42	that	that	WDT
37681	2221	43	when	when	WRB
37681	2221	44	an	an	DT
37681	2221	45	interior	interior	JJ
37681	2221	46	angle	angle	NN
37681	2221	47	becomes	become	VBZ
37681	2221	48	180	180	CD
37681	2221	49	°	°	NNS
37681	2221	50	the	the	DT
37681	2221	51	exterior	exterior	NNP
37681	2221	52	angle	angle	NN
37681	2221	53	becomes	become	VBZ
37681	2221	54	0	0	CD
37681	2221	55	,	,	,
37681	2221	56	and	and	CC
37681	2221	57	when	when	WRB
37681	2221	58	the	the	DT
37681	2221	59	polygon	polygon	NN
37681	2221	60	becomes	become	VBZ
37681	2221	61	concave	concave	NNP
37681	2221	62	the	the	DT
37681	2221	63	exterior	exterior	NNP
37681	2221	64	angle	angle	NN
37681	2221	65	becomes	become	VBZ
37681	2221	66	negative	negative	JJ
37681	2221	67	,	,	,
37681	2221	68	the	the	DT
37681	2221	69	theorem	theorem	NN
37681	2221	70	holding	hold	VBG
37681	2221	71	for	for	IN
37681	2221	72	all	all	PDT
37681	2221	73	these	these	DT
37681	2221	74	cases	case	NNS
37681	2221	75	.	.	.
37681	2222	1	We	-PRON-	PRP
37681	2222	2	have	have	VBP
37681	2222	3	few	few	JJ
37681	2222	4	better	well	JJR
37681	2222	5	illustrations	illustration	NNS
37681	2222	6	of	of	IN
37681	2222	7	the	the	DT
37681	2222	8	significance	significance	NN
37681	2222	9	of	of	IN
37681	2222	10	the	the	DT
37681	2222	11	negative	negative	JJ
37681	2222	12	quantity	quantity	NN
37681	2222	13	,	,	,
37681	2222	14	and	and	CC
37681	2222	15	few	few	JJ
37681	2222	16	better	well	JJR
37681	2222	17	opportunities	opportunity	NNS
37681	2222	18	to	to	TO
37681	2222	19	use	use	VB
37681	2222	20	the	the	DT
37681	2222	21	knowledge	knowledge	NN
37681	2222	22	of	of	IN
37681	2222	23	this	this	DT
37681	2222	24	kind	kind	NN
37681	2222	25	of	of	IN
37681	2222	26	quantity	quantity	NN
37681	2222	27	already	already	RB
37681	2222	28	acquired	acquire	VBN
37681	2222	29	in	in	IN
37681	2222	30	algebra	algebra	NN
37681	2222	31	.	.	.
37681	2223	1	[	[	-LRB-
37681	2223	2	Illustration	illustration	NN
37681	2223	3	]	]	-RRB-
37681	2223	4	In	in	IN
37681	2223	5	the	the	DT
37681	2223	6	hilly	hilly	JJ
37681	2223	7	and	and	CC
37681	2223	8	mountainous	mountainous	JJ
37681	2223	9	parts	part	NNS
37681	2223	10	of	of	IN
37681	2223	11	America	America	NNP
37681	2223	12	,	,	,
37681	2223	13	where	where	WRB
37681	2223	14	irregular	irregular	NN
37681	2223	15	-	-	HYPH
37681	2223	16	shaped	shape	VBN
37681	2223	17	fields	field	NNS
37681	2223	18	are	be	VBP
37681	2223	19	more	more	RBR
37681	2223	20	common	common	JJ
37681	2223	21	than	than	IN
37681	2223	22	in	in	IN
37681	2223	23	the	the	DT
37681	2223	24	more	more	JJR
37681	2223	25	level	level	NN
37681	2223	26	portions	portion	NNS
37681	2223	27	,	,	,
37681	2223	28	a	a	DT
37681	2223	29	common	common	JJ
37681	2223	30	test	test	NN
37681	2223	31	for	for	IN
37681	2223	32	a	a	DT
37681	2223	33	survey	survey	NN
37681	2223	34	is	be	VBZ
37681	2223	35	that	that	DT
37681	2223	36	of	of	IN
37681	2223	37	finding	find	VBG
37681	2223	38	the	the	DT
37681	2223	39	exterior	exterior	NNP
37681	2223	40	angles	angle	NNS
37681	2223	41	when	when	WRB
37681	2223	42	the	the	DT
37681	2223	43	transit	transit	NN
37681	2223	44	instrument	instrument	NN
37681	2223	45	is	be	VBZ
37681	2223	46	set	set	VBN
37681	2223	47	at	at	IN
37681	2223	48	the	the	DT
37681	2223	49	corners	corner	NNS
37681	2223	50	.	.	.
37681	2224	1	In	in	IN
37681	2224	2	this	this	DT
37681	2224	3	field	field	NN
37681	2224	4	these	these	DT
37681	2224	5	angles	angle	NNS
37681	2224	6	are	be	VBP
37681	2224	7	given	give	VBN
37681	2224	8	,	,	,
37681	2224	9	and	and	CC
37681	2224	10	it	-PRON-	PRP
37681	2224	11	will	will	MD
37681	2224	12	be	be	VB
37681	2224	13	seen	see	VBN
37681	2224	14	that	that	IN
37681	2224	15	the	the	DT
37681	2224	16	sum	sum	NN
37681	2224	17	is	be	VBZ
37681	2224	18	360	360	CD
37681	2224	19	°	°	NNS
37681	2224	20	.	.	.
37681	2225	1	In	in	IN
37681	2225	2	the	the	DT
37681	2225	3	absence	absence	NN
37681	2225	4	of	of	IN
37681	2225	5	any	any	DT
37681	2225	6	outdoor	outdoor	JJ
37681	2225	7	work	work	NN
37681	2225	8	a	a	DT
37681	2225	9	protractor	protractor	NN
37681	2225	10	may	may	MD
37681	2225	11	be	be	VB
37681	2225	12	used	use	VBN
37681	2225	13	to	to	TO
37681	2225	14	measure	measure	VB
37681	2225	15	the	the	DT
37681	2225	16	exterior	exterior	JJ
37681	2225	17	angles	angle	NNS
37681	2225	18	of	of	IN
37681	2225	19	a	a	DT
37681	2225	20	polygon	polygon	NN
37681	2225	21	drawn	draw	VBN
37681	2225	22	on	on	IN
37681	2225	23	paper	paper	NN
37681	2225	24	.	.	.
37681	2226	1	If	if	IN
37681	2226	2	there	there	EX
37681	2226	3	is	be	VBZ
37681	2226	4	an	an	DT
37681	2226	5	irregular	irregular	JJ
37681	2226	6	piece	piece	NN
37681	2226	7	of	of	IN
37681	2226	8	land	land	NN
37681	2226	9	near	near	IN
37681	2226	10	the	the	DT
37681	2226	11	school	school	NN
37681	2226	12	,	,	,
37681	2226	13	the	the	DT
37681	2226	14	exterior	exterior	NN
37681	2226	15	angles	angle	NNS
37681	2226	16	can	can	MD
37681	2226	17	be	be	VB
37681	2226	18	fairly	fairly	RB
37681	2226	19	well	well	RB
37681	2226	20	measured	measure	VBN
37681	2226	21	by	by	IN
37681	2226	22	an	an	DT
37681	2226	23	ordinary	ordinary	JJ
37681	2226	24	paper	paper	NN
37681	2226	25	protractor	protractor	NN
37681	2226	26	.	.	.
37681	2227	1	The	the	DT
37681	2227	2	idea	idea	NN
37681	2227	3	of	of	IN
37681	2227	4	locus	locus	NN
37681	2227	5	is	be	VBZ
37681	2227	6	usually	usually	RB
37681	2227	7	introduced	introduce	VBN
37681	2227	8	at	at	IN
37681	2227	9	the	the	DT
37681	2227	10	end	end	NN
37681	2227	11	of	of	IN
37681	2227	12	Book	Book	NNP
37681	2227	13	I.	i.	NN
37681	2228	1	It	-PRON-	PRP
37681	2228	2	is	be	VBZ
37681	2228	3	too	too	RB
37681	2228	4	abstract	abstract	JJ
37681	2228	5	to	to	TO
37681	2228	6	be	be	VB
37681	2228	7	introduced	introduce	VBN
37681	2228	8	successfully	successfully	RB
37681	2228	9	any	any	RB
37681	2228	10	earlier	early	RBR
37681	2228	11	,	,	,
37681	2228	12	although	although	IN
37681	2228	13	authors	author	NNS
37681	2228	14	repeat	repeat	VBP
37681	2228	15	the	the	DT
37681	2228	16	attempt	attempt	NN
37681	2228	17	from	from	IN
37681	2228	18	time	time	NN
37681	2228	19	to	to	IN
37681	2228	20	time	time	NN
37681	2228	21	,	,	,
37681	2228	22	unmindful	unmindful	JJ
37681	2228	23	of	of	IN
37681	2228	24	the	the	DT
37681	2228	25	fact	fact	NN
37681	2228	26	that	that	IN
37681	2228	27	all	all	DT
37681	2228	28	experience	experience	NN
37681	2228	29	is	be	VBZ
37681	2228	30	opposed	opposed	JJ
37681	2228	31	to	to	IN
37681	2228	32	it	-PRON-	PRP
37681	2228	33	.	.	.
37681	2229	1	The	the	DT
37681	2229	2	loci	loci	NN
37681	2229	3	propositions	proposition	NNS
37681	2229	4	are	be	VBP
37681	2229	5	not	not	RB
37681	2229	6	ancient	ancient	JJ
37681	2229	7	.	.	.
37681	2230	1	The	the	DT
37681	2230	2	Greeks	Greeks	NNPS
37681	2230	3	used	use	VBD
37681	2230	4	the	the	DT
37681	2230	5	word	word	NN
37681	2230	6	"	"	``
37681	2230	7	locus	locus	NN
37681	2230	8	"	"	''
37681	2230	9	(	(	-LRB-
37681	2230	10	in	in	IN
37681	2230	11	Greek	Greek	NNP
37681	2230	12	,	,	,
37681	2230	13	_	_	NNP
37681	2230	14	topos	topos	NNP
37681	2230	15	_	_	NNP
37681	2230	16	)	)	-RRB-
37681	2230	17	,	,	,
37681	2230	18	however	however	RB
37681	2230	19	.	.	.
37681	2231	1	Proclus	Proclus	NNP
37681	2231	2	,	,	,
37681	2231	3	for	for	IN
37681	2231	4	example	example	NN
37681	2231	5	,	,	,
37681	2231	6	says	say	VBZ
37681	2231	7	,	,	,
37681	2231	8	"	"	``
37681	2231	9	I	-PRON-	PRP
37681	2231	10	call	call	VBP
37681	2231	11	those	those	DT
37681	2231	12	locus	locus	NN
37681	2231	13	theorems	theorem	NNS
37681	2231	14	in	in	IN
37681	2231	15	which	which	WDT
37681	2231	16	the	the	DT
37681	2231	17	same	same	JJ
37681	2231	18	property	property	NN
37681	2231	19	is	be	VBZ
37681	2231	20	found	find	VBN
37681	2231	21	to	to	TO
37681	2231	22	exist	exist	VB
37681	2231	23	on	on	IN
37681	2231	24	the	the	DT
37681	2231	25	whole	whole	NN
37681	2231	26	of	of	IN
37681	2231	27	some	some	DT
37681	2231	28	locus	locus	NN
37681	2231	29	.	.	.
37681	2231	30	"	"	''
37681	2232	1	Teachers	teacher	NNS
37681	2232	2	should	should	MD
37681	2232	3	be	be	VB
37681	2232	4	careful	careful	JJ
37681	2232	5	to	to	TO
37681	2232	6	have	have	VB
37681	2232	7	the	the	DT
37681	2232	8	pupils	pupil	NNS
37681	2232	9	recognize	recognize	VB
37681	2232	10	the	the	DT
37681	2232	11	necessity	necessity	NN
37681	2232	12	for	for	IN
37681	2232	13	proving	prove	VBG
37681	2232	14	two	two	CD
37681	2232	15	things	thing	NNS
37681	2232	16	with	with	IN
37681	2232	17	respect	respect	NN
37681	2232	18	to	to	IN
37681	2232	19	any	any	DT
37681	2232	20	locus	locus	NN
37681	2232	21	:	:	:
37681	2232	22	(	(	-LRB-
37681	2232	23	1	1	LS
37681	2232	24	)	)	-RRB-
37681	2232	25	that	that	IN
37681	2232	26	any	any	DT
37681	2232	27	point	point	NN
37681	2232	28	on	on	IN
37681	2232	29	the	the	DT
37681	2232	30	supposed	suppose	VBN
37681	2232	31	locus	locus	NN
37681	2232	32	satisfies	satisfy	VBZ
37681	2232	33	the	the	DT
37681	2232	34	condition	condition	NN
37681	2232	35	;	;	,
37681	2232	36	(	(	-LRB-
37681	2232	37	2	2	LS
37681	2232	38	)	)	-RRB-
37681	2232	39	that	that	IN
37681	2232	40	any	any	DT
37681	2232	41	point	point	NN
37681	2232	42	outside	outside	IN
37681	2232	43	the	the	DT
37681	2232	44	supposed	suppose	VBN
37681	2232	45	locus	locus	NN
37681	2232	46	does	do	VBZ
37681	2232	47	not	not	RB
37681	2232	48	satisfy	satisfy	VB
37681	2232	49	the	the	DT
37681	2232	50	given	give	VBN
37681	2232	51	condition	condition	NN
37681	2232	52	.	.	.
37681	2233	1	The	the	DT
37681	2233	2	first	first	JJ
37681	2233	3	of	of	IN
37681	2233	4	these	these	DT
37681	2233	5	is	be	VBZ
37681	2233	6	called	call	VBN
37681	2233	7	the	the	DT
37681	2233	8	"	"	``
37681	2233	9	sufficient	sufficient	JJ
37681	2233	10	condition	condition	NN
37681	2233	11	,	,	,
37681	2233	12	"	"	''
37681	2233	13	and	and	CC
37681	2233	14	the	the	DT
37681	2233	15	second	second	JJ
37681	2233	16	the	the	DT
37681	2233	17	"	"	``
37681	2233	18	necessary	necessary	JJ
37681	2233	19	condition	condition	NN
37681	2233	20	.	.	.
37681	2233	21	"	"	''
37681	2234	1	Thus	thus	RB
37681	2234	2	in	in	IN
37681	2234	3	the	the	DT
37681	2234	4	case	case	NN
37681	2234	5	of	of	IN
37681	2234	6	the	the	DT
37681	2234	7	locus	locus	NN
37681	2234	8	of	of	IN
37681	2234	9	points	point	NNS
37681	2234	10	in	in	IN
37681	2234	11	a	a	DT
37681	2234	12	plane	plane	NN
37681	2234	13	equidistant	equidistant	NN
37681	2234	14	from	from	IN
37681	2234	15	two	two	CD
37681	2234	16	given	give	VBN
37681	2234	17	points	point	NNS
37681	2234	18	,	,	,
37681	2234	19	it	-PRON-	PRP
37681	2234	20	is	be	VBZ
37681	2234	21	_	_	NNP
37681	2234	22	sufficient	sufficient	JJ
37681	2234	23	_	_	NNP
37681	2234	24	that	that	IN
37681	2234	25	the	the	DT
37681	2234	26	point	point	NN
37681	2234	27	be	be	VB
37681	2234	28	on	on	IN
37681	2234	29	the	the	DT
37681	2234	30	perpendicular	perpendicular	JJ
37681	2234	31	bisector	bisector	NN
37681	2234	32	of	of	IN
37681	2234	33	the	the	DT
37681	2234	34	line	line	NN
37681	2234	35	joining	join	VBG
37681	2234	36	the	the	DT
37681	2234	37	given	give	VBN
37681	2234	38	points	point	NNS
37681	2234	39	,	,	,
37681	2234	40	and	and	CC
37681	2234	41	this	this	DT
37681	2234	42	is	be	VBZ
37681	2234	43	the	the	DT
37681	2234	44	first	first	JJ
37681	2234	45	part	part	NN
37681	2234	46	of	of	IN
37681	2234	47	the	the	DT
37681	2234	48	proof	proof	NN
37681	2234	49	;	;	:
37681	2234	50	it	-PRON-	PRP
37681	2234	51	is	be	VBZ
37681	2234	52	also	also	RB
37681	2234	53	_	_	NNP
37681	2234	54	necessary	necessary	JJ
37681	2234	55	_	_	NNP
37681	2234	56	that	that	IN
37681	2234	57	it	-PRON-	PRP
37681	2234	58	be	be	VB
37681	2234	59	on	on	IN
37681	2234	60	this	this	DT
37681	2234	61	line	line	NN
37681	2234	62	,	,	,
37681	2234	63	i.e.	i.e.	FW
37681	2235	1	it	-PRON-	PRP
37681	2235	2	can	can	MD
37681	2235	3	not	not	RB
37681	2235	4	be	be	VB
37681	2235	5	outside	outside	IN
37681	2235	6	this	this	DT
37681	2235	7	line	line	NN
37681	2235	8	,	,	,
37681	2235	9	and	and	CC
37681	2235	10	this	this	DT
37681	2235	11	is	be	VBZ
37681	2235	12	the	the	DT
37681	2235	13	second	second	JJ
37681	2235	14	part	part	NN
37681	2235	15	of	of	IN
37681	2235	16	the	the	DT
37681	2235	17	proof	proof	NN
37681	2235	18	.	.	.
37681	2236	1	The	the	DT
37681	2236	2	proof	proof	NN
37681	2236	3	of	of	IN
37681	2236	4	loci	loci	NN
37681	2236	5	cases	case	NNS
37681	2236	6	,	,	,
37681	2236	7	therefore	therefore	RB
37681	2236	8	,	,	,
37681	2236	9	involves	involve	VBZ
37681	2236	10	a	a	DT
37681	2236	11	consideration	consideration	NN
37681	2236	12	of	of	IN
37681	2236	13	"	"	``
37681	2236	14	the	the	DT
37681	2236	15	necessary	necessary	JJ
37681	2236	16	and	and	CC
37681	2236	17	sufficient	sufficient	JJ
37681	2236	18	condition	condition	NN
37681	2236	19	"	"	''
37681	2236	20	that	that	WDT
37681	2236	21	is	be	VBZ
37681	2236	22	so	so	RB
37681	2236	23	often	often	RB
37681	2236	24	spoken	speak	VBN
37681	2236	25	of	of	IN
37681	2236	26	in	in	IN
37681	2236	27	higher	high	JJR
37681	2236	28	mathematics	mathematic	NNS
37681	2236	29	.	.	.
37681	2237	1	This	this	DT
37681	2237	2	expression	expression	NN
37681	2237	3	might	may	MD
37681	2237	4	well	well	RB
37681	2237	5	be	be	VB
37681	2237	6	incorporated	incorporate	VBN
37681	2237	7	into	into	IN
37681	2237	8	elementary	elementary	JJ
37681	2237	9	geometry	geometry	NN
37681	2237	10	,	,	,
37681	2237	11	and	and	CC
37681	2237	12	when	when	WRB
37681	2237	13	it	-PRON-	PRP
37681	2237	14	becomes	become	VBZ
37681	2237	15	better	well	RBR
37681	2237	16	understood	understand	VBN
37681	2237	17	by	by	IN
37681	2237	18	teachers	teacher	NNS
37681	2237	19	,	,	,
37681	2237	20	it	-PRON-	PRP
37681	2237	21	probably	probably	RB
37681	2237	22	will	will	MD
37681	2237	23	be	be	VB
37681	2237	24	more	more	RBR
37681	2237	25	often	often	RB
37681	2237	26	used	use	VBN
37681	2237	27	.	.	.
37681	2238	1	In	in	IN
37681	2238	2	teaching	teaching	NN
37681	2238	3	loci	loci	NN
37681	2238	4	it	-PRON-	PRP
37681	2238	5	is	be	VBZ
37681	2238	6	helpful	helpful	JJ
37681	2238	7	to	to	TO
37681	2238	8	call	call	VB
37681	2238	9	attention	attention	NN
37681	2238	10	to	to	IN
37681	2238	11	loci	loci	NN
37681	2238	12	in	in	IN
37681	2238	13	space	space	NN
37681	2238	14	(	(	-LRB-
37681	2238	15	meaning	mean	VBG
37681	2238	16	thereby	thereby	RB
37681	2238	17	the	the	DT
37681	2238	18	space	space	NN
37681	2238	19	of	of	IN
37681	2238	20	three	three	CD
37681	2238	21	dimensions	dimension	NNS
37681	2238	22	)	)	-RRB-
37681	2238	23	,	,	,
37681	2238	24	without	without	IN
37681	2238	25	stopping	stop	VBG
37681	2238	26	to	to	TO
37681	2238	27	prove	prove	VB
37681	2238	28	the	the	DT
37681	2238	29	proposition	proposition	NN
37681	2238	30	involved	involve	VBN
37681	2238	31	.	.	.
37681	2239	1	Indeed	indeed	RB
37681	2239	2	,	,	,
37681	2239	3	it	-PRON-	PRP
37681	2239	4	is	be	VBZ
37681	2239	5	desirable	desirable	JJ
37681	2239	6	all	all	RB
37681	2239	7	through	through	IN
37681	2239	8	plane	plane	NN
37681	2239	9	geometry	geometry	NN
37681	2239	10	to	to	TO
37681	2239	11	refer	refer	VB
37681	2239	12	incidentally	incidentally	RB
37681	2239	13	to	to	IN
37681	2239	14	solid	solid	JJ
37681	2239	15	geometry	geometry	NN
37681	2239	16	.	.	.
37681	2240	1	In	in	IN
37681	2240	2	the	the	DT
37681	2240	3	mensuration	mensuration	NN
37681	2240	4	of	of	IN
37681	2240	5	plane	plane	NN
37681	2240	6	figures	figure	NNS
37681	2240	7	,	,	,
37681	2240	8	which	which	WDT
37681	2240	9	may	may	MD
37681	2240	10	be	be	VB
37681	2240	11	boundaries	boundary	NNS
37681	2240	12	of	of	IN
37681	2240	13	solid	solid	JJ
37681	2240	14	figures	figure	NNS
37681	2240	15	,	,	,
37681	2240	16	this	this	DT
37681	2240	17	is	be	VBZ
37681	2240	18	particularly	particularly	RB
37681	2240	19	true	true	JJ
37681	2240	20	.	.	.
37681	2241	1	It	-PRON-	PRP
37681	2241	2	is	be	VBZ
37681	2241	3	a	a	DT
37681	2241	4	great	great	JJ
37681	2241	5	defect	defect	NN
37681	2241	6	in	in	IN
37681	2241	7	most	most	JJS
37681	2241	8	school	school	NN
37681	2241	9	courses	course	NNS
37681	2241	10	in	in	IN
37681	2241	11	geometry	geometry	NN
37681	2241	12	that	that	IN
37681	2241	13	they	-PRON-	PRP
37681	2241	14	are	be	VBP
37681	2241	15	entirely	entirely	RB
37681	2241	16	confined	confine	VBN
37681	2241	17	to	to	IN
37681	2241	18	two	two	CD
37681	2241	19	dimensions	dimension	NNS
37681	2241	20	.	.	.
37681	2242	1	Even	even	RB
37681	2242	2	if	if	IN
37681	2242	3	solid	solid	JJ
37681	2242	4	geometry	geometry	NN
37681	2242	5	in	in	IN
37681	2242	6	the	the	DT
37681	2242	7	usual	usual	JJ
37681	2242	8	sense	sense	NN
37681	2242	9	is	be	VBZ
37681	2242	10	not	not	RB
37681	2242	11	attempted	attempt	VBN
37681	2242	12	,	,	,
37681	2242	13	every	every	DT
37681	2242	14	occasion	occasion	NN
37681	2242	15	should	should	MD
37681	2242	16	be	be	VB
37681	2242	17	taken	take	VBN
37681	2242	18	to	to	TO
37681	2242	19	liberate	liberate	VB
37681	2242	20	boys	boy	NNS
37681	2242	21	'	'	POS
37681	2242	22	minds	mind	NNS
37681	2242	23	from	from	IN
37681	2242	24	what	what	WP
37681	2242	25	becomes	become	VBZ
37681	2242	26	the	the	DT
37681	2242	27	tyranny	tyranny	NN
37681	2242	28	of	of	IN
37681	2242	29	paper	paper	NN
37681	2242	30	.	.	.
37681	2243	1	Thus	thus	RB
37681	2243	2	the	the	DT
37681	2243	3	questions	question	NNS
37681	2243	4	:	:	:
37681	2243	5	"	"	``
37681	2243	6	What	what	WP
37681	2243	7	is	be	VBZ
37681	2243	8	the	the	DT
37681	2243	9	locus	locus	NN
37681	2243	10	of	of	IN
37681	2243	11	a	a	DT
37681	2243	12	point	point	NN
37681	2243	13	equidistant	equidistant	NN
37681	2243	14	from	from	IN
37681	2243	15	two	two	CD
37681	2243	16	given	give	VBN
37681	2243	17	points	point	NNS
37681	2243	18	;	;	:
37681	2243	19	at	at	IN
37681	2243	20	a	a	DT
37681	2243	21	constant	constant	JJ
37681	2243	22	distance	distance	NN
37681	2243	23	from	from	IN
37681	2243	24	a	a	DT
37681	2243	25	given	give	VBN
37681	2243	26	straight	straight	JJ
37681	2243	27	line	line	NN
37681	2243	28	or	or	CC
37681	2243	29	from	from	IN
37681	2243	30	a	a	DT
37681	2243	31	given	give	VBN
37681	2243	32	point	point	NN
37681	2243	33	?	?	.
37681	2243	34	"	"	''
37681	2244	1	should	should	MD
37681	2244	2	be	be	VB
37681	2244	3	extended	extend	VBN
37681	2244	4	to	to	IN
37681	2244	5	space	space	NN
37681	2244	6	.	.	.
37681	2245	1	[	[	-LRB-
37681	2245	2	67	67	CD
37681	2245	3	]	]	-RRB-
37681	2245	4	The	the	DT
37681	2245	5	two	two	CD
37681	2245	6	loci	loci	NN
37681	2245	7	problems	problem	NNS
37681	2245	8	usually	usually	RB
37681	2245	9	given	give	VBN
37681	2245	10	at	at	IN
37681	2245	11	this	this	DT
37681	2245	12	time	time	NN
37681	2245	13	,	,	,
37681	2245	14	referring	refer	VBG
37681	2245	15	to	to	IN
37681	2245	16	a	a	DT
37681	2245	17	point	point	NN
37681	2245	18	equidistant	equidistant	NN
37681	2245	19	from	from	IN
37681	2245	20	the	the	DT
37681	2245	21	extremities	extremity	NNS
37681	2245	22	of	of	IN
37681	2245	23	a	a	DT
37681	2245	24	given	give	VBN
37681	2245	25	line	line	NN
37681	2245	26	,	,	,
37681	2245	27	and	and	CC
37681	2245	28	to	to	IN
37681	2245	29	a	a	DT
37681	2245	30	point	point	NN
37681	2245	31	equidistant	equidistant	NN
37681	2245	32	from	from	IN
37681	2245	33	two	two	CD
37681	2245	34	intersecting	intersect	VBG
37681	2245	35	lines	line	NNS
37681	2245	36	,	,	,
37681	2245	37	both	both	DT
37681	2245	38	permit	permit	NN
37681	2245	39	of	of	IN
37681	2245	40	an	an	DT
37681	2245	41	interesting	interesting	JJ
37681	2245	42	extension	extension	NN
37681	2245	43	to	to	IN
37681	2245	44	three	three	CD
37681	2245	45	dimensions	dimension	NNS
37681	2245	46	without	without	IN
37681	2245	47	any	any	DT
37681	2245	48	formal	formal	JJ
37681	2245	49	proof	proof	NN
37681	2245	50	.	.	.
37681	2246	1	It	-PRON-	PRP
37681	2246	2	is	be	VBZ
37681	2246	3	possible	possible	JJ
37681	2246	4	to	to	TO
37681	2246	5	give	give	VB
37681	2246	6	other	other	JJ
37681	2246	7	loci	loci	NN
37681	2246	8	at	at	IN
37681	2246	9	this	this	DT
37681	2246	10	point	point	NN
37681	2246	11	,	,	,
37681	2246	12	but	but	CC
37681	2246	13	it	-PRON-	PRP
37681	2246	14	is	be	VBZ
37681	2246	15	preferable	preferable	JJ
37681	2246	16	merely	merely	RB
37681	2246	17	to	to	TO
37681	2246	18	introduce	introduce	VB
37681	2246	19	the	the	DT
37681	2246	20	subject	subject	NN
37681	2246	21	in	in	IN
37681	2246	22	Book	Book	NNP
37681	2246	23	I	-PRON-	PRP
37681	2246	24	,	,	,
37681	2246	25	reserving	reserve	VBG
37681	2246	26	the	the	DT
37681	2246	27	further	further	JJ
37681	2246	28	discussion	discussion	NN
37681	2246	29	until	until	IN
37681	2246	30	after	after	IN
37681	2246	31	the	the	DT
37681	2246	32	circle	circle	NN
37681	2246	33	has	have	VBZ
37681	2246	34	been	be	VBN
37681	2246	35	studied	study	VBN
37681	2246	36	.	.	.
37681	2247	1	It	-PRON-	PRP
37681	2247	2	is	be	VBZ
37681	2247	3	well	well	RB
37681	2247	4	,	,	,
37681	2247	5	in	in	IN
37681	2247	6	speaking	speak	VBG
37681	2247	7	of	of	IN
37681	2247	8	loci	loci	NN
37681	2247	9	,	,	,
37681	2247	10	to	to	TO
37681	2247	11	remember	remember	VB
37681	2247	12	that	that	IN
37681	2247	13	it	-PRON-	PRP
37681	2247	14	is	be	VBZ
37681	2247	15	entirely	entirely	RB
37681	2247	16	proper	proper	JJ
37681	2247	17	to	to	TO
37681	2247	18	speak	speak	VB
37681	2247	19	of	of	IN
37681	2247	20	the	the	DT
37681	2247	21	"	"	``
37681	2247	22	locus	locus	NN
37681	2247	23	of	of	IN
37681	2247	24	a	a	DT
37681	2247	25	point	point	NN
37681	2247	26	"	"	''
37681	2247	27	or	or	CC
37681	2247	28	the	the	DT
37681	2247	29	"	"	``
37681	2247	30	locus	locus	NN
37681	2247	31	of	of	IN
37681	2247	32	points	point	NNS
37681	2247	33	.	.	.
37681	2247	34	"	"	''
37681	2248	1	Thus	thus	RB
37681	2248	2	the	the	DT
37681	2248	3	locus	locus	NN
37681	2248	4	of	of	IN
37681	2248	5	a	a	DT
37681	2248	6	_	_	NNP
37681	2248	7	point	point	NN
37681	2248	8	_	_	NNP
37681	2248	9	so	so	RB
37681	2248	10	moving	move	VBG
37681	2248	11	in	in	IN
37681	2248	12	a	a	DT
37681	2248	13	plane	plane	NN
37681	2248	14	as	as	RB
37681	2248	15	constantly	constantly	RB
37681	2248	16	to	to	TO
37681	2248	17	be	be	VB
37681	2248	18	at	at	IN
37681	2248	19	a	a	DT
37681	2248	20	given	give	VBN
37681	2248	21	distance	distance	NN
37681	2248	22	from	from	IN
37681	2248	23	a	a	DT
37681	2248	24	fixed	fix	VBN
37681	2248	25	point	point	NN
37681	2248	26	in	in	IN
37681	2248	27	the	the	DT
37681	2248	28	plane	plane	NN
37681	2248	29	is	be	VBZ
37681	2248	30	a	a	DT
37681	2248	31	circle	circle	NN
37681	2248	32	.	.	.
37681	2249	1	In	in	IN
37681	2249	2	analytic	analytic	JJ
37681	2249	3	geometry	geometry	NN
37681	2249	4	we	-PRON-	PRP
37681	2249	5	usually	usually	RB
37681	2249	6	speak	speak	VBP
37681	2249	7	of	of	IN
37681	2249	8	the	the	DT
37681	2249	9	locus	locus	NN
37681	2249	10	of	of	IN
37681	2249	11	a	a	DT
37681	2249	12	_	_	NNP
37681	2249	13	point	point	NN
37681	2249	14	_	_	NNP
37681	2249	15	,	,	,
37681	2249	16	thinking	think	VBG
37681	2249	17	of	of	IN
37681	2249	18	the	the	DT
37681	2249	19	point	point	NN
37681	2249	20	as	as	IN
37681	2249	21	being	be	VBG
37681	2249	22	anywhere	anywhere	RB
37681	2249	23	on	on	IN
37681	2249	24	the	the	DT
37681	2249	25	locus	locus	NN
37681	2249	26	.	.	.
37681	2250	1	Some	some	DT
37681	2250	2	teachers	teacher	NNS
37681	2250	3	of	of	IN
37681	2250	4	elementary	elementary	JJ
37681	2250	5	geometry	geometry	NN
37681	2250	6	,	,	,
37681	2250	7	however	however	RB
37681	2250	8	,	,	,
37681	2250	9	prefer	prefer	VBP
37681	2250	10	to	to	TO
37681	2250	11	speak	speak	VB
37681	2250	12	of	of	IN
37681	2250	13	the	the	DT
37681	2250	14	locus	locus	NN
37681	2250	15	of	of	IN
37681	2250	16	_	_	NNP
37681	2250	17	points	point	NNS
37681	2250	18	_	_	NNP
37681	2250	19	,	,	,
37681	2250	20	or	or	CC
37681	2250	21	the	the	DT
37681	2250	22	locus	locus	NN
37681	2250	23	of	of	IN
37681	2250	24	_	_	NNP
37681	2250	25	all	all	DT
37681	2250	26	points	point	NNS
37681	2250	27	_	_	NNP
37681	2250	28	,	,	,
37681	2250	29	thus	thus	RB
37681	2250	30	tending	tend	VBG
37681	2250	31	to	to	TO
37681	2250	32	make	make	VB
37681	2250	33	the	the	DT
37681	2250	34	language	language	NN
37681	2250	35	of	of	IN
37681	2250	36	elementary	elementary	JJ
37681	2250	37	geometry	geometry	NN
37681	2250	38	differ	differ	VBP
37681	2250	39	from	from	IN
37681	2250	40	that	that	DT
37681	2250	41	of	of	IN
37681	2250	42	analytic	analytic	JJ
37681	2250	43	geometry	geometry	NN
37681	2250	44	.	.	.
37681	2251	1	Since	since	IN
37681	2251	2	it	-PRON-	PRP
37681	2251	3	is	be	VBZ
37681	2251	4	a	a	DT
37681	2251	5	trivial	trivial	JJ
37681	2251	6	matter	matter	NN
37681	2251	7	of	of	IN
37681	2251	8	phraseology	phraseology	NN
37681	2251	9	,	,	,
37681	2251	10	it	-PRON-	PRP
37681	2251	11	is	be	VBZ
37681	2251	12	better	well	JJR
37681	2251	13	to	to	TO
37681	2251	14	recognize	recognize	VB
37681	2251	15	both	both	DT
37681	2251	16	forms	form	NNS
37681	2251	17	of	of	IN
37681	2251	18	expression	expression	NN
37681	2251	19	and	and	CC
37681	2251	20	to	to	TO
37681	2251	21	let	let	VB
37681	2251	22	pupils	pupil	NNS
37681	2251	23	use	use	VB
37681	2251	24	the	the	DT
37681	2251	25	two	two	CD
37681	2251	26	interchangeably	interchangeably	RB
37681	2251	27	.	.	.
37681	2252	1	FOOTNOTES	footnote	NNS
37681	2252	2	:	:	:
37681	2252	3	[	[	-LRB-
37681	2252	4	57	57	CD
37681	2252	5	]	]	-RRB-
37681	2252	6	Address	address	NN
37681	2252	7	at	at	IN
37681	2252	8	Brussels	Brussels	NNP
37681	2252	9	,	,	,
37681	2252	10	August	August	NNP
37681	2252	11	,	,	,
37681	2252	12	1910	1910	CD
37681	2252	13	.	.	.
37681	2253	1	[	[	-LRB-
37681	2253	2	58	58	CD
37681	2253	3	]	]	-RRB-
37681	2253	4	For	for	IN
37681	2253	5	a	a	DT
37681	2253	6	recent	recent	JJ
37681	2253	7	discussion	discussion	NN
37681	2253	8	of	of	IN
37681	2253	9	this	this	DT
37681	2253	10	general	general	JJ
37681	2253	11	subject	subject	NN
37681	2253	12	,	,	,
37681	2253	13	see	see	VB
37681	2253	14	Professor	Professor	NNP
37681	2253	15	Hobson	Hobson	NNP
37681	2253	16	on	on	IN
37681	2253	17	"	"	``
37681	2253	18	The	the	DT
37681	2253	19	Tendencies	tendency	NNS
37681	2253	20	of	of	IN
37681	2253	21	Modern	Modern	NNP
37681	2253	22	Mathematics	Mathematics	NNP
37681	2253	23	,	,	,
37681	2253	24	"	"	''
37681	2253	25	in	in	IN
37681	2253	26	the	the	DT
37681	2253	27	_	_	NNP
37681	2253	28	Educational	Educational	NNP
37681	2253	29	Review	Review	NNP
37681	2253	30	_	_	NNP
37681	2253	31	,	,	,
37681	2253	32	New	New	NNP
37681	2253	33	York	York	NNP
37681	2253	34	,	,	,
37681	2253	35	1910	1910	CD
37681	2253	36	,	,	,
37681	2253	37	Vol	Vol	NNP
37681	2253	38	.	.	.
37681	2254	1	XL	XL	NNP
37681	2254	2	,	,	,
37681	2254	3	p.	p.	NN
37681	2254	4	524	524	CD
37681	2254	5	.	.	.
37681	2255	1	[	[	-LRB-
37681	2255	2	59	59	CD
37681	2255	3	]	]	-RRB-
37681	2255	4	A	a	DT
37681	2255	5	more	more	RBR
37681	2255	6	extended	extended	JJ
37681	2255	7	list	list	NN
37681	2255	8	of	of	IN
37681	2255	9	applications	application	NNS
37681	2255	10	is	be	VBZ
37681	2255	11	given	give	VBN
37681	2255	12	later	later	RB
37681	2255	13	in	in	IN
37681	2255	14	this	this	DT
37681	2255	15	work	work	NN
37681	2255	16	.	.	.
37681	2256	1	[	[	-LRB-
37681	2256	2	60	60	CD
37681	2256	3	]	]	-RRB-
37681	2256	4	Ab[=u]'l-'Abb[=a]s	ab[=u]'l-'abb[=a]s	FW
37681	2256	5	al	al	NNP
37681	2256	6	-	-	HYPH
37681	2256	7	Fadl	Fadl	NNP
37681	2256	8	ibn	ibn	NNP
37681	2256	9	H[=a]tim	H[=a]tim	NNP
37681	2256	10	al	al	NNP
37681	2256	11	-	-	HYPH
37681	2256	12	Nair[=i]z[=i	Nair[=i]z[=i	NNP
37681	2256	13	]	]	-RRB-
37681	2256	14	,	,	,
37681	2256	15	so	so	RB
37681	2256	16	called	call	VBD
37681	2256	17	from	from	IN
37681	2256	18	his	-PRON-	PRP$
37681	2256	19	birthplace	birthplace	NN
37681	2256	20	,	,	,
37681	2256	21	Nair[=i]z	Nair[=i]z	NNP
37681	2256	22	,	,	,
37681	2256	23	was	be	VBD
37681	2256	24	a	a	DT
37681	2256	25	well	well	RB
37681	2256	26	-	-	HYPH
37681	2256	27	known	know	VBN
37681	2256	28	Arab	arab	JJ
37681	2256	29	writer	writer	NN
37681	2256	30	.	.	.
37681	2257	1	He	-PRON-	PRP
37681	2257	2	died	die	VBD
37681	2257	3	about	about	IN
37681	2257	4	922	922	CD
37681	2257	5	A.D.	A.D.	NNP
37681	2258	1	He	-PRON-	PRP
37681	2258	2	wrote	write	VBD
37681	2258	3	a	a	DT
37681	2258	4	commentary	commentary	NN
37681	2258	5	on	on	IN
37681	2258	6	Euclid	Euclid	NNP
37681	2258	7	.	.	.
37681	2259	1	[	[	-LRB-
37681	2259	2	61	61	CD
37681	2259	3	]	]	-RRB-
37681	2259	4	This	this	DT
37681	2259	5	illustration	illustration	NN
37681	2259	6	,	,	,
37681	2259	7	taken	take	VBN
37681	2259	8	from	from	IN
37681	2259	9	a	a	DT
37681	2259	10	book	book	NN
37681	2259	11	in	in	IN
37681	2259	12	the	the	DT
37681	2259	13	author	author	NN
37681	2259	14	's	's	POS
37681	2259	15	library	library	NN
37681	2259	16	,	,	,
37681	2259	17	appeared	appear	VBD
37681	2259	18	in	in	IN
37681	2259	19	a	a	DT
37681	2259	20	valuable	valuable	JJ
37681	2259	21	monograph	monograph	NN
37681	2259	22	by	by	IN
37681	2259	23	W.	W.	NNP
37681	2259	24	E.	E.	NNP
37681	2259	25	Stark	Stark	NNP
37681	2259	26	,	,	,
37681	2259	27	"	"	``
37681	2259	28	Measuring	measure	VBG
37681	2259	29	Instruments	Instruments	NNPS
37681	2259	30	of	of	IN
37681	2259	31	Long	Long	NNP
37681	2259	32	Ago	ago	RB
37681	2259	33	,	,	,
37681	2259	34	"	"	''
37681	2259	35	published	publish	VBN
37681	2259	36	in	in	IN
37681	2259	37	_	_	NNP
37681	2259	38	School	School	NNP
37681	2259	39	Science	Science	NNP
37681	2259	40	and	and	CC
37681	2259	41	Mathematics	Mathematics	NNP
37681	2259	42	_	_	NNP
37681	2259	43	,	,	,
37681	2259	44	Vol	Vol	NNP
37681	2259	45	.	.	.
37681	2260	1	X	X	NNP
37681	2260	2	,	,	,
37681	2260	3	pp	pp	NNP
37681	2260	4	.	.	.
37681	2261	1	48	48	CD
37681	2261	2	,	,	,
37681	2261	3	126	126	CD
37681	2261	4	.	.	.
37681	2262	1	With	with	IN
37681	2262	2	others	other	NNS
37681	2262	3	of	of	IN
37681	2262	4	the	the	DT
37681	2262	5	same	same	JJ
37681	2262	6	nature	nature	NN
37681	2262	7	it	-PRON-	PRP
37681	2262	8	is	be	VBZ
37681	2262	9	here	here	RB
37681	2262	10	reproduced	reproduce	VBN
37681	2262	11	by	by	IN
37681	2262	12	the	the	DT
37681	2262	13	courtesy	courtesy	NN
37681	2262	14	of	of	IN
37681	2262	15	Principal	Principal	NNP
37681	2262	16	Stark	Stark	NNP
37681	2262	17	and	and	CC
37681	2262	18	of	of	IN
37681	2262	19	the	the	DT
37681	2262	20	editors	editor	NNS
37681	2262	21	of	of	IN
37681	2262	22	the	the	DT
37681	2262	23	journal	journal	NN
37681	2262	24	in	in	IN
37681	2262	25	which	which	WDT
37681	2262	26	it	-PRON-	PRP
37681	2262	27	appeared	appear	VBD
37681	2262	28	.	.	.
37681	2263	1	[	[	-LRB-
37681	2263	2	62	62	CD
37681	2263	3	]	]	-RRB-
37681	2263	4	In	in	IN
37681	2263	5	speaking	speak	VBG
37681	2263	6	of	of	IN
37681	2263	7	two	two	CD
37681	2263	8	congruent	congruent	JJ
37681	2263	9	triangles	triangle	NNS
37681	2263	10	it	-PRON-	PRP
37681	2263	11	is	be	VBZ
37681	2263	12	somewhat	somewhat	RB
37681	2263	13	easier	easy	JJR
37681	2263	14	to	to	TO
37681	2263	15	follow	follow	VB
37681	2263	16	the	the	DT
37681	2263	17	congruence	congruence	NN
37681	2263	18	if	if	IN
37681	2263	19	the	the	DT
37681	2263	20	two	two	CD
37681	2263	21	are	be	VBP
37681	2263	22	read	read	VBN
37681	2263	23	in	in	IN
37681	2263	24	the	the	DT
37681	2263	25	same	same	JJ
37681	2263	26	order	order	NN
37681	2263	27	,	,	,
37681	2263	28	even	even	RB
37681	2263	29	though	though	IN
37681	2263	30	the	the	DT
37681	2263	31	relatively	relatively	RB
37681	2263	32	unimportant	unimportant	JJ
37681	2263	33	counterclockwise	counterclockwise	NN
37681	2263	34	reading	reading	NN
37681	2263	35	is	be	VBZ
37681	2263	36	neglected	neglect	VBN
37681	2263	37	.	.	.
37681	2264	1	No	no	DT
37681	2264	2	one	one	PRP
37681	2264	3	should	should	MD
37681	2264	4	be	be	VB
37681	2264	5	a	a	DT
37681	2264	6	slave	slave	NN
37681	2264	7	to	to	IN
37681	2264	8	such	such	PDT
37681	2264	9	a	a	DT
37681	2264	10	formalism	formalism	NN
37681	2264	11	,	,	,
37681	2264	12	but	but	CC
37681	2264	13	should	should	MD
37681	2264	14	follow	follow	VB
37681	2264	15	the	the	DT
37681	2264	16	plan	plan	NN
37681	2264	17	when	when	WRB
37681	2264	18	convenient	convenient	JJ
37681	2264	19	.	.	.
37681	2265	1	[	[	-LRB-
37681	2265	2	63	63	CD
37681	2265	3	]	]	-RRB-
37681	2265	4	Stark	Stark	NNP
37681	2265	5	,	,	,
37681	2265	6	loc	loc	NN
37681	2265	7	.	.	.
37681	2266	1	cit	cit	NNP
37681	2266	2	.	.	.
37681	2267	1	[	[	-LRB-
37681	2267	2	64	64	CD
37681	2267	3	]	]	-RRB-
37681	2267	4	Of	of	IN
37681	2267	5	which	which	WDT
37681	2267	6	so	so	RB
37681	2267	7	much	much	JJ
37681	2267	8	was	be	VBD
37681	2267	9	made	make	VBN
37681	2267	10	by	by	IN
37681	2267	11	Professor	Professor	NNP
37681	2267	12	Olaus	Olaus	NNP
37681	2267	13	Henrici	Henrici	NNP
37681	2267	14	in	in	IN
37681	2267	15	his	-PRON-	PRP$
37681	2267	16	"	"	``
37681	2267	17	Congruent	congruent	JJ
37681	2267	18	Figures	figure	NNS
37681	2267	19	,	,	,
37681	2267	20	"	"	''
37681	2267	21	London	London	NNP
37681	2267	22	,	,	,
37681	2267	23	1879,--a	1879,--a	CD
37681	2267	24	book	book	NN
37681	2267	25	that	that	WDT
37681	2267	26	every	every	DT
37681	2267	27	teacher	teacher	NN
37681	2267	28	of	of	IN
37681	2267	29	geometry	geometry	NN
37681	2267	30	should	should	MD
37681	2267	31	own	own	VB
37681	2267	32	.	.	.
37681	2268	1	[	[	-LRB-
37681	2268	2	65	65	CD
37681	2268	3	]	]	-RRB-
37681	2268	4	Much	much	JJ
37681	2268	5	is	be	VBZ
37681	2268	6	made	make	VBN
37681	2268	7	of	of	IN
37681	2268	8	this	this	DT
37681	2268	9	in	in	IN
37681	2268	10	the	the	DT
37681	2268	11	excellent	excellent	JJ
37681	2268	12	work	work	NN
37681	2268	13	by	by	IN
37681	2268	14	Henrici	Henrici	NNP
37681	2268	15	and	and	CC
37681	2268	16	Treutlein	Treutlein	NNP
37681	2268	17	,	,	,
37681	2268	18	"	"	''
37681	2268	19	Lehrbuch	lehrbuch	NN
37681	2268	20	der	der	NN
37681	2268	21	Geometrie	Geometrie	NNP
37681	2268	22	,	,	,
37681	2268	23	"	"	''
37681	2268	24	Leipzig	Leipzig	NNP
37681	2268	25	,	,	,
37681	2268	26	1881	1881	CD
37681	2268	27	.	.	.
37681	2269	1	[	[	-LRB-
37681	2269	2	66	66	CD
37681	2269	3	]	]	-RRB-
37681	2269	4	Méray	Méray	NNP
37681	2269	5	did	do	VBD
37681	2269	6	much	much	JJ
37681	2269	7	for	for	IN
37681	2269	8	this	this	DT
37681	2269	9	movement	movement	NN
37681	2269	10	in	in	IN
37681	2269	11	France	France	NNP
37681	2269	12	,	,	,
37681	2269	13	and	and	CC
37681	2269	14	the	the	DT
37681	2269	15	recent	recent	JJ
37681	2269	16	works	work	NNS
37681	2269	17	of	of	IN
37681	2269	18	Bourlet	Bourlet	NNP
37681	2269	19	and	and	CC
37681	2269	20	Borel	Borel	NNP
37681	2269	21	have	have	VBP
37681	2269	22	brought	bring	VBN
37681	2269	23	it	-PRON-	PRP
37681	2269	24	to	to	IN
37681	2269	25	the	the	DT
37681	2269	26	front	front	NN
37681	2269	27	in	in	IN
37681	2269	28	that	that	DT
37681	2269	29	country	country	NN
37681	2269	30	.	.	.
37681	2270	1	[	[	-LRB-
37681	2270	2	67	67	CD
37681	2270	3	]	]	-RRB-
37681	2270	4	W.	W.	NNP
37681	2270	5	N.	N.	NNP
37681	2270	6	Bruce	Bruce	NNP
37681	2270	7	,	,	,
37681	2270	8	"	"	``
37681	2270	9	Teaching	Teaching	NNP
37681	2270	10	of	of	IN
37681	2270	11	Geometry	Geometry	NNP
37681	2270	12	and	and	CC
37681	2270	13	Graphic	Graphic	NNP
37681	2270	14	Algebra	Algebra	NNP
37681	2270	15	in	in	IN
37681	2270	16	Secondary	Secondary	NNP
37681	2270	17	Schools	Schools	NNPS
37681	2270	18	,	,	,
37681	2270	19	"	"	``
37681	2270	20	Board	Board	NNP
37681	2270	21	of	of	IN
37681	2270	22	Education	Education	NNP
37681	2270	23	circular	circular	JJ
37681	2270	24	(	(	-LRB-
37681	2270	25	No	no	UH
37681	2270	26	.	.	.
37681	2271	1	711	711	CD
37681	2271	2	)	)	-RRB-
37681	2271	3	,	,	,
37681	2271	4	p.	p.	NN
37681	2271	5	8	8	CD
37681	2271	6	,	,	,
37681	2271	7	London	London	NNP
37681	2271	8	,	,	,
37681	2271	9	1909	1909	CD
37681	2271	10	.	.	.
37681	2272	1	CHAPTER	chapter	NN
37681	2272	2	XV	XV	NNP
37681	2272	3	THE	the	DT
37681	2272	4	LEADING	lead	VBG
37681	2272	5	PROPOSITIONS	proposition	NNS
37681	2272	6	OF	of	IN
37681	2272	7	BOOK	BOOK	NNP
37681	2272	8	II	ii	CD
37681	2272	9	Having	have	VBG
37681	2272	10	taken	take	VBN
37681	2272	11	up	up	RP
37681	2272	12	all	all	DT
37681	2272	13	of	of	IN
37681	2272	14	the	the	DT
37681	2272	15	propositions	proposition	NNS
37681	2272	16	usually	usually	RB
37681	2272	17	given	give	VBN
37681	2272	18	in	in	IN
37681	2272	19	Book	Book	NNP
37681	2272	20	I	-PRON-	PRP
37681	2272	21	,	,	,
37681	2272	22	it	-PRON-	PRP
37681	2272	23	seems	seem	VBZ
37681	2272	24	unnecessary	unnecessary	JJ
37681	2272	25	to	to	TO
37681	2272	26	consider	consider	VB
37681	2272	27	as	as	IN
37681	2272	28	specifically	specifically	RB
37681	2272	29	all	all	PDT
37681	2272	30	those	those	DT
37681	2272	31	in	in	IN
37681	2272	32	subsequent	subsequent	JJ
37681	2272	33	books	book	NNS
37681	2272	34	.	.	.
37681	2273	1	It	-PRON-	PRP
37681	2273	2	is	be	VBZ
37681	2273	3	therefore	therefore	RB
37681	2273	4	proposed	propose	VBN
37681	2273	5	to	to	TO
37681	2273	6	select	select	VB
37681	2273	7	certain	certain	JJ
37681	2273	8	ones	one	NNS
37681	2273	9	that	that	WDT
37681	2273	10	have	have	VBP
37681	2273	11	some	some	DT
37681	2273	12	special	special	JJ
37681	2273	13	interest	interest	NN
37681	2273	14	,	,	,
37681	2273	15	either	either	CC
37681	2273	16	from	from	IN
37681	2273	17	the	the	DT
37681	2273	18	standpoint	standpoint	NN
37681	2273	19	of	of	IN
37681	2273	20	mathematics	mathematic	NNS
37681	2273	21	or	or	CC
37681	2273	22	from	from	IN
37681	2273	23	that	that	DT
37681	2273	24	of	of	IN
37681	2273	25	history	history	NN
37681	2273	26	or	or	CC
37681	2273	27	application	application	NN
37681	2273	28	,	,	,
37681	2273	29	and	and	CC
37681	2273	30	to	to	TO
37681	2273	31	discuss	discuss	VB
37681	2273	32	them	-PRON-	PRP
37681	2273	33	as	as	RB
37681	2273	34	fully	fully	RB
37681	2273	35	as	as	IN
37681	2273	36	the	the	DT
37681	2273	37	circumstances	circumstance	NNS
37681	2273	38	seem	seem	VBP
37681	2273	39	to	to	TO
37681	2273	40	warrant	warrant	VB
37681	2273	41	.	.	.
37681	2274	1	THEOREMS	THEOREMS	NNP
37681	2274	2	.	.	.
37681	2275	1	_	_	NNP
37681	2275	2	In	in	IN
37681	2275	3	the	the	DT
37681	2275	4	same	same	JJ
37681	2275	5	circle	circle	NN
37681	2275	6	or	or	CC
37681	2275	7	in	in	IN
37681	2275	8	equal	equal	JJ
37681	2275	9	circles	circle	NNS
37681	2275	10	equal	equal	JJ
37681	2275	11	central	central	JJ
37681	2275	12	angles	angle	NNS
37681	2275	13	intercept	intercept	VBP
37681	2275	14	equal	equal	JJ
37681	2275	15	arcs	arc	NNS
37681	2275	16	;	;	:
37681	2275	17	and	and	CC
37681	2275	18	of	of	IN
37681	2275	19	two	two	CD
37681	2275	20	unequal	unequal	JJ
37681	2275	21	central	central	JJ
37681	2275	22	angles	angle	NNS
37681	2275	23	the	the	DT
37681	2275	24	greater	great	JJR
37681	2275	25	intercepts	intercept	NNS
37681	2275	26	the	the	DT
37681	2275	27	greater	great	JJR
37681	2275	28	arc	arc	NNP
37681	2275	29	_	_	NNP
37681	2275	30	,	,	,
37681	2275	31	and	and	CC
37681	2275	32	conversely	conversely	RB
37681	2275	33	for	for	IN
37681	2275	34	both	both	DT
37681	2275	35	of	of	IN
37681	2275	36	these	these	DT
37681	2275	37	cases	case	NNS
37681	2275	38	.	.	.
37681	2276	1	Euclid	Euclid	NNP
37681	2276	2	made	make	VBD
37681	2276	3	these	these	DT
37681	2276	4	the	the	DT
37681	2276	5	twenty	twenty	CD
37681	2276	6	-	-	HYPH
37681	2276	7	sixth	sixth	JJ
37681	2276	8	and	and	CC
37681	2276	9	twenty	twenty	CD
37681	2276	10	-	-	HYPH
37681	2276	11	seventh	seventh	JJ
37681	2276	12	propositions	proposition	NNS
37681	2276	13	of	of	IN
37681	2276	14	his	-PRON-	PRP$
37681	2276	15	Book	Book	NNP
37681	2276	16	III	III	NNP
37681	2276	17	,	,	,
37681	2276	18	but	but	CC
37681	2276	19	he	-PRON-	PRP
37681	2276	20	limited	limit	VBD
37681	2276	21	them	-PRON-	PRP
37681	2276	22	as	as	IN
37681	2276	23	follows	follow	VBZ
37681	2276	24	:	:	:
37681	2276	25	"	"	``
37681	2276	26	In	in	IN
37681	2276	27	equal	equal	JJ
37681	2276	28	circles	circle	NNS
37681	2276	29	equal	equal	JJ
37681	2276	30	angles	angle	NNS
37681	2276	31	stand	stand	VBP
37681	2276	32	on	on	IN
37681	2276	33	equal	equal	JJ
37681	2276	34	circumferences	circumference	NNS
37681	2276	35	,	,	,
37681	2276	36	whether	whether	IN
37681	2276	37	they	-PRON-	PRP
37681	2276	38	stand	stand	VBP
37681	2276	39	at	at	IN
37681	2276	40	the	the	DT
37681	2276	41	centers	center	NNS
37681	2276	42	or	or	CC
37681	2276	43	at	at	IN
37681	2276	44	the	the	DT
37681	2276	45	circumferences	circumference	NNS
37681	2276	46	,	,	,
37681	2276	47	and	and	CC
37681	2276	48	conversely	conversely	RB
37681	2276	49	.	.	.
37681	2276	50	"	"	''
37681	2277	1	He	-PRON-	PRP
37681	2277	2	therefore	therefore	RB
37681	2277	3	included	include	VBD
37681	2277	4	two	two	CD
37681	2277	5	of	of	IN
37681	2277	6	our	-PRON-	PRP$
37681	2277	7	present	present	JJ
37681	2277	8	theorems	theorem	NNS
37681	2277	9	in	in	IN
37681	2277	10	one	one	CD
37681	2277	11	,	,	,
37681	2277	12	thus	thus	RB
37681	2277	13	making	make	VBG
37681	2277	14	the	the	DT
37681	2277	15	proposition	proposition	NN
37681	2277	16	doubly	doubly	RB
37681	2277	17	hard	hard	RB
37681	2277	18	for	for	IN
37681	2277	19	a	a	DT
37681	2277	20	beginner	beginner	NN
37681	2277	21	.	.	.
37681	2278	1	After	after	IN
37681	2278	2	these	these	DT
37681	2278	3	two	two	CD
37681	2278	4	propositions	proposition	NNS
37681	2278	5	the	the	DT
37681	2278	6	Law	Law	NNP
37681	2278	7	of	of	IN
37681	2278	8	Converse	Converse	NNP
37681	2278	9	,	,	,
37681	2278	10	already	already	RB
37681	2278	11	mentioned	mention	VBN
37681	2278	12	on	on	IN
37681	2278	13	page	page	NN
37681	2278	14	190	190	CD
37681	2278	15	,	,	,
37681	2278	16	may	may	MD
37681	2278	17	properly	properly	RB
37681	2278	18	be	be	VB
37681	2278	19	introduced	introduce	VBN
37681	2278	20	.	.	.
37681	2279	1	THEOREMS	THEOREMS	NNP
37681	2279	2	.	.	.
37681	2280	1	_	_	NNP
37681	2280	2	In	in	IN
37681	2280	3	the	the	DT
37681	2280	4	same	same	JJ
37681	2280	5	circle	circle	NN
37681	2280	6	or	or	CC
37681	2280	7	in	in	IN
37681	2280	8	equal	equal	JJ
37681	2280	9	circles	circle	NNS
37681	2280	10	,	,	,
37681	2280	11	if	if	IN
37681	2280	12	two	two	CD
37681	2280	13	arcs	arc	NNS
37681	2280	14	are	be	VBP
37681	2280	15	equal	equal	JJ
37681	2280	16	,	,	,
37681	2280	17	they	-PRON-	PRP
37681	2280	18	are	be	VBP
37681	2280	19	subtended	subtend	VBN
37681	2280	20	by	by	IN
37681	2280	21	equal	equal	JJ
37681	2280	22	chords	chord	NNS
37681	2280	23	;	;	:
37681	2280	24	and	and	CC
37681	2280	25	if	if	IN
37681	2280	26	two	two	CD
37681	2280	27	arcs	arc	NNS
37681	2280	28	are	be	VBP
37681	2280	29	unequal	unequal	JJ
37681	2280	30	,	,	,
37681	2280	31	the	the	DT
37681	2280	32	greater	great	JJR
37681	2280	33	is	be	VBZ
37681	2280	34	subtended	subtend	VBN
37681	2280	35	by	by	IN
37681	2280	36	the	the	DT
37681	2280	37	greater	great	JJR
37681	2280	38	chord	chord	NN
37681	2280	39	_	_	NNP
37681	2280	40	,	,	,
37681	2280	41	and	and	CC
37681	2280	42	conversely	conversely	RB
37681	2280	43	.	.	.
37681	2281	1	Euclid	euclid	JJ
37681	2281	2	dismisses	dismiss	VBZ
37681	2281	3	all	all	PDT
37681	2281	4	this	this	DT
37681	2281	5	with	with	IN
37681	2281	6	the	the	DT
37681	2281	7	simple	simple	JJ
37681	2281	8	theorem	theorem	NN
37681	2281	9	,	,	,
37681	2281	10	"	"	''
37681	2281	11	In	in	IN
37681	2281	12	equal	equal	JJ
37681	2281	13	circles	circle	NNS
37681	2281	14	equal	equal	JJ
37681	2281	15	circumferences	circumference	NNS
37681	2281	16	are	be	VBP
37681	2281	17	subtended	subtend	VBN
37681	2281	18	by	by	IN
37681	2281	19	equal	equal	JJ
37681	2281	20	straight	straight	JJ
37681	2281	21	lines	line	NNS
37681	2281	22	.	.	.
37681	2281	23	"	"	''
37681	2282	1	It	-PRON-	PRP
37681	2282	2	will	will	MD
37681	2282	3	therefore	therefore	RB
37681	2282	4	be	be	VB
37681	2282	5	noticed	notice	VBN
37681	2282	6	that	that	IN
37681	2282	7	he	-PRON-	PRP
37681	2282	8	has	have	VBZ
37681	2282	9	no	no	DT
37681	2282	10	special	special	JJ
37681	2282	11	word	word	NN
37681	2282	12	for	for	IN
37681	2282	13	"	"	``
37681	2282	14	chord	chord	NN
37681	2282	15	"	"	''
37681	2282	16	and	and	CC
37681	2282	17	none	none	NN
37681	2282	18	for	for	IN
37681	2282	19	"	"	``
37681	2282	20	arc	arc	NNP
37681	2282	21	,	,	,
37681	2282	22	"	"	''
37681	2282	23	and	and	CC
37681	2282	24	that	that	IN
37681	2282	25	the	the	DT
37681	2282	26	word	word	NN
37681	2282	27	"	"	``
37681	2282	28	circumference	circumference	NN
37681	2282	29	,	,	,
37681	2282	30	"	"	''
37681	2282	31	which	which	WDT
37681	2282	32	some	some	DT
37681	2282	33	teachers	teacher	NNS
37681	2282	34	are	be	VBP
37681	2282	35	so	so	RB
37681	2282	36	anxious	anxious	JJ
37681	2282	37	to	to	TO
37681	2282	38	retain	retain	VB
37681	2282	39	,	,	,
37681	2282	40	is	be	VBZ
37681	2282	41	used	use	VBN
37681	2282	42	to	to	TO
37681	2282	43	mean	mean	VB
37681	2282	44	both	both	DT
37681	2282	45	the	the	DT
37681	2282	46	whole	whole	JJ
37681	2282	47	circle	circle	NN
37681	2282	48	and	and	CC
37681	2282	49	any	any	DT
37681	2282	50	arc	arc	NN
37681	2282	51	.	.	.
37681	2283	1	It	-PRON-	PRP
37681	2283	2	can	can	MD
37681	2283	3	not	not	RB
37681	2283	4	be	be	VB
37681	2283	5	doubted	doubt	VBN
37681	2283	6	that	that	IN
37681	2283	7	later	later	JJ
37681	2283	8	writers	writer	NNS
37681	2283	9	have	have	VBP
37681	2283	10	greatly	greatly	RB
37681	2283	11	improved	improve	VBN
37681	2283	12	the	the	DT
37681	2283	13	language	language	NN
37681	2283	14	of	of	IN
37681	2283	15	geometry	geometry	NN
37681	2283	16	by	by	IN
37681	2283	17	the	the	DT
37681	2283	18	use	use	NN
37681	2283	19	of	of	IN
37681	2283	20	these	these	DT
37681	2283	21	modern	modern	JJ
37681	2283	22	terms	term	NNS
37681	2283	23	.	.	.
37681	2284	1	The	the	DT
37681	2284	2	word	word	NN
37681	2284	3	"	"	``
37681	2284	4	arc	arc	NN
37681	2284	5	"	"	''
37681	2284	6	is	be	VBZ
37681	2284	7	the	the	DT
37681	2284	8	same	same	JJ
37681	2284	9	,	,	,
37681	2284	10	etymologically	etymologically	RB
37681	2284	11	,	,	,
37681	2284	12	as	as	IN
37681	2284	13	"	"	``
37681	2284	14	arch	arch	JJ
37681	2284	15	,	,	,
37681	2284	16	"	"	''
37681	2284	17	each	each	DT
37681	2284	18	being	be	VBG
37681	2284	19	derived	derive	VBN
37681	2284	20	from	from	IN
37681	2284	21	the	the	DT
37681	2284	22	Latin	Latin	NNP
37681	2284	23	_	_	NNP
37681	2284	24	arcus	arcus	NN
37681	2284	25	_	_	NNP
37681	2284	26	(	(	-LRB-
37681	2284	27	a	a	DT
37681	2284	28	bow	bow	NN
37681	2284	29	)	)	-RRB-
37681	2284	30	.	.	.
37681	2285	1	"	"	``
37681	2285	2	Chord	Chord	NNP
37681	2285	3	"	"	''
37681	2285	4	is	be	VBZ
37681	2285	5	from	from	IN
37681	2285	6	the	the	DT
37681	2285	7	Greek	Greek	NNP
37681	2285	8	,	,	,
37681	2285	9	meaning	mean	VBG
37681	2285	10	"	"	``
37681	2285	11	the	the	DT
37681	2285	12	string	string	NN
37681	2285	13	of	of	IN
37681	2285	14	a	a	DT
37681	2285	15	musical	musical	JJ
37681	2285	16	instrument	instrument	NN
37681	2285	17	.	.	.
37681	2285	18	"	"	''
37681	2286	1	"	"	``
37681	2286	2	Subtend	subtend	NN
37681	2286	3	"	"	''
37681	2286	4	is	be	VBZ
37681	2286	5	from	from	IN
37681	2286	6	the	the	DT
37681	2286	7	Latin	Latin	NNP
37681	2286	8	_	_	NNP
37681	2286	9	sub	sub	NN
37681	2286	10	_	_	NNP
37681	2286	11	(	(	-LRB-
37681	2286	12	under	under	RB
37681	2286	13	)	)	-RRB-
37681	2286	14	,	,	,
37681	2286	15	and	and	CC
37681	2286	16	_	_	NNP
37681	2286	17	tendere	tendere	IN
37681	2286	18	_	_	NNP
37681	2286	19	(	(	-LRB-
37681	2286	20	to	to	TO
37681	2286	21	stretch	stretch	VB
37681	2286	22	)	)	-RRB-
37681	2286	23	.	.	.
37681	2287	1	It	-PRON-	PRP
37681	2287	2	should	should	MD
37681	2287	3	be	be	VB
37681	2287	4	noticed	notice	VBN
37681	2287	5	that	that	IN
37681	2287	6	Euclid	Euclid	NNP
37681	2287	7	speaks	speak	VBZ
37681	2287	8	of	of	IN
37681	2287	9	"	"	``
37681	2287	10	equal	equal	JJ
37681	2287	11	circles	circle	NNS
37681	2287	12	,	,	,
37681	2287	13	"	"	''
37681	2287	14	while	while	IN
37681	2287	15	we	-PRON-	PRP
37681	2287	16	speak	speak	VBP
37681	2287	17	of	of	IN
37681	2287	18	"	"	``
37681	2287	19	the	the	DT
37681	2287	20	same	same	JJ
37681	2287	21	circle	circle	NN
37681	2287	22	or	or	CC
37681	2287	23	equal	equal	JJ
37681	2287	24	circles	circle	NNS
37681	2287	25	,	,	,
37681	2287	26	"	"	''
37681	2287	27	confining	confine	VBG
37681	2287	28	our	-PRON-	PRP$
37681	2287	29	proofs	proof	NNS
37681	2287	30	to	to	IN
37681	2287	31	the	the	DT
37681	2287	32	latter	latter	JJ
37681	2287	33	,	,	,
37681	2287	34	on	on	IN
37681	2287	35	the	the	DT
37681	2287	36	supposition	supposition	NN
37681	2287	37	that	that	IN
37681	2287	38	this	this	DT
37681	2287	39	sufficiently	sufficiently	RB
37681	2287	40	covers	cover	VBZ
37681	2287	41	the	the	DT
37681	2287	42	former	former	JJ
37681	2287	43	.	.	.
37681	2288	1	THEOREM	THEOREM	NNP
37681	2288	2	.	.	.
37681	2289	1	_	_	NNP
37681	2289	2	A	a	DT
37681	2289	3	line	line	NN
37681	2289	4	through	through	IN
37681	2289	5	the	the	DT
37681	2289	6	center	center	NN
37681	2289	7	of	of	IN
37681	2289	8	a	a	DT
37681	2289	9	circle	circle	NN
37681	2289	10	perpendicular	perpendicular	JJ
37681	2289	11	to	to	IN
37681	2289	12	a	a	DT
37681	2289	13	chord	chord	NN
37681	2289	14	bisects	bisect	VBZ
37681	2289	15	the	the	DT
37681	2289	16	chord	chord	NN
37681	2289	17	and	and	CC
37681	2289	18	the	the	DT
37681	2289	19	arcs	arc	NNS
37681	2289	20	subtended	subtend	VBN
37681	2289	21	by	by	IN
37681	2289	22	it	-PRON-	PRP
37681	2289	23	.	.	.
37681	2289	24	_	_	NNP
37681	2289	25	This	this	DT
37681	2289	26	is	be	VBZ
37681	2289	27	an	an	DT
37681	2289	28	improvement	improvement	NN
37681	2289	29	on	on	IN
37681	2289	30	Euclid	Euclid	NNP
37681	2289	31	,	,	,
37681	2289	32	III	III	NNP
37681	2289	33	,	,	,
37681	2289	34	3	3	CD
37681	2289	35	:	:	:
37681	2289	36	"	"	``
37681	2289	37	If	if	IN
37681	2289	38	in	in	IN
37681	2289	39	a	a	DT
37681	2289	40	circle	circle	NN
37681	2289	41	a	a	DT
37681	2289	42	straight	straight	JJ
37681	2289	43	line	line	NN
37681	2289	44	through	through	IN
37681	2289	45	the	the	DT
37681	2289	46	center	center	NN
37681	2289	47	bisects	bisect	VBZ
37681	2289	48	a	a	DT
37681	2289	49	straight	straight	JJ
37681	2289	50	line	line	NN
37681	2289	51	not	not	RB
37681	2289	52	through	through	IN
37681	2289	53	the	the	DT
37681	2289	54	center	center	NN
37681	2289	55	,	,	,
37681	2289	56	it	-PRON-	PRP
37681	2289	57	also	also	RB
37681	2289	58	cuts	cut	VBZ
37681	2289	59	it	-PRON-	PRP
37681	2289	60	at	at	IN
37681	2289	61	right	right	JJ
37681	2289	62	angles	angle	NNS
37681	2289	63	;	;	:
37681	2289	64	and	and	CC
37681	2289	65	if	if	IN
37681	2289	66	it	-PRON-	PRP
37681	2289	67	cuts	cut	VBZ
37681	2289	68	it	-PRON-	PRP
37681	2289	69	at	at	IN
37681	2289	70	right	right	JJ
37681	2289	71	angles	angle	NNS
37681	2289	72	,	,	,
37681	2289	73	it	-PRON-	PRP
37681	2289	74	also	also	RB
37681	2289	75	bisects	bisect	VBZ
37681	2289	76	it	-PRON-	PRP
37681	2289	77	.	.	.
37681	2289	78	"	"	''
37681	2290	1	It	-PRON-	PRP
37681	2290	2	is	be	VBZ
37681	2290	3	a	a	DT
37681	2290	4	very	very	RB
37681	2290	5	important	important	JJ
37681	2290	6	proposition	proposition	NN
37681	2290	7	,	,	,
37681	2290	8	theoretically	theoretically	RB
37681	2290	9	and	and	CC
37681	2290	10	practically	practically	RB
37681	2290	11	,	,	,
37681	2290	12	for	for	IN
37681	2290	13	it	-PRON-	PRP
37681	2290	14	enables	enable	VBZ
37681	2290	15	us	-PRON-	PRP
37681	2290	16	to	to	TO
37681	2290	17	find	find	VB
37681	2290	18	the	the	DT
37681	2290	19	center	center	NN
37681	2290	20	of	of	IN
37681	2290	21	a	a	DT
37681	2290	22	circle	circle	NN
37681	2290	23	if	if	IN
37681	2290	24	we	-PRON-	PRP
37681	2290	25	know	know	VBP
37681	2290	26	any	any	DT
37681	2290	27	part	part	NN
37681	2290	28	of	of	IN
37681	2290	29	its	-PRON-	PRP$
37681	2290	30	arc	arc	NN
37681	2290	31	.	.	.
37681	2291	1	A	a	DT
37681	2291	2	civil	civil	JJ
37681	2291	3	engineer	engineer	NN
37681	2291	4	,	,	,
37681	2291	5	for	for	IN
37681	2291	6	example	example	NN
37681	2291	7	,	,	,
37681	2291	8	who	who	WP
37681	2291	9	wishes	wish	VBZ
37681	2291	10	to	to	TO
37681	2291	11	find	find	VB
37681	2291	12	the	the	DT
37681	2291	13	center	center	NN
37681	2291	14	of	of	IN
37681	2291	15	the	the	DT
37681	2291	16	circle	circle	NN
37681	2291	17	of	of	IN
37681	2291	18	which	which	WDT
37681	2291	19	some	some	DT
37681	2291	20	curve	curve	NN
37681	2291	21	(	(	-LRB-
37681	2291	22	like	like	IN
37681	2291	23	that	that	DT
37681	2291	24	on	on	IN
37681	2291	25	a	a	DT
37681	2291	26	running	run	VBG
37681	2291	27	track	track	NN
37681	2291	28	,	,	,
37681	2291	29	on	on	IN
37681	2291	30	a	a	DT
37681	2291	31	railroad	railroad	NN
37681	2291	32	,	,	,
37681	2291	33	or	or	CC
37681	2291	34	in	in	IN
37681	2291	35	a	a	DT
37681	2291	36	park	park	NN
37681	2291	37	)	)	-RRB-
37681	2291	38	is	be	VBZ
37681	2291	39	an	an	DT
37681	2291	40	arc	arc	NN
37681	2291	41	,	,	,
37681	2291	42	takes	take	VBZ
37681	2291	43	two	two	CD
37681	2291	44	chords	chord	NNS
37681	2291	45	,	,	,
37681	2291	46	say	say	VB
37681	2291	47	of	of	IN
37681	2291	48	one	one	CD
37681	2291	49	hundred	hundred	CD
37681	2291	50	feet	foot	NNS
37681	2291	51	each	each	DT
37681	2291	52	,	,	,
37681	2291	53	and	and	CC
37681	2291	54	erects	erect	VBZ
37681	2291	55	perpendicular	perpendicular	JJ
37681	2291	56	bisectors	bisector	NNS
37681	2291	57	.	.	.
37681	2292	1	It	-PRON-	PRP
37681	2292	2	is	be	VBZ
37681	2292	3	well	well	JJ
37681	2292	4	to	to	TO
37681	2292	5	ask	ask	VB
37681	2292	6	a	a	DT
37681	2292	7	class	class	NN
37681	2292	8	why	why	WRB
37681	2292	9	,	,	,
37681	2292	10	in	in	IN
37681	2292	11	practice	practice	NN
37681	2292	12	,	,	,
37681	2292	13	it	-PRON-	PRP
37681	2292	14	is	be	VBZ
37681	2292	15	better	well	JJR
37681	2292	16	to	to	TO
37681	2292	17	take	take	VB
37681	2292	18	these	these	DT
37681	2292	19	chords	chord	NNS
37681	2292	20	some	some	DT
37681	2292	21	distance	distance	NN
37681	2292	22	apart	apart	RB
37681	2292	23	.	.	.
37681	2293	1	Engineers	engineer	NNS
37681	2293	2	often	often	RB
37681	2293	3	check	check	VBP
37681	2293	4	their	-PRON-	PRP$
37681	2293	5	work	work	NN
37681	2293	6	by	by	IN
37681	2293	7	taking	take	VBG
37681	2293	8	three	three	CD
37681	2293	9	chords	chord	NNS
37681	2293	10	,	,	,
37681	2293	11	the	the	DT
37681	2293	12	perpendicular	perpendicular	JJ
37681	2293	13	bisectors	bisector	NNS
37681	2293	14	of	of	IN
37681	2293	15	the	the	DT
37681	2293	16	three	three	CD
37681	2293	17	passing	pass	VBG
37681	2293	18	through	through	IN
37681	2293	19	a	a	DT
37681	2293	20	single	single	JJ
37681	2293	21	point	point	NN
37681	2293	22	.	.	.
37681	2294	1	Illustrations	illustration	NNS
37681	2294	2	of	of	IN
37681	2294	3	this	this	DT
37681	2294	4	kind	kind	NN
37681	2294	5	of	of	IN
37681	2294	6	work	work	NN
37681	2294	7	are	be	VBP
37681	2294	8	given	give	VBN
37681	2294	9	later	later	RB
37681	2294	10	in	in	IN
37681	2294	11	this	this	DT
37681	2294	12	chapter	chapter	NN
37681	2294	13	.	.	.
37681	2295	1	THEOREM	THEOREM	NNP
37681	2295	2	.	.	.
37681	2296	1	_	_	NNP
37681	2296	2	In	in	IN
37681	2296	3	the	the	DT
37681	2296	4	same	same	JJ
37681	2296	5	circle	circle	NN
37681	2296	6	or	or	CC
37681	2296	7	in	in	IN
37681	2296	8	equal	equal	JJ
37681	2296	9	circles	circle	NNS
37681	2296	10	equal	equal	JJ
37681	2296	11	chords	chord	NNS
37681	2296	12	are	be	VBP
37681	2296	13	equidistant	equidistant	JJ
37681	2296	14	from	from	IN
37681	2296	15	the	the	DT
37681	2296	16	center	center	NN
37681	2296	17	,	,	,
37681	2296	18	and	and	CC
37681	2296	19	chords	chord	NNS
37681	2296	20	equidistant	equidistant	NN
37681	2296	21	from	from	IN
37681	2296	22	the	the	DT
37681	2296	23	center	center	NN
37681	2296	24	are	be	VBP
37681	2296	25	equal	equal	JJ
37681	2296	26	.	.	.
37681	2296	27	_	_	NNP
37681	2296	28	This	this	DT
37681	2296	29	proposition	proposition	NN
37681	2296	30	is	be	VBZ
37681	2296	31	practically	practically	RB
37681	2296	32	used	use	VBN
37681	2296	33	by	by	IN
37681	2296	34	engineers	engineer	NNS
37681	2296	35	in	in	IN
37681	2296	36	locating	locate	VBG
37681	2296	37	points	point	NNS
37681	2296	38	on	on	IN
37681	2296	39	an	an	DT
37681	2296	40	arc	arc	NN
37681	2296	41	of	of	IN
37681	2296	42	a	a	DT
37681	2296	43	circle	circle	NN
37681	2296	44	that	that	WDT
37681	2296	45	is	be	VBZ
37681	2296	46	too	too	RB
37681	2296	47	large	large	JJ
37681	2296	48	to	to	TO
37681	2296	49	be	be	VB
37681	2296	50	described	describe	VBN
37681	2296	51	by	by	IN
37681	2296	52	a	a	DT
37681	2296	53	tape	tape	NN
37681	2296	54	,	,	,
37681	2296	55	or	or	CC
37681	2296	56	that	that	DT
37681	2296	57	can	can	MD
37681	2296	58	not	not	RB
37681	2296	59	easily	easily	RB
37681	2296	60	be	be	VB
37681	2296	61	reached	reach	VBN
37681	2296	62	from	from	IN
37681	2296	63	the	the	DT
37681	2296	64	center	center	NN
37681	2296	65	on	on	IN
37681	2296	66	account	account	NN
37681	2296	67	of	of	IN
37681	2296	68	obstructions	obstruction	NNS
37681	2296	69	.	.	.
37681	2297	1	[	[	-LRB-
37681	2297	2	Illustration	illustration	NN
37681	2297	3	]	]	-RRB-
37681	2297	4	If	if	IN
37681	2297	5	part	part	NN
37681	2297	6	of	of	IN
37681	2297	7	the	the	DT
37681	2297	8	curve	curve	NN
37681	2297	9	_	_	NNP
37681	2297	10	APB	APB	NNP
37681	2297	11	_	_	NNP
37681	2297	12	is	be	VBZ
37681	2297	13	known	know	VBN
37681	2297	14	,	,	,
37681	2297	15	take	take	VB
37681	2297	16	_	_	NNP
37681	2297	17	P	P	NNP
37681	2297	18	_	_	NNP
37681	2297	19	as	as	IN
37681	2297	20	the	the	DT
37681	2297	21	mid	mid	NN
37681	2297	22	-	-	NN
37681	2297	23	point	point	NN
37681	2297	24	.	.	.
37681	2298	1	Then	then	RB
37681	2298	2	stretch	stretch	VB
37681	2298	3	the	the	DT
37681	2298	4	tape	tape	NN
37681	2298	5	from	from	IN
37681	2298	6	_	_	NNP
37681	2298	7	A	A	NNP
37681	2298	8	_	_	NNP
37681	2298	9	to	to	IN
37681	2298	10	_	_	NNP
37681	2298	11	B	B	NNP
37681	2298	12	_	_	NNP
37681	2298	13	and	and	CC
37681	2298	14	draw	draw	VB
37681	2298	15	_	_	NNP
37681	2298	16	PM	PM	NNP
37681	2298	17	_	_	NNP
37681	2298	18	perpendicular	perpendicular	JJ
37681	2298	19	to	to	IN
37681	2298	20	it	-PRON-	PRP
37681	2298	21	.	.	.
37681	2299	1	Then	then	RB
37681	2299	2	swing	swing	VB
37681	2299	3	the	the	DT
37681	2299	4	length	length	NN
37681	2299	5	_	_	NNP
37681	2299	6	AM	AM	NNP
37681	2299	7	_	_	NNP
37681	2299	8	about	about	IN
37681	2299	9	_	_	NNP
37681	2299	10	P	P	NNP
37681	2299	11	_	_	NNP
37681	2299	12	,	,	,
37681	2299	13	and	and	CC
37681	2299	14	_	_	NNP
37681	2299	15	PM	PM	NNP
37681	2299	16	_	_	NNP
37681	2299	17	about	about	IN
37681	2299	18	_	_	NNP
37681	2299	19	B	B	NNP
37681	2299	20	_	_	NNP
37681	2299	21	,	,	,
37681	2299	22	until	until	IN
37681	2299	23	they	-PRON-	PRP
37681	2299	24	meet	meet	VBP
37681	2299	25	at	at	IN
37681	2299	26	_	_	NNP
37681	2299	27	L	L	NNP
37681	2299	28	_	_	NNP
37681	2299	29	,	,	,
37681	2299	30	and	and	CC
37681	2299	31	stretch	stretch	VB
37681	2299	32	the	the	DT
37681	2299	33	length	length	NN
37681	2299	34	_	_	NNP
37681	2299	35	AB	AB	NNP
37681	2299	36	_	_	NNP
37681	2299	37	along	along	IN
37681	2299	38	_	_	NNP
37681	2299	39	PL	PL	NNP
37681	2299	40	_	_	NNP
37681	2299	41	to	to	IN
37681	2299	42	_	_	NNP
37681	2299	43	Q	Q	NNP
37681	2299	44	_	_	NNP
37681	2299	45	.	.	.
37681	2300	1	This	this	DT
37681	2300	2	fixes	fix	VBZ
37681	2300	3	the	the	DT
37681	2300	4	point	point	NN
37681	2300	5	_	_	NNP
37681	2300	6	Q	Q	NNP
37681	2300	7	_	_	NNP
37681	2300	8	.	.	.
37681	2301	1	In	in	IN
37681	2301	2	the	the	DT
37681	2301	3	same	same	JJ
37681	2301	4	way	way	NN
37681	2301	5	fix	fix	VB
37681	2301	6	the	the	DT
37681	2301	7	point	point	NN
37681	2301	8	_	_	NNP
37681	2301	9	C	C	NNP
37681	2301	10	_	_	NNP
37681	2301	11	.	.	.
37681	2302	1	Points	point	NNS
37681	2302	2	on	on	IN
37681	2302	3	the	the	DT
37681	2302	4	curve	curve	NN
37681	2302	5	can	can	MD
37681	2302	6	thus	thus	RB
37681	2302	7	be	be	VB
37681	2302	8	fixed	fix	VBN
37681	2302	9	as	as	IN
37681	2302	10	near	near	RB
37681	2302	11	together	together	RB
37681	2302	12	as	as	IN
37681	2302	13	we	-PRON-	PRP
37681	2302	14	wish	wish	VBP
37681	2302	15	.	.	.
37681	2303	1	The	the	DT
37681	2303	2	chords	chord	NNS
37681	2303	3	_	_	NNP
37681	2303	4	AB	AB	NNP
37681	2303	5	_	_	NNP
37681	2303	6	,	,	,
37681	2303	7	_	_	NNP
37681	2303	8	PQ	PQ	NNP
37681	2303	9	_	_	NNP
37681	2303	10	,	,	,
37681	2303	11	_	_	NNP
37681	2303	12	BC	BC	NNP
37681	2303	13	_	_	NNP
37681	2303	14	,	,	,
37681	2303	15	and	and	CC
37681	2303	16	so	so	RB
37681	2303	17	on	on	RB
37681	2303	18	,	,	,
37681	2303	19	are	be	VBP
37681	2303	20	equal	equal	JJ
37681	2303	21	and	and	CC
37681	2303	22	are	be	VBP
37681	2303	23	equally	equally	RB
37681	2303	24	distant	distant	JJ
37681	2303	25	from	from	IN
37681	2303	26	the	the	DT
37681	2303	27	center	center	NN
37681	2303	28	.	.	.
37681	2304	1	THEOREM	THEOREM	NNP
37681	2304	2	.	.	.
37681	2305	1	_	_	NNP
37681	2305	2	A	a	DT
37681	2305	3	line	line	NN
37681	2305	4	perpendicular	perpendicular	JJ
37681	2305	5	to	to	IN
37681	2305	6	a	a	DT
37681	2305	7	radius	radius	NN
37681	2305	8	at	at	IN
37681	2305	9	its	-PRON-	PRP$
37681	2305	10	extremity	extremity	NN
37681	2305	11	is	be	VBZ
37681	2305	12	tangent	tangent	NN
37681	2305	13	to	to	IN
37681	2305	14	the	the	DT
37681	2305	15	circle	circle	NN
37681	2305	16	.	.	.
37681	2305	17	_	_	NNP
37681	2305	18	The	the	DT
37681	2305	19	enunciation	enunciation	NN
37681	2305	20	of	of	IN
37681	2305	21	this	this	DT
37681	2305	22	proposition	proposition	NN
37681	2305	23	by	by	IN
37681	2305	24	Euclid	Euclid	NNP
37681	2305	25	is	be	VBZ
37681	2305	26	very	very	RB
37681	2305	27	interesting	interesting	JJ
37681	2305	28	.	.	.
37681	2306	1	It	-PRON-	PRP
37681	2306	2	is	be	VBZ
37681	2306	3	as	as	IN
37681	2306	4	follows	follow	VBZ
37681	2306	5	:	:	:
37681	2306	6	The	the	DT
37681	2306	7	straight	straight	JJ
37681	2306	8	line	line	NN
37681	2306	9	drawn	draw	VBN
37681	2306	10	at	at	IN
37681	2306	11	right	right	JJ
37681	2306	12	angles	angle	NNS
37681	2306	13	to	to	IN
37681	2306	14	the	the	DT
37681	2306	15	diameter	diameter	NN
37681	2306	16	of	of	IN
37681	2306	17	a	a	DT
37681	2306	18	circle	circle	NN
37681	2306	19	at	at	IN
37681	2306	20	its	-PRON-	PRP$
37681	2306	21	extremity	extremity	NN
37681	2306	22	will	will	MD
37681	2306	23	fall	fall	VB
37681	2306	24	outside	outside	IN
37681	2306	25	the	the	DT
37681	2306	26	circle	circle	NN
37681	2306	27	,	,	,
37681	2306	28	and	and	CC
37681	2306	29	into	into	IN
37681	2306	30	the	the	DT
37681	2306	31	space	space	NN
37681	2306	32	between	between	IN
37681	2306	33	the	the	DT
37681	2306	34	straight	straight	JJ
37681	2306	35	line	line	NN
37681	2306	36	and	and	CC
37681	2306	37	the	the	DT
37681	2306	38	circumference	circumference	NN
37681	2306	39	another	another	DT
37681	2306	40	straight	straight	JJ
37681	2306	41	line	line	NN
37681	2306	42	can	can	MD
37681	2306	43	not	not	RB
37681	2306	44	be	be	VB
37681	2306	45	interposed	interpose	VBN
37681	2306	46	;	;	:
37681	2306	47	further	further	RB
37681	2306	48	,	,	,
37681	2306	49	the	the	DT
37681	2306	50	angle	angle	NN
37681	2306	51	of	of	IN
37681	2306	52	the	the	DT
37681	2306	53	semicircle	semicircle	NN
37681	2306	54	is	be	VBZ
37681	2306	55	greater	great	JJR
37681	2306	56	and	and	CC
37681	2306	57	the	the	DT
37681	2306	58	remaining	remain	VBG
37681	2306	59	angle	angle	NN
37681	2306	60	less	less	JJR
37681	2306	61	than	than	IN
37681	2306	62	any	any	DT
37681	2306	63	acute	acute	JJ
37681	2306	64	rectilineal	rectilineal	NN
37681	2306	65	angle	angle	NN
37681	2306	66	.	.	.
37681	2307	1	The	the	DT
37681	2307	2	first	first	JJ
37681	2307	3	assertion	assertion	NN
37681	2307	4	is	be	VBZ
37681	2307	5	practically	practically	RB
37681	2307	6	that	that	DT
37681	2307	7	of	of	IN
37681	2307	8	tangency,--"will	tangency,--"will	NNP
37681	2307	9	fall	fall	VB
37681	2307	10	outside	outside	IN
37681	2307	11	the	the	DT
37681	2307	12	circle	circle	NN
37681	2307	13	.	.	.
37681	2307	14	"	"	''
37681	2308	1	The	the	DT
37681	2308	2	second	second	JJ
37681	2308	3	one	one	CD
37681	2308	4	states	state	NNS
37681	2308	5	,	,	,
37681	2308	6	substantially	substantially	RB
37681	2308	7	,	,	,
37681	2308	8	that	that	IN
37681	2308	9	there	there	EX
37681	2308	10	is	be	VBZ
37681	2308	11	only	only	RB
37681	2308	12	one	one	CD
37681	2308	13	such	such	JJ
37681	2308	14	tangent	tangent	NN
37681	2308	15	,	,	,
37681	2308	16	or	or	CC
37681	2308	17	,	,	,
37681	2308	18	as	as	IN
37681	2308	19	we	-PRON-	PRP
37681	2308	20	say	say	VBP
37681	2308	21	in	in	IN
37681	2308	22	modern	modern	JJ
37681	2308	23	mathematics	mathematic	NNS
37681	2308	24	,	,	,
37681	2308	25	the	the	DT
37681	2308	26	tangent	tangent	NN
37681	2308	27	is	be	VBZ
37681	2308	28	unique	unique	JJ
37681	2308	29	.	.	.
37681	2309	1	The	the	DT
37681	2309	2	third	third	JJ
37681	2309	3	statement	statement	NN
37681	2309	4	relates	relate	VBZ
37681	2309	5	to	to	IN
37681	2309	6	the	the	DT
37681	2309	7	angle	angle	NN
37681	2309	8	formed	form	VBN
37681	2309	9	by	by	IN
37681	2309	10	the	the	DT
37681	2309	11	diameter	diameter	NN
37681	2309	12	and	and	CC
37681	2309	13	the	the	DT
37681	2309	14	circumference,--a	circumference,--a	NNP
37681	2309	15	mixed	mixed	JJ
37681	2309	16	angle	angle	NN
37681	2309	17	,	,	,
37681	2309	18	as	as	IN
37681	2309	19	Proclus	Proclus	NNP
37681	2309	20	called	call	VBD
37681	2309	21	it	-PRON-	PRP
37681	2309	22	,	,	,
37681	2309	23	and	and	CC
37681	2309	24	a	a	DT
37681	2309	25	kind	kind	NN
37681	2309	26	of	of	IN
37681	2309	27	angle	angle	NN
37681	2309	28	no	no	RB
37681	2309	29	longer	long	RBR
37681	2309	30	used	use	VBN
37681	2309	31	in	in	IN
37681	2309	32	elementary	elementary	JJ
37681	2309	33	geometry	geometry	NN
37681	2309	34	.	.	.
37681	2310	1	The	the	DT
37681	2310	2	fourth	fourth	JJ
37681	2310	3	statement	statement	NN
37681	2310	4	practically	practically	RB
37681	2310	5	asserts	assert	VBZ
37681	2310	6	that	that	IN
37681	2310	7	the	the	DT
37681	2310	8	angle	angle	NN
37681	2310	9	between	between	IN
37681	2310	10	the	the	DT
37681	2310	11	tangent	tangent	NN
37681	2310	12	and	and	CC
37681	2310	13	circumference	circumference	NN
37681	2310	14	is	be	VBZ
37681	2310	15	less	less	JJR
37681	2310	16	than	than	IN
37681	2310	17	any	any	DT
37681	2310	18	assignable	assignable	JJ
37681	2310	19	quantity	quantity	NN
37681	2310	20	.	.	.
37681	2311	1	This	this	DT
37681	2311	2	gives	give	VBZ
37681	2311	3	rise	rise	NN
37681	2311	4	to	to	IN
37681	2311	5	a	a	DT
37681	2311	6	difficulty	difficulty	NN
37681	2311	7	that	that	WDT
37681	2311	8	seems	seem	VBZ
37681	2311	9	to	to	TO
37681	2311	10	have	have	VB
37681	2311	11	puzzled	puzzle	VBN
37681	2311	12	many	many	JJ
37681	2311	13	of	of	IN
37681	2311	14	Euclid	Euclid	NNP
37681	2311	15	's	's	POS
37681	2311	16	commentators	commentator	NNS
37681	2311	17	,	,	,
37681	2311	18	and	and	CC
37681	2311	19	that	that	DT
37681	2311	20	will	will	MD
37681	2311	21	interest	interest	VB
37681	2311	22	a	a	DT
37681	2311	23	pupil	pupil	NN
37681	2311	24	:	:	:
37681	2311	25	As	as	IN
37681	2311	26	the	the	DT
37681	2311	27	circle	circle	NN
37681	2311	28	diminishes	diminish	VBZ
37681	2311	29	this	this	DT
37681	2311	30	angle	angle	NN
37681	2311	31	apparently	apparently	RB
37681	2311	32	increases	increase	VBZ
37681	2311	33	,	,	,
37681	2311	34	while	while	IN
37681	2311	35	as	as	IN
37681	2311	36	the	the	DT
37681	2311	37	circle	circle	NN
37681	2311	38	increases	increase	VBZ
37681	2311	39	the	the	DT
37681	2311	40	angle	angle	NN
37681	2311	41	decreases	decrease	NNS
37681	2311	42	,	,	,
37681	2311	43	and	and	CC
37681	2311	44	yet	yet	RB
37681	2311	45	the	the	DT
37681	2311	46	angle	angle	NN
37681	2311	47	is	be	VBZ
37681	2311	48	always	always	RB
37681	2311	49	stated	state	VBN
37681	2311	50	to	to	TO
37681	2311	51	be	be	VB
37681	2311	52	zero	zero	CD
37681	2311	53	.	.	.
37681	2312	1	Vieta	Vieta	NNP
37681	2312	2	(	(	-LRB-
37681	2312	3	1540	1540	CD
37681	2312	4	-	-	SYM
37681	2312	5	1603	1603	CD
37681	2312	6	)	)	-RRB-
37681	2312	7	,	,	,
37681	2312	8	who	who	WP
37681	2312	9	did	do	VBD
37681	2312	10	much	much	RB
37681	2312	11	to	to	TO
37681	2312	12	improve	improve	VB
37681	2312	13	the	the	DT
37681	2312	14	science	science	NN
37681	2312	15	of	of	IN
37681	2312	16	algebra	algebra	NN
37681	2312	17	,	,	,
37681	2312	18	attempted	attempt	VBD
37681	2312	19	to	to	TO
37681	2312	20	explain	explain	VB
37681	2312	21	away	away	RB
37681	2312	22	the	the	DT
37681	2312	23	difficulty	difficulty	NN
37681	2312	24	by	by	IN
37681	2312	25	adopting	adopt	VBG
37681	2312	26	a	a	DT
37681	2312	27	notion	notion	NN
37681	2312	28	of	of	IN
37681	2312	29	circle	circle	NN
37681	2312	30	that	that	WDT
37681	2312	31	was	be	VBD
37681	2312	32	prevalent	prevalent	JJ
37681	2312	33	in	in	IN
37681	2312	34	his	-PRON-	PRP$
37681	2312	35	time	time	NN
37681	2312	36	.	.	.
37681	2313	1	He	-PRON-	PRP
37681	2313	2	said	say	VBD
37681	2313	3	that	that	IN
37681	2313	4	a	a	DT
37681	2313	5	circle	circle	NN
37681	2313	6	was	be	VBD
37681	2313	7	a	a	DT
37681	2313	8	polygon	polygon	NN
37681	2313	9	of	of	IN
37681	2313	10	an	an	DT
37681	2313	11	infinite	infinite	JJ
37681	2313	12	number	number	NN
37681	2313	13	of	of	IN
37681	2313	14	sides	side	NNS
37681	2313	15	(	(	-LRB-
37681	2313	16	which	which	WDT
37681	2313	17	it	-PRON-	PRP
37681	2313	18	can	can	MD
37681	2313	19	not	not	RB
37681	2313	20	be	be	VB
37681	2313	21	,	,	,
37681	2313	22	by	by	IN
37681	2313	23	definition	definition	NN
37681	2313	24	)	)	-RRB-
37681	2313	25	,	,	,
37681	2313	26	and	and	CC
37681	2313	27	that	that	IN
37681	2313	28	,	,	,
37681	2313	29	a	a	DT
37681	2313	30	tangent	tangent	NN
37681	2313	31	simply	simply	RB
37681	2313	32	coincided	coincide	VBD
37681	2313	33	with	with	IN
37681	2313	34	one	one	CD
37681	2313	35	of	of	IN
37681	2313	36	the	the	DT
37681	2313	37	sides	side	NNS
37681	2313	38	,	,	,
37681	2313	39	and	and	CC
37681	2313	40	therefore	therefore	RB
37681	2313	41	made	make	VBD
37681	2313	42	no	no	DT
37681	2313	43	angle	angle	NN
37681	2313	44	with	with	IN
37681	2313	45	it	-PRON-	PRP
37681	2313	46	;	;	:
37681	2313	47	and	and	CC
37681	2313	48	this	this	DT
37681	2313	49	view	view	NN
37681	2313	50	was	be	VBD
37681	2313	51	also	also	RB
37681	2313	52	held	hold	VBN
37681	2313	53	by	by	IN
37681	2313	54	Galileo	Galileo	NNP
37681	2313	55	(	(	-LRB-
37681	2313	56	1564	1564	CD
37681	2313	57	-	-	SYM
37681	2313	58	1642	1642	CD
37681	2313	59	)	)	-RRB-
37681	2313	60	,	,	,
37681	2313	61	the	the	DT
37681	2313	62	great	great	JJ
37681	2313	63	physicist	physicist	NNP
37681	2313	64	and	and	CC
37681	2313	65	mathematician	mathematician	NN
37681	2313	66	who	who	WP
37681	2313	67	first	first	RB
37681	2313	68	stated	state	VBD
37681	2313	69	the	the	DT
37681	2313	70	law	law	NN
37681	2313	71	of	of	IN
37681	2313	72	the	the	DT
37681	2313	73	pendulum	pendulum	NN
37681	2313	74	.	.	.
37681	2314	1	THEOREM	THEOREM	NNP
37681	2314	2	.	.	.
37681	2315	1	_	_	NNP
37681	2315	2	Parallel	parallel	JJ
37681	2315	3	lines	line	NNS
37681	2315	4	intercept	intercept	VBP
37681	2315	5	equal	equal	JJ
37681	2315	6	arcs	arc	NNS
37681	2315	7	on	on	IN
37681	2315	8	a	a	DT
37681	2315	9	circle	circle	NN
37681	2315	10	.	.	.
37681	2315	11	_	_	NNP
37681	2315	12	The	the	DT
37681	2315	13	converse	converse	NN
37681	2315	14	of	of	IN
37681	2315	15	this	this	DT
37681	2315	16	proposition	proposition	NN
37681	2315	17	has	have	VBZ
37681	2315	18	an	an	DT
37681	2315	19	interesting	interesting	JJ
37681	2315	20	application	application	NN
37681	2315	21	in	in	IN
37681	2315	22	outdoor	outdoor	JJ
37681	2315	23	work	work	NN
37681	2315	24	.	.	.
37681	2316	1	[	[	-LRB-
37681	2316	2	Illustration	illustration	NN
37681	2316	3	]	]	-RRB-
37681	2316	4	Suppose	suppose	VB
37681	2316	5	we	-PRON-	PRP
37681	2316	6	wish	wish	VBP
37681	2316	7	to	to	TO
37681	2316	8	run	run	VB
37681	2316	9	a	a	DT
37681	2316	10	line	line	NN
37681	2316	11	through	through	IN
37681	2316	12	_	_	NNP
37681	2316	13	P	P	NNP
37681	2316	14	_	_	NNP
37681	2316	15	parallel	parallel	NN
37681	2316	16	to	to	IN
37681	2316	17	a	a	DT
37681	2316	18	given	give	VBN
37681	2316	19	line	line	NN
37681	2316	20	_	_	NNP
37681	2316	21	AB	AB	NNP
37681	2316	22	_	_	NNP
37681	2316	23	.	.	.
37681	2317	1	With	with	IN
37681	2317	2	any	any	DT
37681	2317	3	convenient	convenient	JJ
37681	2317	4	point	point	NN
37681	2317	5	_	_	NNP
37681	2317	6	O	O	NNP
37681	2317	7	_	_	NNP
37681	2317	8	as	as	IN
37681	2317	9	a	a	DT
37681	2317	10	center	center	NN
37681	2317	11	,	,	,
37681	2317	12	and	and	CC
37681	2317	13	_	_	NNP
37681	2317	14	OP	OP	NNP
37681	2317	15	_	_	NNP
37681	2317	16	as	as	IN
37681	2317	17	a	a	DT
37681	2317	18	radius	radius	NN
37681	2317	19	,	,	,
37681	2317	20	describe	describe	VB
37681	2317	21	a	a	DT
37681	2317	22	circle	circle	NN
37681	2317	23	cutting	cut	VBG
37681	2317	24	_	_	NNP
37681	2317	25	AB	AB	NNP
37681	2317	26	_	_	NNP
37681	2317	27	in	in	IN
37681	2317	28	_	_	NNP
37681	2317	29	X	X	NNP
37681	2317	30	_	_	NNP
37681	2317	31	and	and	CC
37681	2317	32	_	_	NNP
37681	2317	33	Y	Y	NNP
37681	2317	34	_	_	NNP
37681	2317	35	.	.	.
37681	2318	1	Draw	Draw	NNP
37681	2318	2	_	_	NNP
37681	2318	3	PX	PX	NNP
37681	2318	4	_	_	NNP
37681	2318	5	.	.	.
37681	2319	1	Then	then	RB
37681	2319	2	with	with	IN
37681	2319	3	_	_	NNP
37681	2319	4	Y	Y	NNP
37681	2319	5	_	_	NNP
37681	2319	6	as	as	IN
37681	2319	7	a	a	DT
37681	2319	8	center	center	NN
37681	2319	9	and	and	CC
37681	2319	10	_	_	NNP
37681	2319	11	PX	PX	NNP
37681	2319	12	_	_	NNP
37681	2319	13	as	as	IN
37681	2319	14	a	a	DT
37681	2319	15	radius	radius	NN
37681	2319	16	draw	draw	VBP
37681	2319	17	an	an	DT
37681	2319	18	arc	arc	NN
37681	2319	19	cutting	cut	VBG
37681	2319	20	the	the	DT
37681	2319	21	circle	circle	NN
37681	2319	22	in	in	IN
37681	2319	23	_	_	NNP
37681	2319	24	Q	Q	NNP
37681	2319	25	_	_	NNP
37681	2319	26	.	.	.
37681	2320	1	Then	then	RB
37681	2320	2	run	run	VB
37681	2320	3	the	the	DT
37681	2320	4	line	line	NN
37681	2320	5	from	from	IN
37681	2320	6	_	_	NNP
37681	2320	7	P	P	NNP
37681	2320	8	_	_	NNP
37681	2320	9	to	to	IN
37681	2320	10	_	_	NNP
37681	2320	11	Q	Q	NNP
37681	2320	12	_	_	NNP
37681	2320	13	.	.	.
37681	2321	1	_	_	NNP
37681	2321	2	PQ	PQ	NNP
37681	2321	3	_	_	NNP
37681	2321	4	is	be	VBZ
37681	2321	5	parallel	parallel	NN
37681	2321	6	to	to	IN
37681	2321	7	_	_	NNP
37681	2321	8	AB	AB	NNP
37681	2321	9	_	_	NNP
37681	2321	10	by	by	IN
37681	2321	11	the	the	DT
37681	2321	12	converse	converse	NN
37681	2321	13	of	of	IN
37681	2321	14	the	the	DT
37681	2321	15	above	above	JJ
37681	2321	16	theorem	theorem	NN
37681	2321	17	,	,	,
37681	2321	18	which	which	WDT
37681	2321	19	is	be	VBZ
37681	2321	20	easily	easily	RB
37681	2321	21	shown	show	VBN
37681	2321	22	to	to	TO
37681	2321	23	be	be	VB
37681	2321	24	true	true	JJ
37681	2321	25	for	for	IN
37681	2321	26	this	this	DT
37681	2321	27	figure	figure	NN
37681	2321	28	.	.	.
37681	2322	1	THEOREM	THEOREM	NNP
37681	2322	2	.	.	.
37681	2323	1	_	_	XX
37681	2323	2	If	if	IN
37681	2323	3	two	two	CD
37681	2323	4	circles	circle	NNS
37681	2323	5	are	be	VBP
37681	2323	6	tangent	tangent	JJ
37681	2323	7	to	to	IN
37681	2323	8	each	each	DT
37681	2323	9	other	other	JJ
37681	2323	10	,	,	,
37681	2323	11	the	the	DT
37681	2323	12	line	line	NN
37681	2323	13	of	of	IN
37681	2323	14	centers	center	NNS
37681	2323	15	passes	pass	VBZ
37681	2323	16	through	through	IN
37681	2323	17	the	the	DT
37681	2323	18	point	point	NN
37681	2323	19	of	of	IN
37681	2323	20	contact	contact	NN
37681	2323	21	.	.	.
37681	2323	22	_	_	NNP
37681	2323	23	There	there	EX
37681	2323	24	are	be	VBP
37681	2323	25	many	many	JJ
37681	2323	26	illustrations	illustration	NNS
37681	2323	27	of	of	IN
37681	2323	28	this	this	DT
37681	2323	29	theorem	theorem	NN
37681	2323	30	in	in	IN
37681	2323	31	practical	practical	JJ
37681	2323	32	work	work	NN
37681	2323	33	,	,	,
37681	2323	34	as	as	IN
37681	2323	35	in	in	IN
37681	2323	36	the	the	DT
37681	2323	37	case	case	NN
37681	2323	38	of	of	IN
37681	2323	39	cogwheels	cogwheel	NNS
37681	2323	40	.	.	.
37681	2324	1	An	an	DT
37681	2324	2	interesting	interesting	JJ
37681	2324	3	application	application	NN
37681	2324	4	to	to	IN
37681	2324	5	engineering	engineering	NN
37681	2324	6	is	be	VBZ
37681	2324	7	seen	see	VBN
37681	2324	8	in	in	IN
37681	2324	9	the	the	DT
37681	2324	10	case	case	NN
37681	2324	11	of	of	IN
37681	2324	12	two	two	CD
37681	2324	13	parallel	parallel	JJ
37681	2324	14	streets	street	NNS
37681	2324	15	or	or	CC
37681	2324	16	lines	line	NNS
37681	2324	17	of	of	IN
37681	2324	18	track	track	NN
37681	2324	19	which	which	WDT
37681	2324	20	are	be	VBP
37681	2324	21	to	to	TO
37681	2324	22	be	be	VB
37681	2324	23	connected	connect	VBN
37681	2324	24	by	by	IN
37681	2324	25	a	a	DT
37681	2324	26	"	"	``
37681	2324	27	reversed	reversed	JJ
37681	2324	28	curve	curve	NN
37681	2324	29	.	.	.
37681	2324	30	"	"	''
37681	2325	1	[	[	-LRB-
37681	2325	2	Illustration	illustration	NN
37681	2325	3	]	]	-RRB-
37681	2325	4	If	if	IN
37681	2325	5	the	the	DT
37681	2325	6	lines	line	NNS
37681	2325	7	are	be	VBP
37681	2325	8	_	_	NNP
37681	2325	9	AB	AB	NNP
37681	2325	10	_	_	NNP
37681	2325	11	and	and	CC
37681	2325	12	_	_	NNP
37681	2325	13	CD	CD	NNP
37681	2325	14	_	_	NNP
37681	2325	15	,	,	,
37681	2325	16	and	and	CC
37681	2325	17	the	the	DT
37681	2325	18	connection	connection	NN
37681	2325	19	is	be	VBZ
37681	2325	20	to	to	TO
37681	2325	21	be	be	VB
37681	2325	22	made	make	VBN
37681	2325	23	,	,	,
37681	2325	24	as	as	IN
37681	2325	25	shown	show	VBN
37681	2325	26	,	,	,
37681	2325	27	from	from	IN
37681	2325	28	_	_	NNP
37681	2325	29	B	B	NNP
37681	2325	30	_	_	NNP
37681	2325	31	to	to	IN
37681	2325	32	_	_	NNP
37681	2325	33	C	C	NNP
37681	2325	34	_	_	NNP
37681	2325	35	,	,	,
37681	2325	36	we	-PRON-	PRP
37681	2325	37	may	may	MD
37681	2325	38	proceed	proceed	VB
37681	2325	39	as	as	IN
37681	2325	40	follows	follow	VBZ
37681	2325	41	:	:	:
37681	2325	42	Draw	Draw	NNP
37681	2325	43	_	_	NNP
37681	2325	44	BC	BC	NNP
37681	2325	45	_	_	NNP
37681	2325	46	and	and	CC
37681	2325	47	bisect	bisect	VB
37681	2325	48	it	-PRON-	PRP
37681	2325	49	at	at	IN
37681	2325	50	_	_	NNP
37681	2325	51	M	M	NNP
37681	2325	52	_	_	NNP
37681	2325	53	.	.	.
37681	2326	1	Erect	Erect	NNP
37681	2326	2	_	_	NNP
37681	2326	3	PO	PO	NNP
37681	2326	4	_	_	NNP
37681	2326	5	,	,	,
37681	2326	6	the	the	DT
37681	2326	7	perpendicular	perpendicular	JJ
37681	2326	8	bisector	bisector	NN
37681	2326	9	of	of	IN
37681	2326	10	_	_	NNP
37681	2326	11	BM	BM	NNP
37681	2326	12	_	_	NNP
37681	2326	13	;	;	:
37681	2326	14	and	and	CC
37681	2326	15	_	_	NNP
37681	2326	16	BO	BO	NNP
37681	2326	17	_	_	NNP
37681	2326	18	,	,	,
37681	2326	19	perpendicular	perpendicular	JJ
37681	2326	20	to	to	IN
37681	2326	21	_	_	NNP
37681	2326	22	AB	AB	NNP
37681	2326	23	_	_	NNP
37681	2326	24	.	.	.
37681	2327	1	Then	then	RB
37681	2327	2	_	_	NNP
37681	2327	3	O	O	NNP
37681	2327	4	_	_	NNP
37681	2327	5	is	be	VBZ
37681	2327	6	one	one	CD
37681	2327	7	center	center	NN
37681	2327	8	of	of	IN
37681	2327	9	curvature	curvature	NN
37681	2327	10	.	.	.
37681	2328	1	In	in	IN
37681	2328	2	the	the	DT
37681	2328	3	same	same	JJ
37681	2328	4	way	way	NN
37681	2328	5	fix	fix	NN
37681	2328	6	_	_	NNP
37681	2328	7	O	O	NNP
37681	2328	8	'	'	''
37681	2328	9	_	_	NN
37681	2328	10	.	.	.
37681	2329	1	Then	then	RB
37681	2329	2	to	to	TO
37681	2329	3	check	check	VB
37681	2329	4	the	the	DT
37681	2329	5	work	work	NN
37681	2329	6	apply	apply	VB
37681	2329	7	this	this	DT
37681	2329	8	theorem	theorem	NN
37681	2329	9	,	,	,
37681	2329	10	_	_	NNP
37681	2329	11	M	M	NNP
37681	2329	12	_	_	NNP
37681	2329	13	being	be	VBG
37681	2329	14	in	in	IN
37681	2329	15	the	the	DT
37681	2329	16	line	line	NN
37681	2329	17	of	of	IN
37681	2329	18	centers	center	NNS
37681	2329	19	_	_	NNP
37681	2329	20	OO	OO	NNP
37681	2329	21	'	'	POS
37681	2329	22	_	_	NNP
37681	2329	23	.	.	.
37681	2330	1	The	the	DT
37681	2330	2	curves	curve	NNS
37681	2330	3	may	may	MD
37681	2330	4	now	now	RB
37681	2330	5	be	be	VB
37681	2330	6	drawn	draw	VBN
37681	2330	7	,	,	,
37681	2330	8	and	and	CC
37681	2330	9	they	-PRON-	PRP
37681	2330	10	will	will	MD
37681	2330	11	be	be	VB
37681	2330	12	tangent	tangent	JJ
37681	2330	13	to	to	IN
37681	2330	14	_	_	NNP
37681	2330	15	AB	AB	NNP
37681	2330	16	_	_	NNP
37681	2330	17	,	,	,
37681	2330	18	to	to	IN
37681	2330	19	_	_	NNP
37681	2330	20	CD	CD	NNP
37681	2330	21	_	_	NNP
37681	2330	22	,	,	,
37681	2330	23	and	and	CC
37681	2330	24	to	to	IN
37681	2330	25	each	each	DT
37681	2330	26	other	other	JJ
37681	2330	27	.	.	.
37681	2331	1	At	at	IN
37681	2331	2	this	this	DT
37681	2331	3	point	point	NN
37681	2331	4	in	in	IN
37681	2331	5	the	the	DT
37681	2331	6	American	american	JJ
37681	2331	7	textbooks	textbook	NNS
37681	2331	8	it	-PRON-	PRP
37681	2331	9	is	be	VBZ
37681	2331	10	the	the	DT
37681	2331	11	custom	custom	NN
37681	2331	12	to	to	TO
37681	2331	13	insert	insert	VB
37681	2331	14	a	a	DT
37681	2331	15	brief	brief	JJ
37681	2331	16	treatment	treatment	NN
37681	2331	17	of	of	IN
37681	2331	18	measurement	measurement	NN
37681	2331	19	,	,	,
37681	2331	20	explaining	explain	VBG
37681	2331	21	what	what	WP
37681	2331	22	is	be	VBZ
37681	2331	23	meant	mean	VBN
37681	2331	24	by	by	IN
37681	2331	25	ratio	ratio	NN
37681	2331	26	,	,	,
37681	2331	27	commensurable	commensurable	JJ
37681	2331	28	and	and	CC
37681	2331	29	incommensurable	incommensurable	JJ
37681	2331	30	quantities	quantity	NNS
37681	2331	31	,	,	,
37681	2331	32	constant	constant	JJ
37681	2331	33	and	and	CC
37681	2331	34	variable	variable	JJ
37681	2331	35	,	,	,
37681	2331	36	and	and	CC
37681	2331	37	limit	limit	VB
37681	2331	38	,	,	,
37681	2331	39	and	and	CC
37681	2331	40	introducing	introduce	VBG
37681	2331	41	one	one	CD
37681	2331	42	or	or	CC
37681	2331	43	more	more	JJR
37681	2331	44	propositions	proposition	NNS
37681	2331	45	relating	relate	VBG
37681	2331	46	to	to	IN
37681	2331	47	limits	limit	NNS
37681	2331	48	.	.	.
37681	2332	1	The	the	DT
37681	2332	2	object	object	NN
37681	2332	3	of	of	IN
37681	2332	4	this	this	DT
37681	2332	5	departure	departure	NN
37681	2332	6	from	from	IN
37681	2332	7	the	the	DT
37681	2332	8	ancient	ancient	JJ
37681	2332	9	sequence	sequence	NN
37681	2332	10	,	,	,
37681	2332	11	which	which	WDT
37681	2332	12	postponed	postpone	VBD
37681	2332	13	this	this	DT
37681	2332	14	subject	subject	NN
37681	2332	15	to	to	IN
37681	2332	16	the	the	DT
37681	2332	17	book	book	NN
37681	2332	18	on	on	IN
37681	2332	19	ratio	ratio	NN
37681	2332	20	and	and	CC
37681	2332	21	proportion	proportion	NN
37681	2332	22	,	,	,
37681	2332	23	is	be	VBZ
37681	2332	24	to	to	TO
37681	2332	25	treat	treat	VB
37681	2332	26	the	the	DT
37681	2332	27	circle	circle	NN
37681	2332	28	more	more	RBR
37681	2332	29	completely	completely	RB
37681	2332	30	in	in	IN
37681	2332	31	Book	Book	NNP
37681	2332	32	III	III	NNP
37681	2332	33	.	.	.
37681	2333	1	It	-PRON-	PRP
37681	2333	2	must	must	MD
37681	2333	3	be	be	VB
37681	2333	4	confessed	confess	VBN
37681	2333	5	that	that	IN
37681	2333	6	the	the	DT
37681	2333	7	treatment	treatment	NN
37681	2333	8	is	be	VBZ
37681	2333	9	not	not	RB
37681	2333	10	as	as	RB
37681	2333	11	scientific	scientific	JJ
37681	2333	12	as	as	IN
37681	2333	13	that	that	DT
37681	2333	14	of	of	IN
37681	2333	15	Euclid	Euclid	NNP
37681	2333	16	,	,	,
37681	2333	17	as	as	IN
37681	2333	18	will	will	MD
37681	2333	19	be	be	VB
37681	2333	20	explained	explain	VBN
37681	2333	21	under	under	IN
37681	2333	22	Book	Book	NNP
37681	2333	23	III	III	NNP
37681	2333	24	,	,	,
37681	2333	25	but	but	CC
37681	2333	26	it	-PRON-	PRP
37681	2333	27	is	be	VBZ
37681	2333	28	far	far	RB
37681	2333	29	better	well	RBR
37681	2333	30	suited	suited	JJ
37681	2333	31	to	to	IN
37681	2333	32	the	the	DT
37681	2333	33	mind	mind	NN
37681	2333	34	of	of	IN
37681	2333	35	a	a	DT
37681	2333	36	boy	boy	NN
37681	2333	37	or	or	CC
37681	2333	38	girl	girl	NN
37681	2333	39	.	.	.
37681	2334	1	It	-PRON-	PRP
37681	2334	2	begins	begin	VBZ
37681	2334	3	by	by	IN
37681	2334	4	defining	define	VBG
37681	2334	5	measurement	measurement	NN
37681	2334	6	in	in	IN
37681	2334	7	a	a	DT
37681	2334	8	practical	practical	JJ
37681	2334	9	way	way	NN
37681	2334	10	,	,	,
37681	2334	11	as	as	IN
37681	2334	12	the	the	DT
37681	2334	13	finding	finding	NN
37681	2334	14	of	of	IN
37681	2334	15	the	the	DT
37681	2334	16	number	number	NN
37681	2334	17	of	of	IN
37681	2334	18	times	time	NNS
37681	2334	19	a	a	DT
37681	2334	20	quantity	quantity	NN
37681	2334	21	of	of	IN
37681	2334	22	any	any	DT
37681	2334	23	kind	kind	NN
37681	2334	24	contains	contain	VBZ
37681	2334	25	a	a	DT
37681	2334	26	known	know	VBN
37681	2334	27	quantity	quantity	NN
37681	2334	28	of	of	IN
37681	2334	29	the	the	DT
37681	2334	30	same	same	JJ
37681	2334	31	kind	kind	NN
37681	2334	32	.	.	.
37681	2335	1	Of	of	RB
37681	2335	2	course	course	RB
37681	2335	3	this	this	DT
37681	2335	4	gives	give	VBZ
37681	2335	5	a	a	DT
37681	2335	6	number	number	NN
37681	2335	7	,	,	,
37681	2335	8	but	but	CC
37681	2335	9	this	this	DT
37681	2335	10	number	number	NN
37681	2335	11	may	may	MD
37681	2335	12	be	be	VB
37681	2335	13	a	a	DT
37681	2335	14	surd	surd	JJ
37681	2335	15	,	,	,
37681	2335	16	like	like	IN
37681	2335	17	[	[	-LRB-
37681	2335	18	sqrt]2	sqrt]2	NN
37681	2335	19	.	.	.
37681	2336	1	In	in	IN
37681	2336	2	other	other	JJ
37681	2336	3	words	word	NNS
37681	2336	4	,	,	,
37681	2336	5	the	the	DT
37681	2336	6	magnitude	magnitude	NN
37681	2336	7	measured	measure	VBN
37681	2336	8	may	may	MD
37681	2336	9	be	be	VB
37681	2336	10	incommensurable	incommensurable	JJ
37681	2336	11	with	with	IN
37681	2336	12	the	the	DT
37681	2336	13	unit	unit	NN
37681	2336	14	of	of	IN
37681	2336	15	measure	measure	NN
37681	2336	16	,	,	,
37681	2336	17	a	a	DT
37681	2336	18	seeming	seeming	JJ
37681	2336	19	paradox	paradox	NN
37681	2336	20	.	.	.
37681	2337	1	With	with	IN
37681	2337	2	this	this	DT
37681	2337	3	difficulty	difficulty	NN
37681	2337	4	,	,	,
37681	2337	5	however	however	RB
37681	2337	6	,	,	,
37681	2337	7	the	the	DT
37681	2337	8	pupil	pupil	NN
37681	2337	9	should	should	MD
37681	2337	10	not	not	RB
37681	2337	11	be	be	VB
37681	2337	12	called	call	VBN
37681	2337	13	upon	upon	IN
37681	2337	14	to	to	TO
37681	2337	15	contend	contend	VB
37681	2337	16	at	at	IN
37681	2337	17	this	this	DT
37681	2337	18	stage	stage	NN
37681	2337	19	in	in	IN
37681	2337	20	his	-PRON-	PRP$
37681	2337	21	progress	progress	NN
37681	2337	22	.	.	.
37681	2338	1	The	the	DT
37681	2338	2	whole	whole	JJ
37681	2338	3	subject	subject	NN
37681	2338	4	of	of	IN
37681	2338	5	incommensurables	incommensurable	NNS
37681	2338	6	might	may	MD
37681	2338	7	safely	safely	RB
37681	2338	8	be	be	VB
37681	2338	9	postponed	postpone	VBN
37681	2338	10	,	,	,
37681	2338	11	although	although	IN
37681	2338	12	it	-PRON-	PRP
37681	2338	13	may	may	MD
37681	2338	14	be	be	VB
37681	2338	15	treated	treat	VBN
37681	2338	16	in	in	IN
37681	2338	17	an	an	DT
37681	2338	18	elementary	elementary	JJ
37681	2338	19	fashion	fashion	NN
37681	2338	20	at	at	IN
37681	2338	21	this	this	DT
37681	2338	22	time	time	NN
37681	2338	23	.	.	.
37681	2339	1	The	the	DT
37681	2339	2	fact	fact	NN
37681	2339	3	that	that	IN
37681	2339	4	the	the	DT
37681	2339	5	measure	measure	NN
37681	2339	6	of	of	IN
37681	2339	7	the	the	DT
37681	2339	8	diagonal	diagonal	JJ
37681	2339	9	of	of	IN
37681	2339	10	a	a	DT
37681	2339	11	square	square	NN
37681	2339	12	,	,	,
37681	2339	13	of	of	IN
37681	2339	14	which	which	WDT
37681	2339	15	a	a	DT
37681	2339	16	side	side	NN
37681	2339	17	is	be	VBZ
37681	2339	18	unity	unity	NN
37681	2339	19	,	,	,
37681	2339	20	is	be	VBZ
37681	2339	21	[	[	-LRB-
37681	2339	22	sqrt]2	sqrt]2	CD
37681	2339	23	,	,	,
37681	2339	24	and	and	CC
37681	2339	25	that	that	IN
37681	2339	26	this	this	DT
37681	2339	27	measure	measure	NN
37681	2339	28	is	be	VBZ
37681	2339	29	an	an	DT
37681	2339	30	incommensurable	incommensurable	JJ
37681	2339	31	number	number	NN
37681	2339	32	,	,	,
37681	2339	33	is	be	VBZ
37681	2339	34	not	not	RB
37681	2339	35	so	so	RB
37681	2339	36	paradoxical	paradoxical	JJ
37681	2339	37	as	as	IN
37681	2339	38	it	-PRON-	PRP
37681	2339	39	seems	seem	VBZ
37681	2339	40	,	,	,
37681	2339	41	the	the	DT
37681	2339	42	paradox	paradox	NN
37681	2339	43	being	be	VBG
37681	2339	44	verbal	verbal	JJ
37681	2339	45	rather	rather	RB
37681	2339	46	than	than	IN
37681	2339	47	actual	actual	JJ
37681	2339	48	.	.	.
37681	2340	1	It	-PRON-	PRP
37681	2340	2	is	be	VBZ
37681	2340	3	then	then	RB
37681	2340	4	customary	customary	JJ
37681	2340	5	to	to	TO
37681	2340	6	define	define	VB
37681	2340	7	ratio	ratio	NN
37681	2340	8	as	as	IN
37681	2340	9	the	the	DT
37681	2340	10	quotient	quotient	NN
37681	2340	11	of	of	IN
37681	2340	12	the	the	DT
37681	2340	13	numerical	numerical	JJ
37681	2340	14	measures	measure	NNS
37681	2340	15	of	of	IN
37681	2340	16	two	two	CD
37681	2340	17	quantities	quantity	NNS
37681	2340	18	in	in	IN
37681	2340	19	terms	term	NNS
37681	2340	20	of	of	IN
37681	2340	21	a	a	DT
37681	2340	22	common	common	JJ
37681	2340	23	unit	unit	NN
37681	2340	24	.	.	.
37681	2341	1	This	this	DT
37681	2341	2	brings	bring	VBZ
37681	2341	3	all	all	DT
37681	2341	4	ratios	ratio	NNS
37681	2341	5	to	to	IN
37681	2341	6	the	the	DT
37681	2341	7	basis	basis	NN
37681	2341	8	of	of	IN
37681	2341	9	numerical	numerical	JJ
37681	2341	10	fractions	fraction	NNS
37681	2341	11	,	,	,
37681	2341	12	and	and	CC
37681	2341	13	while	while	IN
37681	2341	14	it	-PRON-	PRP
37681	2341	15	is	be	VBZ
37681	2341	16	not	not	RB
37681	2341	17	scientifically	scientifically	RB
37681	2341	18	so	so	RB
37681	2341	19	satisfactory	satisfactory	JJ
37681	2341	20	as	as	IN
37681	2341	21	the	the	DT
37681	2341	22	ancient	ancient	JJ
37681	2341	23	concept	concept	NN
37681	2341	24	which	which	WDT
37681	2341	25	considered	consider	VBD
37681	2341	26	the	the	DT
37681	2341	27	terms	term	NNS
37681	2341	28	as	as	IN
37681	2341	29	lines	line	NNS
37681	2341	30	,	,	,
37681	2341	31	surfaces	surface	NNS
37681	2341	32	,	,	,
37681	2341	33	angles	angle	NNS
37681	2341	34	,	,	,
37681	2341	35	or	or	CC
37681	2341	36	solids	solid	NNS
37681	2341	37	,	,	,
37681	2341	38	it	-PRON-	PRP
37681	2341	39	is	be	VBZ
37681	2341	40	more	more	RBR
37681	2341	41	practical	practical	JJ
37681	2341	42	,	,	,
37681	2341	43	and	and	CC
37681	2341	44	it	-PRON-	PRP
37681	2341	45	suffices	suffice	VBZ
37681	2341	46	for	for	IN
37681	2341	47	the	the	DT
37681	2341	48	needs	need	NNS
37681	2341	49	of	of	IN
37681	2341	50	elementary	elementary	JJ
37681	2341	51	pupils	pupil	NNS
37681	2341	52	.	.	.
37681	2342	1	"	"	``
37681	2342	2	Commensurable	commensurable	JJ
37681	2342	3	,	,	,
37681	2342	4	"	"	''
37681	2342	5	"	"	``
37681	2342	6	incommensurable	incommensurable	JJ
37681	2342	7	,	,	,
37681	2342	8	"	"	''
37681	2342	9	"	"	``
37681	2342	10	constant	constant	JJ
37681	2342	11	,	,	,
37681	2342	12	"	"	''
37681	2342	13	and	and	CC
37681	2342	14	"	"	``
37681	2342	15	variable	variable	JJ
37681	2342	16	"	"	''
37681	2342	17	are	be	VBP
37681	2342	18	then	then	RB
37681	2342	19	defined	define	VBN
37681	2342	20	,	,	,
37681	2342	21	and	and	CC
37681	2342	22	these	these	DT
37681	2342	23	definitions	definition	NNS
37681	2342	24	are	be	VBP
37681	2342	25	followed	follow	VBN
37681	2342	26	by	by	IN
37681	2342	27	a	a	DT
37681	2342	28	brief	brief	JJ
37681	2342	29	discussion	discussion	NN
37681	2342	30	of	of	IN
37681	2342	31	limit	limit	NN
37681	2342	32	.	.	.
37681	2343	1	It	-PRON-	PRP
37681	2343	2	simplifies	simplify	VBZ
37681	2343	3	the	the	DT
37681	2343	4	treatment	treatment	NN
37681	2343	5	of	of	IN
37681	2343	6	this	this	DT
37681	2343	7	subject	subject	NN
37681	2343	8	to	to	IN
37681	2343	9	state	state	NN
37681	2343	10	at	at	IN
37681	2343	11	once	once	IN
37681	2343	12	that	that	IN
37681	2343	13	there	there	EX
37681	2343	14	are	be	VBP
37681	2343	15	two	two	CD
37681	2343	16	classes	class	NNS
37681	2343	17	of	of	IN
37681	2343	18	limits,--those	limits,--those	NNP
37681	2343	19	which	which	WDT
37681	2343	20	the	the	DT
37681	2343	21	variable	variable	NN
37681	2343	22	actually	actually	RB
37681	2343	23	reaches	reach	VBZ
37681	2343	24	,	,	,
37681	2343	25	and	and	CC
37681	2343	26	those	those	DT
37681	2343	27	which	which	WDT
37681	2343	28	it	-PRON-	PRP
37681	2343	29	can	can	MD
37681	2343	30	only	only	RB
37681	2343	31	approach	approach	VB
37681	2343	32	indefinitely	indefinitely	RB
37681	2343	33	near	near	RB
37681	2343	34	.	.	.
37681	2344	1	We	-PRON-	PRP
37681	2344	2	find	find	VBP
37681	2344	3	the	the	DT
37681	2344	4	one	one	NN
37681	2344	5	as	as	RB
37681	2344	6	frequently	frequently	RB
37681	2344	7	as	as	IN
37681	2344	8	we	-PRON-	PRP
37681	2344	9	find	find	VBP
37681	2344	10	the	the	DT
37681	2344	11	other	other	JJ
37681	2344	12	,	,	,
37681	2344	13	although	although	IN
37681	2344	14	it	-PRON-	PRP
37681	2344	15	is	be	VBZ
37681	2344	16	the	the	DT
37681	2344	17	latter	latter	JJ
37681	2344	18	that	that	WDT
37681	2344	19	is	be	VBZ
37681	2344	20	referred	refer	VBN
37681	2344	21	to	to	IN
37681	2344	22	in	in	IN
37681	2344	23	geometry	geometry	NN
37681	2344	24	.	.	.
37681	2345	1	For	for	IN
37681	2345	2	example	example	NN
37681	2345	3	,	,	,
37681	2345	4	the	the	DT
37681	2345	5	superior	superior	JJ
37681	2345	6	limit	limit	NN
37681	2345	7	of	of	IN
37681	2345	8	a	a	DT
37681	2345	9	chord	chord	NN
37681	2345	10	is	be	VBZ
37681	2345	11	a	a	DT
37681	2345	12	diameter	diameter	NN
37681	2345	13	,	,	,
37681	2345	14	and	and	CC
37681	2345	15	this	this	DT
37681	2345	16	limit	limit	NN
37681	2345	17	the	the	DT
37681	2345	18	chord	chord	NN
37681	2345	19	may	may	MD
37681	2345	20	reach	reach	VB
37681	2345	21	.	.	.
37681	2346	1	The	the	DT
37681	2346	2	inferior	inferior	JJ
37681	2346	3	limit	limit	NN
37681	2346	4	is	be	VBZ
37681	2346	5	zero	zero	CD
37681	2346	6	,	,	,
37681	2346	7	but	but	CC
37681	2346	8	we	-PRON-	PRP
37681	2346	9	do	do	VBP
37681	2346	10	not	not	RB
37681	2346	11	consider	consider	VB
37681	2346	12	the	the	DT
37681	2346	13	chord	chord	NN
37681	2346	14	as	as	IN
37681	2346	15	reaching	reach	VBG
37681	2346	16	this	this	DT
37681	2346	17	limit	limit	NN
37681	2346	18	.	.	.
37681	2347	1	It	-PRON-	PRP
37681	2347	2	is	be	VBZ
37681	2347	3	also	also	RB
37681	2347	4	well	well	JJ
37681	2347	5	to	to	TO
37681	2347	6	call	call	VB
37681	2347	7	the	the	DT
37681	2347	8	attention	attention	NN
37681	2347	9	of	of	IN
37681	2347	10	pupils	pupil	NNS
37681	2347	11	to	to	IN
37681	2347	12	the	the	DT
37681	2347	13	fact	fact	NN
37681	2347	14	that	that	IN
37681	2347	15	a	a	DT
37681	2347	16	quantity	quantity	NN
37681	2347	17	may	may	MD
37681	2347	18	decrease	decrease	VB
37681	2347	19	towards	towards	IN
37681	2347	20	its	-PRON-	PRP$
37681	2347	21	limit	limit	NN
37681	2347	22	as	as	RB
37681	2347	23	well	well	RB
37681	2347	24	as	as	IN
37681	2347	25	increase	increase	NN
37681	2347	26	towards	towards	IN
37681	2347	27	it	-PRON-	PRP
37681	2347	28	.	.	.
37681	2348	1	Such	such	JJ
37681	2348	2	further	further	JJ
37681	2348	3	definitions	definition	NNS
37681	2348	4	as	as	IN
37681	2348	5	are	be	VBP
37681	2348	6	needed	need	VBN
37681	2348	7	in	in	IN
37681	2348	8	the	the	DT
37681	2348	9	theory	theory	NN
37681	2348	10	of	of	IN
37681	2348	11	limits	limit	NNS
37681	2348	12	are	be	VBP
37681	2348	13	now	now	RB
37681	2348	14	introduced	introduce	VBN
37681	2348	15	.	.	.
37681	2349	1	Among	among	IN
37681	2349	2	these	these	DT
37681	2349	3	is	be	VBZ
37681	2349	4	"	"	``
37681	2349	5	area	area	NN
37681	2349	6	of	of	IN
37681	2349	7	a	a	DT
37681	2349	8	circle	circle	NN
37681	2349	9	.	.	.
37681	2349	10	"	"	''
37681	2350	1	It	-PRON-	PRP
37681	2350	2	might	may	MD
37681	2350	3	occur	occur	VB
37681	2350	4	to	to	IN
37681	2350	5	some	some	DT
37681	2350	6	pupil	pupil	NN
37681	2350	7	that	that	IN
37681	2350	8	since	since	IN
37681	2350	9	a	a	DT
37681	2350	10	circle	circle	NN
37681	2350	11	is	be	VBZ
37681	2350	12	a	a	DT
37681	2350	13	line	line	NN
37681	2350	14	(	(	-LRB-
37681	2350	15	as	as	IN
37681	2350	16	used	use	VBN
37681	2350	17	in	in	IN
37681	2350	18	modern	modern	JJ
37681	2350	19	mathematics	mathematic	NNS
37681	2350	20	)	)	-RRB-
37681	2350	21	,	,	,
37681	2350	22	it	-PRON-	PRP
37681	2350	23	can	can	MD
37681	2350	24	have	have	VB
37681	2350	25	no	no	DT
37681	2350	26	area	area	NN
37681	2350	27	.	.	.
37681	2351	1	This	this	DT
37681	2351	2	is	be	VBZ
37681	2351	3	,	,	,
37681	2351	4	however	however	RB
37681	2351	5	,	,	,
37681	2351	6	a	a	DT
37681	2351	7	mere	mere	JJ
37681	2351	8	quibble	quibble	NN
37681	2351	9	over	over	IN
37681	2351	10	words	word	NNS
37681	2351	11	.	.	.
37681	2352	1	It	-PRON-	PRP
37681	2352	2	is	be	VBZ
37681	2352	3	not	not	RB
37681	2352	4	pretended	pretend	VBN
37681	2352	5	that	that	IN
37681	2352	6	the	the	DT
37681	2352	7	line	line	NN
37681	2352	8	has	have	VBZ
37681	2352	9	area	area	NN
37681	2352	10	,	,	,
37681	2352	11	but	but	CC
37681	2352	12	that	that	IN
37681	2352	13	"	"	``
37681	2352	14	area	area	NN
37681	2352	15	of	of	IN
37681	2352	16	a	a	DT
37681	2352	17	circle	circle	NN
37681	2352	18	"	"	``
37681	2352	19	is	be	VBZ
37681	2352	20	merely	merely	RB
37681	2352	21	a	a	DT
37681	2352	22	shortened	shorten	VBN
37681	2352	23	form	form	NN
37681	2352	24	of	of	IN
37681	2352	25	the	the	DT
37681	2352	26	expression	expression	NN
37681	2352	27	"	"	''
37681	2352	28	area	area	NN
37681	2352	29	inclosed	inclose	VBN
37681	2352	30	by	by	IN
37681	2352	31	a	a	DT
37681	2352	32	circle	circle	NN
37681	2352	33	.	.	.
37681	2352	34	"	"	''
37681	2353	1	The	the	DT
37681	2353	2	Principle	Principle	NNP
37681	2353	3	of	of	IN
37681	2353	4	Limits	Limits	NNPS
37681	2353	5	is	be	VBZ
37681	2353	6	now	now	RB
37681	2353	7	usually	usually	RB
37681	2353	8	given	give	VBN
37681	2353	9	as	as	IN
37681	2353	10	follows	follow	VBZ
37681	2353	11	:	:	:
37681	2353	12	"	"	``
37681	2353	13	If	if	IN
37681	2353	14	,	,	,
37681	2353	15	while	while	IN
37681	2353	16	approaching	approach	VBG
37681	2353	17	their	-PRON-	PRP$
37681	2353	18	respective	respective	JJ
37681	2353	19	limits	limit	NNS
37681	2353	20	,	,	,
37681	2353	21	two	two	CD
37681	2353	22	variables	variable	NNS
37681	2353	23	are	be	VBP
37681	2353	24	always	always	RB
37681	2353	25	equal	equal	JJ
37681	2353	26	,	,	,
37681	2353	27	their	-PRON-	PRP$
37681	2353	28	limits	limit	NNS
37681	2353	29	are	be	VBP
37681	2353	30	equal	equal	JJ
37681	2353	31	.	.	.
37681	2353	32	"	"	''
37681	2354	1	This	this	DT
37681	2354	2	was	be	VBD
37681	2354	3	expressed	express	VBN
37681	2354	4	by	by	IN
37681	2354	5	D'Alembert	D'Alembert	NNP
37681	2354	6	in	in	IN
37681	2354	7	the	the	DT
37681	2354	8	eighteenth	eighteenth	JJ
37681	2354	9	century	century	NN
37681	2354	10	as	as	IN
37681	2354	11	"	"	``
37681	2354	12	Magnitudes	magnitude	NNS
37681	2354	13	which	which	WDT
37681	2354	14	are	be	VBP
37681	2354	15	the	the	DT
37681	2354	16	limits	limit	NNS
37681	2354	17	of	of	IN
37681	2354	18	equal	equal	JJ
37681	2354	19	magnitudes	magnitude	NNS
37681	2354	20	are	be	VBP
37681	2354	21	equal	equal	JJ
37681	2354	22	,	,	,
37681	2354	23	"	"	''
37681	2354	24	or	or	CC
37681	2354	25	this	this	DT
37681	2354	26	in	in	IN
37681	2354	27	substance	substance	NN
37681	2354	28	.	.	.
37681	2355	1	It	-PRON-	PRP
37681	2355	2	would	would	MD
37681	2355	3	easily	easily	RB
37681	2355	4	be	be	VB
37681	2355	5	possible	possible	JJ
37681	2355	6	to	to	TO
37681	2355	7	elaborate	elaborate	VB
37681	2355	8	this	this	DT
37681	2355	9	theory	theory	NN
37681	2355	10	,	,	,
37681	2355	11	proving	prove	VBG
37681	2355	12	,	,	,
37681	2355	13	for	for	IN
37681	2355	14	example	example	NN
37681	2355	15	,	,	,
37681	2355	16	that	that	IN
37681	2355	17	if	if	IN
37681	2355	18	_	_	NNP
37681	2355	19	x	x	NNP
37681	2355	20	_	_	NNP
37681	2355	21	approaches	approach	NNS
37681	2355	22	_	_	NNP
37681	2355	23	y	y	NNP
37681	2355	24	_	_	NNP
37681	2355	25	as	as	IN
37681	2355	26	its	-PRON-	PRP$
37681	2355	27	limit	limit	NN
37681	2355	28	,	,	,
37681	2355	29	then	then	RB
37681	2355	30	_	_	NNP
37681	2355	31	ax	ax	NNP
37681	2355	32	_	_	NNP
37681	2355	33	approaches	approach	VBZ
37681	2355	34	_	_	NNP
37681	2355	35	ay	ay	PRP
37681	2355	36	_	_	NNP
37681	2355	37	as	as	IN
37681	2355	38	its	-PRON-	PRP$
37681	2355	39	limit	limit	NN
37681	2355	40	,	,	,
37681	2355	41	and	and	CC
37681	2355	42	_	_	NNP
37681	2355	43	x	x	NNP
37681	2355	44	/	/	SYM
37681	2355	45	a	a	DT
37681	2355	46	_	_	NNP
37681	2355	47	approaches	approach	VBZ
37681	2355	48	_	_	NNP
37681	2355	49	y	y	NNP
37681	2355	50	/	/	SYM
37681	2355	51	a	a	DT
37681	2355	52	_	_	NNP
37681	2355	53	as	as	IN
37681	2355	54	its	-PRON-	PRP$
37681	2355	55	limit	limit	NN
37681	2355	56	,	,	,
37681	2355	57	and	and	CC
37681	2355	58	so	so	RB
37681	2355	59	on	on	RB
37681	2355	60	.	.	.
37681	2356	1	Very	very	RB
37681	2356	2	much	much	JJ
37681	2356	3	of	of	IN
37681	2356	4	this	this	DT
37681	2356	5	theory	theory	NN
37681	2356	6	,	,	,
37681	2356	7	however	however	RB
37681	2356	8	,	,	,
37681	2356	9	wearies	weary	VBZ
37681	2356	10	a	a	DT
37681	2356	11	pupil	pupil	NN
37681	2356	12	so	so	IN
37681	2356	13	that	that	IN
37681	2356	14	the	the	DT
37681	2356	15	entire	entire	JJ
37681	2356	16	meaning	meaning	NN
37681	2356	17	of	of	IN
37681	2356	18	the	the	DT
37681	2356	19	subject	subject	NN
37681	2356	20	is	be	VBZ
37681	2356	21	lost	lose	VBN
37681	2356	22	,	,	,
37681	2356	23	and	and	CC
37681	2356	24	at	at	IN
37681	2356	25	best	good	JJS
37681	2356	26	the	the	DT
37681	2356	27	treatment	treatment	NN
37681	2356	28	in	in	IN
37681	2356	29	elementary	elementary	JJ
37681	2356	30	geometry	geometry	NN
37681	2356	31	is	be	VBZ
37681	2356	32	not	not	RB
37681	2356	33	rigorous	rigorous	JJ
37681	2356	34	.	.	.
37681	2357	1	It	-PRON-	PRP
37681	2357	2	is	be	VBZ
37681	2357	3	another	another	DT
37681	2357	4	case	case	NN
37681	2357	5	of	of	IN
37681	2357	6	having	have	VBG
37681	2357	7	to	to	TO
37681	2357	8	sacrifice	sacrifice	VB
37681	2357	9	a	a	DT
37681	2357	10	strictly	strictly	RB
37681	2357	11	scientific	scientific	JJ
37681	2357	12	treatment	treatment	NN
37681	2357	13	to	to	IN
37681	2357	14	the	the	DT
37681	2357	15	educational	educational	JJ
37681	2357	16	abilities	ability	NNS
37681	2357	17	of	of	IN
37681	2357	18	the	the	DT
37681	2357	19	pupil	pupil	NN
37681	2357	20	.	.	.
37681	2358	1	Teachers	teacher	NNS
37681	2358	2	wishing	wish	VBG
37681	2358	3	to	to	TO
37681	2358	4	find	find	VB
37681	2358	5	a	a	DT
37681	2358	6	scientific	scientific	JJ
37681	2358	7	treatment	treatment	NN
37681	2358	8	of	of	IN
37681	2358	9	the	the	DT
37681	2358	10	subject	subject	NN
37681	2358	11	should	should	MD
37681	2358	12	consult	consult	VB
37681	2358	13	a	a	DT
37681	2358	14	good	good	JJ
37681	2358	15	work	work	NN
37681	2358	16	on	on	IN
37681	2358	17	the	the	DT
37681	2358	18	calculus	calculus	NN
37681	2358	19	.	.	.
37681	2359	1	THEOREM	THEOREM	NNP
37681	2359	2	.	.	.
37681	2360	1	_	_	NNP
37681	2360	2	In	in	IN
37681	2360	3	the	the	DT
37681	2360	4	same	same	JJ
37681	2360	5	circle	circle	NN
37681	2360	6	or	or	CC
37681	2360	7	in	in	IN
37681	2360	8	equal	equal	JJ
37681	2360	9	circles	circle	NNS
37681	2360	10	two	two	CD
37681	2360	11	central	central	JJ
37681	2360	12	angles	angle	NNS
37681	2360	13	have	have	VBP
37681	2360	14	the	the	DT
37681	2360	15	same	same	JJ
37681	2360	16	ratio	ratio	NN
37681	2360	17	as	as	IN
37681	2360	18	their	-PRON-	PRP$
37681	2360	19	intercepted	intercept	VBN
37681	2360	20	arcs	arc	NNS
37681	2360	21	.	.	.
37681	2360	22	_	_	NNP
37681	2360	23	This	this	DT
37681	2360	24	is	be	VBZ
37681	2360	25	usually	usually	RB
37681	2360	26	proved	prove	VBN
37681	2360	27	first	first	RB
37681	2360	28	for	for	IN
37681	2360	29	the	the	DT
37681	2360	30	commensurable	commensurable	JJ
37681	2360	31	case	case	NN
37681	2360	32	and	and	CC
37681	2360	33	then	then	RB
37681	2360	34	for	for	IN
37681	2360	35	the	the	DT
37681	2360	36	incommensurable	incommensurable	JJ
37681	2360	37	one	one	CD
37681	2360	38	.	.	.
37681	2361	1	The	the	DT
37681	2361	2	latter	latter	JJ
37681	2361	3	is	be	VBZ
37681	2361	4	rarely	rarely	RB
37681	2361	5	understood	understand	VBN
37681	2361	6	by	by	IN
37681	2361	7	all	all	DT
37681	2361	8	of	of	IN
37681	2361	9	the	the	DT
37681	2361	10	class	class	NN
37681	2361	11	,	,	,
37681	2361	12	and	and	CC
37681	2361	13	it	-PRON-	PRP
37681	2361	14	may	may	MD
37681	2361	15	very	very	RB
37681	2361	16	properly	properly	RB
37681	2361	17	be	be	VB
37681	2361	18	required	require	VBN
37681	2361	19	only	only	RB
37681	2361	20	of	of	IN
37681	2361	21	those	those	DT
37681	2361	22	who	who	WP
37681	2361	23	show	show	VBP
37681	2361	24	some	some	DT
37681	2361	25	aptitude	aptitude	NN
37681	2361	26	in	in	IN
37681	2361	27	geometry	geometry	NN
37681	2361	28	.	.	.
37681	2362	1	It	-PRON-	PRP
37681	2362	2	is	be	VBZ
37681	2362	3	better	well	JJR
37681	2362	4	to	to	TO
37681	2362	5	have	have	VB
37681	2362	6	the	the	DT
37681	2362	7	others	other	NNS
37681	2362	8	understand	understand	VB
37681	2362	9	fully	fully	RB
37681	2362	10	the	the	DT
37681	2362	11	commensurable	commensurable	JJ
37681	2362	12	case	case	NN
37681	2362	13	and	and	CC
37681	2362	14	see	see	VB
37681	2362	15	the	the	DT
37681	2362	16	nature	nature	NN
37681	2362	17	of	of	IN
37681	2362	18	its	-PRON-	PRP$
37681	2362	19	applications	application	NNS
37681	2362	20	,	,	,
37681	2362	21	possibly	possibly	RB
37681	2362	22	reading	read	VBG
37681	2362	23	the	the	DT
37681	2362	24	incommensurable	incommensurable	JJ
37681	2362	25	proof	proof	NN
37681	2362	26	with	with	IN
37681	2362	27	the	the	DT
37681	2362	28	teacher	teacher	NN
37681	2362	29	,	,	,
37681	2362	30	than	than	IN
37681	2362	31	to	to	TO
37681	2362	32	stumble	stumble	VB
37681	2362	33	about	about	IN
37681	2362	34	in	in	IN
37681	2362	35	the	the	DT
37681	2362	36	darkness	darkness	NN
37681	2362	37	of	of	IN
37681	2362	38	the	the	DT
37681	2362	39	incommensurable	incommensurable	JJ
37681	2362	40	case	case	NN
37681	2362	41	and	and	CC
37681	2362	42	never	never	RB
37681	2362	43	reach	reach	VB
37681	2362	44	the	the	DT
37681	2362	45	goal	goal	NN
37681	2362	46	.	.	.
37681	2363	1	In	in	IN
37681	2363	2	Euclid	Euclid	NNP
37681	2363	3	there	there	EX
37681	2363	4	was	be	VBD
37681	2363	5	no	no	DT
37681	2363	6	distinction	distinction	NN
37681	2363	7	between	between	IN
37681	2363	8	the	the	DT
37681	2363	9	two	two	CD
37681	2363	10	because	because	IN
37681	2363	11	his	-PRON-	PRP$
37681	2363	12	definition	definition	NN
37681	2363	13	of	of	IN
37681	2363	14	ratio	ratio	NN
37681	2363	15	covered	cover	VBN
37681	2363	16	both	both	CC
37681	2363	17	;	;	:
37681	2363	18	but	but	CC
37681	2363	19	,	,	,
37681	2363	20	as	as	IN
37681	2363	21	we	-PRON-	PRP
37681	2363	22	shall	shall	MD
37681	2363	23	see	see	VB
37681	2363	24	in	in	IN
37681	2363	25	Book	Book	NNP
37681	2363	26	III	III	NNP
37681	2363	27	,	,	,
37681	2363	28	this	this	DT
37681	2363	29	definition	definition	NN
37681	2363	30	is	be	VBZ
37681	2363	31	too	too	RB
37681	2363	32	difficult	difficult	JJ
37681	2363	33	for	for	IN
37681	2363	34	our	-PRON-	PRP$
37681	2363	35	pupils	pupil	NNS
37681	2363	36	.	.	.
37681	2364	1	Theon	Theon	NNP
37681	2364	2	of	of	IN
37681	2364	3	Alexandria	Alexandria	NNP
37681	2364	4	(	(	-LRB-
37681	2364	5	fourth	fourth	JJ
37681	2364	6	century	century	NN
37681	2364	7	A.D.	A.D.	NNP
37681	2364	8	)	)	-RRB-
37681	2364	9	,	,	,
37681	2364	10	the	the	DT
37681	2364	11	father	father	NN
37681	2364	12	of	of	IN
37681	2364	13	the	the	DT
37681	2364	14	Hypatia	Hypatia	NNP
37681	2364	15	who	who	WP
37681	2364	16	is	be	VBZ
37681	2364	17	the	the	DT
37681	2364	18	heroine	heroine	NN
37681	2364	19	of	of	IN
37681	2364	20	Kingsley	Kingsley	NNP
37681	2364	21	's	's	POS
37681	2364	22	well	well	RB
37681	2364	23	-	-	HYPH
37681	2364	24	known	know	VBN
37681	2364	25	novel	novel	NN
37681	2364	26	,	,	,
37681	2364	27	wrote	write	VBD
37681	2364	28	a	a	DT
37681	2364	29	commentary	commentary	NN
37681	2364	30	on	on	IN
37681	2364	31	Euclid	Euclid	NNP
37681	2364	32	,	,	,
37681	2364	33	and	and	CC
37681	2364	34	he	-PRON-	PRP
37681	2364	35	adds	add	VBZ
37681	2364	36	that	that	IN
37681	2364	37	sectors	sector	NNS
37681	2364	38	also	also	RB
37681	2364	39	have	have	VBP
37681	2364	40	the	the	DT
37681	2364	41	same	same	JJ
37681	2364	42	ratio	ratio	NN
37681	2364	43	as	as	IN
37681	2364	44	the	the	DT
37681	2364	45	arcs	arc	NNS
37681	2364	46	,	,	,
37681	2364	47	a	a	DT
37681	2364	48	fact	fact	NN
37681	2364	49	very	very	RB
37681	2364	50	easily	easily	RB
37681	2364	51	proved	prove	VBN
37681	2364	52	.	.	.
37681	2365	1	In	in	IN
37681	2365	2	propositions	proposition	NNS
37681	2365	3	of	of	IN
37681	2365	4	this	this	DT
37681	2365	5	type	type	NN
37681	2365	6	,	,	,
37681	2365	7	referring	refer	VBG
37681	2365	8	to	to	IN
37681	2365	9	the	the	DT
37681	2365	10	same	same	JJ
37681	2365	11	circle	circle	NN
37681	2365	12	or	or	CC
37681	2365	13	to	to	TO
37681	2365	14	equal	equal	JJ
37681	2365	15	circles	circle	NNS
37681	2365	16	,	,	,
37681	2365	17	it	-PRON-	PRP
37681	2365	18	is	be	VBZ
37681	2365	19	not	not	RB
37681	2365	20	worth	worth	JJ
37681	2365	21	while	while	IN
37681	2365	22	to	to	TO
37681	2365	23	ask	ask	VB
37681	2365	24	pupils	pupil	NNS
37681	2365	25	to	to	TO
37681	2365	26	take	take	VB
37681	2365	27	up	up	RP
37681	2365	28	both	both	DT
37681	2365	29	cases	case	NNS
37681	2365	30	,	,	,
37681	2365	31	the	the	DT
37681	2365	32	proof	proof	NN
37681	2365	33	for	for	IN
37681	2365	34	either	either	CC
37681	2365	35	being	be	VBG
37681	2365	36	obviously	obviously	RB
37681	2365	37	a	a	DT
37681	2365	38	proof	proof	NN
37681	2365	39	for	for	IN
37681	2365	40	the	the	DT
37681	2365	41	other	other	JJ
37681	2365	42	.	.	.
37681	2366	1	Many	many	JJ
37681	2366	2	writers	writer	NNS
37681	2366	3	state	state	VBP
37681	2366	4	this	this	DT
37681	2366	5	proposition	proposition	NN
37681	2366	6	so	so	IN
37681	2366	7	that	that	IN
37681	2366	8	it	-PRON-	PRP
37681	2366	9	reads	read	VBZ
37681	2366	10	that	that	IN
37681	2366	11	"	"	``
37681	2366	12	central	central	JJ
37681	2366	13	angles	angle	NNS
37681	2366	14	are	be	VBP
37681	2366	15	_	_	NNP
37681	2366	16	measured	measure	VBN
37681	2366	17	by	by	IN
37681	2366	18	_	_	NNP
37681	2366	19	their	-PRON-	PRP$
37681	2366	20	intercepted	intercept	VBN
37681	2366	21	arcs	arc	NNS
37681	2366	22	.	.	.
37681	2366	23	"	"	''
37681	2367	1	This	this	DT
37681	2367	2	,	,	,
37681	2367	3	of	of	IN
37681	2367	4	course	course	NN
37681	2367	5	,	,	,
37681	2367	6	is	be	VBZ
37681	2367	7	not	not	RB
37681	2367	8	literally	literally	RB
37681	2367	9	true	true	JJ
37681	2367	10	,	,	,
37681	2367	11	since	since	IN
37681	2367	12	we	-PRON-	PRP
37681	2367	13	can	can	MD
37681	2367	14	measure	measure	VB
37681	2367	15	anything	anything	NN
37681	2367	16	only	only	RB
37681	2367	17	by	by	IN
37681	2367	18	some	some	DT
37681	2367	19	thing	thing	NN
37681	2367	20	,	,	,
37681	2367	21	of	of	IN
37681	2367	22	the	the	DT
37681	2367	23	same	same	JJ
37681	2367	24	kind	kind	NN
37681	2367	25	.	.	.
37681	2368	1	Thus	thus	RB
37681	2368	2	we	-PRON-	PRP
37681	2368	3	measure	measure	VBP
37681	2368	4	a	a	DT
37681	2368	5	volume	volume	NN
37681	2368	6	by	by	IN
37681	2368	7	finding	find	VBG
37681	2368	8	how	how	WRB
37681	2368	9	many	many	JJ
37681	2368	10	times	time	NNS
37681	2368	11	it	-PRON-	PRP
37681	2368	12	contains	contain	VBZ
37681	2368	13	another	another	DT
37681	2368	14	volume	volume	NN
37681	2368	15	which	which	WDT
37681	2368	16	we	-PRON-	PRP
37681	2368	17	take	take	VBP
37681	2368	18	as	as	IN
37681	2368	19	a	a	DT
37681	2368	20	unit	unit	NN
37681	2368	21	,	,	,
37681	2368	22	and	and	CC
37681	2368	23	we	-PRON-	PRP
37681	2368	24	measure	measure	VBP
37681	2368	25	a	a	DT
37681	2368	26	length	length	NN
37681	2368	27	by	by	IN
37681	2368	28	taking	take	VBG
37681	2368	29	some	some	DT
37681	2368	30	other	other	JJ
37681	2368	31	length	length	NN
37681	2368	32	as	as	IN
37681	2368	33	a	a	DT
37681	2368	34	unit	unit	NN
37681	2368	35	;	;	:
37681	2368	36	but	but	CC
37681	2368	37	we	-PRON-	PRP
37681	2368	38	can	can	MD
37681	2368	39	not	not	RB
37681	2368	40	measure	measure	VB
37681	2368	41	a	a	DT
37681	2368	42	given	give	VBN
37681	2368	43	length	length	NN
37681	2368	44	in	in	IN
37681	2368	45	quarts	quart	NNS
37681	2368	46	nor	nor	CC
37681	2368	47	a	a	DT
37681	2368	48	given	give	VBN
37681	2368	49	weight	weight	NN
37681	2368	50	in	in	IN
37681	2368	51	feet	foot	NNS
37681	2368	52	,	,	,
37681	2368	53	and	and	CC
37681	2368	54	it	-PRON-	PRP
37681	2368	55	is	be	VBZ
37681	2368	56	equally	equally	RB
37681	2368	57	impossible	impossible	JJ
37681	2368	58	to	to	TO
37681	2368	59	measure	measure	VB
37681	2368	60	an	an	DT
37681	2368	61	arc	arc	NN
37681	2368	62	by	by	IN
37681	2368	63	an	an	DT
37681	2368	64	angle	angle	NN
37681	2368	65	,	,	,
37681	2368	66	and	and	CC
37681	2368	67	vice	vice	NN
37681	2368	68	versa	versa	RB
37681	2368	69	.	.	.
37681	2369	1	Nevertheless	nevertheless	RB
37681	2369	2	it	-PRON-	PRP
37681	2369	3	is	be	VBZ
37681	2369	4	often	often	RB
37681	2369	5	found	find	VBN
37681	2369	6	convenient	convenient	JJ
37681	2369	7	to	to	IN
37681	2369	8	_	_	NNP
37681	2369	9	define	define	NN
37681	2369	10	_	_	IN
37681	2369	11	some	some	DT
37681	2369	12	brief	brief	JJ
37681	2369	13	expression	expression	NN
37681	2369	14	that	that	WDT
37681	2369	15	has	have	VBZ
37681	2369	16	no	no	DT
37681	2369	17	meaning	meaning	NN
37681	2369	18	if	if	IN
37681	2369	19	taken	take	VBN
37681	2369	20	literally	literally	RB
37681	2369	21	,	,	,
37681	2369	22	in	in	IN
37681	2369	23	such	such	JJ
37681	2369	24	way	way	NN
37681	2369	25	that	that	WDT
37681	2369	26	it	-PRON-	PRP
37681	2369	27	shall	shall	MD
37681	2369	28	acquire	acquire	VB
37681	2369	29	a	a	DT
37681	2369	30	meaning	meaning	NN
37681	2369	31	.	.	.
37681	2370	1	Thus	thus	RB
37681	2370	2	we	-PRON-	PRP
37681	2370	3	_	_	IN
37681	2370	4	define	define	NN
37681	2370	5	_	_	NNP
37681	2370	6	"	"	''
37681	2370	7	area	area	NN
37681	2370	8	of	of	IN
37681	2370	9	a	a	DT
37681	2370	10	circle	circle	NN
37681	2370	11	,	,	,
37681	2370	12	"	"	``
37681	2370	13	even	even	RB
37681	2370	14	when	when	WRB
37681	2370	15	we	-PRON-	PRP
37681	2370	16	use	use	VBP
37681	2370	17	"	"	``
37681	2370	18	circle	circle	NN
37681	2370	19	"	"	''
37681	2370	20	to	to	TO
37681	2370	21	mean	mean	VB
37681	2370	22	a	a	DT
37681	2370	23	line	line	NN
37681	2370	24	;	;	,
37681	2370	25	and	and	CC
37681	2370	26	so	so	RB
37681	2370	27	we	-PRON-	PRP
37681	2370	28	may	may	MD
37681	2370	29	define	define	VB
37681	2370	30	the	the	DT
37681	2370	31	expression	expression	NN
37681	2370	32	"	"	``
37681	2370	33	central	central	JJ
37681	2370	34	angles	angle	NNS
37681	2370	35	are	be	VBP
37681	2370	36	measured	measure	VBN
37681	2370	37	by	by	IN
37681	2370	38	their	-PRON-	PRP$
37681	2370	39	intercepted	intercept	VBN
37681	2370	40	arcs	arc	NNS
37681	2370	41	"	"	''
37681	2370	42	to	to	TO
37681	2370	43	mean	mean	VB
37681	2370	44	that	that	IN
37681	2370	45	central	central	JJ
37681	2370	46	angles	angle	NNS
37681	2370	47	have	have	VBP
37681	2370	48	the	the	DT
37681	2370	49	same	same	JJ
37681	2370	50	numerical	numerical	JJ
37681	2370	51	measure	measure	NN
37681	2370	52	as	as	IN
37681	2370	53	these	these	DT
37681	2370	54	arcs	arc	NNS
37681	2370	55	.	.	.
37681	2371	1	This	this	DT
37681	2371	2	is	be	VBZ
37681	2371	3	done	do	VBN
37681	2371	4	by	by	IN
37681	2371	5	most	most	JJS
37681	2371	6	writers	writer	NNS
37681	2371	7	,	,	,
37681	2371	8	and	and	CC
37681	2371	9	is	be	VBZ
37681	2371	10	legitimate	legitimate	JJ
37681	2371	11	as	as	IN
37681	2371	12	explaining	explain	VBG
37681	2371	13	an	an	DT
37681	2371	14	abbreviated	abbreviate	VBN
37681	2371	15	expression	expression	NN
37681	2371	16	.	.	.
37681	2372	1	THEOREM	THEOREM	NNP
37681	2372	2	.	.	.
37681	2373	1	_	_	NNP
37681	2373	2	An	an	DT
37681	2373	3	inscribed	inscribed	JJ
37681	2373	4	angle	angle	NN
37681	2373	5	is	be	VBZ
37681	2373	6	measured	measure	VBN
37681	2373	7	by	by	IN
37681	2373	8	half	half	PDT
37681	2373	9	the	the	DT
37681	2373	10	intercepted	intercept	VBN
37681	2373	11	arc	arc	NN
37681	2373	12	.	.	.
37681	2373	13	_	_	NNP
37681	2373	14	In	in	IN
37681	2373	15	Euclid	Euclid	NNP
37681	2373	16	this	this	DT
37681	2373	17	proposition	proposition	NN
37681	2373	18	is	be	VBZ
37681	2373	19	combined	combine	VBN
37681	2373	20	with	with	IN
37681	2373	21	the	the	DT
37681	2373	22	preceding	precede	VBG
37681	2373	23	one	one	CD
37681	2373	24	in	in	IN
37681	2373	25	his	-PRON-	PRP$
37681	2373	26	Book	Book	NNP
37681	2373	27	VI	VI	NNP
37681	2373	28	,	,	,
37681	2373	29	Proposition	Proposition	NNP
37681	2373	30	33	33	CD
37681	2373	31	.	.	.
37681	2374	1	Such	such	PDT
37681	2374	2	a	a	DT
37681	2374	3	procedure	procedure	NN
37681	2374	4	is	be	VBZ
37681	2374	5	not	not	RB
37681	2374	6	adapted	adapt	VBN
37681	2374	7	to	to	IN
37681	2374	8	the	the	DT
37681	2374	9	needs	need	NNS
37681	2374	10	of	of	IN
37681	2374	11	students	student	NNS
37681	2374	12	to	to	IN
37681	2374	13	-	-	HYPH
37681	2374	14	day	day	NN
37681	2374	15	.	.	.
37681	2375	1	Euclid	Euclid	NNP
37681	2375	2	gave	give	VBD
37681	2375	3	in	in	IN
37681	2375	4	Book	Book	NNP
37681	2375	5	III	III	NNP
37681	2375	6	,	,	,
37681	2375	7	however	however	RB
37681	2375	8	,	,	,
37681	2375	9	the	the	DT
37681	2375	10	proposition	proposition	NN
37681	2375	11	(	(	-LRB-
37681	2375	12	No	no	UH
37681	2375	13	.	.	.
37681	2376	1	20	20	CD
37681	2376	2	)	)	-RRB-
37681	2376	3	that	that	IN
37681	2376	4	a	a	DT
37681	2376	5	central	central	JJ
37681	2376	6	angle	angle	NN
37681	2376	7	is	be	VBZ
37681	2376	8	twice	twice	PDT
37681	2376	9	an	an	DT
37681	2376	10	inscribed	inscribed	JJ
37681	2376	11	angle	angle	NN
37681	2376	12	standing	stand	VBG
37681	2376	13	on	on	IN
37681	2376	14	the	the	DT
37681	2376	15	same	same	JJ
37681	2376	16	arc	arc	NN
37681	2376	17	.	.	.
37681	2377	1	Since	since	IN
37681	2377	2	Euclid	Euclid	NNP
37681	2377	3	never	never	RB
37681	2377	4	considered	consider	VBD
37681	2377	5	an	an	DT
37681	2377	6	angle	angle	NN
37681	2377	7	greater	great	JJR
37681	2377	8	than	than	IN
37681	2377	9	180	180	CD
37681	2377	10	°	°	NNS
37681	2377	11	,	,	,
37681	2377	12	his	-PRON-	PRP$
37681	2377	13	inscribed	inscribed	JJ
37681	2377	14	angle	angle	NN
37681	2377	15	was	be	VBD
37681	2377	16	necessarily	necessarily	RB
37681	2377	17	less	less	JJR
37681	2377	18	than	than	IN
37681	2377	19	a	a	DT
37681	2377	20	right	right	JJ
37681	2377	21	angle	angle	NN
37681	2377	22	.	.	.
37681	2378	1	The	the	DT
37681	2378	2	first	first	JJ
37681	2378	3	one	one	NN
37681	2378	4	who	who	WP
37681	2378	5	is	be	VBZ
37681	2378	6	known	know	VBN
37681	2378	7	to	to	TO
37681	2378	8	have	have	VB
37681	2378	9	given	give	VBN
37681	2378	10	the	the	DT
37681	2378	11	general	general	JJ
37681	2378	12	case	case	NN
37681	2378	13	,	,	,
37681	2378	14	taking	take	VBG
37681	2378	15	the	the	DT
37681	2378	16	central	central	JJ
37681	2378	17	angle	angle	NN
37681	2378	18	as	as	IN
37681	2378	19	being	be	VBG
37681	2378	20	also	also	RB
37681	2378	21	greater	great	JJR
37681	2378	22	than	than	IN
37681	2378	23	180	180	CD
37681	2378	24	°	°	NNS
37681	2378	25	,	,	,
37681	2378	26	was	be	VBD
37681	2378	27	Heron	Heron	NNP
37681	2378	28	of	of	IN
37681	2378	29	Alexandria	Alexandria	NNP
37681	2378	30	,	,	,
37681	2378	31	probably	probably	RB
37681	2378	32	of	of	IN
37681	2378	33	the	the	DT
37681	2378	34	first	first	JJ
37681	2378	35	century	century	NN
37681	2378	36	A.D.[68	a.d.[68	NN
37681	2378	37	]	]	-RRB-
37681	2378	38	In	in	IN
37681	2378	39	this	this	DT
37681	2378	40	he	-PRON-	PRP
37681	2378	41	was	be	VBD
37681	2378	42	followed	follow	VBN
37681	2378	43	by	by	IN
37681	2378	44	various	various	JJ
37681	2378	45	later	later	JJ
37681	2378	46	commentators	commentator	NNS
37681	2378	47	,	,	,
37681	2378	48	including	include	VBG
37681	2378	49	Tartaglia	Tartaglia	NNP
37681	2378	50	and	and	CC
37681	2378	51	Clavius	Clavius	NNP
37681	2378	52	in	in	IN
37681	2378	53	the	the	DT
37681	2378	54	sixteenth	sixteenth	JJ
37681	2378	55	century	century	NN
37681	2378	56	.	.	.
37681	2379	1	One	one	CD
37681	2379	2	of	of	IN
37681	2379	3	the	the	DT
37681	2379	4	many	many	JJ
37681	2379	5	interesting	interesting	JJ
37681	2379	6	exercises	exercise	NNS
37681	2379	7	that	that	WDT
37681	2379	8	may	may	MD
37681	2379	9	be	be	VB
37681	2379	10	derived	derive	VBN
37681	2379	11	from	from	IN
37681	2379	12	this	this	DT
37681	2379	13	theorem	theorem	NN
37681	2379	14	is	be	VBZ
37681	2379	15	seen	see	VBN
37681	2379	16	in	in	IN
37681	2379	17	the	the	DT
37681	2379	18	case	case	NN
37681	2379	19	of	of	IN
37681	2379	20	the	the	DT
37681	2379	21	"	"	``
37681	2379	22	horizontal	horizontal	JJ
37681	2379	23	danger	danger	NN
37681	2379	24	angle	angle	NN
37681	2379	25	"	"	''
37681	2379	26	observed	observe	VBN
37681	2379	27	by	by	IN
37681	2379	28	ships	ship	NNS
37681	2379	29	.	.	.
37681	2380	1	[	[	-LRB-
37681	2380	2	Illustration	illustration	NN
37681	2380	3	]	]	-RRB-
37681	2380	4	If	if	IN
37681	2380	5	some	some	DT
37681	2380	6	dangerous	dangerous	JJ
37681	2380	7	rocks	rock	NNS
37681	2380	8	lie	lie	VBP
37681	2380	9	off	off	IN
37681	2380	10	the	the	DT
37681	2380	11	shore	shore	NN
37681	2380	12	,	,	,
37681	2380	13	and	and	CC
37681	2380	14	_	_	NNP
37681	2380	15	L	L	NNP
37681	2380	16	_	_	NNP
37681	2380	17	and	and	CC
37681	2380	18	_	_	NNP
37681	2380	19	L	L	NNP
37681	2380	20	'	'	''
37681	2380	21	_	_	NNP
37681	2380	22	are	be	VBP
37681	2380	23	two	two	CD
37681	2380	24	lighthouses	lighthouse	NNS
37681	2380	25	,	,	,
37681	2380	26	the	the	DT
37681	2380	27	angle	angle	NN
37681	2380	28	_	_	NNP
37681	2380	29	A	A	NNP
37681	2380	30	_	_	NNP
37681	2380	31	is	be	VBZ
37681	2380	32	determined	determine	VBN
37681	2380	33	by	by	IN
37681	2380	34	observation	observation	NN
37681	2380	35	,	,	,
37681	2380	36	so	so	IN
37681	2380	37	that	that	IN
37681	2380	38	_	_	NNP
37681	2380	39	A	A	NNP
37681	2380	40	_	_	NNP
37681	2380	41	will	will	MD
37681	2380	42	lie	lie	VB
37681	2380	43	on	on	IN
37681	2380	44	a	a	DT
37681	2380	45	circle	circle	NN
37681	2380	46	inclosing	inclose	VBG
37681	2380	47	the	the	DT
37681	2380	48	dangerous	dangerous	JJ
37681	2380	49	area	area	NN
37681	2380	50	.	.	.
37681	2381	1	Angle	Angle	NNP
37681	2381	2	_	_	NNP
37681	2381	3	A	A	NNP
37681	2381	4	_	_	NNP
37681	2381	5	is	be	VBZ
37681	2381	6	called	call	VBN
37681	2381	7	the	the	DT
37681	2381	8	"	"	``
37681	2381	9	horizontal	horizontal	JJ
37681	2381	10	danger	danger	NN
37681	2381	11	angle	angle	NN
37681	2381	12	.	.	.
37681	2381	13	"	"	''
37681	2382	1	Ships	ship	NNS
37681	2382	2	passing	pass	VBG
37681	2382	3	in	in	IN
37681	2382	4	sight	sight	NN
37681	2382	5	of	of	IN
37681	2382	6	the	the	DT
37681	2382	7	two	two	CD
37681	2382	8	lighthouses	lighthouse	NNS
37681	2382	9	_	_	NNP
37681	2382	10	L	L	NNP
37681	2382	11	_	_	NNP
37681	2382	12	and	and	CC
37681	2382	13	_	_	NNP
37681	2382	14	L	L	NNP
37681	2382	15	'	'	''
37681	2382	16	_	_	NNP
37681	2382	17	must	must	MD
37681	2382	18	keep	keep	VB
37681	2382	19	out	out	RP
37681	2382	20	far	far	RB
37681	2382	21	enough	enough	RB
37681	2382	22	so	so	IN
37681	2382	23	that	that	IN
37681	2382	24	the	the	DT
37681	2382	25	angle	angle	NN
37681	2382	26	_	_	NNP
37681	2382	27	L'SL	L'SL	NNP
37681	2382	28	_	_	NNP
37681	2382	29	shall	shall	MD
37681	2382	30	be	be	VB
37681	2382	31	less	less	JJR
37681	2382	32	than	than	IN
37681	2382	33	angle	angle	VB
37681	2382	34	_	_	NNP
37681	2382	35	A	A	NNP
37681	2382	36	_	_	NNP
37681	2382	37	.	.	.
37681	2383	1	To	to	IN
37681	2383	2	this	this	DT
37681	2383	3	proposition	proposition	NN
37681	2383	4	there	there	EX
37681	2383	5	are	be	VBP
37681	2383	6	several	several	JJ
37681	2383	7	important	important	JJ
37681	2383	8	corollaries	corollary	NNS
37681	2383	9	,	,	,
37681	2383	10	including	include	VBG
37681	2383	11	the	the	DT
37681	2383	12	following	follow	VBG
37681	2383	13	:	:	:
37681	2383	14	1	1	CD
37681	2383	15	.	.	.
37681	2384	1	_	_	NNP
37681	2384	2	An	an	DT
37681	2384	3	angle	angle	NN
37681	2384	4	inscribed	inscribe	VBN
37681	2384	5	in	in	IN
37681	2384	6	a	a	DT
37681	2384	7	semicircle	semicircle	NN
37681	2384	8	is	be	VBZ
37681	2384	9	a	a	DT
37681	2384	10	right	right	JJ
37681	2384	11	angle	angle	NN
37681	2384	12	.	.	.
37681	2384	13	_	_	NNP
37681	2384	14	This	this	DT
37681	2384	15	corollary	corollary	NN
37681	2384	16	is	be	VBZ
37681	2384	17	mentioned	mention	VBN
37681	2384	18	by	by	IN
37681	2384	19	Aristotle	Aristotle	NNP
37681	2384	20	and	and	CC
37681	2384	21	is	be	VBZ
37681	2384	22	attributed	attribute	VBN
37681	2384	23	to	to	IN
37681	2384	24	Thales	thale	NNS
37681	2384	25	,	,	,
37681	2384	26	being	be	VBG
37681	2384	27	one	one	CD
37681	2384	28	of	of	IN
37681	2384	29	the	the	DT
37681	2384	30	few	few	JJ
37681	2384	31	propositions	proposition	NNS
37681	2384	32	with	with	IN
37681	2384	33	which	which	WDT
37681	2384	34	his	-PRON-	PRP$
37681	2384	35	name	name	NN
37681	2384	36	is	be	VBZ
37681	2384	37	connected	connect	VBN
37681	2384	38	.	.	.
37681	2385	1	It	-PRON-	PRP
37681	2385	2	enables	enable	VBZ
37681	2385	3	us	-PRON-	PRP
37681	2385	4	to	to	TO
37681	2385	5	describe	describe	VB
37681	2385	6	a	a	DT
37681	2385	7	circle	circle	NN
37681	2385	8	by	by	IN
37681	2385	9	letting	let	VBG
37681	2385	10	the	the	DT
37681	2385	11	arms	arm	NNS
37681	2385	12	of	of	IN
37681	2385	13	a	a	DT
37681	2385	14	carpenter	carpenter	NN
37681	2385	15	's	's	POS
37681	2385	16	square	square	JJ
37681	2385	17	slide	slide	NN
37681	2385	18	along	along	IN
37681	2385	19	two	two	CD
37681	2385	20	nails	nail	NNS
37681	2385	21	driven	drive	VBN
37681	2385	22	in	in	IN
37681	2385	23	a	a	DT
37681	2385	24	board	board	NN
37681	2385	25	,	,	,
37681	2385	26	a	a	DT
37681	2385	27	pencil	pencil	NN
37681	2385	28	being	be	VBG
37681	2385	29	held	hold	VBN
37681	2385	30	at	at	IN
37681	2385	31	the	the	DT
37681	2385	32	vertex	vertex	NNP
37681	2385	33	.	.	.
37681	2386	1	[	[	-LRB-
37681	2386	2	Illustration	illustration	NN
37681	2386	3	]	]	-RRB-
37681	2386	4	A	a	DT
37681	2386	5	more	more	RBR
37681	2386	6	practical	practical	JJ
37681	2386	7	use	use	NN
37681	2386	8	for	for	IN
37681	2386	9	it	-PRON-	PRP
37681	2386	10	is	be	VBZ
37681	2386	11	made	make	VBN
37681	2386	12	by	by	IN
37681	2386	13	machinists	machinist	NNS
37681	2386	14	to	to	TO
37681	2386	15	determine	determine	VB
37681	2386	16	whether	whether	IN
37681	2386	17	a	a	DT
37681	2386	18	casting	casting	NN
37681	2386	19	is	be	VBZ
37681	2386	20	a	a	DT
37681	2386	21	true	true	JJ
37681	2386	22	semicircle	semicircle	NN
37681	2386	23	.	.	.
37681	2387	1	Taking	take	VBG
37681	2387	2	a	a	DT
37681	2387	3	carpenter	carpenter	NN
37681	2387	4	's	's	POS
37681	2387	5	square	square	NN
37681	2387	6	as	as	IN
37681	2387	7	here	here	RB
37681	2387	8	shown	show	VBN
37681	2387	9	,	,	,
37681	2387	10	if	if	IN
37681	2387	11	the	the	DT
37681	2387	12	vertex	vertex	NN
37681	2387	13	touches	touch	VBZ
37681	2387	14	the	the	DT
37681	2387	15	curve	curve	NN
37681	2387	16	at	at	IN
37681	2387	17	every	every	DT
37681	2387	18	point	point	NN
37681	2387	19	as	as	IN
37681	2387	20	the	the	DT
37681	2387	21	square	square	NN
37681	2387	22	slides	slide	VBZ
37681	2387	23	around	around	RB
37681	2387	24	,	,	,
37681	2387	25	it	-PRON-	PRP
37681	2387	26	is	be	VBZ
37681	2387	27	a	a	DT
37681	2387	28	true	true	JJ
37681	2387	29	semicircle	semicircle	NN
37681	2387	30	.	.	.
37681	2388	1	By	by	IN
37681	2388	2	a	a	DT
37681	2388	3	similar	similar	JJ
37681	2388	4	method	method	NN
37681	2388	5	a	a	DT
37681	2388	6	circle	circle	NN
37681	2388	7	may	may	MD
37681	2388	8	be	be	VB
37681	2388	9	described	describe	VBN
37681	2388	10	by	by	IN
37681	2388	11	sliding	slide	VBG
37681	2388	12	a	a	DT
37681	2388	13	draftsman	draftsman	NN
37681	2388	14	's	's	POS
37681	2388	15	triangle	triangle	NN
37681	2388	16	so	so	IN
37681	2388	17	that	that	IN
37681	2388	18	two	two	CD
37681	2388	19	sides	side	NNS
37681	2388	20	touch	touch	VBP
37681	2388	21	two	two	CD
37681	2388	22	tacks	tack	NNS
37681	2388	23	driven	drive	VBN
37681	2388	24	in	in	IN
37681	2388	25	a	a	DT
37681	2388	26	board	board	NN
37681	2388	27	.	.	.
37681	2389	1	[	[	-LRB-
37681	2389	2	Illustration	illustration	NN
37681	2389	3	]	]	-RRB-
37681	2389	4	Another	another	DT
37681	2389	5	interesting	interesting	JJ
37681	2389	6	application	application	NN
37681	2389	7	of	of	IN
37681	2389	8	this	this	DT
37681	2389	9	corollary	corollary	NN
37681	2389	10	may	may	MD
37681	2389	11	be	be	VB
37681	2389	12	seen	see	VBN
37681	2389	13	by	by	IN
37681	2389	14	taking	take	VBG
37681	2389	15	an	an	DT
37681	2389	16	ordinary	ordinary	JJ
37681	2389	17	paper	paper	NN
37681	2389	18	protractor	protractor	NN
37681	2389	19	_	_	NNP
37681	2389	20	ACB	ACB	NNP
37681	2389	21	_	_	NNP
37681	2389	22	,	,	,
37681	2389	23	and	and	CC
37681	2389	24	fastening	fasten	VBG
37681	2389	25	a	a	DT
37681	2389	26	plumb	plumb	JJ
37681	2389	27	line	line	NN
37681	2389	28	at	at	IN
37681	2389	29	_	_	NNP
37681	2389	30	B	B	NNP
37681	2389	31	_	_	NNP
37681	2389	32	.	.	.
37681	2390	1	If	if	IN
37681	2390	2	the	the	DT
37681	2390	3	protractor	protractor	NN
37681	2390	4	is	be	VBZ
37681	2390	5	so	so	RB
37681	2390	6	held	held	JJ
37681	2390	7	that	that	IN
37681	2390	8	the	the	DT
37681	2390	9	plumb	plumb	JJ
37681	2390	10	line	line	NN
37681	2390	11	cuts	cut	VBZ
37681	2390	12	the	the	DT
37681	2390	13	semicircle	semicircle	NN
37681	2390	14	at	at	IN
37681	2390	15	_	_	NNP
37681	2390	16	C	C	NNP
37681	2390	17	_	_	NNP
37681	2390	18	,	,	,
37681	2390	19	then	then	RB
37681	2390	20	_	_	NNP
37681	2390	21	AC	AC	NNP
37681	2390	22	_	_	NNP
37681	2390	23	is	be	VBZ
37681	2390	24	level	level	NN
37681	2390	25	because	because	IN
37681	2390	26	it	-PRON-	PRP
37681	2390	27	is	be	VBZ
37681	2390	28	perpendicular	perpendicular	JJ
37681	2390	29	to	to	IN
37681	2390	30	the	the	DT
37681	2390	31	vertical	vertical	JJ
37681	2390	32	line	line	NN
37681	2390	33	_	_	NNP
37681	2390	34	BC	BC	NNP
37681	2390	35	_	_	NNP
37681	2390	36	.	.	.
37681	2391	1	Thus	thus	RB
37681	2391	2	,	,	,
37681	2391	3	if	if	IN
37681	2391	4	a	a	DT
37681	2391	5	class	class	NN
37681	2391	6	wishes	wish	VBZ
37681	2391	7	to	to	TO
37681	2391	8	determine	determine	VB
37681	2391	9	the	the	DT
37681	2391	10	horizontal	horizontal	JJ
37681	2391	11	line	line	NN
37681	2391	12	_	_	NNP
37681	2391	13	AC	AC	NNP
37681	2391	14	_	_	NNP
37681	2391	15	,	,	,
37681	2391	16	while	while	IN
37681	2391	17	sighting	sight	VBG
37681	2391	18	up	up	RP
37681	2391	19	a	a	DT
37681	2391	20	hill	hill	NN
37681	2391	21	in	in	IN
37681	2391	22	the	the	DT
37681	2391	23	direction	direction	NN
37681	2391	24	_	_	NNP
37681	2391	25	AB	AB	NNP
37681	2391	26	_	_	NNP
37681	2391	27	,	,	,
37681	2391	28	this	this	DT
37681	2391	29	is	be	VBZ
37681	2391	30	easily	easily	RB
37681	2391	31	determined	determine	VBN
37681	2391	32	without	without	IN
37681	2391	33	a	a	DT
37681	2391	34	spirit	spirit	NN
37681	2391	35	level	level	NN
37681	2391	36	.	.	.
37681	2392	1	It	-PRON-	PRP
37681	2392	2	follows	follow	VBZ
37681	2392	3	from	from	IN
37681	2392	4	this	this	DT
37681	2392	5	corollary	corollary	NN
37681	2392	6	,	,	,
37681	2392	7	as	as	IN
37681	2392	8	the	the	DT
37681	2392	9	pupil	pupil	NN
37681	2392	10	has	have	VBZ
37681	2392	11	already	already	RB
37681	2392	12	found	find	VBN
37681	2392	13	,	,	,
37681	2392	14	that	that	IN
37681	2392	15	the	the	DT
37681	2392	16	mid	mid	NN
37681	2392	17	-	-	NN
37681	2392	18	point	point	NN
37681	2392	19	of	of	IN
37681	2392	20	the	the	DT
37681	2392	21	hypotenuse	hypotenuse	NN
37681	2392	22	of	of	IN
37681	2392	23	a	a	DT
37681	2392	24	right	right	JJ
37681	2392	25	triangle	triangle	NN
37681	2392	26	is	be	VBZ
37681	2392	27	equidistant	equidistant	NN
37681	2392	28	from	from	IN
37681	2392	29	the	the	DT
37681	2392	30	three	three	CD
37681	2392	31	vertices	vertex	NNS
37681	2392	32	.	.	.
37681	2393	1	This	this	DT
37681	2393	2	is	be	VBZ
37681	2393	3	useful	useful	JJ
37681	2393	4	in	in	IN
37681	2393	5	outdoor	outdoor	JJ
37681	2393	6	measuring	measuring	NN
37681	2393	7	,	,	,
37681	2393	8	forming	form	VBG
37681	2393	9	the	the	DT
37681	2393	10	basis	basis	NN
37681	2393	11	of	of	IN
37681	2393	12	one	one	CD
37681	2393	13	of	of	IN
37681	2393	14	the	the	DT
37681	2393	15	best	good	JJS
37681	2393	16	methods	method	NNS
37681	2393	17	of	of	IN
37681	2393	18	letting	let	VBG
37681	2393	19	fall	fall	VB
37681	2393	20	a	a	DT
37681	2393	21	perpendicular	perpendicular	NN
37681	2393	22	from	from	IN
37681	2393	23	an	an	DT
37681	2393	24	external	external	JJ
37681	2393	25	point	point	NN
37681	2393	26	to	to	IN
37681	2393	27	a	a	DT
37681	2393	28	line	line	NN
37681	2393	29	.	.	.
37681	2394	1	[	[	-LRB-
37681	2394	2	Illustration	illustration	NN
37681	2394	3	]	]	-RRB-
37681	2394	4	Suppose	Suppose	NNP
37681	2394	5	_	_	NNP
37681	2394	6	XY	XY	NNP
37681	2394	7	_	_	NNP
37681	2394	8	to	to	TO
37681	2394	9	be	be	VB
37681	2394	10	the	the	DT
37681	2394	11	edge	edge	NN
37681	2394	12	of	of	IN
37681	2394	13	a	a	DT
37681	2394	14	sidewalk	sidewalk	NN
37681	2394	15	,	,	,
37681	2394	16	and	and	CC
37681	2394	17	_	_	NNP
37681	2394	18	P	P	NNP
37681	2394	19	_	_	IN
37681	2394	20	a	a	DT
37681	2394	21	point	point	NN
37681	2394	22	in	in	IN
37681	2394	23	the	the	DT
37681	2394	24	street	street	NN
37681	2394	25	from	from	IN
37681	2394	26	which	which	WDT
37681	2394	27	we	-PRON-	PRP
37681	2394	28	wish	wish	VBP
37681	2394	29	to	to	TO
37681	2394	30	lay	lay	VB
37681	2394	31	a	a	DT
37681	2394	32	gas	gas	NN
37681	2394	33	pipe	pipe	NN
37681	2394	34	perpendicular	perpendicular	JJ
37681	2394	35	to	to	IN
37681	2394	36	the	the	DT
37681	2394	37	walk	walk	NN
37681	2394	38	.	.	.
37681	2395	1	From	from	IN
37681	2395	2	_	_	NNP
37681	2395	3	P	P	NNP
37681	2395	4	_	_	NNP
37681	2395	5	swing	swing	VBP
37681	2395	6	a	a	DT
37681	2395	7	cord	cord	NN
37681	2395	8	or	or	CC
37681	2395	9	tape	tape	NN
37681	2395	10	,	,	,
37681	2395	11	say	say	VBP
37681	2395	12	60	60	CD
37681	2395	13	feet	foot	NNS
37681	2395	14	long	long	JJ
37681	2395	15	,	,	,
37681	2395	16	until	until	IN
37681	2395	17	it	-PRON-	PRP
37681	2395	18	meets	meet	VBZ
37681	2395	19	_	_	NNP
37681	2395	20	XY	XY	NNP
37681	2395	21	_	_	NNP
37681	2395	22	at	at	IN
37681	2395	23	_	_	NNP
37681	2395	24	A	A	NNP
37681	2395	25	_	_	NNP
37681	2395	26	.	.	.
37681	2396	1	Then	then	RB
37681	2396	2	take	take	VB
37681	2396	3	_	_	NNP
37681	2396	4	M	M	NNP
37681	2396	5	_	_	NNP
37681	2396	6	,	,	,
37681	2396	7	the	the	DT
37681	2396	8	mid	mid	NN
37681	2396	9	-	-	NN
37681	2396	10	point	point	NN
37681	2396	11	of	of	IN
37681	2396	12	_	_	NNP
37681	2396	13	PA	PA	NNP
37681	2396	14	_	_	NNP
37681	2396	15	,	,	,
37681	2396	16	and	and	CC
37681	2396	17	swing	swing	VB
37681	2396	18	_	_	NNP
37681	2396	19	MP	MP	NNP
37681	2396	20	_	_	NNP
37681	2396	21	about	about	IN
37681	2396	22	_	_	NNP
37681	2396	23	M	M	NNP
37681	2396	24	_	_	NNP
37681	2396	25	,	,	,
37681	2396	26	to	to	TO
37681	2396	27	meet	meet	VB
37681	2396	28	_	_	NNP
37681	2396	29	XY	XY	NNP
37681	2396	30	_	_	NNP
37681	2396	31	at	at	IN
37681	2396	32	_	_	NNP
37681	2396	33	B	B	NNP
37681	2396	34	_	_	NNP
37681	2396	35	.	.	.
37681	2397	1	Then	then	RB
37681	2397	2	_	_	NNP
37681	2397	3	B	B	NNP
37681	2397	4	_	_	NNP
37681	2397	5	is	be	VBZ
37681	2397	6	the	the	DT
37681	2397	7	foot	foot	NN
37681	2397	8	of	of	IN
37681	2397	9	the	the	DT
37681	2397	10	perpendicular	perpendicular	NN
37681	2397	11	,	,	,
37681	2397	12	since	since	IN
37681	2397	13	[	[	-LRB-
37681	2397	14	L]_PBA	L]_PBA	NNP
37681	2397	15	_	_	NNP
37681	2397	16	can	can	MD
37681	2397	17	be	be	VB
37681	2397	18	inscribed	inscribe	VBN
37681	2397	19	in	in	IN
37681	2397	20	a	a	DT
37681	2397	21	semicircle	semicircle	NN
37681	2397	22	.	.	.
37681	2398	1	2	2	LS
37681	2398	2	.	.	.
37681	2399	1	_	_	NNP
37681	2399	2	Angles	Angles	NNP
37681	2399	3	inscribed	inscribe	VBN
37681	2399	4	in	in	IN
37681	2399	5	the	the	DT
37681	2399	6	same	same	JJ
37681	2399	7	segment	segment	NN
37681	2399	8	are	be	VBP
37681	2399	9	equal	equal	JJ
37681	2399	10	.	.	.
37681	2399	11	_	_	NNP
37681	2399	12	[	[	-LRB-
37681	2399	13	Illustration	illustration	NN
37681	2399	14	]	]	-RRB-
37681	2399	15	By	by	IN
37681	2399	16	driving	drive	VBG
37681	2399	17	two	two	CD
37681	2399	18	nails	nail	NNS
37681	2399	19	in	in	IN
37681	2399	20	a	a	DT
37681	2399	21	board	board	NN
37681	2399	22	,	,	,
37681	2399	23	at	at	IN
37681	2399	24	_	_	NNP
37681	2399	25	A	A	NNP
37681	2399	26	_	_	NNP
37681	2399	27	and	and	CC
37681	2399	28	_	_	NNP
37681	2399	29	B	B	NNP
37681	2399	30	_	_	NNP
37681	2399	31	,	,	,
37681	2399	32	and	and	CC
37681	2399	33	taking	take	VBG
37681	2399	34	an	an	DT
37681	2399	35	angle	angle	NN
37681	2399	36	_	_	NNP
37681	2399	37	P	P	NNP
37681	2399	38	_	_	NNP
37681	2399	39	made	make	VBN
37681	2399	40	of	of	IN
37681	2399	41	rigid	rigid	JJ
37681	2399	42	material	material	NN
37681	2399	43	(	(	-LRB-
37681	2399	44	in	in	IN
37681	2399	45	particular	particular	JJ
37681	2399	46	,	,	,
37681	2399	47	as	as	IN
37681	2399	48	already	already	RB
37681	2399	49	stated	state	VBN
37681	2399	50	,	,	,
37681	2399	51	a	a	DT
37681	2399	52	carpenter	carpenter	NN
37681	2399	53	's	's	POS
37681	2399	54	square	square	NN
37681	2399	55	)	)	-RRB-
37681	2399	56	,	,	,
37681	2399	57	a	a	DT
37681	2399	58	pencil	pencil	NN
37681	2399	59	placed	place	VBN
37681	2399	60	at	at	IN
37681	2399	61	_	_	NNP
37681	2399	62	P	P	NNP
37681	2399	63	_	_	NNP
37681	2399	64	will	will	MD
37681	2399	65	generate	generate	VB
37681	2399	66	an	an	DT
37681	2399	67	arc	arc	NN
37681	2399	68	of	of	IN
37681	2399	69	a	a	DT
37681	2399	70	circle	circle	NN
37681	2399	71	if	if	IN
37681	2399	72	the	the	DT
37681	2399	73	arms	arm	NNS
37681	2399	74	slide	slide	NN
37681	2399	75	along	along	IN
37681	2399	76	_	_	NNP
37681	2399	77	A	A	NNP
37681	2399	78	_	_	NNP
37681	2399	79	and	and	CC
37681	2399	80	_	_	NNP
37681	2399	81	B	B	NNP
37681	2399	82	_	_	NNP
37681	2399	83	.	.	.
37681	2400	1	This	this	DT
37681	2400	2	is	be	VBZ
37681	2400	3	an	an	DT
37681	2400	4	interesting	interesting	JJ
37681	2400	5	exercise	exercise	NN
37681	2400	6	for	for	IN
37681	2400	7	pupils	pupil	NNS
37681	2400	8	.	.	.
37681	2401	1	THEOREM	THEOREM	NNP
37681	2401	2	.	.	.
37681	2402	1	_	_	NNP
37681	2402	2	An	an	DT
37681	2402	3	angle	angle	NN
37681	2402	4	formed	form	VBN
37681	2402	5	by	by	IN
37681	2402	6	two	two	CD
37681	2402	7	chords	chord	NNS
37681	2402	8	intersecting	intersect	VBG
37681	2402	9	within	within	IN
37681	2402	10	the	the	DT
37681	2402	11	circle	circle	NN
37681	2402	12	is	be	VBZ
37681	2402	13	measured	measure	VBN
37681	2402	14	by	by	IN
37681	2402	15	half	half	PDT
37681	2402	16	the	the	DT
37681	2402	17	sum	sum	NN
37681	2402	18	of	of	IN
37681	2402	19	the	the	DT
37681	2402	20	intercepted	intercept	VBN
37681	2402	21	arcs	arc	NNS
37681	2402	22	.	.	.
37681	2402	23	_	_	NNP
37681	2402	24	THEOREM	THEOREM	NNP
37681	2402	25	.	.	.
37681	2403	1	_	_	NNP
37681	2403	2	An	an	DT
37681	2403	3	angle	angle	NN
37681	2403	4	formed	form	VBN
37681	2403	5	by	by	IN
37681	2403	6	a	a	DT
37681	2403	7	tangent	tangent	NN
37681	2403	8	and	and	CC
37681	2403	9	a	a	DT
37681	2403	10	chord	chord	NN
37681	2403	11	drawn	draw	VBN
37681	2403	12	from	from	IN
37681	2403	13	the	the	DT
37681	2403	14	point	point	NN
37681	2403	15	of	of	IN
37681	2403	16	tangency	tangency	NN
37681	2403	17	is	be	VBZ
37681	2403	18	measured	measure	VBN
37681	2403	19	by	by	IN
37681	2403	20	half	half	PDT
37681	2403	21	the	the	DT
37681	2403	22	intercepted	intercept	VBN
37681	2403	23	arc	arc	NN
37681	2403	24	.	.	.
37681	2403	25	_	_	NNP
37681	2403	26	THEOREM	THEOREM	NNP
37681	2403	27	.	.	.
37681	2404	1	_	_	NNP
37681	2404	2	An	an	DT
37681	2404	3	angle	angle	NN
37681	2404	4	formed	form	VBN
37681	2404	5	by	by	IN
37681	2404	6	two	two	CD
37681	2404	7	secants	secant	NNS
37681	2404	8	,	,	,
37681	2404	9	a	a	DT
37681	2404	10	secant	secant	NN
37681	2404	11	and	and	CC
37681	2404	12	a	a	DT
37681	2404	13	tangent	tangent	NN
37681	2404	14	,	,	,
37681	2404	15	or	or	CC
37681	2404	16	two	two	CD
37681	2404	17	tangents	tangent	NNS
37681	2404	18	,	,	,
37681	2404	19	drawn	draw	VBN
37681	2404	20	to	to	IN
37681	2404	21	a	a	DT
37681	2404	22	circle	circle	NN
37681	2404	23	from	from	IN
37681	2404	24	an	an	DT
37681	2404	25	external	external	JJ
37681	2404	26	point	point	NN
37681	2404	27	,	,	,
37681	2404	28	is	be	VBZ
37681	2404	29	measured	measure	VBN
37681	2404	30	by	by	IN
37681	2404	31	half	half	PDT
37681	2404	32	the	the	DT
37681	2404	33	difference	difference	NN
37681	2404	34	of	of	IN
37681	2404	35	the	the	DT
37681	2404	36	intercepted	intercept	VBN
37681	2404	37	arcs	arc	NNS
37681	2404	38	.	.	.
37681	2404	39	_	_	NNP
37681	2404	40	These	these	DT
37681	2404	41	three	three	CD
37681	2404	42	theorems	theorem	NNS
37681	2404	43	are	be	VBP
37681	2404	44	all	all	DT
37681	2404	45	special	special	JJ
37681	2404	46	cases	case	NNS
37681	2404	47	of	of	IN
37681	2404	48	the	the	DT
37681	2404	49	general	general	JJ
37681	2404	50	proposition	proposition	NN
37681	2404	51	that	that	IN
37681	2404	52	the	the	DT
37681	2404	53	angle	angle	NN
37681	2404	54	included	include	VBN
37681	2404	55	between	between	IN
37681	2404	56	two	two	CD
37681	2404	57	lines	line	NNS
37681	2404	58	that	that	WDT
37681	2404	59	cut	cut	VBP
37681	2404	60	(	(	-LRB-
37681	2404	61	or	or	CC
37681	2404	62	touch	touch	VB
37681	2404	63	)	)	-RRB-
37681	2404	64	a	a	DT
37681	2404	65	circle	circle	NN
37681	2404	66	is	be	VBZ
37681	2404	67	measured	measure	VBN
37681	2404	68	by	by	IN
37681	2404	69	half	half	PDT
37681	2404	70	the	the	DT
37681	2404	71	sum	sum	NN
37681	2404	72	of	of	IN
37681	2404	73	the	the	DT
37681	2404	74	intercepted	intercept	VBN
37681	2404	75	arcs	arc	NNS
37681	2404	76	.	.	.
37681	2405	1	If	if	IN
37681	2405	2	the	the	DT
37681	2405	3	point	point	NN
37681	2405	4	passes	pass	VBZ
37681	2405	5	from	from	IN
37681	2405	6	within	within	IN
37681	2405	7	the	the	DT
37681	2405	8	circle	circle	NN
37681	2405	9	to	to	IN
37681	2405	10	the	the	DT
37681	2405	11	circle	circle	NN
37681	2405	12	itself	-PRON-	PRP
37681	2405	13	,	,	,
37681	2405	14	one	one	CD
37681	2405	15	arc	arc	NN
37681	2405	16	becomes	become	VBZ
37681	2405	17	zero	zero	CD
37681	2405	18	and	and	CC
37681	2405	19	the	the	DT
37681	2405	20	angle	angle	NN
37681	2405	21	becomes	become	VBZ
37681	2405	22	an	an	DT
37681	2405	23	inscribed	inscribed	JJ
37681	2405	24	angle	angle	NN
37681	2405	25	.	.	.
37681	2406	1	If	if	IN
37681	2406	2	the	the	DT
37681	2406	3	point	point	NN
37681	2406	4	passes	pass	VBZ
37681	2406	5	outside	outside	IN
37681	2406	6	the	the	DT
37681	2406	7	circle	circle	NN
37681	2406	8	,	,	,
37681	2406	9	the	the	DT
37681	2406	10	smaller	small	JJR
37681	2406	11	arc	arc	NN
37681	2406	12	becomes	become	VBZ
37681	2406	13	negative	negative	JJ
37681	2406	14	,	,	,
37681	2406	15	having	have	VBG
37681	2406	16	passed	pass	VBN
37681	2406	17	through	through	IN
37681	2406	18	zero	zero	CD
37681	2406	19	.	.	.
37681	2407	1	The	the	DT
37681	2407	2	point	point	NN
37681	2407	3	may	may	MD
37681	2407	4	even	even	RB
37681	2407	5	"	"	``
37681	2407	6	go	go	VB
37681	2407	7	to	to	IN
37681	2407	8	infinity	infinity	NN
37681	2407	9	,	,	,
37681	2407	10	"	"	''
37681	2407	11	as	as	IN
37681	2407	12	is	be	VBZ
37681	2407	13	said	say	VBN
37681	2407	14	in	in	IN
37681	2407	15	higher	high	JJR
37681	2407	16	mathematics	mathematic	NNS
37681	2407	17	,	,	,
37681	2407	18	the	the	DT
37681	2407	19	lines	line	NNS
37681	2407	20	then	then	RB
37681	2407	21	becoming	become	VBG
37681	2407	22	parallel	parallel	NN
37681	2407	23	,	,	,
37681	2407	24	and	and	CC
37681	2407	25	the	the	DT
37681	2407	26	angle	angle	NN
37681	2407	27	becoming	become	VBG
37681	2407	28	zero	zero	CD
37681	2407	29	,	,	,
37681	2407	30	being	be	VBG
37681	2407	31	measured	measure	VBN
37681	2407	32	by	by	IN
37681	2407	33	half	half	PDT
37681	2407	34	the	the	DT
37681	2407	35	sum	sum	NN
37681	2407	36	of	of	IN
37681	2407	37	one	one	CD
37681	2407	38	arc	arc	NN
37681	2407	39	and	and	CC
37681	2407	40	a	a	DT
37681	2407	41	negative	negative	JJ
37681	2407	42	arc	arc	NN
37681	2407	43	of	of	IN
37681	2407	44	the	the	DT
37681	2407	45	same	same	JJ
37681	2407	46	absolute	absolute	JJ
37681	2407	47	value	value	NN
37681	2407	48	.	.	.
37681	2408	1	This	this	DT
37681	2408	2	is	be	VBZ
37681	2408	3	one	one	CD
37681	2408	4	of	of	IN
37681	2408	5	the	the	DT
37681	2408	6	best	good	JJS
37681	2408	7	illustrations	illustration	NNS
37681	2408	8	of	of	IN
37681	2408	9	the	the	DT
37681	2408	10	Principle	Principle	NNP
37681	2408	11	of	of	IN
37681	2408	12	Continuity	Continuity	NNP
37681	2408	13	to	to	TO
37681	2408	14	be	be	VB
37681	2408	15	found	find	VBN
37681	2408	16	in	in	IN
37681	2408	17	geometry	geometry	NN
37681	2408	18	.	.	.
37681	2409	1	PROBLEM	problem	NN
37681	2409	2	.	.	.
37681	2410	1	_	_	NNP
37681	2410	2	To	to	TO
37681	2410	3	let	let	VB
37681	2410	4	fall	fall	VB
37681	2410	5	a	a	DT
37681	2410	6	perpendicular	perpendicular	NN
37681	2410	7	upon	upon	IN
37681	2410	8	a	a	DT
37681	2410	9	given	give	VBN
37681	2410	10	line	line	NN
37681	2410	11	from	from	IN
37681	2410	12	a	a	DT
37681	2410	13	given	give	VBN
37681	2410	14	external	external	JJ
37681	2410	15	point	point	NN
37681	2410	16	.	.	.
37681	2410	17	_	_	NNP
37681	2410	18	This	this	DT
37681	2410	19	is	be	VBZ
37681	2410	20	the	the	DT
37681	2410	21	first	first	JJ
37681	2410	22	problem	problem	NN
37681	2410	23	that	that	IN
37681	2410	24	a	a	DT
37681	2410	25	student	student	NN
37681	2410	26	meets	meet	VBZ
37681	2410	27	in	in	IN
37681	2410	28	most	most	JJS
37681	2410	29	American	american	JJ
37681	2410	30	geometries	geometry	NNS
37681	2410	31	.	.	.
37681	2411	1	The	the	DT
37681	2411	2	reason	reason	NN
37681	2411	3	for	for	IN
37681	2411	4	treating	treat	VBG
37681	2411	5	the	the	DT
37681	2411	6	problems	problem	NNS
37681	2411	7	by	by	IN
37681	2411	8	themselves	-PRON-	PRP
37681	2411	9	instead	instead	RB
37681	2411	10	of	of	IN
37681	2411	11	mingling	mingle	VBG
37681	2411	12	them	-PRON-	PRP
37681	2411	13	with	with	IN
37681	2411	14	the	the	DT
37681	2411	15	theorems	theorem	NNS
37681	2411	16	has	have	VBZ
37681	2411	17	already	already	RB
37681	2411	18	been	be	VBN
37681	2411	19	discussed	discuss	VBN
37681	2411	20	.	.	.
37681	2412	1	[	[	-LRB-
37681	2412	2	69	69	CD
37681	2412	3	]	]	-RRB-
37681	2412	4	The	the	DT
37681	2412	5	student	student	NN
37681	2412	6	now	now	RB
37681	2412	7	has	have	VBZ
37681	2412	8	a	a	DT
37681	2412	9	sufficient	sufficient	JJ
37681	2412	10	body	body	NN
37681	2412	11	of	of	IN
37681	2412	12	theorems	theorem	NNS
37681	2412	13	,	,	,
37681	2412	14	by	by	IN
37681	2412	15	which	which	WDT
37681	2412	16	he	-PRON-	PRP
37681	2412	17	can	can	MD
37681	2412	18	prove	prove	VB
37681	2412	19	that	that	IN
37681	2412	20	his	-PRON-	PRP$
37681	2412	21	constructions	construction	NNS
37681	2412	22	are	be	VBP
37681	2412	23	correct	correct	JJ
37681	2412	24	,	,	,
37681	2412	25	and	and	CC
37681	2412	26	the	the	DT
37681	2412	27	advantage	advantage	NN
37681	2412	28	of	of	IN
37681	2412	29	treating	treat	VBG
37681	2412	30	these	these	DT
37681	2412	31	constructions	construction	NNS
37681	2412	32	together	together	RB
37681	2412	33	is	be	VBZ
37681	2412	34	greater	great	JJR
37681	2412	35	than	than	IN
37681	2412	36	that	that	DT
37681	2412	37	of	of	IN
37681	2412	38	following	follow	VBG
37681	2412	39	Euclid	Euclid	NNP
37681	2412	40	's	's	POS
37681	2412	41	plan	plan	NN
37681	2412	42	of	of	IN
37681	2412	43	introducing	introduce	VBG
37681	2412	44	them	-PRON-	PRP
37681	2412	45	whenever	whenever	WRB
37681	2412	46	needed	need	VBN
37681	2412	47	.	.	.
37681	2413	1	Proclus	Proclus	NNP
37681	2413	2	tells	tell	VBZ
37681	2413	3	us	-PRON-	PRP
37681	2413	4	that	that	IN
37681	2413	5	"	"	``
37681	2413	6	this	this	DT
37681	2413	7	problem	problem	NN
37681	2413	8	was	be	VBD
37681	2413	9	first	first	RB
37681	2413	10	investigated	investigate	VBN
37681	2413	11	by	by	IN
37681	2413	12	Oenopides,[70	Oenopides,[70	NNP
37681	2413	13	]	]	-RRB-
37681	2413	14	who	who	WP
37681	2413	15	thought	think	VBD
37681	2413	16	it	-PRON-	PRP
37681	2413	17	useful	useful	JJ
37681	2413	18	for	for	IN
37681	2413	19	astronomy	astronomy	NN
37681	2413	20	.	.	.
37681	2413	21	"	"	''
37681	2414	1	Proclus	Proclus	NNP
37681	2414	2	speaks	speak	VBZ
37681	2414	3	of	of	IN
37681	2414	4	such	such	PDT
37681	2414	5	a	a	DT
37681	2414	6	line	line	NN
37681	2414	7	as	as	IN
37681	2414	8	a	a	DT
37681	2414	9	gnomon	gnomon	NN
37681	2414	10	,	,	,
37681	2414	11	a	a	DT
37681	2414	12	common	common	JJ
37681	2414	13	name	name	NN
37681	2414	14	for	for	IN
37681	2414	15	the	the	DT
37681	2414	16	perpendicular	perpendicular	NN
37681	2414	17	on	on	IN
37681	2414	18	a	a	DT
37681	2414	19	sundial	sundial	NN
37681	2414	20	,	,	,
37681	2414	21	which	which	WDT
37681	2414	22	casts	cast	VBZ
37681	2414	23	the	the	DT
37681	2414	24	shadow	shadow	NN
37681	2414	25	by	by	IN
37681	2414	26	which	which	WDT
37681	2414	27	the	the	DT
37681	2414	28	time	time	NN
37681	2414	29	of	of	IN
37681	2414	30	day	day	NN
37681	2414	31	is	be	VBZ
37681	2414	32	known	know	VBN
37681	2414	33	.	.	.
37681	2415	1	He	-PRON-	PRP
37681	2415	2	also	also	RB
37681	2415	3	speaks	speak	VBZ
37681	2415	4	of	of	IN
37681	2415	5	two	two	CD
37681	2415	6	kinds	kind	NNS
37681	2415	7	of	of	IN
37681	2415	8	perpendiculars	perpendicular	NNS
37681	2415	9	,	,	,
37681	2415	10	the	the	DT
37681	2415	11	plane	plane	NN
37681	2415	12	and	and	CC
37681	2415	13	solid	solid	JJ
37681	2415	14	,	,	,
37681	2415	15	the	the	DT
37681	2415	16	former	former	JJ
37681	2415	17	being	be	VBG
37681	2415	18	a	a	DT
37681	2415	19	line	line	NN
37681	2415	20	perpendicular	perpendicular	JJ
37681	2415	21	to	to	IN
37681	2415	22	a	a	DT
37681	2415	23	line	line	NN
37681	2415	24	,	,	,
37681	2415	25	and	and	CC
37681	2415	26	the	the	DT
37681	2415	27	latter	latter	JJ
37681	2415	28	a	a	DT
37681	2415	29	line	line	NN
37681	2415	30	perpendicular	perpendicular	JJ
37681	2415	31	to	to	IN
37681	2415	32	a	a	DT
37681	2415	33	plane	plane	NN
37681	2415	34	.	.	.
37681	2416	1	It	-PRON-	PRP
37681	2416	2	is	be	VBZ
37681	2416	3	interesting	interesting	JJ
37681	2416	4	to	to	TO
37681	2416	5	notice	notice	VB
37681	2416	6	that	that	IN
37681	2416	7	the	the	DT
37681	2416	8	solution	solution	NN
37681	2416	9	tacitly	tacitly	RB
37681	2416	10	assumes	assume	VBZ
37681	2416	11	that	that	IN
37681	2416	12	a	a	DT
37681	2416	13	certain	certain	JJ
37681	2416	14	arc	arc	NN
37681	2416	15	is	be	VBZ
37681	2416	16	going	go	VBG
37681	2416	17	to	to	TO
37681	2416	18	cut	cut	VB
37681	2416	19	the	the	DT
37681	2416	20	given	give	VBN
37681	2416	21	line	line	NN
37681	2416	22	in	in	IN
37681	2416	23	two	two	CD
37681	2416	24	points	point	NNS
37681	2416	25	,	,	,
37681	2416	26	and	and	CC
37681	2416	27	only	only	RB
37681	2416	28	two	two	CD
37681	2416	29	.	.	.
37681	2417	1	Strictly	strictly	RB
37681	2417	2	speaking	speak	VBG
37681	2417	3	,	,	,
37681	2417	4	why	why	WRB
37681	2417	5	may	may	MD
37681	2417	6	it	-PRON-	PRP
37681	2417	7	not	not	RB
37681	2417	8	cut	cut	VB
37681	2417	9	it	-PRON-	PRP
37681	2417	10	in	in	RP
37681	2417	11	only	only	RB
37681	2417	12	one	one	CD
37681	2417	13	point	point	NN
37681	2417	14	,	,	,
37681	2417	15	or	or	CC
37681	2417	16	even	even	RB
37681	2417	17	in	in	IN
37681	2417	18	three	three	CD
37681	2417	19	points	point	NNS
37681	2417	20	?	?	.
37681	2418	1	We	-PRON-	PRP
37681	2418	2	really	really	RB
37681	2418	3	assume	assume	VBP
37681	2418	4	that	that	IN
37681	2418	5	if	if	IN
37681	2418	6	a	a	DT
37681	2418	7	straight	straight	JJ
37681	2418	8	line	line	NN
37681	2418	9	is	be	VBZ
37681	2418	10	drawn	draw	VBN
37681	2418	11	through	through	IN
37681	2418	12	a	a	DT
37681	2418	13	point	point	NN
37681	2418	14	within	within	IN
37681	2418	15	a	a	DT
37681	2418	16	circle	circle	NN
37681	2418	17	,	,	,
37681	2418	18	this	this	DT
37681	2418	19	line	line	NN
37681	2418	20	must	must	MD
37681	2418	21	get	get	VB
37681	2418	22	out	out	IN
37681	2418	23	of	of	IN
37681	2418	24	the	the	DT
37681	2418	25	circle	circle	NN
37681	2418	26	on	on	IN
37681	2418	27	each	each	DT
37681	2418	28	of	of	IN
37681	2418	29	two	two	CD
37681	2418	30	sides	side	NNS
37681	2418	31	of	of	IN
37681	2418	32	the	the	DT
37681	2418	33	given	give	VBN
37681	2418	34	point	point	NN
37681	2418	35	,	,	,
37681	2418	36	and	and	CC
37681	2418	37	in	in	IN
37681	2418	38	getting	get	VBG
37681	2418	39	out	out	RP
37681	2418	40	it	-PRON-	PRP
37681	2418	41	must	must	MD
37681	2418	42	cut	cut	VB
37681	2418	43	the	the	DT
37681	2418	44	circle	circle	NN
37681	2418	45	twice	twice	RB
37681	2418	46	.	.	.
37681	2419	1	Proclus	Proclus	NNP
37681	2419	2	noticed	notice	VBD
37681	2419	3	this	this	DT
37681	2419	4	assumption	assumption	NN
37681	2419	5	and	and	CC
37681	2419	6	endeavored	endeavor	VBD
37681	2419	7	to	to	TO
37681	2419	8	prove	prove	VB
37681	2419	9	it	-PRON-	PRP
37681	2419	10	.	.	.
37681	2420	1	It	-PRON-	PRP
37681	2420	2	is	be	VBZ
37681	2420	3	better	well	JJR
37681	2420	4	,	,	,
37681	2420	5	however	however	RB
37681	2420	6	,	,	,
37681	2420	7	not	not	RB
37681	2420	8	to	to	TO
37681	2420	9	raise	raise	VB
37681	2420	10	the	the	DT
37681	2420	11	question	question	NN
37681	2420	12	with	with	IN
37681	2420	13	beginners	beginner	NNS
37681	2420	14	,	,	,
37681	2420	15	since	since	IN
37681	2420	16	it	-PRON-	PRP
37681	2420	17	seems	seem	VBZ
37681	2420	18	to	to	IN
37681	2420	19	them	-PRON-	PRP
37681	2420	20	like	like	IN
37681	2420	21	hair	hair	NN
37681	2420	22	-	-	HYPH
37681	2420	23	splitting	splitting	NN
37681	2420	24	to	to	IN
37681	2420	25	no	no	DT
37681	2420	26	purpose	purpose	NN
37681	2420	27	.	.	.
37681	2421	1	The	the	DT
37681	2421	2	problem	problem	NN
37681	2421	3	is	be	VBZ
37681	2421	4	of	of	IN
37681	2421	5	much	much	JJ
37681	2421	6	value	value	NN
37681	2421	7	in	in	IN
37681	2421	8	surveying	surveying	NN
37681	2421	9	,	,	,
37681	2421	10	and	and	CC
37681	2421	11	teachers	teacher	NNS
37681	2421	12	would	would	MD
37681	2421	13	do	do	VB
37681	2421	14	well	well	RB
37681	2421	15	to	to	TO
37681	2421	16	ask	ask	VB
37681	2421	17	a	a	DT
37681	2421	18	class	class	NN
37681	2421	19	to	to	TO
37681	2421	20	let	let	VB
37681	2421	21	fall	fall	VB
37681	2421	22	a	a	DT
37681	2421	23	perpendicular	perpendicular	NN
37681	2421	24	to	to	IN
37681	2421	25	the	the	DT
37681	2421	26	edge	edge	NN
37681	2421	27	of	of	IN
37681	2421	28	a	a	DT
37681	2421	29	sidewalk	sidewalk	NN
37681	2421	30	from	from	IN
37681	2421	31	a	a	DT
37681	2421	32	point	point	NN
37681	2421	33	20	20	CD
37681	2421	34	feet	foot	NNS
37681	2421	35	from	from	IN
37681	2421	36	the	the	DT
37681	2421	37	walk	walk	NN
37681	2421	38	,	,	,
37681	2421	39	using	use	VBG
37681	2421	40	an	an	DT
37681	2421	41	ordinary	ordinary	JJ
37681	2421	42	66-foot	66-foot	CD
37681	2421	43	or	or	CC
37681	2421	44	50-foot	50-foot	CD
37681	2421	45	tape	tape	NN
37681	2421	46	.	.	.
37681	2422	1	Practically	practically	RB
37681	2422	2	,	,	,
37681	2422	3	the	the	DT
37681	2422	4	best	good	JJS
37681	2422	5	plan	plan	NN
37681	2422	6	is	be	VBZ
37681	2422	7	to	to	TO
37681	2422	8	swing	swing	VB
37681	2422	9	30	30	CD
37681	2422	10	feet	foot	NNS
37681	2422	11	of	of	IN
37681	2422	12	the	the	DT
37681	2422	13	tape	tape	NN
37681	2422	14	about	about	IN
37681	2422	15	the	the	DT
37681	2422	16	point	point	NN
37681	2422	17	and	and	CC
37681	2422	18	mark	mark	VB
37681	2422	19	the	the	DT
37681	2422	20	two	two	CD
37681	2422	21	points	point	NNS
37681	2422	22	of	of	IN
37681	2422	23	intersection	intersection	NN
37681	2422	24	with	with	IN
37681	2422	25	the	the	DT
37681	2422	26	edge	edge	NN
37681	2422	27	of	of	IN
37681	2422	28	the	the	DT
37681	2422	29	walk	walk	NN
37681	2422	30	.	.	.
37681	2423	1	Then	then	RB
37681	2423	2	measure	measure	VB
37681	2423	3	the	the	DT
37681	2423	4	distance	distance	NN
37681	2423	5	between	between	IN
37681	2423	6	the	the	DT
37681	2423	7	points	point	NNS
37681	2423	8	and	and	CC
37681	2423	9	take	take	VB
37681	2423	10	half	half	NN
37681	2423	11	of	of	IN
37681	2423	12	this	this	DT
37681	2423	13	distance	distance	NN
37681	2423	14	,	,	,
37681	2423	15	thus	thus	RB
37681	2423	16	fixing	fix	VBG
37681	2423	17	the	the	DT
37681	2423	18	foot	foot	NN
37681	2423	19	of	of	IN
37681	2423	20	the	the	DT
37681	2423	21	perpendicular	perpendicular	NN
37681	2423	22	.	.	.
37681	2424	1	PROBLEM	problem	NN
37681	2424	2	.	.	.
37681	2425	1	_	_	NNP
37681	2425	2	At	at	IN
37681	2425	3	a	a	DT
37681	2425	4	given	give	VBN
37681	2425	5	point	point	NN
37681	2425	6	in	in	IN
37681	2425	7	a	a	DT
37681	2425	8	line	line	NN
37681	2425	9	,	,	,
37681	2425	10	to	to	TO
37681	2425	11	erect	erect	VB
37681	2425	12	a	a	DT
37681	2425	13	perpendicular	perpendicular	NN
37681	2425	14	to	to	IN
37681	2425	15	that	that	DT
37681	2425	16	line	line	NN
37681	2425	17	.	.	.
37681	2425	18	_	_	NNP
37681	2425	19	This	this	DT
37681	2425	20	might	may	MD
37681	2425	21	be	be	VB
37681	2425	22	postponed	postpone	VBN
37681	2425	23	until	until	IN
37681	2425	24	after	after	IN
37681	2425	25	the	the	DT
37681	2425	26	problem	problem	NN
37681	2425	27	to	to	TO
37681	2425	28	bisect	bisect	VB
37681	2425	29	an	an	DT
37681	2425	30	angle	angle	NN
37681	2425	31	,	,	,
37681	2425	32	since	since	IN
37681	2425	33	it	-PRON-	PRP
37681	2425	34	merely	merely	RB
37681	2425	35	requires	require	VBZ
37681	2425	36	the	the	DT
37681	2425	37	bisection	bisection	NN
37681	2425	38	of	of	IN
37681	2425	39	a	a	DT
37681	2425	40	straight	straight	JJ
37681	2425	41	angle	angle	NN
37681	2425	42	;	;	:
37681	2425	43	but	but	CC
37681	2425	44	considering	consider	VBG
37681	2425	45	the	the	DT
37681	2425	46	immaturity	immaturity	NN
37681	2425	47	of	of	IN
37681	2425	48	the	the	DT
37681	2425	49	average	average	JJ
37681	2425	50	pupil	pupil	NN
37681	2425	51	,	,	,
37681	2425	52	it	-PRON-	PRP
37681	2425	53	is	be	VBZ
37681	2425	54	better	well	RBR
37681	2425	55	given	give	VBN
37681	2425	56	independently	independently	RB
37681	2425	57	.	.	.
37681	2426	1	The	the	DT
37681	2426	2	usual	usual	JJ
37681	2426	3	case	case	NN
37681	2426	4	considers	consider	VBZ
37681	2426	5	the	the	DT
37681	2426	6	point	point	NN
37681	2426	7	not	not	RB
37681	2426	8	at	at	IN
37681	2426	9	the	the	DT
37681	2426	10	extremity	extremity	NN
37681	2426	11	of	of	IN
37681	2426	12	the	the	DT
37681	2426	13	line	line	NN
37681	2426	14	,	,	,
37681	2426	15	and	and	CC
37681	2426	16	the	the	DT
37681	2426	17	solution	solution	NN
37681	2426	18	is	be	VBZ
37681	2426	19	essentially	essentially	RB
37681	2426	20	that	that	DT
37681	2426	21	of	of	IN
37681	2426	22	Euclid	Euclid	NNP
37681	2426	23	.	.	.
37681	2427	1	In	in	IN
37681	2427	2	practice	practice	NN
37681	2427	3	,	,	,
37681	2427	4	however	however	RB
37681	2427	5	,	,	,
37681	2427	6	as	as	IN
37681	2427	7	for	for	IN
37681	2427	8	example	example	NN
37681	2427	9	in	in	IN
37681	2427	10	surveying	surveying	NN
37681	2427	11	,	,	,
37681	2427	12	the	the	DT
37681	2427	13	point	point	NN
37681	2427	14	may	may	MD
37681	2427	15	be	be	VB
37681	2427	16	at	at	IN
37681	2427	17	the	the	DT
37681	2427	18	extremity	extremity	NN
37681	2427	19	,	,	,
37681	2427	20	and	and	CC
37681	2427	21	it	-PRON-	PRP
37681	2427	22	may	may	MD
37681	2427	23	not	not	RB
37681	2427	24	be	be	VB
37681	2427	25	convenient	convenient	JJ
37681	2427	26	to	to	TO
37681	2427	27	produce	produce	VB
37681	2427	28	the	the	DT
37681	2427	29	line	line	NN
37681	2427	30	.	.	.
37681	2428	1	[	[	-LRB-
37681	2428	2	Illustration	illustration	NN
37681	2428	3	]	]	-RRB-
37681	2428	4	Surveyors	Surveyors	NNPS
37681	2428	5	sometimes	sometimes	RB
37681	2428	6	measure	measure	VBP
37681	2428	7	_	_	NNP
37681	2428	8	PB	PB	NNP
37681	2428	9	_	_	NNP
37681	2428	10	=	=	SYM
37681	2428	11	3	3	CD
37681	2428	12	ft	ft	NN
37681	2428	13	.	.	NNP
37681	2428	14	,	,	,
37681	2428	15	and	and	CC
37681	2428	16	then	then	RB
37681	2428	17	take	take	VB
37681	2428	18	9	9	CD
37681	2428	19	ft	ft	NN
37681	2428	20	.	.	NN
37681	2428	21	of	of	IN
37681	2428	22	tape	tape	NN
37681	2428	23	,	,	,
37681	2428	24	the	the	DT
37681	2428	25	ends	end	NNS
37681	2428	26	being	be	VBG
37681	2428	27	held	hold	VBN
37681	2428	28	at	at	IN
37681	2428	29	_	_	NNP
37681	2428	30	B	B	NNP
37681	2428	31	_	_	NNP
37681	2428	32	and	and	CC
37681	2428	33	_	_	NNP
37681	2428	34	P	P	NNP
37681	2428	35	_	_	NNP
37681	2428	36	,	,	,
37681	2428	37	and	and	CC
37681	2428	38	the	the	DT
37681	2428	39	tape	tape	NN
37681	2428	40	being	be	VBG
37681	2428	41	stretched	stretch	VBN
37681	2428	42	to	to	IN
37681	2428	43	_	_	NNP
37681	2428	44	A	A	NNP
37681	2428	45	_	_	NNP
37681	2428	46	,	,	,
37681	2428	47	so	so	IN
37681	2428	48	that	that	IN
37681	2428	49	_	_	NNP
37681	2428	50	PA	PA	NNP
37681	2428	51	_	_	NNP
37681	2428	52	=	=	SYM
37681	2428	53	4	4	CD
37681	2428	54	ft	ft	NN
37681	2428	55	.	.	.
37681	2428	56	and	and	CC
37681	2428	57	_	_	NNP
37681	2428	58	AB	AB	NNP
37681	2428	59	_	_	NNP
37681	2428	60	=	=	SYM
37681	2428	61	5	5	CD
37681	2428	62	ft	ft	NN
37681	2428	63	.	.	.
37681	2428	64	Then	then	RB
37681	2428	65	_	_	NNP
37681	2428	66	P	P	NNP
37681	2428	67	_	_	NNP
37681	2428	68	is	be	VBZ
37681	2428	69	a	a	DT
37681	2428	70	right	right	JJ
37681	2428	71	angle	angle	NN
37681	2428	72	by	by	IN
37681	2428	73	the	the	DT
37681	2428	74	Pythagorean	Pythagorean	NNP
37681	2428	75	Theorem	Theorem	NNP
37681	2428	76	.	.	.
37681	2429	1	This	this	DT
37681	2429	2	theorem	theorem	NN
37681	2429	3	not	not	RB
37681	2429	4	having	have	VBG
37681	2429	5	yet	yet	RB
37681	2429	6	been	be	VBN
37681	2429	7	proved	prove	VBN
37681	2429	8	,	,	,
37681	2429	9	it	-PRON-	PRP
37681	2429	10	can	can	MD
37681	2429	11	not	not	RB
37681	2429	12	be	be	VB
37681	2429	13	used	use	VBN
37681	2429	14	at	at	IN
37681	2429	15	this	this	DT
37681	2429	16	time	time	NN
37681	2429	17	.	.	.
37681	2430	1	A	a	DT
37681	2430	2	solution	solution	NN
37681	2430	3	for	for	IN
37681	2430	4	the	the	DT
37681	2430	5	problem	problem	NN
37681	2430	6	of	of	IN
37681	2430	7	erecting	erect	VBG
37681	2430	8	a	a	DT
37681	2430	9	perpendicular	perpendicular	NN
37681	2430	10	from	from	IN
37681	2430	11	the	the	DT
37681	2430	12	extremity	extremity	NN
37681	2430	13	of	of	IN
37681	2430	14	a	a	DT
37681	2430	15	line	line	NN
37681	2430	16	that	that	WDT
37681	2430	17	can	can	MD
37681	2430	18	not	not	RB
37681	2430	19	be	be	VB
37681	2430	20	produced	produce	VBN
37681	2430	21	,	,	,
37681	2430	22	depending	depend	VBG
37681	2430	23	,	,	,
37681	2430	24	however	however	RB
37681	2430	25	,	,	,
37681	2430	26	on	on	IN
37681	2430	27	the	the	DT
37681	2430	28	problem	problem	NN
37681	2430	29	of	of	IN
37681	2430	30	bisecting	bisect	VBG
37681	2430	31	an	an	DT
37681	2430	32	angle	angle	NN
37681	2430	33	,	,	,
37681	2430	34	and	and	CC
37681	2430	35	therefore	therefore	RB
37681	2430	36	to	to	TO
37681	2430	37	be	be	VB
37681	2430	38	given	give	VBN
37681	2430	39	after	after	IN
37681	2430	40	that	that	DT
37681	2430	41	problem	problem	NN
37681	2430	42	,	,	,
37681	2430	43	is	be	VBZ
37681	2430	44	attributed	attribute	VBN
37681	2430	45	by	by	IN
37681	2430	46	Al	Al	NNP
37681	2430	47	-	-	HYPH
37681	2430	48	Nair[=i]z[=i	Nair[=i]z[=i	NNP
37681	2430	49	]	]	-RRB-
37681	2430	50	(	(	-LRB-
37681	2430	51	tenth	tenth	JJ
37681	2430	52	century	century	NN
37681	2430	53	A.D.	A.D.	NNP
37681	2430	54	)	)	-RRB-
37681	2430	55	to	to	IN
37681	2430	56	Heron	Heron	NNP
37681	2430	57	of	of	IN
37681	2430	58	Alexandria	Alexandria	NNP
37681	2430	59	.	.	.
37681	2431	1	It	-PRON-	PRP
37681	2431	2	is	be	VBZ
37681	2431	3	also	also	RB
37681	2431	4	given	give	VBN
37681	2431	5	by	by	IN
37681	2431	6	Proclus	Proclus	NNP
37681	2431	7	.	.	.
37681	2432	1	[	[	-LRB-
37681	2432	2	Illustration	illustration	NN
37681	2432	3	]	]	-RRB-
37681	2432	4	Required	require	VBN
37681	2432	5	to	to	TO
37681	2432	6	draw	draw	VB
37681	2432	7	from	from	IN
37681	2432	8	_	_	NNP
37681	2432	9	P	P	NNP
37681	2432	10	_	_	NNP
37681	2432	11	a	a	DT
37681	2432	12	perpendicular	perpendicular	NN
37681	2432	13	to	to	IN
37681	2432	14	_	_	NNP
37681	2432	15	AP	AP	NNP
37681	2432	16	_	_	NNP
37681	2432	17	.	.	.
37681	2433	1	Take	take	VB
37681	2433	2	_	_	NNP
37681	2433	3	X	X	NNP
37681	2433	4	_	_	NNP
37681	2433	5	anywhere	anywhere	RB
37681	2433	6	on	on	IN
37681	2433	7	the	the	DT
37681	2433	8	line	line	NN
37681	2433	9	and	and	CC
37681	2433	10	erect	erect	NN
37681	2433	11	_	_	NNP
37681	2433	12	XY	XY	NNP
37681	2433	13	_	_	NNP
37681	2433	14	[	[	-LRB-
37681	2433	15	perp	perp	NN
37681	2433	16	]	]	-RRB-
37681	2433	17	to	to	IN
37681	2433	18	_	_	NNP
37681	2433	19	AP	AP	NNP
37681	2433	20	_	_	NNP
37681	2433	21	in	in	IN
37681	2433	22	the	the	DT
37681	2433	23	usual	usual	JJ
37681	2433	24	manner	manner	NN
37681	2433	25	.	.	.
37681	2434	1	Bisect	Bisect	NNP
37681	2434	2	[	[	-LRB-
37681	2434	3	L]_PXY	L]_PXY	NNP
37681	2434	4	_	_	NNP
37681	2434	5	by	by	IN
37681	2434	6	the	the	DT
37681	2434	7	line	line	NN
37681	2434	8	_	_	NNP
37681	2434	9	XM	XM	NNP
37681	2434	10	_	_	NNP
37681	2434	11	.	.	.
37681	2435	1	On	on	IN
37681	2435	2	_	_	NNP
37681	2435	3	XY	XY	NNP
37681	2435	4	_	_	NNP
37681	2435	5	take	take	NN
37681	2435	6	_	_	NNP
37681	2435	7	XN	XN	NNP
37681	2435	8	_	_	NNP
37681	2435	9	=	=	SYM
37681	2435	10	_	_	NNP
37681	2435	11	XP	XP	NNP
37681	2435	12	_	_	NNP
37681	2435	13	,	,	,
37681	2435	14	and	and	CC
37681	2435	15	draw	draw	VB
37681	2435	16	_	_	NNP
37681	2435	17	NM	NM	NNP
37681	2435	18	_	_	NNP
37681	2435	19	[	[	-LRB-
37681	2435	20	perp	perp	NN
37681	2435	21	]	]	-RRB-
37681	2435	22	to	to	IN
37681	2435	23	_	_	NNP
37681	2435	24	XY	XY	NNP
37681	2435	25	_	_	NNP
37681	2435	26	.	.	.
37681	2436	1	Then	then	RB
37681	2436	2	draw	draw	VB
37681	2436	3	_	_	NNP
37681	2436	4	PM	PM	NNP
37681	2436	5	_	_	NNP
37681	2436	6	.	.	.
37681	2437	1	The	the	DT
37681	2437	2	proof	proof	NN
37681	2437	3	is	be	VBZ
37681	2437	4	evident	evident	JJ
37681	2437	5	.	.	.
37681	2438	1	These	these	DT
37681	2438	2	may	may	MD
37681	2438	3	at	at	IN
37681	2438	4	the	the	DT
37681	2438	5	proper	proper	JJ
37681	2438	6	time	time	NN
37681	2438	7	be	be	VB
37681	2438	8	given	give	VBN
37681	2438	9	as	as	IN
37681	2438	10	interesting	interesting	JJ
37681	2438	11	variants	variant	NNS
37681	2438	12	of	of	IN
37681	2438	13	the	the	DT
37681	2438	14	usual	usual	JJ
37681	2438	15	solution	solution	NN
37681	2438	16	.	.	.
37681	2439	1	PROBLEM	problem	NN
37681	2439	2	.	.	.
37681	2440	1	_	_	NNP
37681	2440	2	To	to	TO
37681	2440	3	bisect	bisect	VB
37681	2440	4	a	a	DT
37681	2440	5	given	give	VBN
37681	2440	6	line	line	NN
37681	2440	7	.	.	.
37681	2440	8	_	_	NNP
37681	2440	9	Euclid	Euclid	NNP
37681	2440	10	said	say	VBD
37681	2440	11	"	"	``
37681	2440	12	finite	finite	JJ
37681	2440	13	straight	straight	JJ
37681	2440	14	line	line	NN
37681	2440	15	,	,	,
37681	2440	16	"	"	''
37681	2440	17	but	but	CC
37681	2440	18	this	this	DT
37681	2440	19	wording	wording	NN
37681	2440	20	is	be	VBZ
37681	2440	21	not	not	RB
37681	2440	22	commonly	commonly	RB
37681	2440	23	followed	follow	VBN
37681	2440	24	,	,	,
37681	2440	25	because	because	IN
37681	2440	26	it	-PRON-	PRP
37681	2440	27	will	will	MD
37681	2440	28	be	be	VB
37681	2440	29	inferred	infer	VBN
37681	2440	30	that	that	IN
37681	2440	31	the	the	DT
37681	2440	32	line	line	NN
37681	2440	33	is	be	VBZ
37681	2440	34	finite	finite	JJ
37681	2440	35	if	if	IN
37681	2440	36	it	-PRON-	PRP
37681	2440	37	is	be	VBZ
37681	2440	38	to	to	TO
37681	2440	39	be	be	VB
37681	2440	40	bisected	bisect	VBN
37681	2440	41	,	,	,
37681	2440	42	and	and	CC
37681	2440	43	we	-PRON-	PRP
37681	2440	44	use	use	VBP
37681	2440	45	"	"	``
37681	2440	46	line	line	NN
37681	2440	47	"	"	''
37681	2440	48	alone	alone	JJ
37681	2440	49	to	to	TO
37681	2440	50	mean	mean	VB
37681	2440	51	a	a	DT
37681	2440	52	straight	straight	JJ
37681	2440	53	line	line	NN
37681	2440	54	.	.	.
37681	2441	1	Euclid	Euclid	NNP
37681	2441	2	's	's	POS
37681	2441	3	plan	plan	NN
37681	2441	4	was	be	VBD
37681	2441	5	to	to	TO
37681	2441	6	construct	construct	VB
37681	2441	7	an	an	DT
37681	2441	8	equilateral	equilateral	JJ
37681	2441	9	triangle	triangle	NN
37681	2441	10	(	(	-LRB-
37681	2441	11	by	by	IN
37681	2441	12	his	-PRON-	PRP$
37681	2441	13	Proposition	Proposition	NNP
37681	2441	14	1	1	CD
37681	2441	15	of	of	IN
37681	2441	16	Book	Book	NNP
37681	2441	17	I	I	NNP
37681	2441	18	)	)	-RRB-
37681	2441	19	on	on	IN
37681	2441	20	the	the	DT
37681	2441	21	line	line	NN
37681	2441	22	as	as	IN
37681	2441	23	a	a	DT
37681	2441	24	base	base	NN
37681	2441	25	,	,	,
37681	2441	26	and	and	CC
37681	2441	27	then	then	RB
37681	2441	28	to	to	TO
37681	2441	29	bisect	bisect	VB
37681	2441	30	the	the	DT
37681	2441	31	vertical	vertical	JJ
37681	2441	32	angle	angle	NN
37681	2441	33	.	.	.
37681	2442	1	Proclus	Proclus	NNP
37681	2442	2	tells	tell	VBZ
37681	2442	3	us	-PRON-	PRP
37681	2442	4	that	that	IN
37681	2442	5	Apollonius	Apollonius	NNP
37681	2442	6	of	of	IN
37681	2442	7	Perga	Perga	NNP
37681	2442	8	,	,	,
37681	2442	9	who	who	WP
37681	2442	10	wrote	write	VBD
37681	2442	11	the	the	DT
37681	2442	12	first	first	JJ
37681	2442	13	great	great	JJ
37681	2442	14	work	work	NN
37681	2442	15	on	on	IN
37681	2442	16	conic	conic	JJ
37681	2442	17	sections	section	NNS
37681	2442	18	,	,	,
37681	2442	19	used	use	VBD
37681	2442	20	a	a	DT
37681	2442	21	plan	plan	NN
37681	2442	22	which	which	WDT
37681	2442	23	is	be	VBZ
37681	2442	24	substantially	substantially	RB
37681	2442	25	that	that	IN
37681	2442	26	which	which	WDT
37681	2442	27	is	be	VBZ
37681	2442	28	commonly	commonly	RB
37681	2442	29	found	find	VBN
37681	2442	30	in	in	IN
37681	2442	31	textbooks	textbook	NNS
37681	2442	32	to	to	IN
37681	2442	33	-	-	HYPH
37681	2442	34	day,--constructing	day,--constructe	VBG
37681	2442	35	two	two	CD
37681	2442	36	isosceles	isoscele	NNS
37681	2442	37	triangles	triangle	NNS
37681	2442	38	upon	upon	IN
37681	2442	39	the	the	DT
37681	2442	40	line	line	NN
37681	2442	41	as	as	IN
37681	2442	42	a	a	DT
37681	2442	43	common	common	JJ
37681	2442	44	base	base	NN
37681	2442	45	,	,	,
37681	2442	46	and	and	CC
37681	2442	47	connecting	connect	VBG
37681	2442	48	their	-PRON-	PRP$
37681	2442	49	vertices	vertex	NNS
37681	2442	50	.	.	.
37681	2443	1	PROBLEM	problem	NN
37681	2443	2	.	.	.
37681	2444	1	_	_	NNP
37681	2444	2	To	to	TO
37681	2444	3	bisect	bisect	VB
37681	2444	4	a	a	DT
37681	2444	5	given	give	VBN
37681	2444	6	angle	angle	NN
37681	2444	7	.	.	.
37681	2444	8	_	_	NNP
37681	2444	9	It	-PRON-	PRP
37681	2444	10	should	should	MD
37681	2444	11	be	be	VB
37681	2444	12	noticed	notice	VBN
37681	2444	13	that	that	IN
37681	2444	14	in	in	IN
37681	2444	15	the	the	DT
37681	2444	16	usual	usual	JJ
37681	2444	17	solution	solution	NN
37681	2444	18	two	two	CD
37681	2444	19	arcs	arc	NNS
37681	2444	20	intersect	intersect	NN
37681	2444	21	,	,	,
37681	2444	22	and	and	CC
37681	2444	23	the	the	DT
37681	2444	24	point	point	NN
37681	2444	25	thus	thus	RB
37681	2444	26	determined	determine	VBN
37681	2444	27	is	be	VBZ
37681	2444	28	connected	connect	VBN
37681	2444	29	with	with	IN
37681	2444	30	the	the	DT
37681	2444	31	vertex	vertex	NN
37681	2444	32	.	.	.
37681	2445	1	Now	now	RB
37681	2445	2	these	these	DT
37681	2445	3	two	two	CD
37681	2445	4	arcs	arc	NNS
37681	2445	5	intersect	intersect	VBP
37681	2445	6	twice	twice	RB
37681	2445	7	,	,	,
37681	2445	8	and	and	CC
37681	2445	9	since	since	IN
37681	2445	10	one	one	CD
37681	2445	11	of	of	IN
37681	2445	12	the	the	DT
37681	2445	13	points	point	NNS
37681	2445	14	of	of	IN
37681	2445	15	intersection	intersection	NN
37681	2445	16	may	may	MD
37681	2445	17	be	be	VB
37681	2445	18	the	the	DT
37681	2445	19	vertex	vertex	NN
37681	2445	20	itself	-PRON-	PRP
37681	2445	21	,	,	,
37681	2445	22	the	the	DT
37681	2445	23	other	other	JJ
37681	2445	24	point	point	NN
37681	2445	25	of	of	IN
37681	2445	26	intersection	intersection	NN
37681	2445	27	must	must	MD
37681	2445	28	be	be	VB
37681	2445	29	taken	take	VBN
37681	2445	30	.	.	.
37681	2446	1	It	-PRON-	PRP
37681	2446	2	is	be	VBZ
37681	2446	3	not	not	RB
37681	2446	4	,	,	,
37681	2446	5	however	however	RB
37681	2446	6	,	,	,
37681	2446	7	worth	worth	JJ
37681	2446	8	while	while	IN
37681	2446	9	to	to	TO
37681	2446	10	make	make	VB
37681	2446	11	much	much	JJ
37681	2446	12	of	of	IN
37681	2446	13	this	this	DT
37681	2446	14	matter	matter	NN
37681	2446	15	with	with	IN
37681	2446	16	pupils	pupil	NNS
37681	2446	17	.	.	.
37681	2447	1	Proclus	proclus	NN
37681	2447	2	calls	call	VBZ
37681	2447	3	attention	attention	NN
37681	2447	4	to	to	IN
37681	2447	5	the	the	DT
37681	2447	6	possible	possible	JJ
37681	2447	7	suggestion	suggestion	NN
37681	2447	8	that	that	IN
37681	2447	9	the	the	DT
37681	2447	10	point	point	NN
37681	2447	11	of	of	IN
37681	2447	12	intersection	intersection	NN
37681	2447	13	may	may	MD
37681	2447	14	be	be	VB
37681	2447	15	imagined	imagine	VBN
37681	2447	16	to	to	TO
37681	2447	17	lie	lie	VB
37681	2447	18	outside	outside	IN
37681	2447	19	the	the	DT
37681	2447	20	angle	angle	NN
37681	2447	21	,	,	,
37681	2447	22	and	and	CC
37681	2447	23	he	-PRON-	PRP
37681	2447	24	proceeds	proceed	VBZ
37681	2447	25	to	to	TO
37681	2447	26	show	show	VB
37681	2447	27	the	the	DT
37681	2447	28	absurdity	absurdity	NN
37681	2447	29	;	;	:
37681	2447	30	but	but	CC
37681	2447	31	here	here	RB
37681	2447	32	,	,	,
37681	2447	33	again	again	RB
37681	2447	34	,	,	,
37681	2447	35	the	the	DT
37681	2447	36	subject	subject	NN
37681	2447	37	is	be	VBZ
37681	2447	38	not	not	RB
37681	2447	39	one	one	CD
37681	2447	40	of	of	IN
37681	2447	41	value	value	NN
37681	2447	42	to	to	IN
37681	2447	43	beginners	beginner	NNS
37681	2447	44	.	.	.
37681	2448	1	He	-PRON-	PRP
37681	2448	2	also	also	RB
37681	2448	3	contributes	contribute	VBZ
37681	2448	4	to	to	IN
37681	2448	5	the	the	DT
37681	2448	6	history	history	NN
37681	2448	7	of	of	IN
37681	2448	8	the	the	DT
37681	2448	9	trisection	trisection	NN
37681	2448	10	of	of	IN
37681	2448	11	an	an	DT
37681	2448	12	angle	angle	NN
37681	2448	13	.	.	.
37681	2449	1	Any	any	DT
37681	2449	2	angle	angle	NN
37681	2449	3	is	be	VBZ
37681	2449	4	easily	easily	RB
37681	2449	5	trisected	trisect	VBN
37681	2449	6	by	by	IN
37681	2449	7	means	mean	NNS
37681	2449	8	of	of	IN
37681	2449	9	certain	certain	JJ
37681	2449	10	higher	high	JJR
37681	2449	11	curves	curve	NNS
37681	2449	12	,	,	,
37681	2449	13	such	such	JJ
37681	2449	14	as	as	IN
37681	2449	15	the	the	DT
37681	2449	16	conchoid	conchoid	NN
37681	2449	17	of	of	IN
37681	2449	18	Nicomedes	Nicomedes	NNP
37681	2449	19	(	(	-LRB-
37681	2449	20	_	_	NNP
37681	2449	21	ca	ca	NNP
37681	2449	22	.	.	.
37681	2449	23	_	_	NNP
37681	2449	24	180	180	CD
37681	2449	25	B.C.	B.C.	NNP
37681	2450	1	)	)	-RRB-
37681	2450	2	,	,	,
37681	2450	3	the	the	DT
37681	2450	4	quadratrix	quadratrix	NN
37681	2450	5	of	of	IN
37681	2450	6	Hippias	Hippias	NNP
37681	2450	7	of	of	IN
37681	2450	8	Elis	Elis	NNP
37681	2450	9	(	(	-LRB-
37681	2450	10	_	_	NNP
37681	2450	11	ca	ca	NNP
37681	2450	12	.	.	.
37681	2450	13	_	_	NNP
37681	2450	14	420	420	CD
37681	2450	15	B.C.	B.C.	NNP
37681	2451	1	)	)	-RRB-
37681	2451	2	,	,	,
37681	2451	3	or	or	CC
37681	2451	4	the	the	DT
37681	2451	5	spiral	spiral	NN
37681	2451	6	of	of	IN
37681	2451	7	Archimedes	Archimedes	NNP
37681	2451	8	(	(	-LRB-
37681	2451	9	_	_	NNP
37681	2451	10	ca	ca	NNP
37681	2451	11	.	.	.
37681	2451	12	_	_	NNP
37681	2451	13	250	250	CD
37681	2451	14	B.C.	B.C.	NNP
37681	2451	15	)	)	-RRB-
37681	2451	16	.	.	.
37681	2452	1	But	but	CC
37681	2452	2	since	since	IN
37681	2452	3	this	this	DT
37681	2452	4	problem	problem	NN
37681	2452	5	,	,	,
37681	2452	6	stated	state	VBD
37681	2452	7	algebraically	algebraically	RB
37681	2452	8	,	,	,
37681	2452	9	requires	require	VBZ
37681	2452	10	the	the	DT
37681	2452	11	solution	solution	NN
37681	2452	12	of	of	IN
37681	2452	13	a	a	DT
37681	2452	14	cubic	cubic	JJ
37681	2452	15	equation	equation	NN
37681	2452	16	,	,	,
37681	2452	17	and	and	CC
37681	2452	18	this	this	DT
37681	2452	19	involves	involve	VBZ
37681	2452	20	,	,	,
37681	2452	21	geometrically	geometrically	RB
37681	2452	22	,	,	,
37681	2452	23	finding	find	VBG
37681	2452	24	three	three	CD
37681	2452	25	points	point	NNS
37681	2452	26	,	,	,
37681	2452	27	we	-PRON-	PRP
37681	2452	28	can	can	MD
37681	2452	29	not	not	RB
37681	2452	30	solve	solve	VB
37681	2452	31	the	the	DT
37681	2452	32	problem	problem	NN
37681	2452	33	by	by	IN
37681	2452	34	means	mean	NNS
37681	2452	35	of	of	IN
37681	2452	36	straight	straight	JJ
37681	2452	37	lines	line	NNS
37681	2452	38	and	and	CC
37681	2452	39	circles	circle	NNS
37681	2452	40	alone	alone	JJ
37681	2452	41	.	.	.
37681	2453	1	In	in	IN
37681	2453	2	other	other	JJ
37681	2453	3	words	word	NNS
37681	2453	4	,	,	,
37681	2453	5	the	the	DT
37681	2453	6	trisection	trisection	NN
37681	2453	7	of	of	IN
37681	2453	8	_	_	NNP
37681	2453	9	any	any	DT
37681	2453	10	_	_	NNP
37681	2453	11	angle	angle	NN
37681	2453	12	,	,	,
37681	2453	13	by	by	IN
37681	2453	14	the	the	DT
37681	2453	15	use	use	NN
37681	2453	16	of	of	IN
37681	2453	17	the	the	DT
37681	2453	18	straightedge	straightedge	NN
37681	2453	19	and	and	CC
37681	2453	20	compasses	compass	NNS
37681	2453	21	alone	alone	RB
37681	2453	22	,	,	,
37681	2453	23	is	be	VBZ
37681	2453	24	impossible	impossible	JJ
37681	2453	25	.	.	.
37681	2454	1	Special	special	JJ
37681	2454	2	angles	angle	NNS
37681	2454	3	may	may	MD
37681	2454	4	however	however	RB
37681	2454	5	be	be	VB
37681	2454	6	trisected	trisect	VBN
37681	2454	7	.	.	.
37681	2455	1	Thus	thus	RB
37681	2455	2	,	,	,
37681	2455	3	to	to	TO
37681	2455	4	trisect	trisect	VB
37681	2455	5	an	an	DT
37681	2455	6	angle	angle	NN
37681	2455	7	of	of	IN
37681	2455	8	90	90	CD
37681	2455	9	°	°	NNS
37681	2455	10	we	-PRON-	PRP
37681	2455	11	need	need	VBP
37681	2455	12	only	only	RB
37681	2455	13	to	to	TO
37681	2455	14	construct	construct	VB
37681	2455	15	an	an	DT
37681	2455	16	angle	angle	NN
37681	2455	17	of	of	IN
37681	2455	18	60	60	CD
37681	2455	19	°	°	NNS
37681	2455	20	,	,	,
37681	2455	21	and	and	CC
37681	2455	22	this	this	DT
37681	2455	23	can	can	MD
37681	2455	24	be	be	VB
37681	2455	25	done	do	VBN
37681	2455	26	by	by	IN
37681	2455	27	constructing	construct	VBG
37681	2455	28	an	an	DT
37681	2455	29	equilateral	equilateral	JJ
37681	2455	30	triangle	triangle	NN
37681	2455	31	.	.	.
37681	2456	1	But	but	CC
37681	2456	2	while	while	IN
37681	2456	3	we	-PRON-	PRP
37681	2456	4	can	can	MD
37681	2456	5	not	not	RB
37681	2456	6	trisect	trisect	VB
37681	2456	7	the	the	DT
37681	2456	8	angle	angle	NN
37681	2456	9	,	,	,
37681	2456	10	we	-PRON-	PRP
37681	2456	11	may	may	MD
37681	2456	12	easily	easily	RB
37681	2456	13	approximate	approximate	VB
37681	2456	14	trisection	trisection	NN
37681	2456	15	.	.	.
37681	2457	1	For	for	IN
37681	2457	2	since	since	IN
37681	2457	3	,	,	,
37681	2457	4	in	in	IN
37681	2457	5	the	the	DT
37681	2457	6	infinite	infinite	JJ
37681	2457	7	geometric	geometric	NNP
37681	2457	8	series	series	NN
37681	2457	9	1/2	1/2	CD
37681	2457	10	+	+	SYM
37681	2457	11	1/8	1/8	CD
37681	2457	12	+	+	SYM
37681	2457	13	1/32	1/32	CD
37681	2457	14	+	+	CD
37681	2457	15	1/128	1/128	CD
37681	2457	16	+	+	SYM
37681	2457	17	...	...	NFP
37681	2457	18	,	,	,
37681	2457	19	_	_	NNP
37681	2457	20	s	s	NNP
37681	2457	21	_	_	NNP
37681	2457	22	=	=	SYM
37681	2457	23	_	_	NNP
37681	2457	24	a	a	DT
37681	2457	25	_	_	NNP
37681	2457	26	÷	÷	NN
37681	2457	27	(	(	-LRB-
37681	2457	28	1	1	CD
37681	2457	29	-	-	HYPH
37681	2457	30	_	_	NNP
37681	2457	31	r	r	NNP
37681	2457	32	_	_	NNP
37681	2457	33	)	)	-RRB-
37681	2457	34	,	,	,
37681	2457	35	we	-PRON-	PRP
37681	2457	36	have	have	VBP
37681	2457	37	_	_	NNP
37681	2457	38	s	s	NNP
37681	2457	39	_	_	NNP
37681	2457	40	=	=	SYM
37681	2457	41	1/2	1/2	CD
37681	2457	42	÷	÷	NN
37681	2457	43	3/4	3/4	CD
37681	2457	44	=	=	SYM
37681	2457	45	2/3	2/3	CD
37681	2457	46	.	.	.
37681	2458	1	In	in	IN
37681	2458	2	other	other	JJ
37681	2458	3	words	word	NNS
37681	2458	4	,	,	,
37681	2458	5	if	if	IN
37681	2458	6	we	-PRON-	PRP
37681	2458	7	add	add	VBP
37681	2458	8	1/2	1/2	CD
37681	2458	9	of	of	IN
37681	2458	10	the	the	DT
37681	2458	11	angle	angle	NN
37681	2458	12	,	,	,
37681	2458	13	1/8	1/8	CD
37681	2458	14	of	of	IN
37681	2458	15	the	the	DT
37681	2458	16	angle	angle	NN
37681	2458	17	,	,	,
37681	2458	18	1/32	1/32	CD
37681	2458	19	of	of	IN
37681	2458	20	the	the	DT
37681	2458	21	angle	angle	NN
37681	2458	22	,	,	,
37681	2458	23	and	and	CC
37681	2458	24	so	so	RB
37681	2458	25	on	on	RB
37681	2458	26	,	,	,
37681	2458	27	we	-PRON-	PRP
37681	2458	28	approach	approach	VBP
37681	2458	29	as	as	IN
37681	2458	30	a	a	DT
37681	2458	31	limit	limit	NN
37681	2458	32	2/3	2/3	CD
37681	2458	33	of	of	IN
37681	2458	34	the	the	DT
37681	2458	35	angle	angle	NN
37681	2458	36	;	;	:
37681	2458	37	but	but	CC
37681	2458	38	all	all	DT
37681	2458	39	of	of	IN
37681	2458	40	these	these	DT
37681	2458	41	fractions	fraction	NNS
37681	2458	42	can	can	MD
37681	2458	43	be	be	VB
37681	2458	44	obtained	obtain	VBN
37681	2458	45	by	by	IN
37681	2458	46	repeated	repeat	VBN
37681	2458	47	bisections	bisection	NNS
37681	2458	48	,	,	,
37681	2458	49	and	and	CC
37681	2458	50	hence	hence	RB
37681	2458	51	by	by	IN
37681	2458	52	bisections	bisection	NNS
37681	2458	53	we	-PRON-	PRP
37681	2458	54	may	may	MD
37681	2458	55	approximate	approximate	VB
37681	2458	56	the	the	DT
37681	2458	57	trisection	trisection	NN
37681	2458	58	.	.	.
37681	2459	1	The	the	DT
37681	2459	2	approximate	approximate	JJ
37681	2459	3	bisection	bisection	NN
37681	2459	4	(	(	-LRB-
37681	2459	5	or	or	CC
37681	2459	6	any	any	DT
37681	2459	7	other	other	JJ
37681	2459	8	division	division	NN
37681	2459	9	)	)	-RRB-
37681	2459	10	of	of	IN
37681	2459	11	an	an	DT
37681	2459	12	angle	angle	NN
37681	2459	13	may	may	MD
37681	2459	14	of	of	IN
37681	2459	15	course	course	NN
37681	2459	16	be	be	VB
37681	2459	17	effected	effect	VBN
37681	2459	18	by	by	IN
37681	2459	19	the	the	DT
37681	2459	20	help	help	NN
37681	2459	21	of	of	IN
37681	2459	22	the	the	DT
37681	2459	23	protractor	protractor	NN
37681	2459	24	and	and	CC
37681	2459	25	a	a	DT
37681	2459	26	straightedge	straightedge	NN
37681	2459	27	.	.	.
37681	2460	1	The	the	DT
37681	2460	2	geometric	geometric	JJ
37681	2460	3	method	method	NN
37681	2460	4	is	be	VBZ
37681	2460	5	,	,	,
37681	2460	6	however	however	RB
37681	2460	7	,	,	,
37681	2460	8	usually	usually	RB
37681	2460	9	more	more	RBR
37681	2460	10	accurate	accurate	JJ
37681	2460	11	,	,	,
37681	2460	12	and	and	CC
37681	2460	13	it	-PRON-	PRP
37681	2460	14	is	be	VBZ
37681	2460	15	advantageous	advantageous	JJ
37681	2460	16	to	to	TO
37681	2460	17	have	have	VB
37681	2460	18	the	the	DT
37681	2460	19	pupils	pupil	NNS
37681	2460	20	try	try	VB
37681	2460	21	both	both	DT
37681	2460	22	plans	plan	NNS
37681	2460	23	,	,	,
37681	2460	24	say	say	VB
37681	2460	25	for	for	IN
37681	2460	26	bisecting	bisect	VBG
37681	2460	27	an	an	DT
37681	2460	28	angle	angle	NN
37681	2460	29	of	of	IN
37681	2460	30	about	about	RB
37681	2460	31	49	49	CD
37681	2460	32	1/2	1/2	CD
37681	2460	33	°	°	NNS
37681	2460	34	.	.	.
37681	2461	1	[	[	-LRB-
37681	2461	2	Illustration	illustration	NN
37681	2461	3	]	]	-RRB-
37681	2461	4	Applications	Applications	NNPS
37681	2461	5	of	of	IN
37681	2461	6	this	this	DT
37681	2461	7	problem	problem	NN
37681	2461	8	are	be	VBP
37681	2461	9	numerous	numerous	JJ
37681	2461	10	.	.	.
37681	2462	1	It	-PRON-	PRP
37681	2462	2	may	may	MD
37681	2462	3	be	be	VB
37681	2462	4	desired	desire	VBN
37681	2462	5	,	,	,
37681	2462	6	for	for	IN
37681	2462	7	example	example	NN
37681	2462	8	,	,	,
37681	2462	9	to	to	TO
37681	2462	10	set	set	VB
37681	2462	11	a	a	DT
37681	2462	12	lamp	lamp	NN
37681	2462	13	-	-	HYPH
37681	2462	14	post	post	NN
37681	2462	15	on	on	IN
37681	2462	16	a	a	DT
37681	2462	17	line	line	NN
37681	2462	18	bisecting	bisect	VBG
37681	2462	19	the	the	DT
37681	2462	20	angle	angle	NN
37681	2462	21	formed	form	VBN
37681	2462	22	by	by	IN
37681	2462	23	two	two	CD
37681	2462	24	streets	street	NNS
37681	2462	25	that	that	WDT
37681	2462	26	come	come	VBP
37681	2462	27	together	together	RB
37681	2462	28	a	a	DT
37681	2462	29	little	little	JJ
37681	2462	30	unsymmetrically	unsymmetrically	RB
37681	2462	31	,	,	,
37681	2462	32	as	as	IN
37681	2462	33	here	here	RB
37681	2462	34	shown	show	VBN
37681	2462	35	,	,	,
37681	2462	36	in	in	IN
37681	2462	37	which	which	WDT
37681	2462	38	case	case	NN
37681	2462	39	the	the	DT
37681	2462	40	bisecting	bisecting	NN
37681	2462	41	line	line	NN
37681	2462	42	can	can	MD
37681	2462	43	easily	easily	RB
37681	2462	44	be	be	VB
37681	2462	45	run	run	VBN
37681	2462	46	by	by	IN
37681	2462	47	the	the	DT
37681	2462	48	use	use	NN
37681	2462	49	of	of	IN
37681	2462	50	a	a	DT
37681	2462	51	measuring	measuring	NN
37681	2462	52	tape	tape	NN
37681	2462	53	,	,	,
37681	2462	54	or	or	CC
37681	2462	55	even	even	RB
37681	2462	56	of	of	IN
37681	2462	57	a	a	DT
37681	2462	58	stout	stout	JJ
37681	2462	59	cord	cord	NN
37681	2462	60	.	.	.
37681	2463	1	A	a	DT
37681	2463	2	more	more	RBR
37681	2463	3	interesting	interesting	JJ
37681	2463	4	illustration	illustration	NN
37681	2463	5	is	be	VBZ
37681	2463	6	,	,	,
37681	2463	7	however	however	RB
37681	2463	8	,	,	,
37681	2463	9	the	the	DT
37681	2463	10	following	follow	VBG
37681	2463	11	:	:	:
37681	2463	12	[	[	-LRB-
37681	2463	13	Illustration	illustration	NN
37681	2463	14	]	]	-RRB-
37681	2463	15	Let	let	VB
37681	2463	16	the	the	DT
37681	2463	17	pupils	pupil	NNS
37681	2463	18	set	set	VB
37681	2463	19	a	a	DT
37681	2463	20	stake	stake	NN
37681	2463	21	,	,	,
37681	2463	22	say	say	VBP
37681	2463	23	about	about	RB
37681	2463	24	5	5	CD
37681	2463	25	feet	foot	NNS
37681	2463	26	high	high	JJ
37681	2463	27	,	,	,
37681	2463	28	at	at	IN
37681	2463	29	a	a	DT
37681	2463	30	point	point	NN
37681	2463	31	_	_	NNP
37681	2463	32	N	N	NNP
37681	2463	33	_	_	NNP
37681	2463	34	on	on	IN
37681	2463	35	the	the	DT
37681	2463	36	school	school	NN
37681	2463	37	grounds	ground	NNS
37681	2463	38	about	about	RB
37681	2463	39	9	9	CD
37681	2463	40	A.M.	A.M.	NNP
37681	2463	41	,	,	,
37681	2463	42	and	and	CC
37681	2463	43	carefully	carefully	RB
37681	2463	44	measure	measure	VB
37681	2463	45	the	the	DT
37681	2463	46	length	length	NN
37681	2463	47	of	of	IN
37681	2463	48	the	the	DT
37681	2463	49	shadow	shadow	NN
37681	2463	50	,	,	,
37681	2463	51	_	_	NNP
37681	2463	52	NW	NW	NNP
37681	2463	53	_	_	NNP
37681	2463	54	,	,	,
37681	2463	55	placing	place	VBG
37681	2463	56	a	a	DT
37681	2463	57	small	small	JJ
37681	2463	58	wooden	wooden	JJ
37681	2463	59	pin	pin	NN
37681	2463	60	at	at	IN
37681	2463	61	_	_	NNP
37681	2463	62	W	W	NNP
37681	2463	63	_	_	NNP
37681	2463	64	.	.	.
37681	2464	1	Then	then	RB
37681	2464	2	about	about	IN
37681	2464	3	3	3	CD
37681	2464	4	P.M.	P.M.	NNP
37681	2464	5	let	let	VB
37681	2464	6	them	-PRON-	PRP
37681	2464	7	watch	watch	VB
37681	2464	8	until	until	IN
37681	2464	9	the	the	DT
37681	2464	10	shadow	shadow	NN
37681	2464	11	_	_	NNP
37681	2464	12	NE	NE	NNP
37681	2464	13	_	_	NNP
37681	2464	14	is	be	VBZ
37681	2464	15	exactly	exactly	RB
37681	2464	16	the	the	DT
37681	2464	17	same	same	JJ
37681	2464	18	length	length	NN
37681	2464	19	that	that	WDT
37681	2464	20	it	-PRON-	PRP
37681	2464	21	was	be	VBD
37681	2464	22	when	when	WRB
37681	2464	23	_	_	NNP
37681	2464	24	W	W	NNP
37681	2464	25	_	_	NNP
37681	2464	26	was	be	VBD
37681	2464	27	fixed	fix	VBN
37681	2464	28	,	,	,
37681	2464	29	and	and	CC
37681	2464	30	then	then	RB
37681	2464	31	place	place	VB
37681	2464	32	a	a	DT
37681	2464	33	small	small	JJ
37681	2464	34	wooden	wooden	JJ
37681	2464	35	pin	pin	NN
37681	2464	36	at	at	IN
37681	2464	37	_	_	NNP
37681	2464	38	E	E	NNP
37681	2464	39	_	_	NNP
37681	2464	40	.	.	.
37681	2465	1	If	if	IN
37681	2465	2	the	the	DT
37681	2465	3	work	work	NN
37681	2465	4	has	have	VBZ
37681	2465	5	been	be	VBN
37681	2465	6	very	very	RB
37681	2465	7	carefully	carefully	RB
37681	2465	8	done	do	VBN
37681	2465	9	,	,	,
37681	2465	10	and	and	CC
37681	2465	11	they	-PRON-	PRP
37681	2465	12	take	take	VBP
37681	2465	13	the	the	DT
37681	2465	14	tape	tape	NN
37681	2465	15	and	and	CC
37681	2465	16	bisect	bisect	VB
37681	2465	17	the	the	DT
37681	2465	18	line	line	NN
37681	2465	19	_	_	NNP
37681	2465	20	WE	WE	NNP
37681	2465	21	_	_	NNP
37681	2465	22	,	,	,
37681	2465	23	thus	thus	RB
37681	2465	24	fixing	fix	VBG
37681	2465	25	the	the	DT
37681	2465	26	line	line	NN
37681	2465	27	_	_	NNP
37681	2465	28	NS	NS	NNP
37681	2465	29	_	_	NNP
37681	2465	30	,	,	,
37681	2465	31	they	-PRON-	PRP
37681	2465	32	will	will	MD
37681	2465	33	have	have	VB
37681	2465	34	a	a	DT
37681	2465	35	north	north	NN
37681	2465	36	and	and	CC
37681	2465	37	south	south	JJ
37681	2465	38	line	line	NN
37681	2465	39	.	.	.
37681	2466	1	If	if	IN
37681	2466	2	this	this	DT
37681	2466	3	is	be	VBZ
37681	2466	4	marked	mark	VBN
37681	2466	5	out	out	RP
37681	2466	6	for	for	IN
37681	2466	7	a	a	DT
37681	2466	8	short	short	JJ
37681	2466	9	distance	distance	NN
37681	2466	10	from	from	IN
37681	2466	11	_	_	NNP
37681	2466	12	N	N	NNP
37681	2466	13	_	_	NNP
37681	2466	14	,	,	,
37681	2466	15	then	then	RB
37681	2466	16	when	when	WRB
37681	2466	17	the	the	DT
37681	2466	18	shadow	shadow	NN
37681	2466	19	falls	fall	VBZ
37681	2466	20	on	on	IN
37681	2466	21	_	_	NNP
37681	2466	22	NS	NS	NNP
37681	2466	23	_	_	NNP
37681	2466	24	,	,	,
37681	2466	25	it	-PRON-	PRP
37681	2466	26	will	will	MD
37681	2466	27	be	be	VB
37681	2466	28	noon	noon	NN
37681	2466	29	by	by	IN
37681	2466	30	sun	sun	NN
37681	2466	31	time	time	NN
37681	2466	32	(	(	-LRB-
37681	2466	33	not	not	RB
37681	2466	34	standard	standard	JJ
37681	2466	35	time	time	NN
37681	2466	36	)	)	-RRB-
37681	2466	37	at	at	IN
37681	2466	38	the	the	DT
37681	2466	39	school	school	NN
37681	2466	40	.	.	.
37681	2467	1	PROBLEM	problem	NN
37681	2467	2	.	.	.
37681	2468	1	_	_	NNP
37681	2468	2	From	from	IN
37681	2468	3	a	a	DT
37681	2468	4	given	give	VBN
37681	2468	5	point	point	NN
37681	2468	6	in	in	IN
37681	2468	7	a	a	DT
37681	2468	8	given	give	VBN
37681	2468	9	line	line	NN
37681	2468	10	,	,	,
37681	2468	11	to	to	TO
37681	2468	12	draw	draw	VB
37681	2468	13	a	a	DT
37681	2468	14	line	line	NN
37681	2468	15	making	make	VBG
37681	2468	16	an	an	DT
37681	2468	17	angle	angle	NN
37681	2468	18	equal	equal	JJ
37681	2468	19	to	to	IN
37681	2468	20	a	a	DT
37681	2468	21	given	give	VBN
37681	2468	22	angle	angle	NN
37681	2468	23	.	.	.
37681	2468	24	_	_	NNP
37681	2468	25	Proclus	Proclus	NNP
37681	2468	26	says	say	VBZ
37681	2468	27	that	that	IN
37681	2468	28	Eudemus	Eudemus	NNP
37681	2468	29	attributed	attribute	VBD
37681	2468	30	to	to	IN
37681	2468	31	Oenopides	Oenopides	NNP
37681	2468	32	the	the	DT
37681	2468	33	discovery	discovery	NN
37681	2468	34	of	of	IN
37681	2468	35	the	the	DT
37681	2468	36	solution	solution	NN
37681	2468	37	which	which	WDT
37681	2468	38	Euclid	Euclid	NNP
37681	2468	39	gave	give	VBD
37681	2468	40	,	,	,
37681	2468	41	and	and	CC
37681	2468	42	which	which	WDT
37681	2468	43	is	be	VBZ
37681	2468	44	substantially	substantially	RB
37681	2468	45	the	the	DT
37681	2468	46	one	one	NN
37681	2468	47	now	now	RB
37681	2468	48	commonly	commonly	RB
37681	2468	49	seen	see	VBN
37681	2468	50	in	in	IN
37681	2468	51	textbooks	textbook	NNS
37681	2468	52	.	.	.
37681	2469	1	The	the	DT
37681	2469	2	problem	problem	NN
37681	2469	3	was	be	VBD
37681	2469	4	probably	probably	RB
37681	2469	5	solved	solve	VBN
37681	2469	6	in	in	IN
37681	2469	7	some	some	DT
37681	2469	8	fashion	fashion	NN
37681	2469	9	before	before	IN
37681	2469	10	the	the	DT
37681	2469	11	time	time	NN
37681	2469	12	of	of	IN
37681	2469	13	Oenopides	Oenopides	NNP
37681	2469	14	,	,	,
37681	2469	15	however	however	RB
37681	2469	16	.	.	.
37681	2470	1	The	the	DT
37681	2470	2	object	object	NN
37681	2470	3	of	of	IN
37681	2470	4	the	the	DT
37681	2470	5	problem	problem	NN
37681	2470	6	is	be	VBZ
37681	2470	7	primarily	primarily	RB
37681	2470	8	to	to	TO
37681	2470	9	enable	enable	VB
37681	2470	10	us	-PRON-	PRP
37681	2470	11	to	to	TO
37681	2470	12	draw	draw	VB
37681	2470	13	a	a	DT
37681	2470	14	line	line	NN
37681	2470	15	parallel	parallel	JJ
37681	2470	16	to	to	IN
37681	2470	17	a	a	DT
37681	2470	18	given	give	VBN
37681	2470	19	line	line	NN
37681	2470	20	.	.	.
37681	2471	1	Practically	practically	RB
37681	2471	2	,	,	,
37681	2471	3	the	the	DT
37681	2471	4	drawing	drawing	NN
37681	2471	5	of	of	IN
37681	2471	6	one	one	CD
37681	2471	7	line	line	NN
37681	2471	8	parallel	parallel	JJ
37681	2471	9	to	to	IN
37681	2471	10	another	another	DT
37681	2471	11	is	be	VBZ
37681	2471	12	usually	usually	RB
37681	2471	13	effected	effect	VBN
37681	2471	14	by	by	IN
37681	2471	15	means	mean	NNS
37681	2471	16	of	of	IN
37681	2471	17	a	a	DT
37681	2471	18	parallel	parallel	JJ
37681	2471	19	ruler	ruler	NN
37681	2471	20	(	(	-LRB-
37681	2471	21	see	see	VB
37681	2471	22	page	page	NN
37681	2471	23	191	191	CD
37681	2471	24	)	)	-RRB-
37681	2471	25	,	,	,
37681	2471	26	or	or	CC
37681	2471	27	by	by	IN
37681	2471	28	the	the	DT
37681	2471	29	use	use	NN
37681	2471	30	of	of	IN
37681	2471	31	draftsmen	draftsman	NNS
37681	2471	32	's	's	POS
37681	2471	33	triangles	triangle	NNS
37681	2471	34	,	,	,
37681	2471	35	as	as	IN
37681	2471	36	here	here	RB
37681	2471	37	shown	show	VBN
37681	2471	38	,	,	,
37681	2471	39	or	or	CC
37681	2471	40	even	even	RB
37681	2471	41	more	more	RBR
37681	2471	42	commonly	commonly	RB
37681	2471	43	by	by	IN
37681	2471	44	the	the	DT
37681	2471	45	use	use	NN
37681	2471	46	of	of	IN
37681	2471	47	a	a	DT
37681	2471	48	T	T	NNP
37681	2471	49	-	-	HYPH
37681	2471	50	square	square	NN
37681	2471	51	,	,	,
37681	2471	52	such	such	JJ
37681	2471	53	as	as	IN
37681	2471	54	is	be	VBZ
37681	2471	55	here	here	RB
37681	2471	56	seen	see	VBN
37681	2471	57	.	.	.
37681	2472	1	This	this	DT
37681	2472	2	illustration	illustration	NN
37681	2472	3	shows	show	VBZ
37681	2472	4	two	two	CD
37681	2472	5	T	T	NNP
37681	2472	6	-	-	HYPH
37681	2472	7	squares	square	NNS
37681	2472	8	used	use	VBN
37681	2472	9	for	for	IN
37681	2472	10	drawing	draw	VBG
37681	2472	11	lines	line	NNS
37681	2472	12	parallel	parallel	JJ
37681	2472	13	to	to	IN
37681	2472	14	the	the	DT
37681	2472	15	sides	side	NNS
37681	2472	16	of	of	IN
37681	2472	17	a	a	DT
37681	2472	18	board	board	NN
37681	2472	19	upon	upon	IN
37681	2472	20	which	which	WDT
37681	2472	21	the	the	DT
37681	2472	22	drawing	drawing	NN
37681	2472	23	paper	paper	NN
37681	2472	24	is	be	VBZ
37681	2472	25	fastened	fasten	VBN
37681	2472	26	.	.	.
37681	2473	1	[	[	-LRB-
37681	2473	2	71	71	CD
37681	2473	3	]	]	-RRB-
37681	2473	4	[	[	-LRB-
37681	2473	5	Illustration	illustration	NN
37681	2473	6	]	]	-RRB-
37681	2473	7	[	[	-LRB-
37681	2473	8	Illustration	illustration	NN
37681	2473	9	]	]	-RRB-
37681	2473	10	An	an	DT
37681	2473	11	ingenious	ingenious	JJ
37681	2473	12	instrument	instrument	NN
37681	2473	13	described	describe	VBN
37681	2473	14	by	by	IN
37681	2473	15	Baron	Baron	NNP
37681	2473	16	Dupin	Dupin	NNP
37681	2473	17	is	be	VBZ
37681	2473	18	illustrated	illustrate	VBN
37681	2473	19	below	below	RB
37681	2473	20	.	.	.
37681	2474	1	[	[	-LRB-
37681	2474	2	Illustration	illustration	NN
37681	2474	3	]	]	-RRB-
37681	2474	4	To	to	IN
37681	2474	5	the	the	DT
37681	2474	6	bar	bar	NN
37681	2474	7	_	_	NNP
37681	2474	8	A	A	NNP
37681	2474	9	_	_	NNP
37681	2474	10	is	be	VBZ
37681	2474	11	fastened	fasten	VBN
37681	2474	12	the	the	DT
37681	2474	13	sliding	slide	VBG
37681	2474	14	check	check	NN
37681	2474	15	_	_	NNP
37681	2474	16	B	B	NNP
37681	2474	17	_	_	NNP
37681	2474	18	.	.	.
37681	2475	1	A	a	DT
37681	2475	2	movable	movable	JJ
37681	2475	3	check	check	NN
37681	2475	4	_	_	NNP
37681	2475	5	D	D	NNP
37681	2475	6	_	_	NNP
37681	2475	7	may	may	MD
37681	2475	8	be	be	VB
37681	2475	9	fastened	fasten	VBN
37681	2475	10	by	by	IN
37681	2475	11	a	a	DT
37681	2475	12	screw	screw	NN
37681	2475	13	_	_	NNP
37681	2475	14	C	C	NNP
37681	2475	15	_	_	NNP
37681	2475	16	.	.	.
37681	2476	1	A	a	DT
37681	2476	2	sharp	sharp	JJ
37681	2476	3	point	point	NN
37681	2476	4	is	be	VBZ
37681	2476	5	fixed	fix	VBN
37681	2476	6	in	in	IN
37681	2476	7	_	_	NNP
37681	2476	8	B	B	NNP
37681	2476	9	_	_	NNP
37681	2476	10	,	,	,
37681	2476	11	so	so	IN
37681	2476	12	that	that	IN
37681	2476	13	as	as	IN
37681	2476	14	_	_	NNP
37681	2476	15	D	D	NNP
37681	2476	16	_	_	NNP
37681	2476	17	slides	slide	VBZ
37681	2476	18	along	along	IN
37681	2476	19	the	the	DT
37681	2476	20	edge	edge	NN
37681	2476	21	of	of	IN
37681	2476	22	a	a	DT
37681	2476	23	board	board	NN
37681	2476	24	,	,	,
37681	2476	25	the	the	DT
37681	2476	26	point	point	NN
37681	2476	27	marks	mark	VBZ
37681	2476	28	a	a	DT
37681	2476	29	line	line	NN
37681	2476	30	parallel	parallel	JJ
37681	2476	31	to	to	IN
37681	2476	32	the	the	DT
37681	2476	33	edge	edge	NN
37681	2476	34	.	.	.
37681	2477	1	Moreover	moreover	RB
37681	2477	2	,	,	,
37681	2477	3	_	_	NNP
37681	2477	4	F	F	NNP
37681	2477	5	_	_	NNP
37681	2477	6	and	and	CC
37681	2477	7	_	_	NNP
37681	2477	8	G	G	NNP
37681	2477	9	_	_	NNP
37681	2477	10	are	be	VBP
37681	2477	11	two	two	CD
37681	2477	12	brass	brass	NN
37681	2477	13	arms	arm	NNS
37681	2477	14	of	of	IN
37681	2477	15	equal	equal	JJ
37681	2477	16	length	length	NN
37681	2477	17	joined	join	VBN
37681	2477	18	by	by	IN
37681	2477	19	a	a	DT
37681	2477	20	pointed	pointed	JJ
37681	2477	21	screw	screw	NN
37681	2477	22	_	_	NNP
37681	2477	23	H	H	NNP
37681	2477	24	_	_	NNP
37681	2477	25	that	that	DT
37681	2477	26	marks	mark	VBZ
37681	2477	27	a	a	DT
37681	2477	28	line	line	NN
37681	2477	29	midway	midway	NN
37681	2477	30	between	between	IN
37681	2477	31	_	_	NNP
37681	2477	32	B	B	NNP
37681	2477	33	_	_	NNP
37681	2477	34	and	and	CC
37681	2477	35	_	_	NNP
37681	2477	36	D	D	NNP
37681	2477	37	_	_	NNP
37681	2477	38	.	.	.
37681	2478	1	Furthermore	furthermore	RB
37681	2478	2	,	,	,
37681	2478	3	it	-PRON-	PRP
37681	2478	4	is	be	VBZ
37681	2478	5	evident	evident	JJ
37681	2478	6	that	that	IN
37681	2478	7	_	_	NNP
37681	2478	8	H	H	NNP
37681	2478	9	_	_	NNP
37681	2478	10	will	will	MD
37681	2478	11	draw	draw	VB
37681	2478	12	a	a	DT
37681	2478	13	line	line	NN
37681	2478	14	bisecting	bisect	VBG
37681	2478	15	any	any	DT
37681	2478	16	irregular	irregular	JJ
37681	2478	17	board	board	NN
37681	2478	18	if	if	IN
37681	2478	19	the	the	DT
37681	2478	20	checks	check	NNS
37681	2478	21	_	_	NNP
37681	2478	22	B	B	NNP
37681	2478	23	_	_	NNP
37681	2478	24	and	and	CC
37681	2478	25	_	_	NNP
37681	2478	26	D	D	NNP
37681	2478	27	_	_	NNP
37681	2478	28	are	be	VBP
37681	2478	29	kept	keep	VBN
37681	2478	30	in	in	IN
37681	2478	31	contact	contact	NN
37681	2478	32	with	with	IN
37681	2478	33	the	the	DT
37681	2478	34	irregular	irregular	JJ
37681	2478	35	edges	edge	NNS
37681	2478	36	.	.	.
37681	2479	1	Book	Book	NNP
37681	2479	2	II	II	NNP
37681	2479	3	offers	offer	VBZ
37681	2479	4	two	two	CD
37681	2479	5	general	general	JJ
37681	2479	6	lines	line	NNS
37681	2479	7	of	of	IN
37681	2479	8	application	application	NN
37681	2479	9	that	that	WDT
37681	2479	10	may	may	MD
37681	2479	11	be	be	VB
37681	2479	12	introduced	introduce	VBN
37681	2479	13	to	to	TO
37681	2479	14	advantage	advantage	VB
37681	2479	15	,	,	,
37681	2479	16	preferably	preferably	RB
37681	2479	17	as	as	IN
37681	2479	18	additions	addition	NNS
37681	2479	19	to	to	IN
37681	2479	20	the	the	DT
37681	2479	21	textbook	textbook	NN
37681	2479	22	work	work	NN
37681	2479	23	.	.	.
37681	2480	1	One	one	CD
37681	2480	2	of	of	IN
37681	2480	3	these	these	DT
37681	2480	4	has	have	VBZ
37681	2480	5	reference	reference	NN
37681	2480	6	to	to	IN
37681	2480	7	topographical	topographical	JJ
37681	2480	8	drawing	drawing	NN
37681	2480	9	and	and	CC
37681	2480	10	related	related	JJ
37681	2480	11	subjects	subject	NNS
37681	2480	12	,	,	,
37681	2480	13	and	and	CC
37681	2480	14	the	the	DT
37681	2480	15	other	other	JJ
37681	2480	16	to	to	TO
37681	2480	17	geometric	geometric	JJ
37681	2480	18	design	design	NN
37681	2480	19	.	.	.
37681	2481	1	As	as	RB
37681	2481	2	long	long	RB
37681	2481	3	as	as	IN
37681	2481	4	these	these	DT
37681	2481	5	can	can	MD
37681	2481	6	be	be	VB
37681	2481	7	introduced	introduce	VBN
37681	2481	8	to	to	IN
37681	2481	9	the	the	DT
37681	2481	10	pupil	pupil	NN
37681	2481	11	with	with	IN
37681	2481	12	an	an	DT
37681	2481	13	air	air	NN
37681	2481	14	of	of	IN
37681	2481	15	reality	reality	NN
37681	2481	16	,	,	,
37681	2481	17	they	-PRON-	PRP
37681	2481	18	serve	serve	VBP
37681	2481	19	a	a	DT
37681	2481	20	good	good	JJ
37681	2481	21	purpose	purpose	NN
37681	2481	22	,	,	,
37681	2481	23	but	but	CC
37681	2481	24	if	if	IN
37681	2481	25	made	make	VBN
37681	2481	26	a	a	DT
37681	2481	27	part	part	NN
37681	2481	28	of	of	IN
37681	2481	29	textbook	textbook	NN
37681	2481	30	work	work	NN
37681	2481	31	,	,	,
37681	2481	32	they	-PRON-	PRP
37681	2481	33	soon	soon	RB
37681	2481	34	come	come	VBP
37681	2481	35	to	to	TO
37681	2481	36	have	have	VB
37681	2481	37	less	less	JJR
37681	2481	38	interest	interest	NN
37681	2481	39	than	than	IN
37681	2481	40	the	the	DT
37681	2481	41	exercises	exercise	NNS
37681	2481	42	of	of	IN
37681	2481	43	a	a	DT
37681	2481	44	more	more	RBR
37681	2481	45	abstract	abstract	JJ
37681	2481	46	character	character	NN
37681	2481	47	.	.	.
37681	2482	1	If	if	IN
37681	2482	2	a	a	DT
37681	2482	3	teacher	teacher	NN
37681	2482	4	can	can	MD
37681	2482	5	relate	relate	VB
37681	2482	6	the	the	DT
37681	2482	7	problems	problem	NNS
37681	2482	8	in	in	IN
37681	2482	9	topographical	topographical	JJ
37681	2482	10	drawing	drawing	NN
37681	2482	11	to	to	IN
37681	2482	12	the	the	DT
37681	2482	13	pupil	pupil	NN
37681	2482	14	's	's	POS
37681	2482	15	home	home	NN
37681	2482	16	town	town	NN
37681	2482	17	,	,	,
37681	2482	18	and	and	CC
37681	2482	19	can	can	MD
37681	2482	20	occasionally	occasionally	RB
37681	2482	21	set	set	VB
37681	2482	22	some	some	DT
37681	2482	23	outdoor	outdoor	JJ
37681	2482	24	work	work	NN
37681	2482	25	of	of	IN
37681	2482	26	the	the	DT
37681	2482	27	nature	nature	NN
37681	2482	28	here	here	RB
37681	2482	29	suggested	suggest	VBD
37681	2482	30	,	,	,
37681	2482	31	the	the	DT
37681	2482	32	results	result	NNS
37681	2482	33	are	be	VBP
37681	2482	34	usually	usually	RB
37681	2482	35	salutary	salutary	JJ
37681	2482	36	;	;	:
37681	2482	37	but	but	CC
37681	2482	38	if	if	IN
37681	2482	39	he	-PRON-	PRP
37681	2482	40	reiterates	reiterate	VBZ
37681	2482	41	only	only	RB
37681	2482	42	a	a	DT
37681	2482	43	half	half	JJ
37681	2482	44	-	-	HYPH
37681	2482	45	dozen	dozen	NN
37681	2482	46	simple	simple	JJ
37681	2482	47	propositions	proposition	NNS
37681	2482	48	time	time	NN
37681	2482	49	after	after	IN
37681	2482	50	time	time	NN
37681	2482	51	,	,	,
37681	2482	52	with	with	IN
37681	2482	53	only	only	JJ
37681	2482	54	slight	slight	JJ
37681	2482	55	changes	change	NNS
37681	2482	56	in	in	IN
37681	2482	57	the	the	DT
37681	2482	58	nature	nature	NN
37681	2482	59	of	of	IN
37681	2482	60	the	the	DT
37681	2482	61	application	application	NN
37681	2482	62	,	,	,
37681	2482	63	then	then	RB
37681	2482	64	the	the	DT
37681	2482	65	results	result	NNS
37681	2482	66	will	will	MD
37681	2482	67	not	not	RB
37681	2482	68	lead	lead	VB
37681	2482	69	to	to	IN
37681	2482	70	a	a	DT
37681	2482	71	cultivation	cultivation	NN
37681	2482	72	of	of	IN
37681	2482	73	power	power	NN
37681	2482	74	in	in	IN
37681	2482	75	geometry,--a	geometry,--a	NNP
37681	2482	76	point	point	NN
37681	2482	77	which	which	WDT
37681	2482	78	the	the	DT
37681	2482	79	writers	writer	NNS
37681	2482	80	on	on	IN
37681	2482	81	applied	apply	VBN
37681	2482	82	geometry	geometry	NN
37681	2482	83	usually	usually	RB
37681	2482	84	fail	fail	VBP
37681	2482	85	to	to	TO
37681	2482	86	recognize	recognize	VB
37681	2482	87	.	.	.
37681	2483	1	[	[	-LRB-
37681	2483	2	Illustration	illustration	NN
37681	2483	3	]	]	-RRB-
37681	2483	4	One	one	CD
37681	2483	5	of	of	IN
37681	2483	6	the	the	DT
37681	2483	7	simple	simple	JJ
37681	2483	8	applications	application	NNS
37681	2483	9	of	of	IN
37681	2483	10	this	this	DT
37681	2483	11	book	book	NN
37681	2483	12	relates	relate	VBZ
37681	2483	13	to	to	IN
37681	2483	14	the	the	DT
37681	2483	15	rounding	rounding	NN
37681	2483	16	of	of	IN
37681	2483	17	corners	corner	NNS
37681	2483	18	in	in	IN
37681	2483	19	laying	lay	VBG
37681	2483	20	out	out	RP
37681	2483	21	streets	street	NNS
37681	2483	22	in	in	IN
37681	2483	23	some	some	DT
37681	2483	24	of	of	IN
37681	2483	25	our	-PRON-	PRP$
37681	2483	26	modern	modern	JJ
37681	2483	27	towns	town	NNS
37681	2483	28	where	where	WRB
37681	2483	29	there	there	EX
37681	2483	30	is	be	VBZ
37681	2483	31	a	a	DT
37681	2483	32	desire	desire	NN
37681	2483	33	to	to	TO
37681	2483	34	depart	depart	VB
37681	2483	35	from	from	IN
37681	2483	36	the	the	DT
37681	2483	37	conventional	conventional	JJ
37681	2483	38	square	square	JJ
37681	2483	39	corner	corner	NN
37681	2483	40	.	.	.
37681	2484	1	It	-PRON-	PRP
37681	2484	2	is	be	VBZ
37681	2484	3	also	also	RB
37681	2484	4	used	use	VBN
37681	2484	5	in	in	IN
37681	2484	6	laying	lay	VBG
37681	2484	7	out	out	RP
37681	2484	8	park	park	NN
37681	2484	9	walks	walk	VBZ
37681	2484	10	and	and	CC
37681	2484	11	drives	drive	NNS
37681	2484	12	.	.	.
37681	2485	1	[	[	-LRB-
37681	2485	2	Illustration	illustration	NN
37681	2485	3	]	]	-RRB-
37681	2485	4	The	the	DT
37681	2485	5	figure	figure	NN
37681	2485	6	in	in	IN
37681	2485	7	the	the	DT
37681	2485	8	middle	middle	NN
37681	2485	9	of	of	IN
37681	2485	10	the	the	DT
37681	2485	11	page	page	NN
37681	2485	12	represents	represent	VBZ
37681	2485	13	two	two	CD
37681	2485	14	streets	street	NNS
37681	2485	15	,	,	,
37681	2485	16	_	_	NNP
37681	2485	17	AP	AP	NNP
37681	2485	18	_	_	NNP
37681	2485	19	and	and	CC
37681	2485	20	_	_	NNP
37681	2485	21	BQ	BQ	NNP
37681	2485	22	_	_	NNP
37681	2485	23	,	,	,
37681	2485	24	that	that	DT
37681	2485	25	would	would	MD
37681	2485	26	,	,	,
37681	2485	27	if	if	IN
37681	2485	28	prolonged	prolong	VBN
37681	2485	29	,	,	,
37681	2485	30	intersect	intersect	VBP
37681	2485	31	at	at	IN
37681	2485	32	_	_	NNP
37681	2485	33	C	C	NNP
37681	2485	34	_	_	NNP
37681	2485	35	.	.	.
37681	2486	1	It	-PRON-	PRP
37681	2486	2	is	be	VBZ
37681	2486	3	required	require	VBN
37681	2486	4	to	to	TO
37681	2486	5	construct	construct	VB
37681	2486	6	an	an	DT
37681	2486	7	arc	arc	NN
37681	2486	8	so	so	IN
37681	2486	9	that	that	IN
37681	2486	10	they	-PRON-	PRP
37681	2486	11	shall	shall	MD
37681	2486	12	begin	begin	VB
37681	2486	13	to	to	TO
37681	2486	14	curve	curve	VB
37681	2486	15	at	at	IN
37681	2486	16	_	_	NNP
37681	2486	17	P	P	NNP
37681	2486	18	_	_	NNP
37681	2486	19	and	and	CC
37681	2486	20	_	_	NNP
37681	2486	21	Q	Q	NNP
37681	2486	22	_	_	NNP
37681	2486	23	,	,	,
37681	2486	24	where	where	WRB
37681	2486	25	_	_	NNP
37681	2486	26	CP	CP	NNP
37681	2486	27	_	_	NNP
37681	2486	28	=	=	SYM
37681	2486	29	_	_	NNP
37681	2486	30	CQ	CQ	NNP
37681	2486	31	_	_	NNP
37681	2486	32	,	,	,
37681	2486	33	and	and	CC
37681	2486	34	hence	hence	RB
37681	2486	35	the	the	DT
37681	2486	36	"	"	``
37681	2486	37	center	center	NN
37681	2486	38	of	of	IN
37681	2486	39	curvature	curvature	JJ
37681	2486	40	"	"	``
37681	2486	41	_	_	NNP
37681	2486	42	O	O	NNP
37681	2486	43	_	_	NNP
37681	2486	44	must	must	MD
37681	2486	45	be	be	VB
37681	2486	46	found	find	VBN
37681	2486	47	.	.	.
37681	2487	1	The	the	DT
37681	2487	2	problem	problem	NN
37681	2487	3	is	be	VBZ
37681	2487	4	a	a	DT
37681	2487	5	common	common	JJ
37681	2487	6	one	one	NN
37681	2487	7	in	in	IN
37681	2487	8	railroad	railroad	NN
37681	2487	9	work	work	NN
37681	2487	10	,	,	,
37681	2487	11	only	only	RB
37681	2487	12	here	here	RB
37681	2487	13	_	_	NNP
37681	2487	14	AP	AP	NNP
37681	2487	15	_	_	NNP
37681	2487	16	is	be	VBZ
37681	2487	17	usually	usually	RB
37681	2487	18	oblique	oblique	JJ
37681	2487	19	to	to	IN
37681	2487	20	_	_	NNP
37681	2487	21	BQ	BQ	NNP
37681	2487	22	_	_	NNP
37681	2487	23	if	if	IN
37681	2487	24	they	-PRON-	PRP
37681	2487	25	are	be	VBP
37681	2487	26	produced	produce	VBN
37681	2487	27	to	to	TO
37681	2487	28	meet	meet	VB
37681	2487	29	at	at	IN
37681	2487	30	_	_	NNP
37681	2487	31	C	C	NNP
37681	2487	32	_	_	NNP
37681	2487	33	,	,	,
37681	2487	34	as	as	IN
37681	2487	35	in	in	IN
37681	2487	36	the	the	DT
37681	2487	37	second	second	JJ
37681	2487	38	figure	figure	NN
37681	2487	39	on	on	IN
37681	2487	40	page	page	NN
37681	2487	41	218	218	CD
37681	2487	42	.	.	.
37681	2488	1	It	-PRON-	PRP
37681	2488	2	is	be	VBZ
37681	2488	3	required	require	VBN
37681	2488	4	to	to	TO
37681	2488	5	construct	construct	VB
37681	2488	6	an	an	DT
37681	2488	7	arc	arc	NN
37681	2488	8	so	so	IN
37681	2488	9	that	that	IN
37681	2488	10	the	the	DT
37681	2488	11	tracks	track	NNS
37681	2488	12	shall	shall	MD
37681	2488	13	begin	begin	VB
37681	2488	14	to	to	TO
37681	2488	15	curve	curve	VB
37681	2488	16	at	at	IN
37681	2488	17	_	_	NNP
37681	2488	18	P	P	NNP
37681	2488	19	_	_	NNP
37681	2488	20	and	and	CC
37681	2488	21	_	_	NNP
37681	2488	22	Q	Q	NNP
37681	2488	23	_	_	NNP
37681	2488	24	,	,	,
37681	2488	25	where	where	WRB
37681	2488	26	_	_	NNP
37681	2488	27	CP	CP	NNP
37681	2488	28	_	_	NNP
37681	2488	29	=	=	SYM
37681	2488	30	_	_	NNP
37681	2488	31	CQ	CQ	NNP
37681	2488	32	_	_	NNP
37681	2488	33	.	.	.
37681	2489	1	[	[	-LRB-
37681	2489	2	Illustration	illustration	NN
37681	2489	3	]	]	-RRB-
37681	2489	4	The	the	DT
37681	2489	5	problem	problem	NN
37681	2489	6	becomes	become	VBZ
37681	2489	7	a	a	DT
37681	2489	8	little	little	JJ
37681	2489	9	more	more	RBR
37681	2489	10	complicated	complicated	JJ
37681	2489	11	,	,	,
37681	2489	12	and	and	CC
37681	2489	13	correspondingly	correspondingly	RB
37681	2489	14	more	more	RBR
37681	2489	15	interesting	interesting	JJ
37681	2489	16	,	,	,
37681	2489	17	when	when	WRB
37681	2489	18	we	-PRON-	PRP
37681	2489	19	have	have	VBP
37681	2489	20	to	to	TO
37681	2489	21	find	find	VB
37681	2489	22	the	the	DT
37681	2489	23	center	center	NN
37681	2489	24	of	of	IN
37681	2489	25	curvature	curvature	NN
37681	2489	26	for	for	IN
37681	2489	27	a	a	DT
37681	2489	28	street	street	NN
37681	2489	29	railway	railway	NN
37681	2489	30	track	track	NN
37681	2489	31	that	that	WDT
37681	2489	32	must	must	MD
37681	2489	33	turn	turn	VB
37681	2489	34	a	a	DT
37681	2489	35	corner	corner	NN
37681	2489	36	in	in	IN
37681	2489	37	such	such	PDT
37681	2489	38	a	a	DT
37681	2489	39	way	way	NN
37681	2489	40	as	as	IN
37681	2489	41	to	to	TO
37681	2489	42	allow	allow	VB
37681	2489	43	,	,	,
37681	2489	44	say	say	VB
37681	2489	45	,	,	,
37681	2489	46	exactly	exactly	RB
37681	2489	47	5	5	CD
37681	2489	48	feet	foot	NNS
37681	2489	49	from	from	IN
37681	2489	50	the	the	DT
37681	2489	51	point	point	NN
37681	2489	52	_	_	NNP
37681	2489	53	P	P	NNP
37681	2489	54	_	_	NNP
37681	2489	55	,	,	,
37681	2489	56	on	on	IN
37681	2489	57	account	account	NN
37681	2489	58	of	of	IN
37681	2489	59	a	a	DT
37681	2489	60	sidewalk	sidewalk	NN
37681	2489	61	.	.	.
37681	2490	1	[	[	-LRB-
37681	2490	2	Illustration	illustration	NN
37681	2490	3	]	]	-RRB-
37681	2490	4	The	the	DT
37681	2490	5	problem	problem	NN
37681	2490	6	becomes	become	VBZ
37681	2490	7	still	still	RB
37681	2490	8	more	more	RBR
37681	2490	9	difficult	difficult	JJ
37681	2490	10	if	if	IN
37681	2490	11	we	-PRON-	PRP
37681	2490	12	have	have	VBP
37681	2490	13	two	two	CD
37681	2490	14	roads	road	NNS
37681	2490	15	of	of	IN
37681	2490	16	different	different	JJ
37681	2490	17	widths	width	NNS
37681	2490	18	that	that	WDT
37681	2490	19	we	-PRON-	PRP
37681	2490	20	wish	wish	VBP
37681	2490	21	to	to	TO
37681	2490	22	join	join	VB
37681	2490	23	on	on	IN
37681	2490	24	a	a	DT
37681	2490	25	curve	curve	NN
37681	2490	26	.	.	.
37681	2491	1	Here	here	RB
37681	2491	2	the	the	DT
37681	2491	3	two	two	CD
37681	2491	4	centers	center	NNS
37681	2491	5	of	of	IN
37681	2491	6	curvature	curvature	NN
37681	2491	7	are	be	VBP
37681	2491	8	not	not	RB
37681	2491	9	the	the	DT
37681	2491	10	same	same	JJ
37681	2491	11	,	,	,
37681	2491	12	and	and	CC
37681	2491	13	the	the	DT
37681	2491	14	one	one	CD
37681	2491	15	road	road	NN
37681	2491	16	narrows	narrow	VBZ
37681	2491	17	to	to	IN
37681	2491	18	the	the	DT
37681	2491	19	other	other	JJ
37681	2491	20	on	on	IN
37681	2491	21	the	the	DT
37681	2491	22	curve	curve	NN
37681	2491	23	.	.	.
37681	2492	1	The	the	DT
37681	2492	2	solutions	solution	NNS
37681	2492	3	will	will	MD
37681	2492	4	be	be	VB
37681	2492	5	understood	understand	VBN
37681	2492	6	from	from	IN
37681	2492	7	a	a	DT
37681	2492	8	study	study	NN
37681	2492	9	of	of	IN
37681	2492	10	the	the	DT
37681	2492	11	figures	figure	NNS
37681	2492	12	.	.	.
37681	2493	1	The	the	DT
37681	2493	2	number	number	NN
37681	2493	3	of	of	IN
37681	2493	4	problems	problem	NNS
37681	2493	5	of	of	IN
37681	2493	6	this	this	DT
37681	2493	7	kind	kind	NN
37681	2493	8	that	that	WDT
37681	2493	9	can	can	MD
37681	2493	10	easily	easily	RB
37681	2493	11	be	be	VB
37681	2493	12	made	make	VBN
37681	2493	13	is	be	VBZ
37681	2493	14	limitless	limitless	JJ
37681	2493	15	,	,	,
37681	2493	16	and	and	CC
37681	2493	17	it	-PRON-	PRP
37681	2493	18	is	be	VBZ
37681	2493	19	well	well	JJ
37681	2493	20	to	to	TO
37681	2493	21	avoid	avoid	VB
37681	2493	22	the	the	DT
37681	2493	23	danger	danger	NN
37681	2493	24	of	of	IN
37681	2493	25	hobby	hobby	NN
37681	2493	26	riding	ride	VBG
37681	2493	27	on	on	IN
37681	2493	28	this	this	DT
37681	2493	29	or	or	CC
37681	2493	30	any	any	DT
37681	2493	31	similar	similar	JJ
37681	2493	32	topic	topic	NN
37681	2493	33	.	.	.
37681	2494	1	Therefore	therefore	RB
37681	2494	2	a	a	DT
37681	2494	3	single	single	JJ
37681	2494	4	one	one	NN
37681	2494	5	will	will	MD
37681	2494	6	suffice	suffice	VB
37681	2494	7	to	to	TO
37681	2494	8	close	close	VB
37681	2494	9	this	this	DT
37681	2494	10	group	group	NN
37681	2494	11	.	.	.
37681	2495	1	[	[	-LRB-
37681	2495	2	Illustration	illustration	NN
37681	2495	3	]	]	-RRB-
37681	2495	4	If	if	IN
37681	2495	5	a	a	DT
37681	2495	6	road	road	NN
37681	2495	7	_	_	NNP
37681	2495	8	AB	AB	NNP
37681	2495	9	_	_	NNP
37681	2495	10	on	on	IN
37681	2495	11	an	an	DT
37681	2495	12	arc	arc	NN
37681	2495	13	described	describe	VBN
37681	2495	14	about	about	IN
37681	2495	15	_	_	NNP
37681	2495	16	O	O	NNP
37681	2495	17	_	_	NNP
37681	2495	18	,	,	,
37681	2495	19	is	be	VBZ
37681	2495	20	to	to	TO
37681	2495	21	be	be	VB
37681	2495	22	joined	join	VBN
37681	2495	23	to	to	IN
37681	2495	24	road	road	NN
37681	2495	25	_	_	NNP
37681	2495	26	CD	CD	NNP
37681	2495	27	_	_	NNP
37681	2495	28	,	,	,
37681	2495	29	described	describe	VBN
37681	2495	30	about	about	IN
37681	2495	31	_	_	NNP
37681	2495	32	O	O	NNP
37681	2495	33	'	'	''
37681	2495	34	_	_	NNP
37681	2495	35	,	,	,
37681	2495	36	the	the	DT
37681	2495	37	arc	arc	NN
37681	2495	38	_	_	NNP
37681	2495	39	BC	BC	NNP
37681	2495	40	_	_	NNP
37681	2495	41	should	should	MD
37681	2495	42	evidently	evidently	RB
37681	2495	43	be	be	VB
37681	2495	44	internally	internally	RB
37681	2495	45	tangent	tangent	JJ
37681	2495	46	to	to	IN
37681	2495	47	_	_	NNP
37681	2495	48	AB	AB	NNP
37681	2495	49	_	_	NNP
37681	2495	50	and	and	CC
37681	2495	51	externally	externally	RB
37681	2495	52	tangent	tangent	NN
37681	2495	53	to	to	IN
37681	2495	54	_	_	NNP
37681	2495	55	CD	CD	NNP
37681	2495	56	_	_	NNP
37681	2495	57	.	.	.
37681	2496	1	Hence	hence	RB
37681	2496	2	the	the	DT
37681	2496	3	center	center	NN
37681	2496	4	is	be	VBZ
37681	2496	5	on	on	IN
37681	2496	6	_	_	NNP
37681	2496	7	BOX	BOX	NNP
37681	2496	8	_	_	NNP
37681	2496	9	and	and	CC
37681	2496	10	_	_	NNP
37681	2496	11	O'CY	O'CY	NNP
37681	2496	12	_	_	NNP
37681	2496	13	,	,	,
37681	2496	14	and	and	CC
37681	2496	15	is	be	VBZ
37681	2496	16	therefore	therefore	RB
37681	2496	17	at	at	IN
37681	2496	18	_	_	NNP
37681	2496	19	P	P	NNP
37681	2496	20	_	_	NNP
37681	2496	21	.	.	.
37681	2497	1	The	the	DT
37681	2497	2	problem	problem	NN
37681	2497	3	becomes	become	VBZ
37681	2497	4	more	more	RBR
37681	2497	5	real	real	JJ
37681	2497	6	if	if	IN
37681	2497	7	we	-PRON-	PRP
37681	2497	8	give	give	VBP
37681	2497	9	some	some	DT
37681	2497	10	width	width	NN
37681	2497	11	to	to	IN
37681	2497	12	the	the	DT
37681	2497	13	roads	road	NNS
37681	2497	14	in	in	IN
37681	2497	15	making	make	VBG
37681	2497	16	the	the	DT
37681	2497	17	drawing	drawing	NN
37681	2497	18	,	,	,
37681	2497	19	and	and	CC
37681	2497	20	imagine	imagine	VB
37681	2497	21	them	-PRON-	PRP
37681	2497	22	in	in	IN
37681	2497	23	a	a	DT
37681	2497	24	park	park	NN
37681	2497	25	that	that	WDT
37681	2497	26	is	be	VBZ
37681	2497	27	being	be	VBG
37681	2497	28	laid	lay	VBN
37681	2497	29	out	out	RP
37681	2497	30	with	with	IN
37681	2497	31	drives	drive	NNS
37681	2497	32	.	.	.
37681	2498	1	It	-PRON-	PRP
37681	2498	2	will	will	MD
37681	2498	3	be	be	VB
37681	2498	4	noticed	notice	VBN
37681	2498	5	that	that	IN
37681	2498	6	the	the	DT
37681	2498	7	above	above	JJ
37681	2498	8	problems	problem	NNS
37681	2498	9	require	require	VBP
37681	2498	10	the	the	DT
37681	2498	11	erecting	erecting	NN
37681	2498	12	of	of	IN
37681	2498	13	perpendiculars	perpendicular	NNS
37681	2498	14	,	,	,
37681	2498	15	the	the	DT
37681	2498	16	bisecting	bisecting	NN
37681	2498	17	of	of	IN
37681	2498	18	angles	angle	NNS
37681	2498	19	,	,	,
37681	2498	20	and	and	CC
37681	2498	21	the	the	DT
37681	2498	22	application	application	NN
37681	2498	23	of	of	IN
37681	2498	24	the	the	DT
37681	2498	25	propositions	proposition	NNS
37681	2498	26	on	on	IN
37681	2498	27	tangents	tangent	NNS
37681	2498	28	.	.	.
37681	2499	1	A	a	DT
37681	2499	2	somewhat	somewhat	RB
37681	2499	3	different	different	JJ
37681	2499	4	line	line	NN
37681	2499	5	of	of	IN
37681	2499	6	problems	problem	NNS
37681	2499	7	is	be	VBZ
37681	2499	8	that	that	IN
37681	2499	9	relating	relate	VBG
37681	2499	10	to	to	IN
37681	2499	11	the	the	DT
37681	2499	12	passing	passing	NN
37681	2499	13	of	of	IN
37681	2499	14	a	a	DT
37681	2499	15	circle	circle	NN
37681	2499	16	through	through	IN
37681	2499	17	three	three	CD
37681	2499	18	given	give	VBN
37681	2499	19	points	point	NNS
37681	2499	20	.	.	.
37681	2500	1	It	-PRON-	PRP
37681	2500	2	is	be	VBZ
37681	2500	3	very	very	RB
37681	2500	4	easy	easy	JJ
37681	2500	5	to	to	TO
37681	2500	6	manufacture	manufacture	VB
37681	2500	7	problems	problem	NNS
37681	2500	8	of	of	IN
37681	2500	9	this	this	DT
37681	2500	10	kind	kind	NN
37681	2500	11	that	that	WDT
37681	2500	12	have	have	VBP
37681	2500	13	a	a	DT
37681	2500	14	semblance	semblance	NN
37681	2500	15	of	of	IN
37681	2500	16	reality	reality	NN
37681	2500	17	.	.	.
37681	2501	1	[	[	-LRB-
37681	2501	2	Illustration	illustration	NN
37681	2501	3	]	]	-RRB-
37681	2501	4	For	for	IN
37681	2501	5	example	example	NN
37681	2501	6	,	,	,
37681	2501	7	let	let	VB
37681	2501	8	it	-PRON-	PRP
37681	2501	9	be	be	VB
37681	2501	10	required	require	VBN
37681	2501	11	to	to	TO
37681	2501	12	plan	plan	VB
37681	2501	13	a	a	DT
37681	2501	14	driveway	driveway	NN
37681	2501	15	from	from	IN
37681	2501	16	the	the	DT
37681	2501	17	gate	gate	NN
37681	2501	18	_	_	NNP
37681	2501	19	G	G	NNP
37681	2501	20	_	_	NNP
37681	2501	21	to	to	IN
37681	2501	22	the	the	DT
37681	2501	23	porch	porch	NN
37681	2501	24	_	_	NNP
37681	2501	25	P	P	NNP
37681	2501	26	_	_	NNP
37681	2501	27	so	so	IN
37681	2501	28	as	as	IN
37681	2501	29	to	to	TO
37681	2501	30	avoid	avoid	VB
37681	2501	31	a	a	DT
37681	2501	32	mass	mass	NN
37681	2501	33	of	of	IN
37681	2501	34	rocks	rock	NNS
37681	2501	35	_	_	NNP
37681	2501	36	R	R	NNP
37681	2501	37	_	_	NNP
37681	2501	38	,	,	,
37681	2501	39	an	an	DT
37681	2501	40	arc	arc	NN
37681	2501	41	of	of	IN
37681	2501	42	a	a	DT
37681	2501	43	circle	circle	NN
37681	2501	44	to	to	TO
37681	2501	45	be	be	VB
37681	2501	46	taken	take	VBN
37681	2501	47	.	.	.
37681	2502	1	Of	of	RB
37681	2502	2	course	course	RB
37681	2502	3	,	,	,
37681	2502	4	if	if	IN
37681	2502	5	we	-PRON-	PRP
37681	2502	6	allow	allow	VBP
37681	2502	7	pupils	pupil	NNS
37681	2502	8	to	to	TO
37681	2502	9	use	use	VB
37681	2502	10	the	the	DT
37681	2502	11	Pythagorean	Pythagorean	NNP
37681	2502	12	Theorem	Theorem	NNP
37681	2502	13	at	at	IN
37681	2502	14	this	this	DT
37681	2502	15	time	time	NN
37681	2502	16	(	(	-LRB-
37681	2502	17	and	and	CC
37681	2502	18	for	for	IN
37681	2502	19	metrical	metrical	JJ
37681	2502	20	purposes	purpose	NNS
37681	2502	21	this	this	DT
37681	2502	22	is	be	VBZ
37681	2502	23	entirely	entirely	RB
37681	2502	24	proper	proper	JJ
37681	2502	25	,	,	,
37681	2502	26	because	because	IN
37681	2502	27	they	-PRON-	PRP
37681	2502	28	have	have	VBP
37681	2502	29	long	long	RB
37681	2502	30	been	be	VBN
37681	2502	31	familiar	familiar	JJ
37681	2502	32	with	with	IN
37681	2502	33	it	-PRON-	PRP
37681	2502	34	)	)	-RRB-
37681	2502	35	,	,	,
37681	2502	36	then	then	RB
37681	2502	37	we	-PRON-	PRP
37681	2502	38	may	may	MD
37681	2502	39	ask	ask	VB
37681	2502	40	not	not	RB
37681	2502	41	only	only	RB
37681	2502	42	for	for	IN
37681	2502	43	the	the	DT
37681	2502	44	drawing	drawing	NN
37681	2502	45	,	,	,
37681	2502	46	but	but	CC
37681	2502	47	we	-PRON-	PRP
37681	2502	48	may	may	MD
37681	2502	49	,	,	,
37681	2502	50	for	for	IN
37681	2502	51	example	example	NN
37681	2502	52	,	,	,
37681	2502	53	give	give	VB
37681	2502	54	the	the	DT
37681	2502	55	length	length	NN
37681	2502	56	from	from	IN
37681	2502	57	_	_	NNP
37681	2502	58	G	G	NNP
37681	2502	59	_	_	NNP
37681	2502	60	to	to	IN
37681	2502	61	the	the	DT
37681	2502	62	point	point	NN
37681	2502	63	on	on	IN
37681	2502	64	_	_	NNP
37681	2502	65	R	R	NNP
37681	2502	66	_	_	NNP
37681	2502	67	(	(	-LRB-
37681	2502	68	which	which	WDT
37681	2502	69	we	-PRON-	PRP
37681	2502	70	may	may	MD
37681	2502	71	also	also	RB
37681	2502	72	call	call	VB
37681	2502	73	_	_	NNP
37681	2502	74	R	R	NNP
37681	2502	75	_	_	NNP
37681	2502	76	)	)	-RRB-
37681	2502	77	,	,	,
37681	2502	78	and	and	CC
37681	2502	79	the	the	DT
37681	2502	80	angle	angle	NN
37681	2502	81	_	_	NNP
37681	2502	82	RGO	RGO	NNP
37681	2502	83	_	_	NNP
37681	2502	84	as	as	IN
37681	2502	85	60	60	CD
37681	2502	86	°	°	NNS
37681	2502	87	,	,	,
37681	2502	88	to	to	TO
37681	2502	89	find	find	VB
37681	2502	90	the	the	DT
37681	2502	91	radius	radius	NN
37681	2502	92	.	.	.
37681	2503	1	A	a	DT
37681	2503	2	second	second	JJ
37681	2503	3	general	general	JJ
37681	2503	4	line	line	NN
37681	2503	5	of	of	IN
37681	2503	6	exercises	exercise	NNS
37681	2503	7	adapted	adapt	VBN
37681	2503	8	to	to	IN
37681	2503	9	Book	Book	NNP
37681	2503	10	II	II	NNP
37681	2503	11	is	be	VBZ
37681	2503	12	a	a	DT
37681	2503	13	continuation	continuation	NN
37681	2503	14	of	of	IN
37681	2503	15	the	the	DT
37681	2503	16	geometric	geometric	JJ
37681	2503	17	drawing	drawing	NN
37681	2503	18	recommended	recommend	VBN
37681	2503	19	as	as	IN
37681	2503	20	a	a	DT
37681	2503	21	preliminary	preliminary	NN
37681	2503	22	to	to	IN
37681	2503	23	the	the	DT
37681	2503	24	work	work	NN
37681	2503	25	in	in	IN
37681	2503	26	demonstrative	demonstrative	JJ
37681	2503	27	geometry	geometry	NN
37681	2503	28	.	.	.
37681	2504	1	The	the	DT
37681	2504	2	copying	copying	NN
37681	2504	3	or	or	CC
37681	2504	4	the	the	DT
37681	2504	5	making	making	NN
37681	2504	6	of	of	IN
37681	2504	7	designs	design	NNS
37681	2504	8	requiring	require	VBG
37681	2504	9	the	the	DT
37681	2504	10	describing	describing	NN
37681	2504	11	of	of	IN
37681	2504	12	circles	circle	NNS
37681	2504	13	,	,	,
37681	2504	14	their	-PRON-	PRP$
37681	2504	15	inscription	inscription	NN
37681	2504	16	in	in	IN
37681	2504	17	or	or	CC
37681	2504	18	circumscription	circumscription	NN
37681	2504	19	about	about	IN
37681	2504	20	triangles	triangle	NNS
37681	2504	21	,	,	,
37681	2504	22	and	and	CC
37681	2504	23	their	-PRON-	PRP$
37681	2504	24	construction	construction	NN
37681	2504	25	in	in	IN
37681	2504	26	various	various	JJ
37681	2504	27	positions	position	NNS
37681	2504	28	of	of	IN
37681	2504	29	tangency	tangency	NN
37681	2504	30	,	,	,
37681	2504	31	has	have	VBZ
37681	2504	32	some	some	DT
37681	2504	33	value	value	NN
37681	2504	34	as	as	IN
37681	2504	35	applying	apply	VBG
37681	2504	36	the	the	DT
37681	2504	37	various	various	JJ
37681	2504	38	problems	problem	NNS
37681	2504	39	studied	study	VBN
37681	2504	40	in	in	IN
37681	2504	41	this	this	DT
37681	2504	42	book	book	NN
37681	2504	43	.	.	.
37681	2505	1	For	for	IN
37681	2505	2	a	a	DT
37681	2505	3	number	number	NN
37681	2505	4	of	of	IN
37681	2505	5	years	year	NNS
37681	2505	6	past	past	JJ
37681	2505	7	,	,	,
37681	2505	8	several	several	JJ
37681	2505	9	enthusiastic	enthusiastic	JJ
37681	2505	10	teachers	teacher	NNS
37681	2505	11	have	have	VBP
37681	2505	12	made	make	VBN
37681	2505	13	much	much	JJ
37681	2505	14	of	of	IN
37681	2505	15	the	the	DT
37681	2505	16	designs	design	NNS
37681	2505	17	found	find	VBN
37681	2505	18	in	in	IN
37681	2505	19	Gothic	gothic	JJ
37681	2505	20	windows	window	NNS
37681	2505	21	,	,	,
37681	2505	22	having	have	VBG
37681	2505	23	their	-PRON-	PRP$
37681	2505	24	pupils	pupil	NNS
37681	2505	25	make	make	VB
37681	2505	26	the	the	DT
37681	2505	27	outline	outline	JJ
37681	2505	28	drawings	drawing	NNS
37681	2505	29	by	by	IN
37681	2505	30	the	the	DT
37681	2505	31	help	help	NN
37681	2505	32	of	of	IN
37681	2505	33	compasses	compass	NNS
37681	2505	34	and	and	CC
37681	2505	35	straightedge	straightedge	NN
37681	2505	36	.	.	.
37681	2506	1	While	while	IN
37681	2506	2	such	such	JJ
37681	2506	3	work	work	NN
37681	2506	4	has	have	VBZ
37681	2506	5	its	-PRON-	PRP$
37681	2506	6	value	value	NN
37681	2506	7	,	,	,
37681	2506	8	it	-PRON-	PRP
37681	2506	9	is	be	VBZ
37681	2506	10	liable	liable	JJ
37681	2506	11	soon	soon	RB
37681	2506	12	to	to	TO
37681	2506	13	degenerate	degenerate	VB
37681	2506	14	into	into	IN
37681	2506	15	purposeless	purposeless	JJ
37681	2506	16	formalism	formalism	NN
37681	2506	17	,	,	,
37681	2506	18	and	and	CC
37681	2506	19	hence	hence	RB
37681	2506	20	to	to	TO
37681	2506	21	lose	lose	VB
37681	2506	22	interest	interest	NN
37681	2506	23	by	by	IN
37681	2506	24	taking	take	VBG
37681	2506	25	the	the	DT
37681	2506	26	vigorous	vigorous	JJ
37681	2506	27	mind	mind	NN
37681	2506	28	of	of	IN
37681	2506	29	youth	youth	NN
37681	2506	30	from	from	IN
37681	2506	31	the	the	DT
37681	2506	32	strong	strong	JJ
37681	2506	33	study	study	NN
37681	2506	34	of	of	IN
37681	2506	35	geometry	geometry	NN
37681	2506	36	to	to	IN
37681	2506	37	the	the	DT
37681	2506	38	weak	weak	JJ
37681	2506	39	manipulation	manipulation	NN
37681	2506	40	of	of	IN
37681	2506	41	instruments	instrument	NNS
37681	2506	42	.	.	.
37681	2507	1	Nevertheless	nevertheless	RB
37681	2507	2	its	-PRON-	PRP$
37681	2507	3	value	value	NN
37681	2507	4	should	should	MD
37681	2507	5	be	be	VB
37681	2507	6	appreciated	appreciate	VBN
37681	2507	7	and	and	CC
37681	2507	8	conserved	conserve	VBN
37681	2507	9	,	,	,
37681	2507	10	and	and	CC
37681	2507	11	a	a	DT
37681	2507	12	few	few	JJ
37681	2507	13	illustrations	illustration	NNS
37681	2507	14	of	of	IN
37681	2507	15	these	these	DT
37681	2507	16	forms	form	NNS
37681	2507	17	are	be	VBP
37681	2507	18	given	give	VBN
37681	2507	19	in	in	IN
37681	2507	20	order	order	NN
37681	2507	21	that	that	IN
37681	2507	22	the	the	DT
37681	2507	23	teacher	teacher	NN
37681	2507	24	may	may	MD
37681	2507	25	have	have	VB
37681	2507	26	examples	example	NNS
37681	2507	27	from	from	IN
37681	2507	28	which	which	WDT
37681	2507	29	to	to	TO
37681	2507	30	select	select	VB
37681	2507	31	.	.	.
37681	2508	1	The	the	DT
37681	2508	2	best	good	JJS
37681	2508	3	way	way	NN
37681	2508	4	of	of	IN
37681	2508	5	using	use	VBG
37681	2508	6	this	this	DT
37681	2508	7	material	material	NN
37681	2508	8	is	be	VBZ
37681	2508	9	to	to	TO
37681	2508	10	offer	offer	VB
37681	2508	11	it	-PRON-	PRP
37681	2508	12	as	as	IN
37681	2508	13	supplementary	supplementary	JJ
37681	2508	14	work	work	NN
37681	2508	15	,	,	,
37681	2508	16	using	use	VBG
37681	2508	17	much	much	JJ
37681	2508	18	or	or	CC
37681	2508	19	little	little	JJ
37681	2508	20	,	,	,
37681	2508	21	as	as	IN
37681	2508	22	may	may	MD
37681	2508	23	seem	seem	VB
37681	2508	24	best	good	JJS
37681	2508	25	,	,	,
37681	2508	26	thus	thus	RB
37681	2508	27	giving	give	VBG
37681	2508	28	to	to	IN
37681	2508	29	it	-PRON-	PRP
37681	2508	30	a	a	DT
37681	2508	31	freshness	freshness	NN
37681	2508	32	and	and	CC
37681	2508	33	interest	interest	NN
37681	2508	34	that	that	WDT
37681	2508	35	some	some	DT
37681	2508	36	have	have	VBP
37681	2508	37	trouble	trouble	NN
37681	2508	38	in	in	IN
37681	2508	39	imparting	impart	VBG
37681	2508	40	to	to	IN
37681	2508	41	the	the	DT
37681	2508	42	regular	regular	JJ
37681	2508	43	book	book	NN
37681	2508	44	work	work	NN
37681	2508	45	.	.	.
37681	2509	1	The	the	DT
37681	2509	2	best	good	JJS
37681	2509	3	plan	plan	NN
37681	2509	4	is	be	VBZ
37681	2509	5	to	to	TO
37681	2509	6	sketch	sketch	VB
37681	2509	7	rapidly	rapidly	RB
37681	2509	8	the	the	DT
37681	2509	9	outline	outline	NN
37681	2509	10	of	of	IN
37681	2509	11	a	a	DT
37681	2509	12	window	window	NN
37681	2509	13	on	on	IN
37681	2509	14	the	the	DT
37681	2509	15	blackboard	blackboard	NN
37681	2509	16	,	,	,
37681	2509	17	asking	ask	VBG
37681	2509	18	the	the	DT
37681	2509	19	pupils	pupil	NNS
37681	2509	20	to	to	TO
37681	2509	21	make	make	VB
37681	2509	22	a	a	DT
37681	2509	23	rough	rough	JJ
37681	2509	24	drawing	drawing	NN
37681	2509	25	,	,	,
37681	2509	26	and	and	CC
37681	2509	27	to	to	TO
37681	2509	28	bring	bring	VB
37681	2509	29	in	in	RP
37681	2509	30	a	a	DT
37681	2509	31	mathematical	mathematical	JJ
37681	2509	32	drawing	drawing	NN
37681	2509	33	on	on	IN
37681	2509	34	the	the	DT
37681	2509	35	following	follow	VBG
37681	2509	36	day	day	NN
37681	2509	37	.	.	.
37681	2510	1	[	[	-LRB-
37681	2510	2	Illustration	illustration	NN
37681	2510	3	]	]	-RRB-
37681	2510	4	It	-PRON-	PRP
37681	2510	5	might	may	MD
37681	2510	6	be	be	VB
37681	2510	7	said	say	VBN
37681	2510	8	,	,	,
37681	2510	9	for	for	IN
37681	2510	10	example	example	NN
37681	2510	11	,	,	,
37681	2510	12	that	that	IN
37681	2510	13	in	in	IN
37681	2510	14	planning	plan	VBG
37681	2510	15	a	a	DT
37681	2510	16	Gothic	gothic	JJ
37681	2510	17	window	window	NN
37681	2510	18	this	this	DT
37681	2510	19	drawing	drawing	NN
37681	2510	20	is	be	VBZ
37681	2510	21	needed	need	VBN
37681	2510	22	.	.	.
37681	2511	1	The	the	DT
37681	2511	2	arc	arc	NN
37681	2511	3	_	_	NNP
37681	2511	4	BC	BC	NNP
37681	2511	5	_	_	NNP
37681	2511	6	is	be	VBZ
37681	2511	7	drawn	draw	VBN
37681	2511	8	with	with	IN
37681	2511	9	_	_	NNP
37681	2511	10	A	A	NNP
37681	2511	11	_	_	NNP
37681	2511	12	as	as	IN
37681	2511	13	a	a	DT
37681	2511	14	center	center	NN
37681	2511	15	and	and	CC
37681	2511	16	_	_	NNP
37681	2511	17	AB	AB	NNP
37681	2511	18	_	_	NNP
37681	2511	19	as	as	IN
37681	2511	20	a	a	DT
37681	2511	21	radius	radius	NN
37681	2511	22	.	.	.
37681	2512	1	The	the	DT
37681	2512	2	small	small	JJ
37681	2512	3	arches	arch	NNS
37681	2512	4	are	be	VBP
37681	2512	5	described	describe	VBN
37681	2512	6	with	with	IN
37681	2512	7	_	_	NNP
37681	2512	8	A	A	NNP
37681	2512	9	_	_	NNP
37681	2512	10	,	,	,
37681	2512	11	_	_	NNP
37681	2512	12	D	D	NNP
37681	2512	13	_	_	NNP
37681	2512	14	,	,	,
37681	2512	15	and	and	CC
37681	2512	16	_	_	NNP
37681	2512	17	B	B	NNP
37681	2512	18	_	_	NNP
37681	2512	19	as	as	IN
37681	2512	20	centers	center	NNS
37681	2512	21	and	and	CC
37681	2512	22	_	_	NNP
37681	2512	23	AD	AD	NNP
37681	2512	24	_	_	NNP
37681	2512	25	as	as	IN
37681	2512	26	a	a	DT
37681	2512	27	radius	radius	NN
37681	2512	28	.	.	.
37681	2513	1	The	the	DT
37681	2513	2	center	center	NN
37681	2513	3	_	_	NNP
37681	2513	4	P	P	NNP
37681	2513	5	_	_	NNP
37681	2513	6	is	be	VBZ
37681	2513	7	found	find	VBN
37681	2513	8	by	by	IN
37681	2513	9	taking	take	VBG
37681	2513	10	_	_	NNP
37681	2513	11	A	A	NNP
37681	2513	12	_	_	NNP
37681	2513	13	and	and	CC
37681	2513	14	_	_	NNP
37681	2513	15	B	B	NNP
37681	2513	16	_	_	NNP
37681	2513	17	as	as	IN
37681	2513	18	centers	center	NNS
37681	2513	19	and	and	CC
37681	2513	20	_	_	NNP
37681	2513	21	AE	AE	NNP
37681	2513	22	_	_	NNP
37681	2513	23	as	as	IN
37681	2513	24	a	a	DT
37681	2513	25	radius	radius	NN
37681	2513	26	.	.	.
37681	2514	1	How	how	WRB
37681	2514	2	may	may	MD
37681	2514	3	the	the	DT
37681	2514	4	points	point	NNS
37681	2514	5	_	_	NNP
37681	2514	6	D	D	NNP
37681	2514	7	_	_	NNP
37681	2514	8	,	,	,
37681	2514	9	_	_	NNP
37681	2514	10	E	E	NNP
37681	2514	11	_	_	NNP
37681	2514	12	,	,	,
37681	2514	13	and	and	CC
37681	2514	14	_	_	NNP
37681	2514	15	F	F	NNP
37681	2514	16	_	_	NNP
37681	2514	17	be	be	VB
37681	2514	18	found	find	VBN
37681	2514	19	?	?	.
37681	2515	1	Draw	draw	VB
37681	2515	2	the	the	DT
37681	2515	3	figure	figure	NN
37681	2515	4	.	.	.
37681	2516	1	From	from	IN
37681	2516	2	the	the	DT
37681	2516	3	study	study	NN
37681	2516	4	of	of	IN
37681	2516	5	the	the	DT
37681	2516	6	rectilinear	rectilinear	JJ
37681	2516	7	figures	figure	NNS
37681	2516	8	suggested	suggest	VBN
37681	2516	9	by	by	IN
37681	2516	10	such	such	PDT
37681	2516	11	a	a	DT
37681	2516	12	simple	simple	JJ
37681	2516	13	pattern	pattern	NN
37681	2516	14	the	the	DT
37681	2516	15	properties	property	NNS
37681	2516	16	of	of	IN
37681	2516	17	the	the	DT
37681	2516	18	equilateral	equilateral	JJ
37681	2516	19	triangle	triangle	NN
37681	2516	20	may	may	MD
37681	2516	21	be	be	VB
37681	2516	22	inferred	infer	VBN
37681	2516	23	.	.	.
37681	2517	1	The	the	DT
37681	2517	2	Gothic	gothic	JJ
37681	2517	3	window	window	NN
37681	2517	4	also	also	RB
37681	2517	5	offers	offer	VBZ
37681	2517	6	some	some	DT
37681	2517	7	interesting	interesting	JJ
37681	2517	8	possibilities	possibility	NNS
37681	2517	9	in	in	IN
37681	2517	10	connection	connection	NN
37681	2517	11	with	with	IN
37681	2517	12	the	the	DT
37681	2517	13	study	study	NN
37681	2517	14	of	of	IN
37681	2517	15	the	the	DT
37681	2517	16	square	square	NN
37681	2517	17	.	.	.
37681	2518	1	For	for	IN
37681	2518	2	example	example	NN
37681	2518	3	,	,	,
37681	2518	4	the	the	DT
37681	2518	5	illustration	illustration	NN
37681	2518	6	given	give	VBN
37681	2518	7	on	on	IN
37681	2518	8	page	page	NN
37681	2518	9	223	223	CD
37681	2518	10	shows	show	NNS
37681	2518	11	a	a	DT
37681	2518	12	number	number	NN
37681	2518	13	of	of	IN
37681	2518	14	traceries	tracery	NNS
37681	2518	15	involving	involve	VBG
37681	2518	16	the	the	DT
37681	2518	17	construction	construction	NN
37681	2518	18	of	of	IN
37681	2518	19	a	a	DT
37681	2518	20	square	square	NN
37681	2518	21	,	,	,
37681	2518	22	the	the	DT
37681	2518	23	bisecting	bisecting	NN
37681	2518	24	of	of	IN
37681	2518	25	angles	angle	NNS
37681	2518	26	,	,	,
37681	2518	27	and	and	CC
37681	2518	28	the	the	DT
37681	2518	29	describing	describing	NN
37681	2518	30	of	of	IN
37681	2518	31	circles	circle	NNS
37681	2518	32	.	.	.
37681	2519	1	[	[	-LRB-
37681	2519	2	72	72	CD
37681	2519	3	]	]	-RRB-
37681	2519	4	[	[	-LRB-
37681	2519	5	Illustration	illustration	NN
37681	2519	6	]	]	-RRB-
37681	2519	7	The	the	DT
37681	2519	8	properties	property	NNS
37681	2519	9	of	of	IN
37681	2519	10	the	the	DT
37681	2519	11	square	square	NN
37681	2519	12	,	,	,
37681	2519	13	a	a	DT
37681	2519	14	figure	figure	NN
37681	2519	15	now	now	RB
37681	2519	16	easily	easily	RB
37681	2519	17	constructed	construct	VBN
37681	2519	18	by	by	IN
37681	2519	19	the	the	DT
37681	2519	20	pupils	pupil	NNS
37681	2519	21	,	,	,
37681	2519	22	are	be	VBP
37681	2519	23	not	not	RB
37681	2519	24	numerous	numerous	JJ
37681	2519	25	.	.	.
37681	2520	1	What	what	WP
37681	2520	2	few	few	JJ
37681	2520	3	there	there	EX
37681	2520	4	are	be	VBP
37681	2520	5	may	may	MD
37681	2520	6	be	be	VB
37681	2520	7	brought	bring	VBN
37681	2520	8	out	out	RP
37681	2520	9	through	through	IN
37681	2520	10	the	the	DT
37681	2520	11	study	study	NN
37681	2520	12	of	of	IN
37681	2520	13	art	art	NN
37681	2520	14	forms	form	NNS
37681	2520	15	,	,	,
37681	2520	16	if	if	IN
37681	2520	17	desired	desire	VBN
37681	2520	18	.	.	.
37681	2521	1	In	in	IN
37681	2521	2	case	case	NN
37681	2521	3	these	these	DT
37681	2521	4	forms	form	NNS
37681	2521	5	are	be	VBP
37681	2521	6	shown	show	VBN
37681	2521	7	to	to	IN
37681	2521	8	a	a	DT
37681	2521	9	class	class	NN
37681	2521	10	,	,	,
37681	2521	11	it	-PRON-	PRP
37681	2521	12	is	be	VBZ
37681	2521	13	important	important	JJ
37681	2521	14	that	that	IN
37681	2521	15	they	-PRON-	PRP
37681	2521	16	should	should	MD
37681	2521	17	be	be	VB
37681	2521	18	selected	select	VBN
37681	2521	19	from	from	IN
37681	2521	20	good	good	JJ
37681	2521	21	designs	design	NNS
37681	2521	22	.	.	.
37681	2522	1	We	-PRON-	PRP
37681	2522	2	have	have	VBP
37681	2522	3	enough	enough	JJ
37681	2522	4	poor	poor	JJ
37681	2522	5	art	art	NN
37681	2522	6	in	in	IN
37681	2522	7	the	the	DT
37681	2522	8	world	world	NN
37681	2522	9	,	,	,
37681	2522	10	so	so	IN
37681	2522	11	that	that	IN
37681	2522	12	geometry	geometry	NN
37681	2522	13	should	should	MD
37681	2522	14	not	not	RB
37681	2522	15	contribute	contribute	VB
37681	2522	16	any	any	DT
37681	2522	17	more	more	JJR
37681	2522	18	.	.	.
37681	2523	1	This	this	DT
37681	2523	2	illustration	illustration	NN
37681	2523	3	is	be	VBZ
37681	2523	4	a	a	DT
37681	2523	5	type	type	NN
37681	2523	6	of	of	IN
37681	2523	7	the	the	DT
37681	2523	8	best	good	JJS
37681	2523	9	medieval	medieval	JJ
37681	2523	10	Gothic	gothic	JJ
37681	2523	11	parquetry	parquetry	NN
37681	2523	12	.	.	.
37681	2524	1	[	[	-LRB-
37681	2524	2	73	73	CD
37681	2524	3	]	]	-RRB-
37681	2524	4	[	[	-LRB-
37681	2524	5	Illustration	illustration	NN
37681	2524	6	:	:	:
37681	2524	7	GOTHIC	gothic	NN
37681	2524	8	DESIGNS	designs	NN
37681	2524	9	EMPLOYING	employing	NN
37681	2524	10	CIRCLES	circle	NNS
37681	2524	11	AND	and	CC
37681	2524	12	BISECTED	BISECTED	NNP
37681	2524	13	ANGLES	angle	NNS
37681	2524	14	]	]	-RRB-
37681	2524	15	Even	even	RB
37681	2524	16	simple	simple	JJ
37681	2524	17	designs	design	NNS
37681	2524	18	of	of	IN
37681	2524	19	a	a	DT
37681	2524	20	semipuzzling	semipuzzle	VBG
37681	2524	21	nature	nature	NN
37681	2524	22	have	have	VBP
37681	2524	23	their	-PRON-	PRP$
37681	2524	24	advantage	advantage	NN
37681	2524	25	in	in	IN
37681	2524	26	this	this	DT
37681	2524	27	connection	connection	NN
37681	2524	28	.	.	.
37681	2525	1	In	in	IN
37681	2525	2	the	the	DT
37681	2525	3	following	follow	VBG
37681	2525	4	example	example	NN
37681	2525	5	the	the	DT
37681	2525	6	inner	inner	JJ
37681	2525	7	square	square	NN
37681	2525	8	contains	contain	VBZ
37681	2525	9	all	all	DT
37681	2525	10	of	of	IN
37681	2525	11	the	the	DT
37681	2525	12	triangles	triangle	NNS
37681	2525	13	,	,	,
37681	2525	14	the	the	DT
37681	2525	15	letters	letter	NNS
37681	2525	16	showing	show	VBG
37681	2525	17	where	where	WRB
37681	2525	18	they	-PRON-	PRP
37681	2525	19	may	may	MD
37681	2525	20	be	be	VB
37681	2525	21	fitted	fit	VBN
37681	2525	22	.	.	.
37681	2526	1	[	[	-LRB-
37681	2526	2	74	74	CD
37681	2526	3	]	]	-RRB-
37681	2526	4	Still	still	RB
37681	2526	5	more	more	RBR
37681	2526	6	elaborate	elaborate	JJ
37681	2526	7	designs	design	NNS
37681	2526	8	,	,	,
37681	2526	9	based	base	VBN
37681	2526	10	chiefly	chiefly	RB
37681	2526	11	upon	upon	IN
37681	2526	12	the	the	DT
37681	2526	13	square	square	JJ
37681	2526	14	and	and	CC
37681	2526	15	circle	circle	NN
37681	2526	16	,	,	,
37681	2526	17	are	be	VBP
37681	2526	18	shown	show	VBN
37681	2526	19	in	in	IN
37681	2526	20	the	the	DT
37681	2526	21	window	window	NN
37681	2526	22	traceries	tracery	NNS
37681	2526	23	on	on	IN
37681	2526	24	page	page	NN
37681	2526	25	225	225	CD
37681	2526	26	,	,	,
37681	2526	27	and	and	CC
37681	2526	28	others	other	NNS
37681	2526	29	will	will	MD
37681	2526	30	be	be	VB
37681	2526	31	given	give	VBN
37681	2526	32	in	in	IN
37681	2526	33	connection	connection	NN
37681	2526	34	with	with	IN
37681	2526	35	the	the	DT
37681	2526	36	study	study	NN
37681	2526	37	of	of	IN
37681	2526	38	the	the	DT
37681	2526	39	regular	regular	JJ
37681	2526	40	polygons	polygon	NNS
37681	2526	41	.	.	.
37681	2527	1	[	[	-LRB-
37681	2527	2	Illustration	illustration	NN
37681	2527	3	]	]	-RRB-
37681	2527	4	Designs	design	NNS
37681	2527	5	like	like	IN
37681	2527	6	the	the	DT
37681	2527	7	figure	figure	NN
37681	2527	8	below	below	RB
37681	2527	9	are	be	VBP
37681	2527	10	typical	typical	JJ
37681	2527	11	of	of	IN
37681	2527	12	the	the	DT
37681	2527	13	simple	simple	JJ
37681	2527	14	forms	form	NNS
37681	2527	15	,	,	,
37681	2527	16	based	base	VBN
37681	2527	17	on	on	IN
37681	2527	18	the	the	DT
37681	2527	19	square	square	NN
37681	2527	20	and	and	CC
37681	2527	21	circle	circle	NN
37681	2527	22	,	,	,
37681	2527	23	that	that	IN
37681	2527	24	pupils	pupil	NNS
37681	2527	25	may	may	MD
37681	2527	26	profitably	profitably	RB
37681	2527	27	incorporate	incorporate	VB
37681	2527	28	in	in	IN
37681	2527	29	any	any	DT
37681	2527	30	work	work	NN
37681	2527	31	in	in	IN
37681	2527	32	art	art	NN
37681	2527	33	design	design	NN
37681	2527	34	that	that	IN
37681	2527	35	they	-PRON-	PRP
37681	2527	36	may	may	MD
37681	2527	37	be	be	VB
37681	2527	38	doing	do	VBG
37681	2527	39	at	at	IN
37681	2527	40	the	the	DT
37681	2527	41	time	time	NN
37681	2527	42	they	-PRON-	PRP
37681	2527	43	are	be	VBP
37681	2527	44	studying	study	VBG
37681	2527	45	the	the	DT
37681	2527	46	circle	circle	NN
37681	2527	47	and	and	CC
37681	2527	48	the	the	DT
37681	2527	49	problems	problem	NNS
37681	2527	50	relating	relate	VBG
37681	2527	51	to	to	IN
37681	2527	52	perpendiculars	perpendicular	NNS
37681	2527	53	and	and	CC
37681	2527	54	squares	square	NNS
37681	2527	55	.	.	.
37681	2528	1	[	[	-LRB-
37681	2528	2	Illustration	illustration	NN
37681	2528	3	]	]	-RRB-
37681	2528	4	Among	among	IN
37681	2528	5	the	the	DT
37681	2528	6	applications	application	NNS
37681	2528	7	of	of	IN
37681	2528	8	the	the	DT
37681	2528	9	problem	problem	NN
37681	2528	10	to	to	TO
37681	2528	11	draw	draw	VB
37681	2528	12	a	a	DT
37681	2528	13	tangent	tangent	NN
37681	2528	14	to	to	IN
37681	2528	15	a	a	DT
37681	2528	16	given	give	VBN
37681	2528	17	circle	circle	NN
37681	2528	18	is	be	VBZ
37681	2528	19	the	the	DT
37681	2528	20	case	case	NN
37681	2528	21	of	of	IN
37681	2528	22	the	the	DT
37681	2528	23	common	common	JJ
37681	2528	24	tangents	tangent	NNS
37681	2528	25	to	to	IN
37681	2528	26	two	two	CD
37681	2528	27	given	give	VBN
37681	2528	28	circles	circle	NNS
37681	2528	29	.	.	.
37681	2529	1	Some	some	DT
37681	2529	2	authors	author	NNS
37681	2529	3	give	give	VBP
37681	2529	4	this	this	DT
37681	2529	5	as	as	IN
37681	2529	6	a	a	DT
37681	2529	7	basal	basal	NN
37681	2529	8	problem	problem	NN
37681	2529	9	,	,	,
37681	2529	10	although	although	IN
37681	2529	11	it	-PRON-	PRP
37681	2529	12	is	be	VBZ
37681	2529	13	more	more	RBR
37681	2529	14	commonly	commonly	RB
37681	2529	15	given	give	VBN
37681	2529	16	as	as	IN
37681	2529	17	an	an	DT
37681	2529	18	exercise	exercise	NN
37681	2529	19	or	or	CC
37681	2529	20	a	a	DT
37681	2529	21	corollary	corollary	NN
37681	2529	22	.	.	.
37681	2530	1	One	one	CD
37681	2530	2	of	of	IN
37681	2530	3	the	the	DT
37681	2530	4	most	most	RBS
37681	2530	5	obvious	obvious	JJ
37681	2530	6	applications	application	NNS
37681	2530	7	of	of	IN
37681	2530	8	the	the	DT
37681	2530	9	idea	idea	NN
37681	2530	10	is	be	VBZ
37681	2530	11	that	that	IN
37681	2530	12	relating	relate	VBG
37681	2530	13	to	to	IN
37681	2530	14	the	the	DT
37681	2530	15	transmission	transmission	NN
37681	2530	16	of	of	IN
37681	2530	17	circular	circular	JJ
37681	2530	18	motion	motion	NN
37681	2530	19	by	by	IN
37681	2530	20	means	mean	NNS
37681	2530	21	of	of	IN
37681	2530	22	a	a	DT
37681	2530	23	band	band	NN
37681	2530	24	over	over	IN
37681	2530	25	two	two	CD
37681	2530	26	wheels,[75	wheels,[75	CD
37681	2530	27	]	]	-RRB-
37681	2530	28	_	_	NNP
37681	2530	29	A	A	NNP
37681	2530	30	_	_	NNP
37681	2530	31	and	and	CC
37681	2530	32	_	_	NNP
37681	2530	33	B	B	NNP
37681	2530	34	_	_	NNP
37681	2530	35	,	,	,
37681	2530	36	as	as	IN
37681	2530	37	shown	show	VBN
37681	2530	38	on	on	IN
37681	2530	39	page	page	NN
37681	2530	40	226	226	CD
37681	2530	41	.	.	.
37681	2531	1	[	[	-LRB-
37681	2531	2	Illustration	illustration	NN
37681	2531	3	:	:	:
37681	2531	4	GOTHIC	gothic	NN
37681	2531	5	DESIGNS	designs	NN
37681	2531	6	EMPLOYING	employing	NN
37681	2531	7	CIRCLES	circle	NNS
37681	2531	8	AND	and	CC
37681	2531	9	BISECTED	BISECTED	NNP
37681	2531	10	ANGLES	angle	VBN
37681	2531	11	]	]	-RRB-
37681	2531	12	The	the	DT
37681	2531	13	band	band	NN
37681	2531	14	may	may	MD
37681	2531	15	either	either	CC
37681	2531	16	not	not	RB
37681	2531	17	be	be	VB
37681	2531	18	crossed	cross	VBN
37681	2531	19	(	(	-LRB-
37681	2531	20	the	the	DT
37681	2531	21	case	case	NN
37681	2531	22	of	of	IN
37681	2531	23	the	the	DT
37681	2531	24	two	two	CD
37681	2531	25	exterior	exterior	NNP
37681	2531	26	tangents	tangent	NNS
37681	2531	27	)	)	-RRB-
37681	2531	28	,	,	,
37681	2531	29	or	or	CC
37681	2531	30	be	be	VB
37681	2531	31	crossed	cross	VBN
37681	2531	32	(	(	-LRB-
37681	2531	33	the	the	DT
37681	2531	34	interior	interior	JJ
37681	2531	35	tangents	tangent	NNS
37681	2531	36	)	)	-RRB-
37681	2531	37	,	,	,
37681	2531	38	the	the	DT
37681	2531	39	latter	latter	JJ
37681	2531	40	allowing	allow	VBG
37681	2531	41	the	the	DT
37681	2531	42	wheels	wheel	NNS
37681	2531	43	to	to	TO
37681	2531	44	turn	turn	VB
37681	2531	45	in	in	RP
37681	2531	46	opposite	opposite	JJ
37681	2531	47	directions	direction	NNS
37681	2531	48	.	.	.
37681	2532	1	In	in	IN
37681	2532	2	case	case	NN
37681	2532	3	the	the	DT
37681	2532	4	band	band	NN
37681	2532	5	is	be	VBZ
37681	2532	6	liable	liable	JJ
37681	2532	7	to	to	TO
37681	2532	8	change	change	VB
37681	2532	9	its	-PRON-	PRP$
37681	2532	10	length	length	NN
37681	2532	11	,	,	,
37681	2532	12	on	on	IN
37681	2532	13	account	account	NN
37681	2532	14	of	of	IN
37681	2532	15	stretching	stretching	NN
37681	2532	16	or	or	CC
37681	2532	17	variation	variation	NN
37681	2532	18	in	in	IN
37681	2532	19	heat	heat	NN
37681	2532	20	or	or	CC
37681	2532	21	moisture	moisture	NN
37681	2532	22	,	,	,
37681	2532	23	a	a	DT
37681	2532	24	third	third	JJ
37681	2532	25	wheel	wheel	NN
37681	2532	26	,	,	,
37681	2532	27	_	_	NNP
37681	2532	28	D	D	NNP
37681	2532	29	_	_	NNP
37681	2532	30	,	,	,
37681	2532	31	is	be	VBZ
37681	2532	32	used	use	VBN
37681	2532	33	.	.	.
37681	2533	1	We	-PRON-	PRP
37681	2533	2	then	then	RB
37681	2533	3	have	have	VBP
37681	2533	4	the	the	DT
37681	2533	5	case	case	NN
37681	2533	6	of	of	IN
37681	2533	7	tangents	tangent	NNS
37681	2533	8	to	to	IN
37681	2533	9	three	three	CD
37681	2533	10	pairs	pair	NNS
37681	2533	11	of	of	IN
37681	2533	12	circles	circle	NNS
37681	2533	13	.	.	.
37681	2534	1	Illustrations	illustration	NNS
37681	2534	2	of	of	IN
37681	2534	3	this	this	DT
37681	2534	4	nature	nature	NN
37681	2534	5	make	make	VBP
37681	2534	6	the	the	DT
37681	2534	7	exercise	exercise	NN
37681	2534	8	on	on	IN
37681	2534	9	the	the	DT
37681	2534	10	drawing	drawing	NN
37681	2534	11	of	of	IN
37681	2534	12	common	common	JJ
37681	2534	13	tangents	tangent	NNS
37681	2534	14	to	to	IN
37681	2534	15	two	two	CD
37681	2534	16	circles	circle	NNS
37681	2534	17	assume	assume	VBP
37681	2534	18	an	an	DT
37681	2534	19	appearance	appearance	NN
37681	2534	20	of	of	IN
37681	2534	21	genuine	genuine	JJ
37681	2534	22	reality	reality	NN
37681	2534	23	that	that	WDT
37681	2534	24	is	be	VBZ
37681	2534	25	of	of	IN
37681	2534	26	advantage	advantage	NN
37681	2534	27	to	to	IN
37681	2534	28	the	the	DT
37681	2534	29	work	work	NN
37681	2534	30	.	.	.
37681	2535	1	[	[	-LRB-
37681	2535	2	Illustration	illustration	NN
37681	2535	3	]	]	-RRB-
37681	2535	4	FOOTNOTES	FOOTNOTES	NNP
37681	2535	5	:	:	:
37681	2535	6	[	[	-LRB-
37681	2535	7	68	68	CD
37681	2535	8	]	]	-RRB-
37681	2535	9	This	this	DT
37681	2535	10	is	be	VBZ
37681	2535	11	the	the	DT
37681	2535	12	latest	late	JJS
37681	2535	13	opinion	opinion	NN
37681	2535	14	.	.	.
37681	2536	1	He	-PRON-	PRP
37681	2536	2	is	be	VBZ
37681	2536	3	usually	usually	RB
37681	2536	4	assigned	assign	VBN
37681	2536	5	to	to	IN
37681	2536	6	the	the	DT
37681	2536	7	first	first	JJ
37681	2536	8	century	century	NN
37681	2536	9	B.C.	B.C.	NNP
37681	2537	1	[	[	-LRB-
37681	2537	2	69	69	CD
37681	2537	3	]	]	-RRB-
37681	2537	4	See	see	VB
37681	2537	5	page	page	NN
37681	2537	6	54	54	CD
37681	2537	7	.	.	.
37681	2538	1	[	[	-LRB-
37681	2538	2	70	70	CD
37681	2538	3	]	]	-RRB-
37681	2538	4	A	a	DT
37681	2538	5	Greek	greek	JJ
37681	2538	6	philosopher	philosopher	NN
37681	2538	7	and	and	CC
37681	2538	8	mathematician	mathematician	NN
37681	2538	9	of	of	IN
37681	2538	10	the	the	DT
37681	2538	11	fifth	fifth	JJ
37681	2538	12	century	century	NN
37681	2538	13	B.C.	B.C.	NNP
37681	2539	1	[	[	-LRB-
37681	2539	2	71	71	CD
37681	2539	3	]	]	-RRB-
37681	2539	4	This	this	DT
37681	2539	5	illustration	illustration	NN
37681	2539	6	and	and	CC
37681	2539	7	the	the	DT
37681	2539	8	following	follow	VBG
37681	2539	9	two	two	CD
37681	2539	10	are	be	VBP
37681	2539	11	from	from	IN
37681	2539	12	C.	C.	NNP
37681	2539	13	Dupin	Dupin	NNP
37681	2539	14	,	,	,
37681	2539	15	"	"	``
37681	2539	16	Mathematics	Mathematics	NNP
37681	2539	17	Practically	practically	RB
37681	2539	18	Applied	apply	VBN
37681	2539	19	,	,	,
37681	2539	20	"	"	''
37681	2539	21	translated	translate	VBN
37681	2539	22	from	from	IN
37681	2539	23	the	the	DT
37681	2539	24	French	French	NNP
37681	2539	25	by	by	IN
37681	2539	26	G.	G.	NNP
37681	2539	27	Birkbeck	Birkbeck	NNP
37681	2539	28	,	,	,
37681	2539	29	Halifax	Halifax	NNP
37681	2539	30	,	,	,
37681	2539	31	1854	1854	CD
37681	2539	32	.	.	.
37681	2540	1	This	this	DT
37681	2540	2	is	be	VBZ
37681	2540	3	probably	probably	RB
37681	2540	4	the	the	DT
37681	2540	5	most	most	RBS
37681	2540	6	scholarly	scholarly	JJ
37681	2540	7	attempt	attempt	NN
37681	2540	8	ever	ever	RB
37681	2540	9	made	make	VBN
37681	2540	10	at	at	IN
37681	2540	11	constructing	construct	VBG
37681	2540	12	a	a	DT
37681	2540	13	"	"	``
37681	2540	14	practical	practical	JJ
37681	2540	15	geometry	geometry	NN
37681	2540	16	.	.	.
37681	2540	17	"	"	''
37681	2541	1	[	[	-LRB-
37681	2541	2	72	72	CD
37681	2541	3	]	]	-RRB-
37681	2541	4	This	this	DT
37681	2541	5	illustration	illustration	NN
37681	2541	6	and	and	CC
37681	2541	7	others	other	NNS
37681	2541	8	of	of	IN
37681	2541	9	the	the	DT
37681	2541	10	same	same	JJ
37681	2541	11	type	type	NN
37681	2541	12	used	use	VBN
37681	2541	13	in	in	IN
37681	2541	14	this	this	DT
37681	2541	15	work	work	NN
37681	2541	16	are	be	VBP
37681	2541	17	from	from	IN
37681	2541	18	the	the	DT
37681	2541	19	excellent	excellent	JJ
37681	2541	20	drawings	drawing	NNS
37681	2541	21	by	by	IN
37681	2541	22	R.	R.	NNP
37681	2541	23	W.	W.	NNP
37681	2541	24	Billings	Billings	NNP
37681	2541	25	,	,	,
37681	2541	26	in	in	IN
37681	2541	27	"	"	``
37681	2541	28	The	the	DT
37681	2541	29	Infinity	Infinity	NNP
37681	2541	30	of	of	IN
37681	2541	31	Geometric	Geometric	NNP
37681	2541	32	Design	Design	NNP
37681	2541	33	Exemplified	Exemplified	NNP
37681	2541	34	,	,	,
37681	2541	35	"	"	''
37681	2541	36	London	London	NNP
37681	2541	37	,	,	,
37681	2541	38	1849	1849	CD
37681	2541	39	.	.	.
37681	2542	1	[	[	-LRB-
37681	2542	2	73	73	CD
37681	2542	3	]	]	-RRB-
37681	2542	4	From	from	IN
37681	2542	5	H.	H.	NNP
37681	2542	6	Kolb	Kolb	NNP
37681	2542	7	,	,	,
37681	2542	8	"	"	``
37681	2542	9	Der	Der	NNP
37681	2542	10	Ornamentenschatz	Ornamentenschatz	NNP
37681	2542	11	...	...	:
37681	2542	12	aus	aus	NNP
37681	2542	13	allen	allen	NNP
37681	2542	14	Kunst	Kunst	NNP
37681	2542	15	-	-	HYPH
37681	2542	16	Epochen	Epochen	NNP
37681	2542	17	,	,	,
37681	2542	18	"	"	``
37681	2542	19	Stuttgart	Stuttgart	NNP
37681	2542	20	,	,	,
37681	2542	21	1883	1883	CD
37681	2542	22	.	.	.
37681	2543	1	The	the	DT
37681	2543	2	original	original	NN
37681	2543	3	is	be	VBZ
37681	2543	4	in	in	IN
37681	2543	5	the	the	DT
37681	2543	6	Church	Church	NNP
37681	2543	7	of	of	IN
37681	2543	8	Saint	Saint	NNP
37681	2543	9	Anastasia	Anastasia	NNP
37681	2543	10	in	in	IN
37681	2543	11	Verona	Verona	NNP
37681	2543	12	.	.	.
37681	2544	1	[	[	-LRB-
37681	2544	2	74	74	CD
37681	2544	3	]	]	-RRB-
37681	2544	4	From	from	IN
37681	2544	5	J.	J.	NNP
37681	2544	6	Bennett	Bennett	NNP
37681	2544	7	,	,	,
37681	2544	8	"	"	``
37681	2544	9	The	the	DT
37681	2544	10	Arcanum	Arcanum	NNP
37681	2544	11	...	...	:
37681	2544	12	A	a	DT
37681	2544	13	Concise	Concise	NNP
37681	2544	14	Theory	Theory	NNP
37681	2544	15	of	of	IN
37681	2544	16	Practicable	Practicable	NNP
37681	2544	17	Geometry	Geometry	NNP
37681	2544	18	,	,	,
37681	2544	19	"	"	''
37681	2544	20	London	London	NNP
37681	2544	21	,	,	,
37681	2544	22	1838	1838	CD
37681	2544	23	,	,	,
37681	2544	24	one	one	CD
37681	2544	25	of	of	IN
37681	2544	26	the	the	DT
37681	2544	27	many	many	JJ
37681	2544	28	books	book	NNS
37681	2544	29	that	that	WDT
37681	2544	30	have	have	VBP
37681	2544	31	assumed	assume	VBN
37681	2544	32	to	to	TO
37681	2544	33	revolutionize	revolutionize	VB
37681	2544	34	geometry	geometry	NN
37681	2544	35	by	by	IN
37681	2544	36	making	make	VBG
37681	2544	37	it	-PRON-	PRP
37681	2544	38	practical	practical	JJ
37681	2544	39	.	.	.
37681	2545	1	[	[	-LRB-
37681	2545	2	75	75	CD
37681	2545	3	]	]	-RRB-
37681	2545	4	The	the	DT
37681	2545	5	figures	figure	NNS
37681	2545	6	are	be	VBP
37681	2545	7	from	from	IN
37681	2545	8	Dupin	Dupin	NNP
37681	2545	9	,	,	,
37681	2545	10	loc	loc	NNP
37681	2545	11	.	.	.
37681	2546	1	cit	cit	NNP
37681	2546	2	.	.	.
37681	2547	1	CHAPTER	chapter	NN
37681	2547	2	XVI	XVI	NNP
37681	2547	3	THE	the	DT
37681	2547	4	LEADING	lead	VBG
37681	2547	5	PROPOSITIONS	proposition	NNS
37681	2547	6	OF	of	IN
37681	2547	7	BOOK	book	NN
37681	2547	8	III	iii	CD
37681	2547	9	In	in	IN
37681	2547	10	the	the	DT
37681	2547	11	American	american	JJ
37681	2547	12	textbooks	textbook	NNS
37681	2547	13	Book	Book	NNP
37681	2547	14	III	III	NNP
37681	2547	15	is	be	VBZ
37681	2547	16	usually	usually	RB
37681	2547	17	assigned	assign	VBN
37681	2547	18	to	to	IN
37681	2547	19	proportion	proportion	NN
37681	2547	20	.	.	.
37681	2548	1	It	-PRON-	PRP
37681	2548	2	is	be	VBZ
37681	2548	3	therefore	therefore	RB
37681	2548	4	necessary	necessary	JJ
37681	2548	5	at	at	IN
37681	2548	6	the	the	DT
37681	2548	7	beginning	beginning	NN
37681	2548	8	of	of	IN
37681	2548	9	this	this	DT
37681	2548	10	discussion	discussion	NN
37681	2548	11	to	to	TO
37681	2548	12	consider	consider	VB
37681	2548	13	what	what	WP
37681	2548	14	is	be	VBZ
37681	2548	15	meant	mean	VBN
37681	2548	16	by	by	IN
37681	2548	17	ratio	ratio	NN
37681	2548	18	and	and	CC
37681	2548	19	proportion	proportion	NN
37681	2548	20	,	,	,
37681	2548	21	and	and	CC
37681	2548	22	to	to	TO
37681	2548	23	compare	compare	VB
37681	2548	24	the	the	DT
37681	2548	25	ancient	ancient	NN
37681	2548	26	and	and	CC
37681	2548	27	the	the	DT
37681	2548	28	modern	modern	JJ
37681	2548	29	theories	theory	NNS
37681	2548	30	.	.	.
37681	2549	1	The	the	DT
37681	2549	2	subject	subject	NN
37681	2549	3	is	be	VBZ
37681	2549	4	treated	treat	VBN
37681	2549	5	by	by	IN
37681	2549	6	Euclid	Euclid	NNP
37681	2549	7	in	in	IN
37681	2549	8	his	-PRON-	PRP$
37681	2549	9	Book	Book	NNP
37681	2549	10	V	v	NN
37681	2549	11	,	,	,
37681	2549	12	and	and	CC
37681	2549	13	an	an	DT
37681	2549	14	anonymous	anonymous	JJ
37681	2549	15	commentator	commentator	NN
37681	2549	16	has	have	VBZ
37681	2549	17	told	tell	VBN
37681	2549	18	us	-PRON-	PRP
37681	2549	19	that	that	IN
37681	2549	20	it	-PRON-	PRP
37681	2549	21	"	"	``
37681	2549	22	is	be	VBZ
37681	2549	23	the	the	DT
37681	2549	24	discovery	discovery	NN
37681	2549	25	of	of	IN
37681	2549	26	Eudoxus	Eudoxus	NNP
37681	2549	27	,	,	,
37681	2549	28	the	the	DT
37681	2549	29	teacher	teacher	NN
37681	2549	30	of	of	IN
37681	2549	31	Plato	Plato	NNP
37681	2549	32	.	.	.
37681	2549	33	"	"	''
37681	2550	1	Now	now	RB
37681	2550	2	proportion	proportion	NN
37681	2550	3	had	have	VBD
37681	2550	4	been	be	VBN
37681	2550	5	known	know	VBN
37681	2550	6	long	long	RB
37681	2550	7	before	before	IN
37681	2550	8	the	the	DT
37681	2550	9	time	time	NN
37681	2550	10	of	of	IN
37681	2550	11	Eudoxus	Eudoxus	NNP
37681	2550	12	(	(	-LRB-
37681	2550	13	408	408	CD
37681	2550	14	-	-	SYM
37681	2550	15	355	355	CD
37681	2550	16	B.C.	B.C.	NNP
37681	2551	1	)	)	-RRB-
37681	2551	2	,	,	,
37681	2551	3	but	but	CC
37681	2551	4	it	-PRON-	PRP
37681	2551	5	was	be	VBD
37681	2551	6	numerical	numerical	JJ
37681	2551	7	proportion	proportion	NN
37681	2551	8	,	,	,
37681	2551	9	and	and	CC
37681	2551	10	as	as	RB
37681	2551	11	such	such	JJ
37681	2551	12	it	-PRON-	PRP
37681	2551	13	had	have	VBD
37681	2551	14	been	be	VBN
37681	2551	15	studied	study	VBN
37681	2551	16	by	by	IN
37681	2551	17	the	the	DT
37681	2551	18	Pythagoreans	Pythagoreans	NNPS
37681	2551	19	.	.	.
37681	2552	1	They	-PRON-	PRP
37681	2552	2	were	be	VBD
37681	2552	3	also	also	RB
37681	2552	4	the	the	DT
37681	2552	5	first	first	JJ
37681	2552	6	to	to	TO
37681	2552	7	study	study	VB
37681	2552	8	seriously	seriously	RB
37681	2552	9	the	the	DT
37681	2552	10	incommensurable	incommensurable	JJ
37681	2552	11	number	number	NN
37681	2552	12	,	,	,
37681	2552	13	and	and	CC
37681	2552	14	with	with	IN
37681	2552	15	this	this	DT
37681	2552	16	study	study	NN
37681	2552	17	the	the	DT
37681	2552	18	treatment	treatment	NN
37681	2552	19	of	of	IN
37681	2552	20	proportion	proportion	NN
37681	2552	21	from	from	IN
37681	2552	22	the	the	DT
37681	2552	23	standpoint	standpoint	NN
37681	2552	24	of	of	IN
37681	2552	25	rational	rational	JJ
37681	2552	26	numbers	number	NNS
37681	2552	27	lost	lose	VBD
37681	2552	28	its	-PRON-	PRP$
37681	2552	29	scientific	scientific	JJ
37681	2552	30	position	position	NN
37681	2552	31	with	with	IN
37681	2552	32	respect	respect	NN
37681	2552	33	to	to	IN
37681	2552	34	geometry	geometry	NN
37681	2552	35	.	.	.
37681	2553	1	It	-PRON-	PRP
37681	2553	2	was	be	VBD
37681	2553	3	because	because	IN
37681	2553	4	of	of	IN
37681	2553	5	this	this	DT
37681	2553	6	that	that	IN
37681	2553	7	Eudoxus	Eudoxus	NNP
37681	2553	8	worked	work	VBD
37681	2553	9	out	out	RP
37681	2553	10	a	a	DT
37681	2553	11	theory	theory	NN
37681	2553	12	of	of	IN
37681	2553	13	geometric	geometric	JJ
37681	2553	14	proportion	proportion	NN
37681	2553	15	that	that	WDT
37681	2553	16	was	be	VBD
37681	2553	17	independent	independent	JJ
37681	2553	18	of	of	IN
37681	2553	19	number	number	NN
37681	2553	20	as	as	IN
37681	2553	21	an	an	DT
37681	2553	22	expression	expression	NN
37681	2553	23	of	of	IN
37681	2553	24	ratio	ratio	NN
37681	2553	25	.	.	.
37681	2554	1	The	the	DT
37681	2554	2	following	follow	VBG
37681	2554	3	four	four	CD
37681	2554	4	definitions	definition	NNS
37681	2554	5	from	from	IN
37681	2554	6	Euclid	Euclid	NNP
37681	2554	7	are	be	VBP
37681	2554	8	the	the	DT
37681	2554	9	basal	basal	JJ
37681	2554	10	ones	one	NNS
37681	2554	11	of	of	IN
37681	2554	12	the	the	DT
37681	2554	13	ancient	ancient	JJ
37681	2554	14	theory	theory	NN
37681	2554	15	:	:	:
37681	2554	16	A	a	DT
37681	2554	17	ratio	ratio	NN
37681	2554	18	is	be	VBZ
37681	2554	19	a	a	DT
37681	2554	20	sort	sort	NN
37681	2554	21	of	of	IN
37681	2554	22	relation	relation	NN
37681	2554	23	in	in	IN
37681	2554	24	respect	respect	NN
37681	2554	25	of	of	IN
37681	2554	26	size	size	NN
37681	2554	27	between	between	IN
37681	2554	28	two	two	CD
37681	2554	29	magnitudes	magnitude	NNS
37681	2554	30	of	of	IN
37681	2554	31	the	the	DT
37681	2554	32	same	same	JJ
37681	2554	33	kind	kind	NN
37681	2554	34	.	.	.
37681	2555	1	Magnitudes	magnitude	NNS
37681	2555	2	are	be	VBP
37681	2555	3	said	say	VBN
37681	2555	4	to	to	TO
37681	2555	5	have	have	VB
37681	2555	6	a	a	DT
37681	2555	7	ratio	ratio	NN
37681	2555	8	to	to	IN
37681	2555	9	one	one	CD
37681	2555	10	another	another	DT
37681	2555	11	which	which	WDT
37681	2555	12	are	be	VBP
37681	2555	13	capable	capable	JJ
37681	2555	14	,	,	,
37681	2555	15	when	when	WRB
37681	2555	16	multiplied	multiply	VBN
37681	2555	17	,	,	,
37681	2555	18	of	of	IN
37681	2555	19	exceeding	exceed	VBG
37681	2555	20	one	one	NN
37681	2555	21	another	another	DT
37681	2555	22	.	.	.
37681	2556	1	Magnitudes	magnitude	NNS
37681	2556	2	are	be	VBP
37681	2556	3	said	say	VBN
37681	2556	4	to	to	TO
37681	2556	5	be	be	VB
37681	2556	6	in	in	IN
37681	2556	7	the	the	DT
37681	2556	8	same	same	JJ
37681	2556	9	ratio	ratio	NN
37681	2556	10	,	,	,
37681	2556	11	the	the	DT
37681	2556	12	first	first	JJ
37681	2556	13	to	to	IN
37681	2556	14	the	the	DT
37681	2556	15	second	second	JJ
37681	2556	16	and	and	CC
37681	2556	17	the	the	DT
37681	2556	18	third	third	JJ
37681	2556	19	to	to	IN
37681	2556	20	the	the	DT
37681	2556	21	fourth	fourth	JJ
37681	2556	22	,	,	,
37681	2556	23	when	when	WRB
37681	2556	24	,	,	,
37681	2556	25	if	if	IN
37681	2556	26	any	any	DT
37681	2556	27	equimultiples	equimultiple	NNS
37681	2556	28	whatever	whatever	WDT
37681	2556	29	be	be	VBP
37681	2556	30	taken	take	VBN
37681	2556	31	of	of	IN
37681	2556	32	the	the	DT
37681	2556	33	first	first	JJ
37681	2556	34	and	and	CC
37681	2556	35	third	third	JJ
37681	2556	36	,	,	,
37681	2556	37	and	and	CC
37681	2556	38	any	any	DT
37681	2556	39	equimultiples	equimultiple	NNS
37681	2556	40	whatever	whatever	WDT
37681	2556	41	of	of	IN
37681	2556	42	the	the	DT
37681	2556	43	second	second	JJ
37681	2556	44	and	and	CC
37681	2556	45	fourth	fourth	JJ
37681	2556	46	,	,	,
37681	2556	47	the	the	DT
37681	2556	48	former	former	JJ
37681	2556	49	equimultiples	equimultiple	NNS
37681	2556	50	alike	alike	RB
37681	2556	51	exceed	exceed	VBP
37681	2556	52	,	,	,
37681	2556	53	are	be	VBP
37681	2556	54	alike	alike	RB
37681	2556	55	equal	equal	JJ
37681	2556	56	to	to	IN
37681	2556	57	,	,	,
37681	2556	58	or	or	CC
37681	2556	59	alike	alike	RB
37681	2556	60	fall	fall	VB
37681	2556	61	short	short	RB
37681	2556	62	of	of	IN
37681	2556	63	,	,	,
37681	2556	64	the	the	DT
37681	2556	65	latter	latter	JJ
37681	2556	66	equimultiples	equimultiple	NNS
37681	2556	67	respectively	respectively	RB
37681	2556	68	taken	take	VBN
37681	2556	69	in	in	RP
37681	2556	70	corresponding	correspond	VBG
37681	2556	71	order	order	NN
37681	2556	72	.	.	.
37681	2557	1	Let	let	VB
37681	2557	2	magnitudes	magnitude	NNS
37681	2557	3	which	which	WDT
37681	2557	4	have	have	VB
37681	2557	5	the	the	DT
37681	2557	6	same	same	JJ
37681	2557	7	ratio	ratio	NN
37681	2557	8	be	be	VB
37681	2557	9	called	call	VBN
37681	2557	10	proportional	proportional	JJ
37681	2557	11	.	.	.
37681	2558	1	[	[	-LRB-
37681	2558	2	76	76	CD
37681	2558	3	]	]	-RRB-
37681	2558	4	Of	of	IN
37681	2558	5	these	these	DT
37681	2558	6	,	,	,
37681	2558	7	the	the	DT
37681	2558	8	first	first	JJ
37681	2558	9	is	be	VBZ
37681	2558	10	so	so	RB
37681	2558	11	loose	loose	JJ
37681	2558	12	in	in	IN
37681	2558	13	statement	statement	NN
37681	2558	14	as	as	RB
37681	2558	15	often	often	RB
37681	2558	16	to	to	TO
37681	2558	17	have	have	VB
37681	2558	18	been	be	VBN
37681	2558	19	thought	think	VBN
37681	2558	20	to	to	TO
37681	2558	21	be	be	VB
37681	2558	22	an	an	DT
37681	2558	23	interpolation	interpolation	NN
37681	2558	24	of	of	IN
37681	2558	25	some	some	DT
37681	2558	26	later	later	JJ
37681	2558	27	writer	writer	NN
37681	2558	28	.	.	.
37681	2559	1	It	-PRON-	PRP
37681	2559	2	was	be	VBD
37681	2559	3	probably	probably	RB
37681	2559	4	,	,	,
37681	2559	5	however	however	RB
37681	2559	6	,	,	,
37681	2559	7	put	put	VBN
37681	2559	8	into	into	IN
37681	2559	9	the	the	DT
37681	2559	10	original	original	NN
37681	2559	11	for	for	IN
37681	2559	12	the	the	DT
37681	2559	13	sake	sake	NN
37681	2559	14	of	of	IN
37681	2559	15	completeness	completeness	NN
37681	2559	16	,	,	,
37681	2559	17	to	to	TO
37681	2559	18	have	have	VB
37681	2559	19	some	some	DT
37681	2559	20	kind	kind	NN
37681	2559	21	of	of	IN
37681	2559	22	statement	statement	NN
37681	2559	23	concerning	concern	VBG
37681	2559	24	ratio	ratio	NN
37681	2559	25	as	as	IN
37681	2559	26	a	a	DT
37681	2559	27	preliminary	preliminary	NN
37681	2559	28	to	to	IN
37681	2559	29	the	the	DT
37681	2559	30	important	important	JJ
37681	2559	31	definition	definition	NN
37681	2559	32	of	of	IN
37681	2559	33	quantities	quantity	NNS
37681	2559	34	in	in	IN
37681	2559	35	the	the	DT
37681	2559	36	same	same	JJ
37681	2559	37	ratio	ratio	NN
37681	2559	38	.	.	.
37681	2560	1	Like	like	IN
37681	2560	2	the	the	DT
37681	2560	3	definition	definition	NN
37681	2560	4	of	of	IN
37681	2560	5	"	"	``
37681	2560	6	straight	straight	JJ
37681	2560	7	line	line	NN
37681	2560	8	,	,	,
37681	2560	9	"	"	''
37681	2560	10	it	-PRON-	PRP
37681	2560	11	was	be	VBD
37681	2560	12	not	not	RB
37681	2560	13	intended	intend	VBN
37681	2560	14	to	to	TO
37681	2560	15	be	be	VB
37681	2560	16	taken	take	VBN
37681	2560	17	seriously	seriously	RB
37681	2560	18	as	as	IN
37681	2560	19	a	a	DT
37681	2560	20	mathematical	mathematical	JJ
37681	2560	21	statement	statement	NN
37681	2560	22	.	.	.
37681	2561	1	The	the	DT
37681	2561	2	second	second	JJ
37681	2561	3	definition	definition	NN
37681	2561	4	is	be	VBZ
37681	2561	5	intended	intend	VBN
37681	2561	6	to	to	TO
37681	2561	7	exclude	exclude	VB
37681	2561	8	zero	zero	CD
37681	2561	9	and	and	CC
37681	2561	10	infinite	infinite	JJ
37681	2561	11	magnitudes	magnitude	NNS
37681	2561	12	,	,	,
37681	2561	13	and	and	CC
37681	2561	14	to	to	TO
37681	2561	15	show	show	VB
37681	2561	16	that	that	IN
37681	2561	17	incommensurable	incommensurable	JJ
37681	2561	18	magnitudes	magnitude	NNS
37681	2561	19	are	be	VBP
37681	2561	20	included	include	VBN
37681	2561	21	.	.	.
37681	2562	1	The	the	DT
37681	2562	2	third	third	JJ
37681	2562	3	definition	definition	NN
37681	2562	4	is	be	VBZ
37681	2562	5	the	the	DT
37681	2562	6	essential	essential	JJ
37681	2562	7	one	one	CD
37681	2562	8	of	of	IN
37681	2562	9	the	the	DT
37681	2562	10	ancient	ancient	JJ
37681	2562	11	theory	theory	NN
37681	2562	12	.	.	.
37681	2563	1	It	-PRON-	PRP
37681	2563	2	defines	define	VBZ
37681	2563	3	what	what	WP
37681	2563	4	is	be	VBZ
37681	2563	5	meant	mean	VBN
37681	2563	6	by	by	IN
37681	2563	7	saying	say	VBG
37681	2563	8	that	that	IN
37681	2563	9	magnitudes	magnitude	NNS
37681	2563	10	are	be	VBP
37681	2563	11	in	in	IN
37681	2563	12	the	the	DT
37681	2563	13	same	same	JJ
37681	2563	14	ratio	ratio	NN
37681	2563	15	;	;	:
37681	2563	16	in	in	IN
37681	2563	17	other	other	JJ
37681	2563	18	words	word	NNS
37681	2563	19	,	,	,
37681	2563	20	it	-PRON-	PRP
37681	2563	21	defines	define	VBZ
37681	2563	22	a	a	DT
37681	2563	23	proportion	proportion	NN
37681	2563	24	.	.	.
37681	2564	1	Into	into	IN
37681	2564	2	the	the	DT
37681	2564	3	merits	merit	NNS
37681	2564	4	of	of	IN
37681	2564	5	the	the	DT
37681	2564	6	definition	definition	NN
37681	2564	7	it	-PRON-	PRP
37681	2564	8	is	be	VBZ
37681	2564	9	not	not	RB
37681	2564	10	proposed	propose	VBN
37681	2564	11	to	to	TO
37681	2564	12	enter	enter	VB
37681	2564	13	,	,	,
37681	2564	14	for	for	IN
37681	2564	15	the	the	DT
37681	2564	16	reason	reason	NN
37681	2564	17	that	that	IN
37681	2564	18	it	-PRON-	PRP
37681	2564	19	is	be	VBZ
37681	2564	20	no	no	RB
37681	2564	21	longer	long	RBR
37681	2564	22	met	meet	VBN
37681	2564	23	in	in	IN
37681	2564	24	teaching	teaching	NN
37681	2564	25	in	in	IN
37681	2564	26	America	America	NNP
37681	2564	27	,	,	,
37681	2564	28	and	and	CC
37681	2564	29	is	be	VBZ
37681	2564	30	practically	practically	RB
37681	2564	31	abandoned	abandon	VBN
37681	2564	32	even	even	RB
37681	2564	33	where	where	WRB
37681	2564	34	the	the	DT
37681	2564	35	rest	rest	NN
37681	2564	36	of	of	IN
37681	2564	37	Euclid	Euclid	NNP
37681	2564	38	's	's	POS
37681	2564	39	work	work	NN
37681	2564	40	is	be	VBZ
37681	2564	41	in	in	IN
37681	2564	42	use	use	NN
37681	2564	43	.	.	.
37681	2565	1	It	-PRON-	PRP
37681	2565	2	should	should	MD
37681	2565	3	be	be	VB
37681	2565	4	said	say	VBN
37681	2565	5	,	,	,
37681	2565	6	however	however	RB
37681	2565	7	,	,	,
37681	2565	8	that	that	IN
37681	2565	9	it	-PRON-	PRP
37681	2565	10	is	be	VBZ
37681	2565	11	scientifically	scientifically	RB
37681	2565	12	correct	correct	JJ
37681	2565	13	,	,	,
37681	2565	14	that	that	IN
37681	2565	15	it	-PRON-	PRP
37681	2565	16	covers	cover	VBZ
37681	2565	17	the	the	DT
37681	2565	18	case	case	NN
37681	2565	19	of	of	IN
37681	2565	20	incommensurable	incommensurable	JJ
37681	2565	21	magnitudes	magnitude	NNS
37681	2565	22	as	as	RB
37681	2565	23	well	well	RB
37681	2565	24	as	as	IN
37681	2565	25	that	that	DT
37681	2565	26	of	of	IN
37681	2565	27	commensurable	commensurable	JJ
37681	2565	28	ones	one	NNS
37681	2565	29	,	,	,
37681	2565	30	and	and	CC
37681	2565	31	that	that	IN
37681	2565	32	it	-PRON-	PRP
37681	2565	33	is	be	VBZ
37681	2565	34	the	the	DT
37681	2565	35	Greek	greek	JJ
37681	2565	36	forerunner	forerunner	NN
37681	2565	37	of	of	IN
37681	2565	38	the	the	DT
37681	2565	39	modern	modern	JJ
37681	2565	40	theories	theory	NNS
37681	2565	41	of	of	IN
37681	2565	42	irrational	irrational	JJ
37681	2565	43	numbers	number	NNS
37681	2565	44	.	.	.
37681	2566	1	As	as	IN
37681	2566	2	compared	compare	VBN
37681	2566	3	with	with	IN
37681	2566	4	the	the	DT
37681	2566	5	above	above	JJ
37681	2566	6	treatment	treatment	NN
37681	2566	7	,	,	,
37681	2566	8	the	the	DT
37681	2566	9	one	one	NN
37681	2566	10	now	now	RB
37681	2566	11	given	give	VBN
37681	2566	12	in	in	IN
37681	2566	13	textbooks	textbook	NNS
37681	2566	14	is	be	VBZ
37681	2566	15	unscientific	unscientific	JJ
37681	2566	16	.	.	.
37681	2567	1	We	-PRON-	PRP
37681	2567	2	define	define	VBP
37681	2567	3	ratio	ratio	NN
37681	2567	4	as	as	IN
37681	2567	5	"	"	``
37681	2567	6	the	the	DT
37681	2567	7	quotient	quotient	NN
37681	2567	8	of	of	IN
37681	2567	9	the	the	DT
37681	2567	10	numerical	numerical	JJ
37681	2567	11	measures	measure	NNS
37681	2567	12	of	of	IN
37681	2567	13	two	two	CD
37681	2567	14	quantities	quantity	NNS
37681	2567	15	of	of	IN
37681	2567	16	the	the	DT
37681	2567	17	same	same	JJ
37681	2567	18	kind	kind	NN
37681	2567	19	,	,	,
37681	2567	20	"	"	''
37681	2567	21	and	and	CC
37681	2567	22	proportion	proportion	NN
37681	2567	23	as	as	IN
37681	2567	24	"	"	``
37681	2567	25	an	an	DT
37681	2567	26	equality	equality	NN
37681	2567	27	of	of	IN
37681	2567	28	ratios	ratio	NNS
37681	2567	29	.	.	.
37681	2567	30	"	"	''
37681	2568	1	But	but	CC
37681	2568	2	what	what	WP
37681	2568	3	do	do	VBP
37681	2568	4	we	-PRON-	PRP
37681	2568	5	mean	mean	VB
37681	2568	6	by	by	IN
37681	2568	7	the	the	DT
37681	2568	8	quotient	quotient	NN
37681	2568	9	,	,	,
37681	2568	10	say	say	VBP
37681	2568	11	of	of	IN
37681	2568	12	[	[	-LRB-
37681	2568	13	sqrt]2	sqrt]2	CD
37681	2568	14	by	by	IN
37681	2568	15	[	[	-LRB-
37681	2568	16	sqrt]3	sqrt]3	NN
37681	2568	17	?	?	.
37681	2569	1	And	and	CC
37681	2569	2	when	when	WRB
37681	2569	3	we	-PRON-	PRP
37681	2569	4	multiply	multiply	VBP
37681	2569	5	a	a	DT
37681	2569	6	ratio	ratio	NN
37681	2569	7	by	by	IN
37681	2569	8	[	[	-LRB-
37681	2569	9	sqrt]5	sqrt]5	CD
37681	2569	10	,	,	,
37681	2569	11	what	what	WP
37681	2569	12	is	be	VBZ
37681	2569	13	the	the	DT
37681	2569	14	meaning	meaning	NN
37681	2569	15	of	of	IN
37681	2569	16	this	this	DT
37681	2569	17	operation	operation	NN
37681	2569	18	?	?	.
37681	2570	1	If	if	IN
37681	2570	2	we	-PRON-	PRP
37681	2570	3	say	say	VBP
37681	2570	4	that	that	IN
37681	2570	5	[	[	-LRB-
37681	2570	6	sqrt]2	sqrt]2	CD
37681	2570	7	:	:	:
37681	2570	8	[	[	-LRB-
37681	2570	9	sqrt]3	sqrt]3	NN
37681	2570	10	means	mean	VBZ
37681	2570	11	a	a	DT
37681	2570	12	quotient	quotient	NN
37681	2570	13	,	,	,
37681	2570	14	what	what	WP
37681	2570	15	meaning	meaning	NN
37681	2570	16	shall	shall	MD
37681	2570	17	we	-PRON-	PRP
37681	2570	18	assign	assign	VB
37681	2570	19	to	to	TO
37681	2570	20	"	"	``
37681	2570	21	quotient	quotient	VB
37681	2570	22	"	"	''
37681	2570	23	?	?	.
37681	2571	1	If	if	IN
37681	2571	2	it	-PRON-	PRP
37681	2571	3	is	be	VBZ
37681	2571	4	the	the	DT
37681	2571	5	number	number	NN
37681	2571	6	that	that	WDT
37681	2571	7	shows	show	VBZ
37681	2571	8	how	how	WRB
37681	2571	9	many	many	JJ
37681	2571	10	times	time	NNS
37681	2571	11	one	one	CD
37681	2571	12	number	number	NN
37681	2571	13	is	be	VBZ
37681	2571	14	contained	contain	VBN
37681	2571	15	in	in	IN
37681	2571	16	another	another	DT
37681	2571	17	,	,	,
37681	2571	18	how	how	WRB
37681	2571	19	many	many	JJ
37681	2571	20	_	_	NNP
37681	2571	21	times	times	NNP
37681	2571	22	_	_	NNP
37681	2571	23	is	be	VBZ
37681	2571	24	[	[	-LRB-
37681	2571	25	sqrt]3	sqrt]3	NN
37681	2571	26	contained	contain	VBN
37681	2571	27	in	in	IN
37681	2571	28	[	[	-LRB-
37681	2571	29	sqrt]2	sqrt]2	NN
37681	2571	30	?	?	.
37681	2572	1	If	if	IN
37681	2572	2	to	to	TO
37681	2572	3	multiply	multiply	NNP
37681	2572	4	is	be	VBZ
37681	2572	5	to	to	TO
37681	2572	6	take	take	VB
37681	2572	7	a	a	DT
37681	2572	8	number	number	NN
37681	2572	9	a	a	DT
37681	2572	10	certain	certain	JJ
37681	2572	11	number	number	NN
37681	2572	12	of	of	IN
37681	2572	13	times	time	NNS
37681	2572	14	,	,	,
37681	2572	15	how	how	WRB
37681	2572	16	many	many	JJ
37681	2572	17	times	time	NNS
37681	2572	18	do	do	VBP
37681	2572	19	we	-PRON-	PRP
37681	2572	20	take	take	VB
37681	2572	21	it	-PRON-	PRP
37681	2572	22	when	when	WRB
37681	2572	23	we	-PRON-	PRP
37681	2572	24	multiply	multiply	VBP
37681	2572	25	by	by	IN
37681	2572	26	[	[	-LRB-
37681	2572	27	sqrt]5	sqrt]5	IN
37681	2572	28	?	?	.
37681	2573	1	We	-PRON-	PRP
37681	2573	2	certainly	certainly	RB
37681	2573	3	take	take	VBP
37681	2573	4	it	-PRON-	PRP
37681	2573	5	more	more	JJR
37681	2573	6	than	than	IN
37681	2573	7	2	2	CD
37681	2573	8	times	time	NNS
37681	2573	9	and	and	CC
37681	2573	10	less	less	JJR
37681	2573	11	than	than	IN
37681	2573	12	3	3	CD
37681	2573	13	times	time	NNS
37681	2573	14	,	,	,
37681	2573	15	but	but	CC
37681	2573	16	what	what	WDT
37681	2573	17	meaning	meaning	NN
37681	2573	18	can	can	MD
37681	2573	19	we	-PRON-	PRP
37681	2573	20	assign	assign	VB
37681	2573	21	to	to	IN
37681	2573	22	[	[	-LRB-
37681	2573	23	sqrt]5	sqrt]5	CD
37681	2573	24	times	time	NNS
37681	2573	25	?	?	.
37681	2574	1	It	-PRON-	PRP
37681	2574	2	will	will	MD
37681	2574	3	thus	thus	RB
37681	2574	4	be	be	VB
37681	2574	5	seen	see	VBN
37681	2574	6	that	that	IN
37681	2574	7	our	-PRON-	PRP$
37681	2574	8	treatment	treatment	NN
37681	2574	9	of	of	IN
37681	2574	10	proportion	proportion	NN
37681	2574	11	assumes	assume	VBZ
37681	2574	12	that	that	IN
37681	2574	13	we	-PRON-	PRP
37681	2574	14	already	already	RB
37681	2574	15	know	know	VBP
37681	2574	16	the	the	DT
37681	2574	17	theory	theory	NN
37681	2574	18	of	of	IN
37681	2574	19	irrationals	irrational	NNS
37681	2574	20	and	and	CC
37681	2574	21	can	can	MD
37681	2574	22	apply	apply	VB
37681	2574	23	it	-PRON-	PRP
37681	2574	24	to	to	IN
37681	2574	25	geometric	geometric	JJ
37681	2574	26	magnitudes	magnitude	NNS
37681	2574	27	,	,	,
37681	2574	28	while	while	IN
37681	2574	29	the	the	DT
37681	2574	30	ancient	ancient	JJ
37681	2574	31	treatment	treatment	NN
37681	2574	32	is	be	VBZ
37681	2574	33	independent	independent	JJ
37681	2574	34	of	of	IN
37681	2574	35	this	this	DT
37681	2574	36	theory	theory	NN
37681	2574	37	.	.	.
37681	2575	1	Educationally	educationally	RB
37681	2575	2	,	,	,
37681	2575	3	however	however	RB
37681	2575	4	,	,	,
37681	2575	5	we	-PRON-	PRP
37681	2575	6	are	be	VBP
37681	2575	7	forced	force	VBN
37681	2575	8	to	to	TO
37681	2575	9	proceed	proceed	VB
37681	2575	10	as	as	IN
37681	2575	11	we	-PRON-	PRP
37681	2575	12	do	do	VBP
37681	2575	13	.	.	.
37681	2576	1	Just	just	RB
37681	2576	2	as	as	IN
37681	2576	3	Dedekind	Dedekind	NNP
37681	2576	4	's	's	POS
37681	2576	5	theory	theory	NN
37681	2576	6	of	of	IN
37681	2576	7	numbers	number	NNS
37681	2576	8	is	be	VBZ
37681	2576	9	a	a	DT
37681	2576	10	simple	simple	JJ
37681	2576	11	one	one	CD
37681	2576	12	for	for	IN
37681	2576	13	college	college	NN
37681	2576	14	students	student	NNS
37681	2576	15	,	,	,
37681	2576	16	so	so	RB
37681	2576	17	is	be	VBZ
37681	2576	18	the	the	DT
37681	2576	19	ancient	ancient	JJ
37681	2576	20	theory	theory	NN
37681	2576	21	of	of	IN
37681	2576	22	proportion	proportion	NN
37681	2576	23	;	;	:
37681	2576	24	but	but	CC
37681	2576	25	as	as	IN
37681	2576	26	the	the	DT
37681	2576	27	former	former	JJ
37681	2576	28	is	be	VBZ
37681	2576	29	not	not	RB
37681	2576	30	suited	suited	JJ
37681	2576	31	to	to	IN
37681	2576	32	pupils	pupil	NNS
37681	2576	33	in	in	IN
37681	2576	34	the	the	DT
37681	2576	35	high	high	JJ
37681	2576	36	school	school	NN
37681	2576	37	,	,	,
37681	2576	38	so	so	RB
37681	2576	39	the	the	DT
37681	2576	40	latter	latter	JJ
37681	2576	41	must	must	MD
37681	2576	42	be	be	VB
37681	2576	43	relegated	relegate	VBN
37681	2576	44	to	to	IN
37681	2576	45	the	the	DT
37681	2576	46	college	college	NN
37681	2576	47	classes	class	NNS
37681	2576	48	.	.	.
37681	2577	1	And	and	CC
37681	2577	2	in	in	IN
37681	2577	3	this	this	DT
37681	2577	4	we	-PRON-	PRP
37681	2577	5	merely	merely	RB
37681	2577	6	harmonize	harmonize	VBP
37681	2577	7	educational	educational	JJ
37681	2577	8	progress	progress	NN
37681	2577	9	with	with	IN
37681	2577	10	world	world	NN
37681	2577	11	progress	progress	NN
37681	2577	12	,	,	,
37681	2577	13	for	for	IN
37681	2577	14	the	the	DT
37681	2577	15	numerical	numerical	JJ
37681	2577	16	theory	theory	NN
37681	2577	17	of	of	IN
37681	2577	18	proportion	proportion	NN
37681	2577	19	long	long	RB
37681	2577	20	preceded	precede	VBD
37681	2577	21	the	the	DT
37681	2577	22	theory	theory	NN
37681	2577	23	of	of	IN
37681	2577	24	Eudoxus	Eudoxus	NNP
37681	2577	25	.	.	.
37681	2578	1	The	the	DT
37681	2578	2	ancients	ancient	NNS
37681	2578	3	made	make	VBD
37681	2578	4	much	much	JJ
37681	2578	5	of	of	IN
37681	2578	6	such	such	JJ
37681	2578	7	terms	term	NNS
37681	2578	8	as	as	IN
37681	2578	9	duplicate	duplicate	JJ
37681	2578	10	,	,	,
37681	2578	11	triplicate	triplicate	VB
37681	2578	12	,	,	,
37681	2578	13	alternate	alternate	JJ
37681	2578	14	,	,	,
37681	2578	15	and	and	CC
37681	2578	16	inverse	inverse	NN
37681	2578	17	ratio	ratio	NN
37681	2578	18	,	,	,
37681	2578	19	and	and	CC
37681	2578	20	also	also	RB
37681	2578	21	such	such	JJ
37681	2578	22	as	as	IN
37681	2578	23	composition	composition	NN
37681	2578	24	,	,	,
37681	2578	25	separation	separation	NN
37681	2578	26	,	,	,
37681	2578	27	and	and	CC
37681	2578	28	conversion	conversion	NN
37681	2578	29	of	of	IN
37681	2578	30	ratio	ratio	NN
37681	2578	31	.	.	.
37681	2579	1	These	these	DT
37681	2579	2	entered	enter	VBD
37681	2579	3	into	into	IN
37681	2579	4	such	such	JJ
37681	2579	5	propositions	proposition	NNS
37681	2579	6	as	as	IN
37681	2579	7	,	,	,
37681	2579	8	"	"	``
37681	2579	9	If	if	IN
37681	2579	10	four	four	CD
37681	2579	11	magnitudes	magnitude	NNS
37681	2579	12	are	be	VBP
37681	2579	13	proportional	proportional	JJ
37681	2579	14	,	,	,
37681	2579	15	they	-PRON-	PRP
37681	2579	16	will	will	MD
37681	2579	17	also	also	RB
37681	2579	18	be	be	VB
37681	2579	19	proportional	proportional	JJ
37681	2579	20	alternately	alternately	RB
37681	2579	21	.	.	.
37681	2579	22	"	"	''
37681	2580	1	In	in	IN
37681	2580	2	later	later	JJ
37681	2580	3	works	work	NNS
37681	2580	4	they	-PRON-	PRP
37681	2580	5	appear	appear	VBP
37681	2580	6	in	in	IN
37681	2580	7	the	the	DT
37681	2580	8	form	form	NN
37681	2580	9	of	of	IN
37681	2580	10	"	"	``
37681	2580	11	proportion	proportion	NN
37681	2580	12	by	by	IN
37681	2580	13	composition	composition	NN
37681	2580	14	,	,	,
37681	2580	15	"	"	''
37681	2580	16	"	"	``
37681	2580	17	by	by	IN
37681	2580	18	division	division	NN
37681	2580	19	,	,	,
37681	2580	20	"	"	''
37681	2580	21	and	and	CC
37681	2580	22	"	"	``
37681	2580	23	by	by	IN
37681	2580	24	composition	composition	NN
37681	2580	25	and	and	CC
37681	2580	26	division	division	NN
37681	2580	27	.	.	.
37681	2580	28	"	"	''
37681	2581	1	None	none	NN
37681	2581	2	of	of	IN
37681	2581	3	these	these	DT
37681	2581	4	is	be	VBZ
37681	2581	5	to	to	NN
37681	2581	6	-	-	HYPH
37681	2581	7	day	day	NN
37681	2581	8	of	of	IN
37681	2581	9	much	much	JJ
37681	2581	10	importance	importance	NN
37681	2581	11	,	,	,
37681	2581	12	since	since	IN
37681	2581	13	modern	modern	JJ
37681	2581	14	symbolism	symbolism	NN
37681	2581	15	has	have	VBZ
37681	2581	16	greatly	greatly	RB
37681	2581	17	simplified	simplify	VBN
37681	2581	18	the	the	DT
37681	2581	19	ancient	ancient	JJ
37681	2581	20	expressions	expression	NNS
37681	2581	21	,	,	,
37681	2581	22	and	and	CC
37681	2581	23	in	in	IN
37681	2581	24	particular	particular	JJ
37681	2581	25	the	the	DT
37681	2581	26	proposition	proposition	NN
37681	2581	27	concerning	concern	VBG
37681	2581	28	"	"	``
37681	2581	29	composition	composition	NN
37681	2581	30	and	and	CC
37681	2581	31	division	division	NN
37681	2581	32	"	"	''
37681	2581	33	is	be	VBZ
37681	2581	34	no	no	RB
37681	2581	35	longer	long	RBR
37681	2581	36	a	a	DT
37681	2581	37	basal	basal	NN
37681	2581	38	theorem	theorem	NN
37681	2581	39	in	in	IN
37681	2581	40	geometry	geometry	NN
37681	2581	41	.	.	.
37681	2582	1	Indeed	indeed	RB
37681	2582	2	,	,	,
37681	2582	3	if	if	IN
37681	2582	4	our	-PRON-	PRP$
37681	2582	5	course	course	NN
37681	2582	6	of	of	IN
37681	2582	7	study	study	NN
37681	2582	8	were	be	VBD
37681	2582	9	properly	properly	RB
37681	2582	10	arranged	arrange	VBN
37681	2582	11	,	,	,
37681	2582	12	we	-PRON-	PRP
37681	2582	13	might	may	MD
37681	2582	14	well	well	RB
37681	2582	15	relegate	relegate	VB
37681	2582	16	the	the	DT
37681	2582	17	whole	whole	JJ
37681	2582	18	theory	theory	NN
37681	2582	19	of	of	IN
37681	2582	20	proportion	proportion	NN
37681	2582	21	to	to	IN
37681	2582	22	algebra	algebra	NN
37681	2582	23	,	,	,
37681	2582	24	allowing	allow	VBG
37681	2582	25	this	this	DT
37681	2582	26	to	to	TO
37681	2582	27	precede	precede	VB
37681	2582	28	the	the	DT
37681	2582	29	work	work	NN
37681	2582	30	in	in	IN
37681	2582	31	geometry	geometry	NN
37681	2582	32	.	.	.
37681	2583	1	We	-PRON-	PRP
37681	2583	2	shall	shall	MD
37681	2583	3	now	now	RB
37681	2583	4	consider	consider	VB
37681	2583	5	a	a	DT
37681	2583	6	few	few	JJ
37681	2583	7	of	of	IN
37681	2583	8	the	the	DT
37681	2583	9	principal	principal	JJ
37681	2583	10	propositions	proposition	NNS
37681	2583	11	of	of	IN
37681	2583	12	Book	Book	NNP
37681	2583	13	III	III	NNP
37681	2583	14	.	.	.
37681	2584	1	THEOREM	THEOREM	NNP
37681	2584	2	.	.	.
37681	2585	1	_	_	XX
37681	2585	2	If	if	IN
37681	2585	3	a	a	DT
37681	2585	4	line	line	NN
37681	2585	5	is	be	VBZ
37681	2585	6	drawn	draw	VBN
37681	2585	7	through	through	IN
37681	2585	8	two	two	CD
37681	2585	9	sides	side	NNS
37681	2585	10	of	of	IN
37681	2585	11	a	a	DT
37681	2585	12	triangle	triangle	NN
37681	2585	13	parallel	parallel	NN
37681	2585	14	to	to	IN
37681	2585	15	the	the	DT
37681	2585	16	third	third	JJ
37681	2585	17	side	side	NN
37681	2585	18	,	,	,
37681	2585	19	it	-PRON-	PRP
37681	2585	20	divides	divide	VBZ
37681	2585	21	those	those	DT
37681	2585	22	sides	side	NNS
37681	2585	23	proportionally	proportionally	RB
37681	2585	24	.	.	.
37681	2585	25	_	_	NNP
37681	2585	26	In	in	IN
37681	2585	27	addition	addition	NN
37681	2585	28	to	to	IN
37681	2585	29	the	the	DT
37681	2585	30	usual	usual	JJ
37681	2585	31	proof	proof	NN
37681	2585	32	it	-PRON-	PRP
37681	2585	33	is	be	VBZ
37681	2585	34	instructive	instructive	JJ
37681	2585	35	to	to	TO
37681	2585	36	consider	consider	VB
37681	2585	37	in	in	IN
37681	2585	38	class	class	NN
37681	2585	39	the	the	DT
37681	2585	40	cases	case	NNS
37681	2585	41	in	in	IN
37681	2585	42	which	which	WDT
37681	2585	43	the	the	DT
37681	2585	44	parallel	parallel	NN
37681	2585	45	is	be	VBZ
37681	2585	46	drawn	draw	VBN
37681	2585	47	through	through	IN
37681	2585	48	the	the	DT
37681	2585	49	two	two	CD
37681	2585	50	sides	side	NNS
37681	2585	51	produced	produce	VBN
37681	2585	52	,	,	,
37681	2585	53	either	either	CC
37681	2585	54	below	below	IN
37681	2585	55	the	the	DT
37681	2585	56	base	base	NN
37681	2585	57	or	or	CC
37681	2585	58	above	above	IN
37681	2585	59	the	the	DT
37681	2585	60	vertex	vertex	NN
37681	2585	61	,	,	,
37681	2585	62	and	and	CC
37681	2585	63	also	also	RB
37681	2585	64	in	in	IN
37681	2585	65	which	which	WDT
37681	2585	66	the	the	DT
37681	2585	67	parallel	parallel	NN
37681	2585	68	is	be	VBZ
37681	2585	69	drawn	draw	VBN
37681	2585	70	through	through	IN
37681	2585	71	the	the	DT
37681	2585	72	vertex	vertex	NN
37681	2585	73	.	.	.
37681	2586	1	THEOREM	THEOREM	NNP
37681	2586	2	.	.	.
37681	2587	1	_	_	NNP
37681	2587	2	The	the	DT
37681	2587	3	bisector	bisector	NN
37681	2587	4	of	of	IN
37681	2587	5	an	an	DT
37681	2587	6	angle	angle	NN
37681	2587	7	of	of	IN
37681	2587	8	a	a	DT
37681	2587	9	triangle	triangle	NN
37681	2587	10	divides	divide	VBZ
37681	2587	11	the	the	DT
37681	2587	12	opposite	opposite	JJ
37681	2587	13	side	side	NN
37681	2587	14	into	into	IN
37681	2587	15	segments	segment	NNS
37681	2587	16	which	which	WDT
37681	2587	17	are	be	VBP
37681	2587	18	proportional	proportional	JJ
37681	2587	19	to	to	IN
37681	2587	20	the	the	DT
37681	2587	21	adjacent	adjacent	JJ
37681	2587	22	sides	side	NNS
37681	2587	23	.	.	.
37681	2587	24	_	_	NNP
37681	2587	25	The	the	DT
37681	2587	26	proposition	proposition	NN
37681	2587	27	relating	relate	VBG
37681	2587	28	to	to	IN
37681	2587	29	the	the	DT
37681	2587	30	bisector	bisector	NN
37681	2587	31	of	of	IN
37681	2587	32	an	an	DT
37681	2587	33	exterior	exterior	JJ
37681	2587	34	angle	angle	NN
37681	2587	35	may	may	MD
37681	2587	36	be	be	VB
37681	2587	37	considered	consider	VBN
37681	2587	38	as	as	IN
37681	2587	39	a	a	DT
37681	2587	40	part	part	NN
37681	2587	41	of	of	IN
37681	2587	42	this	this	DT
37681	2587	43	one	one	NN
37681	2587	44	,	,	,
37681	2587	45	but	but	CC
37681	2587	46	it	-PRON-	PRP
37681	2587	47	is	be	VBZ
37681	2587	48	usually	usually	RB
37681	2587	49	treated	treat	VBN
37681	2587	50	separately	separately	RB
37681	2587	51	in	in	IN
37681	2587	52	order	order	NN
37681	2587	53	that	that	IN
37681	2587	54	the	the	DT
37681	2587	55	proof	proof	NN
37681	2587	56	shall	shall	MD
37681	2587	57	appear	appear	VB
37681	2587	58	less	less	RBR
37681	2587	59	involved	involved	JJ
37681	2587	60	,	,	,
37681	2587	61	although	although	IN
37681	2587	62	the	the	DT
37681	2587	63	two	two	CD
37681	2587	64	are	be	VBP
37681	2587	65	discussed	discuss	VBN
37681	2587	66	together	together	RB
37681	2587	67	at	at	IN
37681	2587	68	this	this	DT
37681	2587	69	time	time	NN
37681	2587	70	.	.	.
37681	2588	1	The	the	DT
37681	2588	2	proposition	proposition	NN
37681	2588	3	relating	relate	VBG
37681	2588	4	to	to	IN
37681	2588	5	the	the	DT
37681	2588	6	exterior	exterior	NNP
37681	2588	7	angle	angle	NN
37681	2588	8	was	be	VBD
37681	2588	9	recognized	recognize	VBN
37681	2588	10	by	by	IN
37681	2588	11	Pappus	Pappus	NNP
37681	2588	12	of	of	IN
37681	2588	13	Alexandria	Alexandria	NNP
37681	2588	14	.	.	.
37681	2589	1	If	if	IN
37681	2589	2	_	_	NNP
37681	2589	3	ABC	ABC	NNP
37681	2589	4	_	_	NNP
37681	2589	5	is	be	VBZ
37681	2589	6	the	the	DT
37681	2589	7	given	give	VBN
37681	2589	8	triangle	triangle	NN
37681	2589	9	,	,	,
37681	2589	10	and	and	CC
37681	2589	11	_	_	NNP
37681	2589	12	CP__{1	cp__{1	NN
37681	2589	13	}	}	-RRB-
37681	2589	14	,	,	,
37681	2589	15	_	_	NNP
37681	2589	16	CP__{2	cp__{2	NN
37681	2589	17	}	}	-RRB-
37681	2589	18	are	be	VBP
37681	2589	19	respectively	respectively	RB
37681	2589	20	the	the	DT
37681	2589	21	internal	internal	JJ
37681	2589	22	and	and	CC
37681	2589	23	external	external	JJ
37681	2589	24	bisectors	bisector	NNS
37681	2589	25	,	,	,
37681	2589	26	then	then	RB
37681	2589	27	_	_	NNP
37681	2589	28	AB	AB	NNP
37681	2589	29	_	_	NNP
37681	2589	30	is	be	VBZ
37681	2589	31	divided	divide	VBN
37681	2589	32	harmonically	harmonically	RB
37681	2589	33	by	by	IN
37681	2589	34	_	_	NNP
37681	2589	35	P__{1	P__{1	NNP
37681	2589	36	}	}	-RRB-
37681	2589	37	and	and	CC
37681	2589	38	_	_	NNP
37681	2589	39	P__{2	P__{2	NNP
37681	2589	40	}	}	-RRB-
37681	2589	41	.	.	.
37681	2590	1	[	[	-LRB-
37681	2590	2	therefore]_AP__{1	therefore]_ap__{1	NN
37681	2590	3	}	}	-RRB-
37681	2590	4	:	:	:
37681	2590	5	_	_	NNP
37681	2590	6	P__{1}_B	P__{1}_B	NNP
37681	2590	7	_	_	NNP
37681	2590	8	=	=	SYM
37681	2590	9	_	_	NNP
37681	2590	10	AP__{2	AP__{2	NNP
37681	2590	11	}	}	-RRB-
37681	2590	12	:	:	:
37681	2590	13	_	_	NNP
37681	2590	14	P__{2}_B	P__{2}_B	NNP
37681	2590	15	_	_	NNP
37681	2590	16	.	.	.
37681	2591	1	[	[	-LRB-
37681	2591	2	therefore]_AP__{2	therefore]_AP__{2	NNP
37681	2591	3	}	}	-RRB-
37681	2591	4	:	:	:
37681	2591	5	_	_	NNP
37681	2591	6	P__{2}_B	P__{2}_B	NNP
37681	2591	7	_	_	NNP
37681	2591	8	=	=	SYM
37681	2591	9	_	_	NNP
37681	2591	10	AP__{2	AP__{2	NNP
37681	2591	11	}	}	-RRB-
37681	2591	12	-	-	:
37681	2591	13	_	_	NNP
37681	2591	14	P__{1}_P__{2	p__{1}_p__{2	NN
37681	2591	15	}	}	-RRB-
37681	2591	16	:	:	:
37681	2591	17	_	_	NNP
37681	2591	18	P__{1}_P__{2	P__{1}_P__{2	NNP
37681	2591	19	}	}	-RRB-
37681	2591	20	-	-	HYPH
37681	2591	21	_	_	NNP
37681	2591	22	P__{2}_B	P__{2}_B	NNP
37681	2591	23	_	_	NNP
37681	2591	24	,	,	,
37681	2591	25	and	and	CC
37681	2591	26	this	this	DT
37681	2591	27	is	be	VBZ
37681	2591	28	the	the	DT
37681	2591	29	criterion	criterion	NN
37681	2591	30	for	for	IN
37681	2591	31	the	the	DT
37681	2591	32	harmonic	harmonic	JJ
37681	2591	33	progression	progression	NN
37681	2591	34	still	still	RB
37681	2591	35	seen	see	VBN
37681	2591	36	in	in	IN
37681	2591	37	many	many	JJ
37681	2591	38	algebras	algebra	NNS
37681	2591	39	.	.	.
37681	2592	1	For	for	IN
37681	2592	2	,	,	,
37681	2592	3	letting	let	VBG
37681	2592	4	_	_	NNP
37681	2592	5	AP__{2	AP__{2	NNP
37681	2592	6	}	}	-RRB-
37681	2592	7	=	=	SYM
37681	2592	8	_	_	NNP
37681	2592	9	a	a	DT
37681	2592	10	_	_	NNP
37681	2592	11	,	,	,
37681	2592	12	_	_	NNP
37681	2592	13	P__{1}_P__{2	P__{1}_P__{2	NNP
37681	2592	14	}	}	-RRB-
37681	2592	15	=	=	SYM
37681	2592	16	_	_	NNP
37681	2592	17	b	b	NNP
37681	2592	18	_	_	NNP
37681	2592	19	,	,	,
37681	2592	20	_	_	NNP
37681	2592	21	P__{2}_B	P__{2}_B	NNP
37681	2592	22	_	_	NNP
37681	2592	23	=	=	SYM
37681	2592	24	_	_	NNP
37681	2592	25	c	c	NNP
37681	2592	26	_	_	NNP
37681	2592	27	,	,	,
37681	2592	28	we	-PRON-	PRP
37681	2592	29	have	have	VBP
37681	2592	30	_	_	NNP
37681	2592	31	a_/_c	a_/_c	NNP
37681	2592	32	_	_	NNP
37681	2592	33	=	=	NFP
37681	2592	34	(	(	-LRB-
37681	2592	35	_	_	NNP
37681	2592	36	a	a	DT
37681	2592	37	_	_	NNP
37681	2592	38	-	-	HYPH
37681	2592	39	_	_	NNP
37681	2592	40	b_)/(_b	b_)/(_b	IN
37681	2592	41	_	_	NNP
37681	2592	42	-	-	HYPH
37681	2592	43	_	_	NNP
37681	2592	44	c	c	NNP
37681	2592	45	_	_	NNP
37681	2592	46	)	)	-RRB-
37681	2592	47	,	,	,
37681	2592	48	which	which	WDT
37681	2592	49	is	be	VBZ
37681	2592	50	also	also	RB
37681	2592	51	derived	derive	VBN
37681	2592	52	from	from	IN
37681	2592	53	taking	take	VBG
37681	2592	54	the	the	DT
37681	2592	55	reciprocals	reciprocal	NNS
37681	2592	56	of	of	IN
37681	2592	57	_	_	NNP
37681	2592	58	a	a	DT
37681	2592	59	_	_	NNP
37681	2592	60	,	,	,
37681	2592	61	_	_	NNP
37681	2592	62	b	b	NNP
37681	2592	63	_	_	NNP
37681	2592	64	,	,	,
37681	2592	65	_	_	NNP
37681	2592	66	c	c	NNP
37681	2592	67	_	_	NNP
37681	2592	68	,	,	,
37681	2592	69	and	and	CC
37681	2592	70	placing	place	VBG
37681	2592	71	them	-PRON-	PRP
37681	2592	72	in	in	IN
37681	2592	73	an	an	DT
37681	2592	74	arithmetical	arithmetical	JJ
37681	2592	75	progression	progression	NN
37681	2592	76	,	,	,
37681	2592	77	thus	thus	RB
37681	2592	78	:	:	:
37681	2592	79	1/_b	1/_b	CD
37681	2592	80	_	_	NNP
37681	2592	81	-	-	HYPH
37681	2592	82	1/_a	1/_a	NNP
37681	2592	83	_	_	NNP
37681	2592	84	=	=	SYM
37681	2592	85	1/_c	1/_c	CD
37681	2592	86	_	_	NNP
37681	2592	87	-	-	HYPH
37681	2592	88	1/_b	1/_b	NNP
37681	2592	89	_	_	NNP
37681	2592	90	,	,	,
37681	2592	91	whence	whence	NN
37681	2592	92	(	(	-LRB-
37681	2592	93	_	_	NNP
37681	2592	94	a	a	DT
37681	2592	95	_	_	NNP
37681	2592	96	-	-	HYPH
37681	2592	97	_	_	NNP
37681	2592	98	b_)/_ab	b_)/_ab	NNP
37681	2592	99	_	_	NNP
37681	2592	100	=	=	NFP
37681	2592	101	(	(	-LRB-
37681	2592	102	_	_	NNP
37681	2592	103	b	b	NNP
37681	2592	104	_	_	NNP
37681	2592	105	-	-	HYPH
37681	2592	106	_	_	NNP
37681	2592	107	c_)/_bc	c_)/_bc	NNP
37681	2592	108	_	_	NNP
37681	2592	109	,	,	,
37681	2592	110	or	or	CC
37681	2592	111	(	(	-LRB-
37681	2592	112	_	_	NNP
37681	2592	113	a	a	DT
37681	2592	114	_	_	NNP
37681	2592	115	-	-	HYPH
37681	2592	116	_	_	NNP
37681	2592	117	b_)/(_b	b_)/(_b	IN
37681	2592	118	_	_	NNP
37681	2592	119	-	-	HYPH
37681	2592	120	_	_	NNP
37681	2592	121	c	c	NNP
37681	2592	122	_	_	NNP
37681	2592	123	)	)	-RRB-
37681	2592	124	=	=	NFP
37681	2592	125	_	_	NNP
37681	2592	126	ab_/_bc	ab_/_bc	NNP
37681	2592	127	_	_	NNP
37681	2592	128	=	=	SYM
37681	2592	129	_	_	NNP
37681	2592	130	a_/_c	a_/_c	NNP
37681	2592	131	_	_	NNP
37681	2592	132	.	.	.
37681	2593	1	This	this	DT
37681	2593	2	is	be	VBZ
37681	2593	3	the	the	DT
37681	2593	4	reason	reason	NN
37681	2593	5	why	why	WRB
37681	2593	6	the	the	DT
37681	2593	7	line	line	NN
37681	2593	8	_	_	NNP
37681	2593	9	AB	AB	NNP
37681	2593	10	_	_	NNP
37681	2593	11	is	be	VBZ
37681	2593	12	said	say	VBN
37681	2593	13	to	to	TO
37681	2593	14	be	be	VB
37681	2593	15	divided	divide	VBN
37681	2593	16	harmonically	harmonically	RB
37681	2593	17	.	.	.
37681	2594	1	The	the	DT
37681	2594	2	line	line	NN
37681	2594	3	_	_	NNP
37681	2594	4	P__{1}_P__{2	P__{1}_P__{2	NNP
37681	2594	5	}	}	-RRB-
37681	2594	6	is	be	VBZ
37681	2594	7	also	also	RB
37681	2594	8	called	call	VBN
37681	2594	9	the	the	DT
37681	2594	10	_	_	NNP
37681	2594	11	harmonic	harmonic	NNP
37681	2594	12	mean	mean	NN
37681	2594	13	_	_	NNP
37681	2594	14	between	between	IN
37681	2594	15	_	_	NNP
37681	2594	16	AP__{2	AP__{2	NNP
37681	2594	17	}	}	-RRB-
37681	2594	18	and	and	CC
37681	2594	19	_	_	NNP
37681	2594	20	P__{2}_B	P__{2}_B	NNP
37681	2594	21	_	_	NNP
37681	2594	22	,	,	,
37681	2594	23	and	and	CC
37681	2594	24	the	the	DT
37681	2594	25	points	point	NNS
37681	2594	26	_	_	NNP
37681	2594	27	A	A	NNP
37681	2594	28	_	_	NNP
37681	2594	29	,	,	,
37681	2594	30	_	_	NNP
37681	2594	31	P__{1	P__{1	NNP
37681	2594	32	}	}	-RRB-
37681	2594	33	,	,	,
37681	2594	34	_	_	NNP
37681	2594	35	B	B	NNP
37681	2594	36	_	_	NNP
37681	2594	37	,	,	,
37681	2594	38	_	_	NNP
37681	2594	39	P__{2	P__{2	NNP
37681	2594	40	}	}	-RRB-
37681	2594	41	are	be	VBP
37681	2594	42	said	say	VBN
37681	2594	43	to	to	TO
37681	2594	44	form	form	VB
37681	2594	45	an	an	DT
37681	2594	46	_	_	NNP
37681	2594	47	harmonic	harmonic	NNP
37681	2594	48	range	range	NN
37681	2594	49	_	_	NNP
37681	2594	50	.	.	.
37681	2595	1	[	[	-LRB-
37681	2595	2	Illustration	illustration	NN
37681	2595	3	]	]	-RRB-
37681	2595	4	It	-PRON-	PRP
37681	2595	5	may	may	MD
37681	2595	6	be	be	VB
37681	2595	7	noted	note	VBN
37681	2595	8	that	that	IN
37681	2595	9	[	[	-LRB-
37681	2595	10	L]_P__{2}_CP__{1	l]_p__{2}_cp__{1	UH
37681	2595	11	}	}	-RRB-
37681	2595	12	,	,	,
37681	2595	13	being	be	VBG
37681	2595	14	made	make	VBN
37681	2595	15	up	up	RP
37681	2595	16	of	of	IN
37681	2595	17	halves	half	NNS
37681	2595	18	of	of	IN
37681	2595	19	two	two	CD
37681	2595	20	supplementary	supplementary	JJ
37681	2595	21	angles	angle	NNS
37681	2595	22	,	,	,
37681	2595	23	is	be	VBZ
37681	2595	24	a	a	DT
37681	2595	25	right	right	JJ
37681	2595	26	angle	angle	NN
37681	2595	27	.	.	.
37681	2596	1	Furthermore	furthermore	RB
37681	2596	2	,	,	,
37681	2596	3	if	if	IN
37681	2596	4	the	the	DT
37681	2596	5	ratio	ratio	NN
37681	2596	6	_	_	NNP
37681	2596	7	CA	CA	NNP
37681	2596	8	_	_	NNP
37681	2596	9	:	:	:
37681	2596	10	_	_	NNP
37681	2596	11	CB	CB	NNP
37681	2596	12	_	_	NNP
37681	2596	13	is	be	VBZ
37681	2596	14	given	give	VBN
37681	2596	15	,	,	,
37681	2596	16	and	and	CC
37681	2596	17	_	_	NNP
37681	2596	18	AB	AB	NNP
37681	2596	19	_	_	NNP
37681	2596	20	is	be	VBZ
37681	2596	21	given	give	VBN
37681	2596	22	,	,	,
37681	2596	23	then	then	RB
37681	2596	24	_	_	NNP
37681	2596	25	P__{1	P__{1	NNP
37681	2596	26	}	}	-RRB-
37681	2596	27	and	and	CC
37681	2596	28	_	_	NNP
37681	2596	29	P__{2	P__{2	NNP
37681	2596	30	}	}	-RRB-
37681	2596	31	are	be	VBP
37681	2596	32	both	both	DT
37681	2596	33	fixed	fix	VBN
37681	2596	34	.	.	.
37681	2597	1	Hence	hence	RB
37681	2597	2	_	_	NNP
37681	2597	3	C	C	NNP
37681	2597	4	_	_	NNP
37681	2597	5	must	must	MD
37681	2597	6	lie	lie	VB
37681	2597	7	on	on	IN
37681	2597	8	a	a	DT
37681	2597	9	semicircle	semicircle	NN
37681	2597	10	with	with	IN
37681	2597	11	_	_	NNP
37681	2597	12	P__{1}_P__{2	P__{1}_P__{2	NNP
37681	2597	13	}	}	-RRB-
37681	2597	14	as	as	IN
37681	2597	15	a	a	DT
37681	2597	16	diameter	diameter	NN
37681	2597	17	,	,	,
37681	2597	18	and	and	CC
37681	2597	19	therefore	therefore	RB
37681	2597	20	the	the	DT
37681	2597	21	locus	locus	NN
37681	2597	22	of	of	IN
37681	2597	23	a	a	DT
37681	2597	24	point	point	NN
37681	2597	25	such	such	JJ
37681	2597	26	that	that	IN
37681	2597	27	its	-PRON-	PRP$
37681	2597	28	distances	distance	NNS
37681	2597	29	from	from	IN
37681	2597	30	two	two	CD
37681	2597	31	given	give	VBN
37681	2597	32	points	point	NNS
37681	2597	33	are	be	VBP
37681	2597	34	in	in	IN
37681	2597	35	a	a	DT
37681	2597	36	given	give	VBN
37681	2597	37	ratio	ratio	NN
37681	2597	38	is	be	VBZ
37681	2597	39	a	a	DT
37681	2597	40	circle	circle	NN
37681	2597	41	.	.	.
37681	2598	1	This	this	DT
37681	2598	2	fact	fact	NN
37681	2598	3	,	,	,
37681	2598	4	Pappus	Pappus	NNP
37681	2598	5	tells	tell	VBZ
37681	2598	6	us	-PRON-	PRP
37681	2598	7	,	,	,
37681	2598	8	was	be	VBD
37681	2598	9	known	know	VBN
37681	2598	10	to	to	IN
37681	2598	11	Apollonius	Apollonius	NNP
37681	2598	12	.	.	.
37681	2599	1	At	at	IN
37681	2599	2	this	this	DT
37681	2599	3	point	point	NN
37681	2599	4	it	-PRON-	PRP
37681	2599	5	is	be	VBZ
37681	2599	6	customary	customary	JJ
37681	2599	7	to	to	TO
37681	2599	8	define	define	VB
37681	2599	9	similar	similar	JJ
37681	2599	10	polygons	polygon	NNS
37681	2599	11	as	as	RB
37681	2599	12	such	such	JJ
37681	2599	13	as	as	IN
37681	2599	14	have	have	VBP
37681	2599	15	their	-PRON-	PRP$
37681	2599	16	corresponding	corresponding	JJ
37681	2599	17	angles	angle	NNS
37681	2599	18	equal	equal	JJ
37681	2599	19	and	and	CC
37681	2599	20	their	-PRON-	PRP$
37681	2599	21	corresponding	corresponding	JJ
37681	2599	22	sides	side	NNS
37681	2599	23	proportional	proportional	JJ
37681	2599	24	.	.	.
37681	2600	1	Aristotle	Aristotle	NNP
37681	2600	2	gave	give	VBD
37681	2600	3	substantially	substantially	RB
37681	2600	4	this	this	DT
37681	2600	5	definition	definition	NN
37681	2600	6	,	,	,
37681	2600	7	saying	say	VBG
37681	2600	8	that	that	IN
37681	2600	9	such	such	JJ
37681	2600	10	figures	figure	NNS
37681	2600	11	have	have	VBP
37681	2600	12	"	"	``
37681	2600	13	their	-PRON-	PRP$
37681	2600	14	sides	side	NNS
37681	2600	15	proportional	proportional	JJ
37681	2600	16	and	and	CC
37681	2600	17	their	-PRON-	PRP$
37681	2600	18	angles	angle	NNS
37681	2600	19	equal	equal	JJ
37681	2600	20	.	.	.
37681	2600	21	"	"	''
37681	2601	1	Euclid	Euclid	NNP
37681	2601	2	improved	improve	VBD
37681	2601	3	upon	upon	IN
37681	2601	4	this	this	DT
37681	2601	5	by	by	IN
37681	2601	6	saying	say	VBG
37681	2601	7	that	that	IN
37681	2601	8	they	-PRON-	PRP
37681	2601	9	must	must	MD
37681	2601	10	"	"	``
37681	2601	11	have	have	VB
37681	2601	12	their	-PRON-	PRP$
37681	2601	13	angles	angle	NNS
37681	2601	14	severally	severally	RB
37681	2601	15	equal	equal	JJ
37681	2601	16	and	and	CC
37681	2601	17	the	the	DT
37681	2601	18	sides	side	NNS
37681	2601	19	about	about	IN
37681	2601	20	the	the	DT
37681	2601	21	equal	equal	JJ
37681	2601	22	angles	angle	NNS
37681	2601	23	proportional	proportional	JJ
37681	2601	24	.	.	.
37681	2601	25	"	"	''
37681	2602	1	Our	-PRON-	PRP$
37681	2602	2	present	present	JJ
37681	2602	3	phraseology	phraseology	NN
37681	2602	4	seems	seem	VBZ
37681	2602	5	clearer	clear	JJR
37681	2602	6	.	.	.
37681	2603	1	Instead	instead	RB
37681	2603	2	of	of	IN
37681	2603	3	"	"	``
37681	2603	4	corresponding	correspond	VBG
37681	2603	5	angles	angle	NNS
37681	2603	6	"	"	''
37681	2603	7	we	-PRON-	PRP
37681	2603	8	may	may	MD
37681	2603	9	say	say	VB
37681	2603	10	"	"	``
37681	2603	11	homologous	homologous	JJ
37681	2603	12	angles	angle	NNS
37681	2603	13	,	,	,
37681	2603	14	"	"	''
37681	2603	15	but	but	CC
37681	2603	16	there	there	EX
37681	2603	17	seems	seem	VBZ
37681	2603	18	to	to	TO
37681	2603	19	be	be	VB
37681	2603	20	no	no	DT
37681	2603	21	reason	reason	NN
37681	2603	22	for	for	IN
37681	2603	23	using	use	VBG
37681	2603	24	the	the	DT
37681	2603	25	less	less	RBR
37681	2603	26	familiar	familiar	JJ
37681	2603	27	word	word	NN
37681	2603	28	.	.	.
37681	2604	1	[	[	-LRB-
37681	2604	2	Illustration	illustration	NN
37681	2604	3	]	]	-RRB-
37681	2604	4	[	[	-LRB-
37681	2604	5	Illustration	illustration	NN
37681	2604	6	]	]	-RRB-
37681	2604	7	[	[	-LRB-
37681	2604	8	Illustration	illustration	NN
37681	2604	9	]	]	-RRB-
37681	2604	10	It	-PRON-	PRP
37681	2604	11	is	be	VBZ
37681	2604	12	more	more	RBR
37681	2604	13	general	general	JJ
37681	2604	14	to	to	TO
37681	2604	15	proceed	proceed	VB
37681	2604	16	by	by	IN
37681	2604	17	first	first	RB
37681	2604	18	considering	consider	VBG
37681	2604	19	similar	similar	JJ
37681	2604	20	figures	figure	NNS
37681	2604	21	instead	instead	RB
37681	2604	22	of	of	IN
37681	2604	23	similar	similar	JJ
37681	2604	24	polygons	polygon	NNS
37681	2604	25	,	,	,
37681	2604	26	thus	thus	RB
37681	2604	27	including	include	VBG
37681	2604	28	the	the	DT
37681	2604	29	most	most	RBS
37681	2604	30	obviously	obviously	RB
37681	2604	31	similar	similar	JJ
37681	2604	32	of	of	IN
37681	2604	33	all	all	DT
37681	2604	34	figures,--two	figures,--two	CD
37681	2604	35	circles	circle	NNS
37681	2604	36	;	;	:
37681	2604	37	but	but	CC
37681	2604	38	such	such	PDT
37681	2604	39	a	a	DT
37681	2604	40	procedure	procedure	NN
37681	2604	41	is	be	VBZ
37681	2604	42	felt	feel	VBN
37681	2604	43	to	to	TO
37681	2604	44	be	be	VB
37681	2604	45	too	too	RB
37681	2604	46	difficult	difficult	JJ
37681	2604	47	by	by	IN
37681	2604	48	many	many	JJ
37681	2604	49	teachers	teacher	NNS
37681	2604	50	.	.	.
37681	2605	1	By	by	IN
37681	2605	2	this	this	DT
37681	2605	3	plan	plan	NN
37681	2605	4	we	-PRON-	PRP
37681	2605	5	first	first	RB
37681	2605	6	define	define	VBP
37681	2605	7	similar	similar	JJ
37681	2605	8	sets	set	NNS
37681	2605	9	of	of	IN
37681	2605	10	points	point	NNS
37681	2605	11	,	,	,
37681	2605	12	_	_	NNP
37681	2605	13	A__{1	A__{1	NNP
37681	2605	14	}	}	-RRB-
37681	2605	15	,	,	,
37681	2605	16	_	_	NNP
37681	2605	17	A__{2	A__{2	NNP
37681	2605	18	}	}	-RRB-
37681	2605	19	,	,	,
37681	2605	20	_	_	NNP
37681	2605	21	A__{3	A__{3	NNP
37681	2605	22	}	}	-RRB-
37681	2605	23	,	,	,
37681	2605	24	...	...	:
37681	2605	25	,	,	,
37681	2605	26	and	and	CC
37681	2605	27	_	_	NNP
37681	2605	28	B__{1	B__{1	NNP
37681	2605	29	}	}	-RRB-
37681	2605	30	,	,	,
37681	2605	31	_	_	NNP
37681	2605	32	B__{2	B__{2	NNP
37681	2605	33	}	}	-RRB-
37681	2605	34	,	,	,
37681	2605	35	_	_	NNP
37681	2605	36	B__{3	B__{3	NNP
37681	2605	37	}	}	-RRB-
37681	2605	38	,	,	,
37681	2605	39	...	...	:
37681	2605	40	,	,	,
37681	2605	41	as	as	IN
37681	2605	42	such	such	JJ
37681	2605	43	that	that	IN
37681	2605	44	_	_	NNP
37681	2605	45	A__{1}_A__{2	A__{1}_A__{2	NNP
37681	2605	46	}	}	-RRB-
37681	2605	47	,	,	,
37681	2605	48	_	_	NNP
37681	2605	49	B__{1}_B__{2	B__{1}_B__{2	NNP
37681	2605	50	}	}	-RRB-
37681	2605	51	,	,	,
37681	2605	52	_	_	NNP
37681	2605	53	C__{1}_C__{2	C__{1}_C__{2	NNP
37681	2605	54	}	}	-RRB-
37681	2605	55	,	,	,
37681	2605	56	...	...	:
37681	2605	57	are	be	VBP
37681	2605	58	concurrent	concurrent	JJ
37681	2605	59	in	in	IN
37681	2605	60	_	_	NNP
37681	2605	61	O	O	NNP
37681	2605	62	_	_	NNP
37681	2605	63	,	,	,
37681	2605	64	and	and	CC
37681	2605	65	_	_	NNP
37681	2605	66	A__{1}_O	A__{1}_O	NNP
37681	2605	67	_	_	NNP
37681	2605	68	:	:	:
37681	2605	69	_	_	NNP
37681	2605	70	A__{2}_O	A__{2}_O	NNP
37681	2605	71	_	_	NNP
37681	2605	72	=	=	SYM
37681	2605	73	_	_	NNP
37681	2605	74	B__{1}_O	B__{1}_O	NNP
37681	2605	75	_	_	NNP
37681	2605	76	:	:	:
37681	2605	77	_	_	NNP
37681	2605	78	B__{2}_O	B__{2}_O	NNP
37681	2605	79	_	_	NNP
37681	2605	80	=	=	SYM
37681	2605	81	_	_	NNP
37681	2605	82	C__{1}_O	C__{1}_O	NNP
37681	2605	83	_	_	NNP
37681	2605	84	:	:	:
37681	2605	85	_	_	NNP
37681	2605	86	C__{2}_O	C__{2}_O	NNP
37681	2605	87	_	_	NNP
37681	2605	88	=	=	SYM
37681	2605	89	...	...	.
37681	2606	1	Here	here	RB
37681	2606	2	the	the	DT
37681	2606	3	constant	constant	JJ
37681	2606	4	ratio	ratio	NN
37681	2606	5	_	_	NNP
37681	2606	6	A__{1}_O	A__{1}_O	NNP
37681	2606	7	_	_	NNP
37681	2606	8	:	:	:
37681	2606	9	_	_	NNP
37681	2606	10	A__{2}_O	a__{2}_o	CC
37681	2606	11	_	_	NNP
37681	2606	12	is	be	VBZ
37681	2606	13	called	call	VBN
37681	2606	14	the	the	DT
37681	2606	15	_	_	NNP
37681	2606	16	ratio	ratio	NN
37681	2606	17	of	of	IN
37681	2606	18	similitude	similitude	NN
37681	2606	19	_	_	NNP
37681	2606	20	,	,	,
37681	2606	21	and	and	CC
37681	2606	22	_	_	NNP
37681	2606	23	O	O	NNP
37681	2606	24	_	_	NNP
37681	2606	25	is	be	VBZ
37681	2606	26	called	call	VBN
37681	2606	27	the	the	DT
37681	2606	28	_	_	NNP
37681	2606	29	center	center	NN
37681	2606	30	of	of	IN
37681	2606	31	similitude	similitude	NNP
37681	2606	32	_	_	NNP
37681	2606	33	.	.	.
37681	2607	1	Having	have	VBG
37681	2607	2	defined	define	VBN
37681	2607	3	similar	similar	JJ
37681	2607	4	sets	set	NNS
37681	2607	5	of	of	IN
37681	2607	6	points	point	NNS
37681	2607	7	,	,	,
37681	2607	8	we	-PRON-	PRP
37681	2607	9	then	then	RB
37681	2607	10	define	define	VBP
37681	2607	11	similar	similar	JJ
37681	2607	12	figures	figure	NNS
37681	2607	13	as	as	IN
37681	2607	14	those	those	DT
37681	2607	15	figures	figure	NNS
37681	2607	16	whose	whose	WP$
37681	2607	17	points	point	NNS
37681	2607	18	form	form	VBP
37681	2607	19	similar	similar	JJ
37681	2607	20	sets	set	NNS
37681	2607	21	.	.	.
37681	2608	1	Then	then	RB
37681	2608	2	the	the	DT
37681	2608	3	two	two	CD
37681	2608	4	circles	circle	NNS
37681	2608	5	,	,	,
37681	2608	6	the	the	DT
37681	2608	7	four	four	CD
37681	2608	8	triangles	triangle	NNS
37681	2608	9	,	,	,
37681	2608	10	and	and	CC
37681	2608	11	the	the	DT
37681	2608	12	three	three	CD
37681	2608	13	quadrilaterals	quadrilateral	NNS
37681	2608	14	respectively	respectively	RB
37681	2608	15	are	be	VBP
37681	2608	16	similar	similar	JJ
37681	2608	17	figures	figure	NNS
37681	2608	18	.	.	.
37681	2609	1	If	if	IN
37681	2609	2	the	the	DT
37681	2609	3	ratio	ratio	NN
37681	2609	4	of	of	IN
37681	2609	5	similitude	similitude	NN
37681	2609	6	is	be	VBZ
37681	2609	7	1	1	CD
37681	2609	8	,	,	,
37681	2609	9	the	the	DT
37681	2609	10	similar	similar	JJ
37681	2609	11	figures	figure	NNS
37681	2609	12	become	become	VBP
37681	2609	13	symmetric	symmetric	JJ
37681	2609	14	figures	figure	NNS
37681	2609	15	,	,	,
37681	2609	16	and	and	CC
37681	2609	17	they	-PRON-	PRP
37681	2609	18	are	be	VBP
37681	2609	19	therefore	therefore	RB
37681	2609	20	congruent	congruent	JJ
37681	2609	21	.	.	.
37681	2610	1	All	all	DT
37681	2610	2	of	of	IN
37681	2610	3	the	the	DT
37681	2610	4	propositions	proposition	NNS
37681	2610	5	relating	relate	VBG
37681	2610	6	to	to	IN
37681	2610	7	similar	similar	JJ
37681	2610	8	figures	figure	NNS
37681	2610	9	can	can	MD
37681	2610	10	be	be	VB
37681	2610	11	proved	prove	VBN
37681	2610	12	from	from	IN
37681	2610	13	this	this	DT
37681	2610	14	definition	definition	NN
37681	2610	15	,	,	,
37681	2610	16	but	but	CC
37681	2610	17	it	-PRON-	PRP
37681	2610	18	is	be	VBZ
37681	2610	19	customary	customary	JJ
37681	2610	20	to	to	TO
37681	2610	21	use	use	VB
37681	2610	22	the	the	DT
37681	2610	23	Greek	Greek	NNP
37681	2610	24	one	one	NN
37681	2610	25	instead	instead	RB
37681	2610	26	.	.	.
37681	2611	1	[	[	-LRB-
37681	2611	2	Illustration	illustration	NN
37681	2611	3	]	]	-RRB-
37681	2611	4	Among	among	IN
37681	2611	5	the	the	DT
37681	2611	6	interesting	interesting	JJ
37681	2611	7	applications	application	NNS
37681	2611	8	of	of	IN
37681	2611	9	similarity	similarity	NN
37681	2611	10	is	be	VBZ
37681	2611	11	the	the	DT
37681	2611	12	case	case	NN
37681	2611	13	of	of	IN
37681	2611	14	a	a	DT
37681	2611	15	shadow	shadow	NN
37681	2611	16	,	,	,
37681	2611	17	as	as	IN
37681	2611	18	here	here	RB
37681	2611	19	shown	show	VBN
37681	2611	20	,	,	,
37681	2611	21	where	where	WRB
37681	2611	22	the	the	DT
37681	2611	23	light	light	NN
37681	2611	24	is	be	VBZ
37681	2611	25	the	the	DT
37681	2611	26	center	center	NN
37681	2611	27	of	of	IN
37681	2611	28	similitude	similitude	NN
37681	2611	29	.	.	.
37681	2612	1	It	-PRON-	PRP
37681	2612	2	is	be	VBZ
37681	2612	3	also	also	RB
37681	2612	4	well	well	RB
37681	2612	5	known	known	JJ
37681	2612	6	to	to	IN
37681	2612	7	most	most	RBS
37681	2612	8	high	high	JJ
37681	2612	9	school	school	NN
37681	2612	10	pupils	pupil	NNS
37681	2612	11	that	that	IN
37681	2612	12	in	in	IN
37681	2612	13	a	a	DT
37681	2612	14	camera	camera	NN
37681	2612	15	the	the	DT
37681	2612	16	lens	lens	NN
37681	2612	17	reverses	reverse	VBZ
37681	2612	18	the	the	DT
37681	2612	19	image	image	NN
37681	2612	20	.	.	.
37681	2613	1	The	the	DT
37681	2613	2	mathematical	mathematical	JJ
37681	2613	3	arrangement	arrangement	NN
37681	2613	4	is	be	VBZ
37681	2613	5	here	here	RB
37681	2613	6	shown	show	VBN
37681	2613	7	,	,	,
37681	2613	8	the	the	DT
37681	2613	9	lens	lens	NN
37681	2613	10	inclosing	inclose	VBG
37681	2613	11	the	the	DT
37681	2613	12	center	center	NN
37681	2613	13	of	of	IN
37681	2613	14	similitude	similitude	NN
37681	2613	15	.	.	.
37681	2614	1	The	the	DT
37681	2614	2	proposition	proposition	NN
37681	2614	3	may	may	MD
37681	2614	4	also	also	RB
37681	2614	5	be	be	VB
37681	2614	6	applied	apply	VBN
37681	2614	7	to	to	IN
37681	2614	8	the	the	DT
37681	2614	9	enlargement	enlargement	NN
37681	2614	10	of	of	IN
37681	2614	11	maps	map	NNS
37681	2614	12	and	and	CC
37681	2614	13	working	work	VBG
37681	2614	14	drawings	drawing	NNS
37681	2614	15	.	.	.
37681	2615	1	The	the	DT
37681	2615	2	propositions	proposition	NNS
37681	2615	3	concerning	concern	VBG
37681	2615	4	similar	similar	JJ
37681	2615	5	figures	figure	NNS
37681	2615	6	have	have	VBP
37681	2615	7	no	no	RB
37681	2615	8	particularly	particularly	RB
37681	2615	9	interesting	interesting	JJ
37681	2615	10	history	history	NN
37681	2615	11	,	,	,
37681	2615	12	nor	nor	CC
37681	2615	13	do	do	VBP
37681	2615	14	they	-PRON-	PRP
37681	2615	15	present	present	VB
37681	2615	16	any	any	DT
37681	2615	17	difficulties	difficulty	NNS
37681	2615	18	that	that	WDT
37681	2615	19	call	call	VBP
37681	2615	20	for	for	IN
37681	2615	21	discussion	discussion	NN
37681	2615	22	.	.	.
37681	2616	1	In	in	IN
37681	2616	2	schools	school	NNS
37681	2616	3	where	where	WRB
37681	2616	4	there	there	EX
37681	2616	5	is	be	VBZ
37681	2616	6	a	a	DT
37681	2616	7	little	little	JJ
37681	2616	8	time	time	NN
37681	2616	9	for	for	IN
37681	2616	10	trigonometry	trigonometry	NN
37681	2616	11	,	,	,
37681	2616	12	teachers	teacher	NNS
37681	2616	13	sometimes	sometimes	RB
37681	2616	14	find	find	VBP
37681	2616	15	it	-PRON-	PRP
37681	2616	16	helpful	helpful	JJ
37681	2616	17	to	to	TO
37681	2616	18	begin	begin	VB
37681	2616	19	such	such	JJ
37681	2616	20	work	work	NN
37681	2616	21	at	at	IN
37681	2616	22	this	this	DT
37681	2616	23	time	time	NN
37681	2616	24	,	,	,
37681	2616	25	since	since	IN
37681	2616	26	all	all	DT
37681	2616	27	of	of	IN
37681	2616	28	the	the	DT
37681	2616	29	trigonometric	trigonometric	JJ
37681	2616	30	functions	function	NNS
37681	2616	31	depend	depend	VBP
37681	2616	32	upon	upon	IN
37681	2616	33	the	the	DT
37681	2616	34	properties	property	NNS
37681	2616	35	of	of	IN
37681	2616	36	similar	similar	JJ
37681	2616	37	triangles	triangle	NNS
37681	2616	38	,	,	,
37681	2616	39	and	and	CC
37681	2616	40	a	a	DT
37681	2616	41	brief	brief	JJ
37681	2616	42	explanation	explanation	NN
37681	2616	43	of	of	IN
37681	2616	44	the	the	DT
37681	2616	45	simplest	simple	JJS
37681	2616	46	trigonometric	trigonometric	JJ
37681	2616	47	functions	function	NNS
37681	2616	48	may	may	MD
37681	2616	49	add	add	VB
37681	2616	50	a	a	DT
37681	2616	51	little	little	JJ
37681	2616	52	interest	interest	NN
37681	2616	53	to	to	IN
37681	2616	54	the	the	DT
37681	2616	55	work	work	NN
37681	2616	56	.	.	.
37681	2617	1	In	in	IN
37681	2617	2	the	the	DT
37681	2617	3	present	present	JJ
37681	2617	4	state	state	NN
37681	2617	5	of	of	IN
37681	2617	6	our	-PRON-	PRP$
37681	2617	7	curriculum	curriculum	NN
37681	2617	8	we	-PRON-	PRP
37681	2617	9	can	can	MD
37681	2617	10	not	not	RB
37681	2617	11	do	do	VB
37681	2617	12	more	more	JJR
37681	2617	13	than	than	IN
37681	2617	14	mention	mention	VB
37681	2617	15	the	the	DT
37681	2617	16	matter	matter	NN
37681	2617	17	as	as	IN
37681	2617	18	a	a	DT
37681	2617	19	topic	topic	NN
37681	2617	20	of	of	IN
37681	2617	21	general	general	JJ
37681	2617	22	interest	interest	NN
37681	2617	23	in	in	IN
37681	2617	24	this	this	DT
37681	2617	25	connection	connection	NN
37681	2617	26	.	.	.
37681	2618	1	It	-PRON-	PRP
37681	2618	2	is	be	VBZ
37681	2618	3	a	a	DT
37681	2618	4	mistaken	mistaken	JJ
37681	2618	5	idea	idea	NN
37681	2618	6	that	that	IN
37681	2618	7	geometry	geometry	NN
37681	2618	8	is	be	VBZ
37681	2618	9	a	a	DT
37681	2618	10	prerequisite	prerequisite	NN
37681	2618	11	to	to	IN
37681	2618	12	trigonometry	trigonometry	NN
37681	2618	13	.	.	.
37681	2619	1	We	-PRON-	PRP
37681	2619	2	can	can	MD
37681	2619	3	get	get	VB
37681	2619	4	along	along	RP
37681	2619	5	very	very	RB
37681	2619	6	well	well	RB
37681	2619	7	in	in	IN
37681	2619	8	teaching	teach	VBG
37681	2619	9	trigonometry	trigonometry	NN
37681	2619	10	if	if	IN
37681	2619	11	we	-PRON-	PRP
37681	2619	12	have	have	VBP
37681	2619	13	three	three	CD
37681	2619	14	propositions	proposition	NNS
37681	2619	15	:	:	:
37681	2619	16	(	(	-LRB-
37681	2619	17	1	1	LS
37681	2619	18	)	)	-RRB-
37681	2619	19	the	the	DT
37681	2619	20	one	one	NN
37681	2619	21	about	about	IN
37681	2619	22	the	the	DT
37681	2619	23	sum	sum	NN
37681	2619	24	of	of	IN
37681	2619	25	the	the	DT
37681	2619	26	angles	angle	NNS
37681	2619	27	of	of	IN
37681	2619	28	a	a	DT
37681	2619	29	triangle	triangle	NN
37681	2619	30	;	;	:
37681	2619	31	(	(	-LRB-
37681	2619	32	2	2	LS
37681	2619	33	)	)	-RRB-
37681	2619	34	the	the	DT
37681	2619	35	Pythagorean	Pythagorean	NNP
37681	2619	36	Theorem	Theorem	NNP
37681	2619	37	;	;	:
37681	2619	38	(	(	-LRB-
37681	2619	39	3	3	LS
37681	2619	40	)	)	-RRB-
37681	2619	41	the	the	DT
37681	2619	42	one	one	NN
37681	2619	43	that	that	WDT
37681	2619	44	asserts	assert	VBZ
37681	2619	45	that	that	IN
37681	2619	46	two	two	CD
37681	2619	47	right	right	JJ
37681	2619	48	triangles	triangle	NNS
37681	2619	49	are	be	VBP
37681	2619	50	similar	similar	JJ
37681	2619	51	if	if	IN
37681	2619	52	an	an	DT
37681	2619	53	acute	acute	JJ
37681	2619	54	angle	angle	NN
37681	2619	55	of	of	IN
37681	2619	56	the	the	DT
37681	2619	57	one	one	NN
37681	2619	58	equals	equal	VBZ
37681	2619	59	an	an	DT
37681	2619	60	acute	acute	JJ
37681	2619	61	angle	angle	NN
37681	2619	62	of	of	IN
37681	2619	63	the	the	DT
37681	2619	64	other	other	JJ
37681	2619	65	.	.	.
37681	2620	1	For	for	IN
37681	2620	2	teachers	teacher	NNS
37681	2620	3	who	who	WP
37681	2620	4	may	may	MD
37681	2620	5	care	care	VB
37681	2620	6	to	to	TO
37681	2620	7	make	make	VB
37681	2620	8	a	a	DT
37681	2620	9	little	little	JJ
37681	2620	10	digression	digression	NN
37681	2620	11	at	at	IN
37681	2620	12	this	this	DT
37681	2620	13	time	time	NN
37681	2620	14	,	,	,
37681	2620	15	the	the	DT
37681	2620	16	following	follow	VBG
37681	2620	17	brief	brief	JJ
37681	2620	18	statement	statement	NN
37681	2620	19	of	of	IN
37681	2620	20	a	a	DT
37681	2620	21	few	few	JJ
37681	2620	22	of	of	IN
37681	2620	23	the	the	DT
37681	2620	24	facts	fact	NNS
37681	2620	25	of	of	IN
37681	2620	26	trigonometry	trigonometry	NN
37681	2620	27	may	may	MD
37681	2620	28	be	be	VB
37681	2620	29	of	of	IN
37681	2620	30	value	value	NN
37681	2620	31	:	:	:
37681	2620	32	[	[	-LRB-
37681	2620	33	Illustration	illustration	NN
37681	2620	34	]	]	-RRB-
37681	2620	35	In	in	IN
37681	2620	36	the	the	DT
37681	2620	37	right	right	JJ
37681	2620	38	triangle	triangle	NN
37681	2620	39	_	_	NNP
37681	2620	40	OAB	oab	UH
37681	2620	41	_	_	NNP
37681	2620	42	we	-PRON-	PRP
37681	2620	43	shall	shall	MD
37681	2620	44	let	let	VB
37681	2620	45	_	_	NNP
37681	2620	46	AB	AB	NNP
37681	2620	47	_	_	NNP
37681	2620	48	=	=	SYM
37681	2620	49	_	_	NNP
37681	2620	50	y	y	NNP
37681	2620	51	_	_	NNP
37681	2620	52	,	,	,
37681	2620	53	_	_	NNP
37681	2620	54	OA	OA	NNP
37681	2620	55	_	_	NNP
37681	2620	56	=	=	SYM
37681	2620	57	_	_	NNP
37681	2620	58	x	x	NNP
37681	2620	59	_	_	NNP
37681	2620	60	,	,	,
37681	2620	61	_	_	NNP
37681	2620	62	OB	OB	NNP
37681	2620	63	_	_	NNP
37681	2620	64	=	=	SYM
37681	2620	65	_	_	NNP
37681	2620	66	r	r	NNP
37681	2620	67	_	_	NNP
37681	2620	68	,	,	,
37681	2620	69	thus	thus	RB
37681	2620	70	adopting	adopt	VBG
37681	2620	71	the	the	DT
37681	2620	72	letters	letter	NNS
37681	2620	73	of	of	IN
37681	2620	74	higher	high	JJR
37681	2620	75	mathematics	mathematic	NNS
37681	2620	76	.	.	.
37681	2621	1	Then	then	RB
37681	2621	2	,	,	,
37681	2621	3	so	so	RB
37681	2621	4	long	long	RB
37681	2621	5	as	as	IN
37681	2621	6	[	[	-LRB-
37681	2621	7	L]_O	L]_O	NNP
37681	2621	8	_	_	NNP
37681	2621	9	remains	remain	VBZ
37681	2621	10	the	the	DT
37681	2621	11	same	same	JJ
37681	2621	12	,	,	,
37681	2621	13	such	such	JJ
37681	2621	14	ratios	ratio	NNS
37681	2621	15	as	as	IN
37681	2621	16	_	_	NNP
37681	2621	17	y_/_x	y_/_x	NNP
37681	2621	18	_	_	NNP
37681	2621	19	,	,	,
37681	2621	20	_	_	NNP
37681	2621	21	y_/_r	y_/_r	NNP
37681	2621	22	_	_	NNP
37681	2621	23	,	,	,
37681	2621	24	etc	etc	FW
37681	2621	25	.	.	.
37681	2621	26	,	,	,
37681	2621	27	will	will	MD
37681	2621	28	remain	remain	VB
37681	2621	29	the	the	DT
37681	2621	30	same	same	JJ
37681	2621	31	,	,	,
37681	2621	32	whatever	whatever	WDT
37681	2621	33	is	be	VBZ
37681	2621	34	the	the	DT
37681	2621	35	size	size	NN
37681	2621	36	of	of	IN
37681	2621	37	the	the	DT
37681	2621	38	triangle	triangle	NN
37681	2621	39	.	.	.
37681	2622	1	Some	some	DT
37681	2622	2	of	of	IN
37681	2622	3	these	these	DT
37681	2622	4	ratios	ratio	NNS
37681	2622	5	have	have	VBP
37681	2622	6	special	special	JJ
37681	2622	7	names	name	NNS
37681	2622	8	.	.	.
37681	2623	1	For	for	IN
37681	2623	2	example	example	NN
37681	2623	3	,	,	,
37681	2623	4	we	-PRON-	PRP
37681	2623	5	call	call	VBP
37681	2623	6	_	_	NNP
37681	2623	7	y_/_r	y_/_r	NNP
37681	2623	8	_	_	NNP
37681	2623	9	the	the	DT
37681	2623	10	_	_	NNP
37681	2623	11	sine	sine	NN
37681	2623	12	_	_	NNP
37681	2623	13	of	of	IN
37681	2623	14	_	_	NNP
37681	2623	15	O	O	NNP
37681	2623	16	_	_	NNP
37681	2623	17	,	,	,
37681	2623	18	and	and	CC
37681	2623	19	we	-PRON-	PRP
37681	2623	20	write	write	VBP
37681	2623	21	sin	sin	NN
37681	2623	22	_	_	NNP
37681	2623	23	O	O	NNP
37681	2623	24	_	_	NNP
37681	2623	25	=	=	SYM
37681	2623	26	_	_	NNP
37681	2623	27	y_/_r	y_/_r	NNP
37681	2623	28	_	_	NNP
37681	2623	29	;	;	:
37681	2623	30	_	_	NNP
37681	2623	31	x_/_r	x_/_r	NNP
37681	2623	32	_	_	NNP
37681	2623	33	the	the	DT
37681	2623	34	_	_	NNP
37681	2623	35	cosine	cosine	NN
37681	2623	36	_	_	NNP
37681	2623	37	of	of	IN
37681	2623	38	_	_	NNP
37681	2623	39	O	O	NNP
37681	2623	40	_	_	NNP
37681	2623	41	,	,	,
37681	2623	42	and	and	CC
37681	2623	43	we	-PRON-	PRP
37681	2623	44	write	write	VBP
37681	2623	45	cos	cos	NNP
37681	2623	46	_	_	NNP
37681	2623	47	O	O	NNP
37681	2623	48	_	_	NNP
37681	2623	49	=	=	SYM
37681	2623	50	_	_	NNP
37681	2623	51	x_/_r	x_/_r	NNP
37681	2623	52	_	_	NNP
37681	2623	53	;	;	:
37681	2623	54	_	_	NNP
37681	2623	55	y_/_x	y_/_x	NNP
37681	2623	56	_	_	NNP
37681	2623	57	the	the	DT
37681	2623	58	_	_	NNP
37681	2623	59	tangent	tangent	NN
37681	2623	60	_	_	NNP
37681	2623	61	of	of	IN
37681	2623	62	_	_	NNP
37681	2623	63	O	O	NNP
37681	2623	64	_	_	NNP
37681	2623	65	,	,	,
37681	2623	66	and	and	CC
37681	2623	67	we	-PRON-	PRP
37681	2623	68	write	write	VBP
37681	2623	69	tan	tan	NNP
37681	2623	70	_	_	NNP
37681	2623	71	O	O	NNP
37681	2623	72	_	_	NNP
37681	2623	73	=	=	SYM
37681	2623	74	_	_	NNP
37681	2623	75	y_/_x	y_/_x	NNP
37681	2623	76	_	_	NNP
37681	2623	77	.	.	.
37681	2624	1	Now	now	RB
37681	2624	2	because	because	IN
37681	2624	3	sin	sin	NN
37681	2624	4	_	_	NNP
37681	2624	5	O	O	NNP
37681	2624	6	_	_	NNP
37681	2624	7	=	=	SYM
37681	2624	8	_	_	NNP
37681	2624	9	y_/_r	y_/_r	NNP
37681	2624	10	_	_	NNP
37681	2624	11	,	,	,
37681	2624	12	therefore	therefore	RB
37681	2624	13	_	_	NNP
37681	2624	14	r	r	NNP
37681	2624	15	_	_	NNP
37681	2624	16	sin	sin	NN
37681	2624	17	_	_	NNP
37681	2624	18	O	O	NNP
37681	2624	19	_	_	NNP
37681	2624	20	=	=	SYM
37681	2624	21	_	_	NNP
37681	2624	22	y	y	NNP
37681	2624	23	_	_	NNP
37681	2624	24	;	;	:
37681	2624	25	and	and	CC
37681	2624	26	because	because	IN
37681	2624	27	cos	cos	NNP
37681	2624	28	_	_	NNP
37681	2624	29	O	O	NNP
37681	2624	30	_	_	NNP
37681	2624	31	=	=	SYM
37681	2624	32	_	_	NNP
37681	2624	33	x_/_r	x_/_r	NNP
37681	2624	34	_	_	NNP
37681	2624	35	,	,	,
37681	2624	36	therefore	therefore	RB
37681	2624	37	_	_	NNP
37681	2624	38	r	r	NNP
37681	2624	39	_	_	NNP
37681	2624	40	cos	cos	NNP
37681	2624	41	_	_	NNP
37681	2624	42	O	O	NNP
37681	2624	43	_	_	NNP
37681	2624	44	=	=	SYM
37681	2624	45	_	_	NNP
37681	2624	46	x	x	NNP
37681	2624	47	_	_	NNP
37681	2624	48	;	;	:
37681	2624	49	and	and	CC
37681	2624	50	because	because	IN
37681	2624	51	tan	tan	NNP
37681	2624	52	_	_	NNP
37681	2624	53	O	O	NNP
37681	2624	54	_	_	NNP
37681	2624	55	=	=	SYM
37681	2624	56	_	_	NNP
37681	2624	57	y_/_x	y_/_x	NNP
37681	2624	58	_	_	NNP
37681	2624	59	,	,	,
37681	2624	60	therefore	therefore	RB
37681	2624	61	_	_	NNP
37681	2624	62	x	x	NNP
37681	2624	63	_	_	NNP
37681	2624	64	tan	tan	NN
37681	2624	65	_	_	NNP
37681	2624	66	O	O	NNP
37681	2624	67	_	_	NNP
37681	2624	68	=	=	SYM
37681	2624	69	_	_	NNP
37681	2624	70	y	y	NNP
37681	2624	71	_	_	NNP
37681	2624	72	.	.	.
37681	2625	1	Hence	hence	RB
37681	2625	2	,	,	,
37681	2625	3	if	if	IN
37681	2625	4	we	-PRON-	PRP
37681	2625	5	knew	know	VBD
37681	2625	6	the	the	DT
37681	2625	7	values	value	NNS
37681	2625	8	of	of	IN
37681	2625	9	sin	sin	NN
37681	2625	10	_	_	NNP
37681	2625	11	O	O	NNP
37681	2625	12	_	_	NNP
37681	2625	13	,	,	,
37681	2625	14	cos	cos	NNP
37681	2625	15	_	_	NNP
37681	2625	16	O	O	NNP
37681	2625	17	_	_	NNP
37681	2625	18	,	,	,
37681	2625	19	and	and	CC
37681	2625	20	tan	tan	NNP
37681	2625	21	_	_	NNP
37681	2625	22	O	O	NNP
37681	2625	23	_	_	NNP
37681	2625	24	for	for	IN
37681	2625	25	the	the	DT
37681	2625	26	various	various	JJ
37681	2625	27	angles	angle	NNS
37681	2625	28	,	,	,
37681	2625	29	we	-PRON-	PRP
37681	2625	30	could	could	MD
37681	2625	31	find	find	VB
37681	2625	32	_	_	NNP
37681	2625	33	x	x	NNP
37681	2625	34	_	_	NNP
37681	2625	35	,	,	,
37681	2625	36	_	_	NNP
37681	2625	37	y	y	NNP
37681	2625	38	_	_	NNP
37681	2625	39	,	,	,
37681	2625	40	or	or	CC
37681	2625	41	_	_	NNP
37681	2625	42	r	r	NNP
37681	2625	43	_	_	NNP
37681	2625	44	if	if	IN
37681	2625	45	we	-PRON-	PRP
37681	2625	46	knew	know	VBD
37681	2625	47	any	any	DT
37681	2625	48	one	one	CD
37681	2625	49	of	of	IN
37681	2625	50	them	-PRON-	PRP
37681	2625	51	.	.	.
37681	2626	1	Now	now	RB
37681	2626	2	the	the	DT
37681	2626	3	values	value	NNS
37681	2626	4	of	of	IN
37681	2626	5	the	the	DT
37681	2626	6	sine	sine	NN
37681	2626	7	,	,	,
37681	2626	8	cosine	cosine	NN
37681	2626	9	,	,	,
37681	2626	10	and	and	CC
37681	2626	11	tangent	tangent	NN
37681	2626	12	(	(	-LRB-
37681	2626	13	_	_	NNP
37681	2626	14	functions	function	NNS
37681	2626	15	_	_	NNP
37681	2626	16	of	of	IN
37681	2626	17	the	the	DT
37681	2626	18	angles	angle	NNS
37681	2626	19	,	,	,
37681	2626	20	as	as	IN
37681	2626	21	they	-PRON-	PRP
37681	2626	22	are	be	VBP
37681	2626	23	called	call	VBN
37681	2626	24	)	)	-RRB-
37681	2626	25	have	have	VBP
37681	2626	26	been	be	VBN
37681	2626	27	computed	compute	VBN
37681	2626	28	for	for	IN
37681	2626	29	the	the	DT
37681	2626	30	various	various	JJ
37681	2626	31	angles	angle	NNS
37681	2626	32	,	,	,
37681	2626	33	and	and	CC
37681	2626	34	some	some	DT
37681	2626	35	interest	interest	NN
37681	2626	36	may	may	MD
37681	2626	37	be	be	VB
37681	2626	38	developed	develop	VBN
37681	2626	39	by	by	IN
37681	2626	40	obtaining	obtain	VBG
37681	2626	41	them	-PRON-	PRP
37681	2626	42	by	by	IN
37681	2626	43	actual	actual	JJ
37681	2626	44	measurement	measurement	NN
37681	2626	45	,	,	,
37681	2626	46	using	use	VBG
37681	2626	47	the	the	DT
37681	2626	48	protractor	protractor	NN
37681	2626	49	and	and	CC
37681	2626	50	squared	squared	JJ
37681	2626	51	paper	paper	NN
37681	2626	52	.	.	.
37681	2627	1	Some	some	DT
37681	2627	2	of	of	IN
37681	2627	3	those	those	DT
37681	2627	4	needed	need	VBN
37681	2627	5	for	for	IN
37681	2627	6	such	such	JJ
37681	2627	7	angles	angle	NNS
37681	2627	8	as	as	IN
37681	2627	9	a	a	DT
37681	2627	10	pupil	pupil	NN
37681	2627	11	in	in	IN
37681	2627	12	geometry	geometry	NN
37681	2627	13	is	be	VBZ
37681	2627	14	likely	likely	JJ
37681	2627	15	to	to	TO
37681	2627	16	use	use	VB
37681	2627	17	are	be	VBP
37681	2627	18	as	as	IN
37681	2627	19	follows	follow	VBZ
37681	2627	20	:	:	:
37681	2627	21	=	=	LS
37681	2627	22	=	=	NFP
37681	2627	23	=	=	SYM
37681	2627	24	=	=	SYM
37681	2627	25	=	=	SYM
37681	2627	26	=	=	SYM
37681	2627	27	=	=	SYM
37681	2627	28	=	=	SYM
37681	2627	29	=	=	SYM
37681	2627	30	=	=	SYM
37681	2627	31	=	=	SYM
37681	2627	32	=	=	SYM
37681	2627	33	=	=	SYM
37681	2627	34	=	=	SYM
37681	2627	35	=	=	SYM
37681	2627	36	=	=	SYM
37681	2627	37	=	=	SYM
37681	2627	38	=	=	SYM
37681	2627	39	=	=	SYM
37681	2627	40	=	=	SYM
37681	2627	41	=	=	SYM
37681	2627	42	=	=	SYM
37681	2627	43	=	=	SYM
37681	2627	44	=	=	SYM
37681	2627	45	=	=	SYM
37681	2627	46	=	=	SYM
37681	2627	47	=	=	SYM
37681	2627	48	=	=	SYM
37681	2627	49	=	=	SYM
37681	2627	50	=	=	SYM
37681	2627	51	=	=	SYM
37681	2627	52	=	=	SYM
37681	2627	53	=	=	SYM
37681	2627	54	=	=	SYM
37681	2627	55	=	=	SYM
37681	2627	56	=	=	SYM
37681	2627	57	=	=	SYM
37681	2627	58	=	=	SYM
37681	2627	59	=	=	SYM
37681	2627	60	=	=	SYM
37681	2627	61	=	=	SYM
37681	2627	62	=	=	SYM
37681	2627	63	=	=	SYM
37681	2627	64	=	=	SYM
37681	2627	65	=	=	SYM
37681	2627	66	=	=	SYM
37681	2627	67	=	=	SYM
37681	2627	68	=	=	SYM
37681	2627	69	=	=	SYM
37681	2627	70	=	=	SYM
37681	2627	71	=	=	SYM
37681	2627	72	=	=	SYM
37681	2627	73	=	=	SYM
37681	2627	74	=	=	SYM
37681	2627	75	=	=	SYM
37681	2627	76	=	=	SYM
37681	2627	77	=	=	SYM
37681	2627	78	=	=	SYM
37681	2627	79	=	=	SYM
37681	2627	80	=	=	SYM
37681	2627	81	ANGLE	ANGLE	NNP
37681	2627	82	|	|	NNP
37681	2627	83	SINE	SINE	NNP
37681	2627	84	|COSINE|TANGENT||	|cosine|tangent||	JJ
37681	2627	85	ANGLE	ANGLE	NNP
37681	2627	86	|	|	CD
37681	2627	87	SINE	SINE	NNP
37681	2627	88	|COSINE|TANGENT	|cosine|tangent	JJ
37681	2627	89	------+------+------+-------++-------+------+------+--------	------+------+------+-------++-------+------+------+--------	:
37681	2627	90	5	5	CD
37681	2627	91	°	°	,
37681	2627	92	|	|	CD
37681	2627	93	.087	.087	CD
37681	2627	94	|	|	CD
37681	2627	95	.996	.996	CD
37681	2627	96	|	|	CD
37681	2627	97	.087	.087	CD
37681	2627	98	||	||	$
37681	2627	99	50	50	CD
37681	2627	100	°	°	,
37681	2627	101	|	|	CD
37681	2627	102	.766	.766	CD
37681	2627	103	|	|	CD
37681	2627	104	.643	.643	CD
37681	2627	105	|	|	CD
37681	2627	106	1.192	1.192	CD
37681	2627	107	------+------+------+-------++-------+------+------+--------	------+------+------+-------++-------+------+------+--------	SYM
37681	2627	108	10	10	CD
37681	2627	109	°	°	,
37681	2627	110	|	|	CD
37681	2627	111	.174	.174	CD
37681	2627	112	|	|	CD
37681	2627	113	.985	.985	CD
37681	2627	114	|	|	CD
37681	2627	115	.176	.176	CD
37681	2627	116	||	||	$
37681	2627	117	55	55	CD
37681	2627	118	°	°	,
37681	2627	119	|	|	CD
37681	2627	120	.819	.819	CD
37681	2627	121	|	|	CD
37681	2627	122	.574	.574	CD
37681	2627	123	|	|	CD
37681	2627	124	1.428	1.428	CD
37681	2627	125	------+------+------+-------++-------+------+------+--------	------+------+------+-------++-------+------+------+--------	CD
37681	2627	126	15	15	CD
37681	2627	127	°	°	,
37681	2627	128	|	|	CD
37681	2627	129	.259	.259	CD
37681	2627	130	|	|	CD
37681	2627	131	.966	.966	CD
37681	2627	132	|	|	CD
37681	2627	133	.268	.268	CD
37681	2627	134	||	||	NNP
37681	2627	135	60	60	CD
37681	2627	136	°	°	,
37681	2627	137	|	|	CD
37681	2627	138	.866	.866	CD
37681	2627	139	|	|	CD
37681	2627	140	.500	.500	CD
37681	2627	141	|	|	CD
37681	2627	142	1.732	1.732	CD
37681	2627	143	------+------+------+-------++-------+------+------+--------	------+------+------+-------++-------+------+------+--------	NFP
37681	2627	144	20	20	CD
37681	2627	145	°	°	,
37681	2627	146	|	|	CD
37681	2627	147	.342	.342	CD
37681	2627	148	|	|	CD
37681	2627	149	.940	.940	CD
37681	2627	150	|	|	CD
37681	2627	151	.364	.364	CD
37681	2627	152	||	||	NNP
37681	2627	153	65	65	CD
37681	2627	154	°	°	,
37681	2627	155	|	|	NNP
37681	2627	156	.906	.906	CD
37681	2627	157	|	|	CD
37681	2627	158	.423	.423	CD
37681	2627	159	|	|	CD
37681	2627	160	2.145	2.145	CD
37681	2627	161	------+------+------+-------++-------+------+------+--------	------+------+------+-------++-------+------+------+--------	SYM
37681	2627	162	25	25	CD
37681	2627	163	°	°	,
37681	2627	164	|	|	CD
37681	2627	165	.423	.423	CD
37681	2627	166	|	|	NNP
37681	2627	167	.906	.906	CD
37681	2627	168	|	|	CD
37681	2627	169	.466	.466	CD
37681	2627	170	||	||	NNP
37681	2627	171	70	70	CD
37681	2627	172	°	°	,
37681	2627	173	|	|	CD
37681	2627	174	.940	.940	CD
37681	2627	175	|	|	CD
37681	2627	176	.342	.342	CD
37681	2627	177	|	|	CD
37681	2627	178	2.748	2.748	CD
37681	2627	179	------+------+------+-------++-------+------+------+--------	------+------+------+-------++-------+------+------+--------	SYM
37681	2627	180	30	30	CD
37681	2627	181	°	°	,
37681	2627	182	|	|	CD
37681	2627	183	.500	.500	CD
37681	2627	184	|	|	CD
37681	2627	185	.866	.866	CD
37681	2627	186	|	|	CD
37681	2627	187	.577	.577	CD
37681	2627	188	||	||	NNP
37681	2627	189	75	75	CD
37681	2627	190	°	°	,
37681	2627	191	|	|	CD
37681	2627	192	.966	.966	CD
37681	2627	193	|	|	CD
37681	2627	194	.259	.259	CD
37681	2627	195	|	|	CD
37681	2627	196	3.732	3.732	CD
37681	2627	197	------+------+------+-------++-------+------+------+--------	------+------+------+-------++-------+------+------+--------	NFP
37681	2627	198	35	35	CD
37681	2627	199	°	°	,
37681	2627	200	|	|	CD
37681	2627	201	.574	.574	CD
37681	2627	202	|	|	CD
37681	2627	203	.819	.819	CD
37681	2627	204	|	|	CD
37681	2627	205	.700	.700	CD
37681	2627	206	||	||	CD
37681	2627	207	80	80	CD
37681	2627	208	°	°	,
37681	2627	209	|	|	CD
37681	2627	210	.985	.985	CD
37681	2627	211	|	|	CD
37681	2627	212	.174	.174	CD
37681	2627	213	|	|	CD
37681	2627	214	5.671	5.671	CD
37681	2627	215	------+------+------+-------++-------+------+------+--------	------+------+------+-------++-------+------+------+--------	CD
37681	2627	216	40	40	CD
37681	2627	217	°	°	,
37681	2627	218	|	|	CD
37681	2627	219	.643	.643	CD
37681	2627	220	|	|	CD
37681	2627	221	.766	.766	CD
37681	2627	222	|	|	CD
37681	2627	223	.839	.839	CD
37681	2627	224	||	||	CD
37681	2627	225	85	85	CD
37681	2627	226	°	°	,
37681	2627	227	|	|	CD
37681	2627	228	.996	.996	CD
37681	2627	229	|	|	CD
37681	2627	230	.087	.087	CD
37681	2627	231	|11.430	|11.430	CD
37681	2627	232	------+------+------+-------++-------+------+------+--------	------+------+------+-------++-------+------+------+--------	NFP
37681	2627	233	45	45	CD
37681	2627	234	°	°	,
37681	2627	235	|	|	CD
37681	2627	236	.707	.707	CD
37681	2627	237	|	|	CD
37681	2627	238	.707	.707	CD
37681	2627	239	|	|	CD
37681	2627	240	1.000	1.000	CD
37681	2627	241	||	||	NNP
37681	2627	242	90	90	CD
37681	2627	243	°	°	,
37681	2627	244	|	|	CD
37681	2627	245	1.00	1.00	CD
37681	2627	246	|	|	CD
37681	2627	247	.000	.000	CD
37681	2627	248	|[infinity	|[infinity	NNS
37681	2627	249	]	]	-RRB-
37681	2627	250	=	=	NFP
37681	2627	251	=	=	NFP
37681	2627	252	=	=	SYM
37681	2627	253	=	=	SYM
37681	2627	254	=	=	SYM
37681	2627	255	=	=	SYM
37681	2627	256	=	=	SYM
37681	2627	257	=	=	SYM
37681	2627	258	=	=	SYM
37681	2627	259	=	=	SYM
37681	2627	260	=	=	SYM
37681	2627	261	=	=	SYM
37681	2627	262	=	=	SYM
37681	2627	263	=	=	SYM
37681	2627	264	=	=	SYM
37681	2627	265	=	=	SYM
37681	2627	266	=	=	SYM
37681	2627	267	=	=	SYM
37681	2627	268	=	=	SYM
37681	2627	269	=	=	SYM
37681	2627	270	=	=	SYM
37681	2627	271	=	=	SYM
37681	2627	272	=	=	SYM
37681	2627	273	=	=	SYM
37681	2627	274	=	=	SYM
37681	2627	275	=	=	SYM
37681	2627	276	=	=	SYM
37681	2627	277	=	=	SYM
37681	2627	278	=	=	SYM
37681	2627	279	=	=	SYM
37681	2627	280	=	=	SYM
37681	2627	281	=	=	SYM
37681	2627	282	=	=	SYM
37681	2627	283	=	=	SYM
37681	2627	284	=	=	SYM
37681	2627	285	=	=	SYM
37681	2627	286	=	=	SYM
37681	2627	287	=	=	SYM
37681	2627	288	=	=	SYM
37681	2627	289	=	=	SYM
37681	2627	290	=	=	SYM
37681	2627	291	=	=	SYM
37681	2627	292	=	=	SYM
37681	2627	293	=	=	SYM
37681	2627	294	=	=	SYM
37681	2627	295	=	=	SYM
37681	2627	296	=	=	SYM
37681	2627	297	=	=	SYM
37681	2627	298	=	=	SYM
37681	2627	299	=	=	SYM
37681	2627	300	=	=	SYM
37681	2627	301	=	=	SYM
37681	2627	302	=	=	SYM
37681	2627	303	=	=	SYM
37681	2627	304	=	=	SYM
37681	2627	305	=	=	SYM
37681	2627	306	=	=	SYM
37681	2627	307	=	=	NFP
37681	2627	308	=	=	NFP
37681	2627	309	=	=	NFP
37681	2627	310	It	-PRON-	PRP
37681	2627	311	will	will	MD
37681	2627	312	of	of	IN
37681	2627	313	course	course	NN
37681	2627	314	be	be	VB
37681	2627	315	understood	understand	VBN
37681	2627	316	that	that	IN
37681	2627	317	the	the	DT
37681	2627	318	values	value	NNS
37681	2627	319	are	be	VBP
37681	2627	320	correct	correct	JJ
37681	2627	321	only	only	RB
37681	2627	322	to	to	IN
37681	2627	323	the	the	DT
37681	2627	324	nearest	near	JJS
37681	2627	325	thousandth	thousandth	NN
37681	2627	326	.	.	.
37681	2628	1	Thus	thus	RB
37681	2628	2	the	the	DT
37681	2628	3	cosine	cosine	NN
37681	2628	4	of	of	IN
37681	2628	5	5	5	CD
37681	2628	6	°	°	,
37681	2628	7	is	be	VBZ
37681	2628	8	0.99619	0.99619	CD
37681	2628	9	,	,	,
37681	2628	10	and	and	CC
37681	2628	11	the	the	DT
37681	2628	12	sine	sine	NN
37681	2628	13	of	of	IN
37681	2628	14	85	85	CD
37681	2628	15	°	°	NNS
37681	2628	16	is	be	VBZ
37681	2628	17	0.99619	0.99619	CD
37681	2628	18	.	.	.
37681	2629	1	The	the	DT
37681	2629	2	entire	entire	JJ
37681	2629	3	table	table	NN
37681	2629	4	can	can	MD
37681	2629	5	be	be	VB
37681	2629	6	copied	copy	VBN
37681	2629	7	by	by	IN
37681	2629	8	a	a	DT
37681	2629	9	class	class	NN
37681	2629	10	in	in	IN
37681	2629	11	five	five	CD
37681	2629	12	minutes	minute	NNS
37681	2629	13	if	if	IN
37681	2629	14	a	a	DT
37681	2629	15	teacher	teacher	NN
37681	2629	16	wishes	wish	VBZ
37681	2629	17	to	to	TO
37681	2629	18	introduce	introduce	VB
37681	2629	19	this	this	DT
37681	2629	20	phase	phase	NN
37681	2629	21	of	of	IN
37681	2629	22	the	the	DT
37681	2629	23	work	work	NN
37681	2629	24	,	,	,
37681	2629	25	and	and	CC
37681	2629	26	the	the	DT
37681	2629	27	author	author	NN
37681	2629	28	has	have	VBZ
37681	2629	29	frequently	frequently	RB
37681	2629	30	assigned	assign	VBN
37681	2629	31	the	the	DT
37681	2629	32	computing	computing	NN
37681	2629	33	of	of	IN
37681	2629	34	a	a	DT
37681	2629	35	simpler	simple	JJR
37681	2629	36	table	table	NN
37681	2629	37	as	as	IN
37681	2629	38	a	a	DT
37681	2629	39	class	class	NN
37681	2629	40	exercise	exercise	NN
37681	2629	41	.	.	.
37681	2630	1	Referring	refer	VBG
37681	2630	2	to	to	IN
37681	2630	3	the	the	DT
37681	2630	4	figure	figure	NN
37681	2630	5	,	,	,
37681	2630	6	if	if	IN
37681	2630	7	we	-PRON-	PRP
37681	2630	8	know	know	VBP
37681	2630	9	that	that	IN
37681	2630	10	_	_	NNP
37681	2630	11	r	r	NNP
37681	2630	12	_	_	NNP
37681	2630	13	=	=	SYM
37681	2630	14	30	30	CD
37681	2630	15	and	and	CC
37681	2630	16	[	[	-LRB-
37681	2630	17	L]_O	L]_O	NNP
37681	2630	18	_	_	NNP
37681	2630	19	=	=	SYM
37681	2630	20	40	40	CD
37681	2630	21	°	°	NNS
37681	2630	22	,	,	,
37681	2630	23	then	then	RB
37681	2630	24	since	since	IN
37681	2630	25	_	_	NNP
37681	2630	26	y	y	NNP
37681	2630	27	_	_	NNP
37681	2630	28	=	=	SYM
37681	2630	29	_	_	NNP
37681	2630	30	r	r	NNP
37681	2630	31	_	_	NNP
37681	2630	32	sin	sin	NN
37681	2630	33	_	_	NNP
37681	2630	34	O	O	NNP
37681	2630	35	_	_	NNP
37681	2630	36	,	,	,
37681	2630	37	we	-PRON-	PRP
37681	2630	38	have	have	VBP
37681	2630	39	_	_	NNP
37681	2630	40	y	y	NNP
37681	2630	41	_	_	NNP
37681	2630	42	=	=	SYM
37681	2630	43	30	30	CD
37681	2630	44	×	×	CD
37681	2630	45	0.643	0.643	CD
37681	2630	46	=	=	SYM
37681	2630	47	19.29	19.29	CD
37681	2630	48	.	.	.
37681	2631	1	If	if	IN
37681	2631	2	we	-PRON-	PRP
37681	2631	3	know	know	VBP
37681	2631	4	that	that	IN
37681	2631	5	_	_	NNP
37681	2631	6	x	x	NNP
37681	2631	7	_	_	NNP
37681	2631	8	=	=	SYM
37681	2631	9	60	60	CD
37681	2631	10	and	and	CC
37681	2631	11	[	[	-LRB-
37681	2631	12	L]_O	L]_O	NNS
37681	2631	13	_	_	NNP
37681	2631	14	=	=	SYM
37681	2631	15	35	35	CD
37681	2631	16	°	°	NNS
37681	2631	17	,	,	,
37681	2631	18	then	then	RB
37681	2631	19	since	since	IN
37681	2631	20	_	_	NNP
37681	2631	21	y	y	NNP
37681	2631	22	_	_	NNP
37681	2631	23	=	=	SYM
37681	2631	24	_	_	NNP
37681	2631	25	x	x	NNP
37681	2631	26	_	_	NNP
37681	2631	27	tan	tan	NN
37681	2631	28	_	_	NNP
37681	2631	29	O	O	NNP
37681	2631	30	_	_	NNP
37681	2631	31	,	,	,
37681	2631	32	we	-PRON-	PRP
37681	2631	33	have	have	VBP
37681	2631	34	_	_	NNP
37681	2631	35	y	y	NNP
37681	2631	36	_	_	NNP
37681	2631	37	=	=	SYM
37681	2631	38	60	60	CD
37681	2631	39	×	×	CD
37681	2631	40	0.7	0.7	CD
37681	2631	41	=	=	SYM
37681	2631	42	42	42	CD
37681	2631	43	.	.	.
37681	2632	1	We	-PRON-	PRP
37681	2632	2	may	may	MD
37681	2632	3	also	also	RB
37681	2632	4	find	find	VB
37681	2632	5	_	_	NNP
37681	2632	6	r	r	NNP
37681	2632	7	_	_	NNP
37681	2632	8	,	,	,
37681	2632	9	for	for	IN
37681	2632	10	cos	cos	NNP
37681	2632	11	_	_	NNP
37681	2632	12	O	O	NNP
37681	2632	13	_	_	NNP
37681	2632	14	=	=	SYM
37681	2632	15	_	_	NNP
37681	2632	16	x_/_r	x_/_r	NNP
37681	2632	17	_	_	NNP
37681	2632	18	,	,	,
37681	2632	19	whence	whence	NN
37681	2632	20	_	_	NNP
37681	2632	21	r	r	NNP
37681	2632	22	_	_	NNP
37681	2632	23	=	=	SYM
37681	2632	24	_	_	NNP
37681	2632	25	x_/(cos	x_/(cos	NNP
37681	2632	26	_	_	NNP
37681	2632	27	O	O	NNP
37681	2632	28	_	_	NNP
37681	2632	29	)	)	-RRB-
37681	2632	30	=	=	SYM
37681	2632	31	60/0.819	60/0.819	CD
37681	2632	32	=	=	SYM
37681	2632	33	73.26	73.26	CD
37681	2632	34	.	.	.
37681	2633	1	Therefore	therefore	RB
37681	2633	2	,	,	,
37681	2633	3	if	if	IN
37681	2633	4	we	-PRON-	PRP
37681	2633	5	could	could	MD
37681	2633	6	easily	easily	RB
37681	2633	7	measure	measure	VB
37681	2633	8	[	[	-LRB-
37681	2633	9	L]_O	L]_O	NNS
37681	2633	10	_	_	NNP
37681	2633	11	and	and	CC
37681	2633	12	could	could	MD
37681	2633	13	measure	measure	VB
37681	2633	14	the	the	DT
37681	2633	15	distance	distance	NN
37681	2633	16	_	_	NNP
37681	2633	17	x	x	NNP
37681	2633	18	_	_	NNP
37681	2633	19	,	,	,
37681	2633	20	we	-PRON-	PRP
37681	2633	21	could	could	MD
37681	2633	22	find	find	VB
37681	2633	23	the	the	DT
37681	2633	24	height	height	NN
37681	2633	25	of	of	IN
37681	2633	26	a	a	DT
37681	2633	27	building	building	NN
37681	2633	28	_	_	NNP
37681	2633	29	y	y	NNP
37681	2633	30	_	_	NNP
37681	2633	31	.	.	.
37681	2634	1	In	in	IN
37681	2634	2	trigonometry	trigonometry	NN
37681	2634	3	we	-PRON-	PRP
37681	2634	4	use	use	VBP
37681	2634	5	a	a	DT
37681	2634	6	transit	transit	NN
37681	2634	7	for	for	IN
37681	2634	8	measuring	measure	VBG
37681	2634	9	angles	angle	NNS
37681	2634	10	,	,	,
37681	2634	11	but	but	CC
37681	2634	12	it	-PRON-	PRP
37681	2634	13	is	be	VBZ
37681	2634	14	easy	easy	JJ
37681	2634	15	to	to	TO
37681	2634	16	measure	measure	VB
37681	2634	17	them	-PRON-	PRP
37681	2634	18	with	with	IN
37681	2634	19	sufficient	sufficient	JJ
37681	2634	20	accuracy	accuracy	NN
37681	2634	21	for	for	IN
37681	2634	22	illustrative	illustrative	JJ
37681	2634	23	purposes	purpose	NNS
37681	2634	24	by	by	IN
37681	2634	25	placing	place	VBG
37681	2634	26	an	an	DT
37681	2634	27	ordinary	ordinary	JJ
37681	2634	28	paper	paper	NN
37681	2634	29	protractor	protractor	NN
37681	2634	30	upon	upon	IN
37681	2634	31	something	something	NN
37681	2634	32	level	level	NN
37681	2634	33	,	,	,
37681	2634	34	so	so	IN
37681	2634	35	that	that	IN
37681	2634	36	the	the	DT
37681	2634	37	center	center	NN
37681	2634	38	comes	come	VBZ
37681	2634	39	at	at	IN
37681	2634	40	the	the	DT
37681	2634	41	edge	edge	NN
37681	2634	42	,	,	,
37681	2634	43	and	and	CC
37681	2634	44	then	then	RB
37681	2634	45	sighting	sight	VBG
37681	2634	46	along	along	IN
37681	2634	47	a	a	DT
37681	2634	48	ruler	ruler	NN
37681	2634	49	held	hold	VBN
37681	2634	50	against	against	IN
37681	2634	51	it	-PRON-	PRP
37681	2634	52	,	,	,
37681	2634	53	so	so	IN
37681	2634	54	as	as	IN
37681	2634	55	to	to	TO
37681	2634	56	find	find	VB
37681	2634	57	the	the	DT
37681	2634	58	angle	angle	NN
37681	2634	59	of	of	IN
37681	2634	60	elevation	elevation	NN
37681	2634	61	of	of	IN
37681	2634	62	a	a	DT
37681	2634	63	building	building	NN
37681	2634	64	.	.	.
37681	2635	1	We	-PRON-	PRP
37681	2635	2	may	may	MD
37681	2635	3	then	then	RB
37681	2635	4	measure	measure	VB
37681	2635	5	the	the	DT
37681	2635	6	distance	distance	NN
37681	2635	7	to	to	IN
37681	2635	8	the	the	DT
37681	2635	9	building	building	NN
37681	2635	10	and	and	CC
37681	2635	11	apply	apply	VB
37681	2635	12	the	the	DT
37681	2635	13	formula	formula	NN
37681	2635	14	_	_	NNP
37681	2635	15	y	y	NNP
37681	2635	16	_	_	NNP
37681	2635	17	=	=	SYM
37681	2635	18	_	_	NNP
37681	2635	19	x	x	NNP
37681	2635	20	_	_	NNP
37681	2635	21	tan	tan	NN
37681	2635	22	_	_	NNP
37681	2635	23	O	O	NNP
37681	2635	24	_	_	NNP
37681	2635	25	.	.	.
37681	2636	1	[	[	-LRB-
37681	2636	2	Illustration	illustration	NN
37681	2636	3	:	:	:
37681	2636	4	A	a	DT
37681	2636	5	QUADRANT	QUADRANT	NNP
37681	2636	6	OF	of	IN
37681	2636	7	THE	the	DT
37681	2636	8	SIXTEENTH	SIXTEENTH	NNP
37681	2636	9	CENTURY	CENTURY	NNP
37681	2636	10	Finaeus	Finaeus	NNP
37681	2636	11	's	's	POS
37681	2636	12	"	"	``
37681	2636	13	De	De	NNP
37681	2636	14	re	re	NNP
37681	2636	15	et	et	NNP
37681	2636	16	praxi	praxi	NNP
37681	2636	17	geometrica	geometrica	NNP
37681	2636	18	,	,	,
37681	2636	19	"	"	``
37681	2636	20	Paris	Paris	NNP
37681	2636	21	,	,	,
37681	2636	22	1556	1556	CD
37681	2636	23	]	]	-RRB-
37681	2636	24	It	-PRON-	PRP
37681	2636	25	should	should	MD
37681	2636	26	always	always	RB
37681	2636	27	be	be	VB
37681	2636	28	understood	understand	VBN
37681	2636	29	that	that	IN
37681	2636	30	expensive	expensive	JJ
37681	2636	31	apparatus	apparatus	NN
37681	2636	32	is	be	VBZ
37681	2636	33	not	not	RB
37681	2636	34	necessary	necessary	JJ
37681	2636	35	for	for	IN
37681	2636	36	such	such	JJ
37681	2636	37	illustrative	illustrative	JJ
37681	2636	38	work	work	NN
37681	2636	39	.	.	.
37681	2637	1	The	the	DT
37681	2637	2	telescope	telescope	NN
37681	2637	3	used	use	VBN
37681	2637	4	on	on	IN
37681	2637	5	the	the	DT
37681	2637	6	transit	transit	NN
37681	2637	7	is	be	VBZ
37681	2637	8	only	only	RB
37681	2637	9	three	three	CD
37681	2637	10	hundred	hundred	CD
37681	2637	11	years	year	NNS
37681	2637	12	old	old	JJ
37681	2637	13	,	,	,
37681	2637	14	and	and	CC
37681	2637	15	the	the	DT
37681	2637	16	world	world	NN
37681	2637	17	got	get	VBD
37681	2637	18	along	along	RP
37681	2637	19	very	very	RB
37681	2637	20	well	well	RB
37681	2637	21	with	with	IN
37681	2637	22	its	-PRON-	PRP$
37681	2637	23	trigonometry	trigonometry	NN
37681	2637	24	before	before	IN
37681	2637	25	that	that	DT
37681	2637	26	was	be	VBD
37681	2637	27	invented	invent	VBN
37681	2637	28	.	.	.
37681	2638	1	So	so	RB
37681	2638	2	a	a	DT
37681	2638	3	little	little	JJ
37681	2638	4	ingenuity	ingenuity	NN
37681	2638	5	will	will	MD
37681	2638	6	enable	enable	VB
37681	2638	7	any	any	DT
37681	2638	8	one	one	NN
37681	2638	9	to	to	TO
37681	2638	10	make	make	VB
37681	2638	11	from	from	IN
37681	2638	12	cheap	cheap	JJ
37681	2638	13	protractors	protractor	NNS
37681	2638	14	about	about	IN
37681	2638	15	as	as	IN
37681	2638	16	satisfactory	satisfactory	JJ
37681	2638	17	instruments	instrument	NNS
37681	2638	18	as	as	IN
37681	2638	19	the	the	DT
37681	2638	20	world	world	NN
37681	2638	21	used	use	VBN
37681	2638	22	before	before	IN
37681	2638	23	1600	1600	CD
37681	2638	24	.	.	.
37681	2639	1	In	in	IN
37681	2639	2	order	order	NN
37681	2639	3	that	that	IN
37681	2639	4	this	this	DT
37681	2639	5	may	may	MD
37681	2639	6	be	be	VB
37681	2639	7	the	the	DT
37681	2639	8	more	more	RBR
37681	2639	9	fully	fully	RB
37681	2639	10	appreciated	appreciate	VBN
37681	2639	11	,	,	,
37681	2639	12	a	a	DT
37681	2639	13	few	few	JJ
37681	2639	14	illustrations	illustration	NNS
37681	2639	15	are	be	VBP
37681	2639	16	here	here	RB
37681	2639	17	given	give	VBN
37681	2639	18	,	,	,
37681	2639	19	showing	show	VBG
37681	2639	20	the	the	DT
37681	2639	21	old	old	JJ
37681	2639	22	instruments	instrument	NNS
37681	2639	23	and	and	CC
37681	2639	24	methods	method	NNS
37681	2639	25	used	use	VBN
37681	2639	26	in	in	IN
37681	2639	27	practical	practical	JJ
37681	2639	28	surveying	surveying	NN
37681	2639	29	before	before	IN
37681	2639	30	the	the	DT
37681	2639	31	eighteenth	eighteenth	JJ
37681	2639	32	century	century	NN
37681	2639	33	.	.	.
37681	2640	1	[	[	-LRB-
37681	2640	2	Illustration	illustration	NN
37681	2640	3	:	:	:
37681	2640	4	A	a	DT
37681	2640	5	QUADRANT	QUADRANT	NNP
37681	2640	6	OF	of	IN
37681	2640	7	THE	the	DT
37681	2640	8	SEVENTEENTH	SEVENTEENTH	NNP
37681	2640	9	CENTURY	CENTURY	NNP
37681	2640	10	]	]	-RRB-
37681	2640	11	The	the	DT
37681	2640	12	illustration	illustration	NN
37681	2640	13	on	on	IN
37681	2640	14	page	page	NN
37681	2640	15	236	236	CD
37681	2640	16	shows	show	NNS
37681	2640	17	a	a	DT
37681	2640	18	simple	simple	JJ
37681	2640	19	form	form	NN
37681	2640	20	of	of	IN
37681	2640	21	the	the	DT
37681	2640	22	quadrant	quadrant	NN
37681	2640	23	,	,	,
37681	2640	24	an	an	DT
37681	2640	25	instrument	instrument	NN
37681	2640	26	easily	easily	RB
37681	2640	27	made	make	VBN
37681	2640	28	by	by	IN
37681	2640	29	a	a	DT
37681	2640	30	pupil	pupil	NN
37681	2640	31	who	who	WP
37681	2640	32	may	may	MD
37681	2640	33	be	be	VB
37681	2640	34	interested	interested	JJ
37681	2640	35	in	in	IN
37681	2640	36	outdoor	outdoor	JJ
37681	2640	37	work	work	NN
37681	2640	38	.	.	.
37681	2641	1	It	-PRON-	PRP
37681	2641	2	was	be	VBD
37681	2641	3	the	the	DT
37681	2641	4	common	common	JJ
37681	2641	5	surveying	surveying	NN
37681	2641	6	instrument	instrument	NN
37681	2641	7	of	of	IN
37681	2641	8	the	the	DT
37681	2641	9	early	early	JJ
37681	2641	10	days	day	NNS
37681	2641	11	.	.	.
37681	2642	1	A	a	DT
37681	2642	2	more	more	RBR
37681	2642	3	elaborate	elaborate	JJ
37681	2642	4	example	example	NN
37681	2642	5	is	be	VBZ
37681	2642	6	seen	see	VBN
37681	2642	7	in	in	IN
37681	2642	8	the	the	DT
37681	2642	9	illustration	illustration	NN
37681	2642	10	,	,	,
37681	2642	11	on	on	IN
37681	2642	12	page	page	NN
37681	2642	13	237	237	CD
37681	2642	14	,	,	,
37681	2642	15	of	of	IN
37681	2642	16	a	a	DT
37681	2642	17	seventeenth	seventeenth	JJ
37681	2642	18	-	-	HYPH
37681	2642	19	century	century	NN
37681	2642	20	brass	brass	NN
37681	2642	21	specimen	speciman	NNS
37681	2642	22	in	in	IN
37681	2642	23	the	the	DT
37681	2642	24	author	author	NN
37681	2642	25	's	's	POS
37681	2642	26	collection	collection	NN
37681	2642	27	.	.	.
37681	2643	1	[	[	-LRB-
37681	2643	2	77	77	CD
37681	2643	3	]	]	-RRB-
37681	2643	4	[	[	-LRB-
37681	2643	5	Illustration	illustration	NN
37681	2643	6	:	:	:
37681	2643	7	A	a	DT
37681	2643	8	QUADRANT	QUADRANT	NNP
37681	2643	9	OF	of	IN
37681	2643	10	THE	the	DT
37681	2643	11	SEVENTEENTH	SEVENTEENTH	NNP
37681	2643	12	CENTURY	CENTURY	NNP
37681	2643	13	Bartoli	Bartoli	NNP
37681	2643	14	's	's	POS
37681	2643	15	"	"	``
37681	2643	16	Del	Del	NNP
37681	2643	17	modo	modo	NN
37681	2643	18	di	di	NNP
37681	2643	19	misurare	misurare	NN
37681	2643	20	,	,	,
37681	2643	21	"	"	''
37681	2643	22	Venice	Venice	NNP
37681	2643	23	,	,	,
37681	2643	24	1689	1689	CD
37681	2643	25	]	]	-RRB-
37681	2643	26	Another	another	DT
37681	2643	27	type	type	NN
37681	2643	28	,	,	,
37681	2643	29	easily	easily	RB
37681	2643	30	made	make	VBN
37681	2643	31	by	by	IN
37681	2643	32	pupils	pupil	NNS
37681	2643	33	,	,	,
37681	2643	34	is	be	VBZ
37681	2643	35	shown	show	VBN
37681	2643	36	in	in	IN
37681	2643	37	the	the	DT
37681	2643	38	above	above	JJ
37681	2643	39	illustration	illustration	NN
37681	2643	40	from	from	IN
37681	2643	41	Bartoli	Bartoli	NNP
37681	2643	42	,	,	,
37681	2643	43	1689	1689	CD
37681	2643	44	.	.	.
37681	2644	1	Such	such	JJ
37681	2644	2	instruments	instrument	NNS
37681	2644	3	were	be	VBD
37681	2644	4	usually	usually	RB
37681	2644	5	made	make	VBN
37681	2644	6	of	of	IN
37681	2644	7	wood	wood	NN
37681	2644	8	,	,	,
37681	2644	9	brass	brass	NN
37681	2644	10	,	,	,
37681	2644	11	or	or	CC
37681	2644	12	ivory	ivory	NN
37681	2644	13	.	.	.
37681	2645	1	[	[	-LRB-
37681	2645	2	78	78	CD
37681	2645	3	]	]	-RRB-
37681	2645	4	Instruments	instrument	NNS
37681	2645	5	for	for	IN
37681	2645	6	the	the	DT
37681	2645	7	running	running	NN
37681	2645	8	of	of	IN
37681	2645	9	lines	line	NNS
37681	2645	10	perpendicular	perpendicular	JJ
37681	2645	11	to	to	IN
37681	2645	12	other	other	JJ
37681	2645	13	lines	line	NNS
37681	2645	14	were	be	VBD
37681	2645	15	formerly	formerly	RB
37681	2645	16	common	common	JJ
37681	2645	17	,	,	,
37681	2645	18	and	and	CC
37681	2645	19	are	be	VBP
37681	2645	20	easily	easily	RB
37681	2645	21	made	make	VBN
37681	2645	22	.	.	.
37681	2646	1	They	-PRON-	PRP
37681	2646	2	suffice	suffice	VBP
37681	2646	3	,	,	,
37681	2646	4	as	as	IN
37681	2646	5	the	the	DT
37681	2646	6	following	follow	VBG
37681	2646	7	illustration	illustration	NN
37681	2646	8	shows	show	NNS
37681	2646	9	,	,	,
37681	2646	10	for	for	IN
37681	2646	11	surveying	survey	VBG
37681	2646	12	an	an	DT
37681	2646	13	ordinary	ordinary	JJ
37681	2646	14	field	field	NN
37681	2646	15	.	.	.
37681	2647	1	[	[	-LRB-
37681	2647	2	Illustration	illustration	NN
37681	2647	3	:	:	:
37681	2647	4	SURVEYING	survey	VBG
37681	2647	5	INSTRUMENT	instrument	NN
37681	2647	6	OF	of	IN
37681	2647	7	THE	the	DT
37681	2647	8	EIGHTEENTH	EIGHTEENTH	NNP
37681	2647	9	CENTURY	CENTURY	NNP
37681	2647	10	N.	N.	NNP
37681	2647	11	Bion	Bion	NNP
37681	2647	12	's	's	POS
37681	2647	13	"	"	``
37681	2647	14	Traité	Traité	NNP
37681	2647	15	de	de	FW
37681	2647	16	la	la	JJ
37681	2647	17	construction	construction	NN
37681	2647	18	...	...	:
37681	2647	19	des	des	NNP
37681	2647	20	instrumens	instrumen	NNS
37681	2647	21	de	de	IN
37681	2647	22	mathématique	mathématique	NN
37681	2647	23	,	,	,
37681	2647	24	"	"	''
37681	2647	25	The	the	DT
37681	2647	26	Hague	Hague	NNP
37681	2647	27	,	,	,
37681	2647	28	1723	1723	CD
37681	2647	29	]	]	-RRB-
37681	2647	30	[	[	-LRB-
37681	2647	31	Illustration	illustration	NN
37681	2647	32	:	:	:
37681	2647	33	THE	the	DT
37681	2647	34	QUADRANT	QUADRANT	NNP
37681	2647	35	USED	use	VBN
37681	2647	36	FOR	for	IN
37681	2647	37	ALTITUDES	ALTITUDES	NNP
37681	2647	38	Finaeus	Finaeus	NNP
37681	2647	39	's	's	POS
37681	2647	40	"	"	``
37681	2647	41	De	De	NNP
37681	2647	42	re	re	NNP
37681	2647	43	et	et	NNP
37681	2647	44	praxi	praxi	NNP
37681	2647	45	geometrica	geometrica	NNP
37681	2647	46	,	,	,
37681	2647	47	"	"	``
37681	2647	48	Paris	Paris	NNP
37681	2647	49	,	,	,
37681	2647	50	1556	1556	LS
37681	2647	51	]	]	-RRB-
37681	2647	52	The	the	DT
37681	2647	53	quadrant	quadrant	NN
37681	2647	54	was	be	VBD
37681	2647	55	practically	practically	RB
37681	2647	56	used	use	VBN
37681	2647	57	for	for	IN
37681	2647	58	all	all	DT
37681	2647	59	sorts	sort	NNS
37681	2647	60	of	of	IN
37681	2647	61	outdoor	outdoor	JJ
37681	2647	62	measuring	measuring	NN
37681	2647	63	.	.	.
37681	2648	1	For	for	IN
37681	2648	2	example	example	NN
37681	2648	3	,	,	,
37681	2648	4	the	the	DT
37681	2648	5	illustration	illustration	NN
37681	2648	6	from	from	IN
37681	2648	7	Finaeus	Finaeus	NNP
37681	2648	8	,	,	,
37681	2648	9	on	on	IN
37681	2648	10	this	this	DT
37681	2648	11	page	page	NN
37681	2648	12	,	,	,
37681	2648	13	shows	show	VBZ
37681	2648	14	how	how	WRB
37681	2648	15	it	-PRON-	PRP
37681	2648	16	was	be	VBD
37681	2648	17	used	use	VBN
37681	2648	18	for	for	IN
37681	2648	19	altitudes	altitude	NNS
37681	2648	20	,	,	,
37681	2648	21	and	and	CC
37681	2648	22	the	the	DT
37681	2648	23	one	one	NN
37681	2648	24	reproduced	reproduce	VBN
37681	2648	25	on	on	IN
37681	2648	26	page	page	NN
37681	2648	27	240	240	CD
37681	2648	28	shows	show	VBZ
37681	2648	29	how	how	WRB
37681	2648	30	it	-PRON-	PRP
37681	2648	31	was	be	VBD
37681	2648	32	used	use	VBN
37681	2648	33	for	for	IN
37681	2648	34	measuring	measure	VBG
37681	2648	35	depths	depth	NNS
37681	2648	36	.	.	.
37681	2649	1	A	a	DT
37681	2649	2	similar	similar	JJ
37681	2649	3	instrument	instrument	NN
37681	2649	4	from	from	IN
37681	2649	5	the	the	DT
37681	2649	6	work	work	NN
37681	2649	7	of	of	IN
37681	2649	8	Bettinus	Bettinus	NNP
37681	2649	9	is	be	VBZ
37681	2649	10	given	give	VBN
37681	2649	11	on	on	IN
37681	2649	12	page	page	NN
37681	2649	13	241	241	CD
37681	2649	14	,	,	,
37681	2649	15	the	the	DT
37681	2649	16	distance	distance	NN
37681	2649	17	of	of	IN
37681	2649	18	a	a	DT
37681	2649	19	ship	ship	NN
37681	2649	20	being	be	VBG
37681	2649	21	found	find	VBN
37681	2649	22	by	by	IN
37681	2649	23	constructing	construct	VBG
37681	2649	24	an	an	DT
37681	2649	25	isosceles	isoscele	NNS
37681	2649	26	triangle	triangle	NN
37681	2649	27	.	.	.
37681	2650	1	A	a	DT
37681	2650	2	more	more	RBR
37681	2650	3	elaborate	elaborate	JJ
37681	2650	4	form	form	NN
37681	2650	5	,	,	,
37681	2650	6	with	with	IN
37681	2650	7	a	a	DT
37681	2650	8	pendulum	pendulum	NN
37681	2650	9	attachment	attachment	NN
37681	2650	10	,	,	,
37681	2650	11	is	be	VBZ
37681	2650	12	seen	see	VBN
37681	2650	13	in	in	IN
37681	2650	14	the	the	DT
37681	2650	15	illustration	illustration	NN
37681	2650	16	from	from	IN
37681	2650	17	De	De	NNP
37681	2650	18	Judaeis	Judaeis	NNP
37681	2650	19	,	,	,
37681	2650	20	which	which	WDT
37681	2650	21	also	also	RB
37681	2650	22	appears	appear	VBZ
37681	2650	23	on	on	IN
37681	2650	24	page	page	NN
37681	2650	25	241	241	CD
37681	2650	26	.	.	.
37681	2651	1	[	[	-LRB-
37681	2651	2	Illustration	illustration	NN
37681	2651	3	:	:	:
37681	2651	4	THE	the	DT
37681	2651	5	QUADRANT	QUADRANT	NNP
37681	2651	6	USED	use	VBN
37681	2651	7	FOR	for	IN
37681	2651	8	DEPTHS	DEPTHS	NNP
37681	2651	9	Finaeus	Finaeus	NNP
37681	2651	10	's	's	POS
37681	2651	11	"	"	``
37681	2651	12	Protomathesis	Protomathesis	NNP
37681	2651	13	,	,	,
37681	2651	14	"	"	''
37681	2651	15	Paris	Paris	NNP
37681	2651	16	,	,	,
37681	2651	17	1532	1532	CD
37681	2651	18	]	]	-RRB-
37681	2651	19	[	[	-LRB-
37681	2651	20	Illustration	illustration	NN
37681	2651	21	:	:	:
37681	2651	22	A	a	DT
37681	2651	23	QUADRANT	QUADRANT	NNP
37681	2651	24	OF	of	IN
37681	2651	25	THE	the	DT
37681	2651	26	SIXTEENTH	SIXTEENTH	NNP
37681	2651	27	CENTURY	CENTURY	NNP
37681	2651	28	De	De	NNP
37681	2651	29	Judaeis	Judaeis	NNP
37681	2651	30	's	's	POS
37681	2651	31	"	"	``
37681	2651	32	De	De	NNP
37681	2651	33	quadrante	quadrante	NNP
37681	2651	34	geometrico	geometrico	NNP
37681	2651	35	,	,	,
37681	2651	36	"	"	''
37681	2651	37	Nürnberg	Nürnberg	NNP
37681	2651	38	,	,	,
37681	2651	39	1594	1594	CD
37681	2651	40	]	]	-RRB-
37681	2651	41	[	[	-LRB-
37681	2651	42	Illustration	illustration	NN
37681	2651	43	:	:	:
37681	2651	44	THE	the	DT
37681	2651	45	QUADRANT	QUADRANT	NNP
37681	2651	46	USED	use	VBN
37681	2651	47	FOR	for	IN
37681	2651	48	DISTANCES	DISTANCES	NNP
37681	2651	49	Bettinus	Bettinus	NNP
37681	2651	50	's	's	POS
37681	2651	51	"	"	``
37681	2651	52	Apiaria	Apiaria	NNP
37681	2651	53	universae	universae	VB
37681	2651	54	philosophiae	philosophiae	NNS
37681	2651	55	mathematicae	mathematicae	NN
37681	2651	56	,	,	,
37681	2651	57	"	"	``
37681	2651	58	Bologna	Bologna	NNS
37681	2651	59	,	,	,
37681	2651	60	1645	1645	CD
37681	2651	61	]	]	-RRB-
37681	2651	62	The	the	DT
37681	2651	63	quadrant	quadrant	NN
37681	2651	64	finally	finally	RB
37681	2651	65	developed	develop	VBD
37681	2651	66	into	into	IN
37681	2651	67	the	the	DT
37681	2651	68	octant	octant	NN
37681	2651	69	,	,	,
37681	2651	70	as	as	IN
37681	2651	71	shown	show	VBN
37681	2651	72	in	in	IN
37681	2651	73	the	the	DT
37681	2651	74	following	follow	VBG
37681	2651	75	illustration	illustration	NN
37681	2651	76	from	from	IN
37681	2651	77	Hoffmann	Hoffmann	NNP
37681	2651	78	,	,	,
37681	2651	79	and	and	CC
37681	2651	80	this	this	DT
37681	2651	81	in	in	IN
37681	2651	82	turn	turn	NN
37681	2651	83	developed	develop	VBN
37681	2651	84	into	into	IN
37681	2651	85	the	the	DT
37681	2651	86	sextant	sextant	NN
37681	2651	87	,	,	,
37681	2651	88	which	which	WDT
37681	2651	89	is	be	VBZ
37681	2651	90	now	now	RB
37681	2651	91	used	use	VBN
37681	2651	92	by	by	IN
37681	2651	93	all	all	DT
37681	2651	94	navigators	navigator	NNS
37681	2651	95	.	.	.
37681	2652	1	[	[	-LRB-
37681	2652	2	Illustration	illustration	NN
37681	2652	3	:	:	:
37681	2652	4	THE	the	DT
37681	2652	5	OCTANT	OCTANT	NNP
37681	2652	6	Hoffmann	Hoffmann	NNP
37681	2652	7	's	's	POS
37681	2652	8	"	"	``
37681	2652	9	De	De	NNP
37681	2652	10	Octantis	Octantis	NNP
37681	2652	11	,	,	,
37681	2652	12	"	"	''
37681	2652	13	Jena	Jena	NNP
37681	2652	14	,	,	,
37681	2652	15	1612	1612	CD
37681	2652	16	]	]	-RRB-
37681	2652	17	In	in	IN
37681	2652	18	connection	connection	NN
37681	2652	19	with	with	IN
37681	2652	20	this	this	DT
37681	2652	21	general	general	JJ
37681	2652	22	subject	subject	NN
37681	2652	23	the	the	DT
37681	2652	24	use	use	NN
37681	2652	25	of	of	IN
37681	2652	26	the	the	DT
37681	2652	27	speculum	speculum	NN
37681	2652	28	(	(	-LRB-
37681	2652	29	mirror	mirror	NN
37681	2652	30	)	)	-RRB-
37681	2652	31	in	in	IN
37681	2652	32	measuring	measure	VBG
37681	2652	33	heights	height	NNS
37681	2652	34	should	should	MD
37681	2652	35	be	be	VB
37681	2652	36	mentioned	mention	VBN
37681	2652	37	.	.	.
37681	2653	1	The	the	DT
37681	2653	2	illustration	illustration	NN
37681	2653	3	given	give	VBN
37681	2653	4	on	on	IN
37681	2653	5	page	page	NN
37681	2653	6	243	243	CD
37681	2653	7	shows	show	VBZ
37681	2653	8	how	how	WRB
37681	2653	9	in	in	IN
37681	2653	10	early	early	JJ
37681	2653	11	days	day	NNS
37681	2653	12	a	a	DT
37681	2653	13	simple	simple	JJ
37681	2653	14	device	device	NN
37681	2653	15	was	be	VBD
37681	2653	16	used	use	VBN
37681	2653	17	for	for	IN
37681	2653	18	this	this	DT
37681	2653	19	purpose	purpose	NN
37681	2653	20	.	.	.
37681	2654	1	Two	two	CD
37681	2654	2	similar	similar	JJ
37681	2654	3	triangles	triangle	NNS
37681	2654	4	are	be	VBP
37681	2654	5	formed	form	VBN
37681	2654	6	in	in	IN
37681	2654	7	this	this	DT
37681	2654	8	way	way	NN
37681	2654	9	,	,	,
37681	2654	10	and	and	CC
37681	2654	11	we	-PRON-	PRP
37681	2654	12	have	have	VBP
37681	2654	13	only	only	RB
37681	2654	14	to	to	TO
37681	2654	15	measure	measure	VB
37681	2654	16	the	the	DT
37681	2654	17	height	height	NN
37681	2654	18	of	of	IN
37681	2654	19	the	the	DT
37681	2654	20	eye	eye	NN
37681	2654	21	above	above	IN
37681	2654	22	the	the	DT
37681	2654	23	ground	ground	NN
37681	2654	24	,	,	,
37681	2654	25	and	and	CC
37681	2654	26	the	the	DT
37681	2654	27	distances	distance	NNS
37681	2654	28	of	of	IN
37681	2654	29	the	the	DT
37681	2654	30	mirror	mirror	NN
37681	2654	31	from	from	IN
37681	2654	32	the	the	DT
37681	2654	33	tower	tower	NN
37681	2654	34	and	and	CC
37681	2654	35	the	the	DT
37681	2654	36	observer	observer	NN
37681	2654	37	,	,	,
37681	2654	38	to	to	TO
37681	2654	39	have	have	VB
37681	2654	40	three	three	CD
37681	2654	41	terms	term	NNS
37681	2654	42	of	of	IN
37681	2654	43	a	a	DT
37681	2654	44	proportion	proportion	NN
37681	2654	45	.	.	.
37681	2655	1	All	all	DT
37681	2655	2	of	of	IN
37681	2655	3	these	these	DT
37681	2655	4	instruments	instrument	NNS
37681	2655	5	are	be	VBP
37681	2655	6	easily	easily	RB
37681	2655	7	made	make	VBN
37681	2655	8	.	.	.
37681	2656	1	The	the	DT
37681	2656	2	mirror	mirror	NN
37681	2656	3	is	be	VBZ
37681	2656	4	always	always	RB
37681	2656	5	at	at	IN
37681	2656	6	hand	hand	NN
37681	2656	7	,	,	,
37681	2656	8	and	and	CC
37681	2656	9	a	a	DT
37681	2656	10	paper	paper	NN
37681	2656	11	protractor	protractor	NN
37681	2656	12	on	on	IN
37681	2656	13	a	a	DT
37681	2656	14	piece	piece	NN
37681	2656	15	of	of	IN
37681	2656	16	board	board	NN
37681	2656	17	,	,	,
37681	2656	18	with	with	IN
37681	2656	19	a	a	DT
37681	2656	20	plumb	plumb	JJ
37681	2656	21	line	line	NN
37681	2656	22	attached	attach	VBN
37681	2656	23	,	,	,
37681	2656	24	serves	serve	VBZ
37681	2656	25	as	as	IN
37681	2656	26	a	a	DT
37681	2656	27	quadrant	quadrant	NN
37681	2656	28	.	.	.
37681	2657	1	For	for	IN
37681	2657	2	a	a	DT
37681	2657	3	few	few	JJ
37681	2657	4	cents	cent	NNS
37681	2657	5	,	,	,
37681	2657	6	and	and	CC
37681	2657	7	by	by	IN
37681	2657	8	the	the	DT
37681	2657	9	expenditure	expenditure	NN
37681	2657	10	of	of	IN
37681	2657	11	an	an	DT
37681	2657	12	hour	hour	NN
37681	2657	13	or	or	CC
37681	2657	14	so	so	RB
37681	2657	15	,	,	,
37681	2657	16	a	a	DT
37681	2657	17	school	school	NN
37681	2657	18	can	can	MD
37681	2657	19	have	have	VB
37681	2657	20	almost	almost	RB
37681	2657	21	as	as	IN
37681	2657	22	good	good	JJ
37681	2657	23	instruments	instrument	NNS
37681	2657	24	as	as	IN
37681	2657	25	the	the	DT
37681	2657	26	ordinary	ordinary	JJ
37681	2657	27	surveyor	surveyor	NN
37681	2657	28	had	have	VBD
37681	2657	29	before	before	IN
37681	2657	30	the	the	DT
37681	2657	31	nineteenth	nineteenth	JJ
37681	2657	32	century	century	NN
37681	2657	33	.	.	.
37681	2658	1	[	[	-LRB-
37681	2658	2	Illustration	illustration	NN
37681	2658	3	:	:	:
37681	2658	4	THE	the	DT
37681	2658	5	SPECULUM	SPECULUM	NNP
37681	2658	6	Finaeus	Finaeus	NNP
37681	2658	7	's	's	POS
37681	2658	8	"	"	``
37681	2658	9	De	De	NNP
37681	2658	10	re	re	NNP
37681	2658	11	et	et	NNP
37681	2658	12	praxi	praxi	NNP
37681	2658	13	geometrica	geometrica	NNP
37681	2658	14	,	,	,
37681	2658	15	"	"	``
37681	2658	16	Paris	Paris	NNP
37681	2658	17	,	,	,
37681	2658	18	1556	1556	LS
37681	2658	19	]	]	-RRB-
37681	2658	20	A	a	DT
37681	2658	21	well	well	RB
37681	2658	22	-	-	HYPH
37681	2658	23	known	know	VBN
37681	2658	24	method	method	NN
37681	2658	25	of	of	IN
37681	2658	26	measuring	measure	VBG
37681	2658	27	the	the	DT
37681	2658	28	distance	distance	NN
37681	2658	29	across	across	IN
37681	2658	30	a	a	DT
37681	2658	31	stream	stream	NN
37681	2658	32	is	be	VBZ
37681	2658	33	illustrated	illustrate	VBN
37681	2658	34	in	in	IN
37681	2658	35	the	the	DT
37681	2658	36	figure	figure	NN
37681	2658	37	below	below	RB
37681	2658	38	,	,	,
37681	2658	39	where	where	WRB
37681	2658	40	the	the	DT
37681	2658	41	distance	distance	NN
37681	2658	42	from	from	IN
37681	2658	43	_	_	NNP
37681	2658	44	A	A	NNP
37681	2658	45	_	_	NNP
37681	2658	46	to	to	IN
37681	2658	47	some	some	DT
37681	2658	48	point	point	NN
37681	2658	49	_	_	NNP
37681	2658	50	P	P	NNP
37681	2658	51	_	_	NNP
37681	2658	52	is	be	VBZ
37681	2658	53	required	require	VBN
37681	2658	54	.	.	.
37681	2659	1	[	[	-LRB-
37681	2659	2	Illustration	illustration	NN
37681	2659	3	]	]	-RRB-
37681	2659	4	Run	run	VB
37681	2659	5	a	a	DT
37681	2659	6	line	line	NN
37681	2659	7	from	from	IN
37681	2659	8	_	_	NNP
37681	2659	9	A	A	NNP
37681	2659	10	_	_	NNP
37681	2659	11	to	to	IN
37681	2659	12	_	_	NNP
37681	2659	13	C	C	NNP
37681	2659	14	_	_	NNP
37681	2659	15	by	by	IN
37681	2659	16	standing	stand	VBG
37681	2659	17	at	at	IN
37681	2659	18	_	_	NNP
37681	2659	19	C	C	NNP
37681	2659	20	_	_	NNP
37681	2659	21	in	in	IN
37681	2659	22	line	line	NN
37681	2659	23	with	with	IN
37681	2659	24	_	_	NNP
37681	2659	25	A	A	NNP
37681	2659	26	_	_	NNP
37681	2659	27	and	and	CC
37681	2659	28	_	_	NNP
37681	2659	29	P	P	NNP
37681	2659	30	_	_	NNP
37681	2659	31	.	.	.
37681	2660	1	Then	then	RB
37681	2660	2	run	run	VB
37681	2660	3	two	two	CD
37681	2660	4	perpendiculars	perpendicular	NNS
37681	2660	5	from	from	IN
37681	2660	6	_	_	NNP
37681	2660	7	A	A	NNP
37681	2660	8	_	_	NNP
37681	2660	9	and	and	CC
37681	2660	10	_	_	NNP
37681	2660	11	C	C	NNP
37681	2660	12	_	_	NNP
37681	2660	13	by	by	IN
37681	2660	14	any	any	DT
37681	2660	15	of	of	IN
37681	2660	16	the	the	DT
37681	2660	17	methods	method	NNS
37681	2660	18	already	already	RB
37681	2660	19	given,--sighting	given,--sighte	VBG
37681	2660	20	on	on	IN
37681	2660	21	a	a	DT
37681	2660	22	protractor	protractor	NN
37681	2660	23	or	or	CC
37681	2660	24	along	along	IN
37681	2660	25	the	the	DT
37681	2660	26	edge	edge	NN
37681	2660	27	of	of	IN
37681	2660	28	a	a	DT
37681	2660	29	book	book	NN
37681	2660	30	if	if	IN
37681	2660	31	no	no	RB
37681	2660	32	better	well	JJR
37681	2660	33	means	mean	NNS
37681	2660	34	are	be	VBP
37681	2660	35	at	at	IN
37681	2660	36	hand	hand	NN
37681	2660	37	.	.	.
37681	2661	1	Then	then	RB
37681	2661	2	sight	sight	NN
37681	2661	3	from	from	IN
37681	2661	4	some	some	DT
37681	2661	5	point	point	NN
37681	2661	6	_	_	NNP
37681	2661	7	D	D	NNP
37681	2661	8	_	_	NNP
37681	2661	9	,	,	,
37681	2661	10	on	on	IN
37681	2661	11	_	_	NNP
37681	2661	12	CD	CD	NNP
37681	2661	13	_	_	NNP
37681	2661	14	,	,	,
37681	2661	15	to	to	IN
37681	2661	16	_	_	NNP
37681	2661	17	P	P	NNP
37681	2661	18	_	_	NNP
37681	2661	19	,	,	,
37681	2661	20	putting	put	VBG
37681	2661	21	a	a	DT
37681	2661	22	stake	stake	NN
37681	2661	23	at	at	IN
37681	2661	24	_	_	NNP
37681	2661	25	B	B	NNP
37681	2661	26	_	_	NNP
37681	2661	27	.	.	.
37681	2662	1	Then	then	RB
37681	2662	2	run	run	VB
37681	2662	3	the	the	DT
37681	2662	4	perpendicular	perpendicular	JJ
37681	2662	5	_	_	NNP
37681	2662	6	BE	BE	NNP
37681	2662	7	_	_	NNP
37681	2662	8	.	.	.
37681	2663	1	Since	since	IN
37681	2663	2	_	_	NNP
37681	2663	3	DE	DE	NNP
37681	2663	4	_	_	NNP
37681	2663	5	:	:	:
37681	2663	6	_	_	NNP
37681	2663	7	EB	EB	NNP
37681	2663	8	_	_	NNP
37681	2663	9	=	=	SYM
37681	2663	10	_	_	NNP
37681	2663	11	BA	BA	NNP
37681	2663	12	_	_	NNP
37681	2663	13	:	:	:
37681	2663	14	_	_	NNP
37681	2663	15	AP	AP	NNP
37681	2663	16	_	_	NNP
37681	2663	17	,	,	,
37681	2663	18	and	and	CC
37681	2663	19	since	since	IN
37681	2663	20	we	-PRON-	PRP
37681	2663	21	can	can	MD
37681	2663	22	measure	measure	VB
37681	2663	23	_	_	NNP
37681	2663	24	DE	DE	NNP
37681	2663	25	_	_	NNP
37681	2663	26	,	,	,
37681	2663	27	_	_	NNP
37681	2663	28	EB	EB	NNP
37681	2663	29	_	_	NNP
37681	2663	30	,	,	,
37681	2663	31	and	and	CC
37681	2663	32	_	_	NNP
37681	2663	33	BA	BA	NNP
37681	2663	34	_	_	NNP
37681	2663	35	with	with	IN
37681	2663	36	the	the	DT
37681	2663	37	tape	tape	NN
37681	2663	38	,	,	,
37681	2663	39	we	-PRON-	PRP
37681	2663	40	can	can	MD
37681	2663	41	compute	compute	VB
37681	2663	42	the	the	DT
37681	2663	43	distance	distance	NN
37681	2663	44	_	_	NNP
37681	2663	45	AP	AP	NNP
37681	2663	46	_	_	NNP
37681	2663	47	.	.	.
37681	2664	1	There	there	EX
37681	2664	2	are	be	VBP
37681	2664	3	many	many	JJ
37681	2664	4	variations	variation	NNS
37681	2664	5	of	of	IN
37681	2664	6	this	this	DT
37681	2664	7	scheme	scheme	NN
37681	2664	8	of	of	IN
37681	2664	9	measuring	measure	VBG
37681	2664	10	distances	distance	NNS
37681	2664	11	by	by	IN
37681	2664	12	means	mean	NNS
37681	2664	13	of	of	IN
37681	2664	14	similar	similar	JJ
37681	2664	15	triangles	triangle	NNS
37681	2664	16	,	,	,
37681	2664	17	and	and	CC
37681	2664	18	pupils	pupil	NNS
37681	2664	19	may	may	MD
37681	2664	20	be	be	VB
37681	2664	21	encouraged	encourage	VBN
37681	2664	22	to	to	TO
37681	2664	23	try	try	VB
37681	2664	24	some	some	DT
37681	2664	25	of	of	IN
37681	2664	26	them	-PRON-	PRP
37681	2664	27	.	.	.
37681	2665	1	Other	other	JJ
37681	2665	2	figures	figure	NNS
37681	2665	3	are	be	VBP
37681	2665	4	suggested	suggest	VBN
37681	2665	5	on	on	IN
37681	2665	6	page	page	NN
37681	2665	7	244	244	CD
37681	2665	8	,	,	,
37681	2665	9	and	and	CC
37681	2665	10	the	the	DT
37681	2665	11	triangles	triangle	NNS
37681	2665	12	need	nee	MD
37681	2665	13	not	not	RB
37681	2665	14	be	be	VB
37681	2665	15	confined	confine	VBN
37681	2665	16	to	to	IN
37681	2665	17	those	those	DT
37681	2665	18	having	have	VBG
37681	2665	19	a	a	DT
37681	2665	20	right	right	JJ
37681	2665	21	angle	angle	NN
37681	2665	22	.	.	.
37681	2666	1	A	a	DT
37681	2666	2	very	very	RB
37681	2666	3	simple	simple	JJ
37681	2666	4	illustration	illustration	NN
37681	2666	5	of	of	IN
37681	2666	6	the	the	DT
37681	2666	7	use	use	NN
37681	2666	8	of	of	IN
37681	2666	9	similar	similar	JJ
37681	2666	10	triangles	triangle	NNS
37681	2666	11	is	be	VBZ
37681	2666	12	found	find	VBN
37681	2666	13	in	in	IN
37681	2666	14	one	one	CD
37681	2666	15	of	of	IN
37681	2666	16	the	the	DT
37681	2666	17	stories	story	NNS
37681	2666	18	told	tell	VBN
37681	2666	19	of	of	IN
37681	2666	20	Thales	thale	NNS
37681	2666	21	.	.	.
37681	2667	1	It	-PRON-	PRP
37681	2667	2	is	be	VBZ
37681	2667	3	related	relate	VBN
37681	2667	4	that	that	IN
37681	2667	5	he	-PRON-	PRP
37681	2667	6	found	find	VBD
37681	2667	7	the	the	DT
37681	2667	8	height	height	NN
37681	2667	9	of	of	IN
37681	2667	10	the	the	DT
37681	2667	11	pyramids	pyramid	NNS
37681	2667	12	by	by	IN
37681	2667	13	measuring	measure	VBG
37681	2667	14	their	-PRON-	PRP$
37681	2667	15	shadow	shadow	NN
37681	2667	16	at	at	IN
37681	2667	17	the	the	DT
37681	2667	18	instant	instant	NN
37681	2667	19	when	when	WRB
37681	2667	20	his	-PRON-	PRP$
37681	2667	21	own	own	JJ
37681	2667	22	shadow	shadow	NN
37681	2667	23	just	just	RB
37681	2667	24	equaled	equal	VBD
37681	2667	25	his	-PRON-	PRP$
37681	2667	26	height	height	NN
37681	2667	27	.	.	.
37681	2668	1	He	-PRON-	PRP
37681	2668	2	thus	thus	RB
37681	2668	3	had	have	VBD
37681	2668	4	the	the	DT
37681	2668	5	case	case	NN
37681	2668	6	of	of	IN
37681	2668	7	two	two	CD
37681	2668	8	similar	similar	JJ
37681	2668	9	isosceles	isoscele	NNS
37681	2668	10	triangles	triangle	NNS
37681	2668	11	.	.	.
37681	2669	1	This	this	DT
37681	2669	2	is	be	VBZ
37681	2669	3	an	an	DT
37681	2669	4	interesting	interesting	JJ
37681	2669	5	exercise	exercise	NN
37681	2669	6	which	which	WDT
37681	2669	7	may	may	MD
37681	2669	8	be	be	VB
37681	2669	9	tried	try	VBN
37681	2669	10	about	about	IN
37681	2669	11	the	the	DT
37681	2669	12	time	time	NN
37681	2669	13	that	that	WDT
37681	2669	14	pupils	pupil	NNS
37681	2669	15	are	be	VBP
37681	2669	16	leaving	leave	VBG
37681	2669	17	school	school	NN
37681	2669	18	in	in	IN
37681	2669	19	the	the	DT
37681	2669	20	afternoon	afternoon	NN
37681	2669	21	.	.	.
37681	2670	1	[	[	-LRB-
37681	2670	2	Illustration	illustration	NN
37681	2670	3	]	]	-RRB-
37681	2670	4	Another	another	DT
37681	2670	5	application	application	NN
37681	2670	6	of	of	IN
37681	2670	7	the	the	DT
37681	2670	8	same	same	JJ
37681	2670	9	principle	principle	NN
37681	2670	10	is	be	VBZ
37681	2670	11	seen	see	VBN
37681	2670	12	in	in	IN
37681	2670	13	a	a	DT
37681	2670	14	method	method	NN
37681	2670	15	often	often	RB
37681	2670	16	taken	take	VBN
37681	2670	17	for	for	IN
37681	2670	18	measuring	measure	VBG
37681	2670	19	the	the	DT
37681	2670	20	height	height	NN
37681	2670	21	of	of	IN
37681	2670	22	a	a	DT
37681	2670	23	tree	tree	NN
37681	2670	24	.	.	.
37681	2671	1	[	[	-LRB-
37681	2671	2	Illustration	illustration	NN
37681	2671	3	]	]	-RRB-
37681	2671	4	The	the	DT
37681	2671	5	observer	observer	NN
37681	2671	6	has	have	VBZ
37681	2671	7	a	a	DT
37681	2671	8	large	large	JJ
37681	2671	9	right	right	JJ
37681	2671	10	triangle	triangle	NN
37681	2671	11	made	make	VBN
37681	2671	12	of	of	IN
37681	2671	13	wood	wood	NN
37681	2671	14	.	.	.
37681	2672	1	Such	such	PDT
37681	2672	2	a	a	DT
37681	2672	3	triangle	triangle	NN
37681	2672	4	is	be	VBZ
37681	2672	5	shown	show	VBN
37681	2672	6	in	in	IN
37681	2672	7	the	the	DT
37681	2672	8	picture	picture	NN
37681	2672	9	,	,	,
37681	2672	10	in	in	IN
37681	2672	11	which	which	WDT
37681	2672	12	_	_	NNP
37681	2672	13	AB	AB	NNP
37681	2672	14	_	_	NNP
37681	2672	15	=	=	SYM
37681	2672	16	_	_	NNP
37681	2672	17	BC	BC	NNP
37681	2672	18	_	_	NNP
37681	2672	19	.	.	.
37681	2673	1	He	-PRON-	PRP
37681	2673	2	holds	hold	VBZ
37681	2673	3	_	_	NNP
37681	2673	4	AB	AB	NNP
37681	2673	5	_	_	NNP
37681	2673	6	level	level	NN
37681	2673	7	and	and	CC
37681	2673	8	walks	walk	VBZ
37681	2673	9	toward	toward	IN
37681	2673	10	the	the	DT
37681	2673	11	tree	tree	NN
37681	2673	12	until	until	IN
37681	2673	13	he	-PRON-	PRP
37681	2673	14	just	just	RB
37681	2673	15	sees	see	VBZ
37681	2673	16	the	the	DT
37681	2673	17	top	top	NN
37681	2673	18	along	along	IN
37681	2673	19	_	_	NNP
37681	2673	20	AC	AC	NNP
37681	2673	21	_	_	NNP
37681	2673	22	.	.	.
37681	2674	1	Then	then	RB
37681	2674	2	because	because	IN
37681	2674	3	_	_	NNP
37681	2674	4	AB	AB	NNP
37681	2674	5	_	_	NNP
37681	2674	6	=	=	SYM
37681	2674	7	_	_	NNP
37681	2674	8	BC	BC	NNP
37681	2674	9	_	_	NNP
37681	2674	10	,	,	,
37681	2674	11	and	and	CC
37681	2674	12	_	_	NNP
37681	2674	13	AB	AB	NNP
37681	2674	14	_	_	NNP
37681	2674	15	:	:	:
37681	2674	16	_	_	NNP
37681	2674	17	BC	BC	NNP
37681	2674	18	_	_	NNP
37681	2674	19	=	=	SYM
37681	2674	20	_	_	NNP
37681	2674	21	AD	AD	NNP
37681	2674	22	_	_	NNP
37681	2674	23	:	:	:
37681	2674	24	_	_	NNP
37681	2674	25	DE	DE	NNP
37681	2674	26	_	_	NNP
37681	2674	27	,	,	,
37681	2674	28	the	the	DT
37681	2674	29	height	height	NN
37681	2674	30	above	above	IN
37681	2674	31	_	_	NNP
37681	2674	32	D	D	NNP
37681	2674	33	_	_	NNP
37681	2674	34	will	will	MD
37681	2674	35	equal	equal	VB
37681	2674	36	the	the	DT
37681	2674	37	distance	distance	NN
37681	2674	38	_	_	NNP
37681	2674	39	AD	AD	NNP
37681	2674	40	_	_	NNP
37681	2674	41	.	.	.
37681	2675	1	Questions	question	NNS
37681	2675	2	like	like	IN
37681	2675	3	the	the	DT
37681	2675	4	following	follow	VBG
37681	2675	5	may	may	MD
37681	2675	6	be	be	VB
37681	2675	7	given	give	VBN
37681	2675	8	to	to	IN
37681	2675	9	the	the	DT
37681	2675	10	class	class	NN
37681	2675	11	:	:	:
37681	2675	12	1	1	CD
37681	2675	13	.	.	.
37681	2676	1	What	what	WP
37681	2676	2	is	be	VBZ
37681	2676	3	the	the	DT
37681	2676	4	height	height	NN
37681	2676	5	of	of	IN
37681	2676	6	the	the	DT
37681	2676	7	tree	tree	NN
37681	2676	8	in	in	IN
37681	2676	9	the	the	DT
37681	2676	10	picture	picture	NN
37681	2676	11	if	if	IN
37681	2676	12	the	the	DT
37681	2676	13	triangle	triangle	NN
37681	2676	14	is	be	VBZ
37681	2676	15	5	5	CD
37681	2676	16	ft	ft	NN
37681	2676	17	.	.	NNP
37681	2676	18	4	4	CD
37681	2676	19	in	in	IN
37681	2676	20	.	.	.
37681	2677	1	from	from	IN
37681	2677	2	the	the	DT
37681	2677	3	ground	ground	NN
37681	2677	4	,	,	,
37681	2677	5	and	and	CC
37681	2677	6	_	_	NNP
37681	2677	7	AD	AD	NNP
37681	2677	8	_	_	NNP
37681	2677	9	is	be	VBZ
37681	2677	10	23	23	CD
37681	2677	11	ft	ft	NN
37681	2677	12	.	.	NN
37681	2677	13	8	8	CD
37681	2677	14	in	in	IN
37681	2677	15	.	.	.
37681	2677	16	?	?	.
37681	2678	1	2	2	LS
37681	2678	2	.	.	.
37681	2679	1	Suppose	suppose	VB
37681	2679	2	a	a	DT
37681	2679	3	triangle	triangle	NN
37681	2679	4	is	be	VBZ
37681	2679	5	used	use	VBN
37681	2679	6	which	which	WDT
37681	2679	7	has	have	VBZ
37681	2679	8	_	_	NNP
37681	2679	9	AB	AB	NNP
37681	2679	10	_	_	NNP
37681	2679	11	=	=	SYM
37681	2679	12	twice	twice	PDT
37681	2679	13	_	_	NNP
37681	2679	14	BC	BC	NNP
37681	2679	15	_	_	NNP
37681	2679	16	.	.	.
37681	2680	1	What	what	WP
37681	2680	2	is	be	VBZ
37681	2680	3	the	the	DT
37681	2680	4	height	height	NN
37681	2680	5	if	if	IN
37681	2680	6	_	_	NNP
37681	2680	7	AD	AD	NNP
37681	2680	8	_	_	NNP
37681	2680	9	=	=	SYM
37681	2680	10	75	75	CD
37681	2680	11	ft	ft	NN
37681	2680	12	.	.	.
37681	2680	13	?	?	.
37681	2681	1	There	there	EX
37681	2681	2	are	be	VBP
37681	2681	3	many	many	JJ
37681	2681	4	variations	variation	NNS
37681	2681	5	of	of	IN
37681	2681	6	this	this	DT
37681	2681	7	principle	principle	NN
37681	2681	8	.	.	.
37681	2682	1	One	one	PRP
37681	2682	2	consists	consist	VBZ
37681	2682	3	in	in	IN
37681	2682	4	measuring	measure	VBG
37681	2682	5	the	the	DT
37681	2682	6	shadows	shadow	NNS
37681	2682	7	of	of	IN
37681	2682	8	a	a	DT
37681	2682	9	tree	tree	NN
37681	2682	10	and	and	CC
37681	2682	11	a	a	DT
37681	2682	12	staff	staff	NN
37681	2682	13	at	at	IN
37681	2682	14	the	the	DT
37681	2682	15	same	same	JJ
37681	2682	16	time	time	NN
37681	2682	17	.	.	.
37681	2683	1	The	the	DT
37681	2683	2	height	height	NN
37681	2683	3	of	of	IN
37681	2683	4	the	the	DT
37681	2683	5	staff	staff	NN
37681	2683	6	being	be	VBG
37681	2683	7	known	know	VBN
37681	2683	8	,	,	,
37681	2683	9	the	the	DT
37681	2683	10	height	height	NN
37681	2683	11	of	of	IN
37681	2683	12	the	the	DT
37681	2683	13	tree	tree	NN
37681	2683	14	is	be	VBZ
37681	2683	15	found	find	VBN
37681	2683	16	by	by	IN
37681	2683	17	proportion	proportion	NN
37681	2683	18	.	.	.
37681	2684	1	Another	another	DT
37681	2684	2	consists	consist	VBZ
37681	2684	3	in	in	IN
37681	2684	4	sighting	sight	VBG
37681	2684	5	from	from	IN
37681	2684	6	the	the	DT
37681	2684	7	ground	ground	NN
37681	2684	8	,	,	,
37681	2684	9	across	across	IN
37681	2684	10	a	a	DT
37681	2684	11	mark	mark	NN
37681	2684	12	on	on	IN
37681	2684	13	an	an	DT
37681	2684	14	upright	upright	JJ
37681	2684	15	staff	staff	NN
37681	2684	16	,	,	,
37681	2684	17	to	to	IN
37681	2684	18	the	the	DT
37681	2684	19	top	top	NN
37681	2684	20	of	of	IN
37681	2684	21	the	the	DT
37681	2684	22	tree	tree	NN
37681	2684	23	.	.	.
37681	2685	1	The	the	DT
37681	2685	2	height	height	NN
37681	2685	3	of	of	IN
37681	2685	4	the	the	DT
37681	2685	5	mark	mark	NN
37681	2685	6	being	be	VBG
37681	2685	7	known	know	VBN
37681	2685	8	,	,	,
37681	2685	9	and	and	CC
37681	2685	10	the	the	DT
37681	2685	11	distances	distance	NNS
37681	2685	12	from	from	IN
37681	2685	13	the	the	DT
37681	2685	14	eye	eye	NN
37681	2685	15	to	to	IN
37681	2685	16	the	the	DT
37681	2685	17	staff	staff	NN
37681	2685	18	and	and	CC
37681	2685	19	to	to	IN
37681	2685	20	the	the	DT
37681	2685	21	tree	tree	NN
37681	2685	22	being	be	VBG
37681	2685	23	measured	measure	VBN
37681	2685	24	,	,	,
37681	2685	25	the	the	DT
37681	2685	26	height	height	NN
37681	2685	27	of	of	IN
37681	2685	28	the	the	DT
37681	2685	29	tree	tree	NN
37681	2685	30	is	be	VBZ
37681	2685	31	found	find	VBN
37681	2685	32	.	.	.
37681	2686	1	[	[	-LRB-
37681	2686	2	Illustration	illustration	NN
37681	2686	3	]	]	-RRB-
37681	2686	4	An	an	DT
37681	2686	5	instrument	instrument	NN
37681	2686	6	sold	sell	VBN
37681	2686	7	by	by	IN
37681	2686	8	dealers	dealer	NNS
37681	2686	9	for	for	IN
37681	2686	10	the	the	DT
37681	2686	11	measuring	measuring	NN
37681	2686	12	of	of	IN
37681	2686	13	heights	height	NNS
37681	2686	14	is	be	VBZ
37681	2686	15	known	know	VBN
37681	2686	16	as	as	IN
37681	2686	17	the	the	DT
37681	2686	18	hypsometer	hypsometer	NN
37681	2686	19	.	.	.
37681	2687	1	It	-PRON-	PRP
37681	2687	2	is	be	VBZ
37681	2687	3	made	make	VBN
37681	2687	4	of	of	IN
37681	2687	5	brass	brass	NN
37681	2687	6	,	,	,
37681	2687	7	and	and	CC
37681	2687	8	is	be	VBZ
37681	2687	9	of	of	IN
37681	2687	10	the	the	DT
37681	2687	11	form	form	NN
37681	2687	12	here	here	RB
37681	2687	13	shown	show	VBN
37681	2687	14	.	.	.
37681	2688	1	The	the	DT
37681	2688	2	base	base	NN
37681	2688	3	is	be	VBZ
37681	2688	4	graduated	graduate	VBN
37681	2688	5	in	in	IN
37681	2688	6	equal	equal	JJ
37681	2688	7	divisions	division	NNS
37681	2688	8	,	,	,
37681	2688	9	say	say	VBP
37681	2688	10	50	50	CD
37681	2688	11	,	,	,
37681	2688	12	and	and	CC
37681	2688	13	the	the	DT
37681	2688	14	upright	upright	JJ
37681	2688	15	bar	bar	NN
37681	2688	16	is	be	VBZ
37681	2688	17	similarly	similarly	RB
37681	2688	18	divided	divide	VBN
37681	2688	19	.	.	.
37681	2689	1	At	at	IN
37681	2689	2	the	the	DT
37681	2689	3	ends	end	NNS
37681	2689	4	of	of	IN
37681	2689	5	the	the	DT
37681	2689	6	hinged	hinge	VBN
37681	2689	7	radius	radius	NN
37681	2689	8	are	be	VBP
37681	2689	9	two	two	CD
37681	2689	10	sights	sight	NNS
37681	2689	11	.	.	.
37681	2690	1	If	if	IN
37681	2690	2	the	the	DT
37681	2690	3	observer	observer	NN
37681	2690	4	stands	stand	VBZ
37681	2690	5	50	50	CD
37681	2690	6	feet	foot	NNS
37681	2690	7	from	from	IN
37681	2690	8	a	a	DT
37681	2690	9	tree	tree	NN
37681	2690	10	and	and	CC
37681	2690	11	sights	sight	NNS
37681	2690	12	at	at	IN
37681	2690	13	the	the	DT
37681	2690	14	top	top	NN
37681	2690	15	,	,	,
37681	2690	16	so	so	IN
37681	2690	17	that	that	IN
37681	2690	18	the	the	DT
37681	2690	19	hinged	hinge	VBN
37681	2690	20	radius	radius	NN
37681	2690	21	cuts	cut	VBZ
37681	2690	22	the	the	DT
37681	2690	23	upright	upright	JJ
37681	2690	24	bar	bar	NN
37681	2690	25	at	at	IN
37681	2690	26	27	27	CD
37681	2690	27	,	,	,
37681	2690	28	then	then	RB
37681	2690	29	he	-PRON-	PRP
37681	2690	30	knows	know	VBZ
37681	2690	31	at	at	IN
37681	2690	32	once	once	RB
37681	2690	33	that	that	IN
37681	2690	34	the	the	DT
37681	2690	35	tree	tree	NN
37681	2690	36	is	be	VBZ
37681	2690	37	27	27	CD
37681	2690	38	feet	foot	NNS
37681	2690	39	high	high	JJ
37681	2690	40	.	.	.
37681	2691	1	It	-PRON-	PRP
37681	2691	2	is	be	VBZ
37681	2691	3	easy	easy	JJ
37681	2691	4	for	for	IN
37681	2691	5	a	a	DT
37681	2691	6	class	class	NN
37681	2691	7	to	to	TO
37681	2691	8	make	make	VB
37681	2691	9	a	a	DT
37681	2691	10	fairly	fairly	RB
37681	2691	11	good	good	JJ
37681	2691	12	instrument	instrument	NN
37681	2691	13	of	of	IN
37681	2691	14	this	this	DT
37681	2691	15	kind	kind	NN
37681	2691	16	out	out	IN
37681	2691	17	of	of	IN
37681	2691	18	stiff	stiff	JJ
37681	2691	19	pasteboard	pasteboard	NN
37681	2691	20	.	.	.
37681	2692	1	An	an	DT
37681	2692	2	interesting	interesting	JJ
37681	2692	3	application	application	NN
37681	2692	4	of	of	IN
37681	2692	5	the	the	DT
37681	2692	6	theorem	theorem	NN
37681	2692	7	relating	relate	VBG
37681	2692	8	to	to	IN
37681	2692	9	similar	similar	JJ
37681	2692	10	triangles	triangle	NNS
37681	2692	11	is	be	VBZ
37681	2692	12	this	this	DT
37681	2692	13	:	:	:
37681	2692	14	Extend	extend	VB
37681	2692	15	your	-PRON-	PRP$
37681	2692	16	arm	arm	NN
37681	2692	17	and	and	CC
37681	2692	18	point	point	NN
37681	2692	19	to	to	IN
37681	2692	20	a	a	DT
37681	2692	21	distant	distant	JJ
37681	2692	22	object	object	NN
37681	2692	23	,	,	,
37681	2692	24	closing	close	VBG
37681	2692	25	your	-PRON-	PRP$
37681	2692	26	left	left	JJ
37681	2692	27	eye	eye	NN
37681	2692	28	and	and	CC
37681	2692	29	sighting	sight	VBG
37681	2692	30	across	across	IN
37681	2692	31	your	-PRON-	PRP$
37681	2692	32	finger	finger	NN
37681	2692	33	tip	tip	NN
37681	2692	34	with	with	IN
37681	2692	35	your	-PRON-	PRP$
37681	2692	36	right	right	JJ
37681	2692	37	eye	eye	NN
37681	2692	38	.	.	.
37681	2693	1	Now	now	RB
37681	2693	2	keep	keep	VB
37681	2693	3	the	the	DT
37681	2693	4	finger	finger	NN
37681	2693	5	in	in	IN
37681	2693	6	the	the	DT
37681	2693	7	same	same	JJ
37681	2693	8	position	position	NN
37681	2693	9	and	and	CC
37681	2693	10	sight	sight	NN
37681	2693	11	with	with	IN
37681	2693	12	your	-PRON-	PRP$
37681	2693	13	left	left	JJ
37681	2693	14	eye	eye	NN
37681	2693	15	.	.	.
37681	2694	1	The	the	DT
37681	2694	2	finger	finger	NN
37681	2694	3	will	will	MD
37681	2694	4	then	then	RB
37681	2694	5	seem	seem	VB
37681	2694	6	to	to	TO
37681	2694	7	be	be	VB
37681	2694	8	pointing	point	VBG
37681	2694	9	to	to	IN
37681	2694	10	an	an	DT
37681	2694	11	object	object	NN
37681	2694	12	some	some	DT
37681	2694	13	distance	distance	NN
37681	2694	14	to	to	IN
37681	2694	15	the	the	DT
37681	2694	16	right	right	NN
37681	2694	17	of	of	IN
37681	2694	18	the	the	DT
37681	2694	19	one	one	CD
37681	2694	20	at	at	IN
37681	2694	21	which	which	WDT
37681	2694	22	you	-PRON-	PRP
37681	2694	23	were	be	VBD
37681	2694	24	pointing	point	VBG
37681	2694	25	.	.	.
37681	2695	1	If	if	IN
37681	2695	2	you	-PRON-	PRP
37681	2695	3	can	can	MD
37681	2695	4	estimate	estimate	VB
37681	2695	5	the	the	DT
37681	2695	6	distance	distance	NN
37681	2695	7	between	between	IN
37681	2695	8	these	these	DT
37681	2695	9	two	two	CD
37681	2695	10	objects	object	NNS
37681	2695	11	,	,	,
37681	2695	12	which	which	WDT
37681	2695	13	can	can	MD
37681	2695	14	often	often	RB
37681	2695	15	be	be	VB
37681	2695	16	done	do	VBN
37681	2695	17	with	with	IN
37681	2695	18	a	a	DT
37681	2695	19	fair	fair	JJ
37681	2695	20	degree	degree	NN
37681	2695	21	of	of	IN
37681	2695	22	accuracy	accuracy	NN
37681	2695	23	when	when	WRB
37681	2695	24	there	there	EX
37681	2695	25	are	be	VBP
37681	2695	26	houses	house	NNS
37681	2695	27	intervening	intervene	VBG
37681	2695	28	,	,	,
37681	2695	29	then	then	RB
37681	2695	30	you	-PRON-	PRP
37681	2695	31	will	will	MD
37681	2695	32	be	be	VB
37681	2695	33	able	able	JJ
37681	2695	34	to	to	TO
37681	2695	35	tell	tell	VB
37681	2695	36	approximately	approximately	RB
37681	2695	37	your	-PRON-	PRP$
37681	2695	38	distance	distance	NN
37681	2695	39	from	from	IN
37681	2695	40	the	the	DT
37681	2695	41	objects	object	NNS
37681	2695	42	,	,	,
37681	2695	43	for	for	IN
37681	2695	44	it	-PRON-	PRP
37681	2695	45	will	will	MD
37681	2695	46	be	be	VB
37681	2695	47	ten	ten	CD
37681	2695	48	times	time	NNS
37681	2695	49	the	the	DT
37681	2695	50	estimated	estimate	VBN
37681	2695	51	distance	distance	NN
37681	2695	52	between	between	IN
37681	2695	53	them	-PRON-	PRP
37681	2695	54	.	.	.
37681	2696	1	The	the	DT
37681	2696	2	finding	finding	NN
37681	2696	3	of	of	IN
37681	2696	4	the	the	DT
37681	2696	5	reason	reason	NN
37681	2696	6	for	for	IN
37681	2696	7	this	this	DT
37681	2696	8	by	by	IN
37681	2696	9	measuring	measure	VBG
37681	2696	10	the	the	DT
37681	2696	11	distance	distance	NN
37681	2696	12	between	between	IN
37681	2696	13	the	the	DT
37681	2696	14	pupils	pupil	NNS
37681	2696	15	of	of	IN
37681	2696	16	the	the	DT
37681	2696	17	two	two	CD
37681	2696	18	eyes	eye	NNS
37681	2696	19	,	,	,
37681	2696	20	and	and	CC
37681	2696	21	the	the	DT
37681	2696	22	distance	distance	NN
37681	2696	23	from	from	IN
37681	2696	24	the	the	DT
37681	2696	25	eye	eye	NN
37681	2696	26	to	to	IN
37681	2696	27	the	the	DT
37681	2696	28	finger	finger	NN
37681	2696	29	tip	tip	NN
37681	2696	30	,	,	,
37681	2696	31	and	and	CC
37681	2696	32	then	then	RB
37681	2696	33	drawing	draw	VBG
37681	2696	34	the	the	DT
37681	2696	35	figure	figure	NN
37681	2696	36	,	,	,
37681	2696	37	is	be	VBZ
37681	2696	38	an	an	DT
37681	2696	39	interesting	interesting	JJ
37681	2696	40	exercise	exercise	NN
37681	2696	41	.	.	.
37681	2697	1	Perhaps	perhaps	RB
37681	2697	2	some	some	DT
37681	2697	3	pupil	pupil	NN
37681	2697	4	who	who	WP
37681	2697	5	has	have	VBZ
37681	2697	6	read	read	VBN
37681	2697	7	Thoreau	Thoreau	NNP
37681	2697	8	's	's	POS
37681	2697	9	descriptions	description	NNS
37681	2697	10	of	of	IN
37681	2697	11	outdoor	outdoor	JJ
37681	2697	12	life	life	NN
37681	2697	13	may	may	MD
37681	2697	14	be	be	VB
37681	2697	15	interested	interested	JJ
37681	2697	16	in	in	IN
37681	2697	17	what	what	WP
37681	2697	18	he	-PRON-	PRP
37681	2697	19	says	say	VBZ
37681	2697	20	of	of	IN
37681	2697	21	his	-PRON-	PRP$
37681	2697	22	crude	crude	JJ
37681	2697	23	mathematics	mathematic	NNS
37681	2697	24	.	.	.
37681	2698	1	He	-PRON-	PRP
37681	2698	2	writes	write	VBZ
37681	2698	3	,	,	,
37681	2698	4	"	"	``
37681	2698	5	I	-PRON-	PRP
37681	2698	6	borrowed	borrow	VBD
37681	2698	7	the	the	DT
37681	2698	8	plane	plane	NN
37681	2698	9	and	and	CC
37681	2698	10	square	square	JJ
37681	2698	11	,	,	,
37681	2698	12	level	level	NN
37681	2698	13	and	and	CC
37681	2698	14	dividers	divider	NNS
37681	2698	15	,	,	,
37681	2698	16	of	of	IN
37681	2698	17	a	a	DT
37681	2698	18	carpenter	carpenter	NN
37681	2698	19	,	,	,
37681	2698	20	and	and	CC
37681	2698	21	with	with	IN
37681	2698	22	a	a	DT
37681	2698	23	shingle	shingle	NN
37681	2698	24	contrived	contrive	VBN
37681	2698	25	a	a	DT
37681	2698	26	rude	rude	JJ
37681	2698	27	sort	sort	NN
37681	2698	28	of	of	IN
37681	2698	29	a	a	DT
37681	2698	30	quadrant	quadrant	NN
37681	2698	31	,	,	,
37681	2698	32	with	with	IN
37681	2698	33	pins	pin	NNS
37681	2698	34	for	for	IN
37681	2698	35	sights	sight	NNS
37681	2698	36	and	and	CC
37681	2698	37	pivots	pivot	NNS
37681	2698	38	.	.	.
37681	2698	39	"	"	''
37681	2699	1	With	with	IN
37681	2699	2	this	this	DT
37681	2699	3	he	-PRON-	PRP
37681	2699	4	measured	measure	VBD
37681	2699	5	the	the	DT
37681	2699	6	heights	height	NNS
37681	2699	7	of	of	IN
37681	2699	8	a	a	DT
37681	2699	9	cliff	cliff	NN
37681	2699	10	on	on	IN
37681	2699	11	the	the	DT
37681	2699	12	Massachusetts	Massachusetts	NNP
37681	2699	13	coast	coast	NN
37681	2699	14	,	,	,
37681	2699	15	and	and	CC
37681	2699	16	with	with	IN
37681	2699	17	similar	similar	JJ
37681	2699	18	home	home	NN
37681	2699	19	-	-	HYPH
37681	2699	20	made	make	VBN
37681	2699	21	or	or	CC
37681	2699	22	school	school	NN
37681	2699	23	-	-	HYPH
37681	2699	24	made	make	VBN
37681	2699	25	instruments	instrument	NNS
37681	2699	26	a	a	DT
37681	2699	27	pupil	pupil	NN
37681	2699	28	in	in	IN
37681	2699	29	geometry	geometry	NN
37681	2699	30	can	can	MD
37681	2699	31	measure	measure	VB
37681	2699	32	most	most	JJS
37681	2699	33	of	of	IN
37681	2699	34	the	the	DT
37681	2699	35	heights	height	NNS
37681	2699	36	and	and	CC
37681	2699	37	distances	distance	NNS
37681	2699	38	in	in	IN
37681	2699	39	which	which	WDT
37681	2699	40	he	-PRON-	PRP
37681	2699	41	is	be	VBZ
37681	2699	42	interested	interested	JJ
37681	2699	43	.	.	.
37681	2700	1	THEOREM	THEOREM	NNP
37681	2700	2	.	.	.
37681	2701	1	_	_	XX
37681	2701	2	If	if	IN
37681	2701	3	in	in	IN
37681	2701	4	a	a	DT
37681	2701	5	right	right	JJ
37681	2701	6	triangle	triangle	NN
37681	2701	7	a	a	DT
37681	2701	8	perpendicular	perpendicular	NN
37681	2701	9	is	be	VBZ
37681	2701	10	drawn	draw	VBN
37681	2701	11	from	from	IN
37681	2701	12	the	the	DT
37681	2701	13	vertex	vertex	NN
37681	2701	14	of	of	IN
37681	2701	15	the	the	DT
37681	2701	16	right	right	JJ
37681	2701	17	angle	angle	NN
37681	2701	18	to	to	IN
37681	2701	19	the	the	DT
37681	2701	20	hypotenuse	hypotenuse	NN
37681	2701	21	:	:	:
37681	2701	22	_	_	NNP
37681	2701	23	1	1	CD
37681	2701	24	.	.	.
37681	2702	1	_	_	NNP
37681	2702	2	The	the	DT
37681	2702	3	triangles	triangle	NNS
37681	2702	4	thus	thus	RB
37681	2702	5	formed	form	VBN
37681	2702	6	are	be	VBP
37681	2702	7	similar	similar	JJ
37681	2702	8	to	to	IN
37681	2702	9	the	the	DT
37681	2702	10	given	give	VBN
37681	2702	11	triangle	triangle	NN
37681	2702	12	,	,	,
37681	2702	13	and	and	CC
37681	2702	14	are	be	VBP
37681	2702	15	similar	similar	JJ
37681	2702	16	to	to	IN
37681	2702	17	each	each	DT
37681	2702	18	other	other	JJ
37681	2702	19	.	.	.
37681	2702	20	_	_	NNP
37681	2702	21	2	2	CD
37681	2702	22	.	.	.
37681	2703	1	_	_	NNP
37681	2703	2	The	the	DT
37681	2703	3	perpendicular	perpendicular	NN
37681	2703	4	is	be	VBZ
37681	2703	5	the	the	DT
37681	2703	6	mean	mean	NN
37681	2703	7	proportional	proportional	JJ
37681	2703	8	between	between	IN
37681	2703	9	the	the	DT
37681	2703	10	segments	segment	NNS
37681	2703	11	of	of	IN
37681	2703	12	the	the	DT
37681	2703	13	hypotenuse	hypotenuse	NN
37681	2703	14	.	.	.
37681	2703	15	_	_	NNP
37681	2703	16	3	3	CD
37681	2703	17	.	.	.
37681	2704	1	_	_	NNP
37681	2704	2	Each	each	DT
37681	2704	3	of	of	IN
37681	2704	4	the	the	DT
37681	2704	5	other	other	JJ
37681	2704	6	sides	side	NNS
37681	2704	7	is	be	VBZ
37681	2704	8	the	the	DT
37681	2704	9	mean	mean	NN
37681	2704	10	proportional	proportional	JJ
37681	2704	11	between	between	IN
37681	2704	12	the	the	DT
37681	2704	13	hypotenuse	hypotenuse	NN
37681	2704	14	and	and	CC
37681	2704	15	the	the	DT
37681	2704	16	segment	segment	NN
37681	2704	17	of	of	IN
37681	2704	18	the	the	DT
37681	2704	19	hypotenuse	hypotenuse	NN
37681	2704	20	adjacent	adjacent	JJ
37681	2704	21	to	to	IN
37681	2704	22	that	that	DT
37681	2704	23	side	side	NN
37681	2704	24	.	.	.
37681	2704	25	_	_	NNP
37681	2704	26	To	to	IN
37681	2704	27	this	this	DT
37681	2704	28	important	important	JJ
37681	2704	29	proposition	proposition	NN
37681	2704	30	there	there	EX
37681	2704	31	is	be	VBZ
37681	2704	32	one	one	CD
37681	2704	33	corollary	corollary	NN
37681	2704	34	of	of	IN
37681	2704	35	particular	particular	JJ
37681	2704	36	interest	interest	NN
37681	2704	37	,	,	,
37681	2704	38	namely	namely	RB
37681	2704	39	,	,	,
37681	2704	40	_	_	NNP
37681	2704	41	The	the	DT
37681	2704	42	perpendicular	perpendicular	NN
37681	2704	43	from	from	IN
37681	2704	44	any	any	DT
37681	2704	45	point	point	NN
37681	2704	46	on	on	IN
37681	2704	47	a	a	DT
37681	2704	48	circle	circle	NN
37681	2704	49	to	to	IN
37681	2704	50	a	a	DT
37681	2704	51	diameter	diameter	NN
37681	2704	52	is	be	VBZ
37681	2704	53	the	the	DT
37681	2704	54	mean	mean	NN
37681	2704	55	proportional	proportional	JJ
37681	2704	56	between	between	IN
37681	2704	57	the	the	DT
37681	2704	58	segments	segment	NNS
37681	2704	59	of	of	IN
37681	2704	60	the	the	DT
37681	2704	61	diameter	diameter	NN
37681	2704	62	_	_	NNP
37681	2704	63	.	.	.
37681	2705	1	By	by	IN
37681	2705	2	means	mean	NNS
37681	2705	3	of	of	IN
37681	2705	4	this	this	DT
37681	2705	5	corollary	corollary	NN
37681	2705	6	we	-PRON-	PRP
37681	2705	7	can	can	MD
37681	2705	8	easily	easily	RB
37681	2705	9	construct	construct	VB
37681	2705	10	a	a	DT
37681	2705	11	line	line	NN
37681	2705	12	whose	whose	WP$
37681	2705	13	numerical	numerical	JJ
37681	2705	14	value	value	NN
37681	2705	15	is	be	VBZ
37681	2705	16	the	the	DT
37681	2705	17	square	square	JJ
37681	2705	18	root	root	NN
37681	2705	19	of	of	IN
37681	2705	20	any	any	DT
37681	2705	21	number	number	NN
37681	2705	22	we	-PRON-	PRP
37681	2705	23	please	please	VBP
37681	2705	24	.	.	.
37681	2706	1	Thus	thus	RB
37681	2706	2	we	-PRON-	PRP
37681	2706	3	may	may	MD
37681	2706	4	make	make	VB
37681	2706	5	_	_	NNP
37681	2706	6	AD	AD	NNP
37681	2706	7	_	_	NNP
37681	2706	8	=	=	SYM
37681	2706	9	2	2	CD
37681	2706	10	in	in	IN
37681	2706	11	.	.	NNP
37681	2706	12	,	,	,
37681	2706	13	_	_	NNP
37681	2706	14	DB	DB	NNP
37681	2706	15	_	_	NNP
37681	2706	16	=	=	SYM
37681	2706	17	3	3	CD
37681	2706	18	in	in	IN
37681	2706	19	.	.	NNP
37681	2706	20	,	,	,
37681	2706	21	and	and	CC
37681	2706	22	erect	erect	NN
37681	2706	23	_	_	NNP
37681	2706	24	DC	DC	NNP
37681	2706	25	_	_	NNP
37681	2706	26	[	[	-LRB-
37681	2706	27	perp	perp	NN
37681	2706	28	]	]	-RRB-
37681	2706	29	to	to	IN
37681	2706	30	_	_	NNP
37681	2706	31	AB	AB	NNP
37681	2706	32	_	_	NNP
37681	2706	33	.	.	.
37681	2707	1	Then	then	RB
37681	2707	2	the	the	DT
37681	2707	3	length	length	NN
37681	2707	4	of	of	IN
37681	2707	5	_	_	NNP
37681	2707	6	DC	DC	NNP
37681	2707	7	_	_	NNP
37681	2707	8	will	will	MD
37681	2707	9	be	be	VB
37681	2707	10	[	[	-LRB-
37681	2707	11	sqrt]6	sqrt]6	CD
37681	2707	12	in	in	IN
37681	2707	13	.	.	.
37681	2707	14	,	,	,
37681	2707	15	and	and	CC
37681	2707	16	we	-PRON-	PRP
37681	2707	17	may	may	MD
37681	2707	18	find	find	VB
37681	2707	19	[	[	-LRB-
37681	2707	20	sqrt]6	sqrt]6	NN
37681	2707	21	approximately	approximately	RB
37681	2707	22	by	by	IN
37681	2707	23	measuring	measure	VBG
37681	2707	24	_	_	NNP
37681	2707	25	DC	DC	NNP
37681	2707	26	_	_	NNP
37681	2707	27	.	.	.
37681	2708	1	[	[	-LRB-
37681	2708	2	Illustration	illustration	NN
37681	2708	3	]	]	-RRB-
37681	2708	4	Furthermore	furthermore	RB
37681	2708	5	,	,	,
37681	2708	6	if	if	IN
37681	2708	7	we	-PRON-	PRP
37681	2708	8	introduce	introduce	VBP
37681	2708	9	negative	negative	JJ
37681	2708	10	magnitudes	magnitude	NNS
37681	2708	11	into	into	IN
37681	2708	12	geometry	geometry	NN
37681	2708	13	,	,	,
37681	2708	14	and	and	CC
37681	2708	15	let	let	VB
37681	2708	16	_	_	NNP
37681	2708	17	DB	DB	NNP
37681	2708	18	_	_	NNP
37681	2708	19	=	=	SYM
37681	2708	20	+3	+3	NNP
37681	2708	21	and	and	CC
37681	2708	22	_	_	NNP
37681	2708	23	DA	DA	NNP
37681	2708	24	_	_	NNP
37681	2708	25	=	=	SYM
37681	2708	26	-2	-2	:
37681	2708	27	,	,	,
37681	2708	28	then	then	RB
37681	2708	29	_	_	NNP
37681	2708	30	DC	DC	NNP
37681	2708	31	_	_	NNP
37681	2708	32	will	will	MD
37681	2708	33	equal	equal	VB
37681	2708	34	[	[	-LRB-
37681	2708	35	sqrt](-6	sqrt](-6	NNP
37681	2708	36	)	)	-RRB-
37681	2708	37	.	.	.
37681	2709	1	In	in	IN
37681	2709	2	other	other	JJ
37681	2709	3	words	word	NNS
37681	2709	4	,	,	,
37681	2709	5	we	-PRON-	PRP
37681	2709	6	have	have	VBP
37681	2709	7	a	a	DT
37681	2709	8	justification	justification	NN
37681	2709	9	for	for	IN
37681	2709	10	representing	represent	VBG
37681	2709	11	imaginary	imaginary	JJ
37681	2709	12	quantities	quantity	NNS
37681	2709	13	by	by	IN
37681	2709	14	lines	line	NNS
37681	2709	15	perpendicular	perpendicular	JJ
37681	2709	16	to	to	IN
37681	2709	17	the	the	DT
37681	2709	18	line	line	NN
37681	2709	19	on	on	IN
37681	2709	20	which	which	WDT
37681	2709	21	we	-PRON-	PRP
37681	2709	22	represent	represent	VBP
37681	2709	23	real	real	JJ
37681	2709	24	quantities	quantity	NNS
37681	2709	25	,	,	,
37681	2709	26	as	as	IN
37681	2709	27	is	be	VBZ
37681	2709	28	done	do	VBN
37681	2709	29	in	in	IN
37681	2709	30	the	the	DT
37681	2709	31	graphic	graphic	JJ
37681	2709	32	treatment	treatment	NN
37681	2709	33	of	of	IN
37681	2709	34	imaginaries	imaginary	NNS
37681	2709	35	in	in	IN
37681	2709	36	algebra	algebra	NN
37681	2709	37	.	.	.
37681	2710	1	It	-PRON-	PRP
37681	2710	2	is	be	VBZ
37681	2710	3	an	an	DT
37681	2710	4	interesting	interesting	JJ
37681	2710	5	exercise	exercise	NN
37681	2710	6	to	to	TO
37681	2710	7	have	have	VB
37681	2710	8	a	a	DT
37681	2710	9	class	class	NN
37681	2710	10	find	find	NN
37681	2710	11	,	,	,
37681	2710	12	to	to	IN
37681	2710	13	one	one	CD
37681	2710	14	decimal	decimal	JJ
37681	2710	15	place	place	NN
37681	2710	16	,	,	,
37681	2710	17	by	by	IN
37681	2710	18	measuring	measure	VBG
37681	2710	19	as	as	IN
37681	2710	20	above	above	RB
37681	2710	21	,	,	,
37681	2710	22	the	the	DT
37681	2710	23	value	value	NN
37681	2710	24	of	of	IN
37681	2710	25	[	[	-LRB-
37681	2710	26	sqrt]2	sqrt]2	CD
37681	2710	27	,	,	,
37681	2710	28	[	[	-LRB-
37681	2710	29	sqrt]3	sqrt]3	UH
37681	2710	30	,	,	,
37681	2710	31	[	[	-LRB-
37681	2710	32	sqrt]5	sqrt]5	IN
37681	2710	33	,	,	,
37681	2710	34	and	and	CC
37681	2710	35	[	[	-LRB-
37681	2710	36	sqrt]9	sqrt]9	CD
37681	2710	37	,	,	,
37681	2710	38	the	the	DT
37681	2710	39	last	last	JJ
37681	2710	40	being	be	VBG
37681	2710	41	integral	integral	JJ
37681	2710	42	.	.	.
37681	2711	1	If	if	IN
37681	2711	2	,	,	,
37681	2711	3	as	as	IN
37681	2711	4	is	be	VBZ
37681	2711	5	not	not	RB
37681	2711	6	usually	usually	RB
37681	2711	7	the	the	DT
37681	2711	8	case	case	NN
37681	2711	9	,	,	,
37681	2711	10	the	the	DT
37681	2711	11	class	class	NN
37681	2711	12	has	have	VBZ
37681	2711	13	studied	study	VBN
37681	2711	14	the	the	DT
37681	2711	15	complex	complex	JJ
37681	2711	16	number	number	NN
37681	2711	17	,	,	,
37681	2711	18	the	the	DT
37681	2711	19	absolute	absolute	JJ
37681	2711	20	value	value	NN
37681	2711	21	of	of	IN
37681	2711	22	[	[	-LRB-
37681	2711	23	sqrt](-6	sqrt](-6	NNP
37681	2711	24	)	)	-RRB-
37681	2711	25	,	,	,
37681	2711	26	[	[	-LRB-
37681	2711	27	sqrt](-7	sqrt](-7	NNP
37681	2711	28	)	)	-RRB-
37681	2711	29	,	,	,
37681	2711	30	...	...	:
37681	2711	31	,	,	,
37681	2711	32	may	may	MD
37681	2711	33	be	be	VB
37681	2711	34	found	find	VBN
37681	2711	35	in	in	IN
37681	2711	36	the	the	DT
37681	2711	37	same	same	JJ
37681	2711	38	way	way	NN
37681	2711	39	.	.	.
37681	2712	1	A	a	DT
37681	2712	2	practical	practical	JJ
37681	2712	3	illustration	illustration	NN
37681	2712	4	of	of	IN
37681	2712	5	the	the	DT
37681	2712	6	value	value	NN
37681	2712	7	of	of	IN
37681	2712	8	the	the	DT
37681	2712	9	above	above	JJ
37681	2712	10	theorem	theorem	NN
37681	2712	11	is	be	VBZ
37681	2712	12	seen	see	VBN
37681	2712	13	in	in	IN
37681	2712	14	a	a	DT
37681	2712	15	method	method	NN
37681	2712	16	for	for	IN
37681	2712	17	finding	find	VBG
37681	2712	18	distances	distance	NNS
37681	2712	19	that	that	WDT
37681	2712	20	is	be	VBZ
37681	2712	21	frequently	frequently	RB
37681	2712	22	described	describe	VBN
37681	2712	23	in	in	IN
37681	2712	24	early	early	JJ
37681	2712	25	printed	print	VBN
37681	2712	26	books	book	NNS
37681	2712	27	.	.	.
37681	2713	1	It	-PRON-	PRP
37681	2713	2	seems	seem	VBZ
37681	2713	3	to	to	TO
37681	2713	4	have	have	VB
37681	2713	5	come	come	VBN
37681	2713	6	from	from	IN
37681	2713	7	the	the	DT
37681	2713	8	Roman	roman	JJ
37681	2713	9	surveyors	surveyor	NNS
37681	2713	10	.	.	.
37681	2714	1	[	[	-LRB-
37681	2714	2	Illustration	illustration	NN
37681	2714	3	]	]	-RRB-
37681	2714	4	If	if	IN
37681	2714	5	a	a	DT
37681	2714	6	carpenter	carpenter	NN
37681	2714	7	's	's	POS
37681	2714	8	square	square	NN
37681	2714	9	is	be	VBZ
37681	2714	10	put	put	VBN
37681	2714	11	on	on	IN
37681	2714	12	top	top	NN
37681	2714	13	of	of	IN
37681	2714	14	an	an	DT
37681	2714	15	upright	upright	JJ
37681	2714	16	stick	stick	NN
37681	2714	17	,	,	,
37681	2714	18	as	as	IN
37681	2714	19	here	here	RB
37681	2714	20	shown	show	VBN
37681	2714	21	,	,	,
37681	2714	22	and	and	CC
37681	2714	23	an	an	DT
37681	2714	24	observer	observer	NN
37681	2714	25	sights	sight	NNS
37681	2714	26	along	along	IN
37681	2714	27	the	the	DT
37681	2714	28	arms	arm	NNS
37681	2714	29	to	to	IN
37681	2714	30	a	a	DT
37681	2714	31	distant	distant	JJ
37681	2714	32	point	point	NN
37681	2714	33	_	_	NNP
37681	2714	34	B	B	NNP
37681	2714	35	_	_	NNP
37681	2714	36	and	and	CC
37681	2714	37	a	a	DT
37681	2714	38	point	point	NN
37681	2714	39	_	_	NNP
37681	2714	40	A	A	NNP
37681	2714	41	_	_	NNP
37681	2714	42	near	near	IN
37681	2714	43	the	the	DT
37681	2714	44	stick	stick	NN
37681	2714	45	,	,	,
37681	2714	46	then	then	RB
37681	2714	47	the	the	DT
37681	2714	48	two	two	CD
37681	2714	49	triangles	triangle	NNS
37681	2714	50	are	be	VBP
37681	2714	51	similar	similar	JJ
37681	2714	52	.	.	.
37681	2715	1	Hence	hence	RB
37681	2715	2	_	_	NNP
37681	2715	3	AD	AD	NNP
37681	2715	4	_	_	NNP
37681	2715	5	:	:	:
37681	2715	6	_	_	NNP
37681	2715	7	DC	DC	NNP
37681	2715	8	_	_	NNP
37681	2715	9	=	=	SYM
37681	2715	10	_	_	NNP
37681	2715	11	DC	DC	NNP
37681	2715	12	_	_	NNP
37681	2715	13	:	:	:
37681	2715	14	_	_	NNP
37681	2715	15	DB	DB	NNP
37681	2715	16	_	_	NNP
37681	2715	17	.	.	.
37681	2716	1	Hence	hence	RB
37681	2716	2	,	,	,
37681	2716	3	if	if	IN
37681	2716	4	_	_	NNP
37681	2716	5	AD	AD	NNP
37681	2716	6	_	_	NNP
37681	2716	7	and	and	CC
37681	2716	8	_	_	NNP
37681	2716	9	DC	DC	NNP
37681	2716	10	_	_	NNP
37681	2716	11	are	be	VBP
37681	2716	12	measured	measure	VBN
37681	2716	13	,	,	,
37681	2716	14	_	_	NNP
37681	2716	15	DB	DB	NNP
37681	2716	16	_	_	NNP
37681	2716	17	can	can	MD
37681	2716	18	be	be	VB
37681	2716	19	found	find	VBN
37681	2716	20	.	.	.
37681	2717	1	The	the	DT
37681	2717	2	experiment	experiment	NN
37681	2717	3	is	be	VBZ
37681	2717	4	an	an	DT
37681	2717	5	interesting	interesting	JJ
37681	2717	6	and	and	CC
37681	2717	7	instructive	instructive	JJ
37681	2717	8	one	one	CD
37681	2717	9	for	for	IN
37681	2717	10	a	a	DT
37681	2717	11	class	class	NN
37681	2717	12	,	,	,
37681	2717	13	especially	especially	RB
37681	2717	14	as	as	IN
37681	2717	15	the	the	DT
37681	2717	16	square	square	NN
37681	2717	17	can	can	MD
37681	2717	18	easily	easily	RB
37681	2717	19	be	be	VB
37681	2717	20	made	make	VBN
37681	2717	21	out	out	IN
37681	2717	22	of	of	IN
37681	2717	23	heavy	heavy	JJ
37681	2717	24	pasteboard	pasteboard	NN
37681	2717	25	.	.	.
37681	2718	1	THEOREM	THEOREM	NNP
37681	2718	2	.	.	.
37681	2719	1	_	_	XX
37681	2719	2	If	if	IN
37681	2719	3	two	two	CD
37681	2719	4	chords	chord	NNS
37681	2719	5	intersect	intersect	VBP
37681	2719	6	within	within	IN
37681	2719	7	a	a	DT
37681	2719	8	circle	circle	NN
37681	2719	9	,	,	,
37681	2719	10	the	the	DT
37681	2719	11	product	product	NN
37681	2719	12	of	of	IN
37681	2719	13	the	the	DT
37681	2719	14	segments	segment	NNS
37681	2719	15	of	of	IN
37681	2719	16	the	the	DT
37681	2719	17	one	one	NN
37681	2719	18	is	be	VBZ
37681	2719	19	equal	equal	JJ
37681	2719	20	to	to	IN
37681	2719	21	the	the	DT
37681	2719	22	product	product	NN
37681	2719	23	of	of	IN
37681	2719	24	the	the	DT
37681	2719	25	segments	segment	NNS
37681	2719	26	of	of	IN
37681	2719	27	the	the	DT
37681	2719	28	other	other	JJ
37681	2719	29	.	.	.
37681	2719	30	_	_	NNP
37681	2719	31	THEOREM	THEOREM	NNP
37681	2719	32	.	.	.
37681	2720	1	_	_	XX
37681	2720	2	If	if	IN
37681	2720	3	from	from	IN
37681	2720	4	a	a	DT
37681	2720	5	point	point	NN
37681	2720	6	without	without	IN
37681	2720	7	a	a	DT
37681	2720	8	circle	circle	NN
37681	2720	9	a	a	DT
37681	2720	10	secant	secant	NN
37681	2720	11	and	and	CC
37681	2720	12	a	a	DT
37681	2720	13	tangent	tangent	NN
37681	2720	14	are	be	VBP
37681	2720	15	drawn	draw	VBN
37681	2720	16	,	,	,
37681	2720	17	the	the	DT
37681	2720	18	tangent	tangent	NN
37681	2720	19	is	be	VBZ
37681	2720	20	the	the	DT
37681	2720	21	mean	mean	NN
37681	2720	22	proportional	proportional	JJ
37681	2720	23	between	between	IN
37681	2720	24	the	the	DT
37681	2720	25	secant	secant	NN
37681	2720	26	and	and	CC
37681	2720	27	its	-PRON-	PRP$
37681	2720	28	external	external	JJ
37681	2720	29	segment	segment	NN
37681	2720	30	.	.	.
37681	2720	31	_	_	NNP
37681	2720	32	COROLLARY	COROLLARY	NNP
37681	2720	33	.	.	.
37681	2721	1	_	_	XX
37681	2721	2	If	if	IN
37681	2721	3	from	from	IN
37681	2721	4	a	a	DT
37681	2721	5	point	point	NN
37681	2721	6	without	without	IN
37681	2721	7	a	a	DT
37681	2721	8	circle	circle	NN
37681	2721	9	a	a	DT
37681	2721	10	secant	secant	NN
37681	2721	11	is	be	VBZ
37681	2721	12	drawn	draw	VBN
37681	2721	13	,	,	,
37681	2721	14	the	the	DT
37681	2721	15	product	product	NN
37681	2721	16	of	of	IN
37681	2721	17	the	the	DT
37681	2721	18	secant	secant	NN
37681	2721	19	and	and	CC
37681	2721	20	its	-PRON-	PRP$
37681	2721	21	external	external	JJ
37681	2721	22	segment	segment	NN
37681	2721	23	is	be	VBZ
37681	2721	24	constant	constant	JJ
37681	2721	25	in	in	IN
37681	2721	26	whatever	whatever	WDT
37681	2721	27	direction	direction	NN
37681	2721	28	the	the	DT
37681	2721	29	secant	secant	NN
37681	2721	30	is	be	VBZ
37681	2721	31	drawn	draw	VBN
37681	2721	32	.	.	.
37681	2721	33	_	_	NNP
37681	2721	34	These	these	DT
37681	2721	35	two	two	CD
37681	2721	36	propositions	proposition	NNS
37681	2721	37	and	and	CC
37681	2721	38	the	the	DT
37681	2721	39	corollary	corollary	JJ
37681	2721	40	are	be	VBP
37681	2721	41	all	all	DT
37681	2721	42	parts	part	NNS
37681	2721	43	of	of	IN
37681	2721	44	one	one	CD
37681	2721	45	general	general	JJ
37681	2721	46	proposition	proposition	NN
37681	2721	47	:	:	:
37681	2721	48	_	_	XX
37681	2721	49	If	if	IN
37681	2721	50	through	through	IN
37681	2721	51	a	a	DT
37681	2721	52	point	point	NN
37681	2721	53	a	a	DT
37681	2721	54	line	line	NN
37681	2721	55	is	be	VBZ
37681	2721	56	drawn	draw	VBN
37681	2721	57	cutting	cut	VBG
37681	2721	58	a	a	DT
37681	2721	59	circle	circle	NN
37681	2721	60	,	,	,
37681	2721	61	the	the	DT
37681	2721	62	product	product	NN
37681	2721	63	of	of	IN
37681	2721	64	the	the	DT
37681	2721	65	segments	segment	NNS
37681	2721	66	of	of	IN
37681	2721	67	the	the	DT
37681	2721	68	line	line	NN
37681	2721	69	is	be	VBZ
37681	2721	70	constant	constant	JJ
37681	2721	71	_	_	NNP
37681	2721	72	.	.	.
37681	2722	1	[	[	-LRB-
37681	2722	2	Illustration	illustration	NN
37681	2722	3	]	]	-RRB-
37681	2722	4	If	if	IN
37681	2722	5	_	_	NNP
37681	2722	6	P	P	NNP
37681	2722	7	_	_	NNP
37681	2722	8	is	be	VBZ
37681	2722	9	within	within	IN
37681	2722	10	the	the	DT
37681	2722	11	circle	circle	NN
37681	2722	12	,	,	,
37681	2722	13	then	then	RB
37681	2722	14	_	_	NNP
37681	2722	15	xx	xx	IN
37681	2722	16	'	'	``
37681	2722	17	_	_	NNP
37681	2722	18	=	=	SYM
37681	2722	19	_	_	NNP
37681	2722	20	yy	yy	UH
37681	2722	21	'	'	''
37681	2722	22	_	_	NN
37681	2722	23	;	;	:
37681	2722	24	if	if	IN
37681	2722	25	_	_	NNP
37681	2722	26	P	P	NNP
37681	2722	27	_	_	NNP
37681	2722	28	is	be	VBZ
37681	2722	29	on	on	IN
37681	2722	30	the	the	DT
37681	2722	31	circle	circle	NN
37681	2722	32	,	,	,
37681	2722	33	then	then	RB
37681	2722	34	_	_	NNP
37681	2722	35	x	x	NNP
37681	2722	36	_	_	NNP
37681	2722	37	and	and	CC
37681	2722	38	_	_	NNP
37681	2722	39	y	y	NNP
37681	2722	40	_	_	NNP
37681	2722	41	become	become	VBP
37681	2722	42	0	0	CD
37681	2722	43	,	,	,
37681	2722	44	and	and	CC
37681	2722	45	0	0	NFP
37681	2722	46	·	·	NFP
37681	2722	47	_	_	NN
37681	2722	48	x	x	SYM
37681	2722	49	'	'	''
37681	2722	50	_	_	NN
37681	2722	51	=	=	SYM
37681	2722	52	0	0	NFP
37681	2722	53	·	·	NFP
37681	2722	54	_	_	NNP
37681	2722	55	y	y	NNP
37681	2722	56	'	'	''
37681	2722	57	_	_	NNP
37681	2722	58	=	=	SYM
37681	2722	59	0	0	NFP
37681	2722	60	;	;	:
37681	2722	61	if	if	IN
37681	2722	62	_	_	NNP
37681	2722	63	P	P	NNP
37681	2722	64	_	_	NNP
37681	2722	65	is	be	VBZ
37681	2722	66	at	at	IN
37681	2722	67	_	_	NNP
37681	2722	68	P__{3	P__{3	NNP
37681	2722	69	}	}	-RRB-
37681	2722	70	,	,	,
37681	2722	71	then	then	RB
37681	2722	72	_	_	NNP
37681	2722	73	x	x	SYM
37681	2722	74	_	_	NNP
37681	2722	75	and	and	CC
37681	2722	76	_	_	NNP
37681	2722	77	y	y	NNP
37681	2722	78	_	_	NNP
37681	2722	79	,	,	,
37681	2722	80	having	have	VBG
37681	2722	81	passed	pass	VBN
37681	2722	82	through	through	RP
37681	2722	83	0	0	CD
37681	2722	84	,	,	,
37681	2722	85	may	may	MD
37681	2722	86	be	be	VB
37681	2722	87	considered	consider	VBN
37681	2722	88	negative	negative	JJ
37681	2722	89	if	if	IN
37681	2722	90	we	-PRON-	PRP
37681	2722	91	wish	wish	VBP
37681	2722	92	,	,	,
37681	2722	93	although	although	IN
37681	2722	94	the	the	DT
37681	2722	95	two	two	CD
37681	2722	96	negative	negative	JJ
37681	2722	97	signs	sign	NNS
37681	2722	98	would	would	MD
37681	2722	99	cancel	cancel	VB
37681	2722	100	out	out	RP
37681	2722	101	in	in	IN
37681	2722	102	the	the	DT
37681	2722	103	equation	equation	NN
37681	2722	104	;	;	:
37681	2722	105	if	if	IN
37681	2722	106	_	_	NNP
37681	2722	107	P	P	NNP
37681	2722	108	_	_	NNP
37681	2722	109	is	be	VBZ
37681	2722	110	at	at	IN
37681	2722	111	_	_	NNP
37681	2722	112	P__{4	P__{4	NNP
37681	2722	113	}	}	-RRB-
37681	2722	114	,	,	,
37681	2722	115	then	then	RB
37681	2722	116	_	_	NNP
37681	2722	117	y	y	NNP
37681	2722	118	_	_	NNP
37681	2722	119	=	=	SYM
37681	2722	120	_	_	NNP
37681	2722	121	y	y	NNP
37681	2722	122	'	'	''
37681	2722	123	_	_	NNP
37681	2722	124	and	and	CC
37681	2722	125	we	-PRON-	PRP
37681	2722	126	have	have	VBP
37681	2722	127	_	_	NNP
37681	2722	128	xx	xx	IN
37681	2722	129	'	'	``
37681	2722	130	_	_	NNP
37681	2722	131	=	=	SYM
37681	2722	132	_	_	NNP
37681	2722	133	y_^2	y_^2	NNP
37681	2722	134	,	,	,
37681	2722	135	or	or	CC
37681	2722	136	_	_	NNP
37681	2722	137	x	x	NNP
37681	2722	138	_	_	NNP
37681	2722	139	:	:	:
37681	2722	140	_	_	NNP
37681	2722	141	y	y	NNP
37681	2722	142	_	_	NNP
37681	2722	143	=	=	SYM
37681	2722	144	_	_	NNP
37681	2722	145	y	y	NNP
37681	2722	146	_	_	NNP
37681	2722	147	:	:	:
37681	2722	148	_	_	NNP
37681	2722	149	x	x	NNP
37681	2722	150	'	'	''
37681	2722	151	_	_	NNP
37681	2722	152	,	,	,
37681	2722	153	as	as	IN
37681	2722	154	stated	state	VBN
37681	2722	155	in	in	IN
37681	2722	156	the	the	DT
37681	2722	157	proposition	proposition	NN
37681	2722	158	.	.	.
37681	2723	1	We	-PRON-	PRP
37681	2723	2	thus	thus	RB
37681	2723	3	have	have	VBP
37681	2723	4	an	an	DT
37681	2723	5	excellent	excellent	JJ
37681	2723	6	example	example	NN
37681	2723	7	of	of	IN
37681	2723	8	the	the	DT
37681	2723	9	Principle	Principle	NNP
37681	2723	10	of	of	IN
37681	2723	11	Continuity	Continuity	NNP
37681	2723	12	,	,	,
37681	2723	13	and	and	CC
37681	2723	14	classes	class	NNS
37681	2723	15	are	be	VBP
37681	2723	16	always	always	RB
37681	2723	17	interested	interested	JJ
37681	2723	18	to	to	TO
37681	2723	19	consider	consider	VB
37681	2723	20	the	the	DT
37681	2723	21	result	result	NN
37681	2723	22	of	of	IN
37681	2723	23	letting	let	VBG
37681	2723	24	_	_	NNP
37681	2723	25	P	P	NNP
37681	2723	26	_	_	NNP
37681	2723	27	assume	assume	VBP
37681	2723	28	various	various	JJ
37681	2723	29	positions	position	NNS
37681	2723	30	.	.	.
37681	2724	1	Among	among	IN
37681	2724	2	the	the	DT
37681	2724	3	possible	possible	JJ
37681	2724	4	cases	case	NNS
37681	2724	5	is	be	VBZ
37681	2724	6	the	the	DT
37681	2724	7	one	one	CD
37681	2724	8	of	of	IN
37681	2724	9	two	two	CD
37681	2724	10	tangents	tangent	NNS
37681	2724	11	from	from	IN
37681	2724	12	an	an	DT
37681	2724	13	external	external	JJ
37681	2724	14	point	point	NN
37681	2724	15	,	,	,
37681	2724	16	and	and	CC
37681	2724	17	the	the	DT
37681	2724	18	one	one	CD
37681	2724	19	where	where	WRB
37681	2724	20	_	_	NNP
37681	2724	21	P	P	NNP
37681	2724	22	_	_	NNP
37681	2724	23	is	be	VBZ
37681	2724	24	at	at	IN
37681	2724	25	the	the	DT
37681	2724	26	center	center	NN
37681	2724	27	of	of	IN
37681	2724	28	the	the	DT
37681	2724	29	circle	circle	NN
37681	2724	30	.	.	.
37681	2725	1	Students	student	NNS
37681	2725	2	should	should	MD
37681	2725	3	frequently	frequently	RB
37681	2725	4	be	be	VB
37681	2725	5	questioned	question	VBN
37681	2725	6	as	as	IN
37681	2725	7	to	to	IN
37681	2725	8	the	the	DT
37681	2725	9	meaning	meaning	NN
37681	2725	10	of	of	IN
37681	2725	11	"	"	``
37681	2725	12	product	product	NN
37681	2725	13	of	of	IN
37681	2725	14	lines	line	NNS
37681	2725	15	.	.	.
37681	2725	16	"	"	''
37681	2726	1	The	the	DT
37681	2726	2	Greeks	Greeks	NNPS
37681	2726	3	always	always	RB
37681	2726	4	used	use	VBD
37681	2726	5	"	"	''
37681	2726	6	rectangle	rectangle	NN
37681	2726	7	of	of	IN
37681	2726	8	lines	line	NNS
37681	2726	9	,	,	,
37681	2726	10	"	"	''
37681	2726	11	but	but	CC
37681	2726	12	it	-PRON-	PRP
37681	2726	13	is	be	VBZ
37681	2726	14	entirely	entirely	RB
37681	2726	15	legitimate	legitimate	JJ
37681	2726	16	to	to	TO
37681	2726	17	speak	speak	VB
37681	2726	18	of	of	IN
37681	2726	19	"	"	``
37681	2726	20	product	product	NN
37681	2726	21	of	of	IN
37681	2726	22	lines	line	NNS
37681	2726	23	,	,	,
37681	2726	24	"	"	''
37681	2726	25	provided	provide	VBD
37681	2726	26	we	-PRON-	PRP
37681	2726	27	define	define	VBP
37681	2726	28	the	the	DT
37681	2726	29	expression	expression	NN
37681	2726	30	consistently	consistently	RB
37681	2726	31	.	.	.
37681	2727	1	Most	Most	JJS
37681	2727	2	writers	writer	NNS
37681	2727	3	do	do	VBP
37681	2727	4	this	this	DT
37681	2727	5	,	,	,
37681	2727	6	saying	say	VBG
37681	2727	7	that	that	IN
37681	2727	8	by	by	IN
37681	2727	9	the	the	DT
37681	2727	10	product	product	NN
37681	2727	11	of	of	IN
37681	2727	12	lines	line	NNS
37681	2727	13	is	be	VBZ
37681	2727	14	meant	mean	VBN
37681	2727	15	the	the	DT
37681	2727	16	product	product	NN
37681	2727	17	of	of	IN
37681	2727	18	their	-PRON-	PRP$
37681	2727	19	numerical	numerical	JJ
37681	2727	20	values	value	NNS
37681	2727	21	,	,	,
37681	2727	22	a	a	DT
37681	2727	23	subject	subject	NN
37681	2727	24	already	already	RB
37681	2727	25	discussed	discuss	VBN
37681	2727	26	at	at	IN
37681	2727	27	the	the	DT
37681	2727	28	beginning	beginning	NN
37681	2727	29	of	of	IN
37681	2727	30	this	this	DT
37681	2727	31	chapter	chapter	NN
37681	2727	32	.	.	.
37681	2728	1	THEOREM	THEOREM	NNP
37681	2728	2	.	.	.
37681	2729	1	_	_	NNP
37681	2729	2	The	the	DT
37681	2729	3	square	square	NN
37681	2729	4	on	on	IN
37681	2729	5	the	the	DT
37681	2729	6	bisector	bisector	NN
37681	2729	7	of	of	IN
37681	2729	8	an	an	DT
37681	2729	9	angle	angle	NN
37681	2729	10	of	of	IN
37681	2729	11	a	a	DT
37681	2729	12	triangle	triangle	NN
37681	2729	13	is	be	VBZ
37681	2729	14	equal	equal	JJ
37681	2729	15	to	to	IN
37681	2729	16	the	the	DT
37681	2729	17	product	product	NN
37681	2729	18	of	of	IN
37681	2729	19	the	the	DT
37681	2729	20	sides	side	NNS
37681	2729	21	of	of	IN
37681	2729	22	this	this	DT
37681	2729	23	angle	angle	NN
37681	2729	24	diminished	diminish	VBN
37681	2729	25	by	by	IN
37681	2729	26	the	the	DT
37681	2729	27	product	product	NN
37681	2729	28	of	of	IN
37681	2729	29	the	the	DT
37681	2729	30	segments	segment	NNS
37681	2729	31	made	make	VBN
37681	2729	32	by	by	IN
37681	2729	33	the	the	DT
37681	2729	34	bisector	bisector	NN
37681	2729	35	upon	upon	IN
37681	2729	36	the	the	DT
37681	2729	37	third	third	JJ
37681	2729	38	side	side	NN
37681	2729	39	of	of	IN
37681	2729	40	the	the	DT
37681	2729	41	triangle	triangle	NN
37681	2729	42	.	.	.
37681	2729	43	_	_	NNP
37681	2729	44	This	this	DT
37681	2729	45	proposition	proposition	NN
37681	2729	46	enables	enable	VBZ
37681	2729	47	us	-PRON-	PRP
37681	2729	48	to	to	TO
37681	2729	49	compute	compute	VB
37681	2729	50	the	the	DT
37681	2729	51	length	length	NN
37681	2729	52	of	of	IN
37681	2729	53	a	a	DT
37681	2729	54	bisector	bisector	NN
37681	2729	55	of	of	IN
37681	2729	56	a	a	DT
37681	2729	57	triangle	triangle	NN
37681	2729	58	if	if	IN
37681	2729	59	the	the	DT
37681	2729	60	lengths	length	NNS
37681	2729	61	of	of	IN
37681	2729	62	the	the	DT
37681	2729	63	sides	side	NNS
37681	2729	64	are	be	VBP
37681	2729	65	known	know	VBN
37681	2729	66	.	.	.
37681	2730	1	[	[	-LRB-
37681	2730	2	Illustration	illustration	NN
37681	2730	3	]	]	-RRB-
37681	2730	4	For	for	CC
37681	2730	5	,	,	,
37681	2730	6	in	in	IN
37681	2730	7	this	this	DT
37681	2730	8	figure	figure	NN
37681	2730	9	,	,	,
37681	2730	10	let	let	VBD
37681	2730	11	_	_	NNP
37681	2730	12	a	a	DT
37681	2730	13	_	_	NNP
37681	2730	14	=	=	SYM
37681	2730	15	3	3	CD
37681	2730	16	,	,	,
37681	2730	17	_	_	NNP
37681	2730	18	b	b	NNP
37681	2730	19	_	_	NNP
37681	2730	20	=	=	SYM
37681	2730	21	5	5	CD
37681	2730	22	,	,	,
37681	2730	23	and	and	CC
37681	2730	24	_	_	NNP
37681	2730	25	c	c	NNP
37681	2730	26	_	_	NNP
37681	2730	27	=	=	SYM
37681	2730	28	6	6	CD
37681	2730	29	.	.	.
37681	2731	1	Then	then	RB
37681	2731	2	[	[	-LRB-
37681	2731	3	because	because	IN
37681	2731	4	]	]	-RRB-
37681	2731	5	_	_	NNP
37681	2731	6	x	x	NNP
37681	2731	7	_	_	NNP
37681	2731	8	:	:	:
37681	2731	9	_	_	NNP
37681	2731	10	y	y	NNP
37681	2731	11	_	_	NNP
37681	2731	12	=	=	SYM
37681	2731	13	_	_	NNP
37681	2731	14	b	b	NNP
37681	2731	15	_	_	NNP
37681	2731	16	:	:	:
37681	2731	17	_	_	NNP
37681	2731	18	a	a	DT
37681	2731	19	_	_	NNP
37681	2731	20	,	,	,
37681	2731	21	and	and	CC
37681	2731	22	_	_	NNP
37681	2731	23	y	y	NNP
37681	2731	24	_	_	NNP
37681	2731	25	=	=	SYM
37681	2731	26	6	6	CD
37681	2731	27	-	-	HYPH
37681	2731	28	_	_	NN
37681	2731	29	x	x	NNP
37681	2731	30	_	_	NNP
37681	2731	31	,	,	,
37681	2731	32	we	-PRON-	PRP
37681	2731	33	have	have	VBP
37681	2731	34	_	_	NNP
37681	2731	35	x_/(6	x_/(6	NNP
37681	2731	36	-	-	HYPH
37681	2731	37	_	_	NNP
37681	2731	38	x	x	NNP
37681	2731	39	_	_	NNP
37681	2731	40	)	)	-RRB-
37681	2731	41	=	=	SYM
37681	2731	42	5/3	5/3	CD
37681	2731	43	.	.	.
37681	2732	1	[	[	-LRB-
37681	2732	2	therefore	therefore	RB
37681	2732	3	]	]	-RRB-
37681	2732	4	3_x	3_x	CD
37681	2732	5	_	_	NNP
37681	2732	6	=	=	SYM
37681	2732	7	30	30	CD
37681	2732	8	-	-	HYPH
37681	2732	9	5_x	5_x	CD
37681	2732	10	_	_	NNP
37681	2732	11	.	.	.
37681	2733	1	[	[	-LRB-
37681	2733	2	therefore	therefore	RB
37681	2733	3	]	]	-RRB-
37681	2733	4	_	_	NNP
37681	2733	5	x	x	NNP
37681	2733	6	_	_	NNP
37681	2733	7	=	=	SYM
37681	2733	8	3	3	CD
37681	2733	9	3/4	3/4	CD
37681	2733	10	,	,	,
37681	2733	11	_	_	NNP
37681	2733	12	y	y	NNP
37681	2733	13	_	_	NNP
37681	2733	14	=	=	SYM
37681	2733	15	2	2	CD
37681	2733	16	1/4	1/4	CD
37681	2733	17	.	.	.
37681	2734	1	By	by	IN
37681	2734	2	the	the	DT
37681	2734	3	theorem	theorem	NN
37681	2734	4	,	,	,
37681	2734	5	_	_	NNP
37681	2734	6	z_^2	z_^2	NNP
37681	2734	7	=	=	SYM
37681	2734	8	_	_	NNP
37681	2734	9	ab	ab	NNP
37681	2734	10	_	_	NNP
37681	2734	11	-	-	HYPH
37681	2734	12	_	_	NNP
37681	2734	13	xy	xy	NNP
37681	2734	14	_	_	NNP
37681	2734	15	=	=	SYM
37681	2734	16	15	15	CD
37681	2734	17	-	-	HYPH
37681	2734	18	(	(	-LRB-
37681	2734	19	8	8	CD
37681	2734	20	7/16	7/16	CD
37681	2734	21	)	)	-RRB-
37681	2734	22	=	=	SYM
37681	2734	23	6	6	CD
37681	2734	24	9/16	9/16	CD
37681	2734	25	.	.	.
37681	2735	1	[	[	-LRB-
37681	2735	2	therefore	therefore	RB
37681	2735	3	]	]	-RRB-
37681	2735	4	_	_	NNP
37681	2735	5	z	z	NNP
37681	2735	6	_	_	NNP
37681	2735	7	=	=	NFP
37681	2735	8	[	[	-LRB-
37681	2735	9	sqrt](6	sqrt](6	NNP
37681	2735	10	9/16	9/16	CD
37681	2735	11	)	)	-RRB-
37681	2735	12	=	=	SYM
37681	2735	13	1/4	1/4	CD
37681	2735	14	[	[	-LRB-
37681	2735	15	sqrt]105	sqrt]105	NNP
37681	2735	16	=	=	SYM
37681	2735	17	2.5	2.5	CD
37681	2735	18	+	+	CD
37681	2735	19	.	.	.
37681	2736	1	THEOREM	THEOREM	NNP
37681	2736	2	.	.	.
37681	2737	1	_	_	NNP
37681	2737	2	In	in	IN
37681	2737	3	any	any	DT
37681	2737	4	triangle	triangle	NN
37681	2737	5	the	the	DT
37681	2737	6	product	product	NN
37681	2737	7	of	of	IN
37681	2737	8	two	two	CD
37681	2737	9	sides	side	NNS
37681	2737	10	is	be	VBZ
37681	2737	11	equal	equal	JJ
37681	2737	12	to	to	IN
37681	2737	13	the	the	DT
37681	2737	14	product	product	NN
37681	2737	15	of	of	IN
37681	2737	16	the	the	DT
37681	2737	17	diameter	diameter	NN
37681	2737	18	of	of	IN
37681	2737	19	the	the	DT
37681	2737	20	circumscribed	circumscribe	VBN
37681	2737	21	circle	circle	NN
37681	2737	22	by	by	IN
37681	2737	23	the	the	DT
37681	2737	24	altitude	altitude	NN
37681	2737	25	upon	upon	IN
37681	2737	26	the	the	DT
37681	2737	27	third	third	JJ
37681	2737	28	side	side	NN
37681	2737	29	.	.	.
37681	2737	30	_	_	NNP
37681	2737	31	This	this	DT
37681	2737	32	enables	enable	VBZ
37681	2737	33	us	-PRON-	PRP
37681	2737	34	,	,	,
37681	2737	35	after	after	IN
37681	2737	36	the	the	DT
37681	2737	37	Pythagorean	Pythagorean	NNP
37681	2737	38	Theorem	Theorem	NNP
37681	2737	39	has	have	VBZ
37681	2737	40	been	be	VBN
37681	2737	41	studied	study	VBN
37681	2737	42	,	,	,
37681	2737	43	to	to	TO
37681	2737	44	compute	compute	VB
37681	2737	45	the	the	DT
37681	2737	46	length	length	NN
37681	2737	47	of	of	IN
37681	2737	48	the	the	DT
37681	2737	49	diameter	diameter	NN
37681	2737	50	of	of	IN
37681	2737	51	the	the	DT
37681	2737	52	circumscribed	circumscribed	NNP
37681	2737	53	circle	circle	NN
37681	2737	54	in	in	IN
37681	2737	55	terms	term	NNS
37681	2737	56	of	of	IN
37681	2737	57	the	the	DT
37681	2737	58	three	three	CD
37681	2737	59	sides	side	NNS
37681	2737	60	.	.	.
37681	2738	1	[	[	-LRB-
37681	2738	2	Illustration	illustration	NN
37681	2738	3	]	]	-RRB-
37681	2738	4	For	for	CC
37681	2738	5	if	if	IN
37681	2738	6	we	-PRON-	PRP
37681	2738	7	designate	designate	VBP
37681	2738	8	the	the	DT
37681	2738	9	sides	side	NNS
37681	2738	10	by	by	IN
37681	2738	11	_	_	NNP
37681	2738	12	a	a	DT
37681	2738	13	_	_	NNP
37681	2738	14	,	,	,
37681	2738	15	_	_	NNP
37681	2738	16	b	b	NNP
37681	2738	17	_	_	NNP
37681	2738	18	,	,	,
37681	2738	19	and	and	CC
37681	2738	20	_	_	NNP
37681	2738	21	c	c	NNP
37681	2738	22	_	_	NNP
37681	2738	23	,	,	,
37681	2738	24	as	as	IN
37681	2738	25	usual	usual	JJ
37681	2738	26	,	,	,
37681	2738	27	and	and	CC
37681	2738	28	let	let	VB
37681	2738	29	_	_	NNP
37681	2738	30	CD	CD	NNP
37681	2738	31	_	_	NNP
37681	2738	32	=	=	SYM
37681	2738	33	_	_	NNP
37681	2738	34	d	d	NNP
37681	2738	35	_	_	NNP
37681	2738	36	and	and	CC
37681	2738	37	_	_	NNP
37681	2738	38	PB	PB	NNP
37681	2738	39	_	_	NNP
37681	2738	40	=	=	SYM
37681	2738	41	_	_	NNP
37681	2738	42	x	x	NNP
37681	2738	43	_	_	NNP
37681	2738	44	,	,	,
37681	2738	45	then	then	RB
37681	2738	46	(	(	-LRB-
37681	2738	47	_	_	NNP
37681	2738	48	CP_)^2	CP_)^2	NNP
37681	2738	49	=	=	SYM
37681	2738	50	_	_	NNP
37681	2738	51	a_^2	a_^2	NNP
37681	2738	52	-	-	HYPH
37681	2738	53	_	_	NNP
37681	2738	54	x_^2	x_^2	NNP
37681	2738	55	=	=	SYM
37681	2738	56	_	_	NNP
37681	2738	57	b_^2	b_^2	NNP
37681	2738	58	-	-	,
37681	2738	59	(	(	-LRB-
37681	2738	60	_	_	NNP
37681	2738	61	c	c	NNP
37681	2738	62	_	_	NNP
37681	2738	63	-	-	HYPH
37681	2738	64	_	_	NNP
37681	2738	65	x_)^2	x_)^2	NNP
37681	2738	66	.	.	.
37681	2739	1	[	[	-LRB-
37681	2739	2	therefore	therefore	RB
37681	2739	3	]	]	-RRB-
37681	2739	4	_	_	NNP
37681	2739	5	a_^2	a_^2	NNP
37681	2739	6	-	-	HYPH
37681	2739	7	_	_	NNP
37681	2739	8	x_^2	x_^2	NNP
37681	2739	9	=	=	SYM
37681	2739	10	_	_	NNP
37681	2739	11	b_^2	b_^2	NNP
37681	2739	12	-	-	HYPH
37681	2739	13	_	_	NNP
37681	2739	14	c_^2	c_^2	NNP
37681	2739	15	+	+	SYM
37681	2739	16	2_cx	2_cx	CD
37681	2739	17	_	_	NNP
37681	2739	18	-	-	HYPH
37681	2739	19	_	_	NNP
37681	2739	20	x_^2	x_^2	NNP
37681	2739	21	.	.	.
37681	2740	1	[	[	-LRB-
37681	2740	2	therefore	therefore	RB
37681	2740	3	]	]	-RRB-
37681	2740	4	_	_	NNP
37681	2740	5	x	x	NNP
37681	2740	6	_	_	NNP
37681	2740	7	=	=	NFP
37681	2740	8	(	(	-LRB-
37681	2740	9	_	_	NNP
37681	2740	10	a_^2	a_^2	NNP
37681	2740	11	-	-	HYPH
37681	2740	12	_	_	NNP
37681	2740	13	b_^2	b_^2	NNP
37681	2740	14	+	+	NNP
37681	2740	15	_	_	NNP
37681	2740	16	c_^2	c_^2	NNP
37681	2740	17	)	)	-RRB-
37681	2740	18	/	/	SYM
37681	2740	19	2_c	2_c	CD
37681	2740	20	_	_	NNP
37681	2740	21	.	.	.
37681	2741	1	[	[	-LRB-
37681	2741	2	therefore	therefore	RB
37681	2741	3	]	]	-RRB-
37681	2741	4	(	(	-LRB-
37681	2741	5	_	_	NNP
37681	2741	6	CP_)^2	CP_)^2	NNP
37681	2741	7	=	=	SYM
37681	2741	8	_	_	NNP
37681	2741	9	a_^2	a_^2	NNP
37681	2741	10	-	-	,
37681	2741	11	(	(	-LRB-
37681	2741	12	(	(	-LRB-
37681	2741	13	_	_	NNP
37681	2741	14	a_^2	a_^2	NNP
37681	2741	15	-	-	HYPH
37681	2741	16	_	_	NNP
37681	2741	17	b_^2	b_^2	NNP
37681	2741	18	+	+	NNP
37681	2741	19	_	_	NNP
37681	2741	20	c_^2	c_^2	NNP
37681	2741	21	)	)	-RRB-
37681	2741	22	/	/	SYM
37681	2741	23	2_c_)^2	2_c_)^2	CD
37681	2741	24	.	.	.
37681	2742	1	But	but	CC
37681	2742	2	_	_	NNP
37681	2742	3	CP	CP	NNP
37681	2742	4	_	_	NNP
37681	2742	5	·	·	NFP
37681	2742	6	_	_	NNP
37681	2742	7	d	d	NNP
37681	2742	8	_	_	NNP
37681	2742	9	=	=	SYM
37681	2742	10	_	_	NNP
37681	2742	11	ab	ab	NNP
37681	2742	12	_	_	NNP
37681	2742	13	.	.	.
37681	2743	1	[	[	-LRB-
37681	2743	2	therefore	therefore	RB
37681	2743	3	]	]	-RRB-
37681	2743	4	_	_	NNP
37681	2743	5	d	d	NNP
37681	2743	6	_	_	NNP
37681	2743	7	=	=	SYM
37681	2743	8	2_abc	2_abc	CD
37681	2743	9	_	_	NN
37681	2743	10	/	/	SYM
37681	2743	11	[	[	-LRB-
37681	2743	12	sqrt](4_a_^2_c_^2	sqrt](4_a_^2_c_^2	NNP
37681	2743	13	-	-	,
37681	2743	14	(	(	-LRB-
37681	2743	15	_	_	NNP
37681	2743	16	a_^2	a_^2	NNP
37681	2743	17	-	-	HYPH
37681	2743	18	_	_	NNP
37681	2743	19	b_^2	b_^2	NNP
37681	2743	20	+	+	NNP
37681	2743	21	_	_	NNP
37681	2743	22	c_^2)^2	c_^2)^2	NNP
37681	2743	23	)	)	-RRB-
37681	2743	24	.	.	.
37681	2744	1	This	this	DT
37681	2744	2	is	be	VBZ
37681	2744	3	not	not	RB
37681	2744	4	available	available	JJ
37681	2744	5	at	at	IN
37681	2744	6	this	this	DT
37681	2744	7	time	time	NN
37681	2744	8	,	,	,
37681	2744	9	however	however	RB
37681	2744	10	,	,	,
37681	2744	11	because	because	IN
37681	2744	12	the	the	DT
37681	2744	13	Pythagorean	Pythagorean	NNP
37681	2744	14	Theorem	Theorem	NNP
37681	2744	15	has	have	VBZ
37681	2744	16	not	not	RB
37681	2744	17	been	be	VBN
37681	2744	18	proved	prove	VBN
37681	2744	19	.	.	.
37681	2745	1	These	these	DT
37681	2745	2	two	two	CD
37681	2745	3	propositions	proposition	NNS
37681	2745	4	are	be	VBP
37681	2745	5	merely	merely	RB
37681	2745	6	special	special	JJ
37681	2745	7	cases	case	NNS
37681	2745	8	of	of	IN
37681	2745	9	the	the	DT
37681	2745	10	following	follow	VBG
37681	2745	11	general	general	JJ
37681	2745	12	theorem	theorem	NN
37681	2745	13	,	,	,
37681	2745	14	which	which	WDT
37681	2745	15	may	may	MD
37681	2745	16	be	be	VB
37681	2745	17	given	give	VBN
37681	2745	18	as	as	IN
37681	2745	19	an	an	DT
37681	2745	20	interesting	interesting	JJ
37681	2745	21	exercise	exercise	NN
37681	2745	22	:	:	:
37681	2745	23	_	_	XX
37681	2745	24	If	if	IN
37681	2745	25	ABC	ABC	NNP
37681	2745	26	is	be	VBZ
37681	2745	27	an	an	DT
37681	2745	28	inscribed	inscribed	JJ
37681	2745	29	triangle	triangle	NN
37681	2745	30	,	,	,
37681	2745	31	and	and	CC
37681	2745	32	through	through	IN
37681	2745	33	C	c	NN
37681	2745	34	there	there	EX
37681	2745	35	are	be	VBP
37681	2745	36	drawn	draw	VBN
37681	2745	37	two	two	CD
37681	2745	38	straight	straight	JJ
37681	2745	39	lines	line	NNS
37681	2745	40	CD	cd	NN
37681	2745	41	,	,	,
37681	2745	42	meeting	meet	VBG
37681	2745	43	AB	AB	NNP
37681	2745	44	in	in	IN
37681	2745	45	D	d	NN
37681	2745	46	,	,	,
37681	2745	47	and	and	CC
37681	2745	48	CP	CP	NNP
37681	2745	49	,	,	,
37681	2745	50	meeting	meet	VBG
37681	2745	51	the	the	DT
37681	2745	52	circle	circle	NN
37681	2745	53	in	in	IN
37681	2745	54	P	P	NNP
37681	2745	55	,	,	,
37681	2745	56	with	with	IN
37681	2745	57	angles	angle	NNS
37681	2745	58	ACD	ACD	NNP
37681	2745	59	and	and	CC
37681	2745	60	PCB	pcb	NN
37681	2745	61	equal	equal	JJ
37681	2745	62	,	,	,
37681	2745	63	then	then	RB
37681	2745	64	AC	AC	NNP
37681	2745	65	×	×	NN
37681	2745	66	BC	BC	NNP
37681	2745	67	will	will	MD
37681	2745	68	equal	equal	VB
37681	2745	69	CD	cd	NN
37681	2745	70	×	×	NN
37681	2745	71	CP	CP	NNP
37681	2745	72	.	.	.
37681	2745	73	_	_	NNP
37681	2745	74	[	[	-LRB-
37681	2745	75	Illustration	illustration	NN
37681	2745	76	:	:	:
37681	2745	77	FIG	FIG	NNP
37681	2745	78	.	.	.
37681	2746	1	1	1	LS
37681	2746	2	]	]	-RRB-
37681	2746	3	[	[	-LRB-
37681	2746	4	Illustration	illustration	NN
37681	2746	5	:	:	:
37681	2746	6	FIG	FIG	NNP
37681	2746	7	.	.	.
37681	2747	1	2	2	LS
37681	2747	2	]	]	-RRB-
37681	2747	3	[	[	-LRB-
37681	2747	4	Illustration	illustration	NN
37681	2747	5	:	:	:
37681	2747	6	FIG	FIG	NNP
37681	2747	7	.	.	.
37681	2748	1	3	3	LS
37681	2748	2	]	]	-RRB-
37681	2748	3	[	[	-LRB-
37681	2748	4	Illustration	illustration	NN
37681	2748	5	:	:	:
37681	2748	6	FIG	FIG	NNP
37681	2748	7	.	.	.
37681	2749	1	4	4	LS
37681	2749	2	]	]	-RRB-
37681	2749	3	Fig	fig	NN
37681	2749	4	.	.	.
37681	2750	1	1	1	CD
37681	2750	2	is	be	VBZ
37681	2750	3	the	the	DT
37681	2750	4	general	general	JJ
37681	2750	5	case	case	NN
37681	2750	6	where	where	WRB
37681	2750	7	_	_	NNP
37681	2750	8	D	D	NNP
37681	2750	9	_	_	NNP
37681	2750	10	falls	fall	VBZ
37681	2750	11	between	between	IN
37681	2750	12	_	_	NNP
37681	2750	13	A	A	NNP
37681	2750	14	_	_	NNP
37681	2750	15	and	and	CC
37681	2750	16	_	_	NNP
37681	2750	17	B	B	NNP
37681	2750	18	_	_	NNP
37681	2750	19	.	.	.
37681	2751	1	If	if	IN
37681	2751	2	_	_	NNP
37681	2751	3	CP	CP	NNP
37681	2751	4	_	_	NNP
37681	2751	5	is	be	VBZ
37681	2751	6	a	a	DT
37681	2751	7	diameter	diameter	NN
37681	2751	8	,	,	,
37681	2751	9	it	-PRON-	PRP
37681	2751	10	reduces	reduce	VBZ
37681	2751	11	to	to	IN
37681	2751	12	the	the	DT
37681	2751	13	second	second	JJ
37681	2751	14	figure	figure	NN
37681	2751	15	given	give	VBN
37681	2751	16	on	on	IN
37681	2751	17	page	page	NN
37681	2751	18	249	249	CD
37681	2751	19	.	.	.
37681	2752	1	If	if	IN
37681	2752	2	_	_	NNP
37681	2752	3	CP	CP	NNP
37681	2752	4	_	_	NNP
37681	2752	5	bisects	bisect	VBZ
37681	2752	6	[	[	-LRB-
37681	2752	7	L]_ACB	L]_ACB	NNP
37681	2752	8	_	_	NNP
37681	2752	9	,	,	,
37681	2752	10	we	-PRON-	PRP
37681	2752	11	have	have	VBP
37681	2752	12	Fig	Fig	NNP
37681	2752	13	.	.	.
37681	2753	1	3	3	LS
37681	2753	2	,	,	,
37681	2753	3	from	from	IN
37681	2753	4	which	which	WDT
37681	2753	5	may	may	MD
37681	2753	6	be	be	VB
37681	2753	7	proved	prove	VBN
37681	2753	8	the	the	DT
37681	2753	9	proposition	proposition	NN
37681	2753	10	given	give	VBN
37681	2753	11	at	at	IN
37681	2753	12	the	the	DT
37681	2753	13	foot	foot	NN
37681	2753	14	of	of	IN
37681	2753	15	page	page	NN
37681	2753	16	248	248	CD
37681	2753	17	.	.	.
37681	2754	1	If	if	IN
37681	2754	2	_	_	NNP
37681	2754	3	D	D	NNP
37681	2754	4	_	_	NNP
37681	2754	5	lies	lie	VBZ
37681	2754	6	on	on	IN
37681	2754	7	_	_	NNP
37681	2754	8	BA	BA	NNP
37681	2754	9	_	_	NNP
37681	2754	10	produced	produce	VBD
37681	2754	11	,	,	,
37681	2754	12	we	-PRON-	PRP
37681	2754	13	have	have	VBP
37681	2754	14	Fig	Fig	NNP
37681	2754	15	.	.	.
37681	2755	1	2	2	LS
37681	2755	2	.	.	.
37681	2756	1	If	if	IN
37681	2756	2	_	_	NNP
37681	2756	3	D	D	NNP
37681	2756	4	_	_	NNP
37681	2756	5	lies	lie	VBZ
37681	2756	6	on	on	IN
37681	2756	7	_	_	NNP
37681	2756	8	AB	AB	NNP
37681	2756	9	_	_	NNP
37681	2756	10	produced	produce	VBD
37681	2756	11	,	,	,
37681	2756	12	we	-PRON-	PRP
37681	2756	13	have	have	VBP
37681	2756	14	Fig	Fig	NNP
37681	2756	15	.	.	.
37681	2757	1	4	4	LS
37681	2757	2	.	.	.
37681	2758	1	This	this	DT
37681	2758	2	general	general	JJ
37681	2758	3	proposition	proposition	NN
37681	2758	4	is	be	VBZ
37681	2758	5	proved	prove	VBN
37681	2758	6	by	by	IN
37681	2758	7	showing	show	VBG
37681	2758	8	that	that	IN
37681	2758	9	[	[	-LRB-
37681	2758	10	triangles]_ADC	triangles]_adc	UH
37681	2758	11	_	_	NNP
37681	2758	12	and	and	CC
37681	2758	13	_	_	NNP
37681	2758	14	PBC	PBC	NNP
37681	2758	15	_	_	NNP
37681	2758	16	are	be	VBP
37681	2758	17	similar	similar	JJ
37681	2758	18	,	,	,
37681	2758	19	exactly	exactly	RB
37681	2758	20	as	as	IN
37681	2758	21	in	in	IN
37681	2758	22	the	the	DT
37681	2758	23	second	second	JJ
37681	2758	24	proposition	proposition	NN
37681	2758	25	given	give	VBN
37681	2758	26	on	on	IN
37681	2758	27	page	page	NN
37681	2758	28	249	249	CD
37681	2758	29	.	.	.
37681	2759	1	These	these	DT
37681	2759	2	theorems	theorem	NNS
37681	2759	3	are	be	VBP
37681	2759	4	usually	usually	RB
37681	2759	5	followed	follow	VBN
37681	2759	6	by	by	IN
37681	2759	7	problems	problem	NNS
37681	2759	8	of	of	IN
37681	2759	9	construction	construction	NN
37681	2759	10	,	,	,
37681	2759	11	of	of	IN
37681	2759	12	which	which	WDT
37681	2759	13	only	only	RB
37681	2759	14	one	one	CD
37681	2759	15	has	have	VBZ
37681	2759	16	great	great	JJ
37681	2759	17	interest	interest	NN
37681	2759	18	,	,	,
37681	2759	19	namely	namely	RB
37681	2759	20	,	,	,
37681	2759	21	_	_	NNP
37681	2759	22	To	to	TO
37681	2759	23	divide	divide	VB
37681	2759	24	a	a	DT
37681	2759	25	given	give	VBN
37681	2759	26	line	line	NN
37681	2759	27	in	in	IN
37681	2759	28	extreme	extreme	JJ
37681	2759	29	and	and	CC
37681	2759	30	mean	mean	JJ
37681	2759	31	ratio	ratio	NN
37681	2759	32	.	.	.
37681	2759	33	_	_	NNP
37681	2759	34	The	the	DT
37681	2759	35	purpose	purpose	NN
37681	2759	36	of	of	IN
37681	2759	37	this	this	DT
37681	2759	38	problem	problem	NN
37681	2759	39	is	be	VBZ
37681	2759	40	to	to	TO
37681	2759	41	prepare	prepare	VB
37681	2759	42	for	for	IN
37681	2759	43	the	the	DT
37681	2759	44	construction	construction	NN
37681	2759	45	of	of	IN
37681	2759	46	the	the	DT
37681	2759	47	regular	regular	JJ
37681	2759	48	decagon	decagon	NNP
37681	2759	49	and	and	CC
37681	2759	50	pentagon	pentagon	NNP
37681	2759	51	.	.	.
37681	2760	1	The	the	DT
37681	2760	2	division	division	NN
37681	2760	3	of	of	IN
37681	2760	4	a	a	DT
37681	2760	5	line	line	NN
37681	2760	6	in	in	IN
37681	2760	7	extreme	extreme	JJ
37681	2760	8	and	and	CC
37681	2760	9	mean	mean	JJ
37681	2760	10	ratio	ratio	NN
37681	2760	11	is	be	VBZ
37681	2760	12	called	call	VBN
37681	2760	13	"	"	``
37681	2760	14	the	the	DT
37681	2760	15	golden	golden	JJ
37681	2760	16	section	section	NN
37681	2760	17	,	,	,
37681	2760	18	"	"	''
37681	2760	19	and	and	CC
37681	2760	20	is	be	VBZ
37681	2760	21	probably	probably	RB
37681	2760	22	"	"	``
37681	2760	23	the	the	DT
37681	2760	24	section	section	NN
37681	2760	25	"	"	''
37681	2760	26	mentioned	mention	VBN
37681	2760	27	by	by	IN
37681	2760	28	Proclus	Proclus	NNP
37681	2760	29	when	when	WRB
37681	2760	30	he	-PRON-	PRP
37681	2760	31	says	say	VBZ
37681	2760	32	that	that	IN
37681	2760	33	Eudoxus	Eudoxus	NNP
37681	2760	34	"	"	''
37681	2760	35	greatly	greatly	RB
37681	2760	36	added	add	VBN
37681	2760	37	to	to	IN
37681	2760	38	the	the	DT
37681	2760	39	number	number	NN
37681	2760	40	of	of	IN
37681	2760	41	the	the	DT
37681	2760	42	theorems	theorem	NNS
37681	2760	43	which	which	WDT
37681	2760	44	Plato	Plato	NNP
37681	2760	45	originated	originate	VBD
37681	2760	46	regarding	regard	VBG
37681	2760	47	the	the	DT
37681	2760	48	section	section	NN
37681	2760	49	.	.	.
37681	2760	50	"	"	''
37681	2761	1	The	the	DT
37681	2761	2	expression	expression	NN
37681	2761	3	"	"	``
37681	2761	4	golden	golden	JJ
37681	2761	5	section	section	NN
37681	2761	6	"	"	''
37681	2761	7	is	be	VBZ
37681	2761	8	not	not	RB
37681	2761	9	old	old	JJ
37681	2761	10	,	,	,
37681	2761	11	however	however	RB
37681	2761	12	,	,	,
37681	2761	13	and	and	CC
37681	2761	14	its	-PRON-	PRP$
37681	2761	15	origin	origin	NN
37681	2761	16	is	be	VBZ
37681	2761	17	uncertain	uncertain	JJ
37681	2761	18	.	.	.
37681	2762	1	If	if	IN
37681	2762	2	a	a	DT
37681	2762	3	line	line	NN
37681	2762	4	_	_	NNP
37681	2762	5	AB	AB	NNP
37681	2762	6	_	_	NNP
37681	2762	7	is	be	VBZ
37681	2762	8	divided	divide	VBN
37681	2762	9	in	in	IN
37681	2762	10	golden	golden	JJ
37681	2762	11	section	section	NN
37681	2762	12	at	at	IN
37681	2762	13	_	_	NNP
37681	2762	14	P	P	NNP
37681	2762	15	_	_	NNP
37681	2762	16	,	,	,
37681	2762	17	we	-PRON-	PRP
37681	2762	18	have	have	VBP
37681	2762	19	_	_	NNP
37681	2762	20	AB	AB	NNP
37681	2762	21	_	_	NNP
37681	2762	22	×	×	NN
37681	2762	23	_	_	NNP
37681	2762	24	PB	PB	NNP
37681	2762	25	_	_	NNP
37681	2762	26	=	=	NFP
37681	2762	27	(	(	-LRB-
37681	2762	28	_	_	NNP
37681	2762	29	AP_)^2	AP_)^2	NNP
37681	2762	30	.	.	.
37681	2763	1	Therefore	therefore	RB
37681	2763	2	,	,	,
37681	2763	3	if	if	IN
37681	2763	4	_	_	NNP
37681	2763	5	AB	AB	NNP
37681	2763	6	_	_	NNP
37681	2763	7	=	=	SYM
37681	2763	8	_	_	NNP
37681	2763	9	a	a	DT
37681	2763	10	_	_	NNP
37681	2763	11	,	,	,
37681	2763	12	and	and	CC
37681	2763	13	_	_	NNP
37681	2763	14	AP	AP	NNP
37681	2763	15	_	_	NNP
37681	2763	16	=	=	SYM
37681	2763	17	_	_	NNP
37681	2763	18	x	x	NNP
37681	2763	19	_	_	NNP
37681	2763	20	,	,	,
37681	2763	21	we	-PRON-	PRP
37681	2763	22	have	have	VBP
37681	2763	23	_	_	NNP
37681	2763	24	a_(_a	a_(_a	NNP
37681	2763	25	_	_	NNP
37681	2763	26	-	-	HYPH
37681	2763	27	_	_	NNP
37681	2763	28	x	x	NNP
37681	2763	29	_	_	NNP
37681	2763	30	)	)	-RRB-
37681	2763	31	=	=	NFP
37681	2763	32	_	_	NNP
37681	2763	33	x_^2	x_^2	NNP
37681	2763	34	,	,	,
37681	2763	35	or	or	CC
37681	2763	36	_	_	NNP
37681	2763	37	x_^2	x_^2	NNP
37681	2763	38	+	+	SYM
37681	2763	39	_	_	NNP
37681	2763	40	ax	ax	NN
37681	2763	41	_	_	NNP
37681	2763	42	-	-	HYPH
37681	2763	43	_	_	NNP
37681	2763	44	a_^2	a_^2	NNP
37681	2763	45	=	=	SYM
37681	2763	46	0	0	NFP
37681	2763	47	;	;	:
37681	2763	48	whence	whence	NN
37681	2763	49	_	_	NNP
37681	2763	50	x	x	NNP
37681	2763	51	_	_	NNP
37681	2763	52	=	=	SYM
37681	2763	53	-	-	:
37681	2763	54	_	_	NNP
37681	2763	55	a_/2	a_/2	NNP
37681	2763	56	±	±	NNP
37681	2763	57	_	_	NNP
37681	2763	58	a_/2[sqrt]5	a_/2[sqrt]5	NNP
37681	2763	59	=	=	NFP
37681	2763	60	_	_	NNP
37681	2763	61	a_(1.118	a_(1.118	NNP
37681	2763	62	-	-	SYM
37681	2763	63	0.5	0.5	CD
37681	2763	64	)	)	-RRB-
37681	2763	65	=	=	NFP
37681	2763	66	0.618_a	0.618_a	CD
37681	2763	67	_	_	XX
37681	2763	68	,	,	,
37681	2763	69	the	the	DT
37681	2763	70	other	other	JJ
37681	2763	71	root	root	NN
37681	2763	72	representing	represent	VBG
37681	2763	73	the	the	DT
37681	2763	74	external	external	JJ
37681	2763	75	point	point	NN
37681	2763	76	.	.	.
37681	2764	1	That	that	DT
37681	2764	2	is	is	RB
37681	2764	3	,	,	,
37681	2764	4	_	_	NNP
37681	2764	5	x	x	NNP
37681	2764	6	_	_	NNP
37681	2764	7	=	=	SYM
37681	2764	8	about	about	IN
37681	2764	9	0.6_a	0.6_a	NNP
37681	2764	10	_	_	NNP
37681	2764	11	,	,	,
37681	2764	12	and	and	CC
37681	2764	13	_	_	NNP
37681	2764	14	a	a	DT
37681	2764	15	_	_	NNP
37681	2764	16	-	-	HYPH
37681	2764	17	_	_	NNP
37681	2764	18	x	x	NNP
37681	2764	19	_	_	NNP
37681	2764	20	=	=	SYM
37681	2764	21	about	about	IN
37681	2764	22	0.4_a	0.4_a	NNP
37681	2764	23	_	_	NNP
37681	2764	24	,	,	,
37681	2764	25	and	and	CC
37681	2764	26	_	_	NNP
37681	2764	27	a	a	DT
37681	2764	28	_	_	NNP
37681	2764	29	is	be	VBZ
37681	2764	30	therefore	therefore	RB
37681	2764	31	divided	divide	VBN
37681	2764	32	in	in	IN
37681	2764	33	about	about	IN
37681	2764	34	the	the	DT
37681	2764	35	ratio	ratio	NN
37681	2764	36	of	of	IN
37681	2764	37	2	2	CD
37681	2764	38	:	:	SYM
37681	2764	39	3	3	CD
37681	2764	40	.	.	.
37681	2765	1	There	there	EX
37681	2765	2	has	have	VBZ
37681	2765	3	been	be	VBN
37681	2765	4	a	a	DT
37681	2765	5	great	great	JJ
37681	2765	6	deal	deal	NN
37681	2765	7	written	write	VBN
37681	2765	8	upon	upon	IN
37681	2765	9	the	the	DT
37681	2765	10	æsthetic	æsthetic	JJ
37681	2765	11	features	feature	NNS
37681	2765	12	of	of	IN
37681	2765	13	the	the	DT
37681	2765	14	golden	golden	JJ
37681	2765	15	section	section	NN
37681	2765	16	.	.	.
37681	2766	1	It	-PRON-	PRP
37681	2766	2	is	be	VBZ
37681	2766	3	claimed	claim	VBN
37681	2766	4	that	that	IN
37681	2766	5	a	a	DT
37681	2766	6	line	line	NN
37681	2766	7	is	be	VBZ
37681	2766	8	most	most	RBS
37681	2766	9	harmoniously	harmoniously	RB
37681	2766	10	divided	divided	JJ
37681	2766	11	when	when	WRB
37681	2766	12	it	-PRON-	PRP
37681	2766	13	is	be	VBZ
37681	2766	14	either	either	CC
37681	2766	15	bisected	bisect	VBN
37681	2766	16	or	or	CC
37681	2766	17	divided	divide	VBN
37681	2766	18	in	in	IN
37681	2766	19	extreme	extreme	JJ
37681	2766	20	and	and	CC
37681	2766	21	mean	mean	JJ
37681	2766	22	ratio	ratio	NN
37681	2766	23	.	.	.
37681	2767	1	A	a	DT
37681	2767	2	painting	painting	NN
37681	2767	3	has	have	VBZ
37681	2767	4	the	the	DT
37681	2767	5	strong	strong	JJ
37681	2767	6	feature	feature	NN
37681	2767	7	in	in	IN
37681	2767	8	the	the	DT
37681	2767	9	center	center	NN
37681	2767	10	,	,	,
37681	2767	11	or	or	CC
37681	2767	12	more	more	RBR
37681	2767	13	often	often	RB
37681	2767	14	at	at	IN
37681	2767	15	a	a	DT
37681	2767	16	point	point	NN
37681	2767	17	about	about	IN
37681	2767	18	0.4	0.4	CD
37681	2767	19	of	of	IN
37681	2767	20	the	the	DT
37681	2767	21	distance	distance	NN
37681	2767	22	from	from	IN
37681	2767	23	one	one	CD
37681	2767	24	side	side	NN
37681	2767	25	,	,	,
37681	2767	26	that	that	RB
37681	2767	27	is	is	RB
37681	2767	28	,	,	,
37681	2767	29	at	at	IN
37681	2767	30	the	the	DT
37681	2767	31	golden	golden	JJ
37681	2767	32	section	section	NN
37681	2767	33	of	of	IN
37681	2767	34	the	the	DT
37681	2767	35	width	width	NN
37681	2767	36	of	of	IN
37681	2767	37	the	the	DT
37681	2767	38	picture	picture	NN
37681	2767	39	.	.	.
37681	2768	1	It	-PRON-	PRP
37681	2768	2	is	be	VBZ
37681	2768	3	said	say	VBN
37681	2768	4	that	that	IN
37681	2768	5	in	in	IN
37681	2768	6	nature	nature	NN
37681	2768	7	this	this	DT
37681	2768	8	same	same	JJ
37681	2768	9	harmony	harmony	NN
37681	2768	10	is	be	VBZ
37681	2768	11	found	find	VBN
37681	2768	12	,	,	,
37681	2768	13	as	as	IN
37681	2768	14	in	in	IN
37681	2768	15	the	the	DT
37681	2768	16	division	division	NN
37681	2768	17	of	of	IN
37681	2768	18	the	the	DT
37681	2768	19	veins	vein	NNS
37681	2768	20	of	of	IN
37681	2768	21	such	such	JJ
37681	2768	22	leaves	leave	NNS
37681	2768	23	as	as	IN
37681	2768	24	the	the	DT
37681	2768	25	ivy	ivy	NN
37681	2768	26	and	and	CC
37681	2768	27	fern	fern	NN
37681	2768	28	.	.	.
37681	2769	1	FOOTNOTES	footnote	NNS
37681	2769	2	:	:	:
37681	2769	3	[	[	-LRB-
37681	2769	4	76	76	CD
37681	2769	5	]	]	-RRB-
37681	2769	6	For	for	IN
37681	2769	7	a	a	DT
37681	2769	8	very	very	RB
37681	2769	9	full	full	JJ
37681	2769	10	discussion	discussion	NN
37681	2769	11	of	of	IN
37681	2769	12	these	these	DT
37681	2769	13	four	four	CD
37681	2769	14	definitions	definition	NNS
37681	2769	15	see	see	VBP
37681	2769	16	Heath	Heath	NNP
37681	2769	17	's	's	POS
37681	2769	18	"	"	``
37681	2769	19	Euclid	Euclid	NNP
37681	2769	20	,	,	,
37681	2769	21	"	"	''
37681	2769	22	Vol	Vol	NNP
37681	2769	23	.	.	.
37681	2770	1	II	II	NNP
37681	2770	2	,	,	,
37681	2770	3	p.	p.	NN
37681	2770	4	116	116	CD
37681	2770	5	,	,	,
37681	2770	6	and	and	CC
37681	2770	7	authorities	authority	NNS
37681	2770	8	there	there	RB
37681	2770	9	cited	cite	VBD
37681	2770	10	.	.	.
37681	2771	1	[	[	-LRB-
37681	2771	2	77	77	CD
37681	2771	3	]	]	-RRB-
37681	2771	4	These	these	DT
37681	2771	5	two	two	CD
37681	2771	6	and	and	CC
37681	2771	7	several	several	JJ
37681	2771	8	which	which	WDT
37681	2771	9	follow	follow	NN
37681	2771	10	are	be	VBP
37681	2771	11	from	from	IN
37681	2771	12	Stark	Stark	NNP
37681	2771	13	,	,	,
37681	2771	14	loc	loc	NN
37681	2771	15	.	.	.
37681	2772	1	cit	cit	NNP
37681	2772	2	.	.	.
37681	2773	1	[	[	-LRB-
37681	2773	2	78	78	CD
37681	2773	3	]	]	-RRB-
37681	2773	4	The	the	DT
37681	2773	5	author	author	NN
37681	2773	6	has	have	VBZ
37681	2773	7	a	a	DT
37681	2773	8	beautiful	beautiful	JJ
37681	2773	9	ivory	ivory	NN
37681	2773	10	specimen	speciman	NNS
37681	2773	11	of	of	IN
37681	2773	12	the	the	DT
37681	2773	13	Sixteenth	sixteenth	JJ
37681	2773	14	century	century	NN
37681	2773	15	.	.	.
37681	2774	1	CHAPTER	CHAPTER	NNP
37681	2774	2	XVII	XVII	NNP
37681	2774	3	THE	the	DT
37681	2774	4	LEADING	lead	VBG
37681	2774	5	PROPOSITIONS	proposition	NNS
37681	2774	6	OF	of	IN
37681	2774	7	BOOK	BOOK	NNP
37681	2774	8	IV	IV	NNP
37681	2774	9	Book	Book	NNP
37681	2774	10	IV	IV	NNP
37681	2774	11	treats	treat	NNS
37681	2774	12	of	of	IN
37681	2774	13	the	the	DT
37681	2774	14	area	area	NN
37681	2774	15	of	of	IN
37681	2774	16	polygons	polygon	NNS
37681	2774	17	,	,	,
37681	2774	18	and	and	CC
37681	2774	19	offers	offer	VBZ
37681	2774	20	a	a	DT
37681	2774	21	large	large	JJ
37681	2774	22	number	number	NN
37681	2774	23	of	of	IN
37681	2774	24	practical	practical	JJ
37681	2774	25	applications	application	NNS
37681	2774	26	.	.	.
37681	2775	1	Since	since	IN
37681	2775	2	the	the	DT
37681	2775	3	number	number	NN
37681	2775	4	of	of	IN
37681	2775	5	applications	application	NNS
37681	2775	6	to	to	IN
37681	2775	7	the	the	DT
37681	2775	8	measuring	measuring	NN
37681	2775	9	of	of	IN
37681	2775	10	areas	area	NNS
37681	2775	11	of	of	IN
37681	2775	12	various	various	JJ
37681	2775	13	kinds	kind	NNS
37681	2775	14	of	of	IN
37681	2775	15	polygons	polygon	NNS
37681	2775	16	is	be	VBZ
37681	2775	17	unlimited	unlimited	JJ
37681	2775	18	,	,	,
37681	2775	19	while	while	IN
37681	2775	20	in	in	IN
37681	2775	21	the	the	DT
37681	2775	22	first	first	JJ
37681	2775	23	three	three	CD
37681	2775	24	books	book	NNS
37681	2775	25	these	these	DT
37681	2775	26	applications	application	NNS
37681	2775	27	are	be	VBP
37681	2775	28	not	not	RB
37681	2775	29	so	so	RB
37681	2775	30	obvious	obvious	JJ
37681	2775	31	,	,	,
37681	2775	32	less	less	JJR
37681	2775	33	effort	effort	NN
37681	2775	34	is	be	VBZ
37681	2775	35	made	make	VBN
37681	2775	36	in	in	IN
37681	2775	37	this	this	DT
37681	2775	38	chapter	chapter	NN
37681	2775	39	to	to	TO
37681	2775	40	suggest	suggest	VB
37681	2775	41	practical	practical	JJ
37681	2775	42	problems	problem	NNS
37681	2775	43	to	to	IN
37681	2775	44	the	the	DT
37681	2775	45	teachers	teacher	NNS
37681	2775	46	.	.	.
37681	2776	1	The	the	DT
37681	2776	2	survey	survey	NN
37681	2776	3	of	of	IN
37681	2776	4	the	the	DT
37681	2776	5	school	school	NN
37681	2776	6	grounds	ground	NNS
37681	2776	7	or	or	CC
37681	2776	8	of	of	IN
37681	2776	9	vacant	vacant	JJ
37681	2776	10	lots	lot	NNS
37681	2776	11	in	in	IN
37681	2776	12	the	the	DT
37681	2776	13	vicinity	vicinity	NN
37681	2776	14	offers	offer	VBZ
37681	2776	15	all	all	PDT
37681	2776	16	the	the	DT
37681	2776	17	outdoor	outdoor	JJ
37681	2776	18	work	work	NN
37681	2776	19	that	that	WDT
37681	2776	20	is	be	VBZ
37681	2776	21	needed	need	VBN
37681	2776	22	to	to	TO
37681	2776	23	make	make	VB
37681	2776	24	Book	Book	NNP
37681	2776	25	IV	IV	NNP
37681	2776	26	seem	seem	VBP
37681	2776	27	very	very	RB
37681	2776	28	important	important	JJ
37681	2776	29	.	.	.
37681	2777	1	THEOREM	THEOREM	NNP
37681	2777	2	.	.	.
37681	2778	1	_	_	NNP
37681	2778	2	Two	two	CD
37681	2778	3	rectangles	rectangle	NNS
37681	2778	4	having	have	VBG
37681	2778	5	equal	equal	JJ
37681	2778	6	altitudes	altitude	NNS
37681	2778	7	are	be	VBP
37681	2778	8	to	to	IN
37681	2778	9	each	each	DT
37681	2778	10	other	other	JJ
37681	2778	11	as	as	IN
37681	2778	12	their	-PRON-	PRP$
37681	2778	13	bases	basis	NNS
37681	2778	14	.	.	.
37681	2778	15	_	_	NNP
37681	2778	16	Euclid	Euclid	NNP
37681	2778	17	's	's	POS
37681	2778	18	statement	statement	NN
37681	2778	19	(	(	-LRB-
37681	2778	20	Book	Book	NNP
37681	2778	21	VI	VI	NNP
37681	2778	22	,	,	,
37681	2778	23	Proposition	Proposition	NNP
37681	2778	24	1	1	CD
37681	2778	25	)	)	-RRB-
37681	2778	26	was	be	VBD
37681	2778	27	as	as	IN
37681	2778	28	follows	follow	VBZ
37681	2778	29	:	:	:
37681	2778	30	_	_	NNP
37681	2778	31	Triangles	Triangles	NNP
37681	2778	32	and	and	CC
37681	2778	33	parallelograms	parallelogram	NNS
37681	2778	34	which	which	WDT
37681	2778	35	are	be	VBP
37681	2778	36	under	under	IN
37681	2778	37	the	the	DT
37681	2778	38	same	same	JJ
37681	2778	39	height	height	NN
37681	2778	40	are	be	VBP
37681	2778	41	to	to	IN
37681	2778	42	one	one	CD
37681	2778	43	another	another	DT
37681	2778	44	as	as	IN
37681	2778	45	their	-PRON-	PRP$
37681	2778	46	bases	basis	NNS
37681	2778	47	_	_	NNP
37681	2778	48	.	.	.
37681	2779	1	Our	-PRON-	PRP$
37681	2779	2	plan	plan	NN
37681	2779	3	of	of	IN
37681	2779	4	treating	treat	VBG
37681	2779	5	the	the	DT
37681	2779	6	two	two	CD
37681	2779	7	figures	figure	NNS
37681	2779	8	separately	separately	RB
37681	2779	9	is	be	VBZ
37681	2779	10	manifestly	manifestly	RB
37681	2779	11	better	well	JJR
37681	2779	12	from	from	IN
37681	2779	13	the	the	DT
37681	2779	14	educational	educational	JJ
37681	2779	15	standpoint	standpoint	NN
37681	2779	16	.	.	.
37681	2780	1	In	in	IN
37681	2780	2	the	the	DT
37681	2780	3	modern	modern	JJ
37681	2780	4	treatment	treatment	NN
37681	2780	5	by	by	IN
37681	2780	6	limits	limit	NNS
37681	2780	7	the	the	DT
37681	2780	8	proof	proof	NN
37681	2780	9	is	be	VBZ
37681	2780	10	divided	divide	VBN
37681	2780	11	into	into	IN
37681	2780	12	two	two	CD
37681	2780	13	parts	part	NNS
37681	2780	14	:	:	:
37681	2780	15	first	first	RB
37681	2780	16	,	,	,
37681	2780	17	for	for	IN
37681	2780	18	commensurable	commensurable	JJ
37681	2780	19	bases	basis	NNS
37681	2780	20	;	;	:
37681	2780	21	and	and	CC
37681	2780	22	second	second	RB
37681	2780	23	,	,	,
37681	2780	24	for	for	IN
37681	2780	25	incommensurable	incommensurable	JJ
37681	2780	26	ones	one	NNS
37681	2780	27	.	.	.
37681	2781	1	Of	of	IN
37681	2781	2	these	these	DT
37681	2781	3	the	the	DT
37681	2781	4	second	second	JJ
37681	2781	5	may	may	MD
37681	2781	6	well	well	RB
37681	2781	7	be	be	VB
37681	2781	8	omitted	omit	VBN
37681	2781	9	,	,	,
37681	2781	10	or	or	CC
37681	2781	11	merely	merely	RB
37681	2781	12	be	be	VB
37681	2781	13	read	read	VBN
37681	2781	14	over	over	RP
37681	2781	15	by	by	IN
37681	2781	16	the	the	DT
37681	2781	17	teacher	teacher	NN
37681	2781	18	and	and	CC
37681	2781	19	class	class	NN
37681	2781	20	and	and	CC
37681	2781	21	the	the	DT
37681	2781	22	reasons	reason	NNS
37681	2781	23	explained	explain	VBD
37681	2781	24	.	.	.
37681	2782	1	In	in	IN
37681	2782	2	general	general	JJ
37681	2782	3	,	,	,
37681	2782	4	it	-PRON-	PRP
37681	2782	5	is	be	VBZ
37681	2782	6	doubtful	doubtful	JJ
37681	2782	7	if	if	IN
37681	2782	8	the	the	DT
37681	2782	9	majority	majority	NN
37681	2782	10	of	of	IN
37681	2782	11	an	an	DT
37681	2782	12	American	american	JJ
37681	2782	13	class	class	NN
37681	2782	14	in	in	IN
37681	2782	15	geometry	geometry	NN
37681	2782	16	get	get	VBP
37681	2782	17	much	much	RB
37681	2782	18	out	out	IN
37681	2782	19	of	of	IN
37681	2782	20	the	the	DT
37681	2782	21	incommensurable	incommensurable	JJ
37681	2782	22	case	case	NN
37681	2782	23	.	.	.
37681	2783	1	Of	of	RB
37681	2783	2	course	course	RB
37681	2783	3	,	,	,
37681	2783	4	with	with	IN
37681	2783	5	a	a	DT
37681	2783	6	bright	bright	JJ
37681	2783	7	class	class	NN
37681	2783	8	a	a	DT
37681	2783	9	teacher	teacher	NN
37681	2783	10	may	may	MD
37681	2783	11	well	well	RB
37681	2783	12	afford	afford	VB
37681	2783	13	to	to	TO
37681	2783	14	take	take	VB
37681	2783	15	it	-PRON-	PRP
37681	2783	16	as	as	IN
37681	2783	17	it	-PRON-	PRP
37681	2783	18	is	be	VBZ
37681	2783	19	given	give	VBN
37681	2783	20	in	in	IN
37681	2783	21	the	the	DT
37681	2783	22	textbook	textbook	NN
37681	2783	23	,	,	,
37681	2783	24	but	but	CC
37681	2783	25	the	the	DT
37681	2783	26	important	important	JJ
37681	2783	27	thing	thing	NN
37681	2783	28	is	be	VBZ
37681	2783	29	that	that	IN
37681	2783	30	the	the	DT
37681	2783	31	commensurable	commensurable	JJ
37681	2783	32	case	case	NN
37681	2783	33	should	should	MD
37681	2783	34	be	be	VB
37681	2783	35	proved	prove	VBN
37681	2783	36	and	and	CC
37681	2783	37	the	the	DT
37681	2783	38	incommensurable	incommensurable	JJ
37681	2783	39	one	one	NN
37681	2783	40	recognized	recognize	VBD
37681	2783	41	.	.	.
37681	2784	1	Euclid	Euclid	NNP
37681	2784	2	's	's	POS
37681	2784	3	treatment	treatment	NN
37681	2784	4	of	of	IN
37681	2784	5	proportion	proportion	NN
37681	2784	6	was	be	VBD
37681	2784	7	so	so	RB
37681	2784	8	rigorous	rigorous	JJ
37681	2784	9	that	that	IN
37681	2784	10	no	no	DT
37681	2784	11	special	special	JJ
37681	2784	12	treatment	treatment	NN
37681	2784	13	of	of	IN
37681	2784	14	the	the	DT
37681	2784	15	incommensurable	incommensurable	NN
37681	2784	16	was	be	VBD
37681	2784	17	necessary	necessary	JJ
37681	2784	18	.	.	.
37681	2785	1	The	the	DT
37681	2785	2	French	french	JJ
37681	2785	3	geometer	geometer	NN
37681	2785	4	,	,	,
37681	2785	5	Legendre	Legendre	NNP
37681	2785	6	,	,	,
37681	2785	7	gave	give	VBD
37681	2785	8	a	a	DT
37681	2785	9	rigorous	rigorous	JJ
37681	2785	10	proof	proof	NN
37681	2785	11	by	by	IN
37681	2785	12	_	_	NNP
37681	2785	13	reductio	reductio	NNP
37681	2785	14	ad	ad	NN
37681	2785	15	absurdum	absurdum	NN
37681	2785	16	_	_	NNP
37681	2785	17	.	.	.
37681	2786	1	In	in	IN
37681	2786	2	America	America	NNP
37681	2786	3	the	the	DT
37681	2786	4	pupils	pupil	NNS
37681	2786	5	are	be	VBP
37681	2786	6	hardly	hardly	RB
37681	2786	7	ready	ready	JJ
37681	2786	8	for	for	IN
37681	2786	9	these	these	DT
37681	2786	10	proofs	proof	NNS
37681	2786	11	,	,	,
37681	2786	12	and	and	CC
37681	2786	13	so	so	RB
37681	2786	14	our	-PRON-	PRP$
37681	2786	15	treatment	treatment	NN
37681	2786	16	by	by	IN
37681	2786	17	limits	limit	NNS
37681	2786	18	is	be	VBZ
37681	2786	19	less	less	RBR
37681	2786	20	rigorous	rigorous	JJ
37681	2786	21	than	than	IN
37681	2786	22	these	these	DT
37681	2786	23	earlier	early	JJR
37681	2786	24	ones	one	NNS
37681	2786	25	.	.	.
37681	2787	1	THEOREM	THEOREM	NNP
37681	2787	2	.	.	.
37681	2788	1	_	_	NNP
37681	2788	2	The	the	DT
37681	2788	3	area	area	NN
37681	2788	4	of	of	IN
37681	2788	5	a	a	DT
37681	2788	6	rectangle	rectangle	NN
37681	2788	7	is	be	VBZ
37681	2788	8	equal	equal	JJ
37681	2788	9	to	to	IN
37681	2788	10	the	the	DT
37681	2788	11	product	product	NN
37681	2788	12	of	of	IN
37681	2788	13	its	-PRON-	PRP$
37681	2788	14	base	base	NN
37681	2788	15	by	by	IN
37681	2788	16	its	-PRON-	PRP$
37681	2788	17	altitude	altitude	NN
37681	2788	18	.	.	.
37681	2788	19	_	_	NNP
37681	2788	20	The	the	DT
37681	2788	21	easiest	easy	JJS
37681	2788	22	way	way	NN
37681	2788	23	to	to	TO
37681	2788	24	introduce	introduce	VB
37681	2788	25	this	this	DT
37681	2788	26	is	be	VBZ
37681	2788	27	to	to	TO
37681	2788	28	mark	mark	VB
37681	2788	29	a	a	DT
37681	2788	30	rectangle	rectangle	NN
37681	2788	31	,	,	,
37681	2788	32	with	with	IN
37681	2788	33	commensurable	commensurable	JJ
37681	2788	34	sides	side	NNS
37681	2788	35	,	,	,
37681	2788	36	on	on	IN
37681	2788	37	squared	squared	JJ
37681	2788	38	paper	paper	NN
37681	2788	39	,	,	,
37681	2788	40	and	and	CC
37681	2788	41	count	count	VB
37681	2788	42	up	up	RP
37681	2788	43	the	the	DT
37681	2788	44	squares	square	NNS
37681	2788	45	;	;	:
37681	2788	46	or	or	CC
37681	2788	47	,	,	,
37681	2788	48	what	what	WP
37681	2788	49	is	be	VBZ
37681	2788	50	more	more	RBR
37681	2788	51	convenient	convenient	JJ
37681	2788	52	,	,	,
37681	2788	53	to	to	TO
37681	2788	54	draw	draw	VB
37681	2788	55	the	the	DT
37681	2788	56	rectangle	rectangle	NN
37681	2788	57	and	and	CC
37681	2788	58	mark	mark	VB
37681	2788	59	the	the	DT
37681	2788	60	area	area	NN
37681	2788	61	off	off	RB
37681	2788	62	in	in	IN
37681	2788	63	squares	square	NNS
37681	2788	64	.	.	.
37681	2789	1	It	-PRON-	PRP
37681	2789	2	is	be	VBZ
37681	2789	3	interesting	interesting	JJ
37681	2789	4	and	and	CC
37681	2789	5	valuable	valuable	JJ
37681	2789	6	to	to	IN
37681	2789	7	a	a	DT
37681	2789	8	class	class	NN
37681	2789	9	to	to	TO
37681	2789	10	have	have	VB
37681	2789	11	its	-PRON-	PRP$
37681	2789	12	attention	attention	NN
37681	2789	13	called	call	VBN
37681	2789	14	to	to	IN
37681	2789	15	the	the	DT
37681	2789	16	fact	fact	NN
37681	2789	17	that	that	IN
37681	2789	18	the	the	DT
37681	2789	19	perimeter	perimeter	NN
37681	2789	20	of	of	IN
37681	2789	21	a	a	DT
37681	2789	22	rectangle	rectangle	NN
37681	2789	23	is	be	VBZ
37681	2789	24	no	no	DT
37681	2789	25	criterion	criterion	NN
37681	2789	26	as	as	IN
37681	2789	27	to	to	IN
37681	2789	28	the	the	DT
37681	2789	29	area	area	NN
37681	2789	30	.	.	.
37681	2790	1	Thus	thus	RB
37681	2790	2	,	,	,
37681	2790	3	if	if	IN
37681	2790	4	a	a	DT
37681	2790	5	rectangle	rectangle	NN
37681	2790	6	has	have	VBZ
37681	2790	7	an	an	DT
37681	2790	8	area	area	NN
37681	2790	9	of	of	IN
37681	2790	10	1	1	CD
37681	2790	11	square	square	JJ
37681	2790	12	foot	foot	NN
37681	2790	13	and	and	CC
37681	2790	14	is	be	VBZ
37681	2790	15	only	only	RB
37681	2790	16	1/440	1/440	CD
37681	2790	17	of	of	IN
37681	2790	18	an	an	DT
37681	2790	19	inch	inch	NN
37681	2790	20	high	high	JJ
37681	2790	21	,	,	,
37681	2790	22	the	the	DT
37681	2790	23	perimeter	perimeter	NN
37681	2790	24	is	be	VBZ
37681	2790	25	over	over	IN
37681	2790	26	2	2	CD
37681	2790	27	miles	mile	NNS
37681	2790	28	.	.	.
37681	2791	1	The	the	DT
37681	2791	2	story	story	NN
37681	2791	3	of	of	IN
37681	2791	4	how	how	WRB
37681	2791	5	Indians	Indians	NNPS
37681	2791	6	were	be	VBD
37681	2791	7	induced	induce	VBN
37681	2791	8	to	to	TO
37681	2791	9	sell	sell	VB
37681	2791	10	their	-PRON-	PRP$
37681	2791	11	land	land	NN
37681	2791	12	by	by	IN
37681	2791	13	measuring	measure	VBG
37681	2791	14	the	the	DT
37681	2791	15	perimeter	perimeter	NN
37681	2791	16	is	be	VBZ
37681	2791	17	a	a	DT
37681	2791	18	very	very	RB
37681	2791	19	old	old	JJ
37681	2791	20	one	one	CD
37681	2791	21	.	.	.
37681	2792	1	Proclus	Proclus	NNP
37681	2792	2	speaks	speak	VBZ
37681	2792	3	of	of	IN
37681	2792	4	travelers	traveler	NNS
37681	2792	5	who	who	WP
37681	2792	6	described	describe	VBD
37681	2792	7	the	the	DT
37681	2792	8	size	size	NN
37681	2792	9	of	of	IN
37681	2792	10	cities	city	NNS
37681	2792	11	by	by	IN
37681	2792	12	the	the	DT
37681	2792	13	perimeters	perimeter	NNS
37681	2792	14	,	,	,
37681	2792	15	and	and	CC
37681	2792	16	of	of	IN
37681	2792	17	men	man	NNS
37681	2792	18	who	who	WP
37681	2792	19	cheated	cheat	VBD
37681	2792	20	others	other	NNS
37681	2792	21	by	by	IN
37681	2792	22	pretending	pretend	VBG
37681	2792	23	to	to	TO
37681	2792	24	give	give	VB
37681	2792	25	them	-PRON-	PRP
37681	2792	26	as	as	RB
37681	2792	27	much	much	JJ
37681	2792	28	land	land	NN
37681	2792	29	as	as	IN
37681	2792	30	they	-PRON-	PRP
37681	2792	31	themselves	-PRON-	PRP
37681	2792	32	had	have	VBD
37681	2792	33	,	,	,
37681	2792	34	when	when	WRB
37681	2792	35	really	really	RB
37681	2792	36	they	-PRON-	PRP
37681	2792	37	made	make	VBD
37681	2792	38	only	only	RB
37681	2792	39	the	the	DT
37681	2792	40	perimeters	perimeter	NNS
37681	2792	41	equal	equal	JJ
37681	2792	42	.	.	.
37681	2793	1	Thucydides	thucydide	NNS
37681	2793	2	estimated	estimate	VBD
37681	2793	3	the	the	DT
37681	2793	4	size	size	NN
37681	2793	5	of	of	IN
37681	2793	6	Sicily	Sicily	NNP
37681	2793	7	by	by	IN
37681	2793	8	the	the	DT
37681	2793	9	time	time	NN
37681	2793	10	it	-PRON-	PRP
37681	2793	11	took	take	VBD
37681	2793	12	to	to	TO
37681	2793	13	sail	sail	VB
37681	2793	14	round	round	IN
37681	2793	15	it	-PRON-	PRP
37681	2793	16	.	.	.
37681	2794	1	Pupils	pupil	NNS
37681	2794	2	will	will	MD
37681	2794	3	be	be	VB
37681	2794	4	interested	interested	JJ
37681	2794	5	to	to	TO
37681	2794	6	know	know	VB
37681	2794	7	in	in	IN
37681	2794	8	this	this	DT
37681	2794	9	connection	connection	NN
37681	2794	10	that	that	IN
37681	2794	11	of	of	IN
37681	2794	12	polygons	polygon	NNS
37681	2794	13	having	have	VBG
37681	2794	14	the	the	DT
37681	2794	15	same	same	JJ
37681	2794	16	perimeter	perimeter	NN
37681	2794	17	and	and	CC
37681	2794	18	the	the	DT
37681	2794	19	same	same	JJ
37681	2794	20	number	number	NN
37681	2794	21	of	of	IN
37681	2794	22	sides	side	NNS
37681	2794	23	,	,	,
37681	2794	24	the	the	DT
37681	2794	25	one	one	NN
37681	2794	26	having	have	VBG
37681	2794	27	equal	equal	JJ
37681	2794	28	sides	side	NNS
37681	2794	29	and	and	CC
37681	2794	30	equal	equal	JJ
37681	2794	31	angles	angle	NNS
37681	2794	32	is	be	VBZ
37681	2794	33	the	the	DT
37681	2794	34	greatest	great	JJS
37681	2794	35	,	,	,
37681	2794	36	and	and	CC
37681	2794	37	that	that	DT
37681	2794	38	of	of	IN
37681	2794	39	plane	plane	NN
37681	2794	40	figures	figure	NNS
37681	2794	41	having	have	VBG
37681	2794	42	the	the	DT
37681	2794	43	same	same	JJ
37681	2794	44	perimeter	perimeter	NN
37681	2794	45	,	,	,
37681	2794	46	the	the	DT
37681	2794	47	circle	circle	NN
37681	2794	48	is	be	VBZ
37681	2794	49	the	the	DT
37681	2794	50	greatest	great	JJS
37681	2794	51	.	.	.
37681	2795	1	These	these	DT
37681	2795	2	facts	fact	NNS
37681	2795	3	were	be	VBD
37681	2795	4	known	know	VBN
37681	2795	5	to	to	IN
37681	2795	6	the	the	DT
37681	2795	7	Greek	greek	JJ
37681	2795	8	writers	writer	NNS
37681	2795	9	,	,	,
37681	2795	10	Zenodorus	Zenodorus	NNP
37681	2795	11	(	(	-LRB-
37681	2795	12	_	_	NNP
37681	2795	13	ca	ca	NNP
37681	2795	14	.	.	.
37681	2795	15	_	_	NNP
37681	2795	16	150	150	CD
37681	2795	17	B.C.	B.C.	NNP
37681	2795	18	)	)	-RRB-
37681	2796	1	and	and	CC
37681	2796	2	Proclus	Proclus	NNP
37681	2796	3	(	(	-LRB-
37681	2796	4	410	410	CD
37681	2796	5	-	-	SYM
37681	2796	6	485	485	CD
37681	2796	7	A.D.	A.D.	NNP
37681	2796	8	)	)	-RRB-
37681	2796	9	.	.	.
37681	2797	1	The	the	DT
37681	2797	2	surfaces	surface	NNS
37681	2797	3	of	of	IN
37681	2797	4	rectangular	rectangular	JJ
37681	2797	5	solids	solid	NNS
37681	2797	6	may	may	MD
37681	2797	7	now	now	RB
37681	2797	8	be	be	VB
37681	2797	9	found	find	VBN
37681	2797	10	,	,	,
37681	2797	11	there	there	EX
37681	2797	12	being	be	VBG
37681	2797	13	an	an	DT
37681	2797	14	advantage	advantage	NN
37681	2797	15	in	in	IN
37681	2797	16	thus	thus	RB
37681	2797	17	incidentally	incidentally	RB
37681	2797	18	connecting	connect	VBG
37681	2797	19	plane	plane	NN
37681	2797	20	and	and	CC
37681	2797	21	solid	solid	JJ
37681	2797	22	geometry	geometry	NN
37681	2797	23	wherever	wherever	WRB
37681	2797	24	it	-PRON-	PRP
37681	2797	25	is	be	VBZ
37681	2797	26	natural	natural	JJ
37681	2797	27	to	to	TO
37681	2797	28	do	do	VB
37681	2797	29	so	so	RB
37681	2797	30	.	.	.
37681	2798	1	THEOREM	THEOREM	NNP
37681	2798	2	.	.	.
37681	2799	1	_	_	NNP
37681	2799	2	The	the	DT
37681	2799	3	area	area	NN
37681	2799	4	of	of	IN
37681	2799	5	a	a	DT
37681	2799	6	parallelogram	parallelogram	NN
37681	2799	7	is	be	VBZ
37681	2799	8	equal	equal	JJ
37681	2799	9	to	to	IN
37681	2799	10	the	the	DT
37681	2799	11	product	product	NN
37681	2799	12	of	of	IN
37681	2799	13	its	-PRON-	PRP$
37681	2799	14	base	base	NN
37681	2799	15	by	by	IN
37681	2799	16	its	-PRON-	PRP$
37681	2799	17	altitude	altitude	NN
37681	2799	18	.	.	.
37681	2799	19	_	_	NNP
37681	2799	20	The	the	DT
37681	2799	21	best	good	JJS
37681	2799	22	way	way	NN
37681	2799	23	to	to	TO
37681	2799	24	introduce	introduce	VB
37681	2799	25	this	this	DT
37681	2799	26	theorem	theorem	NN
37681	2799	27	is	be	VBZ
37681	2799	28	to	to	TO
37681	2799	29	cut	cut	VB
37681	2799	30	a	a	DT
37681	2799	31	parallelogram	parallelogram	NN
37681	2799	32	from	from	IN
37681	2799	33	paper	paper	NN
37681	2799	34	,	,	,
37681	2799	35	and	and	CC
37681	2799	36	then	then	RB
37681	2799	37	,	,	,
37681	2799	38	with	with	IN
37681	2799	39	the	the	DT
37681	2799	40	class	class	NN
37681	2799	41	,	,	,
37681	2799	42	separate	separate	VB
37681	2799	43	it	-PRON-	PRP
37681	2799	44	into	into	IN
37681	2799	45	two	two	CD
37681	2799	46	parts	part	NNS
37681	2799	47	by	by	IN
37681	2799	48	a	a	DT
37681	2799	49	cut	cut	NN
37681	2799	50	perpendicular	perpendicular	NN
37681	2799	51	to	to	IN
37681	2799	52	the	the	DT
37681	2799	53	base	base	NN
37681	2799	54	.	.	.
37681	2800	1	The	the	DT
37681	2800	2	two	two	CD
37681	2800	3	parts	part	NNS
37681	2800	4	may	may	MD
37681	2800	5	then	then	RB
37681	2800	6	be	be	VB
37681	2800	7	fitted	fit	VBN
37681	2800	8	together	together	RB
37681	2800	9	to	to	TO
37681	2800	10	make	make	VB
37681	2800	11	a	a	DT
37681	2800	12	rectangle	rectangle	NN
37681	2800	13	.	.	.
37681	2801	1	In	in	IN
37681	2801	2	particular	particular	JJ
37681	2801	3	,	,	,
37681	2801	4	if	if	IN
37681	2801	5	we	-PRON-	PRP
37681	2801	6	cut	cut	VBD
37681	2801	7	off	off	RP
37681	2801	8	a	a	DT
37681	2801	9	triangle	triangle	NN
37681	2801	10	from	from	IN
37681	2801	11	one	one	CD
37681	2801	12	end	end	NN
37681	2801	13	and	and	CC
37681	2801	14	fit	fit	VB
37681	2801	15	it	-PRON-	PRP
37681	2801	16	on	on	IN
37681	2801	17	the	the	DT
37681	2801	18	other	other	JJ
37681	2801	19	,	,	,
37681	2801	20	we	-PRON-	PRP
37681	2801	21	have	have	VBP
37681	2801	22	the	the	DT
37681	2801	23	basis	basis	NN
37681	2801	24	for	for	IN
37681	2801	25	the	the	DT
37681	2801	26	proof	proof	NN
37681	2801	27	of	of	IN
37681	2801	28	the	the	DT
37681	2801	29	textbooks	textbook	NNS
37681	2801	30	.	.	.
37681	2802	1	The	the	DT
37681	2802	2	use	use	NN
37681	2802	3	of	of	IN
37681	2802	4	squared	squared	JJ
37681	2802	5	paper	paper	NN
37681	2802	6	for	for	IN
37681	2802	7	such	such	PDT
37681	2802	8	a	a	DT
37681	2802	9	proposition	proposition	NN
37681	2802	10	is	be	VBZ
37681	2802	11	not	not	RB
37681	2802	12	wise	wise	JJ
37681	2802	13	,	,	,
37681	2802	14	since	since	IN
37681	2802	15	it	-PRON-	PRP
37681	2802	16	makes	make	VBZ
37681	2802	17	the	the	DT
37681	2802	18	measurement	measurement	NN
37681	2802	19	appear	appear	VB
37681	2802	20	to	to	TO
37681	2802	21	be	be	VB
37681	2802	22	merely	merely	RB
37681	2802	23	an	an	DT
37681	2802	24	approximation	approximation	NN
37681	2802	25	.	.	.
37681	2803	1	The	the	DT
37681	2803	2	cutting	cutting	NN
37681	2803	3	of	of	IN
37681	2803	4	the	the	DT
37681	2803	5	paper	paper	NN
37681	2803	6	is	be	VBZ
37681	2803	7	in	in	IN
37681	2803	8	every	every	DT
37681	2803	9	way	way	NN
37681	2803	10	more	more	RBR
37681	2803	11	satisfactory	satisfactory	JJ
37681	2803	12	.	.	.
37681	2804	1	THEOREM	THEOREM	NNP
37681	2804	2	.	.	.
37681	2805	1	_	_	NNP
37681	2805	2	The	the	DT
37681	2805	3	area	area	NN
37681	2805	4	of	of	IN
37681	2805	5	a	a	DT
37681	2805	6	triangle	triangle	NN
37681	2805	7	is	be	VBZ
37681	2805	8	equal	equal	JJ
37681	2805	9	to	to	IN
37681	2805	10	half	half	PDT
37681	2805	11	the	the	DT
37681	2805	12	product	product	NN
37681	2805	13	of	of	IN
37681	2805	14	its	-PRON-	PRP$
37681	2805	15	base	base	NN
37681	2805	16	by	by	IN
37681	2805	17	its	-PRON-	PRP$
37681	2805	18	altitude	altitude	NN
37681	2805	19	.	.	.
37681	2805	20	_	_	NNP
37681	2805	21	Of	of	RB
37681	2805	22	course	course	RB
37681	2805	23	,	,	,
37681	2805	24	the	the	DT
37681	2805	25	Greeks	Greeks	NNPS
37681	2805	26	would	would	MD
37681	2805	27	never	never	RB
37681	2805	28	have	have	VB
37681	2805	29	used	use	VBN
37681	2805	30	the	the	DT
37681	2805	31	wording	wording	NN
37681	2805	32	of	of	IN
37681	2805	33	either	either	DT
37681	2805	34	of	of	IN
37681	2805	35	these	these	DT
37681	2805	36	two	two	CD
37681	2805	37	propositions	proposition	NNS
37681	2805	38	.	.	.
37681	2806	1	Euclid	euclid	JJ
37681	2806	2	,	,	,
37681	2806	3	for	for	IN
37681	2806	4	example	example	NN
37681	2806	5	,	,	,
37681	2806	6	gives	give	VBZ
37681	2806	7	this	this	DT
37681	2806	8	one	one	NN
37681	2806	9	as	as	IN
37681	2806	10	follows	follow	VBZ
37681	2806	11	:	:	:
37681	2806	12	_	_	XX
37681	2806	13	If	if	IN
37681	2806	14	a	a	DT
37681	2806	15	parallelogram	parallelogram	NN
37681	2806	16	have	have	VBP
37681	2806	17	the	the	DT
37681	2806	18	same	same	JJ
37681	2806	19	base	base	NN
37681	2806	20	with	with	IN
37681	2806	21	a	a	DT
37681	2806	22	triangle	triangle	NN
37681	2806	23	and	and	CC
37681	2806	24	be	be	VB
37681	2806	25	in	in	IN
37681	2806	26	the	the	DT
37681	2806	27	same	same	JJ
37681	2806	28	parallels	parallel	NNS
37681	2806	29	,	,	,
37681	2806	30	the	the	DT
37681	2806	31	parallelogram	parallelogram	NN
37681	2806	32	is	be	VBZ
37681	2806	33	double	double	JJ
37681	2806	34	of	of	IN
37681	2806	35	the	the	DT
37681	2806	36	triangle	triangle	NN
37681	2806	37	.	.	.
37681	2806	38	_	_	NNP
37681	2806	39	As	as	IN
37681	2806	40	to	to	IN
37681	2806	41	the	the	DT
37681	2806	42	parallelogram	parallelogram	NN
37681	2806	43	,	,	,
37681	2806	44	he	-PRON-	PRP
37681	2806	45	simply	simply	RB
37681	2806	46	says	say	VBZ
37681	2806	47	it	-PRON-	PRP
37681	2806	48	is	be	VBZ
37681	2806	49	equal	equal	JJ
37681	2806	50	to	to	IN
37681	2806	51	a	a	DT
37681	2806	52	parallelogram	parallelogram	NN
37681	2806	53	of	of	IN
37681	2806	54	equal	equal	JJ
37681	2806	55	base	base	NN
37681	2806	56	and	and	CC
37681	2806	57	"	"	``
37681	2806	58	in	in	IN
37681	2806	59	the	the	DT
37681	2806	60	same	same	JJ
37681	2806	61	parallels	parallel	NNS
37681	2806	62	,	,	,
37681	2806	63	"	"	''
37681	2806	64	which	which	WDT
37681	2806	65	makes	make	VBZ
37681	2806	66	it	-PRON-	PRP
37681	2806	67	equal	equal	JJ
37681	2806	68	to	to	IN
37681	2806	69	a	a	DT
37681	2806	70	rectangle	rectangle	NN
37681	2806	71	of	of	IN
37681	2806	72	the	the	DT
37681	2806	73	same	same	JJ
37681	2806	74	base	base	NN
37681	2806	75	and	and	CC
37681	2806	76	the	the	DT
37681	2806	77	same	same	JJ
37681	2806	78	altitude	altitude	NN
37681	2806	79	.	.	.
37681	2807	1	The	the	DT
37681	2807	2	number	number	NN
37681	2807	3	of	of	IN
37681	2807	4	applications	application	NNS
37681	2807	5	of	of	IN
37681	2807	6	these	these	DT
37681	2807	7	two	two	CD
37681	2807	8	theorems	theorem	NNS
37681	2807	9	is	be	VBZ
37681	2807	10	so	so	RB
37681	2807	11	great	great	JJ
37681	2807	12	that	that	IN
37681	2807	13	the	the	DT
37681	2807	14	teacher	teacher	NN
37681	2807	15	will	will	MD
37681	2807	16	not	not	RB
37681	2807	17	be	be	VB
37681	2807	18	at	at	IN
37681	2807	19	a	a	DT
37681	2807	20	loss	loss	NN
37681	2807	21	to	to	TO
37681	2807	22	find	find	VB
37681	2807	23	genuine	genuine	JJ
37681	2807	24	ones	one	NNS
37681	2807	25	that	that	WDT
37681	2807	26	appeal	appeal	VBP
37681	2807	27	to	to	IN
37681	2807	28	the	the	DT
37681	2807	29	class	class	NN
37681	2807	30	.	.	.
37681	2808	1	Teachers	teacher	NNS
37681	2808	2	may	may	MD
37681	2808	3	now	now	RB
37681	2808	4	introduce	introduce	VB
37681	2808	5	pyramids	pyramid	NNS
37681	2808	6	,	,	,
37681	2808	7	requiring	require	VBG
37681	2808	8	the	the	DT
37681	2808	9	areas	area	NNS
37681	2808	10	of	of	IN
37681	2808	11	the	the	DT
37681	2808	12	triangular	triangular	NN
37681	2808	13	faces	face	VBZ
37681	2808	14	to	to	TO
37681	2808	15	be	be	VB
37681	2808	16	found	find	VBN
37681	2808	17	.	.	.
37681	2809	1	The	the	DT
37681	2809	2	Ahmes	Ahmes	NNP
37681	2809	3	papyrus	papyrus	NN
37681	2809	4	(	(	-LRB-
37681	2809	5	_	_	NNP
37681	2809	6	ca	ca	NNP
37681	2809	7	.	.	.
37681	2809	8	_	_	NNP
37681	2809	9	1700	1700	CD
37681	2809	10	B.C.	B.C.	NNP
37681	2809	11	)	)	-RRB-
37681	2810	1	gives	give	VBZ
37681	2810	2	the	the	DT
37681	2810	3	area	area	NN
37681	2810	4	of	of	IN
37681	2810	5	an	an	DT
37681	2810	6	isosceles	isoscele	NNS
37681	2810	7	triangle	triangle	NN
37681	2810	8	as	as	IN
37681	2810	9	1/2	1/2	CD
37681	2810	10	_	_	NNP
37681	2810	11	bs	bs	NNP
37681	2810	12	_	_	NNP
37681	2810	13	,	,	,
37681	2810	14	where	where	WRB
37681	2810	15	_	_	NNP
37681	2810	16	s	s	NNP
37681	2810	17	_	_	NNP
37681	2810	18	is	be	VBZ
37681	2810	19	one	one	CD
37681	2810	20	of	of	IN
37681	2810	21	the	the	DT
37681	2810	22	equal	equal	JJ
37681	2810	23	sides	side	NNS
37681	2810	24	,	,	,
37681	2810	25	thus	thus	RB
37681	2810	26	taking	take	VBG
37681	2810	27	_	_	NNP
37681	2810	28	s	s	NNP
37681	2810	29	_	_	NNP
37681	2810	30	for	for	IN
37681	2810	31	the	the	DT
37681	2810	32	altitude	altitude	NN
37681	2810	33	.	.	.
37681	2811	1	This	this	DT
37681	2811	2	shows	show	VBZ
37681	2811	3	the	the	DT
37681	2811	4	primitive	primitive	JJ
37681	2811	5	state	state	NN
37681	2811	6	of	of	IN
37681	2811	7	geometry	geometry	NN
37681	2811	8	at	at	IN
37681	2811	9	that	that	DT
37681	2811	10	time	time	NN
37681	2811	11	.	.	.
37681	2812	1	THEOREM	THEOREM	NNP
37681	2812	2	.	.	.
37681	2813	1	_	_	NNP
37681	2813	2	The	the	DT
37681	2813	3	area	area	NN
37681	2813	4	of	of	IN
37681	2813	5	a	a	DT
37681	2813	6	trapezoid	trapezoid	NN
37681	2813	7	is	be	VBZ
37681	2813	8	equal	equal	JJ
37681	2813	9	to	to	IN
37681	2813	10	half	half	PDT
37681	2813	11	the	the	DT
37681	2813	12	sum	sum	NN
37681	2813	13	of	of	IN
37681	2813	14	its	-PRON-	PRP$
37681	2813	15	bases	basis	NNS
37681	2813	16	multiplied	multiply	VBN
37681	2813	17	by	by	IN
37681	2813	18	the	the	DT
37681	2813	19	altitude	altitude	NN
37681	2813	20	.	.	.
37681	2813	21	_	_	NNP
37681	2813	22	[	[	-LRB-
37681	2813	23	Illustration	illustration	NN
37681	2813	24	]	]	-RRB-
37681	2813	25	An	an	DT
37681	2813	26	interesting	interesting	JJ
37681	2813	27	variation	variation	NN
37681	2813	28	of	of	IN
37681	2813	29	the	the	DT
37681	2813	30	ordinary	ordinary	JJ
37681	2813	31	proof	proof	NN
37681	2813	32	is	be	VBZ
37681	2813	33	made	make	VBN
37681	2813	34	by	by	IN
37681	2813	35	placing	place	VBG
37681	2813	36	a	a	DT
37681	2813	37	trapezoid	trapezoid	NN
37681	2813	38	_	_	NNP
37681	2813	39	T	T	NNP
37681	2813	40	'	'	''
37681	2813	41	_	_	NNP
37681	2813	42	,	,	,
37681	2813	43	congruent	congruent	JJ
37681	2813	44	to	to	IN
37681	2813	45	_	_	NNP
37681	2813	46	T	T	NNP
37681	2813	47	_	_	NNP
37681	2813	48	,	,	,
37681	2813	49	in	in	IN
37681	2813	50	the	the	DT
37681	2813	51	position	position	NN
37681	2813	52	here	here	RB
37681	2813	53	shown	show	VBN
37681	2813	54	.	.	.
37681	2814	1	The	the	DT
37681	2814	2	parallelogram	parallelogram	NN
37681	2814	3	formed	form	VBD
37681	2814	4	equals	equal	NNS
37681	2814	5	_	_	NNP
37681	2814	6	a_(_b	a_(_b	NNP
37681	2814	7	_	_	NNP
37681	2814	8	+	+	SYM
37681	2814	9	_	_	NNP
37681	2814	10	b	b	NNP
37681	2814	11	'	'	``
37681	2814	12	_	_	NNP
37681	2814	13	)	)	-RRB-
37681	2814	14	,	,	,
37681	2814	15	and	and	CC
37681	2814	16	therefore	therefore	RB
37681	2814	17	_	_	NNP
37681	2814	18	T	T	NNP
37681	2814	19	_	_	NNP
37681	2814	20	=	=	SYM
37681	2814	21	_	_	NNP
37681	2814	22	a	a	DT
37681	2814	23	_	_	NNP
37681	2814	24	·	·	NFP
37681	2814	25	(	(	-LRB-
37681	2814	26	_	_	NNP
37681	2814	27	b	b	NNP
37681	2814	28	_	_	NNP
37681	2814	29	+	+	NNP
37681	2814	30	_	_	NNP
37681	2814	31	b'_)/2	b'_)/2	''
37681	2814	32	.	.	.
37681	2815	1	The	the	DT
37681	2815	2	proposition	proposition	NN
37681	2815	3	should	should	MD
37681	2815	4	be	be	VB
37681	2815	5	discussed	discuss	VBN
37681	2815	6	for	for	IN
37681	2815	7	the	the	DT
37681	2815	8	case	case	NN
37681	2815	9	_	_	NNP
37681	2815	10	b	b	NNP
37681	2815	11	_	_	NNP
37681	2815	12	=	=	SYM
37681	2815	13	_	_	NNP
37681	2815	14	b	b	NNP
37681	2815	15	'	'	``
37681	2815	16	_	_	NNP
37681	2815	17	,	,	,
37681	2815	18	when	when	WRB
37681	2815	19	it	-PRON-	PRP
37681	2815	20	reduces	reduce	VBZ
37681	2815	21	to	to	IN
37681	2815	22	the	the	DT
37681	2815	23	one	one	CD
37681	2815	24	about	about	IN
37681	2815	25	the	the	DT
37681	2815	26	area	area	NN
37681	2815	27	of	of	IN
37681	2815	28	a	a	DT
37681	2815	29	parallelogram	parallelogram	NN
37681	2815	30	.	.	.
37681	2816	1	If	if	IN
37681	2816	2	_	_	NNP
37681	2816	3	b'_=	b'_=	NNP
37681	2816	4	0	0	CD
37681	2816	5	,	,	,
37681	2816	6	the	the	DT
37681	2816	7	trapezoid	trapezoid	NN
37681	2816	8	reduces	reduce	VBZ
37681	2816	9	to	to	IN
37681	2816	10	a	a	DT
37681	2816	11	triangle	triangle	NN
37681	2816	12	,	,	,
37681	2816	13	and	and	CC
37681	2816	14	_	_	NNP
37681	2816	15	T	T	NNP
37681	2816	16	_	_	NNP
37681	2816	17	=	=	SYM
37681	2816	18	_	_	NNP
37681	2816	19	a	a	DT
37681	2816	20	_	_	NNP
37681	2816	21	·	·	NFP
37681	2816	22	_	_	NNP
37681	2816	23	b_/2	b_/2	NNP
37681	2816	24	.	.	.
37681	2817	1	This	this	DT
37681	2817	2	proposition	proposition	NN
37681	2817	3	is	be	VBZ
37681	2817	4	the	the	DT
37681	2817	5	basis	basis	NN
37681	2817	6	of	of	IN
37681	2817	7	the	the	DT
37681	2817	8	theory	theory	NN
37681	2817	9	of	of	IN
37681	2817	10	land	land	NN
37681	2817	11	surveying	surveying	NN
37681	2817	12	,	,	,
37681	2817	13	a	a	DT
37681	2817	14	piece	piece	NN
37681	2817	15	of	of	IN
37681	2817	16	land	land	NN
37681	2817	17	being	being	NN
37681	2817	18	,	,	,
37681	2817	19	for	for	IN
37681	2817	20	purposes	purpose	NNS
37681	2817	21	of	of	IN
37681	2817	22	measurement	measurement	NN
37681	2817	23	,	,	,
37681	2817	24	divided	divide	VBN
37681	2817	25	into	into	IN
37681	2817	26	trapezoids	trapezoid	NNS
37681	2817	27	and	and	CC
37681	2817	28	triangles	triangle	NNS
37681	2817	29	,	,	,
37681	2817	30	the	the	DT
37681	2817	31	latter	latter	JJ
37681	2817	32	being	being	NN
37681	2817	33	,	,	,
37681	2817	34	as	as	IN
37681	2817	35	we	-PRON-	PRP
37681	2817	36	have	have	VBP
37681	2817	37	seen	see	VBN
37681	2817	38	,	,	,
37681	2817	39	a	a	DT
37681	2817	40	kind	kind	NN
37681	2817	41	of	of	IN
37681	2817	42	special	special	JJ
37681	2817	43	trapezoid	trapezoid	NN
37681	2817	44	.	.	.
37681	2818	1	The	the	DT
37681	2818	2	proposition	proposition	NN
37681	2818	3	is	be	VBZ
37681	2818	4	not	not	RB
37681	2818	5	in	in	IN
37681	2818	6	Euclid	Euclid	NNP
37681	2818	7	,	,	,
37681	2818	8	but	but	CC
37681	2818	9	is	be	VBZ
37681	2818	10	given	give	VBN
37681	2818	11	by	by	IN
37681	2818	12	Proclus	Proclus	NNP
37681	2818	13	in	in	IN
37681	2818	14	the	the	DT
37681	2818	15	fifth	fifth	JJ
37681	2818	16	century	century	NN
37681	2818	17	.	.	.
37681	2819	1	The	the	DT
37681	2819	2	term	term	NN
37681	2819	3	"	"	``
37681	2819	4	isosceles	isoscele	NNS
37681	2819	5	trapezoid	trapezoid	NN
37681	2819	6	"	"	''
37681	2819	7	is	be	VBZ
37681	2819	8	used	use	VBN
37681	2819	9	to	to	TO
37681	2819	10	mean	mean	VB
37681	2819	11	a	a	DT
37681	2819	12	trapezoid	trapezoid	NN
37681	2819	13	with	with	IN
37681	2819	14	two	two	CD
37681	2819	15	opposite	opposite	JJ
37681	2819	16	sides	side	NNS
37681	2819	17	equal	equal	JJ
37681	2819	18	,	,	,
37681	2819	19	but	but	CC
37681	2819	20	not	not	RB
37681	2819	21	parallel	parallel	JJ
37681	2819	22	.	.	.
37681	2820	1	The	the	DT
37681	2820	2	area	area	NN
37681	2820	3	of	of	IN
37681	2820	4	such	such	PDT
37681	2820	5	a	a	DT
37681	2820	6	figure	figure	NN
37681	2820	7	was	be	VBD
37681	2820	8	incorrectly	incorrectly	RB
37681	2820	9	given	give	VBN
37681	2820	10	by	by	IN
37681	2820	11	the	the	DT
37681	2820	12	Ahmes	Ahmes	NNP
37681	2820	13	papyrus	papyru	NNS
37681	2820	14	as	as	IN
37681	2820	15	1/2(_b	1/2(_b	CD
37681	2820	16	_	_	NNP
37681	2820	17	+	+	SYM
37681	2820	18	_	_	NNP
37681	2820	19	b'_)_s	b'_)_s	NNP
37681	2820	20	_	_	NNP
37681	2820	21	,	,	,
37681	2820	22	where	where	WRB
37681	2820	23	_	_	NNP
37681	2820	24	s	s	NNP
37681	2820	25	_	_	NNP
37681	2820	26	is	be	VBZ
37681	2820	27	one	one	CD
37681	2820	28	of	of	IN
37681	2820	29	the	the	DT
37681	2820	30	equal	equal	JJ
37681	2820	31	sides	side	NNS
37681	2820	32	.	.	.
37681	2821	1	This	this	DT
37681	2821	2	amounts	amount	VBZ
37681	2821	3	to	to	IN
37681	2821	4	taking	take	VBG
37681	2821	5	_	_	NNP
37681	2821	6	s	s	NNP
37681	2821	7	_	_	NNP
37681	2821	8	=	=	SYM
37681	2821	9	_	_	NNP
37681	2821	10	a	a	DT
37681	2821	11	_	_	NNP
37681	2821	12	.	.	.
37681	2822	1	The	the	DT
37681	2822	2	proposition	proposition	NN
37681	2822	3	is	be	VBZ
37681	2822	4	particularly	particularly	RB
37681	2822	5	important	important	JJ
37681	2822	6	in	in	IN
37681	2822	7	the	the	DT
37681	2822	8	surveying	surveying	NN
37681	2822	9	of	of	IN
37681	2822	10	an	an	DT
37681	2822	11	irregular	irregular	JJ
37681	2822	12	field	field	NN
37681	2822	13	such	such	JJ
37681	2822	14	as	as	IN
37681	2822	15	is	be	VBZ
37681	2822	16	found	find	VBN
37681	2822	17	in	in	IN
37681	2822	18	hilly	hilly	JJ
37681	2822	19	districts	district	NNS
37681	2822	20	.	.	.
37681	2823	1	It	-PRON-	PRP
37681	2823	2	is	be	VBZ
37681	2823	3	customary	customary	JJ
37681	2823	4	to	to	TO
37681	2823	5	consider	consider	VB
37681	2823	6	the	the	DT
37681	2823	7	field	field	NN
37681	2823	8	as	as	IN
37681	2823	9	a	a	DT
37681	2823	10	polygon	polygon	NN
37681	2823	11	,	,	,
37681	2823	12	and	and	CC
37681	2823	13	to	to	TO
37681	2823	14	draw	draw	VB
37681	2823	15	a	a	DT
37681	2823	16	meridian	meridian	JJ
37681	2823	17	line	line	NN
37681	2823	18	,	,	,
37681	2823	19	letting	let	VBG
37681	2823	20	fall	fall	VB
37681	2823	21	perpendiculars	perpendicular	NNS
37681	2823	22	upon	upon	IN
37681	2823	23	it	-PRON-	PRP
37681	2823	24	from	from	IN
37681	2823	25	the	the	DT
37681	2823	26	vertices	vertex	NNS
37681	2823	27	,	,	,
37681	2823	28	thus	thus	RB
37681	2823	29	forming	form	VBG
37681	2823	30	triangles	triangle	NNS
37681	2823	31	and	and	CC
37681	2823	32	trapezoids	trapezoid	NNS
37681	2823	33	that	that	WDT
37681	2823	34	can	can	MD
37681	2823	35	easily	easily	RB
37681	2823	36	be	be	VB
37681	2823	37	measured	measure	VBN
37681	2823	38	.	.	.
37681	2824	1	An	an	DT
37681	2824	2	older	old	JJR
37681	2824	3	plan	plan	NN
37681	2824	4	,	,	,
37681	2824	5	but	but	CC
37681	2824	6	one	one	CD
37681	2824	7	better	better	RB
37681	2824	8	suited	suit	VBN
37681	2824	9	to	to	IN
37681	2824	10	the	the	DT
37681	2824	11	use	use	NN
37681	2824	12	of	of	IN
37681	2824	13	pupils	pupil	NNS
37681	2824	14	who	who	WP
37681	2824	15	may	may	MD
37681	2824	16	be	be	VB
37681	2824	17	working	work	VBG
37681	2824	18	only	only	RB
37681	2824	19	with	with	IN
37681	2824	20	the	the	DT
37681	2824	21	tape	tape	NN
37681	2824	22	,	,	,
37681	2824	23	is	be	VBZ
37681	2824	24	given	give	VBN
37681	2824	25	on	on	IN
37681	2824	26	page	page	NN
37681	2824	27	99	99	CD
37681	2824	28	.	.	.
37681	2825	1	THEOREM	THEOREM	NNP
37681	2825	2	.	.	.
37681	2826	1	_	_	NNP
37681	2826	2	The	the	DT
37681	2826	3	areas	area	NNS
37681	2826	4	of	of	IN
37681	2826	5	two	two	CD
37681	2826	6	triangles	triangle	NNS
37681	2826	7	which	which	WDT
37681	2826	8	have	have	VBP
37681	2826	9	an	an	DT
37681	2826	10	angle	angle	NN
37681	2826	11	of	of	IN
37681	2826	12	the	the	DT
37681	2826	13	one	one	NN
37681	2826	14	equal	equal	JJ
37681	2826	15	to	to	IN
37681	2826	16	an	an	DT
37681	2826	17	angle	angle	NN
37681	2826	18	of	of	IN
37681	2826	19	the	the	DT
37681	2826	20	other	other	JJ
37681	2826	21	are	be	VBP
37681	2826	22	to	to	IN
37681	2826	23	each	each	DT
37681	2826	24	other	other	JJ
37681	2826	25	as	as	IN
37681	2826	26	the	the	DT
37681	2826	27	products	product	NNS
37681	2826	28	of	of	IN
37681	2826	29	the	the	DT
37681	2826	30	sides	side	NNS
37681	2826	31	including	include	VBG
37681	2826	32	the	the	DT
37681	2826	33	equal	equal	JJ
37681	2826	34	angles	angle	NNS
37681	2826	35	.	.	.
37681	2826	36	_	_	NNP
37681	2826	37	This	this	DT
37681	2826	38	proposition	proposition	NN
37681	2826	39	may	may	MD
37681	2826	40	be	be	VB
37681	2826	41	omitted	omit	VBN
37681	2826	42	as	as	RB
37681	2826	43	far	far	RB
37681	2826	44	as	as	IN
37681	2826	45	its	-PRON-	PRP$
37681	2826	46	use	use	NN
37681	2826	47	in	in	IN
37681	2826	48	plane	plane	NN
37681	2826	49	geometry	geometry	NN
37681	2826	50	is	be	VBZ
37681	2826	51	concerned	concern	VBN
37681	2826	52	,	,	,
37681	2826	53	for	for	IN
37681	2826	54	we	-PRON-	PRP
37681	2826	55	can	can	MD
37681	2826	56	prove	prove	VB
37681	2826	57	the	the	DT
37681	2826	58	next	next	JJ
37681	2826	59	proposition	proposition	NN
37681	2826	60	here	here	RB
37681	2826	61	given	give	VBN
37681	2826	62	without	without	IN
37681	2826	63	using	use	VBG
37681	2826	64	it	-PRON-	PRP
37681	2826	65	.	.	.
37681	2827	1	In	in	IN
37681	2827	2	solid	solid	JJ
37681	2827	3	geometry	geometry	NN
37681	2827	4	it	-PRON-	PRP
37681	2827	5	is	be	VBZ
37681	2827	6	used	use	VBN
37681	2827	7	only	only	RB
37681	2827	8	in	in	IN
37681	2827	9	a	a	DT
37681	2827	10	proposition	proposition	NN
37681	2827	11	relating	relate	VBG
37681	2827	12	to	to	IN
37681	2827	13	the	the	DT
37681	2827	14	volumes	volume	NNS
37681	2827	15	of	of	IN
37681	2827	16	two	two	CD
37681	2827	17	triangular	triangular	JJ
37681	2827	18	pyramids	pyramid	NNS
37681	2827	19	having	have	VBG
37681	2827	20	a	a	DT
37681	2827	21	common	common	JJ
37681	2827	22	trihedral	trihedral	JJ
37681	2827	23	angle	angle	NN
37681	2827	24	,	,	,
37681	2827	25	and	and	CC
37681	2827	26	this	this	DT
37681	2827	27	is	be	VBZ
37681	2827	28	usually	usually	RB
37681	2827	29	omitted	omit	VBN
37681	2827	30	.	.	.
37681	2828	1	But	but	CC
37681	2828	2	the	the	DT
37681	2828	3	theorem	theorem	NN
37681	2828	4	is	be	VBZ
37681	2828	5	so	so	RB
37681	2828	6	simple	simple	JJ
37681	2828	7	that	that	IN
37681	2828	8	it	-PRON-	PRP
37681	2828	9	takes	take	VBZ
37681	2828	10	but	but	CC
37681	2828	11	little	little	JJ
37681	2828	12	time	time	NN
37681	2828	13	,	,	,
37681	2828	14	and	and	CC
37681	2828	15	it	-PRON-	PRP
37681	2828	16	adds	add	VBZ
37681	2828	17	greatly	greatly	RB
37681	2828	18	to	to	IN
37681	2828	19	the	the	DT
37681	2828	20	student	student	NN
37681	2828	21	's	's	POS
37681	2828	22	appreciation	appreciation	NN
37681	2828	23	of	of	IN
37681	2828	24	similar	similar	JJ
37681	2828	25	triangles	triangle	NNS
37681	2828	26	.	.	.
37681	2829	1	It	-PRON-	PRP
37681	2829	2	not	not	RB
37681	2829	3	only	only	RB
37681	2829	4	simplifies	simplify	VBZ
37681	2829	5	the	the	DT
37681	2829	6	next	next	JJ
37681	2829	7	one	one	NN
37681	2829	8	here	here	RB
37681	2829	9	given	give	VBN
37681	2829	10	,	,	,
37681	2829	11	but	but	CC
37681	2829	12	teachers	teacher	NNS
37681	2829	13	can	can	MD
37681	2829	14	at	at	IN
37681	2829	15	once	once	RB
37681	2829	16	deduce	deduce	VB
37681	2829	17	the	the	DT
37681	2829	18	latter	latter	JJ
37681	2829	19	from	from	IN
37681	2829	20	it	-PRON-	PRP
37681	2829	21	as	as	IN
37681	2829	22	a	a	DT
37681	2829	23	special	special	JJ
37681	2829	24	case	case	NN
37681	2829	25	by	by	IN
37681	2829	26	asking	ask	VBG
37681	2829	27	to	to	IN
37681	2829	28	what	what	WP
37681	2829	29	it	-PRON-	PRP
37681	2829	30	reduces	reduce	VBZ
37681	2829	31	if	if	IN
37681	2829	32	a	a	DT
37681	2829	33	second	second	JJ
37681	2829	34	angle	angle	NN
37681	2829	35	of	of	IN
37681	2829	36	one	one	CD
37681	2829	37	triangle	triangle	NN
37681	2829	38	is	be	VBZ
37681	2829	39	also	also	RB
37681	2829	40	equal	equal	JJ
37681	2829	41	to	to	IN
37681	2829	42	a	a	DT
37681	2829	43	second	second	JJ
37681	2829	44	angle	angle	NN
37681	2829	45	of	of	IN
37681	2829	46	the	the	DT
37681	2829	47	other	other	JJ
37681	2829	48	triangle	triangle	NN
37681	2829	49	.	.	.
37681	2830	1	It	-PRON-	PRP
37681	2830	2	is	be	VBZ
37681	2830	3	helpful	helpful	JJ
37681	2830	4	to	to	TO
37681	2830	5	give	give	VB
37681	2830	6	numerical	numerical	JJ
37681	2830	7	values	value	NNS
37681	2830	8	to	to	IN
37681	2830	9	the	the	DT
37681	2830	10	sides	side	NNS
37681	2830	11	of	of	IN
37681	2830	12	a	a	DT
37681	2830	13	few	few	JJ
37681	2830	14	triangles	triangle	NNS
37681	2830	15	having	have	VBG
37681	2830	16	such	such	JJ
37681	2830	17	equal	equal	JJ
37681	2830	18	angles	angle	NNS
37681	2830	19	,	,	,
37681	2830	20	and	and	CC
37681	2830	21	to	to	TO
37681	2830	22	find	find	VB
37681	2830	23	the	the	DT
37681	2830	24	numerical	numerical	JJ
37681	2830	25	ratio	ratio	NN
37681	2830	26	of	of	IN
37681	2830	27	the	the	DT
37681	2830	28	areas	area	NNS
37681	2830	29	.	.	.
37681	2831	1	THEOREM	THEOREM	NNP
37681	2831	2	.	.	.
37681	2832	1	_	_	NNP
37681	2832	2	The	the	DT
37681	2832	3	areas	area	NNS
37681	2832	4	of	of	IN
37681	2832	5	two	two	CD
37681	2832	6	similar	similar	JJ
37681	2832	7	triangles	triangle	NNS
37681	2832	8	are	be	VBP
37681	2832	9	to	to	IN
37681	2832	10	each	each	DT
37681	2832	11	other	other	JJ
37681	2832	12	as	as	IN
37681	2832	13	the	the	DT
37681	2832	14	squares	square	NNS
37681	2832	15	on	on	IN
37681	2832	16	any	any	DT
37681	2832	17	two	two	CD
37681	2832	18	corresponding	corresponding	JJ
37681	2832	19	sides	side	NNS
37681	2832	20	.	.	.
37681	2832	21	_	_	NNP
37681	2832	22	[	[	-LRB-
37681	2832	23	Illustration	illustration	NN
37681	2832	24	]	]	-RRB-
37681	2832	25	This	this	DT
37681	2832	26	may	may	MD
37681	2832	27	be	be	VB
37681	2832	28	proved	prove	VBN
37681	2832	29	independently	independently	RB
37681	2832	30	of	of	IN
37681	2832	31	the	the	DT
37681	2832	32	preceding	precede	VBG
37681	2832	33	proposition	proposition	NN
37681	2832	34	by	by	IN
37681	2832	35	drawing	draw	VBG
37681	2832	36	the	the	DT
37681	2832	37	altitudes	altitude	NNS
37681	2832	38	_	_	NNP
37681	2832	39	p	p	NNP
37681	2832	40	_	_	NNP
37681	2832	41	and	and	CC
37681	2832	42	_	_	NNP
37681	2832	43	p	p	NNP
37681	2832	44	'	'	''
37681	2832	45	_	_	NNP
37681	2832	46	.	.	.
37681	2833	1	Then	then	RB
37681	2833	2	[	[	-LRB-
37681	2833	3	triangle]_ABC_/[triangle]_A'B'C	triangle]_ABC_/[triangle]_A'B'C	NNP
37681	2833	4	'	'	''
37681	2833	5	_	_	NNP
37681	2833	6	=	=	SYM
37681	2833	7	_	_	NNP
37681	2833	8	cp_/_c'p	cp_/_c'p	NNP
37681	2833	9	'	'	``
37681	2833	10	_	_	NN
37681	2833	11	.	.	.
37681	2834	1	But	but	CC
37681	2834	2	_	_	NNP
37681	2834	3	c_/_c	c_/_c	NNP
37681	2834	4	'	'	''
37681	2834	5	_	_	NNP
37681	2834	6	=	=	SYM
37681	2834	7	_	_	NNP
37681	2834	8	p_/_p	p_/_p	NNP
37681	2834	9	'	'	POS
37681	2834	10	_	_	NNP
37681	2834	11	,	,	,
37681	2834	12	by	by	IN
37681	2834	13	similar	similar	JJ
37681	2834	14	triangles	triangle	NNS
37681	2834	15	.	.	.
37681	2835	1	[	[	-LRB-
37681	2835	2	therefore	therefore	RB
37681	2835	3	]	]	-RRB-
37681	2835	4	[	[	-LRB-
37681	2835	5	triangle]_ABC_/[triangle]_A'B'C	triangle]_ABC_/[triangle]_A'B'C	NNP
37681	2835	6	'	'	''
37681	2835	7	_	_	NNP
37681	2835	8	=	=	SYM
37681	2835	9	_	_	NNP
37681	2835	10	c_^2/_c'_^2	c_^2/_c'_^2	NN
37681	2835	11	,	,	,
37681	2835	12	and	and	CC
37681	2835	13	so	so	RB
37681	2835	14	for	for	IN
37681	2835	15	other	other	JJ
37681	2835	16	sides	side	NNS
37681	2835	17	.	.	.
37681	2836	1	This	this	DT
37681	2836	2	proof	proof	NN
37681	2836	3	is	be	VBZ
37681	2836	4	unnecessarily	unnecessarily	RB
37681	2836	5	long	long	JJ
37681	2836	6	,	,	,
37681	2836	7	however	however	RB
37681	2836	8	,	,	,
37681	2836	9	because	because	IN
37681	2836	10	of	of	IN
37681	2836	11	the	the	DT
37681	2836	12	introduction	introduction	NN
37681	2836	13	of	of	IN
37681	2836	14	the	the	DT
37681	2836	15	altitudes	altitude	NNS
37681	2836	16	.	.	.
37681	2837	1	In	in	IN
37681	2837	2	this	this	DT
37681	2837	3	and	and	CC
37681	2837	4	several	several	JJ
37681	2837	5	other	other	JJ
37681	2837	6	propositions	proposition	NNS
37681	2837	7	in	in	IN
37681	2837	8	Book	Book	NNP
37681	2837	9	IV	IV	NNP
37681	2837	10	occurs	occur	VBZ
37681	2837	11	the	the	DT
37681	2837	12	expression	expression	NN
37681	2837	13	"	"	``
37681	2837	14	the	the	DT
37681	2837	15	square	square	NN
37681	2837	16	_	_	NNP
37681	2837	17	on	on	IN
37681	2837	18	_	_	NNP
37681	2837	19	a	a	DT
37681	2837	20	line	line	NN
37681	2837	21	.	.	.
37681	2837	22	"	"	''
37681	2838	1	We	-PRON-	PRP
37681	2838	2	have	have	VBP
37681	2838	3	,	,	,
37681	2838	4	in	in	IN
37681	2838	5	our	-PRON-	PRP$
37681	2838	6	departure	departure	NN
37681	2838	7	from	from	IN
37681	2838	8	Euclid	Euclid	NNP
37681	2838	9	,	,	,
37681	2838	10	treated	treat	VBD
37681	2838	11	a	a	DT
37681	2838	12	line	line	NN
37681	2838	13	either	either	CC
37681	2838	14	as	as	IN
37681	2838	15	a	a	DT
37681	2838	16	geometric	geometric	JJ
37681	2838	17	figure	figure	NN
37681	2838	18	or	or	CC
37681	2838	19	as	as	IN
37681	2838	20	a	a	DT
37681	2838	21	number	number	NN
37681	2838	22	(	(	-LRB-
37681	2838	23	the	the	DT
37681	2838	24	length	length	NN
37681	2838	25	of	of	IN
37681	2838	26	the	the	DT
37681	2838	27	line	line	NN
37681	2838	28	)	)	-RRB-
37681	2838	29	,	,	,
37681	2838	30	as	as	IN
37681	2838	31	was	be	VBD
37681	2838	32	the	the	DT
37681	2838	33	more	more	RBR
37681	2838	34	convenient	convenient	JJ
37681	2838	35	.	.	.
37681	2839	1	Of	of	RB
37681	2839	2	course	course	RB
37681	2839	3	if	if	IN
37681	2839	4	we	-PRON-	PRP
37681	2839	5	are	be	VBP
37681	2839	6	speaking	speak	VBG
37681	2839	7	of	of	IN
37681	2839	8	a	a	DT
37681	2839	9	line	line	NN
37681	2839	10	,	,	,
37681	2839	11	the	the	DT
37681	2839	12	preferable	preferable	JJ
37681	2839	13	expression	expression	NN
37681	2839	14	is	be	VBZ
37681	2839	15	"	"	``
37681	2839	16	square	square	JJ
37681	2839	17	_	_	NNP
37681	2839	18	on	on	IN
37681	2839	19	_	_	NNP
37681	2839	20	the	the	DT
37681	2839	21	line	line	NN
37681	2839	22	,	,	,
37681	2839	23	"	"	``
37681	2839	24	whereas	whereas	IN
37681	2839	25	if	if	IN
37681	2839	26	we	-PRON-	PRP
37681	2839	27	speak	speak	VBP
37681	2839	28	of	of	IN
37681	2839	29	a	a	DT
37681	2839	30	number	number	NN
37681	2839	31	,	,	,
37681	2839	32	we	-PRON-	PRP
37681	2839	33	say	say	VBP
37681	2839	34	"	"	``
37681	2839	35	square	square	JJ
37681	2839	36	_	_	NNP
37681	2839	37	of	of	IN
37681	2839	38	_	_	NNP
37681	2839	39	the	the	DT
37681	2839	40	number	number	NN
37681	2839	41	.	.	.
37681	2839	42	"	"	''
37681	2840	1	In	in	IN
37681	2840	2	the	the	DT
37681	2840	3	case	case	NN
37681	2840	4	of	of	IN
37681	2840	5	a	a	DT
37681	2840	6	rectangle	rectangle	NN
37681	2840	7	of	of	IN
37681	2840	8	two	two	CD
37681	2840	9	lines	line	NNS
37681	2840	10	we	-PRON-	PRP
37681	2840	11	have	have	VBP
37681	2840	12	come	come	VBN
37681	2840	13	to	to	TO
37681	2840	14	speak	speak	VB
37681	2840	15	of	of	IN
37681	2840	16	the	the	DT
37681	2840	17	"	"	``
37681	2840	18	product	product	NN
37681	2840	19	of	of	IN
37681	2840	20	the	the	DT
37681	2840	21	lines	line	NNS
37681	2840	22	,	,	,
37681	2840	23	"	"	''
37681	2840	24	meaning	mean	VBG
37681	2840	25	the	the	DT
37681	2840	26	product	product	NN
37681	2840	27	of	of	IN
37681	2840	28	their	-PRON-	PRP$
37681	2840	29	numerical	numerical	JJ
37681	2840	30	values	value	NNS
37681	2840	31	.	.	.
37681	2841	1	We	-PRON-	PRP
37681	2841	2	are	be	VBP
37681	2841	3	therefore	therefore	RB
37681	2841	4	not	not	RB
37681	2841	5	as	as	RB
37681	2841	6	accurate	accurate	JJ
37681	2841	7	in	in	IN
37681	2841	8	our	-PRON-	PRP$
37681	2841	9	phraseology	phraseology	NN
37681	2841	10	as	as	IN
37681	2841	11	Euclid	Euclid	NNP
37681	2841	12	,	,	,
37681	2841	13	and	and	CC
37681	2841	14	we	-PRON-	PRP
37681	2841	15	do	do	VBP
37681	2841	16	not	not	RB
37681	2841	17	pretend	pretend	VB
37681	2841	18	to	to	TO
37681	2841	19	be	be	VB
37681	2841	20	,	,	,
37681	2841	21	for	for	IN
37681	2841	22	reasons	reason	NNS
37681	2841	23	already	already	RB
37681	2841	24	given	give	VBN
37681	2841	25	.	.	.
37681	2842	1	But	but	CC
37681	2842	2	when	when	WRB
37681	2842	3	it	-PRON-	PRP
37681	2842	4	comes	come	VBZ
37681	2842	5	to	to	IN
37681	2842	6	"	"	``
37681	2842	7	square	square	JJ
37681	2842	8	_	_	NNP
37681	2842	9	on	on	IN
37681	2842	10	_	_	NNP
37681	2842	11	a	a	DT
37681	2842	12	line	line	NN
37681	2842	13	"	"	''
37681	2842	14	or	or	CC
37681	2842	15	"	"	``
37681	2842	16	square	square	JJ
37681	2842	17	_	_	NNP
37681	2842	18	of	of	IN
37681	2842	19	_	_	NNP
37681	2842	20	a	a	DT
37681	2842	21	line	line	NN
37681	2842	22	,	,	,
37681	2842	23	"	"	''
37681	2842	24	the	the	DT
37681	2842	25	former	former	JJ
37681	2842	26	is	be	VBZ
37681	2842	27	the	the	DT
37681	2842	28	one	one	NN
37681	2842	29	demanding	demand	VBG
37681	2842	30	no	no	DT
37681	2842	31	explanation	explanation	NN
37681	2842	32	or	or	CC
37681	2842	33	apology	apology	NN
37681	2842	34	,	,	,
37681	2842	35	and	and	CC
37681	2842	36	it	-PRON-	PRP
37681	2842	37	is	be	VBZ
37681	2842	38	even	even	RB
37681	2842	39	better	well	RBR
37681	2842	40	understood	understand	VBN
37681	2842	41	than	than	IN
37681	2842	42	the	the	DT
37681	2842	43	latter	latter	JJ
37681	2842	44	.	.	.
37681	2843	1	THEOREM	THEOREM	NNP
37681	2843	2	.	.	.
37681	2844	1	_	_	NNP
37681	2844	2	The	the	DT
37681	2844	3	areas	area	NNS
37681	2844	4	of	of	IN
37681	2844	5	two	two	CD
37681	2844	6	similar	similar	JJ
37681	2844	7	polygons	polygon	NNS
37681	2844	8	are	be	VBP
37681	2844	9	to	to	IN
37681	2844	10	each	each	DT
37681	2844	11	other	other	JJ
37681	2844	12	as	as	IN
37681	2844	13	the	the	DT
37681	2844	14	squares	square	NNS
37681	2844	15	on	on	IN
37681	2844	16	any	any	DT
37681	2844	17	two	two	CD
37681	2844	18	corresponding	corresponding	JJ
37681	2844	19	sides	side	NNS
37681	2844	20	.	.	.
37681	2844	21	_	_	NNP
37681	2844	22	This	this	DT
37681	2844	23	is	be	VBZ
37681	2844	24	a	a	DT
37681	2844	25	proposition	proposition	NN
37681	2844	26	of	of	IN
37681	2844	27	great	great	JJ
37681	2844	28	importance	importance	NN
37681	2844	29	,	,	,
37681	2844	30	and	and	CC
37681	2844	31	in	in	IN
37681	2844	32	due	due	JJ
37681	2844	33	time	time	NN
37681	2844	34	the	the	DT
37681	2844	35	pupil	pupil	NN
37681	2844	36	sees	see	VBZ
37681	2844	37	that	that	IN
37681	2844	38	it	-PRON-	PRP
37681	2844	39	applies	apply	VBZ
37681	2844	40	to	to	IN
37681	2844	41	circles	circle	NNS
37681	2844	42	,	,	,
37681	2844	43	with	with	IN
37681	2844	44	the	the	DT
37681	2844	45	necessary	necessary	JJ
37681	2844	46	change	change	NN
37681	2844	47	of	of	IN
37681	2844	48	the	the	DT
37681	2844	49	word	word	NN
37681	2844	50	"	"	``
37681	2844	51	sides	side	NNS
37681	2844	52	"	"	''
37681	2844	53	to	to	IN
37681	2844	54	"	"	``
37681	2844	55	lines	line	NNS
37681	2844	56	.	.	.
37681	2844	57	"	"	''
37681	2845	1	It	-PRON-	PRP
37681	2845	2	is	be	VBZ
37681	2845	3	well	well	JJ
37681	2845	4	to	to	TO
37681	2845	5	ask	ask	VB
37681	2845	6	a	a	DT
37681	2845	7	few	few	JJ
37681	2845	8	questions	question	NNS
37681	2845	9	like	like	IN
37681	2845	10	the	the	DT
37681	2845	11	following	follow	VBG
37681	2845	12	:	:	:
37681	2845	13	If	if	IN
37681	2845	14	one	one	CD
37681	2845	15	square	square	NN
37681	2845	16	is	be	VBZ
37681	2845	17	twice	twice	RB
37681	2845	18	as	as	RB
37681	2845	19	high	high	JJ
37681	2845	20	as	as	IN
37681	2845	21	another	another	DT
37681	2845	22	,	,	,
37681	2845	23	how	how	WRB
37681	2845	24	do	do	VBP
37681	2845	25	the	the	DT
37681	2845	26	areas	area	NNS
37681	2845	27	compare	compare	VB
37681	2845	28	?	?	.
37681	2846	1	If	if	IN
37681	2846	2	the	the	DT
37681	2846	3	side	side	NN
37681	2846	4	of	of	IN
37681	2846	5	one	one	CD
37681	2846	6	equilateral	equilateral	JJ
37681	2846	7	triangle	triangle	NN
37681	2846	8	is	be	VBZ
37681	2846	9	three	three	CD
37681	2846	10	times	time	NNS
37681	2846	11	as	as	RB
37681	2846	12	long	long	RB
37681	2846	13	as	as	IN
37681	2846	14	that	that	DT
37681	2846	15	of	of	IN
37681	2846	16	another	another	DT
37681	2846	17	,	,	,
37681	2846	18	how	how	WRB
37681	2846	19	do	do	VBP
37681	2846	20	the	the	DT
37681	2846	21	perimeters	perimeter	NNS
37681	2846	22	compare	compare	VB
37681	2846	23	?	?	.
37681	2847	1	how	how	WRB
37681	2847	2	do	do	VBP
37681	2847	3	the	the	DT
37681	2847	4	areas	area	NNS
37681	2847	5	compare	compare	VB
37681	2847	6	?	?	.
37681	2848	1	If	if	IN
37681	2848	2	the	the	DT
37681	2848	3	area	area	NN
37681	2848	4	of	of	IN
37681	2848	5	one	one	CD
37681	2848	6	square	square	NN
37681	2848	7	is	be	VBZ
37681	2848	8	twenty	twenty	CD
37681	2848	9	-	-	HYPH
37681	2848	10	five	five	CD
37681	2848	11	times	time	NNS
37681	2848	12	the	the	DT
37681	2848	13	area	area	NN
37681	2848	14	of	of	IN
37681	2848	15	another	another	DT
37681	2848	16	square	square	NN
37681	2848	17	,	,	,
37681	2848	18	the	the	DT
37681	2848	19	side	side	NN
37681	2848	20	of	of	IN
37681	2848	21	the	the	DT
37681	2848	22	first	first	JJ
37681	2848	23	is	be	VBZ
37681	2848	24	how	how	WRB
37681	2848	25	many	many	JJ
37681	2848	26	times	time	NNS
37681	2848	27	as	as	RB
37681	2848	28	long	long	RB
37681	2848	29	as	as	IN
37681	2848	30	the	the	DT
37681	2848	31	side	side	NN
37681	2848	32	of	of	IN
37681	2848	33	the	the	DT
37681	2848	34	second	second	JJ
37681	2848	35	?	?	.
37681	2849	1	If	if	IN
37681	2849	2	a	a	DT
37681	2849	3	photograph	photograph	NN
37681	2849	4	is	be	VBZ
37681	2849	5	enlarged	enlarge	VBN
37681	2849	6	so	so	IN
37681	2849	7	that	that	IN
37681	2849	8	a	a	DT
37681	2849	9	tree	tree	NN
37681	2849	10	is	be	VBZ
37681	2849	11	four	four	CD
37681	2849	12	times	time	NNS
37681	2849	13	as	as	RB
37681	2849	14	high	high	RB
37681	2849	15	as	as	IN
37681	2849	16	it	-PRON-	PRP
37681	2849	17	was	be	VBD
37681	2849	18	before	before	RB
37681	2849	19	,	,	,
37681	2849	20	what	what	WP
37681	2849	21	is	be	VBZ
37681	2849	22	the	the	DT
37681	2849	23	ratio	ratio	NN
37681	2849	24	of	of	IN
37681	2849	25	corresponding	correspond	VBG
37681	2849	26	dimensions	dimension	NNS
37681	2849	27	?	?	.
37681	2850	1	The	the	DT
37681	2850	2	area	area	NN
37681	2850	3	of	of	IN
37681	2850	4	the	the	DT
37681	2850	5	enlarged	enlarged	JJ
37681	2850	6	photograph	photograph	NN
37681	2850	7	is	be	VBZ
37681	2850	8	how	how	WRB
37681	2850	9	many	many	JJ
37681	2850	10	times	time	NNS
37681	2850	11	as	as	RB
37681	2850	12	great	great	JJ
37681	2850	13	as	as	IN
37681	2850	14	the	the	DT
37681	2850	15	area	area	NN
37681	2850	16	of	of	IN
37681	2850	17	the	the	DT
37681	2850	18	original	original	NN
37681	2850	19	?	?	.
37681	2851	1	THEOREM	THEOREM	NNP
37681	2851	2	.	.	.
37681	2852	1	_	_	NNP
37681	2852	2	The	the	DT
37681	2852	3	square	square	NN
37681	2852	4	on	on	IN
37681	2852	5	the	the	DT
37681	2852	6	hypotenuse	hypotenuse	NN
37681	2852	7	of	of	IN
37681	2852	8	a	a	DT
37681	2852	9	right	right	JJ
37681	2852	10	triangle	triangle	NN
37681	2852	11	is	be	VBZ
37681	2852	12	equivalent	equivalent	JJ
37681	2852	13	to	to	IN
37681	2852	14	the	the	DT
37681	2852	15	sum	sum	NN
37681	2852	16	of	of	IN
37681	2852	17	the	the	DT
37681	2852	18	squares	square	NNS
37681	2852	19	on	on	IN
37681	2852	20	the	the	DT
37681	2852	21	other	other	JJ
37681	2852	22	two	two	CD
37681	2852	23	sides	side	NNS
37681	2852	24	.	.	.
37681	2852	25	_	_	XX
37681	2852	26	Of	of	IN
37681	2852	27	all	all	PDT
37681	2852	28	the	the	DT
37681	2852	29	propositions	proposition	NNS
37681	2852	30	of	of	IN
37681	2852	31	geometry	geometry	NN
37681	2852	32	this	this	DT
37681	2852	33	is	be	VBZ
37681	2852	34	the	the	DT
37681	2852	35	most	most	RBS
37681	2852	36	famous	famous	JJ
37681	2852	37	and	and	CC
37681	2852	38	perhaps	perhaps	RB
37681	2852	39	the	the	DT
37681	2852	40	most	most	RBS
37681	2852	41	valuable	valuable	JJ
37681	2852	42	.	.	.
37681	2853	1	Trigonometry	Trigonometry	NNP
37681	2853	2	is	be	VBZ
37681	2853	3	based	base	VBN
37681	2853	4	chiefly	chiefly	RB
37681	2853	5	upon	upon	IN
37681	2853	6	two	two	CD
37681	2853	7	facts	fact	NNS
37681	2853	8	of	of	IN
37681	2853	9	plane	plane	NN
37681	2853	10	geometry	geometry	NN
37681	2853	11	:	:	:
37681	2853	12	(	(	-LRB-
37681	2853	13	1	1	LS
37681	2853	14	)	)	-RRB-
37681	2853	15	in	in	IN
37681	2853	16	similar	similar	JJ
37681	2853	17	triangles	triangle	NNS
37681	2853	18	the	the	DT
37681	2853	19	corresponding	corresponding	JJ
37681	2853	20	sides	side	NNS
37681	2853	21	are	be	VBP
37681	2853	22	proportional	proportional	JJ
37681	2853	23	,	,	,
37681	2853	24	and	and	CC
37681	2853	25	(	(	-LRB-
37681	2853	26	2	2	LS
37681	2853	27	)	)	-RRB-
37681	2853	28	this	this	DT
37681	2853	29	proposition	proposition	NN
37681	2853	30	.	.	.
37681	2854	1	In	in	IN
37681	2854	2	mensuration	mensuration	NN
37681	2854	3	,	,	,
37681	2854	4	in	in	IN
37681	2854	5	general	general	JJ
37681	2854	6	,	,	,
37681	2854	7	this	this	DT
37681	2854	8	proposition	proposition	NN
37681	2854	9	enters	enter	VBZ
37681	2854	10	more	more	RBR
37681	2854	11	often	often	RB
37681	2854	12	than	than	IN
37681	2854	13	any	any	DT
37681	2854	14	others	other	NNS
37681	2854	15	,	,	,
37681	2854	16	except	except	IN
37681	2854	17	those	those	DT
37681	2854	18	on	on	IN
37681	2854	19	the	the	DT
37681	2854	20	measuring	measuring	NN
37681	2854	21	of	of	IN
37681	2854	22	the	the	DT
37681	2854	23	rectangle	rectangle	NN
37681	2854	24	and	and	CC
37681	2854	25	triangle	triangle	NNP
37681	2854	26	.	.	.
37681	2855	1	It	-PRON-	PRP
37681	2855	2	is	be	VBZ
37681	2855	3	proposed	propose	VBN
37681	2855	4	,	,	,
37681	2855	5	therefore	therefore	RB
37681	2855	6	,	,	,
37681	2855	7	to	to	TO
37681	2855	8	devote	devote	VB
37681	2855	9	considerable	considerable	JJ
37681	2855	10	space	space	NN
37681	2855	11	to	to	IN
37681	2855	12	speaking	speak	VBG
37681	2855	13	of	of	IN
37681	2855	14	the	the	DT
37681	2855	15	history	history	NN
37681	2855	16	of	of	IN
37681	2855	17	the	the	DT
37681	2855	18	theorem	theorem	NN
37681	2855	19	,	,	,
37681	2855	20	and	and	CC
37681	2855	21	to	to	IN
37681	2855	22	certain	certain	JJ
37681	2855	23	proofs	proof	NNS
37681	2855	24	that	that	WDT
37681	2855	25	may	may	MD
37681	2855	26	profitably	profitably	RB
37681	2855	27	be	be	VB
37681	2855	28	suggested	suggest	VBN
37681	2855	29	from	from	IN
37681	2855	30	time	time	NN
37681	2855	31	to	to	IN
37681	2855	32	time	time	NN
37681	2855	33	to	to	IN
37681	2855	34	different	different	JJ
37681	2855	35	classes	class	NNS
37681	2855	36	for	for	IN
37681	2855	37	the	the	DT
37681	2855	38	purpose	purpose	NN
37681	2855	39	of	of	IN
37681	2855	40	adding	add	VBG
37681	2855	41	interest	interest	NN
37681	2855	42	to	to	IN
37681	2855	43	the	the	DT
37681	2855	44	work	work	NN
37681	2855	45	.	.	.
37681	2856	1	Proclus	Proclus	NNP
37681	2856	2	,	,	,
37681	2856	3	the	the	DT
37681	2856	4	old	old	JJ
37681	2856	5	Greek	greek	JJ
37681	2856	6	commentator	commentator	NN
37681	2856	7	on	on	IN
37681	2856	8	Euclid	Euclid	NNP
37681	2856	9	,	,	,
37681	2856	10	has	have	VBZ
37681	2856	11	this	this	DT
37681	2856	12	to	to	TO
37681	2856	13	say	say	VB
37681	2856	14	of	of	IN
37681	2856	15	the	the	DT
37681	2856	16	history	history	NN
37681	2856	17	:	:	:
37681	2856	18	"	"	``
37681	2856	19	If	if	IN
37681	2856	20	we	-PRON-	PRP
37681	2856	21	listen	listen	VBP
37681	2856	22	to	to	IN
37681	2856	23	those	those	DT
37681	2856	24	who	who	WP
37681	2856	25	wish	wish	VBP
37681	2856	26	to	to	TO
37681	2856	27	recount	recount	VB
37681	2856	28	ancient	ancient	JJ
37681	2856	29	history	history	NN
37681	2856	30	,	,	,
37681	2856	31	we	-PRON-	PRP
37681	2856	32	may	may	MD
37681	2856	33	find	find	VB
37681	2856	34	some	some	DT
37681	2856	35	of	of	IN
37681	2856	36	them	-PRON-	PRP
37681	2856	37	referring	refer	VBG
37681	2856	38	this	this	DT
37681	2856	39	theorem	theorem	NN
37681	2856	40	to	to	IN
37681	2856	41	Pythagoras	Pythagoras	NNP
37681	2856	42	and	and	CC
37681	2856	43	saying	say	VBG
37681	2856	44	that	that	IN
37681	2856	45	he	-PRON-	PRP
37681	2856	46	sacrificed	sacrifice	VBD
37681	2856	47	an	an	DT
37681	2856	48	ox	ox	NN
37681	2856	49	in	in	IN
37681	2856	50	honor	honor	NN
37681	2856	51	of	of	IN
37681	2856	52	his	-PRON-	PRP$
37681	2856	53	discovery	discovery	NN
37681	2856	54	.	.	.
37681	2857	1	But	but	CC
37681	2857	2	for	for	IN
37681	2857	3	my	-PRON-	PRP$
37681	2857	4	part	part	NN
37681	2857	5	,	,	,
37681	2857	6	while	while	IN
37681	2857	7	I	-PRON-	PRP
37681	2857	8	admire	admire	VBP
37681	2857	9	those	those	DT
37681	2857	10	who	who	WP
37681	2857	11	first	first	RB
37681	2857	12	observed	observe	VBD
37681	2857	13	the	the	DT
37681	2857	14	truth	truth	NN
37681	2857	15	of	of	IN
37681	2857	16	this	this	DT
37681	2857	17	theorem	theorem	NN
37681	2857	18	,	,	,
37681	2857	19	I	-PRON-	PRP
37681	2857	20	marvel	marvel	VBP
37681	2857	21	more	more	RBR
37681	2857	22	at	at	IN
37681	2857	23	the	the	DT
37681	2857	24	writer	writer	NN
37681	2857	25	of	of	IN
37681	2857	26	the	the	DT
37681	2857	27	'	'	``
37681	2857	28	Elements	element	NNS
37681	2857	29	'	'	''
37681	2857	30	(	(	-LRB-
37681	2857	31	Euclid	euclid	NN
37681	2857	32	)	)	-RRB-
37681	2857	33	,	,	,
37681	2857	34	not	not	RB
37681	2857	35	only	only	RB
37681	2857	36	because	because	IN
37681	2857	37	he	-PRON-	PRP
37681	2857	38	made	make	VBD
37681	2857	39	it	-PRON-	PRP
37681	2857	40	fast	fast	JJ
37681	2857	41	by	by	IN
37681	2857	42	a	a	DT
37681	2857	43	most	most	RBS
37681	2857	44	lucid	lucid	JJ
37681	2857	45	demonstration	demonstration	NN
37681	2857	46	,	,	,
37681	2857	47	but	but	CC
37681	2857	48	because	because	IN
37681	2857	49	he	-PRON-	PRP
37681	2857	50	compelled	compel	VBD
37681	2857	51	assent	assent	NN
37681	2857	52	to	to	IN
37681	2857	53	the	the	DT
37681	2857	54	still	still	RB
37681	2857	55	more	more	RBR
37681	2857	56	general	general	JJ
37681	2857	57	theorem	theorem	NN
37681	2857	58	by	by	IN
37681	2857	59	the	the	DT
37681	2857	60	irrefragable	irrefragable	JJ
37681	2857	61	arguments	argument	NNS
37681	2857	62	of	of	IN
37681	2857	63	science	science	NN
37681	2857	64	in	in	IN
37681	2857	65	Book	Book	NNP
37681	2857	66	VI	VI	NNP
37681	2857	67	.	.	.
37681	2858	1	For	for	IN
37681	2858	2	in	in	IN
37681	2858	3	that	that	DT
37681	2858	4	book	book	NN
37681	2858	5	he	-PRON-	PRP
37681	2858	6	proves	prove	VBZ
37681	2858	7	,	,	,
37681	2858	8	generally	generally	RB
37681	2858	9	,	,	,
37681	2858	10	that	that	IN
37681	2858	11	in	in	IN
37681	2858	12	right	right	JJ
37681	2858	13	triangles	triangle	NNS
37681	2858	14	the	the	DT
37681	2858	15	figure	figure	NN
37681	2858	16	on	on	IN
37681	2858	17	the	the	DT
37681	2858	18	side	side	NN
37681	2858	19	subtending	subtend	VBG
37681	2858	20	the	the	DT
37681	2858	21	right	right	JJ
37681	2858	22	angle	angle	NN
37681	2858	23	is	be	VBZ
37681	2858	24	equal	equal	JJ
37681	2858	25	to	to	IN
37681	2858	26	the	the	DT
37681	2858	27	similar	similar	JJ
37681	2858	28	and	and	CC
37681	2858	29	similarly	similarly	RB
37681	2858	30	placed	place	VBN
37681	2858	31	figures	figure	NNS
37681	2858	32	described	describe	VBN
37681	2858	33	on	on	IN
37681	2858	34	the	the	DT
37681	2858	35	sides	side	NNS
37681	2858	36	about	about	IN
37681	2858	37	the	the	DT
37681	2858	38	right	right	JJ
37681	2858	39	angle	angle	NN
37681	2858	40	.	.	.
37681	2858	41	"	"	''
37681	2859	1	Now	now	RB
37681	2859	2	it	-PRON-	PRP
37681	2859	3	appears	appear	VBZ
37681	2859	4	from	from	IN
37681	2859	5	this	this	DT
37681	2859	6	that	that	DT
37681	2859	7	Proclus	Proclus	NNP
37681	2859	8	,	,	,
37681	2859	9	in	in	IN
37681	2859	10	the	the	DT
37681	2859	11	fifth	fifth	JJ
37681	2859	12	century	century	NN
37681	2859	13	A.D.	A.D.	NNP
37681	2859	14	,	,	,
37681	2859	15	thought	think	VBD
37681	2859	16	that	that	IN
37681	2859	17	Pythagoras	Pythagoras	NNP
37681	2859	18	discovered	discover	VBD
37681	2859	19	the	the	DT
37681	2859	20	proposition	proposition	NN
37681	2859	21	in	in	IN
37681	2859	22	the	the	DT
37681	2859	23	sixth	sixth	JJ
37681	2859	24	century	century	NN
37681	2859	25	B.C.	B.C.	NNP
37681	2859	26	,	,	,
37681	2859	27	that	that	IN
37681	2859	28	the	the	DT
37681	2859	29	usual	usual	JJ
37681	2859	30	proof	proof	NN
37681	2859	31	,	,	,
37681	2859	32	as	as	IN
37681	2859	33	given	give	VBN
37681	2859	34	in	in	IN
37681	2859	35	most	most	JJS
37681	2859	36	of	of	IN
37681	2859	37	our	-PRON-	PRP$
37681	2859	38	American	american	JJ
37681	2859	39	textbooks	textbook	NNS
37681	2859	40	,	,	,
37681	2859	41	was	be	VBD
37681	2859	42	due	due	JJ
37681	2859	43	to	to	IN
37681	2859	44	Euclid	Euclid	NNP
37681	2859	45	,	,	,
37681	2859	46	and	and	CC
37681	2859	47	that	that	IN
37681	2859	48	the	the	DT
37681	2859	49	generalized	generalize	VBN
37681	2859	50	form	form	NN
37681	2859	51	was	be	VBD
37681	2859	52	also	also	RB
37681	2859	53	due	due	JJ
37681	2859	54	to	to	IN
37681	2859	55	the	the	DT
37681	2859	56	latter	latter	JJ
37681	2859	57	.	.	.
37681	2860	1	For	for	IN
37681	2860	2	it	-PRON-	PRP
37681	2860	3	should	should	MD
37681	2860	4	be	be	VB
37681	2860	5	made	make	VBN
37681	2860	6	known	known	JJ
37681	2860	7	to	to	IN
37681	2860	8	students	student	NNS
37681	2860	9	that	that	IN
37681	2860	10	the	the	DT
37681	2860	11	proposition	proposition	NN
37681	2860	12	is	be	VBZ
37681	2860	13	true	true	JJ
37681	2860	14	not	not	RB
37681	2860	15	only	only	RB
37681	2860	16	for	for	IN
37681	2860	17	squares	square	NNS
37681	2860	18	,	,	,
37681	2860	19	but	but	CC
37681	2860	20	for	for	IN
37681	2860	21	any	any	DT
37681	2860	22	similar	similar	JJ
37681	2860	23	figures	figure	NNS
37681	2860	24	,	,	,
37681	2860	25	such	such	JJ
37681	2860	26	as	as	IN
37681	2860	27	equilateral	equilateral	JJ
37681	2860	28	triangles	triangle	NNS
37681	2860	29	,	,	,
37681	2860	30	parallelograms	parallelogram	NNS
37681	2860	31	,	,	,
37681	2860	32	semicircles	semicircles	NNP
37681	2860	33	,	,	,
37681	2860	34	and	and	CC
37681	2860	35	irregular	irregular	JJ
37681	2860	36	figures	figure	NNS
37681	2860	37	,	,	,
37681	2860	38	provided	provide	VBN
37681	2860	39	they	-PRON-	PRP
37681	2860	40	are	be	VBP
37681	2860	41	similarly	similarly	RB
37681	2860	42	placed	place	VBN
37681	2860	43	on	on	IN
37681	2860	44	the	the	DT
37681	2860	45	three	three	CD
37681	2860	46	sides	side	NNS
37681	2860	47	of	of	IN
37681	2860	48	the	the	DT
37681	2860	49	right	right	JJ
37681	2860	50	triangle	triangle	NN
37681	2860	51	.	.	.
37681	2861	1	Besides	besides	IN
37681	2861	2	Proclus	Proclus	NNP
37681	2861	3	,	,	,
37681	2861	4	Plutarch	Plutarch	NNP
37681	2861	5	testifies	testify	VBZ
37681	2861	6	to	to	IN
37681	2861	7	the	the	DT
37681	2861	8	fact	fact	NN
37681	2861	9	that	that	IN
37681	2861	10	Pythagoras	Pythagoras	NNP
37681	2861	11	was	be	VBD
37681	2861	12	the	the	DT
37681	2861	13	discoverer	discoverer	NN
37681	2861	14	,	,	,
37681	2861	15	saying	say	VBG
37681	2861	16	that	that	IN
37681	2861	17	"	"	``
37681	2861	18	Pythagoras	Pythagoras	NNP
37681	2861	19	sacrificed	sacrifice	VBD
37681	2861	20	an	an	DT
37681	2861	21	ox	ox	NN
37681	2861	22	on	on	IN
37681	2861	23	the	the	DT
37681	2861	24	strength	strength	NN
37681	2861	25	of	of	IN
37681	2861	26	his	-PRON-	PRP$
37681	2861	27	proposition	proposition	NN
37681	2861	28	as	as	IN
37681	2861	29	Apollodotus	Apollodotus	NNP
37681	2861	30	says	say	VBZ
37681	2861	31	,	,	,
37681	2861	32	"	"	``
37681	2861	33	but	but	CC
37681	2861	34	saying	say	VBG
37681	2861	35	that	that	IN
37681	2861	36	there	there	EX
37681	2861	37	were	be	VBD
37681	2861	38	two	two	CD
37681	2861	39	possible	possible	JJ
37681	2861	40	propositions	proposition	NNS
37681	2861	41	to	to	TO
37681	2861	42	which	which	WDT
37681	2861	43	this	this	DT
37681	2861	44	refers	refer	VBZ
37681	2861	45	.	.	.
37681	2862	1	This	this	DT
37681	2862	2	Apollodotus	Apollodotus	NNP
37681	2862	3	was	be	VBD
37681	2862	4	probably	probably	RB
37681	2862	5	Apollodorus	Apollodorus	NNP
37681	2862	6	,	,	,
37681	2862	7	surnamed	surname	VBD
37681	2862	8	Logisticus	Logisticus	NNP
37681	2862	9	(	(	-LRB-
37681	2862	10	the	the	DT
37681	2862	11	Calculator	Calculator	NNP
37681	2862	12	)	)	-RRB-
37681	2862	13	,	,	,
37681	2862	14	whose	whose	WP$
37681	2862	15	date	date	NN
37681	2862	16	is	be	VBZ
37681	2862	17	quite	quite	RB
37681	2862	18	uncertain	uncertain	JJ
37681	2862	19	,	,	,
37681	2862	20	and	and	CC
37681	2862	21	who	who	WP
37681	2862	22	speaks	speak	VBZ
37681	2862	23	in	in	IN
37681	2862	24	some	some	DT
37681	2862	25	verses	verse	NNS
37681	2862	26	of	of	IN
37681	2862	27	a	a	DT
37681	2862	28	"	"	``
37681	2862	29	famous	famous	JJ
37681	2862	30	proposition	proposition	NN
37681	2862	31	"	"	''
37681	2862	32	discovered	discover	VBN
37681	2862	33	by	by	IN
37681	2862	34	Pythagoras	Pythagoras	NNP
37681	2862	35	,	,	,
37681	2862	36	and	and	CC
37681	2862	37	all	all	DT
37681	2862	38	tradition	tradition	NN
37681	2862	39	makes	make	VBZ
37681	2862	40	this	this	DT
37681	2862	41	the	the	DT
37681	2862	42	one	one	CD
37681	2862	43	.	.	.
37681	2863	1	Cicero	Cicero	NNP
37681	2863	2	,	,	,
37681	2863	3	who	who	WP
37681	2863	4	comments	comment	VBZ
37681	2863	5	upon	upon	IN
37681	2863	6	these	these	DT
37681	2863	7	verses	verse	NNS
37681	2863	8	,	,	,
37681	2863	9	does	do	VBZ
37681	2863	10	not	not	RB
37681	2863	11	question	question	VB
37681	2863	12	the	the	DT
37681	2863	13	discovery	discovery	NN
37681	2863	14	,	,	,
37681	2863	15	but	but	CC
37681	2863	16	doubts	doubt	VBZ
37681	2863	17	the	the	DT
37681	2863	18	story	story	NN
37681	2863	19	of	of	IN
37681	2863	20	the	the	DT
37681	2863	21	sacrifice	sacrifice	NN
37681	2863	22	of	of	IN
37681	2863	23	the	the	DT
37681	2863	24	ox	ox	NN
37681	2863	25	.	.	.
37681	2864	1	Of	of	IN
37681	2864	2	other	other	JJ
37681	2864	3	early	early	JJ
37681	2864	4	writers	writer	NNS
37681	2864	5	,	,	,
37681	2864	6	Diogenes	Diogenes	NNP
37681	2864	7	Laertius	Laertius	NNP
37681	2864	8	,	,	,
37681	2864	9	whose	whose	WP$
37681	2864	10	date	date	NN
37681	2864	11	is	be	VBZ
37681	2864	12	entirely	entirely	RB
37681	2864	13	uncertain	uncertain	JJ
37681	2864	14	(	(	-LRB-
37681	2864	15	perhaps	perhaps	RB
37681	2864	16	the	the	DT
37681	2864	17	second	second	JJ
37681	2864	18	century	century	NN
37681	2864	19	A.D.	A.D.	NNP
37681	2864	20	)	)	-RRB-
37681	2864	21	,	,	,
37681	2864	22	and	and	CC
37681	2864	23	Athenæus	Athenæus	NNP
37681	2864	24	(	(	-LRB-
37681	2864	25	third	third	JJ
37681	2864	26	century	century	NN
37681	2864	27	A.D.	A.D.	NNP
37681	2864	28	)	)	-RRB-
37681	2864	29	may	may	MD
37681	2864	30	be	be	VB
37681	2864	31	mentioned	mention	VBN
37681	2864	32	as	as	IN
37681	2864	33	attributing	attribute	VBG
37681	2864	34	the	the	DT
37681	2864	35	theorem	theorem	NN
37681	2864	36	to	to	IN
37681	2864	37	Pythagoras	Pythagoras	NNP
37681	2864	38	,	,	,
37681	2864	39	while	while	IN
37681	2864	40	Heron	Heron	NNP
37681	2864	41	(	(	-LRB-
37681	2864	42	first	first	JJ
37681	2864	43	century	century	NN
37681	2864	44	A.D.	A.D.	NNP
37681	2864	45	)	)	-RRB-
37681	2864	46	says	say	VBZ
37681	2864	47	that	that	IN
37681	2864	48	he	-PRON-	PRP
37681	2864	49	gave	give	VBD
37681	2864	50	a	a	DT
37681	2864	51	rule	rule	NN
37681	2864	52	for	for	IN
37681	2864	53	forming	form	VBG
37681	2864	54	right	right	JJ
37681	2864	55	triangles	triangle	NNS
37681	2864	56	with	with	IN
37681	2864	57	rational	rational	JJ
37681	2864	58	integers	integer	NNS
37681	2864	59	for	for	IN
37681	2864	60	the	the	DT
37681	2864	61	sides	side	NNS
37681	2864	62	,	,	,
37681	2864	63	like	like	IN
37681	2864	64	3	3	CD
37681	2864	65	,	,	,
37681	2864	66	4	4	CD
37681	2864	67	,	,	,
37681	2864	68	5	5	CD
37681	2864	69	,	,	,
37681	2864	70	where	where	WRB
37681	2864	71	3	3	CD
37681	2864	72	^	^	NN
37681	2864	73	2	2	CD
37681	2864	74	+	+	SYM
37681	2864	75	4	4	CD
37681	2864	76	^	^	SYM
37681	2864	77	2	2	CD
37681	2864	78	=	=	SYM
37681	2864	79	5	5	CD
37681	2864	80	^	^	SYM
37681	2864	81	2	2	CD
37681	2864	82	.	.	.
37681	2865	1	It	-PRON-	PRP
37681	2865	2	should	should	MD
37681	2865	3	be	be	VB
37681	2865	4	said	say	VBN
37681	2865	5	,	,	,
37681	2865	6	however	however	RB
37681	2865	7	,	,	,
37681	2865	8	that	that	IN
37681	2865	9	the	the	DT
37681	2865	10	Pythagorean	pythagorean	JJ
37681	2865	11	origin	origin	NN
37681	2865	12	has	have	VBZ
37681	2865	13	been	be	VBN
37681	2865	14	doubted	doubt	VBN
37681	2865	15	,	,	,
37681	2865	16	notably	notably	RB
37681	2865	17	in	in	IN
37681	2865	18	an	an	DT
37681	2865	19	article	article	NN
37681	2865	20	by	by	IN
37681	2865	21	H.	H.	NNP
37681	2865	22	Vogt	Vogt	NNP
37681	2865	23	,	,	,
37681	2865	24	published	publish	VBN
37681	2865	25	in	in	IN
37681	2865	26	the	the	DT
37681	2865	27	_	_	NNP
37681	2865	28	Bibliotheca	Bibliotheca	NNP
37681	2865	29	Mathematica	Mathematica	NNP
37681	2865	30	_	_	NNP
37681	2865	31	in	in	IN
37681	2865	32	1908	1908	CD
37681	2865	33	(	(	-LRB-
37681	2865	34	Vol	Vol	NNP
37681	2865	35	.	.	.
37681	2866	1	IX	ix	NN
37681	2866	2	(	(	-LRB-
37681	2866	3	3	3	CD
37681	2866	4	)	)	-RRB-
37681	2866	5	,	,	,
37681	2866	6	p.	p.	NN
37681	2866	7	15	15	CD
37681	2866	8	)	)	-RRB-
37681	2866	9	,	,	,
37681	2866	10	entitled	entitle	VBN
37681	2866	11	"	"	``
37681	2866	12	Die	Die	NNP
37681	2866	13	Geometrie	Geometrie	NNP
37681	2866	14	des	des	FW
37681	2866	15	Pythagoras	Pythagoras	NNP
37681	2866	16	,	,	,
37681	2866	17	"	"	''
37681	2866	18	and	and	CC
37681	2866	19	by	by	IN
37681	2866	20	G.	G.	NNP
37681	2866	21	Junge	Junge	NNP
37681	2866	22	,	,	,
37681	2866	23	in	in	IN
37681	2866	24	his	-PRON-	PRP$
37681	2866	25	work	work	NN
37681	2866	26	entitled	entitle	VBN
37681	2866	27	"	"	``
37681	2866	28	Wann	Wann	NNP
37681	2866	29	haben	haben	NNP
37681	2866	30	die	die	VBP
37681	2866	31	Griechen	Griechen	NNP
37681	2866	32	das	das	NNP
37681	2866	33	Irrationale	Irrationale	NNP
37681	2866	34	entdeckt	entdeckt	VBZ
37681	2866	35	?	?	.
37681	2866	36	"	"	''
37681	2867	1	(	(	-LRB-
37681	2867	2	Halle	Halle	NNP
37681	2867	3	,	,	,
37681	2867	4	1907	1907	CD
37681	2867	5	)	)	-RRB-
37681	2867	6	.	.	.
37681	2868	1	These	these	DT
37681	2868	2	writers	writer	NNS
37681	2868	3	claim	claim	VBP
37681	2868	4	that	that	IN
37681	2868	5	all	all	PDT
37681	2868	6	the	the	DT
37681	2868	7	authorities	authority	NNS
37681	2868	8	attributing	attribute	VBG
37681	2868	9	the	the	DT
37681	2868	10	proposition	proposition	NN
37681	2868	11	to	to	IN
37681	2868	12	Pythagoras	Pythagoras	NNP
37681	2868	13	are	be	VBP
37681	2868	14	centuries	century	NNS
37681	2868	15	later	later	RB
37681	2868	16	than	than	IN
37681	2868	17	his	-PRON-	PRP$
37681	2868	18	time	time	NN
37681	2868	19	,	,	,
37681	2868	20	and	and	CC
37681	2868	21	are	be	VBP
37681	2868	22	open	open	JJ
37681	2868	23	to	to	IN
37681	2868	24	grave	grave	JJ
37681	2868	25	suspicion	suspicion	NN
37681	2868	26	.	.	.
37681	2869	1	Nevertheless	nevertheless	RB
37681	2869	2	it	-PRON-	PRP
37681	2869	3	is	be	VBZ
37681	2869	4	hardly	hardly	RB
37681	2869	5	possible	possible	JJ
37681	2869	6	that	that	IN
37681	2869	7	such	such	PDT
37681	2869	8	a	a	DT
37681	2869	9	general	general	JJ
37681	2869	10	tradition	tradition	NN
37681	2869	11	,	,	,
37681	2869	12	and	and	CC
37681	2869	13	one	one	CD
37681	2869	14	so	so	RB
37681	2869	15	universally	universally	RB
37681	2869	16	accepted	accept	VBN
37681	2869	17	,	,	,
37681	2869	18	should	should	MD
37681	2869	19	have	have	VB
37681	2869	20	arisen	arise	VBN
37681	2869	21	without	without	IN
37681	2869	22	good	good	JJ
37681	2869	23	foundation	foundation	NN
37681	2869	24	.	.	.
37681	2870	1	The	the	DT
37681	2870	2	evidence	evidence	NN
37681	2870	3	has	have	VBZ
37681	2870	4	been	be	VBN
37681	2870	5	carefully	carefully	RB
37681	2870	6	studied	study	VBN
37681	2870	7	by	by	IN
37681	2870	8	Heath	Heath	NNP
37681	2870	9	in	in	IN
37681	2870	10	his	-PRON-	PRP$
37681	2870	11	"	"	``
37681	2870	12	Euclid	Euclid	NNP
37681	2870	13	,	,	,
37681	2870	14	"	"	''
37681	2870	15	who	who	WP
37681	2870	16	concludes	conclude	VBZ
37681	2870	17	with	with	IN
37681	2870	18	these	these	DT
37681	2870	19	words	word	NNS
37681	2870	20	:	:	:
37681	2870	21	"	"	``
37681	2870	22	On	on	IN
37681	2870	23	the	the	DT
37681	2870	24	whole	whole	NN
37681	2870	25	,	,	,
37681	2870	26	therefore	therefore	RB
37681	2870	27	,	,	,
37681	2870	28	I	-PRON-	PRP
37681	2870	29	see	see	VBP
37681	2870	30	no	no	DT
37681	2870	31	sufficient	sufficient	JJ
37681	2870	32	reason	reason	NN
37681	2870	33	to	to	TO
37681	2870	34	question	question	VB
37681	2870	35	the	the	DT
37681	2870	36	tradition	tradition	NN
37681	2870	37	that	that	WDT
37681	2870	38	,	,	,
37681	2870	39	so	so	RB
37681	2870	40	far	far	RB
37681	2870	41	as	as	IN
37681	2870	42	Greek	greek	JJ
37681	2870	43	geometry	geometry	NN
37681	2870	44	is	be	VBZ
37681	2870	45	concerned	concern	VBN
37681	2870	46	...	...	NFP
37681	2870	47	,	,	,
37681	2870	48	Pythagoras	Pythagoras	NNP
37681	2870	49	was	be	VBD
37681	2870	50	the	the	DT
37681	2870	51	first	first	JJ
37681	2870	52	to	to	TO
37681	2870	53	introduce	introduce	VB
37681	2870	54	the	the	DT
37681	2870	55	theorem	theorem	NN
37681	2870	56	...	...	NFP
37681	2870	57	and	and	CC
37681	2870	58	to	to	TO
37681	2870	59	give	give	VB
37681	2870	60	a	a	DT
37681	2870	61	general	general	JJ
37681	2870	62	proof	proof	NN
37681	2870	63	of	of	IN
37681	2870	64	it	-PRON-	PRP
37681	2870	65	.	.	.
37681	2870	66	"	"	''
37681	2871	1	That	that	IN
37681	2871	2	the	the	DT
37681	2871	3	fact	fact	NN
37681	2871	4	was	be	VBD
37681	2871	5	known	know	VBN
37681	2871	6	earlier	early	RBR
37681	2871	7	,	,	,
37681	2871	8	probably	probably	RB
37681	2871	9	without	without	IN
37681	2871	10	the	the	DT
37681	2871	11	general	general	JJ
37681	2871	12	proof	proof	NN
37681	2871	13	,	,	,
37681	2871	14	is	be	VBZ
37681	2871	15	recognized	recognize	VBN
37681	2871	16	by	by	IN
37681	2871	17	all	all	DT
37681	2871	18	modern	modern	JJ
37681	2871	19	writers	writer	NNS
37681	2871	20	.	.	.
37681	2872	1	[	[	-LRB-
37681	2872	2	Illustration	illustration	NN
37681	2872	3	]	]	-RRB-
37681	2872	4	Pythagoras	Pythagoras	NNP
37681	2872	5	had	have	VBD
37681	2872	6	studied	study	VBN
37681	2872	7	in	in	IN
37681	2872	8	Egypt	Egypt	NNP
37681	2872	9	and	and	CC
37681	2872	10	possibly	possibly	RB
37681	2872	11	in	in	IN
37681	2872	12	the	the	DT
37681	2872	13	East	East	NNP
37681	2872	14	before	before	IN
37681	2872	15	he	-PRON-	PRP
37681	2872	16	established	establish	VBD
37681	2872	17	his	-PRON-	PRP$
37681	2872	18	school	school	NN
37681	2872	19	at	at	IN
37681	2872	20	Crotona	Crotona	NNP
37681	2872	21	,	,	,
37681	2872	22	in	in	IN
37681	2872	23	southern	southern	JJ
37681	2872	24	Italy	Italy	NNP
37681	2872	25	.	.	.
37681	2873	1	In	in	IN
37681	2873	2	Egypt	Egypt	NNP
37681	2873	3	,	,	,
37681	2873	4	at	at	IN
37681	2873	5	any	any	DT
37681	2873	6	rate	rate	NN
37681	2873	7	,	,	,
37681	2873	8	he	-PRON-	PRP
37681	2873	9	could	could	MD
37681	2873	10	easily	easily	RB
37681	2873	11	have	have	VB
37681	2873	12	found	find	VBN
37681	2873	13	that	that	IN
37681	2873	14	a	a	DT
37681	2873	15	triangle	triangle	NN
37681	2873	16	with	with	IN
37681	2873	17	the	the	DT
37681	2873	18	sides	side	NNS
37681	2873	19	3	3	CD
37681	2873	20	,	,	,
37681	2873	21	4	4	CD
37681	2873	22	,	,	,
37681	2873	23	5	5	CD
37681	2873	24	,	,	,
37681	2873	25	is	be	VBZ
37681	2873	26	a	a	DT
37681	2873	27	right	right	JJ
37681	2873	28	triangle	triangle	NN
37681	2873	29	,	,	,
37681	2873	30	and	and	CC
37681	2873	31	Vitruvius	Vitruvius	NNP
37681	2873	32	(	(	-LRB-
37681	2873	33	first	first	JJ
37681	2873	34	century	century	NN
37681	2873	35	B.C.	B.C.	NNP
37681	2873	36	)	)	-RRB-
37681	2874	1	tells	tell	VBZ
37681	2874	2	us	-PRON-	PRP
37681	2874	3	that	that	IN
37681	2874	4	he	-PRON-	PRP
37681	2874	5	taught	teach	VBD
37681	2874	6	this	this	DT
37681	2874	7	fact	fact	NN
37681	2874	8	.	.	.
37681	2875	1	The	the	DT
37681	2875	2	Egyptian	Egyptian	NNP
37681	2875	3	_	_	NNP
37681	2875	4	harpedonaptae	harpedonaptae	NN
37681	2875	5	_	_	NNP
37681	2875	6	(	(	-LRB-
37681	2875	7	rope	rope	NN
37681	2875	8	stretchers	stretcher	NNS
37681	2875	9	)	)	-RRB-
37681	2875	10	stretched	stretch	VBD
37681	2875	11	ropes	rope	NNS
37681	2875	12	about	about	IN
37681	2875	13	pegs	peg	NNS
37681	2875	14	so	so	IN
37681	2875	15	as	as	IN
37681	2875	16	to	to	TO
37681	2875	17	make	make	VB
37681	2875	18	such	such	PDT
37681	2875	19	a	a	DT
37681	2875	20	triangle	triangle	NN
37681	2875	21	for	for	IN
37681	2875	22	the	the	DT
37681	2875	23	purpose	purpose	NN
37681	2875	24	of	of	IN
37681	2875	25	laying	lay	VBG
37681	2875	26	out	out	RP
37681	2875	27	a	a	DT
37681	2875	28	right	right	JJ
37681	2875	29	angle	angle	NN
37681	2875	30	in	in	IN
37681	2875	31	their	-PRON-	PRP$
37681	2875	32	surveying	surveying	NN
37681	2875	33	,	,	,
37681	2875	34	just	just	RB
37681	2875	35	as	as	IN
37681	2875	36	our	-PRON-	PRP$
37681	2875	37	surveyors	surveyor	NNS
37681	2875	38	do	do	VBP
37681	2875	39	to	to	IN
37681	2875	40	-	-	HYPH
37681	2875	41	day	day	NN
37681	2875	42	.	.	.
37681	2876	1	The	the	DT
37681	2876	2	great	great	JJ
37681	2876	3	pyramids	pyramid	NNS
37681	2876	4	have	have	VBP
37681	2876	5	an	an	DT
37681	2876	6	angle	angle	NN
37681	2876	7	of	of	IN
37681	2876	8	slope	slope	NN
37681	2876	9	such	such	JJ
37681	2876	10	as	as	IN
37681	2876	11	is	be	VBZ
37681	2876	12	given	give	VBN
37681	2876	13	by	by	IN
37681	2876	14	this	this	DT
37681	2876	15	triangle	triangle	NN
37681	2876	16	.	.	.
37681	2877	1	Indeed	indeed	RB
37681	2877	2	,	,	,
37681	2877	3	a	a	DT
37681	2877	4	papyrus	papyrus	NN
37681	2877	5	of	of	IN
37681	2877	6	the	the	DT
37681	2877	7	twelfth	twelfth	JJ
37681	2877	8	dynasty	dynasty	NN
37681	2877	9	,	,	,
37681	2877	10	lately	lately	RB
37681	2877	11	discovered	discover	VBN
37681	2877	12	at	at	IN
37681	2877	13	Kahun	Kahun	NNP
37681	2877	14	,	,	,
37681	2877	15	in	in	IN
37681	2877	16	Egypt	Egypt	NNP
37681	2877	17	,	,	,
37681	2877	18	refers	refer	VBZ
37681	2877	19	to	to	IN
37681	2877	20	four	four	CD
37681	2877	21	of	of	IN
37681	2877	22	these	these	DT
37681	2877	23	triangles	triangle	NNS
37681	2877	24	,	,	,
37681	2877	25	such	such	JJ
37681	2877	26	as	as	IN
37681	2877	27	1	1	CD
37681	2877	28	^	^	NN
37681	2877	29	2	2	CD
37681	2877	30	+	+	SYM
37681	2877	31	(	(	-LRB-
37681	2877	32	3/4)^2	3/4)^2	CD
37681	2877	33	=	=	SYM
37681	2877	34	(	(	-LRB-
37681	2877	35	1	1	CD
37681	2877	36	1/4)^2	1/4)^2	CD
37681	2877	37	.	.	.
37681	2878	1	This	this	DT
37681	2878	2	property	property	NN
37681	2878	3	seems	seem	VBZ
37681	2878	4	to	to	TO
37681	2878	5	have	have	VB
37681	2878	6	been	be	VBN
37681	2878	7	a	a	DT
37681	2878	8	matter	matter	NN
37681	2878	9	of	of	IN
37681	2878	10	common	common	JJ
37681	2878	11	knowledge	knowledge	NN
37681	2878	12	long	long	RB
37681	2878	13	before	before	IN
37681	2878	14	Pythagoras	Pythagoras	NNP
37681	2878	15	,	,	,
37681	2878	16	even	even	RB
37681	2878	17	as	as	IN
37681	2878	18	far	far	RB
37681	2878	19	east	east	RB
37681	2878	20	as	as	IN
37681	2878	21	China	China	NNP
37681	2878	22	.	.	.
37681	2879	1	He	-PRON-	PRP
37681	2879	2	was	be	VBD
37681	2879	3	,	,	,
37681	2879	4	therefore	therefore	RB
37681	2879	5	,	,	,
37681	2879	6	naturally	naturally	RB
37681	2879	7	led	lead	VBD
37681	2879	8	to	to	TO
37681	2879	9	attempt	attempt	VB
37681	2879	10	to	to	TO
37681	2879	11	prove	prove	VB
37681	2879	12	the	the	DT
37681	2879	13	general	general	JJ
37681	2879	14	property	property	NN
37681	2879	15	which	which	WDT
37681	2879	16	had	have	VBD
37681	2879	17	already	already	RB
37681	2879	18	been	be	VBN
37681	2879	19	recognized	recognize	VBN
37681	2879	20	for	for	IN
37681	2879	21	special	special	JJ
37681	2879	22	cases	case	NNS
37681	2879	23	,	,	,
37681	2879	24	and	and	CC
37681	2879	25	in	in	IN
37681	2879	26	particular	particular	JJ
37681	2879	27	for	for	IN
37681	2879	28	the	the	DT
37681	2879	29	isosceles	isoscele	NNS
37681	2879	30	right	right	JJ
37681	2879	31	triangle	triangle	NN
37681	2879	32	.	.	.
37681	2880	1	How	how	WRB
37681	2880	2	Pythagoras	Pythagoras	NNP
37681	2880	3	proved	prove	VBD
37681	2880	4	the	the	DT
37681	2880	5	proposition	proposition	NN
37681	2880	6	is	be	VBZ
37681	2880	7	not	not	RB
37681	2880	8	known	know	VBN
37681	2880	9	.	.	.
37681	2881	1	It	-PRON-	PRP
37681	2881	2	has	have	VBZ
37681	2881	3	been	be	VBN
37681	2881	4	thought	think	VBN
37681	2881	5	that	that	IN
37681	2881	6	he	-PRON-	PRP
37681	2881	7	used	use	VBD
37681	2881	8	a	a	DT
37681	2881	9	proof	proof	NN
37681	2881	10	by	by	IN
37681	2881	11	proportion	proportion	NN
37681	2881	12	,	,	,
37681	2881	13	because	because	IN
37681	2881	14	Proclus	Proclus	NNP
37681	2881	15	says	say	VBZ
37681	2881	16	that	that	IN
37681	2881	17	Euclid	Euclid	NNP
37681	2881	18	gave	give	VBD
37681	2881	19	a	a	DT
37681	2881	20	new	new	JJ
37681	2881	21	style	style	NN
37681	2881	22	of	of	IN
37681	2881	23	proof	proof	NN
37681	2881	24	,	,	,
37681	2881	25	and	and	CC
37681	2881	26	Euclid	Euclid	NNP
37681	2881	27	does	do	VBZ
37681	2881	28	not	not	RB
37681	2881	29	use	use	VB
37681	2881	30	proportion	proportion	NN
37681	2881	31	for	for	IN
37681	2881	32	this	this	DT
37681	2881	33	purpose	purpose	NN
37681	2881	34	,	,	,
37681	2881	35	while	while	IN
37681	2881	36	the	the	DT
37681	2881	37	subject	subject	NN
37681	2881	38	,	,	,
37681	2881	39	in	in	IN
37681	2881	40	incomplete	incomplete	JJ
37681	2881	41	form	form	NN
37681	2881	42	,	,	,
37681	2881	43	was	be	VBD
37681	2881	44	highly	highly	RB
37681	2881	45	esteemed	esteem	VBN
37681	2881	46	by	by	IN
37681	2881	47	the	the	DT
37681	2881	48	Pythagoreans	Pythagoreans	NNPS
37681	2881	49	.	.	.
37681	2882	1	Heath	Heath	NNP
37681	2882	2	suggests	suggest	VBZ
37681	2882	3	that	that	IN
37681	2882	4	this	this	DT
37681	2882	5	is	be	VBZ
37681	2882	6	among	among	IN
37681	2882	7	the	the	DT
37681	2882	8	possibilities	possibility	NNS
37681	2882	9	:	:	:
37681	2882	10	[	[	-LRB-
37681	2882	11	Illustration	illustration	NN
37681	2882	12	]	]	-RRB-
37681	2882	13	[	[	-LRB-
37681	2882	14	triangles]_ABC	triangles]_ABC	NNP
37681	2882	15	_	_	NNP
37681	2882	16	and	and	CC
37681	2882	17	_	_	NNP
37681	2882	18	APC	APC	NNP
37681	2882	19	_	_	NNP
37681	2882	20	are	be	VBP
37681	2882	21	similar	similar	JJ
37681	2882	22	.	.	.
37681	2883	1	[	[	-LRB-
37681	2883	2	therefore	therefore	RB
37681	2883	3	]	]	-RRB-
37681	2883	4	_	_	NNP
37681	2883	5	AB	AB	NNP
37681	2883	6	_	_	NNP
37681	2883	7	×	×	NN
37681	2883	8	_	_	NNP
37681	2883	9	AP	AP	NNP
37681	2883	10	_	_	NNP
37681	2883	11	=	=	NFP
37681	2883	12	(	(	-LRB-
37681	2883	13	_	_	NNP
37681	2883	14	AC_)^2	AC_)^2	NNP
37681	2883	15	.	.	.
37681	2884	1	Similarly	similarly	RB
37681	2884	2	,	,	,
37681	2884	3	_	_	NNP
37681	2884	4	AB	AB	NNP
37681	2884	5	_	_	NNP
37681	2884	6	×	×	NN
37681	2884	7	_	_	NNP
37681	2884	8	PB	PB	NNP
37681	2884	9	_	_	NNP
37681	2884	10	=	=	NFP
37681	2884	11	(	(	-LRB-
37681	2884	12	_	_	NNP
37681	2884	13	BC_)^2	BC_)^2	NNP
37681	2884	14	.	.	.
37681	2885	1	[	[	-LRB-
37681	2885	2	therefore	therefore	RB
37681	2885	3	]	]	-RRB-
37681	2885	4	_	_	NNP
37681	2885	5	AB_(_AP	AB_(_AP	NNP
37681	2885	6	_	_	NNP
37681	2885	7	+	+	CC
37681	2885	8	_	_	NNP
37681	2885	9	PB	PB	NNP
37681	2885	10	_	_	NNP
37681	2885	11	)	)	-RRB-
37681	2885	12	=	=	NFP
37681	2885	13	(	(	-LRB-
37681	2885	14	_	_	NNP
37681	2885	15	AC_)^2	AC_)^2	NNP
37681	2885	16	+	+	CC
37681	2885	17	(	(	-LRB-
37681	2885	18	_	_	NNP
37681	2885	19	BC_)^2	BC_)^2	NNP
37681	2885	20	,	,	,
37681	2885	21	or	or	CC
37681	2885	22	(	(	-LRB-
37681	2885	23	_	_	NNP
37681	2885	24	AB_)^2	AB_)^2	NNP
37681	2885	25	=	=	FW
37681	2885	26	(	(	-LRB-
37681	2885	27	_	_	NNP
37681	2885	28	AC_)^2	AC_)^2	NNP
37681	2885	29	+	+	CC
37681	2885	30	(	(	-LRB-
37681	2885	31	_	_	NNP
37681	2885	32	BC_)^2	BC_)^2	NNP
37681	2885	33	.	.	.
37681	2886	1	Others	other	NNS
37681	2886	2	have	have	VBP
37681	2886	3	thought	think	VBN
37681	2886	4	that	that	IN
37681	2886	5	Pythagoras	Pythagoras	NNP
37681	2886	6	derived	derive	VBD
37681	2886	7	his	-PRON-	PRP$
37681	2886	8	proof	proof	NN
37681	2886	9	from	from	IN
37681	2886	10	dissecting	dissect	VBG
37681	2886	11	a	a	DT
37681	2886	12	square	square	NN
37681	2886	13	and	and	CC
37681	2886	14	showing	show	VBG
37681	2886	15	that	that	IN
37681	2886	16	the	the	DT
37681	2886	17	square	square	NN
37681	2886	18	on	on	IN
37681	2886	19	the	the	DT
37681	2886	20	hypotenuse	hypotenuse	NN
37681	2886	21	must	must	MD
37681	2886	22	equal	equal	VB
37681	2886	23	the	the	DT
37681	2886	24	sum	sum	NN
37681	2886	25	of	of	IN
37681	2886	26	the	the	DT
37681	2886	27	squares	square	NNS
37681	2886	28	on	on	IN
37681	2886	29	the	the	DT
37681	2886	30	other	other	JJ
37681	2886	31	two	two	CD
37681	2886	32	sides	side	NNS
37681	2886	33	,	,	,
37681	2886	34	in	in	IN
37681	2886	35	some	some	DT
37681	2886	36	such	such	JJ
37681	2886	37	manner	manner	NN
37681	2886	38	as	as	IN
37681	2886	39	this	this	DT
37681	2886	40	:	:	:
37681	2886	41	[	[	-LRB-
37681	2886	42	Illustration	illustration	NN
37681	2886	43	:	:	:
37681	2886	44	FIG	FIG	NNP
37681	2886	45	.	.	.
37681	2887	1	1	1	LS
37681	2887	2	]	]	-RRB-
37681	2887	3	[	[	-LRB-
37681	2887	4	Illustration	illustration	NN
37681	2887	5	:	:	:
37681	2887	6	FIG	FIG	NNP
37681	2887	7	.	.	.
37681	2888	1	2	2	LS
37681	2888	2	]	]	-RRB-
37681	2888	3	Here	here	RB
37681	2888	4	Fig	fig	NN
37681	2888	5	.	.	.
37681	2889	1	1	1	CD
37681	2889	2	is	be	VBZ
37681	2889	3	evidently	evidently	RB
37681	2889	4	_	_	NNP
37681	2889	5	h_^2	h_^2	NNP
37681	2889	6	+	+	SYM
37681	2889	7	4	4	CD
37681	2889	8	[	[	-LRB-
37681	2889	9	triangles	triangle	NNS
37681	2889	10	]	]	-RRB-
37681	2889	11	.	.	.
37681	2890	1	Fig	fig	NN
37681	2890	2	.	.	.
37681	2891	1	2	2	CD
37681	2891	2	is	be	VBZ
37681	2891	3	evidently	evidently	RB
37681	2891	4	_	_	NNP
37681	2891	5	a_^2	a_^2	NNP
37681	2891	6	+	+	SYM
37681	2891	7	_	_	NNP
37681	2891	8	b_^2	b_^2	NNP
37681	2891	9	+	+	CC
37681	2891	10	4	4	CD
37681	2891	11	[	[	-LRB-
37681	2891	12	triangles	triangle	NNS
37681	2891	13	]	]	-RRB-
37681	2891	14	.	.	.
37681	2892	1	[	[	-LRB-
37681	2892	2	therefore	therefore	RB
37681	2892	3	]	]	-RRB-
37681	2892	4	_	_	NNP
37681	2892	5	h_^2	h_^2	NNP
37681	2892	6	+	+	SYM
37681	2892	7	4	4	CD
37681	2892	8	[	[	-LRB-
37681	2892	9	triangles	triangle	NNS
37681	2892	10	]	]	-RRB-
37681	2892	11	=	=	NFP
37681	2892	12	_	_	NNP
37681	2892	13	a_^2	a_^2	NNP
37681	2892	14	+	+	SYM
37681	2892	15	_	_	NNP
37681	2892	16	b_^2	b_^2	NNP
37681	2892	17	+	+	CC
37681	2892	18	4	4	CD
37681	2892	19	[	[	-LRB-
37681	2892	20	triangles	triangle	NNS
37681	2892	21	]	]	-RRB-
37681	2892	22	,	,	,
37681	2892	23	the	the	DT
37681	2892	24	[	[	-LRB-
37681	2892	25	triangles	triangle	NNS
37681	2892	26	]	]	-RRB-
37681	2892	27	all	all	DT
37681	2892	28	being	be	VBG
37681	2892	29	congruent	congruent	JJ
37681	2892	30	.	.	.
37681	2893	1	[	[	-LRB-
37681	2893	2	therefore	therefore	RB
37681	2893	3	]	]	-RRB-
37681	2893	4	_	_	NNP
37681	2893	5	h_^2	h_^2	NNP
37681	2893	6	=	=	SYM
37681	2893	7	_	_	NNP
37681	2893	8	a_^2	a_^2	NNP
37681	2893	9	+	+	SYM
37681	2893	10	_	_	NNP
37681	2893	11	b_^2	b_^2	NNP
37681	2893	12	.	.	.
37681	2894	1	The	the	DT
37681	2894	2	great	great	JJ
37681	2894	3	Hindu	Hindu	NNP
37681	2894	4	mathematician	mathematician	NN
37681	2894	5	,	,	,
37681	2894	6	Bhaskara	Bhaskara	NNP
37681	2894	7	(	(	-LRB-
37681	2894	8	born	bear	VBN
37681	2894	9	1114	1114	CD
37681	2894	10	A.D.	A.D.	NNP
37681	2894	11	)	)	-RRB-
37681	2894	12	,	,	,
37681	2894	13	proceeds	proceed	VBZ
37681	2894	14	in	in	IN
37681	2894	15	a	a	DT
37681	2894	16	somewhat	somewhat	RB
37681	2894	17	similar	similar	JJ
37681	2894	18	manner	manner	NN
37681	2894	19	.	.	.
37681	2895	1	He	-PRON-	PRP
37681	2895	2	draws	draw	VBZ
37681	2895	3	this	this	DT
37681	2895	4	figure	figure	NN
37681	2895	5	,	,	,
37681	2895	6	but	but	CC
37681	2895	7	gives	give	VBZ
37681	2895	8	no	no	DT
37681	2895	9	proof	proof	NN
37681	2895	10	.	.	.
37681	2896	1	It	-PRON-	PRP
37681	2896	2	is	be	VBZ
37681	2896	3	evident	evident	JJ
37681	2896	4	that	that	IN
37681	2896	5	he	-PRON-	PRP
37681	2896	6	had	have	VBD
37681	2896	7	in	in	IN
37681	2896	8	mind	mind	NN
37681	2896	9	this	this	DT
37681	2896	10	relation	relation	NN
37681	2896	11	:	:	:
37681	2896	12	[	[	-LRB-
37681	2896	13	Illustration	illustration	NN
37681	2896	14	]	]	-RRB-
37681	2896	15	_	_	NNP
37681	2896	16	h_^2	h_^2	NNP
37681	2896	17	=	=	SYM
37681	2896	18	4	4	CD
37681	2896	19	·	·	NFP
37681	2896	20	_	_	NNP
37681	2896	21	ab_/2	ab_/2	NNP
37681	2896	22	+	+	NFP
37681	2896	23	(	(	-LRB-
37681	2896	24	_	_	NNP
37681	2896	25	b	b	NNP
37681	2896	26	_	_	NNP
37681	2896	27	-	-	HYPH
37681	2896	28	_	_	NNP
37681	2896	29	a_)^2	a_)^2	NNP
37681	2896	30	=	=	SYM
37681	2896	31	_	_	NNP
37681	2896	32	a_^2	a_^2	NNP
37681	2896	33	+	+	SYM
37681	2896	34	_	_	NNP
37681	2896	35	b_^2	b_^2	NNP
37681	2896	36	.	.	.
37681	2897	1	A	a	DT
37681	2897	2	somewhat	somewhat	RB
37681	2897	3	similar	similar	JJ
37681	2897	4	proof	proof	NN
37681	2897	5	can	can	MD
37681	2897	6	be	be	VB
37681	2897	7	based	base	VBN
37681	2897	8	upon	upon	IN
37681	2897	9	the	the	DT
37681	2897	10	following	following	JJ
37681	2897	11	figure	figure	NN
37681	2897	12	:	:	:
37681	2897	13	[	[	-LRB-
37681	2897	14	Illustration	illustration	NN
37681	2897	15	]	]	-RRB-
37681	2897	16	If	if	IN
37681	2897	17	the	the	DT
37681	2897	18	four	four	CD
37681	2897	19	triangles	triangle	NNS
37681	2897	20	,	,	,
37681	2897	21	1	1	CD
37681	2897	22	+	+	SYM
37681	2897	23	2	2	CD
37681	2897	24	+	+	SYM
37681	2897	25	3	3	CD
37681	2897	26	+	+	SYM
37681	2897	27	4	4	CD
37681	2897	28	,	,	,
37681	2897	29	are	be	VBP
37681	2897	30	taken	take	VBN
37681	2897	31	away	away	RB
37681	2897	32	,	,	,
37681	2897	33	there	there	EX
37681	2897	34	remains	remain	VBZ
37681	2897	35	the	the	DT
37681	2897	36	square	square	NN
37681	2897	37	on	on	IN
37681	2897	38	the	the	DT
37681	2897	39	hypotenuse	hypotenuse	NN
37681	2897	40	.	.	.
37681	2898	1	But	but	CC
37681	2898	2	if	if	IN
37681	2898	3	we	-PRON-	PRP
37681	2898	4	take	take	VBP
37681	2898	5	away	away	RB
37681	2898	6	the	the	DT
37681	2898	7	two	two	CD
37681	2898	8	shaded	shaded	JJ
37681	2898	9	rectangles	rectangle	NNS
37681	2898	10	,	,	,
37681	2898	11	which	which	WDT
37681	2898	12	equal	equal	VBP
37681	2898	13	the	the	DT
37681	2898	14	four	four	CD
37681	2898	15	triangles	triangle	NNS
37681	2898	16	,	,	,
37681	2898	17	there	there	EX
37681	2898	18	remain	remain	VBP
37681	2898	19	the	the	DT
37681	2898	20	squares	square	NNS
37681	2898	21	on	on	IN
37681	2898	22	the	the	DT
37681	2898	23	two	two	CD
37681	2898	24	sides	side	NNS
37681	2898	25	.	.	.
37681	2899	1	Therefore	therefore	RB
37681	2899	2	the	the	DT
37681	2899	3	square	square	NN
37681	2899	4	on	on	IN
37681	2899	5	the	the	DT
37681	2899	6	hypotenuse	hypotenuse	NN
37681	2899	7	must	must	MD
37681	2899	8	equal	equal	VB
37681	2899	9	the	the	DT
37681	2899	10	sum	sum	NN
37681	2899	11	of	of	IN
37681	2899	12	these	these	DT
37681	2899	13	two	two	CD
37681	2899	14	squares	square	NNS
37681	2899	15	.	.	.
37681	2900	1	[	[	-LRB-
37681	2900	2	Illustration	illustration	NN
37681	2900	3	]	]	-RRB-
37681	2900	4	It	-PRON-	PRP
37681	2900	5	has	have	VBZ
37681	2900	6	long	long	RB
37681	2900	7	been	be	VBN
37681	2900	8	thought	think	VBN
37681	2900	9	that	that	IN
37681	2900	10	the	the	DT
37681	2900	11	truth	truth	NN
37681	2900	12	of	of	IN
37681	2900	13	the	the	DT
37681	2900	14	proposition	proposition	NN
37681	2900	15	was	be	VBD
37681	2900	16	first	first	RB
37681	2900	17	observed	observe	VBN
37681	2900	18	by	by	IN
37681	2900	19	seeing	see	VBG
37681	2900	20	the	the	DT
37681	2900	21	tiles	tile	NNS
37681	2900	22	on	on	IN
37681	2900	23	the	the	DT
37681	2900	24	floors	floor	NNS
37681	2900	25	of	of	IN
37681	2900	26	ancient	ancient	JJ
37681	2900	27	temples	temple	NNS
37681	2900	28	.	.	.
37681	2901	1	If	if	IN
37681	2901	2	they	-PRON-	PRP
37681	2901	3	were	be	VBD
37681	2901	4	arranged	arrange	VBN
37681	2901	5	as	as	IN
37681	2901	6	here	here	RB
37681	2901	7	shown	show	VBN
37681	2901	8	,	,	,
37681	2901	9	the	the	DT
37681	2901	10	proposition	proposition	NN
37681	2901	11	would	would	MD
37681	2901	12	be	be	VB
37681	2901	13	evident	evident	JJ
37681	2901	14	for	for	IN
37681	2901	15	the	the	DT
37681	2901	16	special	special	JJ
37681	2901	17	case	case	NN
37681	2901	18	of	of	IN
37681	2901	19	an	an	DT
37681	2901	20	isosceles	isoscele	NNS
37681	2901	21	right	right	JJ
37681	2901	22	triangle	triangle	NN
37681	2901	23	.	.	.
37681	2902	1	The	the	DT
37681	2902	2	Hindus	Hindus	NNPS
37681	2902	3	knew	know	VBD
37681	2902	4	the	the	DT
37681	2902	5	proposition	proposition	NN
37681	2902	6	long	long	RB
37681	2902	7	before	before	IN
37681	2902	8	Bhaskara	Bhaskara	NNP
37681	2902	9	,	,	,
37681	2902	10	however	however	RB
37681	2902	11	,	,	,
37681	2902	12	and	and	CC
37681	2902	13	possibly	possibly	RB
37681	2902	14	before	before	IN
37681	2902	15	Pythagoras	Pythagoras	NNP
37681	2902	16	.	.	.
37681	2903	1	It	-PRON-	PRP
37681	2903	2	is	be	VBZ
37681	2903	3	referred	refer	VBN
37681	2903	4	to	to	IN
37681	2903	5	in	in	IN
37681	2903	6	the	the	DT
37681	2903	7	old	old	JJ
37681	2903	8	religious	religious	JJ
37681	2903	9	poems	poem	NNS
37681	2903	10	of	of	IN
37681	2903	11	the	the	DT
37681	2903	12	Brahmans	Brahmans	NNPS
37681	2903	13	,	,	,
37681	2903	14	the	the	DT
37681	2903	15	"	"	``
37681	2903	16	Sulvasutras	sulvasutra	NNS
37681	2903	17	,	,	,
37681	2903	18	"	"	''
37681	2903	19	but	but	CC
37681	2903	20	the	the	DT
37681	2903	21	date	date	NN
37681	2903	22	of	of	IN
37681	2903	23	these	these	DT
37681	2903	24	poems	poem	NNS
37681	2903	25	is	be	VBZ
37681	2903	26	so	so	RB
37681	2903	27	uncertain	uncertain	JJ
37681	2903	28	that	that	IN
37681	2903	29	it	-PRON-	PRP
37681	2903	30	is	be	VBZ
37681	2903	31	impossible	impossible	JJ
37681	2903	32	to	to	TO
37681	2903	33	state	state	VB
37681	2903	34	that	that	IN
37681	2903	35	they	-PRON-	PRP
37681	2903	36	preceded	precede	VBD
37681	2903	37	the	the	DT
37681	2903	38	sixth	sixth	JJ
37681	2903	39	century	century	NN
37681	2903	40	B.C.,[79	b.c.,[79	NN
37681	2903	41	]	]	-RRB-
37681	2903	42	in	in	IN
37681	2903	43	which	which	WDT
37681	2903	44	Pythagoras	Pythagoras	NNP
37681	2903	45	lived	live	VBD
37681	2903	46	.	.	.
37681	2904	1	The	the	DT
37681	2904	2	"	"	``
37681	2904	3	Sulvasutra	Sulvasutra	NNP
37681	2904	4	"	"	''
37681	2904	5	of	of	IN
37681	2904	6	Apastamba	Apastamba	NNP
37681	2904	7	has	have	VBZ
37681	2904	8	a	a	DT
37681	2904	9	collection	collection	NN
37681	2904	10	of	of	IN
37681	2904	11	rules	rule	NNS
37681	2904	12	,	,	,
37681	2904	13	without	without	IN
37681	2904	14	proofs	proofs	NNP
37681	2904	15	,	,	,
37681	2904	16	for	for	IN
37681	2904	17	constructing	construct	VBG
37681	2904	18	various	various	JJ
37681	2904	19	figures	figure	NNS
37681	2904	20	.	.	.
37681	2905	1	Among	among	IN
37681	2905	2	these	these	DT
37681	2905	3	is	be	VBZ
37681	2905	4	one	one	CD
37681	2905	5	for	for	IN
37681	2905	6	constructing	construct	VBG
37681	2905	7	right	right	JJ
37681	2905	8	angles	angle	NNS
37681	2905	9	by	by	IN
37681	2905	10	stretching	stretch	VBG
37681	2905	11	cords	cord	NNS
37681	2905	12	of	of	IN
37681	2905	13	the	the	DT
37681	2905	14	following	following	JJ
37681	2905	15	lengths	length	NNS
37681	2905	16	:	:	:
37681	2905	17	3	3	CD
37681	2905	18	,	,	,
37681	2905	19	4	4	CD
37681	2905	20	,	,	,
37681	2905	21	5	5	CD
37681	2905	22	;	;	SYM
37681	2905	23	12	12	CD
37681	2905	24	,	,	,
37681	2905	25	16	16	CD
37681	2905	26	,	,	,
37681	2905	27	20	20	CD
37681	2905	28	;	;	SYM
37681	2905	29	15	15	CD
37681	2905	30	,	,	,
37681	2905	31	20	20	CD
37681	2905	32	,	,	,
37681	2905	33	25	25	CD
37681	2905	34	(	(	-LRB-
37681	2905	35	the	the	DT
37681	2905	36	two	two	CD
37681	2905	37	latter	latter	JJ
37681	2905	38	being	be	VBG
37681	2905	39	multiples	multiple	NNS
37681	2905	40	of	of	IN
37681	2905	41	the	the	DT
37681	2905	42	first	first	JJ
37681	2905	43	)	)	-RRB-
37681	2905	44	;	;	:
37681	2905	45	5	5	CD
37681	2905	46	,	,	,
37681	2905	47	12	12	CD
37681	2905	48	,	,	,
37681	2905	49	13	13	CD
37681	2905	50	;	;	SYM
37681	2905	51	15	15	CD
37681	2905	52	,	,	,
37681	2905	53	36	36	CD
37681	2905	54	,	,	,
37681	2905	55	39	39	CD
37681	2905	56	;	;	SYM
37681	2905	57	8	8	CD
37681	2905	58	,	,	,
37681	2905	59	15	15	CD
37681	2905	60	,	,	,
37681	2905	61	17	17	CD
37681	2905	62	;	;	SYM
37681	2905	63	12	12	CD
37681	2905	64	,	,	,
37681	2905	65	35	35	CD
37681	2905	66	,	,	,
37681	2905	67	37	37	CD
37681	2905	68	.	.	.
37681	2906	1	Whatever	whatever	WDT
37681	2906	2	the	the	DT
37681	2906	3	date	date	NN
37681	2906	4	of	of	IN
37681	2906	5	these	these	DT
37681	2906	6	"	"	``
37681	2906	7	Sulvasutras	sulvasutra	NNS
37681	2906	8	,	,	,
37681	2906	9	"	"	''
37681	2906	10	there	there	EX
37681	2906	11	is	be	VBZ
37681	2906	12	no	no	DT
37681	2906	13	evidence	evidence	NN
37681	2906	14	that	that	IN
37681	2906	15	the	the	DT
37681	2906	16	Indians	Indians	NNPS
37681	2906	17	had	have	VBD
37681	2906	18	a	a	DT
37681	2906	19	definite	definite	JJ
37681	2906	20	proof	proof	NN
37681	2906	21	of	of	IN
37681	2906	22	the	the	DT
37681	2906	23	theorem	theorem	NN
37681	2906	24	,	,	,
37681	2906	25	even	even	RB
37681	2906	26	though	though	IN
37681	2906	27	they	-PRON-	PRP
37681	2906	28	,	,	,
37681	2906	29	like	like	IN
37681	2906	30	the	the	DT
37681	2906	31	early	early	JJ
37681	2906	32	Egyptians	Egyptians	NNPS
37681	2906	33	,	,	,
37681	2906	34	recognized	recognize	VBD
37681	2906	35	the	the	DT
37681	2906	36	general	general	JJ
37681	2906	37	fact	fact	NN
37681	2906	38	.	.	.
37681	2907	1	It	-PRON-	PRP
37681	2907	2	is	be	VBZ
37681	2907	3	always	always	RB
37681	2907	4	interesting	interesting	JJ
37681	2907	5	to	to	IN
37681	2907	6	a	a	DT
37681	2907	7	class	class	NN
37681	2907	8	to	to	TO
37681	2907	9	see	see	VB
37681	2907	10	more	more	JJR
37681	2907	11	than	than	IN
37681	2907	12	one	one	CD
37681	2907	13	proof	proof	NN
37681	2907	14	of	of	IN
37681	2907	15	a	a	DT
37681	2907	16	famous	famous	JJ
37681	2907	17	theorem	theorem	NN
37681	2907	18	,	,	,
37681	2907	19	and	and	CC
37681	2907	20	many	many	JJ
37681	2907	21	teachers	teacher	NNS
37681	2907	22	find	find	VBP
37681	2907	23	it	-PRON-	PRP
37681	2907	24	profitable	profitable	JJ
37681	2907	25	to	to	TO
37681	2907	26	ask	ask	VB
37681	2907	27	their	-PRON-	PRP$
37681	2907	28	pupils	pupil	NNS
37681	2907	29	to	to	TO
37681	2907	30	work	work	VB
37681	2907	31	out	out	RP
37681	2907	32	proofs	proof	NNS
37681	2907	33	that	that	WDT
37681	2907	34	are	be	VBP
37681	2907	35	(	(	-LRB-
37681	2907	36	to	to	IN
37681	2907	37	them	-PRON-	PRP
37681	2907	38	)	)	-RRB-
37681	2907	39	original	original	JJ
37681	2907	40	,	,	,
37681	2907	41	often	often	RB
37681	2907	42	suggesting	suggest	VBG
37681	2907	43	the	the	DT
37681	2907	44	figure	figure	NN
37681	2907	45	.	.	.
37681	2908	1	Two	two	CD
37681	2908	2	of	of	IN
37681	2908	3	the	the	DT
37681	2908	4	best	well	RBS
37681	2908	5	known	know	VBN
37681	2908	6	historic	historic	JJ
37681	2908	7	proofs	proof	NNS
37681	2908	8	are	be	VBP
37681	2908	9	here	here	RB
37681	2908	10	given	give	VBN
37681	2908	11	.	.	.
37681	2909	1	The	the	DT
37681	2909	2	first	first	JJ
37681	2909	3	makes	make	VBZ
37681	2909	4	the	the	DT
37681	2909	5	Pythagorean	Pythagorean	NNP
37681	2909	6	Theorem	Theorem	NNP
37681	2909	7	a	a	DT
37681	2909	8	special	special	JJ
37681	2909	9	case	case	NN
37681	2909	10	of	of	IN
37681	2909	11	a	a	DT
37681	2909	12	proposition	proposition	NN
37681	2909	13	due	due	IN
37681	2909	14	to	to	IN
37681	2909	15	Pappus	Pappus	NNP
37681	2909	16	(	(	-LRB-
37681	2909	17	fourth	fourth	JJ
37681	2909	18	century	century	NN
37681	2909	19	A.D.	A.D.	NNP
37681	2909	20	)	)	-RRB-
37681	2909	21	,	,	,
37681	2909	22	relating	relate	VBG
37681	2909	23	to	to	IN
37681	2909	24	any	any	DT
37681	2909	25	kind	kind	NN
37681	2909	26	of	of	IN
37681	2909	27	a	a	DT
37681	2909	28	triangle	triangle	NN
37681	2909	29	.	.	.
37681	2910	1	[	[	-LRB-
37681	2910	2	Illustration	illustration	NN
37681	2910	3	]	]	-RRB-
37681	2910	4	Somewhat	somewhat	RB
37681	2910	5	simplified	simplify	VBN
37681	2910	6	,	,	,
37681	2910	7	this	this	DT
37681	2910	8	proposition	proposition	NN
37681	2910	9	asserts	assert	VBZ
37681	2910	10	that	that	IN
37681	2910	11	if	if	IN
37681	2910	12	_	_	NNP
37681	2910	13	ABC	ABC	NNP
37681	2910	14	_	_	NNP
37681	2910	15	is	be	VBZ
37681	2910	16	_	_	NNP
37681	2910	17	any	any	DT
37681	2910	18	_	_	NNP
37681	2910	19	kind	kind	NN
37681	2910	20	of	of	IN
37681	2910	21	triangle	triangle	NN
37681	2910	22	,	,	,
37681	2910	23	and	and	CC
37681	2910	24	_	_	NNP
37681	2910	25	MC	MC	NNP
37681	2910	26	_	_	NNP
37681	2910	27	,	,	,
37681	2910	28	_	_	NNP
37681	2910	29	NC	NC	NNP
37681	2910	30	_	_	NNP
37681	2910	31	are	be	VBP
37681	2910	32	parallelograms	parallelogram	NNS
37681	2910	33	on	on	IN
37681	2910	34	_	_	NNP
37681	2910	35	AC	AC	NNP
37681	2910	36	_	_	NNP
37681	2910	37	,	,	,
37681	2910	38	_	_	NNP
37681	2910	39	BC	BC	NNP
37681	2910	40	_	_	NNP
37681	2910	41	,	,	,
37681	2910	42	the	the	DT
37681	2910	43	opposite	opposite	JJ
37681	2910	44	sides	side	NNS
37681	2910	45	being	be	VBG
37681	2910	46	produced	produce	VBN
37681	2910	47	to	to	TO
37681	2910	48	meet	meet	VB
37681	2910	49	at	at	IN
37681	2910	50	_	_	NNP
37681	2910	51	P	P	NNP
37681	2910	52	_	_	NNP
37681	2910	53	;	;	:
37681	2910	54	and	and	CC
37681	2910	55	if	if	IN
37681	2910	56	_	_	NNP
37681	2910	57	PC	PC	NNP
37681	2910	58	_	_	NNP
37681	2910	59	is	be	VBZ
37681	2910	60	produced	produce	VBN
37681	2910	61	making	make	VBG
37681	2910	62	_	_	NNP
37681	2910	63	QR	QR	NNP
37681	2910	64	_	_	NNP
37681	2910	65	=	=	SYM
37681	2910	66	_	_	NNP
37681	2910	67	PC	PC	NNP
37681	2910	68	_	_	NNP
37681	2910	69	;	;	:
37681	2910	70	and	and	CC
37681	2910	71	if	if	IN
37681	2910	72	the	the	DT
37681	2910	73	parallelogram	parallelogram	NN
37681	2910	74	_	_	NNP
37681	2910	75	AT	AT	NNP
37681	2910	76	_	_	NNP
37681	2910	77	is	be	VBZ
37681	2910	78	constructed	construct	VBN
37681	2910	79	,	,	,
37681	2910	80	then	then	RB
37681	2910	81	_	_	NNP
37681	2910	82	AT	AT	NNP
37681	2910	83	_	_	NNP
37681	2910	84	=	=	SYM
37681	2910	85	_	_	NNP
37681	2910	86	MC	MC	NNP
37681	2910	87	_	_	NNP
37681	2910	88	+	+	NNP
37681	2910	89	_	_	NNP
37681	2910	90	NC	NC	NNP
37681	2910	91	_	_	NNP
37681	2910	92	.	.	.
37681	2911	1	For	for	IN
37681	2911	2	_	_	NNP
37681	2911	3	MC	MC	NNP
37681	2911	4	_	_	NNP
37681	2911	5	=	=	SYM
37681	2911	6	_	_	NNP
37681	2911	7	AP	AP	NNP
37681	2911	8	_	_	NNP
37681	2911	9	=	=	SYM
37681	2911	10	_	_	NNP
37681	2911	11	AR	AR	NNP
37681	2911	12	_	_	NNP
37681	2911	13	,	,	,
37681	2911	14	having	have	VBG
37681	2911	15	equal	equal	JJ
37681	2911	16	bases	basis	NNS
37681	2911	17	and	and	CC
37681	2911	18	equal	equal	JJ
37681	2911	19	altitudes	altitude	NNS
37681	2911	20	.	.	.
37681	2912	1	Similarly	similarly	RB
37681	2912	2	,	,	,
37681	2912	3	_	_	NNP
37681	2912	4	NC	NC	NNP
37681	2912	5	_	_	NNP
37681	2912	6	=	=	SYM
37681	2912	7	_	_	NNP
37681	2912	8	QT	QT	NNP
37681	2912	9	_	_	NNP
37681	2912	10	.	.	.
37681	2913	1	Adding	add	VBG
37681	2913	2	,	,	,
37681	2913	3	_	_	NNP
37681	2913	4	MC	MC	NNP
37681	2913	5	_	_	NNP
37681	2913	6	+	+	NNP
37681	2913	7	_	_	NNP
37681	2913	8	NC	NC	NNP
37681	2913	9	_	_	NNP
37681	2913	10	=	=	SYM
37681	2913	11	_	_	NNP
37681	2913	12	AT	AT	NNP
37681	2913	13	_	_	NNP
37681	2913	14	.	.	.
37681	2914	1	If	if	IN
37681	2914	2	,	,	,
37681	2914	3	now	now	RB
37681	2914	4	,	,	,
37681	2914	5	_	_	NNP
37681	2914	6	ABC	ABC	NNP
37681	2914	7	_	_	NNP
37681	2914	8	is	be	VBZ
37681	2914	9	a	a	DT
37681	2914	10	right	right	JJ
37681	2914	11	triangle	triangle	NN
37681	2914	12	,	,	,
37681	2914	13	and	and	CC
37681	2914	14	if	if	IN
37681	2914	15	_	_	NNP
37681	2914	16	MC	MC	NNP
37681	2914	17	_	_	NNP
37681	2914	18	and	and	CC
37681	2914	19	_	_	NNP
37681	2914	20	NC	NC	NNP
37681	2914	21	_	_	NNP
37681	2914	22	are	be	VBP
37681	2914	23	squares	square	NNS
37681	2914	24	,	,	,
37681	2914	25	it	-PRON-	PRP
37681	2914	26	is	be	VBZ
37681	2914	27	easy	easy	JJ
37681	2914	28	to	to	TO
37681	2914	29	show	show	VB
37681	2914	30	that	that	IN
37681	2914	31	_	_	NNP
37681	2914	32	AT	AT	NNP
37681	2914	33	_	_	NNP
37681	2914	34	is	be	VBZ
37681	2914	35	a	a	DT
37681	2914	36	square	square	NN
37681	2914	37	,	,	,
37681	2914	38	and	and	CC
37681	2914	39	the	the	DT
37681	2914	40	proposition	proposition	NN
37681	2914	41	reduces	reduce	VBZ
37681	2914	42	to	to	IN
37681	2914	43	the	the	DT
37681	2914	44	Pythagorean	Pythagorean	NNP
37681	2914	45	Theorem	Theorem	NNP
37681	2914	46	.	.	.
37681	2915	1	The	the	DT
37681	2915	2	Arab	arab	JJ
37681	2915	3	writer	writer	NN
37681	2915	4	,	,	,
37681	2915	5	Al	Al	NNP
37681	2915	6	-	-	HYPH
37681	2915	7	Nair[=i]z[=i	Nair[=i]z[=i	NNP
37681	2915	8	]	]	-RRB-
37681	2915	9	(	(	-LRB-
37681	2915	10	died	die	VBN
37681	2915	11	about	about	RB
37681	2915	12	922	922	CD
37681	2915	13	A.D.	A.D.	NNP
37681	2915	14	)	)	-RRB-
37681	2915	15	,	,	,
37681	2915	16	attributes	attribute	VBZ
37681	2915	17	to	to	IN
37681	2915	18	Th[=a]bit	Th[=a]bit	NNP
37681	2915	19	ben	ben	NNP
37681	2915	20	Qurra	Qurra	NNP
37681	2915	21	(	(	-LRB-
37681	2915	22	826	826	CD
37681	2915	23	-	-	SYM
37681	2915	24	901	901	CD
37681	2915	25	A.D.	A.D.	NNP
37681	2915	26	)	)	-RRB-
37681	2915	27	a	a	DT
37681	2915	28	proof	proof	NN
37681	2915	29	substantially	substantially	RB
37681	2915	30	as	as	IN
37681	2915	31	follows	follow	VBZ
37681	2915	32	:	:	:
37681	2915	33	[	[	-LRB-
37681	2915	34	Illustration	illustration	NN
37681	2915	35	]	]	-RRB-
37681	2915	36	The	the	DT
37681	2915	37	four	four	CD
37681	2915	38	triangles	triangle	NNS
37681	2915	39	_	_	NNP
37681	2915	40	T	T	NNP
37681	2915	41	_	_	NNP
37681	2915	42	can	can	MD
37681	2915	43	be	be	VB
37681	2915	44	proved	prove	VBN
37681	2915	45	congruent	congruent	JJ
37681	2915	46	.	.	.
37681	2916	1	Then	then	RB
37681	2916	2	if	if	IN
37681	2916	3	we	-PRON-	PRP
37681	2916	4	take	take	VBP
37681	2916	5	from	from	IN
37681	2916	6	the	the	DT
37681	2916	7	whole	whole	JJ
37681	2916	8	figure	figure	NN
37681	2916	9	_	_	NNP
37681	2916	10	T	T	NNP
37681	2916	11	_	_	NNP
37681	2916	12	and	and	CC
37681	2916	13	_	_	NNP
37681	2916	14	T	T	NNP
37681	2916	15	'	'	''
37681	2916	16	_	_	NNP
37681	2916	17	,	,	,
37681	2916	18	we	-PRON-	PRP
37681	2916	19	have	have	VBP
37681	2916	20	left	leave	VBN
37681	2916	21	the	the	DT
37681	2916	22	squares	square	NNS
37681	2916	23	on	on	IN
37681	2916	24	the	the	DT
37681	2916	25	two	two	CD
37681	2916	26	sides	side	NNS
37681	2916	27	of	of	IN
37681	2916	28	the	the	DT
37681	2916	29	right	right	JJ
37681	2916	30	angle	angle	NN
37681	2916	31	.	.	.
37681	2917	1	If	if	IN
37681	2917	2	we	-PRON-	PRP
37681	2917	3	take	take	VBP
37681	2917	4	away	away	RB
37681	2917	5	the	the	DT
37681	2917	6	other	other	JJ
37681	2917	7	two	two	CD
37681	2917	8	triangles	triangle	NNS
37681	2917	9	instead	instead	RB
37681	2917	10	,	,	,
37681	2917	11	we	-PRON-	PRP
37681	2917	12	have	have	VBP
37681	2917	13	left	leave	VBN
37681	2917	14	the	the	DT
37681	2917	15	square	square	NN
37681	2917	16	on	on	IN
37681	2917	17	the	the	DT
37681	2917	18	hypotenuse	hypotenuse	NN
37681	2917	19	.	.	.
37681	2918	1	Therefore	therefore	RB
37681	2918	2	the	the	DT
37681	2918	3	former	former	JJ
37681	2918	4	is	be	VBZ
37681	2918	5	equivalent	equivalent	JJ
37681	2918	6	to	to	IN
37681	2918	7	the	the	DT
37681	2918	8	latter	latter	JJ
37681	2918	9	.	.	.
37681	2919	1	A	a	DT
37681	2919	2	proof	proof	NN
37681	2919	3	attributed	attribute	VBN
37681	2919	4	to	to	IN
37681	2919	5	the	the	DT
37681	2919	6	great	great	JJ
37681	2919	7	artist	artist	NN
37681	2919	8	,	,	,
37681	2919	9	Leonardo	Leonardo	NNP
37681	2919	10	da	da	NNP
37681	2919	11	Vinci	Vinci	NNP
37681	2919	12	(	(	-LRB-
37681	2919	13	1452	1452	CD
37681	2919	14	-	-	SYM
37681	2919	15	1519	1519	CD
37681	2919	16	)	)	-RRB-
37681	2919	17	,	,	,
37681	2919	18	is	be	VBZ
37681	2919	19	as	as	IN
37681	2919	20	follows	follow	VBZ
37681	2919	21	:	:	:
37681	2919	22	[	[	-LRB-
37681	2919	23	Illustration	illustration	NN
37681	2919	24	]	]	-RRB-
37681	2919	25	The	the	DT
37681	2919	26	construction	construction	NN
37681	2919	27	of	of	IN
37681	2919	28	the	the	DT
37681	2919	29	following	follow	VBG
37681	2919	30	figure	figure	NN
37681	2919	31	is	be	VBZ
37681	2919	32	evident	evident	JJ
37681	2919	33	.	.	.
37681	2920	1	It	-PRON-	PRP
37681	2920	2	is	be	VBZ
37681	2920	3	easily	easily	RB
37681	2920	4	shown	show	VBN
37681	2920	5	that	that	IN
37681	2920	6	the	the	DT
37681	2920	7	four	four	CD
37681	2920	8	quadrilaterals	quadrilateral	NNS
37681	2920	9	_	_	NNP
37681	2920	10	ABMX	ABMX	NNP
37681	2920	11	_	_	NNP
37681	2920	12	,	,	,
37681	2920	13	_	_	NNP
37681	2920	14	XNCA	XNCA	NNP
37681	2920	15	_	_	NNP
37681	2920	16	,	,	,
37681	2920	17	_	_	NNP
37681	2920	18	SBCP	SBCP	NNP
37681	2920	19	_	_	NNP
37681	2920	20	,	,	,
37681	2920	21	and	and	CC
37681	2920	22	_	_	NNP
37681	2920	23	SRQP	SRQP	NNP
37681	2920	24	_	_	NNP
37681	2920	25	are	be	VBP
37681	2920	26	congruent	congruent	JJ
37681	2920	27	.	.	.
37681	2921	1	[	[	-LRB-
37681	2921	2	therefore	therefore	RB
37681	2921	3	]	]	-RRB-
37681	2921	4	_	_	NNP
37681	2921	5	ABMXNCA	ABMXNCA	NNP
37681	2921	6	_	_	NNP
37681	2921	7	equals	equal	VBZ
37681	2921	8	_	_	NNP
37681	2921	9	SBCPQRS	SBCPQRS	NNP
37681	2921	10	_	_	NNP
37681	2921	11	but	but	CC
37681	2921	12	is	be	VBZ
37681	2921	13	not	not	RB
37681	2921	14	congruent	congruent	JJ
37681	2921	15	to	to	IN
37681	2921	16	it	-PRON-	PRP
37681	2921	17	,	,	,
37681	2921	18	the	the	DT
37681	2921	19	congruent	congruent	JJ
37681	2921	20	quadrilaterals	quadrilateral	NNS
37681	2921	21	being	be	VBG
37681	2921	22	differently	differently	RB
37681	2921	23	arranged	arrange	VBN
37681	2921	24	.	.	.
37681	2922	1	Subtract	subtract	VB
37681	2922	2	the	the	DT
37681	2922	3	congruent	congruent	JJ
37681	2922	4	triangles	triangle	NNS
37681	2922	5	_	_	NNP
37681	2922	6	MXN	MXN	NNP
37681	2922	7	_	_	NNP
37681	2922	8	,	,	,
37681	2922	9	_	_	NNP
37681	2922	10	ABC	ABC	NNP
37681	2922	11	_	_	NNP
37681	2922	12	,	,	,
37681	2922	13	_	_	NNP
37681	2922	14	RAQ	RAQ	NNP
37681	2922	15	_	_	NNP
37681	2922	16	,	,	,
37681	2922	17	and	and	CC
37681	2922	18	the	the	DT
37681	2922	19	proposition	proposition	NN
37681	2922	20	is	be	VBZ
37681	2922	21	proved	prove	VBN
37681	2922	22	.	.	.
37681	2923	1	[	[	-LRB-
37681	2923	2	80	80	CD
37681	2923	3	]	]	-RRB-
37681	2923	4	The	the	DT
37681	2923	5	following	follow	VBG
37681	2923	6	is	be	VBZ
37681	2923	7	an	an	DT
37681	2923	8	interesting	interesting	JJ
37681	2923	9	proof	proof	NN
37681	2923	10	of	of	IN
37681	2923	11	the	the	DT
37681	2923	12	proposition	proposition	NN
37681	2923	13	:	:	:
37681	2923	14	Let	let	VB
37681	2923	15	_	_	NNP
37681	2923	16	ABC	ABC	NNP
37681	2923	17	_	_	NNP
37681	2923	18	be	be	VB
37681	2923	19	the	the	DT
37681	2923	20	original	original	JJ
37681	2923	21	triangle	triangle	NN
37681	2923	22	,	,	,
37681	2923	23	with	with	IN
37681	2923	24	_	_	NNP
37681	2923	25	AB	AB	NNP
37681	2923	26	_	_	NNP
37681	2923	27	<	<	XX
37681	2923	28	_	_	NNP
37681	2923	29	BC	BC	NNP
37681	2923	30	_	_	NNP
37681	2923	31	.	.	.
37681	2924	1	Turn	turn	VB
37681	2924	2	the	the	DT
37681	2924	3	triangle	triangle	NN
37681	2924	4	about	about	IN
37681	2924	5	_	_	NNP
37681	2924	6	B	B	NNP
37681	2924	7	_	_	NNP
37681	2924	8	,	,	,
37681	2924	9	through	through	IN
37681	2924	10	90	90	CD
37681	2924	11	°	°	NNS
37681	2924	12	,	,	,
37681	2924	13	until	until	IN
37681	2924	14	it	-PRON-	PRP
37681	2924	15	comes	come	VBZ
37681	2924	16	into	into	IN
37681	2924	17	the	the	DT
37681	2924	18	position	position	NN
37681	2924	19	_	_	NNP
37681	2924	20	A'BC	A'BC	NNP
37681	2924	21	'	'	``
37681	2924	22	_	_	XX
37681	2924	23	.	.	.
37681	2925	1	Then	then	RB
37681	2925	2	because	because	IN
37681	2925	3	it	-PRON-	PRP
37681	2925	4	has	have	VBZ
37681	2925	5	been	be	VBN
37681	2925	6	turned	turn	VBN
37681	2925	7	through	through	RP
37681	2925	8	90	90	CD
37681	2925	9	°	°	NNS
37681	2925	10	,	,	,
37681	2925	11	_	_	NNP
37681	2925	12	C'A'P	C'A'P	NNP
37681	2925	13	_	_	NNP
37681	2925	14	will	will	MD
37681	2925	15	be	be	VB
37681	2925	16	perpendicular	perpendicular	JJ
37681	2925	17	to	to	IN
37681	2925	18	_	_	NNP
37681	2925	19	AC	AC	NNP
37681	2925	20	_	_	NNP
37681	2925	21	.	.	.
37681	2926	1	Then	then	RB
37681	2926	2	1/2(_AB_)^2	1/2(_ab_)^2	CD
37681	2926	3	=	=	SYM
37681	2926	4	[	[	-LRB-
37681	2926	5	triangle]_ABA	triangle]_aba	UH
37681	2926	6	'	'	``
37681	2926	7	_	_	NNP
37681	2926	8	,	,	,
37681	2926	9	and	and	CC
37681	2926	10	1/2(_BC'_)^2	1/2(_bc'_)^2	CD
37681	2926	11	=	=	SYM
37681	2926	12	[	[	-LRB-
37681	2926	13	triangle]_BC'C	triangle]_BC'C	NNP
37681	2926	14	_	_	NNP
37681	2926	15	,	,	,
37681	2926	16	because	because	IN
37681	2926	17	_	_	NNP
37681	2926	18	BC	BC	NNP
37681	2926	19	_	_	NNP
37681	2926	20	=	=	SYM
37681	2926	21	_	_	NNP
37681	2926	22	BC	BC	NNP
37681	2926	23	'	'	POS
37681	2926	24	_	_	NNP
37681	2926	25	.	.	.
37681	2927	1	[	[	-LRB-
37681	2927	2	therefore	therefore	RB
37681	2927	3	]	]	-RRB-
37681	2927	4	1/2((_AB_)^2	1/2((_ab_)^2	CD
37681	2927	5	+	+	NFP
37681	2927	6	(	(	-LRB-
37681	2927	7	_	_	NNP
37681	2927	8	BC_)^2	BC_)^2	NNP
37681	2927	9	)	)	-RRB-
37681	2927	10	=	=	NFP
37681	2927	11	[	[	-LRB-
37681	2927	12	triangle]_ABA	triangle]_aba	UH
37681	2927	13	'	'	``
37681	2927	14	_	_	NN
37681	2927	15	+	+	CC
37681	2927	16	[	[	-LRB-
37681	2927	17	triangle]_BC'C	triangle]_BC'C	NNP
37681	2927	18	_	_	NNP
37681	2927	19	.	.	.
37681	2928	1	[	[	-LRB-
37681	2928	2	therefore	therefore	RB
37681	2928	3	]	]	-RRB-
37681	2928	4	1/2((_AB_)^2	1/2((_ab_)^2	CD
37681	2928	5	+	+	NFP
37681	2928	6	(	(	-LRB-
37681	2928	7	_	_	NNP
37681	2928	8	BC_)^2	BC_)^2	NNP
37681	2928	9	)	)	-RRB-
37681	2928	10	=	=	NFP
37681	2928	11	[	[	-LRB-
37681	2928	12	triangle]_AC'A	triangle]_ac'a	NN
37681	2928	13	'	'	``
37681	2928	14	_	_	NN
37681	2928	15	+	+	CC
37681	2928	16	[	[	-LRB-
37681	2928	17	triangle]_A'C'C	triangle]_A'C'C	NNP
37681	2928	18	_	_	NNP
37681	2928	19	[	[	-LRB-
37681	2928	20	Illustration	illustration	NN
37681	2928	21	]	]	-RRB-
37681	2928	22	(	(	-LRB-
37681	2928	23	For	for	IN
37681	2928	24	[	[	-LRB-
37681	2928	25	triangle]_ABA	triangle]_ABA	NNP
37681	2928	26	'	'	``
37681	2928	27	_	_	NN
37681	2928	28	+	+	CC
37681	2928	29	[	[	-LRB-
37681	2928	30	triangle]_BC'A	triangle]_bc'a	NN
37681	2928	31	'	'	``
37681	2928	32	_	_	NN
37681	2928	33	+	+	CC
37681	2928	34	[	[	-LRB-
37681	2928	35	triangle]_A'C'C	triangle]_A'C'C	NNP
37681	2928	36	_	_	NNP
37681	2928	37	is	be	VBZ
37681	2928	38	the	the	DT
37681	2928	39	second	second	JJ
37681	2928	40	member	member	NN
37681	2928	41	of	of	IN
37681	2928	42	both	both	DT
37681	2928	43	equations	equation	NNS
37681	2928	44	.	.	.
37681	2928	45	)	)	-RRB-
37681	2929	1	=	=	SYM
37681	2929	2	1/2_A'C	1/2_a'c	LS
37681	2929	3	'	'	``
37681	2929	4	_	_	NNP
37681	2929	5	·	·	NFP
37681	2929	6	_	_	NNP
37681	2929	7	AP	AP	NNP
37681	2929	8	_	_	NNP
37681	2929	9	+	+	CC
37681	2929	10	1/2_A'C	1/2_a'c	NN
37681	2929	11	'	'	''
37681	2929	12	_	_	NNP
37681	2929	13	·	·	NFP
37681	2929	14	_	_	NNP
37681	2929	15	PC	PC	NNP
37681	2929	16	_	_	NN
37681	2929	17	=	=	SYM
37681	2929	18	1/2_A'C	1/2_a'c	NN
37681	2929	19	'	'	``
37681	2929	20	_	_	NN
37681	2929	21	·	·	NFP
37681	2929	22	_	_	NNP
37681	2929	23	AC	AC	NNP
37681	2929	24	_	_	NNP
37681	2929	25	=	=	SYM
37681	2929	26	1/2(_AC_)^2	1/2(_ac_)^2	CD
37681	2929	27	.	.	.
37681	2930	1	[	[	-LRB-
37681	2930	2	therefore	therefore	RB
37681	2930	3	]	]	-RRB-
37681	2930	4	(	(	-LRB-
37681	2930	5	_	_	NNP
37681	2930	6	AB_)^2	AB_)^2	NNP
37681	2930	7	+	+	NFP
37681	2930	8	(	(	-LRB-
37681	2930	9	_	_	NNP
37681	2930	10	BC_)^2	BC_)^2	NNP
37681	2930	11	=	=	NFP
37681	2930	12	(	(	-LRB-
37681	2930	13	_	_	NNP
37681	2930	14	AC_)^2	AC_)^2	NNP
37681	2930	15	.	.	.
37681	2931	1	The	the	DT
37681	2931	2	Pythagorean	Pythagorean	NNP
37681	2931	3	Theorem	Theorem	NNP
37681	2931	4	,	,	,
37681	2931	5	as	as	IN
37681	2931	6	it	-PRON-	PRP
37681	2931	7	is	be	VBZ
37681	2931	8	generally	generally	RB
37681	2931	9	called	call	VBN
37681	2931	10	,	,	,
37681	2931	11	has	have	VBZ
37681	2931	12	had	have	VBN
37681	2931	13	other	other	JJ
37681	2931	14	names	name	NNS
37681	2931	15	.	.	.
37681	2932	1	It	-PRON-	PRP
37681	2932	2	is	be	VBZ
37681	2932	3	not	not	RB
37681	2932	4	uncommonly	uncommonly	RB
37681	2932	5	called	call	VBN
37681	2932	6	the	the	DT
37681	2932	7	_	_	NNP
37681	2932	8	pons	pons	NNP
37681	2932	9	asinorum	asinorum	NNP
37681	2932	10	_	_	NNP
37681	2932	11	(	(	-LRB-
37681	2932	12	see	see	VB
37681	2932	13	page	page	NN
37681	2932	14	174	174	CD
37681	2932	15	)	)	-RRB-
37681	2932	16	in	in	IN
37681	2932	17	France	France	NNP
37681	2932	18	.	.	.
37681	2933	1	The	the	DT
37681	2933	2	Arab	arab	JJ
37681	2933	3	writers	writer	NNS
37681	2933	4	called	call	VBD
37681	2933	5	it	-PRON-	PRP
37681	2933	6	the	the	DT
37681	2933	7	Figure	figure	NN
37681	2933	8	of	of	IN
37681	2933	9	the	the	DT
37681	2933	10	Bride	Bride	NNP
37681	2933	11	,	,	,
37681	2933	12	although	although	IN
37681	2933	13	the	the	DT
37681	2933	14	reason	reason	NN
37681	2933	15	for	for	IN
37681	2933	16	this	this	DT
37681	2933	17	name	name	NN
37681	2933	18	is	be	VBZ
37681	2933	19	unknown	unknown	JJ
37681	2933	20	;	;	:
37681	2933	21	possibly	possibly	RB
37681	2933	22	two	two	CD
37681	2933	23	being	be	VBG
37681	2933	24	joined	join	VBN
37681	2933	25	in	in	IN
37681	2933	26	one	one	NN
37681	2933	27	has	have	VBZ
37681	2933	28	something	something	NN
37681	2933	29	to	to	TO
37681	2933	30	do	do	VB
37681	2933	31	with	with	IN
37681	2933	32	it	-PRON-	PRP
37681	2933	33	.	.	.
37681	2934	1	It	-PRON-	PRP
37681	2934	2	has	have	VBZ
37681	2934	3	also	also	RB
37681	2934	4	been	be	VBN
37681	2934	5	called	call	VBN
37681	2934	6	the	the	DT
37681	2934	7	Bride	Bride	NNP
37681	2934	8	's	's	POS
37681	2934	9	Chair	Chair	NNP
37681	2934	10	,	,	,
37681	2934	11	and	and	CC
37681	2934	12	the	the	DT
37681	2934	13	shape	shape	NN
37681	2934	14	of	of	IN
37681	2934	15	the	the	DT
37681	2934	16	Euclid	euclid	JJ
37681	2934	17	figure	figure	NN
37681	2934	18	is	be	VBZ
37681	2934	19	not	not	RB
37681	2934	20	unlike	unlike	IN
37681	2934	21	the	the	DT
37681	2934	22	chair	chair	NN
37681	2934	23	that	that	WDT
37681	2934	24	a	a	DT
37681	2934	25	slave	slave	NN
37681	2934	26	carries	carry	VBZ
37681	2934	27	on	on	IN
37681	2934	28	his	-PRON-	PRP$
37681	2934	29	back	back	NN
37681	2934	30	,	,	,
37681	2934	31	in	in	IN
37681	2934	32	which	which	WDT
37681	2934	33	the	the	DT
37681	2934	34	Eastern	eastern	JJ
37681	2934	35	bride	bride	NN
37681	2934	36	is	be	VBZ
37681	2934	37	sometimes	sometimes	RB
37681	2934	38	transported	transport	VBN
37681	2934	39	to	to	IN
37681	2934	40	the	the	DT
37681	2934	41	wedding	wedding	NN
37681	2934	42	ceremony	ceremony	NN
37681	2934	43	.	.	.
37681	2935	1	Schopenhauer	Schopenhauer	NNP
37681	2935	2	,	,	,
37681	2935	3	the	the	DT
37681	2935	4	German	german	JJ
37681	2935	5	philosopher	philosopher	NN
37681	2935	6	,	,	,
37681	2935	7	referring	refer	VBG
37681	2935	8	to	to	IN
37681	2935	9	the	the	DT
37681	2935	10	figure	figure	NN
37681	2935	11	,	,	,
37681	2935	12	speaks	speak	VBZ
37681	2935	13	of	of	IN
37681	2935	14	it	-PRON-	PRP
37681	2935	15	as	as	IN
37681	2935	16	"	"	``
37681	2935	17	a	a	DT
37681	2935	18	proof	proof	NN
37681	2935	19	walking	walk	VBG
37681	2935	20	on	on	IN
37681	2935	21	stilts	stilt	NNS
37681	2935	22	,	,	,
37681	2935	23	"	"	''
37681	2935	24	and	and	CC
37681	2935	25	as	as	IN
37681	2935	26	"	"	``
37681	2935	27	a	a	DT
37681	2935	28	mouse	mouse	NN
37681	2935	29	-	-	HYPH
37681	2935	30	trap	trap	NN
37681	2935	31	proof	proof	NN
37681	2935	32	.	.	.
37681	2935	33	"	"	''
37681	2936	1	An	an	DT
37681	2936	2	interesting	interesting	JJ
37681	2936	3	theory	theory	NN
37681	2936	4	suggested	suggest	VBN
37681	2936	5	by	by	IN
37681	2936	6	the	the	DT
37681	2936	7	proposition	proposition	NN
37681	2936	8	is	be	VBZ
37681	2936	9	that	that	DT
37681	2936	10	of	of	IN
37681	2936	11	computing	compute	VBG
37681	2936	12	the	the	DT
37681	2936	13	sides	side	NNS
37681	2936	14	of	of	IN
37681	2936	15	right	right	JJ
37681	2936	16	triangles	triangle	NNS
37681	2936	17	so	so	IN
37681	2936	18	that	that	IN
37681	2936	19	they	-PRON-	PRP
37681	2936	20	shall	shall	MD
37681	2936	21	be	be	VB
37681	2936	22	represented	represent	VBN
37681	2936	23	by	by	IN
37681	2936	24	rational	rational	JJ
37681	2936	25	numbers	number	NNS
37681	2936	26	.	.	.
37681	2937	1	Pythagoras	Pythagoras	NNP
37681	2937	2	seems	seem	VBZ
37681	2937	3	to	to	TO
37681	2937	4	have	have	VB
37681	2937	5	been	be	VBN
37681	2937	6	the	the	DT
37681	2937	7	first	first	JJ
37681	2937	8	to	to	TO
37681	2937	9	take	take	VB
37681	2937	10	up	up	RP
37681	2937	11	this	this	DT
37681	2937	12	theory	theory	NN
37681	2937	13	,	,	,
37681	2937	14	although	although	IN
37681	2937	15	such	such	JJ
37681	2937	16	numbers	number	NNS
37681	2937	17	were	be	VBD
37681	2937	18	applied	apply	VBN
37681	2937	19	to	to	IN
37681	2937	20	the	the	DT
37681	2937	21	right	right	JJ
37681	2937	22	triangle	triangle	NN
37681	2937	23	before	before	IN
37681	2937	24	his	-PRON-	PRP$
37681	2937	25	time	time	NN
37681	2937	26	,	,	,
37681	2937	27	and	and	CC
37681	2937	28	Proclus	Proclus	NNP
37681	2937	29	tells	tell	VBZ
37681	2937	30	us	-PRON-	PRP
37681	2937	31	that	that	IN
37681	2937	32	Plato	Plato	NNP
37681	2937	33	also	also	RB
37681	2937	34	contributed	contribute	VBD
37681	2937	35	to	to	IN
37681	2937	36	it	-PRON-	PRP
37681	2937	37	.	.	.
37681	2938	1	The	the	DT
37681	2938	2	rule	rule	NN
37681	2938	3	of	of	IN
37681	2938	4	Pythagoras	Pythagoras	NNP
37681	2938	5	,	,	,
37681	2938	6	put	put	VBN
37681	2938	7	in	in	IN
37681	2938	8	modern	modern	JJ
37681	2938	9	symbols	symbol	NNS
37681	2938	10	,	,	,
37681	2938	11	was	be	VBD
37681	2938	12	as	as	IN
37681	2938	13	follows	follow	VBZ
37681	2938	14	:	:	:
37681	2938	15	_	_	NNP
37681	2938	16	n_^2	n_^2	NNP
37681	2938	17	+	+	NFP
37681	2938	18	(	(	-LRB-
37681	2938	19	(	(	-LRB-
37681	2938	20	_	_	NNP
37681	2938	21	n_^2	n_^2	NNP
37681	2938	22	-	-	HYPH
37681	2938	23	1)/2)^2	1)/2)^2	NNP
37681	2938	24	=	=	NFP
37681	2938	25	(	(	-LRB-
37681	2938	26	(	(	-LRB-
37681	2938	27	_	_	NNP
37681	2938	28	n_^2	n_^2	NNP
37681	2938	29	+	+	SYM
37681	2938	30	1)/2)^2	1)/2)^2	CD
37681	2938	31	,	,	,
37681	2938	32	the	the	DT
37681	2938	33	sides	side	NNS
37681	2938	34	being	be	VBG
37681	2938	35	_	_	NNP
37681	2938	36	n	n	CC
37681	2938	37	_	_	NNP
37681	2938	38	,	,	,
37681	2938	39	(	(	-LRB-
37681	2938	40	_	_	NNP
37681	2938	41	n_^2	n_^2	NNP
37681	2938	42	-	-	HYPH
37681	2938	43	1)/2	1)/2	CD
37681	2938	44	,	,	,
37681	2938	45	and	and	CC
37681	2938	46	(	(	-LRB-
37681	2938	47	_	_	NNP
37681	2938	48	n_^2	n_^2	NNP
37681	2938	49	+	+	SYM
37681	2938	50	1)/2	1)/2	CD
37681	2938	51	.	.	.
37681	2939	1	If	if	IN
37681	2939	2	for	for	IN
37681	2939	3	_	_	NNP
37681	2939	4	n	n	CC
37681	2939	5	_	_	NNP
37681	2939	6	we	-PRON-	PRP
37681	2939	7	put	put	VBD
37681	2939	8	3	3	CD
37681	2939	9	,	,	,
37681	2939	10	we	-PRON-	PRP
37681	2939	11	have	have	VBP
37681	2939	12	3	3	CD
37681	2939	13	,	,	,
37681	2939	14	4	4	CD
37681	2939	15	,	,	,
37681	2939	16	5	5	CD
37681	2939	17	.	.	.
37681	2940	1	If	if	IN
37681	2940	2	we	-PRON-	PRP
37681	2940	3	take	take	VBP
37681	2940	4	the	the	DT
37681	2940	5	various	various	JJ
37681	2940	6	odd	odd	JJ
37681	2940	7	numbers	number	NNS
37681	2940	8	,	,	,
37681	2940	9	we	-PRON-	PRP
37681	2940	10	have	have	VBP
37681	2940	11	_	_	NNP
37681	2940	12	n	n	CC
37681	2940	13	_	_	NNP
37681	2940	14	=	=	SYM
37681	2940	15	1	1	CD
37681	2940	16	,	,	,
37681	2940	17	3	3	CD
37681	2940	18	,	,	,
37681	2940	19	5	5	CD
37681	2940	20	,	,	,
37681	2940	21	7	7	CD
37681	2940	22	,	,	,
37681	2940	23	9	9	CD
37681	2940	24	,	,	,
37681	2940	25	·	·	NFP
37681	2940	26	·	·	NFP
37681	2940	27	·	·	NFP
37681	2940	28	,	,	,
37681	2940	29	(	(	-LRB-
37681	2940	30	_	_	NNP
37681	2940	31	n_^2	n_^2	NNP
37681	2940	32	-	-	HYPH
37681	2940	33	1)/2	1)/2	NNP
37681	2940	34	=	=	SYM
37681	2940	35	0	0	CD
37681	2940	36	,	,	,
37681	2940	37	4	4	CD
37681	2940	38	,	,	,
37681	2940	39	12	12	CD
37681	2940	40	,	,	,
37681	2940	41	24	24	CD
37681	2940	42	,	,	,
37681	2940	43	40	40	CD
37681	2940	44	,	,	,
37681	2940	45	·	·	NFP
37681	2940	46	·	·	NFP
37681	2940	47	·	·	NFP
37681	2940	48	,	,	,
37681	2940	49	(	(	-LRB-
37681	2940	50	_	_	NNP
37681	2940	51	n_^2	n_^2	NNP
37681	2940	52	+	+	SYM
37681	2940	53	1)/2	1)/2	CD
37681	2940	54	=	=	SYM
37681	2940	55	1	1	CD
37681	2940	56	,	,	,
37681	2940	57	5	5	CD
37681	2940	58	,	,	,
37681	2940	59	13	13	CD
37681	2940	60	,	,	,
37681	2940	61	25	25	CD
37681	2940	62	,	,	,
37681	2940	63	41	41	CD
37681	2940	64	,	,	,
37681	2940	65	·	·	NFP
37681	2940	66	·	·	NFP
37681	2940	67	·	·	NFP
37681	2940	68	.	.	.
37681	2941	1	Of	of	RB
37681	2941	2	course	course	RB
37681	2941	3	_	_	NNP
37681	2941	4	n	n	CC
37681	2941	5	_	_	NNP
37681	2941	6	may	may	MD
37681	2941	7	be	be	VB
37681	2941	8	even	even	RB
37681	2941	9	,	,	,
37681	2941	10	giving	give	VBG
37681	2941	11	fractional	fractional	JJ
37681	2941	12	values	value	NNS
37681	2941	13	.	.	.
37681	2942	1	Thus	thus	RB
37681	2942	2	,	,	,
37681	2942	3	for	for	IN
37681	2942	4	_	_	NNP
37681	2942	5	n	n	CC
37681	2942	6	_	_	NNP
37681	2942	7	=	=	SYM
37681	2942	8	2	2	CD
37681	2942	9	we	-PRON-	PRP
37681	2942	10	have	have	VBP
37681	2942	11	for	for	IN
37681	2942	12	the	the	DT
37681	2942	13	three	three	CD
37681	2942	14	sides	side	NNS
37681	2942	15	,	,	,
37681	2942	16	2	2	CD
37681	2942	17	,	,	,
37681	2942	18	1	1	CD
37681	2942	19	1/2	1/2	CD
37681	2942	20	,	,	,
37681	2942	21	2	2	CD
37681	2942	22	1/2	1/2	CD
37681	2942	23	.	.	.
37681	2943	1	Other	other	JJ
37681	2943	2	formulas	formula	NNS
37681	2943	3	are	be	VBP
37681	2943	4	also	also	RB
37681	2943	5	known	know	VBN
37681	2943	6	.	.	.
37681	2944	1	Plato	Plato	NNP
37681	2944	2	's	's	POS
37681	2944	3	,	,	,
37681	2944	4	for	for	IN
37681	2944	5	example	example	NN
37681	2944	6	,	,	,
37681	2944	7	is	be	VBZ
37681	2944	8	as	as	IN
37681	2944	9	follows	follow	VBZ
37681	2944	10	:	:	:
37681	2944	11	(	(	-LRB-
37681	2944	12	2_n_)^2	2_n_)^2	CD
37681	2944	13	+	+	NFP
37681	2944	14	(	(	-LRB-
37681	2944	15	_	_	NNP
37681	2944	16	n_^2	n_^2	NNP
37681	2944	17	-	-	HYPH
37681	2944	18	1)^2	1)^2	NNP
37681	2944	19	=	=	NFP
37681	2944	20	(	(	-LRB-
37681	2944	21	_	_	NNP
37681	2944	22	n_^2	n_^2	NNP
37681	2944	23	+	+	SYM
37681	2944	24	1)^2	1)^2	NNP
37681	2944	25	.	.	.
37681	2945	1	If	if	IN
37681	2945	2	2_n	2_n	CD
37681	2945	3	_	_	NNP
37681	2945	4	=	=	SYM
37681	2945	5	2	2	CD
37681	2945	6	,	,	,
37681	2945	7	4	4	CD
37681	2945	8	,	,	,
37681	2945	9	6	6	CD
37681	2945	10	,	,	,
37681	2945	11	8	8	CD
37681	2945	12	,	,	,
37681	2945	13	10	10	CD
37681	2945	14	,	,	,
37681	2945	15	·	·	NFP
37681	2945	16	·	·	NFP
37681	2945	17	·	·	NFP
37681	2945	18	,	,	,
37681	2945	19	then	then	RB
37681	2945	20	_	_	NNP
37681	2945	21	n_^2	n_^2	NNP
37681	2945	22	-	-	HYPH
37681	2945	23	1	1	NNP
37681	2945	24	=	=	SYM
37681	2945	25	0	0	CD
37681	2945	26	,	,	,
37681	2945	27	3	3	CD
37681	2945	28	,	,	,
37681	2945	29	8	8	CD
37681	2945	30	,	,	,
37681	2945	31	15	15	CD
37681	2945	32	,	,	,
37681	2945	33	24	24	CD
37681	2945	34	,	,	,
37681	2945	35	·	·	NFP
37681	2945	36	·	·	NFP
37681	2945	37	·	·	NFP
37681	2945	38	,	,	,
37681	2945	39	and	and	CC
37681	2945	40	_	_	NNP
37681	2945	41	n_^2	n_^2	NNP
37681	2945	42	+	+	SYM
37681	2945	43	1	1	CD
37681	2945	44	=	=	SYM
37681	2945	45	2	2	CD
37681	2945	46	,	,	,
37681	2945	47	5	5	CD
37681	2945	48	,	,	,
37681	2945	49	10	10	CD
37681	2945	50	,	,	,
37681	2945	51	17	17	CD
37681	2945	52	,	,	,
37681	2945	53	26	26	CD
37681	2945	54	,	,	,
37681	2945	55	·	·	NFP
37681	2945	56	·	·	NFP
37681	2945	57	·	·	NFP
37681	2945	58	.	.	.
37681	2946	1	This	this	DT
37681	2946	2	formula	formula	NN
37681	2946	3	evidently	evidently	RB
37681	2946	4	comes	come	VBZ
37681	2946	5	from	from	IN
37681	2946	6	that	that	DT
37681	2946	7	of	of	IN
37681	2946	8	Pythagoras	Pythagoras	NNP
37681	2946	9	by	by	IN
37681	2946	10	doubling	double	VBG
37681	2946	11	the	the	DT
37681	2946	12	sides	side	NNS
37681	2946	13	of	of	IN
37681	2946	14	the	the	DT
37681	2946	15	squares	square	NNS
37681	2946	16	.	.	.
37681	2947	1	[	[	-LRB-
37681	2947	2	81	81	CD
37681	2947	3	]	]	-RRB-
37681	2947	4	THEOREM	theorem	NN
37681	2947	5	.	.	.
37681	2948	1	_	_	NNP
37681	2948	2	In	in	IN
37681	2948	3	any	any	DT
37681	2948	4	triangle	triangle	NN
37681	2948	5	the	the	DT
37681	2948	6	square	square	NN
37681	2948	7	of	of	IN
37681	2948	8	the	the	DT
37681	2948	9	side	side	NN
37681	2948	10	opposite	opposite	IN
37681	2948	11	an	an	DT
37681	2948	12	acute	acute	JJ
37681	2948	13	angle	angle	NN
37681	2948	14	is	be	VBZ
37681	2948	15	equal	equal	JJ
37681	2948	16	to	to	IN
37681	2948	17	the	the	DT
37681	2948	18	sum	sum	NN
37681	2948	19	of	of	IN
37681	2948	20	the	the	DT
37681	2948	21	squares	square	NNS
37681	2948	22	of	of	IN
37681	2948	23	the	the	DT
37681	2948	24	other	other	JJ
37681	2948	25	two	two	CD
37681	2948	26	sides	side	NNS
37681	2948	27	diminished	diminish	VBN
37681	2948	28	by	by	IN
37681	2948	29	twice	twice	PDT
37681	2948	30	the	the	DT
37681	2948	31	product	product	NN
37681	2948	32	of	of	IN
37681	2948	33	one	one	CD
37681	2948	34	of	of	IN
37681	2948	35	those	those	DT
37681	2948	36	sides	side	NNS
37681	2948	37	by	by	IN
37681	2948	38	the	the	DT
37681	2948	39	projection	projection	NN
37681	2948	40	of	of	IN
37681	2948	41	the	the	DT
37681	2948	42	other	other	JJ
37681	2948	43	upon	upon	IN
37681	2948	44	that	that	DT
37681	2948	45	side	side	NN
37681	2948	46	.	.	.
37681	2948	47	_	_	NNP
37681	2948	48	THEOREM	THEOREM	NNP
37681	2948	49	.	.	.
37681	2949	1	_	_	NNP
37681	2949	2	A	a	DT
37681	2949	3	similar	similar	JJ
37681	2949	4	statement	statement	NN
37681	2949	5	for	for	IN
37681	2949	6	the	the	DT
37681	2949	7	obtuse	obtuse	JJ
37681	2949	8	triangle	triangle	NN
37681	2949	9	.	.	.
37681	2949	10	_	_	NNP
37681	2949	11	These	these	DT
37681	2949	12	two	two	CD
37681	2949	13	propositions	proposition	NNS
37681	2949	14	are	be	VBP
37681	2949	15	usually	usually	RB
37681	2949	16	proved	prove	VBN
37681	2949	17	by	by	IN
37681	2949	18	the	the	DT
37681	2949	19	help	help	NN
37681	2949	20	of	of	IN
37681	2949	21	the	the	DT
37681	2949	22	Pythagorean	Pythagorean	NNP
37681	2949	23	Theorem	Theorem	NNP
37681	2949	24	.	.	.
37681	2950	1	Some	some	DT
37681	2950	2	writers	writer	NNS
37681	2950	3	,	,	,
37681	2950	4	however	however	RB
37681	2950	5	,	,	,
37681	2950	6	actually	actually	RB
37681	2950	7	construct	construct	VBP
37681	2950	8	the	the	DT
37681	2950	9	squares	square	NNS
37681	2950	10	and	and	CC
37681	2950	11	give	give	VB
37681	2950	12	a	a	DT
37681	2950	13	proof	proof	NN
37681	2950	14	similar	similar	JJ
37681	2950	15	to	to	IN
37681	2950	16	the	the	DT
37681	2950	17	one	one	CD
37681	2950	18	in	in	IN
37681	2950	19	that	that	DT
37681	2950	20	proposition	proposition	NN
37681	2950	21	.	.	.
37681	2951	1	This	this	DT
37681	2951	2	plan	plan	NN
37681	2951	3	goes	go	VBZ
37681	2951	4	back	back	RB
37681	2951	5	at	at	IN
37681	2951	6	least	least	RBS
37681	2951	7	to	to	IN
37681	2951	8	Gregoire	Gregoire	NNP
37681	2951	9	de	de	NNP
37681	2951	10	St.	St.	NNP
37681	2951	11	Vincent	Vincent	NNP
37681	2951	12	(	(	-LRB-
37681	2951	13	1647	1647	CD
37681	2951	14	)	)	-RRB-
37681	2951	15	.	.	.
37681	2952	1	[	[	-LRB-
37681	2952	2	Illustration	illustration	NN
37681	2952	3	]	]	-RRB-
37681	2952	4	It	-PRON-	PRP
37681	2952	5	should	should	MD
37681	2952	6	be	be	VB
37681	2952	7	observed	observe	VBN
37681	2952	8	that	that	IN
37681	2952	9	_	_	NNP
37681	2952	10	a_^2	a_^2	NNP
37681	2952	11	=	=	SYM
37681	2952	12	_	_	NNP
37681	2952	13	b_^2	b_^2	NNP
37681	2952	14	+	+	NNP
37681	2952	15	_	_	NNP
37681	2952	16	c_^2	c_^2	NNP
37681	2952	17	-	-	HYPH
37681	2952	18	2_b'c	2_b'c	CD
37681	2952	19	_	_	NNP
37681	2952	20	.	.	.
37681	2953	1	If	if	IN
37681	2953	2	[	[	-LRB-
37681	2953	3	L]_A	L]_A	NNS
37681	2953	4	_	_	NNP
37681	2953	5	=	=	SYM
37681	2953	6	90	90	CD
37681	2953	7	°	°	NNS
37681	2953	8	,	,	,
37681	2953	9	then	then	RB
37681	2953	10	_	_	NNP
37681	2953	11	b	b	NNP
37681	2953	12	'	'	``
37681	2953	13	_	_	NNP
37681	2953	14	=	=	SYM
37681	2953	15	0	0	CD
37681	2953	16	,	,	,
37681	2953	17	and	and	CC
37681	2953	18	this	this	DT
37681	2953	19	becomes	become	VBZ
37681	2953	20	_	_	NNP
37681	2953	21	a_^2	a_^2	NNP
37681	2953	22	=	=	SYM
37681	2953	23	_	_	NNP
37681	2953	24	b_^2	b_^2	NNP
37681	2953	25	+	+	NNP
37681	2953	26	_	_	NNP
37681	2953	27	c_^2	c_^2	NNP
37681	2953	28	.	.	.
37681	2954	1	If	if	IN
37681	2954	2	[	[	-LRB-
37681	2954	3	L]_A	L]_A	NNP
37681	2954	4	_	_	NNP
37681	2954	5	is	be	VBZ
37681	2954	6	obtuse	obtuse	NN
37681	2954	7	,	,	,
37681	2954	8	then	then	RB
37681	2954	9	_	_	NNP
37681	2954	10	b	b	NNP
37681	2954	11	'	'	''
37681	2954	12	_	_	NNP
37681	2954	13	passes	pass	VBZ
37681	2954	14	through	through	IN
37681	2954	15	0	0	CD
37681	2954	16	and	and	CC
37681	2954	17	becomes	become	VBZ
37681	2954	18	negative	negative	JJ
37681	2954	19	,	,	,
37681	2954	20	and	and	CC
37681	2954	21	_	_	NNP
37681	2954	22	a_^2	a_^2	NNP
37681	2954	23	=	=	SYM
37681	2954	24	_	_	NNP
37681	2954	25	b_^2	b_^2	NNP
37681	2954	26	+	+	NNP
37681	2954	27	_	_	NNP
37681	2954	28	c_^2	c_^2	NNP
37681	2954	29	+	+	CC
37681	2954	30	2_b'c	2_b'c	CD
37681	2954	31	_	_	NNP
37681	2954	32	.	.	.
37681	2955	1	Thus	thus	RB
37681	2955	2	we	-PRON-	PRP
37681	2955	3	have	have	VBP
37681	2955	4	three	three	CD
37681	2955	5	propositions	proposition	NNS
37681	2955	6	in	in	IN
37681	2955	7	one	one	CD
37681	2955	8	.	.	.
37681	2956	1	[	[	-LRB-
37681	2956	2	Illustration	illustration	NN
37681	2956	3	]	]	-RRB-
37681	2956	4	At	at	IN
37681	2956	5	the	the	DT
37681	2956	6	close	close	NN
37681	2956	7	of	of	IN
37681	2956	8	Book	Book	NNP
37681	2956	9	IV	IV	NNP
37681	2956	10	many	many	JJ
37681	2956	11	geometries	geometry	NNS
37681	2956	12	give	give	VBP
37681	2956	13	as	as	IN
37681	2956	14	an	an	DT
37681	2956	15	exercise	exercise	NN
37681	2956	16	,	,	,
37681	2956	17	and	and	CC
37681	2956	18	some	some	DT
37681	2956	19	give	give	VBP
37681	2956	20	as	as	IN
37681	2956	21	a	a	DT
37681	2956	22	regular	regular	JJ
37681	2956	23	proposition	proposition	NN
37681	2956	24	,	,	,
37681	2956	25	the	the	DT
37681	2956	26	celebrated	celebrated	JJ
37681	2956	27	problem	problem	NN
37681	2956	28	that	that	WDT
37681	2956	29	bears	bear	VBZ
37681	2956	30	the	the	DT
37681	2956	31	name	name	NN
37681	2956	32	of	of	IN
37681	2956	33	Heron	Heron	NNP
37681	2956	34	of	of	IN
37681	2956	35	Alexandria	Alexandria	NNP
37681	2956	36	,	,	,
37681	2956	37	namely	namely	RB
37681	2956	38	,	,	,
37681	2956	39	to	to	TO
37681	2956	40	compute	compute	VB
37681	2956	41	the	the	DT
37681	2956	42	area	area	NN
37681	2956	43	of	of	IN
37681	2956	44	a	a	DT
37681	2956	45	triangle	triangle	NN
37681	2956	46	in	in	IN
37681	2956	47	terms	term	NNS
37681	2956	48	of	of	IN
37681	2956	49	its	-PRON-	PRP$
37681	2956	50	sides	side	NNS
37681	2956	51	.	.	.
37681	2957	1	The	the	DT
37681	2957	2	result	result	NN
37681	2957	3	is	be	VBZ
37681	2957	4	the	the	DT
37681	2957	5	important	important	JJ
37681	2957	6	formula	formula	NN
37681	2957	7	Area	area	NN
37681	2957	8	=	=	NFP
37681	2957	9	[	[	-LRB-
37681	2957	10	sqrt](_s_(_s	sqrt](_s_(_s	NNP
37681	2957	11	_	_	NNP
37681	2957	12	-	-	HYPH
37681	2957	13	_	_	NNP
37681	2957	14	a_)(_s	a_)(_s	NN
37681	2957	15	_	_	NNP
37681	2957	16	-	-	HYPH
37681	2957	17	_	_	NNP
37681	2957	18	b_)(_s	b_)(_s	NN
37681	2957	19	_	_	NNP
37681	2957	20	-	-	HYPH
37681	2957	21	_	_	NNP
37681	2957	22	c	c	NNP
37681	2957	23	_	_	NNP
37681	2957	24	)	)	-RRB-
37681	2957	25	)	)	-RRB-
37681	2957	26	,	,	,
37681	2957	27	where	where	WRB
37681	2957	28	_	_	NNP
37681	2957	29	a	a	DT
37681	2957	30	_	_	NNP
37681	2957	31	,	,	,
37681	2957	32	_	_	NNP
37681	2957	33	b	b	NNP
37681	2957	34	_	_	NNP
37681	2957	35	,	,	,
37681	2957	36	and	and	CC
37681	2957	37	_	_	NNP
37681	2957	38	c	c	NNP
37681	2957	39	_	_	NNP
37681	2957	40	are	be	VBP
37681	2957	41	the	the	DT
37681	2957	42	sides	side	NNS
37681	2957	43	,	,	,
37681	2957	44	and	and	CC
37681	2957	45	_	_	NNP
37681	2957	46	s	s	NNP
37681	2957	47	_	_	NNP
37681	2957	48	is	be	VBZ
37681	2957	49	the	the	DT
37681	2957	50	semiperimeter	semiperimeter	JJ
37681	2957	51	1/2(_a	1/2(_a	CD
37681	2957	52	_	_	NNP
37681	2957	53	+	+	NNP
37681	2957	54	_	_	NNP
37681	2957	55	b	b	NNP
37681	2957	56	_	_	NNP
37681	2957	57	+	+	NNP
37681	2957	58	_	_	NNP
37681	2957	59	c	c	NNP
37681	2957	60	_	_	NNP
37681	2957	61	)	)	-RRB-
37681	2957	62	.	.	.
37681	2958	1	As	as	IN
37681	2958	2	a	a	DT
37681	2958	3	practical	practical	JJ
37681	2958	4	application	application	NN
37681	2958	5	the	the	DT
37681	2958	6	class	class	NN
37681	2958	7	may	may	MD
37681	2958	8	be	be	VB
37681	2958	9	able	able	JJ
37681	2958	10	to	to	TO
37681	2958	11	find	find	VB
37681	2958	12	a	a	DT
37681	2958	13	triangular	triangular	JJ
37681	2958	14	piece	piece	NN
37681	2958	15	of	of	IN
37681	2958	16	land	land	NN
37681	2958	17	,	,	,
37681	2958	18	as	as	IN
37681	2958	19	here	here	RB
37681	2958	20	shown	show	VBN
37681	2958	21	,	,	,
37681	2958	22	and	and	CC
37681	2958	23	to	to	TO
37681	2958	24	measure	measure	VB
37681	2958	25	the	the	DT
37681	2958	26	sides	side	NNS
37681	2958	27	.	.	.
37681	2959	1	If	if	IN
37681	2959	2	the	the	DT
37681	2959	3	piece	piece	NN
37681	2959	4	is	be	VBZ
37681	2959	5	clear	clear	JJ
37681	2959	6	,	,	,
37681	2959	7	the	the	DT
37681	2959	8	result	result	NN
37681	2959	9	may	may	MD
37681	2959	10	be	be	VB
37681	2959	11	checked	check	VBN
37681	2959	12	by	by	IN
37681	2959	13	measuring	measure	VBG
37681	2959	14	the	the	DT
37681	2959	15	altitude	altitude	NN
37681	2959	16	and	and	CC
37681	2959	17	applying	apply	VBG
37681	2959	18	the	the	DT
37681	2959	19	formula	formula	NN
37681	2959	20	_	_	NNP
37681	2959	21	a	a	DT
37681	2959	22	_	_	NNP
37681	2959	23	=	=	SYM
37681	2959	24	1/2_bh	1/2_bh	CD
37681	2959	25	_	_	XX
37681	2959	26	.	.	.
37681	2960	1	It	-PRON-	PRP
37681	2960	2	may	may	MD
37681	2960	3	be	be	VB
37681	2960	4	stated	state	VBN
37681	2960	5	to	to	IN
37681	2960	6	the	the	DT
37681	2960	7	class	class	NN
37681	2960	8	that	that	WDT
37681	2960	9	Heron	Heron	NNP
37681	2960	10	's	's	POS
37681	2960	11	formula	formula	NN
37681	2960	12	is	be	VBZ
37681	2960	13	only	only	RB
37681	2960	14	a	a	DT
37681	2960	15	special	special	JJ
37681	2960	16	case	case	NN
37681	2960	17	of	of	IN
37681	2960	18	the	the	DT
37681	2960	19	more	more	RBR
37681	2960	20	general	general	JJ
37681	2960	21	one	one	NN
37681	2960	22	developed	develop	VBN
37681	2960	23	about	about	RB
37681	2960	24	640	640	CD
37681	2960	25	A.D.	A.D.	NNP
37681	2960	26	,	,	,
37681	2960	27	by	by	IN
37681	2960	28	a	a	DT
37681	2960	29	famous	famous	JJ
37681	2960	30	Hindu	Hindu	NNP
37681	2960	31	mathematician	mathematician	NN
37681	2960	32	,	,	,
37681	2960	33	Brahmagupta	Brahmagupta	NNP
37681	2960	34	.	.	.
37681	2961	1	This	this	DT
37681	2961	2	formula	formula	NN
37681	2961	3	gives	give	VBZ
37681	2961	4	the	the	DT
37681	2961	5	area	area	NN
37681	2961	6	of	of	IN
37681	2961	7	an	an	DT
37681	2961	8	inscribed	inscribe	VBN
37681	2961	9	quadrilateral	quadrilateral	NN
37681	2961	10	as	as	IN
37681	2961	11	[	[	-LRB-
37681	2961	12	sqrt]((_s	sqrt]((_s	NNP
37681	2961	13	_	_	NNP
37681	2961	14	-	-	HYPH
37681	2961	15	_	_	NNP
37681	2961	16	a_)(_s	a_)(_s	NN
37681	2961	17	_	_	NNP
37681	2961	18	-	-	HYPH
37681	2961	19	_	_	NNP
37681	2961	20	b_)(_s	b_)(_s	NN
37681	2961	21	_	_	NNP
37681	2961	22	-	-	HYPH
37681	2961	23	_	_	NNP
37681	2961	24	c_)(_s	c_)(_s	NN
37681	2961	25	_	_	NNP
37681	2961	26	-	-	HYPH
37681	2961	27	_	_	NNP
37681	2961	28	d	d	NNP
37681	2961	29	_	_	NNP
37681	2961	30	)	)	-RRB-
37681	2961	31	)	)	-RRB-
37681	2961	32	,	,	,
37681	2961	33	where	where	WRB
37681	2961	34	_	_	NNP
37681	2961	35	a	a	DT
37681	2961	36	_	_	NNP
37681	2961	37	,	,	,
37681	2961	38	_	_	NNP
37681	2961	39	b	b	NNP
37681	2961	40	_	_	NNP
37681	2961	41	,	,	,
37681	2961	42	_	_	NNP
37681	2961	43	c	c	NNP
37681	2961	44	_	_	NNP
37681	2961	45	,	,	,
37681	2961	46	and	and	CC
37681	2961	47	_	_	NNP
37681	2961	48	d	d	NNP
37681	2961	49	_	_	NNP
37681	2961	50	are	be	VBP
37681	2961	51	the	the	DT
37681	2961	52	sides	side	NNS
37681	2961	53	and	and	CC
37681	2961	54	_	_	NNP
37681	2961	55	s	s	NNP
37681	2961	56	_	_	NNP
37681	2961	57	is	be	VBZ
37681	2961	58	the	the	DT
37681	2961	59	semiperimeter	semiperimeter	NN
37681	2961	60	.	.	.
37681	2962	1	If	if	IN
37681	2962	2	_	_	NNP
37681	2962	3	d	d	NNP
37681	2962	4	_	_	NNP
37681	2962	5	=	=	SYM
37681	2962	6	0	0	CD
37681	2962	7	,	,	,
37681	2962	8	the	the	DT
37681	2962	9	quadrilateral	quadrilateral	NN
37681	2962	10	becomes	become	VBZ
37681	2962	11	a	a	DT
37681	2962	12	triangle	triangle	NN
37681	2962	13	and	and	CC
37681	2962	14	we	-PRON-	PRP
37681	2962	15	have	have	VBP
37681	2962	16	Heron	Heron	NNP
37681	2962	17	's	's	POS
37681	2962	18	formula	formula	NN
37681	2962	19	.	.	.
37681	2963	1	[	[	-LRB-
37681	2963	2	82	82	CD
37681	2963	3	]	]	-RRB-
37681	2963	4	At	at	IN
37681	2963	5	the	the	DT
37681	2963	6	close	close	NN
37681	2963	7	of	of	IN
37681	2963	8	Book	Book	NNP
37681	2963	9	IV	IV	NNP
37681	2963	10	,	,	,
37681	2963	11	also	also	RB
37681	2963	12	,	,	,
37681	2963	13	the	the	DT
37681	2963	14	geometric	geometric	JJ
37681	2963	15	equivalents	equivalent	NNS
37681	2963	16	of	of	IN
37681	2963	17	the	the	DT
37681	2963	18	algebraic	algebraic	NNP
37681	2963	19	formulas	formula	NNS
37681	2963	20	for	for	IN
37681	2963	21	(	(	-LRB-
37681	2963	22	_	_	NNP
37681	2963	23	a	a	DT
37681	2963	24	_	_	NNP
37681	2963	25	+	+	CC
37681	2963	26	_	_	NNP
37681	2963	27	b_)^2	b_)^2	RB
37681	2963	28	,	,	,
37681	2963	29	(	(	-LRB-
37681	2963	30	_	_	NNP
37681	2963	31	a	a	DT
37681	2963	32	_	_	NNP
37681	2963	33	-	-	HYPH
37681	2963	34	_	_	NNP
37681	2963	35	b_)^2	b_)^2	RB
37681	2963	36	,	,	,
37681	2963	37	and	and	CC
37681	2963	38	(	(	-LRB-
37681	2963	39	_	_	NNP
37681	2963	40	a	a	DT
37681	2963	41	_	_	NNP
37681	2963	42	+	+	NNP
37681	2963	43	_	_	NNP
37681	2963	44	b_)(_a	b_)(_a	NN
37681	2963	45	_	_	NNP
37681	2963	46	-	-	HYPH
37681	2963	47	_	_	NNP
37681	2963	48	b	b	NNP
37681	2963	49	_	_	NNP
37681	2963	50	)	)	-RRB-
37681	2963	51	are	be	VBP
37681	2963	52	given	give	VBN
37681	2963	53	.	.	.
37681	2964	1	The	the	DT
37681	2964	2	class	class	NN
37681	2964	3	may	may	MD
37681	2964	4	like	like	VB
37681	2964	5	to	to	TO
37681	2964	6	know	know	VB
37681	2964	7	that	that	IN
37681	2964	8	Euclid	Euclid	NNP
37681	2964	9	had	have	VBD
37681	2964	10	no	no	DT
37681	2964	11	algebra	algebra	NN
37681	2964	12	and	and	CC
37681	2964	13	was	be	VBD
37681	2964	14	compelled	compel	VBN
37681	2964	15	to	to	TO
37681	2964	16	prove	prove	VB
37681	2964	17	such	such	JJ
37681	2964	18	relations	relation	NNS
37681	2964	19	as	as	IN
37681	2964	20	these	these	DT
37681	2964	21	by	by	IN
37681	2964	22	geometry	geometry	NN
37681	2964	23	,	,	,
37681	2964	24	while	while	IN
37681	2964	25	we	-PRON-	PRP
37681	2964	26	do	do	VBP
37681	2964	27	it	-PRON-	PRP
37681	2964	28	now	now	RB
37681	2964	29	much	much	RB
37681	2964	30	more	more	RBR
37681	2964	31	easily	easily	RB
37681	2964	32	by	by	IN
37681	2964	33	algebraic	algebraic	NNP
37681	2964	34	multiplication	multiplication	NNP
37681	2964	35	.	.	.
37681	2965	1	FOOTNOTES	footnote	NNS
37681	2965	2	:	:	:
37681	2965	3	[	[	-LRB-
37681	2965	4	79	79	CD
37681	2965	5	]	]	-RRB-
37681	2965	6	See	see	VB
37681	2965	7	,	,	,
37681	2965	8	for	for	IN
37681	2965	9	example	example	NN
37681	2965	10	,	,	,
37681	2965	11	G.	G.	NNP
37681	2965	12	B.	B.	NNP
37681	2965	13	Kaye	Kaye	NNP
37681	2965	14	,	,	,
37681	2965	15	"	"	``
37681	2965	16	The	the	DT
37681	2965	17	Source	Source	NNP
37681	2965	18	of	of	IN
37681	2965	19	Hindu	Hindu	NNP
37681	2965	20	Mathematics	Mathematics	NNP
37681	2965	21	,	,	,
37681	2965	22	"	"	''
37681	2965	23	in	in	IN
37681	2965	24	the	the	DT
37681	2965	25	_	_	NNP
37681	2965	26	Journal	Journal	NNP
37681	2965	27	of	of	IN
37681	2965	28	the	the	DT
37681	2965	29	Royal	Royal	NNP
37681	2965	30	Asiatic	Asiatic	NNP
37681	2965	31	Society	Society	NNP
37681	2965	32	_	_	NNP
37681	2965	33	,	,	,
37681	2965	34	July	July	NNP
37681	2965	35	,	,	,
37681	2965	36	1910	1910	CD
37681	2965	37	.	.	.
37681	2966	1	[	[	-LRB-
37681	2966	2	80	80	CD
37681	2966	3	]	]	-RRB-
37681	2966	4	An	an	DT
37681	2966	5	interesting	interesting	JJ
37681	2966	6	Japanese	japanese	JJ
37681	2966	7	proof	proof	NN
37681	2966	8	of	of	IN
37681	2966	9	this	this	DT
37681	2966	10	general	general	JJ
37681	2966	11	character	character	NN
37681	2966	12	may	may	MD
37681	2966	13	be	be	VB
37681	2966	14	seen	see	VBN
37681	2966	15	in	in	IN
37681	2966	16	Y.	Y.	NNP
37681	2966	17	Mikami	Mikami	NNP
37681	2966	18	,	,	,
37681	2966	19	"	"	``
37681	2966	20	Mathematical	Mathematical	NNP
37681	2966	21	Papers	Papers	NNPS
37681	2966	22	from	from	IN
37681	2966	23	the	the	DT
37681	2966	24	Far	Far	NNP
37681	2966	25	East	East	NNP
37681	2966	26	,	,	,
37681	2966	27	"	"	''
37681	2966	28	p.	p.	NN
37681	2966	29	127	127	CD
37681	2966	30	,	,	,
37681	2966	31	Leipzig	Leipzig	NNP
37681	2966	32	,	,	,
37681	2966	33	1910	1910	CD
37681	2966	34	.	.	.
37681	2967	1	[	[	-LRB-
37681	2967	2	81	81	CD
37681	2967	3	]	]	-RRB-
37681	2967	4	Special	special	JJ
37681	2967	5	recognition	recognition	NN
37681	2967	6	of	of	IN
37681	2967	7	indebtedness	indebtedness	NN
37681	2967	8	to	to	IN
37681	2967	9	H.	H.	NNP
37681	2967	10	A.	A.	NNP
37681	2967	11	Naber	Naber	NNP
37681	2967	12	's	's	POS
37681	2967	13	"	"	``
37681	2967	14	Das	Das	NNP
37681	2967	15	Theorem	Theorem	NNP
37681	2967	16	des	des	FW
37681	2967	17	Pythagoras	Pythagoras	NNP
37681	2967	18	"	"	''
37681	2967	19	(	(	-LRB-
37681	2967	20	Haarlem	Haarlem	NNP
37681	2967	21	,	,	,
37681	2967	22	1908	1908	CD
37681	2967	23	)	)	-RRB-
37681	2967	24	,	,	,
37681	2967	25	Heath	Heath	NNP
37681	2967	26	's	's	POS
37681	2967	27	"	"	``
37681	2967	28	Euclid	Euclid	NNP
37681	2967	29	,	,	,
37681	2967	30	"	"	''
37681	2967	31	Gow	Gow	NNP
37681	2967	32	's	's	POS
37681	2967	33	"	"	``
37681	2967	34	History	History	NNP
37681	2967	35	of	of	IN
37681	2967	36	Greek	Greek	NNP
37681	2967	37	Mathematics	Mathematics	NNP
37681	2967	38	,	,	,
37681	2967	39	"	"	''
37681	2967	40	and	and	CC
37681	2967	41	Cantor	Cantor	NNP
37681	2967	42	's	's	POS
37681	2967	43	"	"	``
37681	2967	44	Geschichte	Geschichte	NNP
37681	2967	45	"	"	''
37681	2967	46	is	be	VBZ
37681	2967	47	due	due	JJ
37681	2967	48	in	in	IN
37681	2967	49	connection	connection	NN
37681	2967	50	with	with	IN
37681	2967	51	the	the	DT
37681	2967	52	Pythagorean	Pythagorean	NNP
37681	2967	53	Theorem	Theorem	NNP
37681	2967	54	.	.	.
37681	2968	1	[	[	-LRB-
37681	2968	2	82	82	CD
37681	2968	3	]	]	-RRB-
37681	2968	4	The	the	DT
37681	2968	5	rule	rule	NN
37681	2968	6	was	be	VBD
37681	2968	7	so	so	RB
37681	2968	8	ill	ill	JJ
37681	2968	9	understood	understand	VBD
37681	2968	10	that	that	IN
37681	2968	11	Bhaskara	Bhaskara	NNP
37681	2968	12	(	(	-LRB-
37681	2968	13	twelfth	twelfth	JJ
37681	2968	14	century	century	NN
37681	2968	15	)	)	-RRB-
37681	2968	16	said	say	VBD
37681	2968	17	that	that	IN
37681	2968	18	Brahmagupta	Brahmagupta	NNP
37681	2968	19	was	be	VBD
37681	2968	20	a	a	DT
37681	2968	21	"	"	``
37681	2968	22	blundering	blunder	VBG
37681	2968	23	devil	devil	NN
37681	2968	24	"	"	''
37681	2968	25	for	for	IN
37681	2968	26	giving	give	VBG
37681	2968	27	it	-PRON-	PRP
37681	2968	28	(	(	-LRB-
37681	2968	29	"	"	``
37681	2968	30	Lilavati	Lilavati	NNS
37681	2968	31	,	,	,
37681	2968	32	"	"	''
37681	2968	33	§	§	-LRB-
37681	2968	34	172	172	CD
37681	2968	35	)	)	-RRB-
37681	2968	36	.	.	.
37681	2969	1	CHAPTER	chapter	NN
37681	2969	2	XVIII	xviii	VBP
37681	2969	3	THE	the	DT
37681	2969	4	LEADING	lead	VBG
37681	2969	5	PROPOSITIONS	proposition	NNS
37681	2969	6	OF	of	IN
37681	2969	7	BOOK	book	NN
37681	2969	8	V	v	NN
37681	2969	9	[	[	-LRB-
37681	2969	10	Illustration	illustration	NN
37681	2969	11	]	]	-RRB-
37681	2969	12	Book	Book	NNP
37681	2969	13	V	v	NN
37681	2969	14	treats	treat	NNS
37681	2969	15	of	of	IN
37681	2969	16	regular	regular	JJ
37681	2969	17	polygons	polygon	NNS
37681	2969	18	and	and	CC
37681	2969	19	circles	circle	NNS
37681	2969	20	,	,	,
37681	2969	21	and	and	CC
37681	2969	22	includes	include	VBZ
37681	2969	23	the	the	DT
37681	2969	24	computation	computation	NN
37681	2969	25	of	of	IN
37681	2969	26	the	the	DT
37681	2969	27	approximate	approximate	JJ
37681	2969	28	value	value	NN
37681	2969	29	of	of	IN
37681	2969	30	[	[	-LRB-
37681	2969	31	pi	pi	NN
37681	2969	32	]	]	-RRB-
37681	2969	33	.	.	.
37681	2970	1	It	-PRON-	PRP
37681	2970	2	opens	open	VBZ
37681	2970	3	with	with	IN
37681	2970	4	a	a	DT
37681	2970	5	definition	definition	NN
37681	2970	6	of	of	IN
37681	2970	7	a	a	DT
37681	2970	8	regular	regular	JJ
37681	2970	9	polygon	polygon	NN
37681	2970	10	as	as	IN
37681	2970	11	one	one	CD
37681	2970	12	that	that	WDT
37681	2970	13	is	be	VBZ
37681	2970	14	both	both	DT
37681	2970	15	equilateral	equilateral	JJ
37681	2970	16	and	and	CC
37681	2970	17	equiangular	equiangular	JJ
37681	2970	18	.	.	.
37681	2971	1	While	while	IN
37681	2971	2	in	in	IN
37681	2971	3	elementary	elementary	JJ
37681	2971	4	geometry	geometry	NN
37681	2971	5	the	the	DT
37681	2971	6	only	only	JJ
37681	2971	7	regular	regular	JJ
37681	2971	8	polygons	polygon	NNS
37681	2971	9	studied	study	VBN
37681	2971	10	are	be	VBP
37681	2971	11	convex	convex	NNP
37681	2971	12	,	,	,
37681	2971	13	it	-PRON-	PRP
37681	2971	14	is	be	VBZ
37681	2971	15	interesting	interesting	JJ
37681	2971	16	to	to	IN
37681	2971	17	a	a	DT
37681	2971	18	class	class	NN
37681	2971	19	to	to	TO
37681	2971	20	see	see	VB
37681	2971	21	that	that	IN
37681	2971	22	there	there	EX
37681	2971	23	are	be	VBP
37681	2971	24	also	also	RB
37681	2971	25	regular	regular	JJ
37681	2971	26	cross	cross	NN
37681	2971	27	polygons	polygon	NNS
37681	2971	28	.	.	.
37681	2972	1	Indeed	indeed	RB
37681	2972	2	,	,	,
37681	2972	3	the	the	DT
37681	2972	4	regular	regular	JJ
37681	2972	5	cross	cross	NN
37681	2972	6	pentagon	pentagon	NNP
37681	2972	7	was	be	VBD
37681	2972	8	the	the	DT
37681	2972	9	badge	badge	NN
37681	2972	10	of	of	IN
37681	2972	11	the	the	DT
37681	2972	12	Pythagoreans	Pythagoreans	NNPS
37681	2972	13	,	,	,
37681	2972	14	as	as	IN
37681	2972	15	Lucian	Lucian	NNP
37681	2972	16	(	(	-LRB-
37681	2972	17	_	_	NNP
37681	2972	18	ca	ca	NNP
37681	2972	19	.	.	.
37681	2972	20	_	_	NNP
37681	2972	21	100	100	CD
37681	2972	22	B.C.	B.C.	NNP
37681	2972	23	)	)	-RRB-
37681	2973	1	and	and	CC
37681	2973	2	an	an	DT
37681	2973	3	unknown	unknown	JJ
37681	2973	4	commentator	commentator	NN
37681	2973	5	on	on	IN
37681	2973	6	Aristophanes	Aristophanes	NNP
37681	2973	7	(	(	-LRB-
37681	2973	8	_	_	NNP
37681	2973	9	ca	ca	NNP
37681	2973	10	.	.	.
37681	2973	11	_	_	NNP
37681	2973	12	400	400	CD
37681	2973	13	B.C.	B.C.	NNP
37681	2973	14	)	)	-RRB-
37681	2974	1	tell	tell	VB
37681	2974	2	us	-PRON-	PRP
37681	2974	3	.	.	.
37681	2975	1	At	at	IN
37681	2975	2	the	the	DT
37681	2975	3	vertices	vertex	NNS
37681	2975	4	of	of	IN
37681	2975	5	this	this	DT
37681	2975	6	polygon	polygon	NN
37681	2975	7	the	the	DT
37681	2975	8	Pythagoreans	Pythagoreans	NNPS
37681	2975	9	placed	place	VBD
37681	2975	10	the	the	DT
37681	2975	11	Greek	greek	JJ
37681	2975	12	letters	letter	NNS
37681	2975	13	signifying	signify	VBG
37681	2975	14	"	"	``
37681	2975	15	health	health	NN
37681	2975	16	.	.	.
37681	2975	17	"	"	''
37681	2976	1	Euclid	Euclid	NNP
37681	2976	2	was	be	VBD
37681	2976	3	not	not	RB
37681	2976	4	interested	interested	JJ
37681	2976	5	in	in	IN
37681	2976	6	the	the	DT
37681	2976	7	measure	measure	NN
37681	2976	8	of	of	IN
37681	2976	9	the	the	DT
37681	2976	10	circle	circle	NN
37681	2976	11	,	,	,
37681	2976	12	and	and	CC
37681	2976	13	there	there	EX
37681	2976	14	is	be	VBZ
37681	2976	15	nothing	nothing	NN
37681	2976	16	in	in	IN
37681	2976	17	his	-PRON-	PRP$
37681	2976	18	"	"	``
37681	2976	19	Elements	Elements	NNPS
37681	2976	20	"	"	''
37681	2976	21	on	on	IN
37681	2976	22	the	the	DT
37681	2976	23	value	value	NN
37681	2976	24	of	of	IN
37681	2976	25	[	[	-LRB-
37681	2976	26	pi	pi	NN
37681	2976	27	]	]	-RRB-
37681	2976	28	.	.	.
37681	2977	1	Indeed	indeed	RB
37681	2977	2	,	,	,
37681	2977	3	he	-PRON-	PRP
37681	2977	4	expressly	expressly	RB
37681	2977	5	avoided	avoid	VBD
37681	2977	6	numerical	numerical	JJ
37681	2977	7	measures	measure	NNS
37681	2977	8	of	of	IN
37681	2977	9	all	all	DT
37681	2977	10	kinds	kind	NNS
37681	2977	11	in	in	IN
37681	2977	12	his	-PRON-	PRP$
37681	2977	13	geometry	geometry	NN
37681	2977	14	,	,	,
37681	2977	15	wishing	wish	VBG
37681	2977	16	the	the	DT
37681	2977	17	science	science	NN
37681	2977	18	to	to	TO
37681	2977	19	be	be	VB
37681	2977	20	kept	keep	VBN
37681	2977	21	distinct	distinct	JJ
37681	2977	22	from	from	IN
37681	2977	23	that	that	DT
37681	2977	24	form	form	NN
37681	2977	25	of	of	IN
37681	2977	26	arithmetic	arithmetic	JJ
37681	2977	27	known	know	VBN
37681	2977	28	to	to	IN
37681	2977	29	the	the	DT
37681	2977	30	Greeks	Greeks	NNPS
37681	2977	31	as	as	IN
37681	2977	32	logistic	logistic	JJ
37681	2977	33	,	,	,
37681	2977	34	or	or	CC
37681	2977	35	calculation	calculation	NN
37681	2977	36	.	.	.
37681	2978	1	His	-PRON-	PRP$
37681	2978	2	Book	Book	NNP
37681	2978	3	IV	IV	NNP
37681	2978	4	is	be	VBZ
37681	2978	5	devoted	devote	VBN
37681	2978	6	to	to	IN
37681	2978	7	the	the	DT
37681	2978	8	construction	construction	NN
37681	2978	9	of	of	IN
37681	2978	10	certain	certain	JJ
37681	2978	11	regular	regular	JJ
37681	2978	12	polygons	polygon	NNS
37681	2978	13	,	,	,
37681	2978	14	and	and	CC
37681	2978	15	his	-PRON-	PRP$
37681	2978	16	propositions	proposition	NNS
37681	2978	17	on	on	IN
37681	2978	18	this	this	DT
37681	2978	19	subject	subject	NN
37681	2978	20	are	be	VBP
37681	2978	21	now	now	RB
37681	2978	22	embodied	embody	VBN
37681	2978	23	in	in	IN
37681	2978	24	Book	Book	NNP
37681	2978	25	V	V	NNP
37681	2978	26	as	as	IN
37681	2978	27	it	-PRON-	PRP
37681	2978	28	is	be	VBZ
37681	2978	29	usually	usually	RB
37681	2978	30	taught	teach	VBN
37681	2978	31	in	in	IN
37681	2978	32	America	America	NNP
37681	2978	33	.	.	.
37681	2979	1	If	if	IN
37681	2979	2	we	-PRON-	PRP
37681	2979	3	consider	consider	VBP
37681	2979	4	Book	Book	NNP
37681	2979	5	V	V	NNP
37681	2979	6	as	as	IN
37681	2979	7	a	a	DT
37681	2979	8	whole	whole	NN
37681	2979	9	,	,	,
37681	2979	10	we	-PRON-	PRP
37681	2979	11	are	be	VBP
37681	2979	12	struck	strike	VBN
37681	2979	13	by	by	IN
37681	2979	14	three	three	CD
37681	2979	15	features	feature	NNS
37681	2979	16	.	.	.
37681	2980	1	Of	of	IN
37681	2980	2	these	these	DT
37681	2980	3	the	the	DT
37681	2980	4	first	first	JJ
37681	2980	5	is	be	VBZ
37681	2980	6	the	the	DT
37681	2980	7	pure	pure	JJ
37681	2980	8	geometry	geometry	NN
37681	2980	9	involved	involve	VBN
37681	2980	10	,	,	,
37681	2980	11	and	and	CC
37681	2980	12	this	this	DT
37681	2980	13	is	be	VBZ
37681	2980	14	the	the	DT
37681	2980	15	essential	essential	JJ
37681	2980	16	feature	feature	NN
37681	2980	17	to	to	TO
37681	2980	18	be	be	VB
37681	2980	19	emphasized	emphasize	VBN
37681	2980	20	.	.	.
37681	2981	1	The	the	DT
37681	2981	2	second	second	JJ
37681	2981	3	is	be	VBZ
37681	2981	4	the	the	DT
37681	2981	5	mensuration	mensuration	NN
37681	2981	6	of	of	IN
37681	2981	7	the	the	DT
37681	2981	8	circle	circle	NN
37681	2981	9	,	,	,
37681	2981	10	a	a	DT
37681	2981	11	relatively	relatively	RB
37681	2981	12	unimportant	unimportant	JJ
37681	2981	13	piece	piece	NN
37681	2981	14	of	of	IN
37681	2981	15	theory	theory	NN
37681	2981	16	in	in	IN
37681	2981	17	view	view	NN
37681	2981	18	of	of	IN
37681	2981	19	the	the	DT
37681	2981	20	fact	fact	NN
37681	2981	21	that	that	IN
37681	2981	22	the	the	DT
37681	2981	23	pupil	pupil	NN
37681	2981	24	is	be	VBZ
37681	2981	25	not	not	RB
37681	2981	26	ready	ready	JJ
37681	2981	27	for	for	IN
37681	2981	28	incommensurables	incommensurable	NNS
37681	2981	29	,	,	,
37681	2981	30	and	and	CC
37681	2981	31	a	a	DT
37681	2981	32	feature	feature	NN
37681	2981	33	that	that	WDT
37681	2981	34	imparts	impart	VBZ
37681	2981	35	no	no	DT
37681	2981	36	information	information	NN
37681	2981	37	that	that	IN
37681	2981	38	the	the	DT
37681	2981	39	pupil	pupil	NN
37681	2981	40	did	do	VBD
37681	2981	41	not	not	RB
37681	2981	42	find	find	VB
37681	2981	43	in	in	IN
37681	2981	44	arithmetic	arithmetic	JJ
37681	2981	45	.	.	.
37681	2982	1	The	the	DT
37681	2982	2	third	third	JJ
37681	2982	3	is	be	VBZ
37681	2982	4	the	the	DT
37681	2982	5	somewhat	somewhat	RB
37681	2982	6	interesting	interesting	JJ
37681	2982	7	but	but	CC
37681	2982	8	mathematically	mathematically	RB
37681	2982	9	unimportant	unimportant	JJ
37681	2982	10	application	application	NN
37681	2982	11	of	of	IN
37681	2982	12	the	the	DT
37681	2982	13	regular	regular	JJ
37681	2982	14	polygons	polygon	NNS
37681	2982	15	to	to	IN
37681	2982	16	geometric	geometric	JJ
37681	2982	17	design	design	NN
37681	2982	18	.	.	.
37681	2983	1	As	as	IN
37681	2983	2	to	to	IN
37681	2983	3	the	the	DT
37681	2983	4	mensuration	mensuration	NN
37681	2983	5	of	of	IN
37681	2983	6	the	the	DT
37681	2983	7	circle	circle	NN
37681	2983	8	it	-PRON-	PRP
37681	2983	9	is	be	VBZ
37681	2983	10	well	well	JJ
37681	2983	11	for	for	IN
37681	2983	12	us	-PRON-	PRP
37681	2983	13	to	to	TO
37681	2983	14	take	take	VB
37681	2983	15	a	a	DT
37681	2983	16	broad	broad	JJ
37681	2983	17	view	view	NN
37681	2983	18	before	before	IN
37681	2983	19	coming	come	VBG
37681	2983	20	down	down	RP
37681	2983	21	to	to	IN
37681	2983	22	details	detail	NNS
37681	2983	23	.	.	.
37681	2984	1	There	there	EX
37681	2984	2	are	be	VBP
37681	2984	3	only	only	RB
37681	2984	4	four	four	CD
37681	2984	5	leading	lead	VBG
37681	2984	6	propositions	proposition	NNS
37681	2984	7	necessary	necessary	JJ
37681	2984	8	for	for	IN
37681	2984	9	the	the	DT
37681	2984	10	mensuration	mensuration	NN
37681	2984	11	of	of	IN
37681	2984	12	the	the	DT
37681	2984	13	circle	circle	NN
37681	2984	14	and	and	CC
37681	2984	15	the	the	DT
37681	2984	16	determination	determination	NN
37681	2984	17	of	of	IN
37681	2984	18	the	the	DT
37681	2984	19	value	value	NN
37681	2984	20	of	of	IN
37681	2984	21	[	[	-LRB-
37681	2984	22	pi	pi	NN
37681	2984	23	]	]	-RRB-
37681	2984	24	.	.	.
37681	2985	1	These	these	DT
37681	2985	2	are	be	VBP
37681	2985	3	as	as	IN
37681	2985	4	follows	follow	VBZ
37681	2985	5	:	:	:
37681	2985	6	(	(	-LRB-
37681	2985	7	1	1	LS
37681	2985	8	)	)	-RRB-
37681	2985	9	The	the	DT
37681	2985	10	inscribing	inscribing	NN
37681	2985	11	of	of	IN
37681	2985	12	a	a	DT
37681	2985	13	regular	regular	JJ
37681	2985	14	hexagon	hexagon	NN
37681	2985	15	,	,	,
37681	2985	16	or	or	CC
37681	2985	17	any	any	DT
37681	2985	18	other	other	JJ
37681	2985	19	regular	regular	JJ
37681	2985	20	polygon	polygon	NN
37681	2985	21	of	of	IN
37681	2985	22	which	which	WDT
37681	2985	23	the	the	DT
37681	2985	24	side	side	NN
37681	2985	25	is	be	VBZ
37681	2985	26	easily	easily	RB
37681	2985	27	computed	compute	VBN
37681	2985	28	in	in	IN
37681	2985	29	terms	term	NNS
37681	2985	30	of	of	IN
37681	2985	31	the	the	DT
37681	2985	32	radius	radius	NN
37681	2985	33	.	.	.
37681	2986	1	We	-PRON-	PRP
37681	2986	2	may	may	MD
37681	2986	3	start	start	VB
37681	2986	4	with	with	IN
37681	2986	5	a	a	DT
37681	2986	6	square	square	NN
37681	2986	7	,	,	,
37681	2986	8	for	for	IN
37681	2986	9	example	example	NN
37681	2986	10	,	,	,
37681	2986	11	but	but	CC
37681	2986	12	this	this	DT
37681	2986	13	is	be	VBZ
37681	2986	14	not	not	RB
37681	2986	15	so	so	RB
37681	2986	16	good	good	JJ
37681	2986	17	as	as	IN
37681	2986	18	the	the	DT
37681	2986	19	hexagon	hexagon	NN
37681	2986	20	because	because	IN
37681	2986	21	its	-PRON-	PRP$
37681	2986	22	side	side	NN
37681	2986	23	is	be	VBZ
37681	2986	24	incommensurable	incommensurable	JJ
37681	2986	25	with	with	IN
37681	2986	26	the	the	DT
37681	2986	27	radius	radius	NN
37681	2986	28	,	,	,
37681	2986	29	and	and	CC
37681	2986	30	its	-PRON-	PRP$
37681	2986	31	perimeter	perimeter	NN
37681	2986	32	is	be	VBZ
37681	2986	33	not	not	RB
37681	2986	34	as	as	RB
37681	2986	35	near	near	IN
37681	2986	36	the	the	DT
37681	2986	37	circumference	circumference	NN
37681	2986	38	.	.	.
37681	2987	1	(	(	-LRB-
37681	2987	2	2	2	LS
37681	2987	3	)	)	-RRB-
37681	2987	4	The	the	DT
37681	2987	5	perimeters	perimeter	NNS
37681	2987	6	of	of	IN
37681	2987	7	similar	similar	JJ
37681	2987	8	regular	regular	JJ
37681	2987	9	polygons	polygon	NNS
37681	2987	10	are	be	VBP
37681	2987	11	proportional	proportional	JJ
37681	2987	12	to	to	IN
37681	2987	13	their	-PRON-	PRP$
37681	2987	14	radii	radii	NN
37681	2987	15	,	,	,
37681	2987	16	and	and	CC
37681	2987	17	their	-PRON-	PRP$
37681	2987	18	areas	area	NNS
37681	2987	19	to	to	IN
37681	2987	20	the	the	DT
37681	2987	21	squares	square	NNS
37681	2987	22	of	of	IN
37681	2987	23	the	the	DT
37681	2987	24	radii	radii	NN
37681	2987	25	.	.	.
37681	2988	1	It	-PRON-	PRP
37681	2988	2	is	be	VBZ
37681	2988	3	now	now	RB
37681	2988	4	necessary	necessary	JJ
37681	2988	5	to	to	IN
37681	2988	6	state	state	NN
37681	2988	7	,	,	,
37681	2988	8	in	in	IN
37681	2988	9	the	the	DT
37681	2988	10	form	form	NN
37681	2988	11	of	of	IN
37681	2988	12	a	a	DT
37681	2988	13	postulate	postulate	NN
37681	2988	14	if	if	IN
37681	2988	15	desired	desire	VBN
37681	2988	16	,	,	,
37681	2988	17	that	that	IN
37681	2988	18	the	the	DT
37681	2988	19	circle	circle	NN
37681	2988	20	is	be	VBZ
37681	2988	21	the	the	DT
37681	2988	22	limit	limit	NN
37681	2988	23	of	of	IN
37681	2988	24	regular	regular	JJ
37681	2988	25	inscribed	inscribed	JJ
37681	2988	26	and	and	CC
37681	2988	27	circumscribed	circumscribed	JJ
37681	2988	28	polygons	polygon	NNS
37681	2988	29	as	as	IN
37681	2988	30	the	the	DT
37681	2988	31	number	number	NN
37681	2988	32	of	of	IN
37681	2988	33	sides	side	NNS
37681	2988	34	increases	increase	VBZ
37681	2988	35	indefinitely	indefinitely	RB
37681	2988	36	,	,	,
37681	2988	37	and	and	CC
37681	2988	38	hence	hence	RB
37681	2988	39	that	that	DT
37681	2988	40	(	(	-LRB-
37681	2988	41	2	2	LS
37681	2988	42	)	)	-RRB-
37681	2988	43	holds	hold	VBZ
37681	2988	44	for	for	IN
37681	2988	45	circles	circle	NNS
37681	2988	46	.	.	.
37681	2989	1	(	(	-LRB-
37681	2989	2	3	3	LS
37681	2989	3	)	)	-RRB-
37681	2989	4	The	the	DT
37681	2989	5	proposition	proposition	NN
37681	2989	6	relating	relate	VBG
37681	2989	7	to	to	IN
37681	2989	8	the	the	DT
37681	2989	9	area	area	NN
37681	2989	10	of	of	IN
37681	2989	11	a	a	DT
37681	2989	12	regular	regular	JJ
37681	2989	13	polygon	polygon	NN
37681	2989	14	,	,	,
37681	2989	15	and	and	CC
37681	2989	16	the	the	DT
37681	2989	17	resulting	result	VBG
37681	2989	18	proposition	proposition	NN
37681	2989	19	relating	relate	VBG
37681	2989	20	to	to	IN
37681	2989	21	the	the	DT
37681	2989	22	circle	circle	NN
37681	2989	23	.	.	.
37681	2990	1	(	(	-LRB-
37681	2990	2	4	4	LS
37681	2990	3	)	)	-RRB-
37681	2990	4	Given	give	VBN
37681	2990	5	the	the	DT
37681	2990	6	side	side	NN
37681	2990	7	of	of	IN
37681	2990	8	a	a	DT
37681	2990	9	regular	regular	JJ
37681	2990	10	inscribed	inscribe	VBN
37681	2990	11	polygon	polygon	NN
37681	2990	12	,	,	,
37681	2990	13	to	to	TO
37681	2990	14	find	find	VB
37681	2990	15	the	the	DT
37681	2990	16	side	side	NN
37681	2990	17	of	of	IN
37681	2990	18	a	a	DT
37681	2990	19	regular	regular	JJ
37681	2990	20	inscribed	inscribe	VBN
37681	2990	21	polygon	polygon	NN
37681	2990	22	of	of	IN
37681	2990	23	double	double	PDT
37681	2990	24	the	the	DT
37681	2990	25	number	number	NN
37681	2990	26	of	of	IN
37681	2990	27	sides	side	NNS
37681	2990	28	.	.	.
37681	2991	1	It	-PRON-	PRP
37681	2991	2	will	will	MD
37681	2991	3	thus	thus	RB
37681	2991	4	be	be	VB
37681	2991	5	seen	see	VBN
37681	2991	6	that	that	IN
37681	2991	7	if	if	IN
37681	2991	8	we	-PRON-	PRP
37681	2991	9	were	be	VBD
37681	2991	10	merely	merely	RB
37681	2991	11	desirous	desirous	JJ
37681	2991	12	of	of	IN
37681	2991	13	approximating	approximate	VBG
37681	2991	14	the	the	DT
37681	2991	15	value	value	NN
37681	2991	16	of	of	IN
37681	2991	17	[	[	-LRB-
37681	2991	18	pi	pi	NN
37681	2991	19	]	]	-RRB-
37681	2991	20	,	,	,
37681	2991	21	and	and	CC
37681	2991	22	of	of	IN
37681	2991	23	finding	find	VBG
37681	2991	24	the	the	DT
37681	2991	25	two	two	CD
37681	2991	26	formulas	formula	NNS
37681	2991	27	_	_	NNP
37681	2991	28	c	c	NNP
37681	2991	29	_	_	NNP
37681	2991	30	=	=	SYM
37681	2991	31	2[pi]_r	2[pi]_r	CD
37681	2991	32	_	_	NNP
37681	2991	33	and	and	CC
37681	2991	34	_	_	NNP
37681	2991	35	a	a	DT
37681	2991	36	_	_	NNP
37681	2991	37	=	=	NFP
37681	2991	38	[	[	-LRB-
37681	2991	39	pi]_r_^2	pi]_r_^2	UH
37681	2991	40	,	,	,
37681	2991	41	we	-PRON-	PRP
37681	2991	42	should	should	MD
37681	2991	43	need	need	VB
37681	2991	44	only	only	RB
37681	2991	45	four	four	CD
37681	2991	46	propositions	proposition	NNS
37681	2991	47	in	in	IN
37681	2991	48	this	this	DT
37681	2991	49	book	book	NN
37681	2991	50	upon	upon	IN
37681	2991	51	which	which	WDT
37681	2991	52	to	to	TO
37681	2991	53	base	base	VB
37681	2991	54	our	-PRON-	PRP$
37681	2991	55	work	work	NN
37681	2991	56	.	.	.
37681	2992	1	It	-PRON-	PRP
37681	2992	2	is	be	VBZ
37681	2992	3	also	also	RB
37681	2992	4	apparent	apparent	JJ
37681	2992	5	that	that	IN
37681	2992	6	even	even	RB
37681	2992	7	if	if	IN
37681	2992	8	the	the	DT
37681	2992	9	incommensurable	incommensurable	JJ
37681	2992	10	cases	case	NNS
37681	2992	11	are	be	VBP
37681	2992	12	generally	generally	RB
37681	2992	13	omitted	omit	VBN
37681	2992	14	,	,	,
37681	2992	15	the	the	DT
37681	2992	16	notion	notion	NN
37681	2992	17	of	of	IN
37681	2992	18	_	_	NNP
37681	2992	19	limit	limit	NN
37681	2992	20	_	_	NNP
37681	2992	21	is	be	VBZ
37681	2992	22	needed	need	VBN
37681	2992	23	at	at	IN
37681	2992	24	this	this	DT
37681	2992	25	time	time	NN
37681	2992	26	,	,	,
37681	2992	27	and	and	CC
37681	2992	28	that	that	IN
37681	2992	29	it	-PRON-	PRP
37681	2992	30	must	must	MD
37681	2992	31	briefly	briefly	RB
37681	2992	32	be	be	VB
37681	2992	33	reviewed	review	VBN
37681	2992	34	before	before	IN
37681	2992	35	proceeding	proceed	VBG
37681	2992	36	further	further	RB
37681	2992	37	.	.	.
37681	2993	1	There	there	EX
37681	2993	2	is	be	VBZ
37681	2993	3	,	,	,
37681	2993	4	however	however	RB
37681	2993	5	,	,	,
37681	2993	6	a	a	DT
37681	2993	7	much	much	RB
37681	2993	8	more	more	RBR
37681	2993	9	worthy	worthy	JJ
37681	2993	10	interest	interest	NN
37681	2993	11	than	than	IN
37681	2993	12	the	the	DT
37681	2993	13	mere	mere	JJ
37681	2993	14	mensuration	mensuration	NN
37681	2993	15	of	of	IN
37681	2993	16	the	the	DT
37681	2993	17	circle	circle	NN
37681	2993	18	,	,	,
37681	2993	19	namely	namely	RB
37681	2993	20	,	,	,
37681	2993	21	the	the	DT
37681	2993	22	construction	construction	NN
37681	2993	23	of	of	IN
37681	2993	24	such	such	JJ
37681	2993	25	polygons	polygon	NNS
37681	2993	26	as	as	IN
37681	2993	27	can	can	MD
37681	2993	28	readily	readily	RB
37681	2993	29	be	be	VB
37681	2993	30	formed	form	VBN
37681	2993	31	by	by	IN
37681	2993	32	the	the	DT
37681	2993	33	use	use	NN
37681	2993	34	of	of	IN
37681	2993	35	compasses	compass	NNS
37681	2993	36	and	and	CC
37681	2993	37	straightedge	straightedge	NN
37681	2993	38	alone	alone	RB
37681	2993	39	.	.	.
37681	2994	1	The	the	DT
37681	2994	2	pleasure	pleasure	NN
37681	2994	3	of	of	IN
37681	2994	4	constructing	construct	VBG
37681	2994	5	such	such	JJ
37681	2994	6	figures	figure	NNS
37681	2994	7	and	and	CC
37681	2994	8	of	of	IN
37681	2994	9	proving	prove	VBG
37681	2994	10	that	that	IN
37681	2994	11	the	the	DT
37681	2994	12	construction	construction	NN
37681	2994	13	is	be	VBZ
37681	2994	14	correct	correct	JJ
37681	2994	15	is	be	VBZ
37681	2994	16	of	of	IN
37681	2994	17	itself	-PRON-	PRP
37681	2994	18	sufficient	sufficient	JJ
37681	2994	19	justification	justification	NN
37681	2994	20	for	for	IN
37681	2994	21	the	the	DT
37681	2994	22	work	work	NN
37681	2994	23	.	.	.
37681	2995	1	As	as	IN
37681	2995	2	to	to	IN
37681	2995	3	the	the	DT
37681	2995	4	use	use	NN
37681	2995	5	of	of	IN
37681	2995	6	such	such	JJ
37681	2995	7	figures	figure	NNS
37681	2995	8	in	in	IN
37681	2995	9	geometric	geometric	JJ
37681	2995	10	design	design	NN
37681	2995	11	,	,	,
37681	2995	12	some	some	DT
37681	2995	13	discussion	discussion	NN
37681	2995	14	will	will	MD
37681	2995	15	be	be	VB
37681	2995	16	offered	offer	VBN
37681	2995	17	at	at	IN
37681	2995	18	the	the	DT
37681	2995	19	close	close	NN
37681	2995	20	of	of	IN
37681	2995	21	this	this	DT
37681	2995	22	chapter	chapter	NN
37681	2995	23	.	.	.
37681	2996	1	The	the	DT
37681	2996	2	first	first	JJ
37681	2996	3	few	few	JJ
37681	2996	4	propositions	proposition	NNS
37681	2996	5	include	include	VBP
37681	2996	6	those	those	DT
37681	2996	7	that	that	WDT
37681	2996	8	lead	lead	VBP
37681	2996	9	up	up	IN
37681	2996	10	to	to	IN
37681	2996	11	the	the	DT
37681	2996	12	mensuration	mensuration	NN
37681	2996	13	of	of	IN
37681	2996	14	the	the	DT
37681	2996	15	circle	circle	NN
37681	2996	16	.	.	.
37681	2997	1	After	after	IN
37681	2997	2	they	-PRON-	PRP
37681	2997	3	are	be	VBP
37681	2997	4	proved	prove	VBN
37681	2997	5	it	-PRON-	PRP
37681	2997	6	is	be	VBZ
37681	2997	7	assumed	assume	VBN
37681	2997	8	that	that	IN
37681	2997	9	the	the	DT
37681	2997	10	circle	circle	NN
37681	2997	11	is	be	VBZ
37681	2997	12	the	the	DT
37681	2997	13	limit	limit	NN
37681	2997	14	of	of	IN
37681	2997	15	the	the	DT
37681	2997	16	regular	regular	JJ
37681	2997	17	inscribed	inscribed	JJ
37681	2997	18	and	and	CC
37681	2997	19	circumscribed	circumscribed	JJ
37681	2997	20	polygons	polygon	NNS
37681	2997	21	as	as	IN
37681	2997	22	the	the	DT
37681	2997	23	number	number	NN
37681	2997	24	of	of	IN
37681	2997	25	sides	side	NNS
37681	2997	26	increases	increase	VBZ
37681	2997	27	indefinitely	indefinitely	RB
37681	2997	28	.	.	.
37681	2998	1	This	this	DT
37681	2998	2	may	may	MD
37681	2998	3	often	often	RB
37681	2998	4	be	be	VB
37681	2998	5	proved	prove	VBN
37681	2998	6	with	with	IN
37681	2998	7	some	some	DT
37681	2998	8	approach	approach	NN
37681	2998	9	to	to	TO
37681	2998	10	rigor	rigor	VB
37681	2998	11	by	by	IN
37681	2998	12	a	a	DT
37681	2998	13	few	few	JJ
37681	2998	14	members	member	NNS
37681	2998	15	of	of	IN
37681	2998	16	an	an	DT
37681	2998	17	elementary	elementary	JJ
37681	2998	18	class	class	NN
37681	2998	19	,	,	,
37681	2998	20	but	but	CC
37681	2998	21	it	-PRON-	PRP
37681	2998	22	is	be	VBZ
37681	2998	23	the	the	DT
37681	2998	24	experience	experience	NN
37681	2998	25	of	of	IN
37681	2998	26	teachers	teacher	NNS
37681	2998	27	that	that	IN
37681	2998	28	the	the	DT
37681	2998	29	proof	proof	NN
37681	2998	30	is	be	VBZ
37681	2998	31	too	too	RB
37681	2998	32	difficult	difficult	JJ
37681	2998	33	for	for	IN
37681	2998	34	most	most	JJS
37681	2998	35	beginners	beginner	NNS
37681	2998	36	,	,	,
37681	2998	37	and	and	CC
37681	2998	38	so	so	RB
37681	2998	39	the	the	DT
37681	2998	40	assumption	assumption	NN
37681	2998	41	is	be	VBZ
37681	2998	42	usually	usually	RB
37681	2998	43	made	make	VBN
37681	2998	44	in	in	IN
37681	2998	45	the	the	DT
37681	2998	46	form	form	NN
37681	2998	47	of	of	IN
37681	2998	48	an	an	DT
37681	2998	49	unproved	unproved	JJ
37681	2998	50	theorem	theorem	NN
37681	2998	51	.	.	.
37681	2999	1	The	the	DT
37681	2999	2	following	follow	VBG
37681	2999	3	are	be	VBP
37681	2999	4	some	some	DT
37681	2999	5	of	of	IN
37681	2999	6	the	the	DT
37681	2999	7	leading	lead	VBG
37681	2999	8	propositions	proposition	NNS
37681	2999	9	of	of	IN
37681	2999	10	this	this	DT
37681	2999	11	book	book	NN
37681	2999	12	:	:	:
37681	2999	13	THEOREM	theorem	NN
37681	2999	14	.	.	.
37681	3000	1	_	_	NNP
37681	3000	2	Two	two	CD
37681	3000	3	circumferences	circumference	NNS
37681	3000	4	have	have	VBP
37681	3000	5	the	the	DT
37681	3000	6	same	same	JJ
37681	3000	7	ratio	ratio	NN
37681	3000	8	as	as	IN
37681	3000	9	their	-PRON-	PRP$
37681	3000	10	radii	radii	NN
37681	3000	11	.	.	.
37681	3000	12	_	_	NNP
37681	3000	13	This	this	DT
37681	3000	14	leads	lead	VBZ
37681	3000	15	to	to	IN
37681	3000	16	defining	define	VBG
37681	3000	17	the	the	DT
37681	3000	18	ratio	ratio	NN
37681	3000	19	of	of	IN
37681	3000	20	the	the	DT
37681	3000	21	circumference	circumference	NN
37681	3000	22	to	to	IN
37681	3000	23	the	the	DT
37681	3000	24	diameter	diameter	NN
37681	3000	25	as	as	IN
37681	3000	26	[	[	-LRB-
37681	3000	27	pi	pi	NN
37681	3000	28	]	]	-RRB-
37681	3000	29	.	.	.
37681	3001	1	Although	although	IN
37681	3001	2	this	this	DT
37681	3001	3	is	be	VBZ
37681	3001	4	a	a	DT
37681	3001	5	Greek	greek	JJ
37681	3001	6	letter	letter	NN
37681	3001	7	,	,	,
37681	3001	8	it	-PRON-	PRP
37681	3001	9	was	be	VBD
37681	3001	10	not	not	RB
37681	3001	11	used	use	VBN
37681	3001	12	by	by	IN
37681	3001	13	the	the	DT
37681	3001	14	Greeks	Greeks	NNPS
37681	3001	15	to	to	TO
37681	3001	16	represent	represent	VB
37681	3001	17	this	this	DT
37681	3001	18	ratio	ratio	NN
37681	3001	19	.	.	.
37681	3002	1	Indeed	indeed	RB
37681	3002	2	,	,	,
37681	3002	3	it	-PRON-	PRP
37681	3002	4	was	be	VBD
37681	3002	5	not	not	RB
37681	3002	6	until	until	IN
37681	3002	7	1706	1706	CD
37681	3002	8	that	that	IN
37681	3002	9	an	an	DT
37681	3002	10	English	english	JJ
37681	3002	11	writer	writer	NN
37681	3002	12	,	,	,
37681	3002	13	William	William	NNP
37681	3002	14	Jones	Jones	NNP
37681	3002	15	,	,	,
37681	3002	16	in	in	IN
37681	3002	17	his	-PRON-	PRP$
37681	3002	18	"	"	``
37681	3002	19	Synopsis	Synopsis	NNP
37681	3002	20	Palmariorum	Palmariorum	NNP
37681	3002	21	Matheseos	Matheseos	NNP
37681	3002	22	,	,	,
37681	3002	23	"	"	''
37681	3002	24	used	use	VBD
37681	3002	25	it	-PRON-	PRP
37681	3002	26	in	in	IN
37681	3002	27	this	this	DT
37681	3002	28	way	way	NN
37681	3002	29	,	,	,
37681	3002	30	it	-PRON-	PRP
37681	3002	31	being	be	VBG
37681	3002	32	the	the	DT
37681	3002	33	initial	initial	JJ
37681	3002	34	letter	letter	NN
37681	3002	35	of	of	IN
37681	3002	36	the	the	DT
37681	3002	37	Greek	greek	JJ
37681	3002	38	word	word	NN
37681	3002	39	for	for	IN
37681	3002	40	"	"	``
37681	3002	41	periphery	periphery	NN
37681	3002	42	.	.	.
37681	3002	43	"	"	''
37681	3003	1	After	after	IN
37681	3003	2	establishing	establish	VBG
37681	3003	3	the	the	DT
37681	3003	4	properties	property	NNS
37681	3003	5	that	that	WDT
37681	3003	6	_	_	NNP
37681	3003	7	c	c	NNP
37681	3003	8	_	_	NNP
37681	3003	9	=	=	SYM
37681	3003	10	2[pi]_r	2[pi]_r	CD
37681	3003	11	_	_	NNP
37681	3003	12	,	,	,
37681	3003	13	and	and	CC
37681	3003	14	_	_	NNP
37681	3003	15	a	a	DT
37681	3003	16	_	_	NNP
37681	3003	17	=	=	NFP
37681	3003	18	[	[	-LRB-
37681	3003	19	pi]_r_^2	pi]_r_^2	NNP
37681	3003	20	,	,	,
37681	3003	21	the	the	DT
37681	3003	22	textbooks	textbook	NNS
37681	3003	23	follow	follow	VBP
37681	3003	24	the	the	DT
37681	3003	25	Greek	greek	JJ
37681	3003	26	custom	custom	NN
37681	3003	27	and	and	CC
37681	3003	28	proceed	proceed	VBP
37681	3003	29	to	to	TO
37681	3003	30	show	show	VB
37681	3003	31	how	how	WRB
37681	3003	32	to	to	TO
37681	3003	33	inscribe	inscribe	NNP
37681	3003	34	and	and	CC
37681	3003	35	circumscribe	circumscribe	VB
37681	3003	36	various	various	JJ
37681	3003	37	regular	regular	JJ
37681	3003	38	polygons	polygon	NNS
37681	3003	39	,	,	,
37681	3003	40	the	the	DT
37681	3003	41	purpose	purpose	NN
37681	3003	42	being	be	VBG
37681	3003	43	to	to	TO
37681	3003	44	use	use	VB
37681	3003	45	these	these	DT
37681	3003	46	in	in	IN
37681	3003	47	computing	compute	VBG
37681	3003	48	the	the	DT
37681	3003	49	approximate	approximate	JJ
37681	3003	50	numerical	numerical	JJ
37681	3003	51	value	value	NN
37681	3003	52	of	of	IN
37681	3003	53	[	[	-LRB-
37681	3003	54	pi	pi	NN
37681	3003	55	]	]	-RRB-
37681	3003	56	.	.	.
37681	3004	1	Of	of	IN
37681	3004	2	these	these	DT
37681	3004	3	regular	regular	JJ
37681	3004	4	polygons	polygon	NNS
37681	3004	5	two	two	CD
37681	3004	6	are	be	VBP
37681	3004	7	of	of	IN
37681	3004	8	special	special	JJ
37681	3004	9	interest	interest	NN
37681	3004	10	,	,	,
37681	3004	11	and	and	CC
37681	3004	12	these	these	DT
37681	3004	13	will	will	MD
37681	3004	14	now	now	RB
37681	3004	15	be	be	VB
37681	3004	16	considered	consider	VBN
37681	3004	17	.	.	.
37681	3005	1	PROBLEM	problem	NN
37681	3005	2	.	.	.
37681	3006	1	_	_	NNP
37681	3006	2	To	to	TO
37681	3006	3	inscribe	inscribe	VB
37681	3006	4	a	a	DT
37681	3006	5	regular	regular	JJ
37681	3006	6	hexagon	hexagon	NN
37681	3006	7	in	in	IN
37681	3006	8	a	a	DT
37681	3006	9	circle	circle	NN
37681	3006	10	.	.	.
37681	3006	11	_	_	IN
37681	3006	12	That	that	IN
37681	3006	13	the	the	DT
37681	3006	14	side	side	NN
37681	3006	15	of	of	IN
37681	3006	16	a	a	DT
37681	3006	17	regular	regular	JJ
37681	3006	18	inscribed	inscribed	JJ
37681	3006	19	hexagon	hexagon	NNP
37681	3006	20	equals	equal	VBZ
37681	3006	21	the	the	DT
37681	3006	22	radius	radius	NN
37681	3006	23	must	must	MD
37681	3006	24	have	have	VB
37681	3006	25	been	be	VBN
37681	3006	26	recognized	recognize	VBN
37681	3006	27	very	very	RB
37681	3006	28	early	early	RB
37681	3006	29	.	.	.
37681	3007	1	The	the	DT
37681	3007	2	common	common	JJ
37681	3007	3	divisions	division	NNS
37681	3007	4	of	of	IN
37681	3007	5	the	the	DT
37681	3007	6	circle	circle	NN
37681	3007	7	in	in	IN
37681	3007	8	ancient	ancient	JJ
37681	3007	9	art	art	NN
37681	3007	10	are	be	VBP
37681	3007	11	into	into	IN
37681	3007	12	four	four	CD
37681	3007	13	,	,	,
37681	3007	14	six	six	CD
37681	3007	15	,	,	,
37681	3007	16	and	and	CC
37681	3007	17	eight	eight	CD
37681	3007	18	equal	equal	JJ
37681	3007	19	parts	part	NNS
37681	3007	20	.	.	.
37681	3008	1	No	no	DT
37681	3008	2	draftsman	draftsman	NN
37681	3008	3	could	could	MD
37681	3008	4	have	have	VB
37681	3008	5	worked	work	VBN
37681	3008	6	with	with	IN
37681	3008	7	a	a	DT
37681	3008	8	pair	pair	NN
37681	3008	9	of	of	IN
37681	3008	10	compasses	compass	NNS
37681	3008	11	without	without	IN
37681	3008	12	quickly	quickly	RB
37681	3008	13	learning	learn	VBG
37681	3008	14	how	how	WRB
37681	3008	15	to	to	TO
37681	3008	16	effect	effect	VB
37681	3008	17	these	these	DT
37681	3008	18	divisions	division	NNS
37681	3008	19	,	,	,
37681	3008	20	and	and	CC
37681	3008	21	that	that	IN
37681	3008	22	compasses	compass	NNS
37681	3008	23	were	be	VBD
37681	3008	24	early	early	RB
37681	3008	25	used	use	VBN
37681	3008	26	is	be	VBZ
37681	3008	27	attested	attest	VBN
37681	3008	28	by	by	IN
37681	3008	29	the	the	DT
37681	3008	30	specimens	specimen	NNS
37681	3008	31	of	of	IN
37681	3008	32	these	these	DT
37681	3008	33	instruments	instrument	NNS
37681	3008	34	often	often	RB
37681	3008	35	seen	see	VBN
37681	3008	36	in	in	IN
37681	3008	37	museums	museum	NNS
37681	3008	38	.	.	.
37681	3009	1	There	there	EX
37681	3009	2	is	be	VBZ
37681	3009	3	a	a	DT
37681	3009	4	tradition	tradition	NN
37681	3009	5	that	that	WDT
37681	3009	6	the	the	DT
37681	3009	7	ancient	ancient	JJ
37681	3009	8	Babylonians	Babylonians	NNPS
37681	3009	9	considered	consider	VBD
37681	3009	10	the	the	DT
37681	3009	11	circle	circle	NN
37681	3009	12	of	of	IN
37681	3009	13	the	the	DT
37681	3009	14	year	year	NN
37681	3009	15	as	as	IN
37681	3009	16	made	make	VBN
37681	3009	17	up	up	RP
37681	3009	18	of	of	IN
37681	3009	19	360	360	CD
37681	3009	20	days	day	NNS
37681	3009	21	,	,	,
37681	3009	22	whence	whence	NN
37681	3009	23	they	-PRON-	PRP
37681	3009	24	took	take	VBD
37681	3009	25	the	the	DT
37681	3009	26	circle	circle	NN
37681	3009	27	as	as	IN
37681	3009	28	composed	compose	VBN
37681	3009	29	of	of	IN
37681	3009	30	360	360	CD
37681	3009	31	steps	step	NNS
37681	3009	32	or	or	CC
37681	3009	33	grades	grade	NNS
37681	3009	34	(	(	-LRB-
37681	3009	35	degrees	degree	NNS
37681	3009	36	)	)	-RRB-
37681	3009	37	.	.	.
37681	3010	1	This	this	DT
37681	3010	2	tradition	tradition	NN
37681	3010	3	is	be	VBZ
37681	3010	4	without	without	IN
37681	3010	5	historic	historic	JJ
37681	3010	6	foundation	foundation	NN
37681	3010	7	,	,	,
37681	3010	8	however	however	RB
37681	3010	9	,	,	,
37681	3010	10	there	there	EX
37681	3010	11	being	be	VBG
37681	3010	12	no	no	DT
37681	3010	13	authority	authority	NN
37681	3010	14	in	in	IN
37681	3010	15	the	the	DT
37681	3010	16	inscriptions	inscription	NNS
37681	3010	17	for	for	IN
37681	3010	18	this	this	DT
37681	3010	19	assumption	assumption	NN
37681	3010	20	of	of	IN
37681	3010	21	the	the	DT
37681	3010	22	360-division	360-division	CD
37681	3010	23	by	by	IN
37681	3010	24	the	the	DT
37681	3010	25	Babylonians	Babylonians	NNPS
37681	3010	26	,	,	,
37681	3010	27	who	who	WP
37681	3010	28	seem	seem	VBP
37681	3010	29	rather	rather	RB
37681	3010	30	to	to	TO
37681	3010	31	have	have	VB
37681	3010	32	preferred	prefer	VBN
37681	3010	33	8	8	CD
37681	3010	34	,	,	,
37681	3010	35	12	12	CD
37681	3010	36	,	,	,
37681	3010	37	120	120	CD
37681	3010	38	,	,	,
37681	3010	39	240	240	CD
37681	3010	40	,	,	,
37681	3010	41	and	and	CC
37681	3010	42	480	480	CD
37681	3010	43	as	as	IN
37681	3010	44	their	-PRON-	PRP$
37681	3010	45	division	division	NN
37681	3010	46	numbers	number	NNS
37681	3010	47	.	.	.
37681	3011	1	The	the	DT
37681	3011	2	story	story	NN
37681	3011	3	of	of	IN
37681	3011	4	360	360	CD
37681	3011	5	°	°	NNS
37681	3011	6	in	in	IN
37681	3011	7	the	the	DT
37681	3011	8	Babylonian	babylonian	JJ
37681	3011	9	circle	circle	NN
37681	3011	10	seems	seem	VBZ
37681	3011	11	to	to	TO
37681	3011	12	start	start	VB
37681	3011	13	with	with	IN
37681	3011	14	Achilles	Achilles	NNP
37681	3011	15	Tatius	Tatius	NNP
37681	3011	16	,	,	,
37681	3011	17	an	an	DT
37681	3011	18	Alexandrian	alexandrian	JJ
37681	3011	19	grammarian	grammarian	NN
37681	3011	20	of	of	IN
37681	3011	21	the	the	DT
37681	3011	22	second	second	JJ
37681	3011	23	or	or	CC
37681	3011	24	third	third	JJ
37681	3011	25	century	century	NN
37681	3011	26	A.D.	A.D.	NNP
37681	3012	1	It	-PRON-	PRP
37681	3012	2	is	be	VBZ
37681	3012	3	possible	possible	JJ
37681	3012	4	,	,	,
37681	3012	5	however	however	RB
37681	3012	6	,	,	,
37681	3012	7	that	that	IN
37681	3012	8	the	the	DT
37681	3012	9	Babylonians	Babylonians	NNPS
37681	3012	10	got	get	VBD
37681	3012	11	their	-PRON-	PRP$
37681	3012	12	favorite	favorite	JJ
37681	3012	13	number	number	NN
37681	3012	14	60	60	CD
37681	3012	15	(	(	-LRB-
37681	3012	16	as	as	IN
37681	3012	17	in	in	IN
37681	3012	18	60	60	CD
37681	3012	19	seconds	second	NNS
37681	3012	20	make	make	VBP
37681	3012	21	a	a	DT
37681	3012	22	minute	minute	NN
37681	3012	23	,	,	,
37681	3012	24	60	60	CD
37681	3012	25	minutes	minute	NNS
37681	3012	26	make	make	VBP
37681	3012	27	an	an	DT
37681	3012	28	hour	hour	NN
37681	3012	29	or	or	CC
37681	3012	30	degree	degree	NN
37681	3012	31	)	)	-RRB-
37681	3012	32	from	from	IN
37681	3012	33	the	the	DT
37681	3012	34	hexagon	hexagon	NNP
37681	3012	35	in	in	IN
37681	3012	36	a	a	DT
37681	3012	37	circle	circle	NN
37681	3012	38	(	(	-LRB-
37681	3012	39	1/6	1/6	CD
37681	3012	40	of	of	IN
37681	3012	41	360	360	CD
37681	3012	42	°	°	NNS
37681	3012	43	=	=	SYM
37681	3012	44	60	60	CD
37681	3012	45	°	°	NNS
37681	3012	46	)	)	-RRB-
37681	3012	47	,	,	,
37681	3012	48	although	although	IN
37681	3012	49	the	the	DT
37681	3012	50	probabilities	probability	NNS
37681	3012	51	seem	seem	VBP
37681	3012	52	to	to	TO
37681	3012	53	be	be	VB
37681	3012	54	that	that	IN
37681	3012	55	there	there	EX
37681	3012	56	is	be	VBZ
37681	3012	57	no	no	DT
37681	3012	58	such	such	JJ
37681	3012	59	connection	connection	NN
37681	3012	60	.	.	.
37681	3013	1	[	[	-LRB-
37681	3013	2	83	83	CD
37681	3013	3	]	]	-RRB-
37681	3013	4	The	the	DT
37681	3013	5	applications	application	NNS
37681	3013	6	of	of	IN
37681	3013	7	this	this	DT
37681	3013	8	problem	problem	NN
37681	3013	9	to	to	IN
37681	3013	10	mensuration	mensuration	NN
37681	3013	11	are	be	VBP
37681	3013	12	numerous	numerous	JJ
37681	3013	13	.	.	.
37681	3014	1	The	the	DT
37681	3014	2	fact	fact	NN
37681	3014	3	that	that	IN
37681	3014	4	we	-PRON-	PRP
37681	3014	5	may	may	MD
37681	3014	6	use	use	VB
37681	3014	7	for	for	IN
37681	3014	8	tiles	tile	NNS
37681	3014	9	on	on	IN
37681	3014	10	a	a	DT
37681	3014	11	floor	floor	NN
37681	3014	12	three	three	CD
37681	3014	13	regular	regular	JJ
37681	3014	14	polygons	polygon	NNS
37681	3014	15	--	--	:
37681	3014	16	the	the	DT
37681	3014	17	triangle	triangle	NN
37681	3014	18	,	,	,
37681	3014	19	square	square	NN
37681	3014	20	,	,	,
37681	3014	21	and	and	CC
37681	3014	22	hexagon	hexagon	NNP
37681	3014	23	--	--	:
37681	3014	24	is	be	VBZ
37681	3014	25	noteworthy	noteworthy	JJ
37681	3014	26	,	,	,
37681	3014	27	a	a	DT
37681	3014	28	fact	fact	NN
37681	3014	29	that	that	IN
37681	3014	30	Proclus	Proclus	NNP
37681	3014	31	tells	tell	VBZ
37681	3014	32	us	-PRON-	PRP
37681	3014	33	was	be	VBD
37681	3014	34	recognized	recognize	VBN
37681	3014	35	by	by	IN
37681	3014	36	Pythagoras	Pythagoras	NNP
37681	3014	37	.	.	.
37681	3015	1	The	the	DT
37681	3015	2	measurement	measurement	NN
37681	3015	3	of	of	IN
37681	3015	4	the	the	DT
37681	3015	5	regular	regular	JJ
37681	3015	6	hexagon	hexagon	NNP
37681	3015	7	,	,	,
37681	3015	8	given	give	VBN
37681	3015	9	one	one	CD
37681	3015	10	side	side	NN
37681	3015	11	,	,	,
37681	3015	12	may	may	MD
37681	3015	13	be	be	VB
37681	3015	14	used	use	VBN
37681	3015	15	in	in	IN
37681	3015	16	computing	compute	VBG
37681	3015	17	sections	section	NNS
37681	3015	18	of	of	IN
37681	3015	19	hexagonal	hexagonal	JJ
37681	3015	20	columns	column	NNS
37681	3015	21	,	,	,
37681	3015	22	in	in	IN
37681	3015	23	finding	find	VBG
37681	3015	24	areas	area	NNS
37681	3015	25	of	of	IN
37681	3015	26	flower	flower	NN
37681	3015	27	beds	bed	NNS
37681	3015	28	,	,	,
37681	3015	29	and	and	CC
37681	3015	30	in	in	IN
37681	3015	31	other	other	JJ
37681	3015	32	similar	similar	JJ
37681	3015	33	cases	case	NNS
37681	3015	34	.	.	.
37681	3016	1	This	this	DT
37681	3016	2	review	review	NN
37681	3016	3	of	of	IN
37681	3016	4	the	the	DT
37681	3016	5	names	name	NNS
37681	3016	6	of	of	IN
37681	3016	7	the	the	DT
37681	3016	8	polygons	polygon	NNS
37681	3016	9	offers	offer	VBZ
37681	3016	10	an	an	DT
37681	3016	11	opportunity	opportunity	NN
37681	3016	12	to	to	TO
37681	3016	13	impress	impress	VB
37681	3016	14	their	-PRON-	PRP$
37681	3016	15	etymology	etymology	NN
37681	3016	16	again	again	RB
37681	3016	17	on	on	IN
37681	3016	18	the	the	DT
37681	3016	19	mind	mind	NN
37681	3016	20	.	.	.
37681	3017	1	In	in	IN
37681	3017	2	this	this	DT
37681	3017	3	case	case	NN
37681	3017	4	,	,	,
37681	3017	5	for	for	IN
37681	3017	6	example	example	NN
37681	3017	7	,	,	,
37681	3017	8	we	-PRON-	PRP
37681	3017	9	have	have	VBP
37681	3017	10	"	"	``
37681	3017	11	hexagon	hexagon	NNP
37681	3017	12	"	"	''
37681	3017	13	from	from	IN
37681	3017	14	the	the	DT
37681	3017	15	Greek	greek	JJ
37681	3017	16	words	word	NNS
37681	3017	17	for	for	IN
37681	3017	18	"	"	``
37681	3017	19	six	six	CD
37681	3017	20	"	"	''
37681	3017	21	and	and	CC
37681	3017	22	"	"	``
37681	3017	23	angle	angle	NN
37681	3017	24	.	.	.
37681	3017	25	"	"	''
37681	3018	1	PROBLEM	problem	NN
37681	3018	2	.	.	.
37681	3019	1	_	_	NNP
37681	3019	2	To	to	TO
37681	3019	3	inscribe	inscribe	VB
37681	3019	4	a	a	DT
37681	3019	5	regular	regular	JJ
37681	3019	6	decagon	decagon	NN
37681	3019	7	in	in	IN
37681	3019	8	a	a	DT
37681	3019	9	given	give	VBN
37681	3019	10	circle	circle	NN
37681	3019	11	.	.	.
37681	3019	12	_	_	NNP
37681	3019	13	Euclid	Euclid	NNP
37681	3019	14	states	state	VBZ
37681	3019	15	the	the	DT
37681	3019	16	problem	problem	NN
37681	3019	17	thus	thus	RB
37681	3019	18	:	:	:
37681	3019	19	_	_	NNP
37681	3019	20	To	to	TO
37681	3019	21	construct	construct	VB
37681	3019	22	an	an	DT
37681	3019	23	isosceles	isoscele	NNS
37681	3019	24	triangle	triangle	NN
37681	3019	25	having	have	VBG
37681	3019	26	each	each	DT
37681	3019	27	of	of	IN
37681	3019	28	the	the	DT
37681	3019	29	angles	angle	NNS
37681	3019	30	at	at	IN
37681	3019	31	the	the	DT
37681	3019	32	base	base	NN
37681	3019	33	double	double	JJ
37681	3019	34	of	of	IN
37681	3019	35	the	the	DT
37681	3019	36	remaining	remain	VBG
37681	3019	37	one	one	CD
37681	3019	38	.	.	.
37681	3019	39	_	_	NNP
37681	3019	40	This	this	DT
37681	3019	41	makes	make	VBZ
37681	3019	42	each	each	DT
37681	3019	43	base	base	NN
37681	3019	44	angle	angle	NN
37681	3019	45	72	72	CD
37681	3019	46	°	°	NNS
37681	3019	47	and	and	CC
37681	3019	48	the	the	DT
37681	3019	49	vertical	vertical	JJ
37681	3019	50	angle	angle	NN
37681	3019	51	36	36	CD
37681	3019	52	°	°	NNS
37681	3019	53	,	,	,
37681	3019	54	the	the	DT
37681	3019	55	latter	latter	JJ
37681	3019	56	being	be	VBG
37681	3019	57	the	the	DT
37681	3019	58	central	central	JJ
37681	3019	59	angle	angle	NN
37681	3019	60	of	of	IN
37681	3019	61	a	a	DT
37681	3019	62	regular	regular	JJ
37681	3019	63	decagon,--essentially	decagon,--essentially	RB
37681	3019	64	our	-PRON-	PRP$
37681	3019	65	present	present	JJ
37681	3019	66	method	method	NN
37681	3019	67	.	.	.
37681	3020	1	This	this	DT
37681	3020	2	proposition	proposition	NN
37681	3020	3	seems	seem	VBZ
37681	3020	4	undoubtedly	undoubtedly	RB
37681	3020	5	due	due	JJ
37681	3020	6	to	to	IN
37681	3020	7	the	the	DT
37681	3020	8	Pythagoreans	Pythagoreans	NNPS
37681	3020	9	,	,	,
37681	3020	10	as	as	IN
37681	3020	11	tradition	tradition	NN
37681	3020	12	has	have	VBZ
37681	3020	13	always	always	RB
37681	3020	14	asserted	assert	VBN
37681	3020	15	.	.	.
37681	3021	1	Proclus	Proclus	NNP
37681	3021	2	tells	tell	VBZ
37681	3021	3	us	-PRON-	PRP
37681	3021	4	that	that	IN
37681	3021	5	Pythagoras	Pythagoras	NNP
37681	3021	6	discovered	discover	VBD
37681	3021	7	"	"	``
37681	3021	8	the	the	DT
37681	3021	9	construction	construction	NN
37681	3021	10	of	of	IN
37681	3021	11	the	the	DT
37681	3021	12	cosmic	cosmic	JJ
37681	3021	13	figures	figure	NNS
37681	3021	14	,	,	,
37681	3021	15	"	"	''
37681	3021	16	or	or	CC
37681	3021	17	the	the	DT
37681	3021	18	five	five	CD
37681	3021	19	regular	regular	JJ
37681	3021	20	polyhedrons	polyhedron	NNS
37681	3021	21	,	,	,
37681	3021	22	and	and	CC
37681	3021	23	one	one	CD
37681	3021	24	of	of	IN
37681	3021	25	these	these	DT
37681	3021	26	(	(	-LRB-
37681	3021	27	the	the	DT
37681	3021	28	dodecahedron	dodecahedron	FW
37681	3021	29	)	)	-RRB-
37681	3021	30	involves	involve	VBZ
37681	3021	31	the	the	DT
37681	3021	32	construction	construction	NN
37681	3021	33	of	of	IN
37681	3021	34	the	the	DT
37681	3021	35	regular	regular	JJ
37681	3021	36	pentagon	pentagon	NNP
37681	3021	37	.	.	.
37681	3022	1	Iamblichus	Iamblichus	NNP
37681	3022	2	(	(	-LRB-
37681	3022	3	_	_	NNP
37681	3022	4	ca	ca	NNP
37681	3022	5	.	.	.
37681	3022	6	_	_	NNP
37681	3022	7	325	325	CD
37681	3022	8	A.D.	A.D.	NNP
37681	3022	9	)	)	-RRB-
37681	3022	10	tells	tell	VBZ
37681	3022	11	us	-PRON-	PRP
37681	3022	12	that	that	IN
37681	3022	13	Hippasus	Hippasus	NNP
37681	3022	14	,	,	,
37681	3022	15	a	a	DT
37681	3022	16	Pythagorean	Pythagorean	NNP
37681	3022	17	,	,	,
37681	3022	18	was	be	VBD
37681	3022	19	said	say	VBN
37681	3022	20	to	to	TO
37681	3022	21	have	have	VB
37681	3022	22	been	be	VBN
37681	3022	23	drowned	drown	VBN
37681	3022	24	for	for	IN
37681	3022	25	daring	dare	VBG
37681	3022	26	to	to	TO
37681	3022	27	claim	claim	VB
37681	3022	28	credit	credit	NN
37681	3022	29	for	for	IN
37681	3022	30	the	the	DT
37681	3022	31	construction	construction	NN
37681	3022	32	of	of	IN
37681	3022	33	the	the	DT
37681	3022	34	regular	regular	JJ
37681	3022	35	dodecahedron	dodecahedron	NN
37681	3022	36	,	,	,
37681	3022	37	when	when	WRB
37681	3022	38	by	by	IN
37681	3022	39	the	the	DT
37681	3022	40	rules	rule	NNS
37681	3022	41	of	of	IN
37681	3022	42	the	the	DT
37681	3022	43	brotherhood	brotherhood	NN
37681	3022	44	all	all	DT
37681	3022	45	credit	credit	NN
37681	3022	46	should	should	MD
37681	3022	47	have	have	VB
37681	3022	48	been	be	VBN
37681	3022	49	assigned	assign	VBN
37681	3022	50	to	to	IN
37681	3022	51	Pythagoras	Pythagoras	NNP
37681	3022	52	.	.	.
37681	3023	1	If	if	IN
37681	3023	2	a	a	DT
37681	3023	3	regular	regular	JJ
37681	3023	4	polygon	polygon	NN
37681	3023	5	of	of	IN
37681	3023	6	_	_	NNP
37681	3023	7	s	s	NNP
37681	3023	8	_	_	NNP
37681	3023	9	sides	side	NNS
37681	3023	10	can	can	MD
37681	3023	11	be	be	VB
37681	3023	12	inscribed	inscribe	VBN
37681	3023	13	,	,	,
37681	3023	14	we	-PRON-	PRP
37681	3023	15	may	may	MD
37681	3023	16	bisect	bisect	VB
37681	3023	17	the	the	DT
37681	3023	18	central	central	JJ
37681	3023	19	angles	angle	NNS
37681	3023	20	,	,	,
37681	3023	21	and	and	CC
37681	3023	22	therefore	therefore	RB
37681	3023	23	inscribe	inscribe	VBP
37681	3023	24	one	one	CD
37681	3023	25	of	of	IN
37681	3023	26	2_s	2_s	CD
37681	3023	27	_	_	NNP
37681	3023	28	sides	side	NNS
37681	3023	29	,	,	,
37681	3023	30	and	and	CC
37681	3023	31	then	then	RB
37681	3023	32	of	of	IN
37681	3023	33	4_s	4_s	CD
37681	3023	34	_	_	NNP
37681	3023	35	sides	side	NNS
37681	3023	36	,	,	,
37681	3023	37	and	and	CC
37681	3023	38	then	then	RB
37681	3023	39	of	of	IN
37681	3023	40	8_s	8_s	CD
37681	3023	41	_	_	NNP
37681	3023	42	sides	side	NNS
37681	3023	43	,	,	,
37681	3023	44	and	and	CC
37681	3023	45	in	in	IN
37681	3023	46	general	general	JJ
37681	3023	47	of	of	IN
37681	3023	48	2^{_n_}_s	2^{_n_}_s	NNP
37681	3023	49	_	_	NNP
37681	3023	50	sides	side	NNS
37681	3023	51	.	.	.
37681	3024	1	This	this	DT
37681	3024	2	includes	include	VBZ
37681	3024	3	the	the	DT
37681	3024	4	case	case	NN
37681	3024	5	of	of	IN
37681	3024	6	_	_	NNP
37681	3024	7	s	s	NNP
37681	3024	8	_	_	NNP
37681	3024	9	=	=	SYM
37681	3024	10	2	2	CD
37681	3024	11	and	and	CC
37681	3024	12	_	_	NNP
37681	3024	13	n	n	CC
37681	3024	14	_	_	NNP
37681	3024	15	=	=	SYM
37681	3024	16	0	0	NFP
37681	3024	17	,	,	,
37681	3024	18	for	for	IN
37681	3024	19	we	-PRON-	PRP
37681	3024	20	can	can	MD
37681	3024	21	inscribe	inscribe	VB
37681	3024	22	a	a	DT
37681	3024	23	regular	regular	JJ
37681	3024	24	polygon	polygon	NN
37681	3024	25	of	of	IN
37681	3024	26	two	two	CD
37681	3024	27	sides	side	NNS
37681	3024	28	,	,	,
37681	3024	29	the	the	DT
37681	3024	30	angles	angle	NNS
37681	3024	31	being	be	VBG
37681	3024	32	,	,	,
37681	3024	33	by	by	IN
37681	3024	34	the	the	DT
37681	3024	35	usual	usual	JJ
37681	3024	36	formula	formula	NN
37681	3024	37	,	,	,
37681	3024	38	2(2	2(2	NNP
37681	3024	39	-	-	HYPH
37681	3024	40	2)/2	2)/2	NNP
37681	3024	41	=	=	SYM
37681	3024	42	0	0	CD
37681	3024	43	,	,	,
37681	3024	44	although	although	IN
37681	3024	45	,	,	,
37681	3024	46	of	of	IN
37681	3024	47	course	course	NN
37681	3024	48	,	,	,
37681	3024	49	we	-PRON-	PRP
37681	3024	50	never	never	RB
37681	3024	51	think	think	VBP
37681	3024	52	of	of	IN
37681	3024	53	two	two	CD
37681	3024	54	equal	equal	JJ
37681	3024	55	and	and	CC
37681	3024	56	coincident	coincident	JJ
37681	3024	57	lines	line	NNS
37681	3024	58	as	as	IN
37681	3024	59	forming	form	VBG
37681	3024	60	what	what	WP
37681	3024	61	we	-PRON-	PRP
37681	3024	62	might	may	MD
37681	3024	63	call	call	VB
37681	3024	64	a	a	DT
37681	3024	65	_	_	NNP
37681	3024	66	digon	digon	NN
37681	3024	67	_	_	NNP
37681	3024	68	.	.	.
37681	3025	1	We	-PRON-	PRP
37681	3025	2	therefore	therefore	RB
37681	3025	3	have	have	VBP
37681	3025	4	the	the	DT
37681	3025	5	following	following	JJ
37681	3025	6	regular	regular	JJ
37681	3025	7	polygons	polygon	NNS
37681	3025	8	:	:	:
37681	3025	9	From	from	IN
37681	3025	10	the	the	DT
37681	3025	11	equilateral	equilateral	JJ
37681	3025	12	triangle	triangle	NN
37681	3025	13	,	,	,
37681	3025	14	regular	regular	JJ
37681	3025	15	polygons	polygon	NNS
37681	3025	16	of	of	IN
37681	3025	17	2^_n	2^_n	NNP
37681	3025	18	_	_	NNP
37681	3025	19	·	·	NFP
37681	3025	20	3	3	CD
37681	3025	21	sides	side	NNS
37681	3025	22	;	;	:
37681	3025	23	From	from	IN
37681	3025	24	the	the	DT
37681	3025	25	square	square	JJ
37681	3025	26	,	,	,
37681	3025	27	regular	regular	JJ
37681	3025	28	polygons	polygon	NNS
37681	3025	29	of	of	IN
37681	3025	30	2^_n	2^_n	NNP
37681	3025	31	_	_	NNP
37681	3025	32	sides	side	NNS
37681	3025	33	;	;	:
37681	3025	34	From	from	IN
37681	3025	35	the	the	DT
37681	3025	36	regular	regular	JJ
37681	3025	37	pentagon	pentagon	NNP
37681	3025	38	,	,	,
37681	3025	39	regular	regular	JJ
37681	3025	40	polygons	polygon	NNS
37681	3025	41	of	of	IN
37681	3025	42	2^_n	2^_n	NNP
37681	3025	43	_	_	NNP
37681	3025	44	·	·	NFP
37681	3025	45	5	5	CD
37681	3025	46	sides	side	NNS
37681	3025	47	;	;	:
37681	3025	48	From	from	IN
37681	3025	49	the	the	DT
37681	3025	50	regular	regular	JJ
37681	3025	51	pentedecagon	pentedecagon	NN
37681	3025	52	,	,	,
37681	3025	53	regular	regular	JJ
37681	3025	54	polygons	polygon	NNS
37681	3025	55	of	of	IN
37681	3025	56	2^_n	2^_n	NNP
37681	3025	57	_	_	NNP
37681	3025	58	·	·	NFP
37681	3025	59	15	15	CD
37681	3025	60	sides	side	NNS
37681	3025	61	.	.	.
37681	3026	1	This	this	DT
37681	3026	2	gives	give	VBZ
37681	3026	3	us	-PRON-	PRP
37681	3026	4	,	,	,
37681	3026	5	for	for	IN
37681	3026	6	successive	successive	JJ
37681	3026	7	values	value	NNS
37681	3026	8	of	of	IN
37681	3026	9	_	_	NNP
37681	3026	10	n	n	NNP
37681	3026	11	_	_	NNP
37681	3026	12	,	,	,
37681	3026	13	the	the	DT
37681	3026	14	following	follow	VBG
37681	3026	15	regular	regular	JJ
37681	3026	16	polygons	polygon	NNS
37681	3026	17	of	of	IN
37681	3026	18	less	less	JJR
37681	3026	19	than	than	IN
37681	3026	20	100	100	CD
37681	3026	21	sides	side	NNS
37681	3026	22	:	:	:
37681	3026	23	From	from	IN
37681	3026	24	2^_n	2^_n	NNP
37681	3026	25	_	_	NNP
37681	3026	26	·	·	NFP
37681	3026	27	3	3	CD
37681	3026	28	,	,	,
37681	3026	29	3	3	CD
37681	3026	30	,	,	,
37681	3026	31	6	6	CD
37681	3026	32	,	,	,
37681	3026	33	12	12	CD
37681	3026	34	,	,	,
37681	3026	35	24	24	CD
37681	3026	36	,	,	,
37681	3026	37	48	48	CD
37681	3026	38	,	,	,
37681	3026	39	96	96	CD
37681	3026	40	;	;	:
37681	3026	41	From	from	IN
37681	3026	42	2^_n	2^_n	NNP
37681	3026	43	_	_	NNP
37681	3026	44	,	,	,
37681	3026	45	2	2	CD
37681	3026	46	,	,	,
37681	3026	47	4	4	CD
37681	3026	48	,	,	,
37681	3026	49	8	8	CD
37681	3026	50	,	,	,
37681	3026	51	16	16	CD
37681	3026	52	,	,	,
37681	3026	53	32	32	CD
37681	3026	54	,	,	,
37681	3026	55	64	64	CD
37681	3026	56	;	;	:
37681	3026	57	From	from	IN
37681	3026	58	2^_n	2^_n	NNP
37681	3026	59	_	_	NNP
37681	3026	60	·	·	NFP
37681	3026	61	5	5	CD
37681	3026	62	,	,	,
37681	3026	63	5	5	CD
37681	3026	64	,	,	,
37681	3026	65	10	10	CD
37681	3026	66	,	,	,
37681	3026	67	20	20	CD
37681	3026	68	,	,	,
37681	3026	69	40	40	CD
37681	3026	70	,	,	,
37681	3026	71	80	80	CD
37681	3026	72	;	;	:
37681	3026	73	From	from	IN
37681	3026	74	2^_n	2^_n	NNP
37681	3026	75	_	_	NNP
37681	3026	76	·	·	NFP
37681	3026	77	15	15	CD
37681	3026	78	,	,	,
37681	3026	79	15	15	CD
37681	3026	80	,	,	,
37681	3026	81	30	30	CD
37681	3026	82	,	,	,
37681	3026	83	60	60	CD
37681	3026	84	.	.	.
37681	3027	1	[	[	-LRB-
37681	3027	2	Illustration	illustration	NN
37681	3027	3	:	:	:
37681	3027	4	ROMAN	ROMAN	NNP
37681	3027	5	MOSAIC	MOSAIC	NNP
37681	3027	6	FOUND	find	VBD
37681	3027	7	AT	at	IN
37681	3027	8	POMPEII	POMPEII	NNP
37681	3027	9	]	]	-RRB-
37681	3027	10	Gauss	Gauss	NNP
37681	3027	11	(	(	-LRB-
37681	3027	12	1777	1777	CD
37681	3027	13	-	-	SYM
37681	3027	14	1855	1855	CD
37681	3027	15	)	)	-RRB-
37681	3027	16	,	,	,
37681	3027	17	a	a	DT
37681	3027	18	celebrated	celebrated	JJ
37681	3027	19	German	german	JJ
37681	3027	20	mathematician	mathematician	NN
37681	3027	21	,	,	,
37681	3027	22	proved	prove	VBN
37681	3027	23	(	(	-LRB-
37681	3027	24	in	in	IN
37681	3027	25	1796	1796	CD
37681	3027	26	)	)	-RRB-
37681	3027	27	that	that	IN
37681	3027	28	it	-PRON-	PRP
37681	3027	29	is	be	VBZ
37681	3027	30	possible	possible	JJ
37681	3027	31	also	also	RB
37681	3027	32	to	to	TO
37681	3027	33	inscribe	inscribe	VB
37681	3027	34	a	a	DT
37681	3027	35	regular	regular	JJ
37681	3027	36	polygon	polygon	NN
37681	3027	37	of	of	IN
37681	3027	38	17	17	CD
37681	3027	39	sides	side	NNS
37681	3027	40	,	,	,
37681	3027	41	and	and	CC
37681	3027	42	hence	hence	RB
37681	3027	43	polygons	polygon	NNS
37681	3027	44	of	of	IN
37681	3027	45	2^_n	2^_n	NNP
37681	3027	46	_	_	NNP
37681	3027	47	·	·	NFP
37681	3027	48	17	17	CD
37681	3027	49	sides	side	NNS
37681	3027	50	,	,	,
37681	3027	51	or	or	CC
37681	3027	52	17	17	CD
37681	3027	53	,	,	,
37681	3027	54	34	34	CD
37681	3027	55	,	,	,
37681	3027	56	68	68	CD
37681	3027	57	,	,	,
37681	3027	58	...	...	NFP
37681	3027	59	,	,	,
37681	3027	60	sides	side	NNS
37681	3027	61	,	,	,
37681	3027	62	and	and	CC
37681	3027	63	also	also	RB
37681	3027	64	3	3	CD
37681	3027	65	·	·	SYM
37681	3027	66	17	17	CD
37681	3027	67	=	=	SYM
37681	3027	68	51	51	CD
37681	3027	69	and	and	CC
37681	3027	70	5	5	CD
37681	3027	71	·	·	SYM
37681	3027	72	17	17	CD
37681	3027	73	=	=	SYM
37681	3027	74	85	85	CD
37681	3027	75	sides	side	NNS
37681	3027	76	,	,	,
37681	3027	77	by	by	IN
37681	3027	78	the	the	DT
37681	3027	79	use	use	NN
37681	3027	80	of	of	IN
37681	3027	81	the	the	DT
37681	3027	82	compasses	compass	NNS
37681	3027	83	and	and	CC
37681	3027	84	straightedge	straightedge	NN
37681	3027	85	,	,	,
37681	3027	86	but	but	CC
37681	3027	87	the	the	DT
37681	3027	88	proof	proof	NN
37681	3027	89	is	be	VBZ
37681	3027	90	not	not	RB
37681	3027	91	adapted	adapt	VBN
37681	3027	92	to	to	IN
37681	3027	93	elementary	elementary	JJ
37681	3027	94	geometry	geometry	NN
37681	3027	95	.	.	.
37681	3028	1	In	in	IN
37681	3028	2	connection	connection	NN
37681	3028	3	with	with	IN
37681	3028	4	the	the	DT
37681	3028	5	study	study	NN
37681	3028	6	of	of	IN
37681	3028	7	the	the	DT
37681	3028	8	regular	regular	JJ
37681	3028	9	polygons	polygon	NNS
37681	3028	10	some	some	DT
37681	3028	11	interest	interest	NN
37681	3028	12	attaches	attach	VBZ
37681	3028	13	to	to	IN
37681	3028	14	the	the	DT
37681	3028	15	reference	reference	NN
37681	3028	16	to	to	IN
37681	3028	17	various	various	JJ
37681	3028	18	forms	form	NNS
37681	3028	19	of	of	IN
37681	3028	20	decorative	decorative	JJ
37681	3028	21	design	design	NN
37681	3028	22	.	.	.
37681	3029	1	The	the	DT
37681	3029	2	mosaic	mosaic	JJ
37681	3029	3	floor	floor	NN
37681	3029	4	,	,	,
37681	3029	5	parquetry	parquetry	NN
37681	3029	6	,	,	,
37681	3029	7	Gothic	gothic	JJ
37681	3029	8	windows	window	NNS
37681	3029	9	,	,	,
37681	3029	10	and	and	CC
37681	3029	11	patterns	pattern	NNS
37681	3029	12	of	of	IN
37681	3029	13	various	various	JJ
37681	3029	14	kinds	kind	NNS
37681	3029	15	often	often	RB
37681	3029	16	involve	involve	VBP
37681	3029	17	the	the	DT
37681	3029	18	regular	regular	JJ
37681	3029	19	figures	figure	NNS
37681	3029	20	.	.	.
37681	3030	1	If	if	IN
37681	3030	2	the	the	DT
37681	3030	3	teacher	teacher	NN
37681	3030	4	uses	use	VBZ
37681	3030	5	such	such	JJ
37681	3030	6	material	material	NN
37681	3030	7	,	,	,
37681	3030	8	care	care	NN
37681	3030	9	should	should	MD
37681	3030	10	be	be	VB
37681	3030	11	taken	take	VBN
37681	3030	12	to	to	TO
37681	3030	13	exemplify	exemplify	VB
37681	3030	14	good	good	JJ
37681	3030	15	art	art	NN
37681	3030	16	.	.	.
37681	3031	1	For	for	IN
37681	3031	2	example	example	NN
37681	3031	3	,	,	,
37681	3031	4	the	the	DT
37681	3031	5	equilateral	equilateral	JJ
37681	3031	6	triangle	triangle	NN
37681	3031	7	and	and	CC
37681	3031	8	its	-PRON-	PRP$
37681	3031	9	relation	relation	NN
37681	3031	10	to	to	IN
37681	3031	11	the	the	DT
37681	3031	12	regular	regular	JJ
37681	3031	13	hexagon	hexagon	NNP
37681	3031	14	is	be	VBZ
37681	3031	15	shown	show	VBN
37681	3031	16	in	in	IN
37681	3031	17	the	the	DT
37681	3031	18	picture	picture	NN
37681	3031	19	of	of	IN
37681	3031	20	an	an	DT
37681	3031	21	ancient	ancient	JJ
37681	3031	22	Roman	roman	JJ
37681	3031	23	mosaic	mosaic	JJ
37681	3031	24	floor	floor	NN
37681	3031	25	on	on	IN
37681	3031	26	page	page	NN
37681	3031	27	274	274	CD
37681	3031	28	.	.	.
37681	3032	1	[	[	-LRB-
37681	3032	2	84	84	CD
37681	3032	3	]	]	-RRB-
37681	3032	4	In	in	IN
37681	3032	5	the	the	DT
37681	3032	6	next	next	JJ
37681	3032	7	illustration	illustration	NN
37681	3032	8	some	some	DT
37681	3032	9	characteristic	characteristic	JJ
37681	3032	10	Moorish	Moorish	NNP
37681	3032	11	mosaic	mosaic	JJ
37681	3032	12	work	work	NN
37681	3032	13	appears	appear	VBZ
37681	3032	14	,	,	,
37681	3032	15	in	in	IN
37681	3032	16	which	which	WDT
37681	3032	17	it	-PRON-	PRP
37681	3032	18	will	will	MD
37681	3032	19	be	be	VB
37681	3032	20	seen	see	VBN
37681	3032	21	that	that	IN
37681	3032	22	the	the	DT
37681	3032	23	basal	basal	NN
37681	3032	24	figure	figure	NN
37681	3032	25	is	be	VBZ
37681	3032	26	the	the	DT
37681	3032	27	square	square	NN
37681	3032	28	,	,	,
37681	3032	29	although	although	IN
37681	3032	30	at	at	IN
37681	3032	31	first	first	JJ
37681	3032	32	sight	sight	NN
37681	3032	33	this	this	DT
37681	3032	34	would	would	MD
37681	3032	35	not	not	RB
37681	3032	36	seem	seem	VB
37681	3032	37	to	to	TO
37681	3032	38	be	be	VB
37681	3032	39	the	the	DT
37681	3032	40	case	case	NN
37681	3032	41	.	.	.
37681	3033	1	[	[	-LRB-
37681	3033	2	85	85	CD
37681	3033	3	]	]	-RRB-
37681	3033	4	This	this	DT
37681	3033	5	is	be	VBZ
37681	3033	6	followed	follow	VBN
37681	3033	7	by	by	IN
37681	3033	8	a	a	DT
37681	3033	9	beautiful	beautiful	JJ
37681	3033	10	Byzantine	Byzantine	NNP
37681	3033	11	mosaic	mosaic	JJ
37681	3033	12	,	,	,
37681	3033	13	the	the	DT
37681	3033	14	original	original	NN
37681	3033	15	of	of	IN
37681	3033	16	which	which	WDT
37681	3033	17	was	be	VBD
37681	3033	18	in	in	IN
37681	3033	19	five	five	CD
37681	3033	20	colors	color	NNS
37681	3033	21	of	of	IN
37681	3033	22	marble	marble	NN
37681	3033	23	.	.	.
37681	3034	1	Here	here	RB
37681	3034	2	it	-PRON-	PRP
37681	3034	3	will	will	MD
37681	3034	4	be	be	VB
37681	3034	5	seen	see	VBN
37681	3034	6	that	that	IN
37681	3034	7	the	the	DT
37681	3034	8	equilateral	equilateral	JJ
37681	3034	9	triangle	triangle	NN
37681	3034	10	and	and	CC
37681	3034	11	the	the	DT
37681	3034	12	regular	regular	JJ
37681	3034	13	hexagon	hexagon	NNP
37681	3034	14	are	be	VBP
37681	3034	15	the	the	DT
37681	3034	16	basal	basal	NN
37681	3034	17	figures	figure	NNS
37681	3034	18	,	,	,
37681	3034	19	and	and	CC
37681	3034	20	a	a	DT
37681	3034	21	few	few	JJ
37681	3034	22	of	of	IN
37681	3034	23	the	the	DT
37681	3034	24	properties	property	NNS
37681	3034	25	of	of	IN
37681	3034	26	these	these	DT
37681	3034	27	polygons	polygon	NNS
37681	3034	28	might	may	MD
37681	3034	29	be	be	VB
37681	3034	30	derived	derive	VBN
37681	3034	31	from	from	IN
37681	3034	32	the	the	DT
37681	3034	33	study	study	NN
37681	3034	34	of	of	IN
37681	3034	35	such	such	PDT
37681	3034	36	a	a	DT
37681	3034	37	design	design	NN
37681	3034	38	.	.	.
37681	3035	1	In	in	IN
37681	3035	2	the	the	DT
37681	3035	3	Arabic	arabic	JJ
37681	3035	4	pattern	pattern	NN
37681	3035	5	on	on	IN
37681	3035	6	page	page	NN
37681	3035	7	276	276	CD
37681	3035	8	the	the	DT
37681	3035	9	dodecagon	dodecagon	NNP
37681	3035	10	appears	appear	VBZ
37681	3035	11	as	as	IN
37681	3035	12	the	the	DT
37681	3035	13	basis	basis	NN
37681	3035	14	,	,	,
37681	3035	15	and	and	CC
37681	3035	16	the	the	DT
37681	3035	17	remarkable	remarkable	JJ
37681	3035	18	powers	power	NNS
37681	3035	19	of	of	IN
37681	3035	20	the	the	DT
37681	3035	21	Arab	arab	JJ
37681	3035	22	designer	designer	NN
37681	3035	23	are	be	VBP
37681	3035	24	shown	show	VBN
37681	3035	25	in	in	IN
37681	3035	26	the	the	DT
37681	3035	27	use	use	NN
37681	3035	28	of	of	IN
37681	3035	29	symmetry	symmetry	NN
37681	3035	30	without	without	IN
37681	3035	31	employing	employ	VBG
37681	3035	32	regular	regular	JJ
37681	3035	33	figures	figure	NNS
37681	3035	34	.	.	.
37681	3036	1	[	[	-LRB-
37681	3036	2	Illustration	illustration	NN
37681	3036	3	:	:	:
37681	3036	4	MOSAIC	MOSAIC	NNP
37681	3036	5	FROM	from	IN
37681	3036	6	DAMASCUS	DAMASCUS	NNP
37681	3036	7	]	]	-RRB-
37681	3036	8	[	[	-LRB-
37681	3036	9	Illustration	illustration	NN
37681	3036	10	:	:	:
37681	3036	11	MOSAIC	mosaic	IN
37681	3036	12	FROM	from	IN
37681	3036	13	AN	an	DT
37681	3036	14	ANCIENT	ancient	NN
37681	3036	15	BYZANTINE	BYZANTINE	NNS
37681	3036	16	CHURCH	church	NN
37681	3036	17	]	]	-RRB-
37681	3036	18	PROBLEM	PROBLEM	NNP
37681	3036	19	.	.	.
37681	3037	1	_	_	NNP
37681	3037	2	Given	give	VBN
37681	3037	3	the	the	DT
37681	3037	4	side	side	NN
37681	3037	5	and	and	CC
37681	3037	6	the	the	DT
37681	3037	7	radius	radius	NN
37681	3037	8	of	of	IN
37681	3037	9	a	a	DT
37681	3037	10	regular	regular	JJ
37681	3037	11	inscribed	inscribe	VBN
37681	3037	12	polygon	polygon	NN
37681	3037	13	,	,	,
37681	3037	14	to	to	TO
37681	3037	15	find	find	VB
37681	3037	16	the	the	DT
37681	3037	17	side	side	NN
37681	3037	18	of	of	IN
37681	3037	19	the	the	DT
37681	3037	20	regular	regular	JJ
37681	3037	21	inscribed	inscribe	VBN
37681	3037	22	polygon	polygon	NN
37681	3037	23	of	of	IN
37681	3037	24	double	double	PDT
37681	3037	25	the	the	DT
37681	3037	26	number	number	NN
37681	3037	27	of	of	IN
37681	3037	28	sides	side	NNS
37681	3037	29	.	.	.
37681	3037	30	_	_	NNP
37681	3037	31	[	[	-LRB-
37681	3037	32	Illustration	illustration	NN
37681	3037	33	:	:	:
37681	3037	34	ARABIC	arabic	JJ
37681	3037	35	PATTERN	pattern	NN
37681	3037	36	]	]	-RRB-
37681	3037	37	The	the	DT
37681	3037	38	object	object	NN
37681	3037	39	of	of	IN
37681	3037	40	this	this	DT
37681	3037	41	proposition	proposition	NN
37681	3037	42	is	be	VBZ
37681	3037	43	,	,	,
37681	3037	44	of	of	IN
37681	3037	45	course	course	NN
37681	3037	46	,	,	,
37681	3037	47	to	to	TO
37681	3037	48	prepare	prepare	VB
37681	3037	49	the	the	DT
37681	3037	50	way	way	NN
37681	3037	51	for	for	IN
37681	3037	52	finding	find	VBG
37681	3037	53	the	the	DT
37681	3037	54	perimeter	perimeter	NN
37681	3037	55	of	of	IN
37681	3037	56	a	a	DT
37681	3037	57	polygon	polygon	NN
37681	3037	58	of	of	IN
37681	3037	59	2_n	2_n	CD
37681	3037	60	_	_	NNP
37681	3037	61	sides	side	NNS
37681	3037	62	,	,	,
37681	3037	63	knowing	know	VBG
37681	3037	64	that	that	DT
37681	3037	65	of	of	IN
37681	3037	66	_	_	NNP
37681	3037	67	n	n	CC
37681	3037	68	_	_	NNP
37681	3037	69	sides	side	NNS
37681	3037	70	.	.	.
37681	3038	1	The	the	DT
37681	3038	2	Greek	Greek	NNP
37681	3038	3	plan	plan	NN
37681	3038	4	was	be	VBD
37681	3038	5	generally	generally	RB
37681	3038	6	to	to	TO
37681	3038	7	use	use	VB
37681	3038	8	both	both	CC
37681	3038	9	an	an	DT
37681	3038	10	inscribed	inscribed	JJ
37681	3038	11	and	and	CC
37681	3038	12	a	a	DT
37681	3038	13	circumscribed	circumscribe	VBN
37681	3038	14	polygon	polygon	NN
37681	3038	15	,	,	,
37681	3038	16	thus	thus	RB
37681	3038	17	approaching	approach	VBG
37681	3038	18	the	the	DT
37681	3038	19	circle	circle	NN
37681	3038	20	as	as	IN
37681	3038	21	a	a	DT
37681	3038	22	limit	limit	NN
37681	3038	23	both	both	CC
37681	3038	24	from	from	IN
37681	3038	25	without	without	IN
37681	3038	26	and	and	CC
37681	3038	27	within	within	RB
37681	3038	28	.	.	.
37681	3039	1	This	this	DT
37681	3039	2	is	be	VBZ
37681	3039	3	more	more	RBR
37681	3039	4	conclusive	conclusive	JJ
37681	3039	5	from	from	IN
37681	3039	6	the	the	DT
37681	3039	7	ultrascientific	ultrascientific	JJ
37681	3039	8	point	point	NN
37681	3039	9	of	of	IN
37681	3039	10	view	view	NN
37681	3039	11	,	,	,
37681	3039	12	but	but	CC
37681	3039	13	it	-PRON-	PRP
37681	3039	14	is	be	VBZ
37681	3039	15	,	,	,
37681	3039	16	if	if	IN
37681	3039	17	anything	anything	NN
37681	3039	18	,	,	,
37681	3039	19	less	less	RBR
37681	3039	20	conclusive	conclusive	JJ
37681	3039	21	to	to	IN
37681	3039	22	a	a	DT
37681	3039	23	beginner	beginner	NN
37681	3039	24	,	,	,
37681	3039	25	because	because	IN
37681	3039	26	he	-PRON-	PRP
37681	3039	27	does	do	VBZ
37681	3039	28	not	not	RB
37681	3039	29	so	so	RB
37681	3039	30	readily	readily	RB
37681	3039	31	follow	follow	VB
37681	3039	32	the	the	DT
37681	3039	33	proof	proof	NN
37681	3039	34	.	.	.
37681	3040	1	The	the	DT
37681	3040	2	plan	plan	NN
37681	3040	3	of	of	IN
37681	3040	4	using	use	VBG
37681	3040	5	the	the	DT
37681	3040	6	two	two	CD
37681	3040	7	polygons	polygon	NNS
37681	3040	8	was	be	VBD
37681	3040	9	carried	carry	VBN
37681	3040	10	out	out	RP
37681	3040	11	by	by	IN
37681	3040	12	Archimedes	archimede	NNS
37681	3040	13	of	of	IN
37681	3040	14	Syracuse	Syracuse	NNP
37681	3040	15	(	(	-LRB-
37681	3040	16	287	287	CD
37681	3040	17	-	-	SYM
37681	3040	18	212	212	CD
37681	3040	19	B.C.	B.C.	NNP
37681	3040	20	)	)	-RRB-
37681	3041	1	in	in	IN
37681	3041	2	his	-PRON-	PRP$
37681	3041	3	famous	famous	JJ
37681	3041	4	method	method	NN
37681	3041	5	of	of	IN
37681	3041	6	approximating	approximate	VBG
37681	3041	7	the	the	DT
37681	3041	8	value	value	NN
37681	3041	9	of	of	IN
37681	3041	10	[	[	-LRB-
37681	3041	11	pi	pi	NN
37681	3041	12	]	]	-RRB-
37681	3041	13	,	,	,
37681	3041	14	although	although	IN
37681	3041	15	before	before	IN
37681	3041	16	him	-PRON-	PRP
37681	3041	17	Antiphon	Antiphon	NNP
37681	3041	18	(	(	-LRB-
37681	3041	19	fifth	fifth	JJ
37681	3041	20	century	century	NN
37681	3041	21	B.C.	B.C.	NNP
37681	3041	22	)	)	-RRB-
37681	3042	1	had	have	VBD
37681	3042	2	inscribed	inscribe	VBN
37681	3042	3	a	a	DT
37681	3042	4	square	square	JJ
37681	3042	5	(	(	-LRB-
37681	3042	6	or	or	CC
37681	3042	7	equilateral	equilateral	JJ
37681	3042	8	triangle	triangle	NN
37681	3042	9	)	)	-RRB-
37681	3042	10	as	as	IN
37681	3042	11	a	a	DT
37681	3042	12	basis	basis	NN
37681	3042	13	for	for	IN
37681	3042	14	the	the	DT
37681	3042	15	work	work	NN
37681	3042	16	,	,	,
37681	3042	17	and	and	CC
37681	3042	18	Bryson	Bryson	NNP
37681	3042	19	(	(	-LRB-
37681	3042	20	his	-PRON-	PRP$
37681	3042	21	contemporary	contemporary	NN
37681	3042	22	)	)	-RRB-
37681	3042	23	had	have	VBD
37681	3042	24	attacked	attack	VBN
37681	3042	25	the	the	DT
37681	3042	26	problem	problem	NN
37681	3042	27	by	by	IN
37681	3042	28	circumscribing	circumscribe	VBG
37681	3042	29	as	as	RB
37681	3042	30	well	well	RB
37681	3042	31	as	as	IN
37681	3042	32	inscribing	inscribe	VBG
37681	3042	33	a	a	DT
37681	3042	34	regular	regular	JJ
37681	3042	35	polygon	polygon	NN
37681	3042	36	.	.	.
37681	3043	1	PROBLEM	problem	NN
37681	3043	2	.	.	.
37681	3044	1	_	_	NNP
37681	3044	2	To	to	TO
37681	3044	3	find	find	VB
37681	3044	4	the	the	DT
37681	3044	5	numerical	numerical	JJ
37681	3044	6	value	value	NN
37681	3044	7	of	of	IN
37681	3044	8	the	the	DT
37681	3044	9	ratio	ratio	NN
37681	3044	10	of	of	IN
37681	3044	11	the	the	DT
37681	3044	12	circumference	circumference	NN
37681	3044	13	of	of	IN
37681	3044	14	a	a	DT
37681	3044	15	circle	circle	NN
37681	3044	16	to	to	IN
37681	3044	17	its	-PRON-	PRP$
37681	3044	18	diameter	diameter	NN
37681	3044	19	.	.	.
37681	3044	20	_	_	NNP
37681	3044	21	As	as	RB
37681	3044	22	already	already	RB
37681	3044	23	stated	state	VBN
37681	3044	24	,	,	,
37681	3044	25	the	the	DT
37681	3044	26	usual	usual	JJ
37681	3044	27	plan	plan	NN
37681	3044	28	of	of	IN
37681	3044	29	the	the	DT
37681	3044	30	textbooks	textbook	NNS
37681	3044	31	is	be	VBZ
37681	3044	32	in	in	IN
37681	3044	33	part	part	NN
37681	3044	34	the	the	DT
37681	3044	35	method	method	NN
37681	3044	36	followed	follow	VBN
37681	3044	37	by	by	IN
37681	3044	38	Archimedes	archimede	NNS
37681	3044	39	.	.	.
37681	3045	1	It	-PRON-	PRP
37681	3045	2	is	be	VBZ
37681	3045	3	possible	possible	JJ
37681	3045	4	to	to	TO
37681	3045	5	start	start	VB
37681	3045	6	with	with	IN
37681	3045	7	any	any	DT
37681	3045	8	regular	regular	JJ
37681	3045	9	polygon	polygon	NN
37681	3045	10	of	of	IN
37681	3045	11	which	which	WDT
37681	3045	12	the	the	DT
37681	3045	13	side	side	NN
37681	3045	14	can	can	MD
37681	3045	15	conveniently	conveniently	RB
37681	3045	16	be	be	VB
37681	3045	17	found	find	VBN
37681	3045	18	in	in	IN
37681	3045	19	terms	term	NNS
37681	3045	20	of	of	IN
37681	3045	21	the	the	DT
37681	3045	22	radius	radius	NN
37681	3045	23	.	.	.
37681	3046	1	In	in	IN
37681	3046	2	particular	particular	JJ
37681	3046	3	we	-PRON-	PRP
37681	3046	4	might	may	MD
37681	3046	5	begin	begin	VB
37681	3046	6	with	with	IN
37681	3046	7	an	an	DT
37681	3046	8	inscribed	inscribe	VBN
37681	3046	9	square	square	NN
37681	3046	10	instead	instead	RB
37681	3046	11	of	of	IN
37681	3046	12	a	a	DT
37681	3046	13	regular	regular	JJ
37681	3046	14	hexagon	hexagon	NN
37681	3046	15	.	.	.
37681	3047	1	In	in	IN
37681	3047	2	this	this	DT
37681	3047	3	case	case	NN
37681	3047	4	we	-PRON-	PRP
37681	3047	5	should	should	MD
37681	3047	6	have	have	VB
37681	3047	7	_	_	NNP
37681	3047	8	Length	Length	NNP
37681	3047	9	of	of	IN
37681	3047	10	Side	Side	NNP
37681	3047	11	_	_	NNP
37681	3047	12	_	_	NNP
37681	3047	13	Perimeter	Perimeter	NNP
37681	3047	14	_	_	NNP
37681	3047	15	_	_	NNP
37681	3047	16	s__{4	s__{4	NNP
37681	3047	17	}	}	-RRB-
37681	3047	18	=	=	SYM
37681	3047	19	1.414	1.414	CD
37681	3047	20	...	...	NFP
37681	3047	21	=	=	SYM
37681	3047	22	1.41	1.41	CD
37681	3047	23	5.66	5.66	CD
37681	3047	24	_	_	NNP
37681	3047	25	s__{8	s__{8	NN
37681	3047	26	}	}	-RRB-
37681	3047	27	=	=	NFP
37681	3047	28	[	[	-LRB-
37681	3047	29	sqrt](2	sqrt](2	NN
37681	3047	30	-	-	HYPH
37681	3047	31	[	[	-LRB-
37681	3047	32	sqrt](4	sqrt](4	NN
37681	3047	33	-	-	HYPH
37681	3047	34	1.414	1.414	CD
37681	3047	35	^	^	NN
37681	3047	36	2	2	CD
37681	3047	37	)	)	-RRB-
37681	3047	38	)	)	-RRB-
37681	3047	39	=	=	NFP
37681	3047	40	0.72	0.72	CD
37681	3047	41	5.76	5.76	CD
37681	3047	42	and	and	CC
37681	3047	43	so	so	RB
37681	3047	44	on	on	RB
37681	3047	45	.	.	.
37681	3048	1	It	-PRON-	PRP
37681	3048	2	is	be	VBZ
37681	3048	3	a	a	DT
37681	3048	4	little	little	JJ
37681	3048	5	easier	easy	JJR
37681	3048	6	to	to	TO
37681	3048	7	start	start	VB
37681	3048	8	with	with	IN
37681	3048	9	the	the	DT
37681	3048	10	hexagon	hexagon	NNP
37681	3048	11	,	,	,
37681	3048	12	however	however	RB
37681	3048	13	,	,	,
37681	3048	14	for	for	IN
37681	3048	15	we	-PRON-	PRP
37681	3048	16	are	be	VBP
37681	3048	17	already	already	RB
37681	3048	18	nearer	nearer	IN
37681	3048	19	the	the	DT
37681	3048	20	circle	circle	NN
37681	3048	21	,	,	,
37681	3048	22	and	and	CC
37681	3048	23	the	the	DT
37681	3048	24	side	side	NN
37681	3048	25	and	and	CC
37681	3048	26	perimeter	perimeter	NN
37681	3048	27	are	be	VBP
37681	3048	28	both	both	DT
37681	3048	29	commensurable	commensurable	JJ
37681	3048	30	with	with	IN
37681	3048	31	the	the	DT
37681	3048	32	radius	radius	NN
37681	3048	33	.	.	.
37681	3049	1	It	-PRON-	PRP
37681	3049	2	is	be	VBZ
37681	3049	3	not	not	RB
37681	3049	4	,	,	,
37681	3049	5	of	of	IN
37681	3049	6	course	course	NN
37681	3049	7	,	,	,
37681	3049	8	intended	intend	VBD
37681	3049	9	that	that	IN
37681	3049	10	pupils	pupil	NNS
37681	3049	11	should	should	MD
37681	3049	12	make	make	VB
37681	3049	13	the	the	DT
37681	3049	14	long	long	JJ
37681	3049	15	numerical	numerical	JJ
37681	3049	16	calculations	calculation	NNS
37681	3049	17	.	.	.
37681	3050	1	They	-PRON-	PRP
37681	3050	2	may	may	MD
37681	3050	3	be	be	VB
37681	3050	4	required	require	VBN
37681	3050	5	to	to	TO
37681	3050	6	compute	compute	VB
37681	3050	7	_	_	NNP
37681	3050	8	s__{12	s__{12	NNP
37681	3050	9	}	}	-RRB-
37681	3050	10	and	and	CC
37681	3050	11	possibly	possibly	RB
37681	3050	12	_	_	NNP
37681	3050	13	s__{24	s__{24	NNP
37681	3050	14	}	}	-RRB-
37681	3050	15	,	,	,
37681	3050	16	but	but	CC
37681	3050	17	aside	aside	RB
37681	3050	18	from	from	IN
37681	3050	19	this	this	DT
37681	3050	20	they	-PRON-	PRP
37681	3050	21	are	be	VBP
37681	3050	22	expected	expect	VBN
37681	3050	23	merely	merely	RB
37681	3050	24	to	to	TO
37681	3050	25	know	know	VB
37681	3050	26	the	the	DT
37681	3050	27	process	process	NN
37681	3050	28	.	.	.
37681	3051	1	If	if	IN
37681	3051	2	it	-PRON-	PRP
37681	3051	3	were	be	VBD
37681	3051	4	possible	possible	JJ
37681	3051	5	to	to	TO
37681	3051	6	find	find	VB
37681	3051	7	the	the	DT
37681	3051	8	value	value	NN
37681	3051	9	of	of	IN
37681	3051	10	[	[	-LRB-
37681	3051	11	pi	pi	NN
37681	3051	12	]	]	-RRB-
37681	3051	13	exactly	exactly	RB
37681	3051	14	,	,	,
37681	3051	15	we	-PRON-	PRP
37681	3051	16	could	could	MD
37681	3051	17	find	find	VB
37681	3051	18	the	the	DT
37681	3051	19	circumference	circumference	NN
37681	3051	20	exactly	exactly	RB
37681	3051	21	in	in	IN
37681	3051	22	terms	term	NNS
37681	3051	23	of	of	IN
37681	3051	24	the	the	DT
37681	3051	25	radius	radius	NN
37681	3051	26	,	,	,
37681	3051	27	since	since	IN
37681	3051	28	c	c	NN
37681	3051	29	=	=	SYM
37681	3051	30	2[pi]_r	2[pi]_r	CD
37681	3051	31	_	_	NNP
37681	3051	32	.	.	.
37681	3052	1	If	if	IN
37681	3052	2	we	-PRON-	PRP
37681	3052	3	could	could	MD
37681	3052	4	find	find	VB
37681	3052	5	the	the	DT
37681	3052	6	circumference	circumference	NN
37681	3052	7	exactly	exactly	RB
37681	3052	8	,	,	,
37681	3052	9	we	-PRON-	PRP
37681	3052	10	could	could	MD
37681	3052	11	find	find	VB
37681	3052	12	the	the	DT
37681	3052	13	area	area	NN
37681	3052	14	exactly	exactly	RB
37681	3052	15	,	,	,
37681	3052	16	since	since	IN
37681	3052	17	_	_	NNP
37681	3052	18	a	a	DT
37681	3052	19	_	_	NNP
37681	3052	20	=	=	NFP
37681	3052	21	[	[	-LRB-
37681	3052	22	pi]_r_^2	pi]_r_^2	NNP
37681	3052	23	.	.	.
37681	3053	1	If	if	IN
37681	3053	2	we	-PRON-	PRP
37681	3053	3	could	could	MD
37681	3053	4	find	find	VB
37681	3053	5	the	the	DT
37681	3053	6	area	area	NN
37681	3053	7	exactly	exactly	RB
37681	3053	8	in	in	IN
37681	3053	9	this	this	DT
37681	3053	10	form	form	NN
37681	3053	11	,	,	,
37681	3053	12	[	[	-LRB-
37681	3053	13	pi	pi	NN
37681	3053	14	]	]	-RRB-
37681	3053	15	times	time	NNS
37681	3053	16	a	a	DT
37681	3053	17	square	square	NN
37681	3053	18	,	,	,
37681	3053	19	we	-PRON-	PRP
37681	3053	20	should	should	MD
37681	3053	21	have	have	VB
37681	3053	22	a	a	DT
37681	3053	23	rectangle	rectangle	NN
37681	3053	24	,	,	,
37681	3053	25	and	and	CC
37681	3053	26	it	-PRON-	PRP
37681	3053	27	is	be	VBZ
37681	3053	28	easy	easy	JJ
37681	3053	29	to	to	TO
37681	3053	30	construct	construct	VB
37681	3053	31	a	a	DT
37681	3053	32	square	square	JJ
37681	3053	33	equivalent	equivalent	NN
37681	3053	34	to	to	IN
37681	3053	35	any	any	DT
37681	3053	36	rectangle	rectangle	NN
37681	3053	37	.	.	.
37681	3054	1	Therefore	therefore	RB
37681	3054	2	,	,	,
37681	3054	3	if	if	IN
37681	3054	4	we	-PRON-	PRP
37681	3054	5	could	could	MD
37681	3054	6	find	find	VB
37681	3054	7	the	the	DT
37681	3054	8	value	value	NN
37681	3054	9	of	of	IN
37681	3054	10	[	[	-LRB-
37681	3054	11	pi	pi	NN
37681	3054	12	]	]	-RRB-
37681	3054	13	exactly	exactly	RB
37681	3054	14	,	,	,
37681	3054	15	we	-PRON-	PRP
37681	3054	16	could	could	MD
37681	3054	17	construct	construct	VB
37681	3054	18	a	a	DT
37681	3054	19	square	square	NN
37681	3054	20	with	with	IN
37681	3054	21	area	area	NN
37681	3054	22	equivalent	equivalent	JJ
37681	3054	23	to	to	IN
37681	3054	24	the	the	DT
37681	3054	25	area	area	NN
37681	3054	26	of	of	IN
37681	3054	27	the	the	DT
37681	3054	28	circle	circle	NN
37681	3054	29	;	;	:
37681	3054	30	in	in	IN
37681	3054	31	other	other	JJ
37681	3054	32	words	word	NNS
37681	3054	33	,	,	,
37681	3054	34	we	-PRON-	PRP
37681	3054	35	could	could	MD
37681	3054	36	"	"	``
37681	3054	37	square	square	VB
37681	3054	38	the	the	DT
37681	3054	39	circle	circle	NN
37681	3054	40	.	.	.
37681	3054	41	"	"	''
37681	3055	1	We	-PRON-	PRP
37681	3055	2	could	could	MD
37681	3055	3	also	also	RB
37681	3055	4	,	,	,
37681	3055	5	as	as	IN
37681	3055	6	already	already	RB
37681	3055	7	stated	state	VBN
37681	3055	8	,	,	,
37681	3055	9	construct	construct	VB
37681	3055	10	a	a	DT
37681	3055	11	straight	straight	JJ
37681	3055	12	line	line	NN
37681	3055	13	equivalent	equivalent	JJ
37681	3055	14	to	to	IN
37681	3055	15	the	the	DT
37681	3055	16	circumference	circumference	NN
37681	3055	17	;	;	:
37681	3055	18	in	in	IN
37681	3055	19	other	other	JJ
37681	3055	20	words	word	NNS
37681	3055	21	,	,	,
37681	3055	22	we	-PRON-	PRP
37681	3055	23	could	could	MD
37681	3055	24	"	"	``
37681	3055	25	rectify	rectify	VB
37681	3055	26	the	the	DT
37681	3055	27	circumference	circumference	NN
37681	3055	28	.	.	.
37681	3055	29	"	"	''
37681	3056	1	These	these	DT
37681	3056	2	two	two	CD
37681	3056	3	problems	problem	NNS
37681	3056	4	have	have	VBP
37681	3056	5	attracted	attract	VBN
37681	3056	6	the	the	DT
37681	3056	7	attention	attention	NN
37681	3056	8	of	of	IN
37681	3056	9	the	the	DT
37681	3056	10	world	world	NN
37681	3056	11	for	for	IN
37681	3056	12	over	over	IN
37681	3056	13	two	two	CD
37681	3056	14	thousand	thousand	CD
37681	3056	15	years	year	NNS
37681	3056	16	,	,	,
37681	3056	17	but	but	CC
37681	3056	18	on	on	IN
37681	3056	19	account	account	NN
37681	3056	20	of	of	IN
37681	3056	21	their	-PRON-	PRP$
37681	3056	22	interrelation	interrelation	NN
37681	3056	23	they	-PRON-	PRP
37681	3056	24	are	be	VBP
37681	3056	25	usually	usually	RB
37681	3056	26	spoken	speak	VBN
37681	3056	27	of	of	IN
37681	3056	28	as	as	IN
37681	3056	29	a	a	DT
37681	3056	30	single	single	JJ
37681	3056	31	problem	problem	NN
37681	3056	32	,	,	,
37681	3056	33	"	"	''
37681	3056	34	to	to	TO
37681	3056	35	square	square	VB
37681	3056	36	the	the	DT
37681	3056	37	circle	circle	NN
37681	3056	38	.	.	.
37681	3056	39	"	"	''
37681	3057	1	Since	since	IN
37681	3057	2	we	-PRON-	PRP
37681	3057	3	can	can	MD
37681	3057	4	construct	construct	VB
37681	3057	5	[	[	-LRB-
37681	3057	6	sqrt]_a	sqrt]_a	NNP
37681	3057	7	_	_	NNP
37681	3057	8	by	by	IN
37681	3057	9	means	mean	NNS
37681	3057	10	of	of	IN
37681	3057	11	the	the	DT
37681	3057	12	straightedge	straightedge	NN
37681	3057	13	and	and	CC
37681	3057	14	compasses	compass	NNS
37681	3057	15	,	,	,
37681	3057	16	it	-PRON-	PRP
37681	3057	17	would	would	MD
37681	3057	18	be	be	VB
37681	3057	19	possible	possible	JJ
37681	3057	20	for	for	IN
37681	3057	21	us	-PRON-	PRP
37681	3057	22	to	to	TO
37681	3057	23	square	square	VB
37681	3057	24	the	the	DT
37681	3057	25	circle	circle	NN
37681	3057	26	if	if	IN
37681	3057	27	we	-PRON-	PRP
37681	3057	28	could	could	MD
37681	3057	29	express	express	VB
37681	3057	30	[	[	-LRB-
37681	3057	31	pi	pi	NN
37681	3057	32	]	]	-RRB-
37681	3057	33	by	by	IN
37681	3057	34	a	a	DT
37681	3057	35	finite	finite	JJ
37681	3057	36	number	number	NN
37681	3057	37	of	of	IN
37681	3057	38	square	square	JJ
37681	3057	39	roots	root	NNS
37681	3057	40	.	.	.
37681	3058	1	Conversely	conversely	RB
37681	3058	2	,	,	,
37681	3058	3	every	every	DT
37681	3058	4	geometric	geometric	JJ
37681	3058	5	construction	construction	NN
37681	3058	6	reduces	reduce	VBZ
37681	3058	7	to	to	IN
37681	3058	8	the	the	DT
37681	3058	9	intersection	intersection	NN
37681	3058	10	of	of	IN
37681	3058	11	two	two	CD
37681	3058	12	straight	straight	JJ
37681	3058	13	lines	line	NNS
37681	3058	14	,	,	,
37681	3058	15	of	of	IN
37681	3058	16	a	a	DT
37681	3058	17	straight	straight	JJ
37681	3058	18	line	line	NN
37681	3058	19	and	and	CC
37681	3058	20	a	a	DT
37681	3058	21	circle	circle	NN
37681	3058	22	,	,	,
37681	3058	23	or	or	CC
37681	3058	24	of	of	IN
37681	3058	25	two	two	CD
37681	3058	26	circles	circle	NNS
37681	3058	27	,	,	,
37681	3058	28	and	and	CC
37681	3058	29	is	be	VBZ
37681	3058	30	therefore	therefore	RB
37681	3058	31	equivalent	equivalent	JJ
37681	3058	32	to	to	IN
37681	3058	33	a	a	DT
37681	3058	34	rational	rational	JJ
37681	3058	35	operation	operation	NN
37681	3058	36	or	or	CC
37681	3058	37	to	to	IN
37681	3058	38	the	the	DT
37681	3058	39	extracting	extracting	NN
37681	3058	40	of	of	IN
37681	3058	41	a	a	DT
37681	3058	42	square	square	JJ
37681	3058	43	root	root	NN
37681	3058	44	.	.	.
37681	3059	1	Hence	hence	RB
37681	3059	2	a	a	DT
37681	3059	3	geometric	geometric	JJ
37681	3059	4	construction	construction	NN
37681	3059	5	can	can	MD
37681	3059	6	not	not	RB
37681	3059	7	be	be	VB
37681	3059	8	effected	effect	VBN
37681	3059	9	by	by	IN
37681	3059	10	the	the	DT
37681	3059	11	straightedge	straightedge	NN
37681	3059	12	and	and	CC
37681	3059	13	compasses	compass	NNS
37681	3059	14	unless	unless	IN
37681	3059	15	it	-PRON-	PRP
37681	3059	16	is	be	VBZ
37681	3059	17	equivalent	equivalent	JJ
37681	3059	18	to	to	IN
37681	3059	19	a	a	DT
37681	3059	20	series	series	NN
37681	3059	21	of	of	IN
37681	3059	22	rational	rational	JJ
37681	3059	23	operations	operation	NNS
37681	3059	24	or	or	CC
37681	3059	25	to	to	IN
37681	3059	26	the	the	DT
37681	3059	27	extracting	extracting	NN
37681	3059	28	of	of	IN
37681	3059	29	a	a	DT
37681	3059	30	finite	finite	JJ
37681	3059	31	number	number	NN
37681	3059	32	of	of	IN
37681	3059	33	square	square	JJ
37681	3059	34	roots	root	NNS
37681	3059	35	.	.	.
37681	3060	1	It	-PRON-	PRP
37681	3060	2	was	be	VBD
37681	3060	3	proved	prove	VBN
37681	3060	4	by	by	IN
37681	3060	5	a	a	DT
37681	3060	6	German	german	JJ
37681	3060	7	professor	professor	NN
37681	3060	8	,	,	,
37681	3060	9	Lindemann	Lindemann	NNP
37681	3060	10	,	,	,
37681	3060	11	in	in	IN
37681	3060	12	1882	1882	CD
37681	3060	13	,	,	,
37681	3060	14	that	that	IN
37681	3060	15	[	[	-LRB-
37681	3060	16	pi	pi	NN
37681	3060	17	]	]	-RRB-
37681	3060	18	can	can	MD
37681	3060	19	not	not	RB
37681	3060	20	be	be	VB
37681	3060	21	expressed	express	VBN
37681	3060	22	as	as	IN
37681	3060	23	an	an	DT
37681	3060	24	algebraic	algebraic	NN
37681	3060	25	number	number	NN
37681	3060	26	,	,	,
37681	3060	27	that	that	RB
37681	3060	28	is	is	RB
37681	3060	29	,	,	,
37681	3060	30	as	as	IN
37681	3060	31	the	the	DT
37681	3060	32	root	root	NN
37681	3060	33	of	of	IN
37681	3060	34	an	an	DT
37681	3060	35	equation	equation	NN
37681	3060	36	with	with	IN
37681	3060	37	rational	rational	JJ
37681	3060	38	coefficients	coefficient	NNS
37681	3060	39	,	,	,
37681	3060	40	and	and	CC
37681	3060	41	hence	hence	RB
37681	3060	42	it	-PRON-	PRP
37681	3060	43	can	can	MD
37681	3060	44	not	not	RB
37681	3060	45	be	be	VB
37681	3060	46	found	find	VBN
37681	3060	47	by	by	IN
37681	3060	48	the	the	DT
37681	3060	49	above	above	JJ
37681	3060	50	operations	operation	NNS
37681	3060	51	,	,	,
37681	3060	52	and	and	CC
37681	3060	53	,	,	,
37681	3060	54	furthermore	furthermore	RB
37681	3060	55	,	,	,
37681	3060	56	that	that	IN
37681	3060	57	the	the	DT
37681	3060	58	solution	solution	NN
37681	3060	59	of	of	IN
37681	3060	60	this	this	DT
37681	3060	61	famous	famous	JJ
37681	3060	62	problem	problem	NN
37681	3060	63	is	be	VBZ
37681	3060	64	impossible	impossible	JJ
37681	3060	65	by	by	IN
37681	3060	66	elementary	elementary	JJ
37681	3060	67	geometry	geometry	NN
37681	3060	68	.	.	.
37681	3061	1	[	[	-LRB-
37681	3061	2	86	86	CD
37681	3061	3	]	]	-RRB-
37681	3061	4	It	-PRON-	PRP
37681	3061	5	should	should	MD
37681	3061	6	also	also	RB
37681	3061	7	be	be	VB
37681	3061	8	pointed	point	VBN
37681	3061	9	out	out	RP
37681	3061	10	to	to	IN
37681	3061	11	the	the	DT
37681	3061	12	student	student	NN
37681	3061	13	that	that	IN
37681	3061	14	for	for	IN
37681	3061	15	many	many	JJ
37681	3061	16	practical	practical	JJ
37681	3061	17	purposes	purpose	NNS
37681	3061	18	one	one	CD
37681	3061	19	of	of	IN
37681	3061	20	the	the	DT
37681	3061	21	limits	limit	NNS
37681	3061	22	of	of	IN
37681	3061	23	[	[	-LRB-
37681	3061	24	pi	pi	NN
37681	3061	25	]	]	-RRB-
37681	3061	26	stated	state	VBN
37681	3061	27	by	by	IN
37681	3061	28	Archimedes	archimede	NNS
37681	3061	29	,	,	,
37681	3061	30	namely	namely	RB
37681	3061	31	,	,	,
37681	3061	32	3	3	CD
37681	3061	33	1/7	1/7	CD
37681	3061	34	,	,	,
37681	3061	35	is	be	VBZ
37681	3061	36	sufficient	sufficient	JJ
37681	3061	37	.	.	.
37681	3062	1	For	for	IN
37681	3062	2	more	more	JJR
37681	3062	3	accurate	accurate	JJ
37681	3062	4	work	work	NN
37681	3062	5	3.1416	3.1416	CD
37681	3062	6	is	be	VBZ
37681	3062	7	usually	usually	RB
37681	3062	8	a	a	DT
37681	3062	9	satisfactory	satisfactory	JJ
37681	3062	10	approximation	approximation	NN
37681	3062	11	.	.	.
37681	3063	1	Indeed	indeed	RB
37681	3063	2	,	,	,
37681	3063	3	the	the	DT
37681	3063	4	late	late	JJ
37681	3063	5	Professor	Professor	NNP
37681	3063	6	Newcomb	Newcomb	NNP
37681	3063	7	stated	state	VBD
37681	3063	8	that	that	IN
37681	3063	9	"	"	``
37681	3063	10	ten	ten	CD
37681	3063	11	decimal	decimal	JJ
37681	3063	12	places	place	NNS
37681	3063	13	are	be	VBP
37681	3063	14	sufficient	sufficient	JJ
37681	3063	15	to	to	TO
37681	3063	16	give	give	VB
37681	3063	17	the	the	DT
37681	3063	18	circumference	circumference	NN
37681	3063	19	of	of	IN
37681	3063	20	the	the	DT
37681	3063	21	earth	earth	NN
37681	3063	22	to	to	IN
37681	3063	23	the	the	DT
37681	3063	24	fraction	fraction	NN
37681	3063	25	of	of	IN
37681	3063	26	an	an	DT
37681	3063	27	inch	inch	NN
37681	3063	28	,	,	,
37681	3063	29	and	and	CC
37681	3063	30	thirty	thirty	CD
37681	3063	31	decimal	decimal	JJ
37681	3063	32	places	place	NNS
37681	3063	33	would	would	MD
37681	3063	34	give	give	VB
37681	3063	35	the	the	DT
37681	3063	36	circumference	circumference	NN
37681	3063	37	of	of	IN
37681	3063	38	the	the	DT
37681	3063	39	whole	whole	JJ
37681	3063	40	visible	visible	JJ
37681	3063	41	universe	universe	NN
37681	3063	42	to	to	IN
37681	3063	43	a	a	DT
37681	3063	44	quantity	quantity	NN
37681	3063	45	imperceptible	imperceptible	JJ
37681	3063	46	with	with	IN
37681	3063	47	the	the	DT
37681	3063	48	most	most	RBS
37681	3063	49	powerful	powerful	JJ
37681	3063	50	microscope	microscope	NN
37681	3063	51	.	.	.
37681	3063	52	"	"	''
37681	3064	1	Probably	probably	RB
37681	3064	2	the	the	DT
37681	3064	3	earliest	early	JJS
37681	3064	4	approximation	approximation	NN
37681	3064	5	of	of	IN
37681	3064	6	the	the	DT
37681	3064	7	value	value	NN
37681	3064	8	of	of	IN
37681	3064	9	[	[	-LRB-
37681	3064	10	pi	pi	NN
37681	3064	11	]	]	-RRB-
37681	3064	12	was	be	VBD
37681	3064	13	3	3	CD
37681	3064	14	.	.	.
37681	3065	1	This	this	DT
37681	3065	2	appears	appear	VBZ
37681	3065	3	very	very	RB
37681	3065	4	commonly	commonly	RB
37681	3065	5	in	in	IN
37681	3065	6	antiquity	antiquity	NN
37681	3065	7	,	,	,
37681	3065	8	as	as	IN
37681	3065	9	in	in	IN
37681	3065	10	I	-PRON-	PRP
37681	3065	11	Kings	king	NNS
37681	3065	12	vii	vii	VBP
37681	3065	13	,	,	,
37681	3065	14	23	23	CD
37681	3065	15	,	,	,
37681	3065	16	and	and	CC
37681	3065	17	2	2	CD
37681	3065	18	Chronicles	Chronicles	NNPS
37681	3065	19	iv	iv	NNS
37681	3065	20	,	,	,
37681	3065	21	2	2	CD
37681	3065	22	.	.	.
37681	3066	1	In	in	IN
37681	3066	2	the	the	DT
37681	3066	3	Ahmes	Ahmes	NNP
37681	3066	4	papyrus	papyru	NNS
37681	3066	5	(	(	-LRB-
37681	3066	6	_	_	NNP
37681	3066	7	ca	ca	NNP
37681	3066	8	.	.	.
37681	3066	9	_	_	NNP
37681	3066	10	1700	1700	CD
37681	3066	11	B.C.	B.C.	NNP
37681	3066	12	)	)	-RRB-
37681	3067	1	there	there	EX
37681	3067	2	is	be	VBZ
37681	3067	3	a	a	DT
37681	3067	4	rule	rule	NN
37681	3067	5	for	for	IN
37681	3067	6	finding	find	VBG
37681	3067	7	the	the	DT
37681	3067	8	area	area	NN
37681	3067	9	of	of	IN
37681	3067	10	the	the	DT
37681	3067	11	circle	circle	NN
37681	3067	12	,	,	,
37681	3067	13	expressed	express	VBN
37681	3067	14	in	in	IN
37681	3067	15	modern	modern	JJ
37681	3067	16	symbols	symbol	NNS
37681	3067	17	as	as	IN
37681	3067	18	(	(	-LRB-
37681	3067	19	8/9)^2_d_^2	8/9)^2_d_^2	NNP
37681	3067	20	,	,	,
37681	3067	21	which	which	WDT
37681	3067	22	makes	make	VBZ
37681	3067	23	[	[	-LRB-
37681	3067	24	pi	pi	NN
37681	3067	25	]	]	-RRB-
37681	3067	26	=	=	SYM
37681	3067	27	256/81	256/81	CD
37681	3067	28	or	or	CC
37681	3067	29	3.1604	3.1604	CD
37681	3067	30	....	....	.
37681	3067	31	Archimedes	archimede	NNS
37681	3067	32	,	,	,
37681	3067	33	using	use	VBG
37681	3067	34	a	a	DT
37681	3067	35	plan	plan	NN
37681	3067	36	somewhat	somewhat	RB
37681	3067	37	similar	similar	JJ
37681	3067	38	to	to	IN
37681	3067	39	ours	-PRON-	PRP
37681	3067	40	,	,	,
37681	3067	41	found	find	VBD
37681	3067	42	that	that	IN
37681	3067	43	[	[	-LRB-
37681	3067	44	pi	pi	NN
37681	3067	45	]	]	-RRB-
37681	3067	46	lay	lie	VBD
37681	3067	47	between	between	IN
37681	3067	48	3	3	CD
37681	3067	49	1/7	1/7	CD
37681	3067	50	and	and	CC
37681	3067	51	3	3	CD
37681	3067	52	10/71	10/71	CD
37681	3067	53	.	.	.
37681	3068	1	Ptolemy	Ptolemy	NNP
37681	3068	2	,	,	,
37681	3068	3	the	the	DT
37681	3068	4	great	great	JJ
37681	3068	5	Greek	greek	JJ
37681	3068	6	astronomer	astronomer	NN
37681	3068	7	,	,	,
37681	3068	8	expressed	express	VBD
37681	3068	9	the	the	DT
37681	3068	10	value	value	NN
37681	3068	11	as	as	IN
37681	3068	12	3	3	CD
37681	3068	13	17/120	17/120	CD
37681	3068	14	,	,	,
37681	3068	15	or	or	CC
37681	3068	16	3.14166	3.14166	CD
37681	3068	17	....	....	.
37681	3069	1	The	the	DT
37681	3069	2	fact	fact	NN
37681	3069	3	that	that	IN
37681	3069	4	Ptolemy	Ptolemy	NNP
37681	3069	5	divided	divide	VBD
37681	3069	6	his	-PRON-	PRP$
37681	3069	7	diameter	diameter	NN
37681	3069	8	into	into	IN
37681	3069	9	120	120	CD
37681	3069	10	units	unit	NNS
37681	3069	11	and	and	CC
37681	3069	12	his	-PRON-	PRP$
37681	3069	13	circumference	circumference	NN
37681	3069	14	into	into	IN
37681	3069	15	360	360	CD
37681	3069	16	units	unit	NNS
37681	3069	17	probably	probably	RB
37681	3069	18	shows	show	VBZ
37681	3069	19	,	,	,
37681	3069	20	however	however	RB
37681	3069	21	,	,	,
37681	3069	22	the	the	DT
37681	3069	23	influence	influence	NN
37681	3069	24	of	of	IN
37681	3069	25	the	the	DT
37681	3069	26	ancient	ancient	JJ
37681	3069	27	value	value	NN
37681	3069	28	3	3	CD
37681	3069	29	.	.	.
37681	3070	1	In	in	IN
37681	3070	2	India	India	NNP
37681	3070	3	an	an	DT
37681	3070	4	approximate	approximate	JJ
37681	3070	5	value	value	NN
37681	3070	6	appears	appear	VBZ
37681	3070	7	in	in	IN
37681	3070	8	a	a	DT
37681	3070	9	certain	certain	JJ
37681	3070	10	poem	poem	NN
37681	3070	11	written	write	VBN
37681	3070	12	before	before	IN
37681	3070	13	the	the	DT
37681	3070	14	Christian	christian	JJ
37681	3070	15	era	era	NN
37681	3070	16	,	,	,
37681	3070	17	but	but	CC
37681	3070	18	the	the	DT
37681	3070	19	date	date	NN
37681	3070	20	is	be	VBZ
37681	3070	21	uncertain	uncertain	JJ
37681	3070	22	.	.	.
37681	3071	1	About	about	RB
37681	3071	2	500	500	CD
37681	3071	3	A.D.	A.D.	NNP
37681	3071	4	Aryabhatta	Aryabhatta	NNP
37681	3071	5	(	(	-LRB-
37681	3071	6	or	or	CC
37681	3071	7	possibly	possibly	RB
37681	3071	8	a	a	DT
37681	3071	9	later	later	JJ
37681	3071	10	writer	writer	NN
37681	3071	11	of	of	IN
37681	3071	12	the	the	DT
37681	3071	13	same	same	JJ
37681	3071	14	name	name	NN
37681	3071	15	)	)	-RRB-
37681	3071	16	gave	give	VBD
37681	3071	17	the	the	DT
37681	3071	18	value	value	NN
37681	3071	19	62832/20000	62832/20000	CD
37681	3071	20	,	,	,
37681	3071	21	or	or	CC
37681	3071	22	3.1416	3.1416	CD
37681	3071	23	.	.	.
37681	3072	1	Brahmagupta	Brahmagupta	NNP
37681	3072	2	,	,	,
37681	3072	3	another	another	DT
37681	3072	4	Hindu	Hindu	NNP
37681	3072	5	(	(	-LRB-
37681	3072	6	born	bear	VBN
37681	3072	7	598	598	CD
37681	3072	8	A.D.	A.D.	NNP
37681	3072	9	)	)	-RRB-
37681	3072	10	,	,	,
37681	3072	11	gave	give	VBD
37681	3072	12	[	[	-LRB-
37681	3072	13	sqrt](10	sqrt](10	NNP
37681	3072	14	)	)	-RRB-
37681	3072	15	,	,	,
37681	3072	16	and	and	CC
37681	3072	17	this	this	DT
37681	3072	18	also	also	RB
37681	3072	19	appears	appear	VBZ
37681	3072	20	in	in	IN
37681	3072	21	the	the	DT
37681	3072	22	writings	writing	NNS
37681	3072	23	of	of	IN
37681	3072	24	the	the	DT
37681	3072	25	Chinese	chinese	JJ
37681	3072	26	mathematician	mathematician	NN
37681	3072	27	Chang	Chang	NNP
37681	3072	28	Hêng	Hêng	NNP
37681	3072	29	(	(	-LRB-
37681	3072	30	78	78	CD
37681	3072	31	-	-	SYM
37681	3072	32	139	139	CD
37681	3072	33	A.D.	A.D.	NNP
37681	3072	34	)	)	-RRB-
37681	3072	35	.	.	.
37681	3073	1	A	a	DT
37681	3073	2	little	little	JJ
37681	3073	3	later	later	RB
37681	3073	4	in	in	IN
37681	3073	5	China	China	NNP
37681	3073	6	,	,	,
37681	3073	7	Wang	Wang	NNP
37681	3073	8	Fan	Fan	NNP
37681	3073	9	(	(	-LRB-
37681	3073	10	229	229	CD
37681	3073	11	-	-	SYM
37681	3073	12	267	267	CD
37681	3073	13	)	)	-RRB-
37681	3073	14	gave	give	VBD
37681	3073	15	142	142	CD
37681	3073	16	÷	÷	NN
37681	3073	17	45	45	CD
37681	3073	18	,	,	,
37681	3073	19	or	or	CC
37681	3073	20	3.1555	3.1555	CD
37681	3073	21	...	...	NFP
37681	3073	22	;	;	:
37681	3073	23	and	and	CC
37681	3073	24	one	one	CD
37681	3073	25	of	of	IN
37681	3073	26	his	-PRON-	PRP$
37681	3073	27	contemporaries	contemporary	NNS
37681	3073	28	,	,	,
37681	3073	29	Lui	Lui	NNP
37681	3073	30	Hui	Hui	NNP
37681	3073	31	,	,	,
37681	3073	32	gave	give	VBD
37681	3073	33	157	157	CD
37681	3073	34	÷	÷	NN
37681	3073	35	50	50	CD
37681	3073	36	,	,	,
37681	3073	37	or	or	CC
37681	3073	38	3.14	3.14	CD
37681	3073	39	.	.	.
37681	3074	1	In	in	IN
37681	3074	2	the	the	DT
37681	3074	3	fifth	fifth	JJ
37681	3074	4	century	century	NN
37681	3074	5	Ch'ung	Ch'ung	NNP
37681	3074	6	-	-	HYPH
37681	3074	7	chih	chih	NNP
37681	3074	8	gave	give	VBD
37681	3074	9	as	as	IN
37681	3074	10	the	the	DT
37681	3074	11	limits	limit	NNS
37681	3074	12	of	of	IN
37681	3074	13	[	[	-LRB-
37681	3074	14	pi	pi	NN
37681	3074	15	]	]	-RRB-
37681	3074	16	,	,	,
37681	3074	17	3.1415927	3.1415927	CD
37681	3074	18	and	and	CC
37681	3074	19	3.1415926	3.1415926	CD
37681	3074	20	,	,	,
37681	3074	21	from	from	IN
37681	3074	22	which	which	WDT
37681	3074	23	he	-PRON-	PRP
37681	3074	24	inferred	infer	VBD
37681	3074	25	that	that	IN
37681	3074	26	22/7	22/7	CD
37681	3074	27	and	and	CC
37681	3074	28	355/113	355/113	NN
37681	3074	29	were	be	VBD
37681	3074	30	good	good	JJ
37681	3074	31	approximations	approximation	NNS
37681	3074	32	,	,	,
37681	3074	33	although	although	IN
37681	3074	34	he	-PRON-	PRP
37681	3074	35	does	do	VBZ
37681	3074	36	not	not	RB
37681	3074	37	state	state	VB
37681	3074	38	how	how	WRB
37681	3074	39	he	-PRON-	PRP
37681	3074	40	came	come	VBD
37681	3074	41	to	to	IN
37681	3074	42	this	this	DT
37681	3074	43	conclusion	conclusion	NN
37681	3074	44	.	.	.
37681	3075	1	In	in	IN
37681	3075	2	the	the	DT
37681	3075	3	Middle	Middle	NNP
37681	3075	4	Ages	Ages	NNP
37681	3075	5	the	the	DT
37681	3075	6	greatest	great	JJS
37681	3075	7	mathematician	mathematician	NN
37681	3075	8	of	of	IN
37681	3075	9	Italy	Italy	NNP
37681	3075	10	,	,	,
37681	3075	11	Leonardo	Leonardo	NNP
37681	3075	12	Fibonacci	Fibonacci	NNP
37681	3075	13	,	,	,
37681	3075	14	or	or	CC
37681	3075	15	Leonardo	Leonardo	NNP
37681	3075	16	of	of	IN
37681	3075	17	Pisa	Pisa	NNP
37681	3075	18	(	(	-LRB-
37681	3075	19	about	about	RB
37681	3075	20	1200	1200	CD
37681	3075	21	A.D.	A.D.	NNP
37681	3075	22	)	)	-RRB-
37681	3075	23	,	,	,
37681	3075	24	found	find	VBN
37681	3075	25	as	as	IN
37681	3075	26	limits	limit	NNS
37681	3075	27	3.1427	3.1427	CD
37681	3075	28	...	...	NFP
37681	3075	29	and	and	CC
37681	3075	30	3.1410	3.1410	CD
37681	3075	31	....	....	NFP
37681	3075	32	About	about	RB
37681	3075	33	1600	1600	CD
37681	3075	34	the	the	DT
37681	3075	35	Chinese	chinese	JJ
37681	3075	36	value	value	NN
37681	3075	37	355/113	355/113	NNP
37681	3075	38	was	be	VBD
37681	3075	39	rediscovered	rediscover	VBN
37681	3075	40	by	by	IN
37681	3075	41	Adriaen	Adriaen	NNP
37681	3075	42	Anthonisz	Anthonisz	NNP
37681	3075	43	(	(	-LRB-
37681	3075	44	1527	1527	CD
37681	3075	45	-	-	SYM
37681	3075	46	1607	1607	CD
37681	3075	47	)	)	-RRB-
37681	3075	48	,	,	,
37681	3075	49	being	be	VBG
37681	3075	50	published	publish	VBN
37681	3075	51	by	by	IN
37681	3075	52	his	-PRON-	PRP$
37681	3075	53	son	son	NN
37681	3075	54	,	,	,
37681	3075	55	who	who	WP
37681	3075	56	is	be	VBZ
37681	3075	57	known	know	VBN
37681	3075	58	as	as	IN
37681	3075	59	Metius	Metius	NNP
37681	3075	60	(	(	-LRB-
37681	3075	61	1571	1571	CD
37681	3075	62	-	-	SYM
37681	3075	63	1635	1635	CD
37681	3075	64	)	)	-RRB-
37681	3075	65	,	,	,
37681	3075	66	in	in	IN
37681	3075	67	the	the	DT
37681	3075	68	year	year	NN
37681	3075	69	1625	1625	CD
37681	3075	70	.	.	.
37681	3076	1	About	about	RB
37681	3076	2	the	the	DT
37681	3076	3	same	same	JJ
37681	3076	4	period	period	NN
37681	3076	5	the	the	DT
37681	3076	6	French	french	JJ
37681	3076	7	mathematician	mathematician	NN
37681	3076	8	Vieta	vieta	NN
37681	3076	9	(	(	-LRB-
37681	3076	10	1540	1540	CD
37681	3076	11	-	-	SYM
37681	3076	12	1603	1603	CD
37681	3076	13	)	)	-RRB-
37681	3076	14	found	find	VBD
37681	3076	15	the	the	DT
37681	3076	16	value	value	NN
37681	3076	17	of	of	IN
37681	3076	18	[	[	-LRB-
37681	3076	19	pi	pi	NN
37681	3076	20	]	]	-RRB-
37681	3076	21	to	to	IN
37681	3076	22	9	9	CD
37681	3076	23	decimal	decimal	JJ
37681	3076	24	places	place	NNS
37681	3076	25	,	,	,
37681	3076	26	and	and	CC
37681	3076	27	Adriaen	Adriaen	NNP
37681	3076	28	van	van	NNP
37681	3076	29	Rooman	Rooman	NNP
37681	3076	30	(	(	-LRB-
37681	3076	31	1561	1561	CD
37681	3076	32	-	-	SYM
37681	3076	33	1615	1615	CD
37681	3076	34	)	)	-RRB-
37681	3076	35	carried	carry	VBD
37681	3076	36	it	-PRON-	PRP
37681	3076	37	to	to	IN
37681	3076	38	17	17	CD
37681	3076	39	decimal	decimal	JJ
37681	3076	40	places	place	NNS
37681	3076	41	,	,	,
37681	3076	42	and	and	CC
37681	3076	43	Ludolph	Ludolph	NNP
37681	3076	44	van	van	NNP
37681	3076	45	Ceulen	Ceulen	NNP
37681	3076	46	(	(	-LRB-
37681	3076	47	1540	1540	CD
37681	3076	48	-	-	SYM
37681	3076	49	1610	1610	CD
37681	3076	50	)	)	-RRB-
37681	3076	51	to	to	IN
37681	3076	52	35	35	CD
37681	3076	53	decimal	decimal	JJ
37681	3076	54	places	place	NNS
37681	3076	55	.	.	.
37681	3077	1	It	-PRON-	PRP
37681	3077	2	was	be	VBD
37681	3077	3	carried	carry	VBN
37681	3077	4	to	to	IN
37681	3077	5	140	140	CD
37681	3077	6	decimal	decimal	JJ
37681	3077	7	places	place	NNS
37681	3077	8	by	by	IN
37681	3077	9	Georg	Georg	NNP
37681	3077	10	Vega	Vega	NNP
37681	3077	11	(	(	-LRB-
37681	3077	12	died	die	VBD
37681	3077	13	in	in	IN
37681	3077	14	1793	1793	CD
37681	3077	15	)	)	-RRB-
37681	3077	16	,	,	,
37681	3077	17	to	to	IN
37681	3077	18	200	200	CD
37681	3077	19	by	by	IN
37681	3077	20	Zacharias	Zacharias	NNP
37681	3077	21	Dase	Dase	NNP
37681	3077	22	(	(	-LRB-
37681	3077	23	died	die	VBD
37681	3077	24	in	in	IN
37681	3077	25	1844	1844	CD
37681	3077	26	)	)	-RRB-
37681	3077	27	,	,	,
37681	3077	28	to	to	IN
37681	3077	29	500	500	CD
37681	3077	30	by	by	IN
37681	3077	31	Richter	Richter	NNP
37681	3077	32	(	(	-LRB-
37681	3077	33	died	die	VBN
37681	3077	34	in	in	IN
37681	3077	35	1854	1854	CD
37681	3077	36	)	)	-RRB-
37681	3077	37	,	,	,
37681	3077	38	and	and	CC
37681	3077	39	more	more	RBR
37681	3077	40	recently	recently	RB
37681	3077	41	by	by	IN
37681	3077	42	Shanks	shank	NNS
37681	3077	43	to	to	IN
37681	3077	44	707	707	CD
37681	3077	45	decimal	decimal	JJ
37681	3077	46	places	place	NNS
37681	3077	47	.	.	.
37681	3078	1	There	there	EX
37681	3078	2	have	have	VBP
37681	3078	3	been	be	VBN
37681	3078	4	many	many	JJ
37681	3078	5	interesting	interesting	JJ
37681	3078	6	formulas	formula	NNS
37681	3078	7	for	for	IN
37681	3078	8	[	[	-LRB-
37681	3078	9	pi	pi	NN
37681	3078	10	]	]	-RRB-
37681	3078	11	,	,	,
37681	3078	12	among	among	IN
37681	3078	13	them	-PRON-	PRP
37681	3078	14	being	be	VBG
37681	3078	15	the	the	DT
37681	3078	16	following	follow	VBG
37681	3078	17	:	:	:
37681	3078	18	[	[	-LRB-
37681	3078	19	pi]/2	pi]/2	NN
37681	3078	20	=	=	SYM
37681	3078	21	2/1	2/1	CD
37681	3078	22	·	·	NFP
37681	3078	23	2/3	2/3	CD
37681	3078	24	·	·	NFP
37681	3078	25	4/3	4/3	CD
37681	3078	26	·	·	NFP
37681	3078	27	4/5	4/5	CD
37681	3078	28	·	·	NFP
37681	3078	29	6/5	6/5	CD
37681	3078	30	·	·	NFP
37681	3078	31	6/7	6/7	CD
37681	3078	32	·	·	NFP
37681	3078	33	8/7	8/7	CD
37681	3078	34	·	·	NFP
37681	3078	35	8/9	8/9	CD
37681	3078	36	·	·	NFP
37681	3078	37	....	....	.
37681	3078	38	(	(	-LRB-
37681	3078	39	Wallis	Wallis	NNP
37681	3078	40	,	,	,
37681	3078	41	1616	1616	CD
37681	3078	42	-	-	SYM
37681	3078	43	1703	1703	CD
37681	3078	44	)	)	-RRB-
37681	3078	45	4/[pi	4/[pi	NN
37681	3078	46	]	]	-RRB-
37681	3078	47	=	=	SYM
37681	3078	48	1	1	CD
37681	3078	49	+	+	SYM
37681	3078	50	1/2	1/2	CD
37681	3078	51	+	+	SYM
37681	3078	52	9/2	9/2	CD
37681	3078	53	+	+	SYM
37681	3078	54	25/2	25/2	CD
37681	3078	55	+	+	CC
37681	3078	56	49/2	49/2	CD
37681	3078	57	+	+	SYM
37681	3078	58	....	....	.
37681	3078	59	(	(	-LRB-
37681	3078	60	Brouncker	Brouncker	NNP
37681	3078	61	,	,	,
37681	3078	62	1620	1620	CD
37681	3078	63	-	-	SYM
37681	3078	64	1684	1684	CD
37681	3078	65	)	)	-RRB-
37681	3078	66	[	[	-LRB-
37681	3078	67	pi]/4	pi]/4	NNP
37681	3078	68	=	=	SYM
37681	3078	69	1	1	CD
37681	3078	70	-	-	SYM
37681	3078	71	1/3	1/3	CD
37681	3078	72	+	+	SYM
37681	3078	73	1/5	1/5	CD
37681	3078	74	-	-	SYM
37681	3078	75	1/7	1/7	CD
37681	3078	76	+	+	SYM
37681	3078	77	....	....	.
37681	3078	78	(	(	-LRB-
37681	3078	79	Gregory	Gregory	NNP
37681	3078	80	,	,	,
37681	3078	81	1638	1638	CD
37681	3078	82	-	-	SYM
37681	3078	83	1675	1675	CD
37681	3078	84	)	)	-RRB-
37681	3078	85	[	[	-LRB-
37681	3078	86	pi]/6	pi]/6	NNP
37681	3078	87	=	=	NFP
37681	3078	88	[	[	-LRB-
37681	3078	89	sqrt](1/3	sqrt](1/3	NN
37681	3078	90	)	)	-RRB-
37681	3078	91	·	·	NFP
37681	3078	92	(	(	-LRB-
37681	3078	93	1	1	CD
37681	3078	94	-	-	SYM
37681	3078	95	1/(3	1/(3	CD
37681	3078	96	·	·	SYM
37681	3078	97	3	3	CD
37681	3078	98	)	)	-RRB-
37681	3078	99	+	+	CC
37681	3078	100	1/(3	1/(3	CD
37681	3078	101	^	^	NN
37681	3078	102	2	2	CD
37681	3078	103	·	·	SYM
37681	3078	104	5	5	CD
37681	3078	105	)	)	-RRB-
37681	3078	106	-	-	.
37681	3078	107	1/(3	1/(3	VBN
37681	3078	108	^	^	NN
37681	3078	109	3	3	CD
37681	3078	110	·	·	SYM
37681	3078	111	7	7	CD
37681	3078	112	)	)	-RRB-
37681	3078	113	+	+	SYM
37681	3078	114	...	...	NFP
37681	3078	115	)	)	-RRB-
37681	3078	116	.	.	.
37681	3079	1	[	[	-LRB-
37681	3079	2	pi]/2	pi]/2	NNP
37681	3079	3	=	=	NFP
37681	3079	4	(	(	-LRB-
37681	3079	5	log	log	NNP
37681	3079	6	_	_	NNP
37681	3079	7	i	i	PRP
37681	3079	8	_	_	NNP
37681	3079	9	)	)	-RRB-
37681	3079	10	/	/	SYM
37681	3079	11	_	_	NNP
37681	3079	12	i	i	PRP
37681	3079	13	_	_	NNP
37681	3079	14	.	.	.
37681	3080	1	(	(	-LRB-
37681	3080	2	Bernoulli	Bernoulli	NNP
37681	3080	3	)	)	-RRB-
37681	3080	4	[	[	-LRB-
37681	3080	5	pi]/(2[sqrt](3	pi]/(2[sqrt](3	NNP
37681	3080	6	)	)	-RRB-
37681	3080	7	)	)	-RRB-
37681	3080	8	=	=	NFP
37681	3080	9	1	1	CD
37681	3080	10	-	-	SYM
37681	3080	11	1/5	1/5	CD
37681	3080	12	+	+	SYM
37681	3080	13	1/7	1/7	CD
37681	3080	14	-	-	SYM
37681	3080	15	1/11	1/11	CD
37681	3080	16	+	+	CD
37681	3080	17	1/13	1/13	CD
37681	3080	18	-	-	HYPH
37681	3080	19	1/17	1/17	CD
37681	3080	20	+	+	SYM
37681	3080	21	1/19	1/19	CD
37681	3080	22	...	...	NFP
37681	3080	23	,	,	,
37681	3080	24	thus	thus	RB
37681	3080	25	connecting	connect	VBG
37681	3080	26	the	the	DT
37681	3080	27	primes	prime	NNS
37681	3080	28	.	.	.
37681	3081	1	[	[	-LRB-
37681	3081	2	pi]^2/16	pi]^2/16	IN
37681	3081	3	=	=	SYM
37681	3081	4	1	1	CD
37681	3081	5	-	-	SYM
37681	3081	6	1/2	1/2	CD
37681	3081	7	^	^	NN
37681	3081	8	2	2	CD
37681	3081	9	-	-	SYM
37681	3081	10	1/3	1/3	CD
37681	3081	11	^	^	NN
37681	3081	12	2	2	CD
37681	3081	13	+	+	SYM
37681	3081	14	1/4	1/4	CD
37681	3081	15	^	^	NN
37681	3081	16	2	2	CD
37681	3081	17	-	-	SYM
37681	3081	18	1/5	1/5	CD
37681	3081	19	^	^	NN
37681	3081	20	2	2	CD
37681	3081	21	+	+	CC
37681	3081	22	1/6	1/6	CD
37681	3081	23	^	^	NN
37681	3081	24	2	2	CD
37681	3081	25	-	-	SYM
37681	3081	26	1/7	1/7	CD
37681	3081	27	^	^	NN
37681	3081	28	2	2	CD
37681	3081	29	-	-	SYM
37681	3081	30	1/8	1/8	CD
37681	3081	31	^	^	NN
37681	3081	32	2	2	CD
37681	3081	33	+	+	SYM
37681	3081	34	1/9	1/9	CD
37681	3081	35	^	^	NN
37681	3081	36	2	2	CD
37681	3081	37	+	+	SYM
37681	3081	38	....	....	.
37681	3081	39	[	[	-LRB-
37681	3081	40	pi]/2	pi]/2	NNP
37681	3081	41	=	=	SYM
37681	3081	42	_	_	NNP
37681	3081	43	x_/2	x_/2	NNP
37681	3081	44	+	+	CC
37681	3081	45	sin	sin	NN
37681	3081	46	_	_	NNP
37681	3081	47	x	x	NNP
37681	3081	48	_	_	NNP
37681	3081	49	+	+	NFP
37681	3081	50	(	(	-LRB-
37681	3081	51	sin^2	sin^2	``
37681	3081	52	_	_	NNP
37681	3081	53	x	x	NNP
37681	3081	54	_	_	NNP
37681	3081	55	)	)	-RRB-
37681	3081	56	/	/	SYM
37681	3081	57	2	2	CD
37681	3081	58	+	+	SYM
37681	3081	59	(	(	-LRB-
37681	3081	60	sin^3	sin^3	``
37681	3081	61	_	_	NNP
37681	3081	62	x	x	NNP
37681	3081	63	_	_	NNP
37681	3081	64	)	)	-RRB-
37681	3081	65	/	/	SYM
37681	3081	66	3	3	CD
37681	3081	67	+	+	SYM
37681	3081	68	....	....	NFP
37681	3081	69	(	(	-LRB-
37681	3081	70	0	0	NFP
37681	3081	71	<	<	XX
37681	3081	72	_	_	NNP
37681	3081	73	x	x	NNP
37681	3081	74	_	_	NNP
37681	3081	75	<	<	XX
37681	3081	76	2[pi	2[pi	LS
37681	3081	77	]	]	-RRB-
37681	3081	78	)	)	-RRB-
37681	3081	79	[	[	-LRB-
37681	3081	80	pi]/4	pi]/4	NNP
37681	3081	81	=	=	NNP
37681	3081	82	3/4	3/4	CD
37681	3081	83	+	+	SYM
37681	3081	84	1/(2	1/(2	CD
37681	3081	85	·	·	NFP
37681	3081	86	3	3	CD
37681	3081	87	·	·	SYM
37681	3081	88	4	4	CD
37681	3081	89	)	)	-RRB-
37681	3081	90	-	-	:
37681	3081	91	1/(4	1/(4	CD
37681	3081	92	·	·	NFP
37681	3081	93	5	5	CD
37681	3081	94	·	·	SYM
37681	3081	95	6	6	CD
37681	3081	96	)	)	-RRB-
37681	3081	97	+	+	CC
37681	3081	98	1/(6	1/(6	CD
37681	3081	99	·	·	NFP
37681	3081	100	7	7	CD
37681	3081	101	·	·	SYM
37681	3081	102	8)	8)	CD
37681	3081	103	-	-	HYPH
37681	3081	104	....	....	NFP
37681	3081	105	2[pi]^2/3	2[pi]^2/3	CD
37681	3081	106	=	=	SYM
37681	3081	107	7	7	CD
37681	3081	108	-	-	HYPH
37681	3081	109	(	(	-LRB-
37681	3081	110	1/(1	1/(1	CD
37681	3081	111	·	·	NFP
37681	3081	112	3	3	CD
37681	3081	113	)	)	-RRB-
37681	3081	114	+	+	CC
37681	3081	115	1/(3	1/(3	CD
37681	3081	116	·	·	SYM
37681	3081	117	6	6	CD
37681	3081	118	)	)	-RRB-
37681	3081	119	+	+	CC
37681	3081	120	1/(6	1/(6	CD
37681	3081	121	·	·	SYM
37681	3081	122	10	10	CD
37681	3081	123	)	)	-RRB-
37681	3081	124	+	+	SYM
37681	3081	125	...	...	NFP
37681	3081	126	)	)	-RRB-
37681	3081	127	.	.	.
37681	3082	1	[	[	-LRB-
37681	3082	2	pi	pi	NN
37681	3082	3	]	]	-RRB-
37681	3082	4	=	=	SYM
37681	3082	5	2^_n_[sqrt](2	2^_n_[sqrt](2	CD
37681	3082	6	-	-	:
37681	3082	7	[	[	-LRB-
37681	3082	8	sqrt](2	sqrt](2	NN
37681	3082	9	+	+	SYM
37681	3082	10	[	[	-LRB-
37681	3082	11	sqrt](2	sqrt](2	NN
37681	3082	12	+	+	SYM
37681	3082	13	[	[	-LRB-
37681	3082	14	sqrt](2	sqrt](2	NN
37681	3082	15	+	+	SYM
37681	3082	16	[	[	-LRB-
37681	3082	17	sqrt](2	sqrt](2	NN
37681	3082	18	...	...	NFP
37681	3082	19	)	)	-RRB-
37681	3082	20	)	)	-RRB-
37681	3082	21	)	)	-RRB-
37681	3082	22	)	)	-RRB-
37681	3082	23	)	)	-RRB-
37681	3082	24	.	.	.
37681	3083	1	Students	student	NNS
37681	3083	2	of	of	IN
37681	3083	3	elementary	elementary	JJ
37681	3083	4	geometry	geometry	NN
37681	3083	5	are	be	VBP
37681	3083	6	not	not	RB
37681	3083	7	prepared	prepared	JJ
37681	3083	8	to	to	TO
37681	3083	9	appreciate	appreciate	VB
37681	3083	10	it	-PRON-	PRP
37681	3083	11	,	,	,
37681	3083	12	but	but	CC
37681	3083	13	teachers	teacher	NNS
37681	3083	14	will	will	MD
37681	3083	15	be	be	VB
37681	3083	16	interested	interested	JJ
37681	3083	17	in	in	IN
37681	3083	18	the	the	DT
37681	3083	19	remarkable	remarkable	JJ
37681	3083	20	formula	formula	NN
37681	3083	21	discovered	discover	VBN
37681	3083	22	by	by	IN
37681	3083	23	Euler	Euler	NNP
37681	3083	24	(	(	-LRB-
37681	3083	25	1707	1707	CD
37681	3083	26	-	-	SYM
37681	3083	27	1783	1783	CD
37681	3083	28	)	)	-RRB-
37681	3083	29	,	,	,
37681	3083	30	the	the	DT
37681	3083	31	great	great	JJ
37681	3083	32	Swiss	swiss	JJ
37681	3083	33	mathematician	mathematician	NN
37681	3083	34	,	,	,
37681	3083	35	namely	namely	RB
37681	3083	36	,	,	,
37681	3083	37	1	1	CD
37681	3083	38	+	+	SYM
37681	3083	39	_	_	NNP
37681	3083	40	e_^{_i_[pi	e_^{_i_[pi	NN
37681	3083	41	]	]	-RRB-
37681	3083	42	}	}	-RRB-
37681	3083	43	=	=	NFP
37681	3083	44	0	0	NFP
37681	3083	45	.	.	.
37681	3084	1	In	in	IN
37681	3084	2	this	this	DT
37681	3084	3	relation	relation	NN
37681	3084	4	are	be	VBP
37681	3084	5	included	include	VBN
37681	3084	6	the	the	DT
37681	3084	7	five	five	CD
37681	3084	8	most	most	RBS
37681	3084	9	interesting	interesting	JJ
37681	3084	10	quantities	quantity	NNS
37681	3084	11	in	in	IN
37681	3084	12	mathematics,--zero	mathematics,--zero	NNP
37681	3084	13	,	,	,
37681	3084	14	the	the	DT
37681	3084	15	unit	unit	NN
37681	3084	16	,	,	,
37681	3084	17	the	the	DT
37681	3084	18	base	base	NN
37681	3084	19	of	of	IN
37681	3084	20	the	the	DT
37681	3084	21	so	so	RB
37681	3084	22	-	-	HYPH
37681	3084	23	called	call	VBN
37681	3084	24	Napierian	napierian	JJ
37681	3084	25	logarithms	logarithm	NNS
37681	3084	26	,	,	,
37681	3084	27	_	_	NNP
37681	3084	28	i	i	PRP
37681	3084	29	_	_	NNP
37681	3084	30	=	=	NFP
37681	3084	31	[	[	-LRB-
37681	3084	32	sqrt](-1	sqrt](-1	NNP
37681	3084	33	)	)	-RRB-
37681	3084	34	,	,	,
37681	3084	35	and	and	CC
37681	3084	36	[	[	-LRB-
37681	3084	37	pi	pi	NN
37681	3084	38	]	]	-RRB-
37681	3084	39	.	.	.
37681	3085	1	It	-PRON-	PRP
37681	3085	2	was	be	VBD
37681	3085	3	by	by	IN
37681	3085	4	means	mean	NNS
37681	3085	5	of	of	IN
37681	3085	6	this	this	DT
37681	3085	7	relation	relation	NN
37681	3085	8	that	that	IN
37681	3085	9	the	the	DT
37681	3085	10	transcendence	transcendence	NN
37681	3085	11	of	of	IN
37681	3085	12	_	_	NNP
37681	3085	13	e	e	NNP
37681	3085	14	_	_	NNP
37681	3085	15	was	be	VBD
37681	3085	16	proved	prove	VBN
37681	3085	17	by	by	IN
37681	3085	18	the	the	DT
37681	3085	19	French	french	JJ
37681	3085	20	mathematician	mathematician	NN
37681	3085	21	Hermite	Hermite	NNP
37681	3085	22	,	,	,
37681	3085	23	and	and	CC
37681	3085	24	the	the	DT
37681	3085	25	transcendence	transcendence	NN
37681	3085	26	of	of	IN
37681	3085	27	[	[	-LRB-
37681	3085	28	pi	pi	NN
37681	3085	29	]	]	-RRB-
37681	3085	30	by	by	IN
37681	3085	31	the	the	DT
37681	3085	32	German	german	JJ
37681	3085	33	Lindemann	Lindemann	NNP
37681	3085	34	.	.	.
37681	3086	1	[	[	-LRB-
37681	3086	2	Illustration	illustration	NN
37681	3086	3	]	]	-RRB-
37681	3086	4	There	there	EX
37681	3086	5	should	should	MD
37681	3086	6	be	be	VB
37681	3086	7	introduced	introduce	VBN
37681	3086	8	at	at	IN
37681	3086	9	this	this	DT
37681	3086	10	time	time	NN
37681	3086	11	,	,	,
37681	3086	12	if	if	IN
37681	3086	13	it	-PRON-	PRP
37681	3086	14	has	have	VBZ
37681	3086	15	not	not	RB
37681	3086	16	already	already	RB
37681	3086	17	been	be	VBN
37681	3086	18	done	do	VBN
37681	3086	19	,	,	,
37681	3086	20	the	the	DT
37681	3086	21	proposition	proposition	NN
37681	3086	22	of	of	IN
37681	3086	23	the	the	DT
37681	3086	24	lunes	lune	NNS
37681	3086	25	of	of	IN
37681	3086	26	Hippocrates	Hippocrates	NNPS
37681	3086	27	(	(	-LRB-
37681	3086	28	_	_	NNP
37681	3086	29	ca	ca	NNP
37681	3086	30	.	.	.
37681	3086	31	_	_	NNP
37681	3086	32	470	470	CD
37681	3086	33	B.C.	B.C.	NNP
37681	3087	1	)	)	-RRB-
37681	3087	2	,	,	,
37681	3087	3	who	who	WP
37681	3087	4	proved	prove	VBD
37681	3087	5	a	a	DT
37681	3087	6	theorem	theorem	NN
37681	3087	7	that	that	WDT
37681	3087	8	asserts	assert	VBZ
37681	3087	9	,	,	,
37681	3087	10	in	in	IN
37681	3087	11	somewhat	somewhat	RB
37681	3087	12	more	more	RBR
37681	3087	13	general	general	JJ
37681	3087	14	form	form	NN
37681	3087	15	,	,	,
37681	3087	16	that	that	IN
37681	3087	17	if	if	IN
37681	3087	18	three	three	CD
37681	3087	19	semicircles	semicircle	NNS
37681	3087	20	be	be	VB
37681	3087	21	described	describe	VBN
37681	3087	22	on	on	IN
37681	3087	23	the	the	DT
37681	3087	24	sides	side	NNS
37681	3087	25	of	of	IN
37681	3087	26	a	a	DT
37681	3087	27	right	right	JJ
37681	3087	28	triangle	triangle	NN
37681	3087	29	as	as	IN
37681	3087	30	diameters	diameter	NNS
37681	3087	31	,	,	,
37681	3087	32	as	as	IN
37681	3087	33	shown	show	VBN
37681	3087	34	,	,	,
37681	3087	35	the	the	DT
37681	3087	36	lunes	lune	NNS
37681	3087	37	_	_	NNP
37681	3087	38	L	L	NNP
37681	3087	39	_	_	NNP
37681	3087	40	+	+	SYM
37681	3087	41	_	_	NNP
37681	3087	42	L	L	NNP
37681	3087	43	'	'	''
37681	3087	44	_	_	NNP
37681	3087	45	are	be	VBP
37681	3087	46	together	together	RB
37681	3087	47	equivalent	equivalent	JJ
37681	3087	48	to	to	IN
37681	3087	49	the	the	DT
37681	3087	50	triangle	triangle	NN
37681	3087	51	_	_	NNP
37681	3087	52	T	T	NNP
37681	3087	53	_	_	NNP
37681	3087	54	.	.	.
37681	3088	1	[	[	-LRB-
37681	3088	2	Illustration	illustration	NN
37681	3088	3	]	]	-RRB-
37681	3088	4	In	in	IN
37681	3088	5	the	the	DT
37681	3088	6	use	use	NN
37681	3088	7	of	of	IN
37681	3088	8	the	the	DT
37681	3088	9	circle	circle	NN
37681	3088	10	in	in	IN
37681	3088	11	design	design	NN
37681	3088	12	one	one	CD
37681	3088	13	of	of	IN
37681	3088	14	the	the	DT
37681	3088	15	simplest	simple	JJS
37681	3088	16	forms	form	NNS
37681	3088	17	suggested	suggest	VBN
37681	3088	18	by	by	IN
37681	3088	19	Book	Book	NNP
37681	3088	20	V	V	NNP
37681	3088	21	is	be	VBZ
37681	3088	22	the	the	DT
37681	3088	23	trefoil	trefoil	NN
37681	3088	24	(	(	-LRB-
37681	3088	25	three	three	CD
37681	3088	26	-	-	HYPH
37681	3088	27	leaf	leaf	NN
37681	3088	28	)	)	-RRB-
37681	3088	29	,	,	,
37681	3088	30	as	as	IN
37681	3088	31	here	here	RB
37681	3088	32	shown	show	VBN
37681	3088	33	,	,	,
37681	3088	34	with	with	IN
37681	3088	35	the	the	DT
37681	3088	36	necessary	necessary	JJ
37681	3088	37	construction	construction	NN
37681	3088	38	lines	line	NNS
37681	3088	39	.	.	.
37681	3089	1	This	this	DT
37681	3089	2	is	be	VBZ
37681	3089	3	a	a	DT
37681	3089	4	very	very	RB
37681	3089	5	common	common	JJ
37681	3089	6	ornament	ornament	NN
37681	3089	7	in	in	IN
37681	3089	8	architecture	architecture	NN
37681	3089	9	,	,	,
37681	3089	10	both	both	CC
37681	3089	11	with	with	IN
37681	3089	12	rounded	rounded	JJ
37681	3089	13	ends	end	NNS
37681	3089	14	and	and	CC
37681	3089	15	with	with	IN
37681	3089	16	the	the	DT
37681	3089	17	ends	end	NNS
37681	3089	18	slightly	slightly	RB
37681	3089	19	pointed	point	VBN
37681	3089	20	.	.	.
37681	3090	1	The	the	DT
37681	3090	2	trefoil	trefoil	NN
37681	3090	3	is	be	VBZ
37681	3090	4	closely	closely	RB
37681	3090	5	connected	connect	VBN
37681	3090	6	with	with	IN
37681	3090	7	hexagonal	hexagonal	JJ
37681	3090	8	designs	design	NNS
37681	3090	9	,	,	,
37681	3090	10	since	since	IN
37681	3090	11	the	the	DT
37681	3090	12	regular	regular	JJ
37681	3090	13	hexagon	hexagon	NNP
37681	3090	14	is	be	VBZ
37681	3090	15	formed	form	VBN
37681	3090	16	from	from	IN
37681	3090	17	the	the	DT
37681	3090	18	inscribed	inscribe	VBN
37681	3090	19	equilateral	equilateral	JJ
37681	3090	20	triangle	triangle	NN
37681	3090	21	by	by	IN
37681	3090	22	doubling	double	VBG
37681	3090	23	the	the	DT
37681	3090	24	number	number	NN
37681	3090	25	of	of	IN
37681	3090	26	sides	side	NNS
37681	3090	27	.	.	.
37681	3091	1	The	the	DT
37681	3091	2	following	follow	VBG
37681	3091	3	are	be	VBP
37681	3091	4	designs	design	NNS
37681	3091	5	that	that	WDT
37681	3091	6	are	be	VBP
37681	3091	7	easily	easily	RB
37681	3091	8	made	make	VBN
37681	3091	9	:	:	:
37681	3091	10	[	[	-LRB-
37681	3091	11	Illustration	illustration	NN
37681	3091	12	]	]	-RRB-
37681	3091	13	It	-PRON-	PRP
37681	3091	14	is	be	VBZ
37681	3091	15	not	not	RB
37681	3091	16	very	very	RB
37681	3091	17	profitable	profitable	JJ
37681	3091	18	,	,	,
37681	3091	19	because	because	IN
37681	3091	20	it	-PRON-	PRP
37681	3091	21	is	be	VBZ
37681	3091	22	manifestly	manifestly	RB
37681	3091	23	unreal	unreal	JJ
37681	3091	24	,	,	,
37681	3091	25	to	to	TO
37681	3091	26	measure	measure	VB
37681	3091	27	the	the	DT
37681	3091	28	parts	part	NNS
37681	3091	29	of	of	IN
37681	3091	30	such	such	JJ
37681	3091	31	figures	figure	NNS
37681	3091	32	,	,	,
37681	3091	33	but	but	CC
37681	3091	34	it	-PRON-	PRP
37681	3091	35	offers	offer	VBZ
37681	3091	36	plenty	plenty	NN
37681	3091	37	of	of	IN
37681	3091	38	practice	practice	NN
37681	3091	39	in	in	IN
37681	3091	40	numerical	numerical	JJ
37681	3091	41	work	work	NN
37681	3091	42	.	.	.
37681	3092	1	[	[	-LRB-
37681	3092	2	Illustration	illustration	NN
37681	3092	3	:	:	:
37681	3092	4	CHOIR	CHOIR	NNP
37681	3092	5	OF	of	IN
37681	3092	6	LINCOLN	LINCOLN	NNP
37681	3092	7	CATHEDRAL	CATHEDRAL	NNP
37681	3092	8	]	]	-RRB-
37681	3092	9	[	[	-LRB-
37681	3092	10	Illustration	illustration	NN
37681	3092	11	:	:	:
37681	3092	12	PORCH	porch	NN
37681	3092	13	OF	of	IN
37681	3092	14	LINCOLN	LINCOLN	NNP
37681	3092	15	CATHEDRAL	CATHEDRAL	NNPS
37681	3092	16	]	]	-RRB-
37681	3092	17	In	in	IN
37681	3092	18	the	the	DT
37681	3092	19	illustrations	illustration	NNS
37681	3092	20	of	of	IN
37681	3092	21	the	the	DT
37681	3092	22	Gothic	gothic	JJ
37681	3092	23	windows	window	NNS
37681	3092	24	given	give	VBN
37681	3092	25	in	in	IN
37681	3092	26	Chapter	Chapter	NNP
37681	3092	27	XV	XV	NNP
37681	3092	28	only	only	RB
37681	3092	29	the	the	DT
37681	3092	30	square	square	NN
37681	3092	31	and	and	CC
37681	3092	32	circle	circle	NN
37681	3092	33	were	be	VBD
37681	3092	34	generally	generally	RB
37681	3092	35	involved	involve	VBN
37681	3092	36	.	.	.
37681	3093	1	Teachers	teacher	NNS
37681	3093	2	who	who	WP
37681	3093	3	feel	feel	VBP
37681	3093	4	it	-PRON-	PRP
37681	3093	5	necessary	necessary	JJ
37681	3093	6	or	or	CC
37681	3093	7	advisable	advisable	JJ
37681	3093	8	to	to	TO
37681	3093	9	go	go	VB
37681	3093	10	outside	outside	IN
37681	3093	11	the	the	DT
37681	3093	12	regular	regular	JJ
37681	3093	13	work	work	NN
37681	3093	14	of	of	IN
37681	3093	15	geometry	geometry	NN
37681	3093	16	for	for	IN
37681	3093	17	the	the	DT
37681	3093	18	purpose	purpose	NN
37681	3093	19	of	of	IN
37681	3093	20	increasing	increase	VBG
37681	3093	21	the	the	DT
37681	3093	22	pupil	pupil	NN
37681	3093	23	's	's	POS
37681	3093	24	interest	interest	NN
37681	3093	25	or	or	CC
37681	3093	26	of	of	IN
37681	3093	27	training	train	VBG
37681	3093	28	his	-PRON-	PRP$
37681	3093	29	hand	hand	NN
37681	3093	30	in	in	IN
37681	3093	31	the	the	DT
37681	3093	32	drawing	drawing	NN
37681	3093	33	of	of	IN
37681	3093	34	figures	figure	NNS
37681	3093	35	will	will	MD
37681	3093	36	find	find	VB
37681	3093	37	plenty	plenty	NN
37681	3093	38	of	of	IN
37681	3093	39	designs	design	NNS
37681	3093	40	given	give	VBN
37681	3093	41	in	in	IN
37681	3093	42	any	any	DT
37681	3093	43	pictures	picture	NNS
37681	3093	44	of	of	IN
37681	3093	45	Gothic	gothic	JJ
37681	3093	46	cathedrals	cathedral	NNS
37681	3093	47	.	.	.
37681	3094	1	For	for	IN
37681	3094	2	example	example	NN
37681	3094	3	,	,	,
37681	3094	4	this	this	DT
37681	3094	5	picture	picture	NN
37681	3094	6	of	of	IN
37681	3094	7	the	the	DT
37681	3094	8	noble	noble	JJ
37681	3094	9	window	window	NN
37681	3094	10	in	in	IN
37681	3094	11	the	the	DT
37681	3094	12	choir	choir	NN
37681	3094	13	of	of	IN
37681	3094	14	Lincoln	Lincoln	NNP
37681	3094	15	Cathedral	Cathedral	NNP
37681	3094	16	shows	show	VBZ
37681	3094	17	the	the	DT
37681	3094	18	use	use	NN
37681	3094	19	of	of	IN
37681	3094	20	the	the	DT
37681	3094	21	square	square	NN
37681	3094	22	,	,	,
37681	3094	23	hexagon	hexagon	NNP
37681	3094	24	,	,	,
37681	3094	25	and	and	CC
37681	3094	26	pentagon	pentagon	NNP
37681	3094	27	.	.	.
37681	3095	1	In	in	IN
37681	3095	2	the	the	DT
37681	3095	3	porch	porch	NN
37681	3095	4	of	of	IN
37681	3095	5	the	the	DT
37681	3095	6	same	same	JJ
37681	3095	7	cathedral	cathedral	NN
37681	3095	8	,	,	,
37681	3095	9	shown	show	VBN
37681	3095	10	in	in	IN
37681	3095	11	the	the	DT
37681	3095	12	next	next	JJ
37681	3095	13	illustration	illustration	NN
37681	3095	14	,	,	,
37681	3095	15	the	the	DT
37681	3095	16	architect	architect	NN
37681	3095	17	has	have	VBZ
37681	3095	18	made	make	VBN
37681	3095	19	use	use	NN
37681	3095	20	of	of	IN
37681	3095	21	the	the	DT
37681	3095	22	triangle	triangle	NN
37681	3095	23	,	,	,
37681	3095	24	square	square	NN
37681	3095	25	,	,	,
37681	3095	26	and	and	CC
37681	3095	27	pentagon	pentagon	NNP
37681	3095	28	in	in	IN
37681	3095	29	planning	plan	VBG
37681	3095	30	his	-PRON-	PRP$
37681	3095	31	ornamental	ornamental	JJ
37681	3095	32	stonework	stonework	NN
37681	3095	33	.	.	.
37681	3096	1	It	-PRON-	PRP
37681	3096	2	is	be	VBZ
37681	3096	3	possible	possible	JJ
37681	3096	4	to	to	TO
37681	3096	5	add	add	VB
37681	3096	6	to	to	IN
37681	3096	7	the	the	DT
37681	3096	8	work	work	NN
37681	3096	9	in	in	IN
37681	3096	10	pure	pure	JJ
37681	3096	11	geometry	geometry	NN
37681	3096	12	some	some	DT
37681	3096	13	work	work	NN
37681	3096	14	in	in	IN
37681	3096	15	the	the	DT
37681	3096	16	mensuration	mensuration	NN
37681	3096	17	of	of	IN
37681	3096	18	the	the	DT
37681	3096	19	curvilinear	curvilinear	NN
37681	3096	20	figures	figure	NNS
37681	3096	21	shown	show	VBN
37681	3096	22	in	in	IN
37681	3096	23	these	these	DT
37681	3096	24	designs	design	NNS
37681	3096	25	.	.	.
37681	3097	1	This	this	DT
37681	3097	2	form	form	NN
37681	3097	3	of	of	IN
37681	3097	4	mensuration	mensuration	NN
37681	3097	5	is	be	VBZ
37681	3097	6	not	not	RB
37681	3097	7	of	of	IN
37681	3097	8	much	much	JJ
37681	3097	9	value	value	NN
37681	3097	10	,	,	,
37681	3097	11	however	however	RB
37681	3097	12	,	,	,
37681	3097	13	since	since	IN
37681	3097	14	it	-PRON-	PRP
37681	3097	15	places	place	VBZ
37681	3097	16	before	before	IN
37681	3097	17	the	the	DT
37681	3097	18	pupil	pupil	NN
37681	3097	19	a	a	DT
37681	3097	20	problem	problem	NN
37681	3097	21	that	that	WDT
37681	3097	22	he	-PRON-	PRP
37681	3097	23	sees	see	VBZ
37681	3097	24	at	at	IN
37681	3097	25	once	once	RB
37681	3097	26	is	be	VBZ
37681	3097	27	fictitious	fictitious	JJ
37681	3097	28	,	,	,
37681	3097	29	and	and	CC
37681	3097	30	that	that	DT
37681	3097	31	has	have	VBZ
37681	3097	32	no	no	DT
37681	3097	33	human	human	JJ
37681	3097	34	interest	interest	NN
37681	3097	35	.	.	.
37681	3098	1	[	[	-LRB-
37681	3098	2	Illustration	illustration	NN
37681	3098	3	:	:	:
37681	3098	4	GOTHIC	gothic	NN
37681	3098	5	DESIGNS	designs	NN
37681	3098	6	EMPLOYING	employing	NN
37681	3098	7	CIRCLES	circle	NNS
37681	3098	8	AND	and	CC
37681	3098	9	BISECTED	BISECTED	NNP
37681	3098	10	ANGLES	angle	NNS
37681	3098	11	]	]	-RRB-
37681	3098	12	[	[	-LRB-
37681	3098	13	Illustration	illustration	NN
37681	3098	14	:	:	:
37681	3098	15	GOTHIC	gothic	NN
37681	3098	16	DESIGNS	designs	NN
37681	3098	17	EMPLOYING	employing	NN
37681	3098	18	CIRCLES	circle	NNS
37681	3098	19	AND	and	CC
37681	3098	20	SQUARES	squares	NN
37681	3098	21	]	]	-RRB-
37681	3098	22	[	[	-LRB-
37681	3098	23	Illustration	illustration	NN
37681	3098	24	:	:	:
37681	3098	25	GOTHIC	gothic	NN
37681	3098	26	DESIGNS	designs	NN
37681	3098	27	EMPLOYING	employing	NN
37681	3098	28	CIRCLES	circle	NNS
37681	3098	29	AND	and	CC
37681	3098	30	THE	the	DT
37681	3098	31	EQUILATERAL	equilateral	JJ
37681	3098	32	TRIANGLE	triangle	NN
37681	3098	33	]	]	-RRB-
37681	3098	34	[	[	-LRB-
37681	3098	35	Illustration	illustration	NN
37681	3098	36	:	:	:
37681	3098	37	GOTHIC	gothic	NN
37681	3098	38	DESIGNS	designs	NN
37681	3098	39	EMPLOYING	employing	NN
37681	3098	40	CIRCLES	circle	NNS
37681	3098	41	AND	and	CC
37681	3098	42	THE	the	DT
37681	3098	43	REGULAR	REGULAR	NNP
37681	3098	44	HEXAGON	HEXAGON	NNP
37681	3098	45	]	]	-RRB-
37681	3098	46	The	the	DT
37681	3098	47	designs	design	NNS
37681	3098	48	given	give	VBN
37681	3098	49	on	on	IN
37681	3098	50	page	page	NN
37681	3098	51	283	283	CD
37681	3098	52	involve	involve	VBP
37681	3098	53	chiefly	chiefly	RB
37681	3098	54	the	the	DT
37681	3098	55	square	square	NN
37681	3098	56	as	as	IN
37681	3098	57	a	a	DT
37681	3098	58	basis	basis	NN
37681	3098	59	,	,	,
37681	3098	60	but	but	CC
37681	3098	61	it	-PRON-	PRP
37681	3098	62	will	will	MD
37681	3098	63	be	be	VB
37681	3098	64	seen	see	VBN
37681	3098	65	from	from	IN
37681	3098	66	one	one	CD
37681	3098	67	of	of	IN
37681	3098	68	the	the	DT
37681	3098	69	figures	figure	NNS
37681	3098	70	that	that	WDT
37681	3098	71	the	the	DT
37681	3098	72	equilateral	equilateral	JJ
37681	3098	73	triangle	triangle	NNP
37681	3098	74	and	and	CC
37681	3098	75	the	the	DT
37681	3098	76	hexagon	hexagon	NN
37681	3098	77	also	also	RB
37681	3098	78	enter	enter	VBP
37681	3098	79	.	.	.
37681	3099	1	The	the	DT
37681	3099	2	possibilities	possibility	NNS
37681	3099	3	of	of	IN
37681	3099	4	endless	endless	JJ
37681	3099	5	variation	variation	NN
37681	3099	6	of	of	IN
37681	3099	7	a	a	DT
37681	3099	8	single	single	JJ
37681	3099	9	design	design	NN
37681	3099	10	are	be	VBP
37681	3099	11	shown	show	VBN
37681	3099	12	in	in	IN
37681	3099	13	the	the	DT
37681	3099	14	illustration	illustration	NN
37681	3099	15	on	on	IN
37681	3099	16	page	page	NN
37681	3099	17	284	284	CD
37681	3099	18	,	,	,
37681	3099	19	the	the	DT
37681	3099	20	basis	basis	NN
37681	3099	21	in	in	IN
37681	3099	22	this	this	DT
37681	3099	23	case	case	NN
37681	3099	24	being	be	VBG
37681	3099	25	the	the	DT
37681	3099	26	square	square	NN
37681	3099	27	.	.	.
37681	3100	1	The	the	DT
37681	3100	2	variations	variation	NNS
37681	3100	3	in	in	IN
37681	3100	4	the	the	DT
37681	3100	5	use	use	NN
37681	3100	6	of	of	IN
37681	3100	7	the	the	DT
37681	3100	8	triangle	triangle	NNP
37681	3100	9	and	and	CC
37681	3100	10	hexagon	hexagon	NNP
37681	3100	11	have	have	VBP
37681	3100	12	been	be	VBN
37681	3100	13	the	the	DT
37681	3100	14	object	object	NN
37681	3100	15	of	of	IN
37681	3100	16	study	study	NN
37681	3100	17	of	of	IN
37681	3100	18	many	many	JJ
37681	3100	19	designers	designer	NNS
37681	3100	20	of	of	IN
37681	3100	21	Gothic	gothic	JJ
37681	3100	22	windows	window	NNS
37681	3100	23	,	,	,
37681	3100	24	and	and	CC
37681	3100	25	some	some	DT
37681	3100	26	examples	example	NNS
37681	3100	27	of	of	IN
37681	3100	28	these	these	DT
37681	3100	29	forms	form	NNS
37681	3100	30	are	be	VBP
37681	3100	31	shown	show	VBN
37681	3100	32	on	on	IN
37681	3100	33	page	page	NN
37681	3100	34	285	285	CD
37681	3100	35	.	.	.
37681	3101	1	In	in	IN
37681	3101	2	more	more	JJR
37681	3101	3	simple	simple	JJ
37681	3101	4	form	form	NN
37681	3101	5	this	this	DT
37681	3101	6	ringing	ringing	NN
37681	3101	7	of	of	IN
37681	3101	8	the	the	DT
37681	3101	9	changes	change	NNS
37681	3101	10	on	on	IN
37681	3101	11	elementary	elementary	JJ
37681	3101	12	figures	figure	NNS
37681	3101	13	is	be	VBZ
37681	3101	14	shown	show	VBN
37681	3101	15	on	on	IN
37681	3101	16	page	page	NN
37681	3101	17	286	286	CD
37681	3101	18	.	.	.
37681	3102	1	Some	some	DT
37681	3102	2	teachers	teacher	NNS
37681	3102	3	have	have	VBP
37681	3102	4	used	use	VBN
37681	3102	5	color	color	NN
37681	3102	6	work	work	NN
37681	3102	7	with	with	IN
37681	3102	8	such	such	JJ
37681	3102	9	designs	design	NNS
37681	3102	10	for	for	IN
37681	3102	11	the	the	DT
37681	3102	12	purpose	purpose	NN
37681	3102	13	of	of	IN
37681	3102	14	increasing	increase	VBG
37681	3102	15	the	the	DT
37681	3102	16	interest	interest	NN
37681	3102	17	of	of	IN
37681	3102	18	their	-PRON-	PRP$
37681	3102	19	pupils	pupil	NNS
37681	3102	20	,	,	,
37681	3102	21	but	but	CC
37681	3102	22	the	the	DT
37681	3102	23	danger	danger	NN
37681	3102	24	of	of	IN
37681	3102	25	thus	thus	RB
37681	3102	26	using	use	VBG
37681	3102	27	the	the	DT
37681	3102	28	time	time	NN
37681	3102	29	with	with	IN
37681	3102	30	no	no	DT
37681	3102	31	serious	serious	JJ
37681	3102	32	end	end	NN
37681	3102	33	in	in	IN
37681	3102	34	view	view	NN
37681	3102	35	will	will	MD
37681	3102	36	be	be	VB
37681	3102	37	apparent	apparent	JJ
37681	3102	38	.	.	.
37681	3103	1	[	[	-LRB-
37681	3103	2	Illustration	illustration	NN
37681	3103	3	]	]	-RRB-
37681	3103	4	In	in	IN
37681	3103	5	the	the	DT
37681	3103	6	matter	matter	NN
37681	3103	7	of	of	IN
37681	3103	8	the	the	DT
37681	3103	9	mensuration	mensuration	NN
37681	3103	10	of	of	IN
37681	3103	11	the	the	DT
37681	3103	12	circle	circle	NN
37681	3103	13	the	the	DT
37681	3103	14	annexed	annex	VBN
37681	3103	15	design	design	NN
37681	3103	16	has	have	VBZ
37681	3103	17	some	some	DT
37681	3103	18	interest	interest	NN
37681	3103	19	.	.	.
37681	3104	1	The	the	DT
37681	3104	2	figure	figure	NN
37681	3104	3	is	be	VBZ
37681	3104	4	not	not	RB
37681	3104	5	uncommon	uncommon	JJ
37681	3104	6	in	in	IN
37681	3104	7	decoration	decoration	NN
37681	3104	8	,	,	,
37681	3104	9	and	and	CC
37681	3104	10	it	-PRON-	PRP
37681	3104	11	is	be	VBZ
37681	3104	12	interesting	interesting	JJ
37681	3104	13	to	to	TO
37681	3104	14	show	show	VB
37681	3104	15	,	,	,
37681	3104	16	as	as	IN
37681	3104	17	a	a	DT
37681	3104	18	matter	matter	NN
37681	3104	19	of	of	IN
37681	3104	20	pure	pure	JJ
37681	3104	21	geometry	geometry	NN
37681	3104	22	,	,	,
37681	3104	23	that	that	IN
37681	3104	24	the	the	DT
37681	3104	25	area	area	NN
37681	3104	26	of	of	IN
37681	3104	27	the	the	DT
37681	3104	28	circle	circle	NN
37681	3104	29	is	be	VBZ
37681	3104	30	divided	divide	VBN
37681	3104	31	into	into	IN
37681	3104	32	three	three	CD
37681	3104	33	equal	equal	JJ
37681	3104	34	portions	portion	NNS
37681	3104	35	by	by	IN
37681	3104	36	means	mean	NNS
37681	3104	37	of	of	IN
37681	3104	38	the	the	DT
37681	3104	39	four	four	CD
37681	3104	40	interior	interior	JJ
37681	3104	41	semicircles	semicircle	NNS
37681	3104	42	.	.	.
37681	3105	1	[	[	-LRB-
37681	3105	2	Illustration	illustration	NN
37681	3105	3	]	]	-RRB-
37681	3105	4	An	an	DT
37681	3105	5	important	important	JJ
37681	3105	6	application	application	NN
37681	3105	7	of	of	IN
37681	3105	8	the	the	DT
37681	3105	9	formula	formula	NN
37681	3105	10	_	_	NNP
37681	3105	11	a	a	DT
37681	3105	12	_	_	NNP
37681	3105	13	=	=	NFP
37681	3105	14	[	[	-LRB-
37681	3105	15	pi]_r_^2	pi]_r_^2	NNP
37681	3105	16	is	be	VBZ
37681	3105	17	seen	see	VBN
37681	3105	18	in	in	IN
37681	3105	19	the	the	DT
37681	3105	20	area	area	NN
37681	3105	21	of	of	IN
37681	3105	22	the	the	DT
37681	3105	23	annulus	annulus	NN
37681	3105	24	,	,	,
37681	3105	25	or	or	CC
37681	3105	26	ring	ring	NN
37681	3105	27	,	,	,
37681	3105	28	the	the	DT
37681	3105	29	formula	formula	NN
37681	3105	30	being	be	VBG
37681	3105	31	_	_	NNP
37681	3105	32	a	a	DT
37681	3105	33	_	_	NN
37681	3105	34	=	=	NFP
37681	3105	35	[	[	-LRB-
37681	3105	36	pi]_r_^2	pi]_r_^2	NN
37681	3105	37	-	-	,
37681	3105	38	[	[	-LRB-
37681	3105	39	pi]_r'_^2	pi]_r'_^2	NNP
37681	3105	40	=	=	NFP
37681	3105	41	[	[	-LRB-
37681	3105	42	pi](_r_^2	pi](_r_^2	NNP
37681	3105	43	-	-	HYPH
37681	3105	44	_	_	NNP
37681	3105	45	r'_^2	r'_^2	NNP
37681	3105	46	)	)	-RRB-
37681	3105	47	=	=	NFP
37681	3105	48	[	[	-LRB-
37681	3105	49	pi](_r	pi](_r	NNP
37681	3105	50	_	_	NNP
37681	3105	51	+	+	NNP
37681	3105	52	_	_	NNP
37681	3105	53	r'_)(_r	r'_)(_r	NNP
37681	3105	54	_	_	NNP
37681	3105	55	-	-	HYPH
37681	3105	56	_	_	NNP
37681	3105	57	r	r	NNP
37681	3105	58	'	'	''
37681	3105	59	_	_	NNP
37681	3105	60	)	)	-RRB-
37681	3105	61	.	.	.
37681	3106	1	It	-PRON-	PRP
37681	3106	2	is	be	VBZ
37681	3106	3	used	use	VBN
37681	3106	4	in	in	IN
37681	3106	5	finding	find	VBG
37681	3106	6	the	the	DT
37681	3106	7	area	area	NN
37681	3106	8	of	of	IN
37681	3106	9	the	the	DT
37681	3106	10	cross	cross	NN
37681	3106	11	section	section	NN
37681	3106	12	of	of	IN
37681	3106	13	pipes	pipe	NNS
37681	3106	14	,	,	,
37681	3106	15	and	and	CC
37681	3106	16	this	this	DT
37681	3106	17	is	be	VBZ
37681	3106	18	needed	need	VBN
37681	3106	19	when	when	WRB
37681	3106	20	we	-PRON-	PRP
37681	3106	21	wish	wish	VBP
37681	3106	22	to	to	TO
37681	3106	23	compute	compute	VB
37681	3106	24	the	the	DT
37681	3106	25	volume	volume	NN
37681	3106	26	of	of	IN
37681	3106	27	the	the	DT
37681	3106	28	iron	iron	NN
37681	3106	29	used	use	VBN
37681	3106	30	.	.	.
37681	3107	1	Another	another	DT
37681	3107	2	excellent	excellent	JJ
37681	3107	3	application	application	NN
37681	3107	4	is	be	VBZ
37681	3107	5	that	that	DT
37681	3107	6	of	of	IN
37681	3107	7	finding	find	VBG
37681	3107	8	the	the	DT
37681	3107	9	area	area	NN
37681	3107	10	of	of	IN
37681	3107	11	the	the	DT
37681	3107	12	surface	surface	NN
37681	3107	13	of	of	IN
37681	3107	14	a	a	DT
37681	3107	15	cylinder	cylinder	NN
37681	3107	16	,	,	,
37681	3107	17	there	there	EX
37681	3107	18	being	be	VBG
37681	3107	19	no	no	DT
37681	3107	20	reason	reason	NN
37681	3107	21	why	why	WRB
37681	3107	22	such	such	JJ
37681	3107	23	simple	simple	JJ
37681	3107	24	cases	case	NNS
37681	3107	25	from	from	IN
37681	3107	26	solid	solid	JJ
37681	3107	27	geometry	geometry	NN
37681	3107	28	should	should	MD
37681	3107	29	not	not	RB
37681	3107	30	furnish	furnish	VB
37681	3107	31	working	working	NN
37681	3107	32	material	material	NN
37681	3107	33	for	for	IN
37681	3107	34	plane	plane	NN
37681	3107	35	geometry	geometry	NN
37681	3107	36	,	,	,
37681	3107	37	particularly	particularly	RB
37681	3107	38	as	as	IN
37681	3107	39	they	-PRON-	PRP
37681	3107	40	have	have	VBP
37681	3107	41	already	already	RB
37681	3107	42	been	be	VBN
37681	3107	43	met	meet	VBN
37681	3107	44	by	by	IN
37681	3107	45	the	the	DT
37681	3107	46	pupils	pupil	NNS
37681	3107	47	in	in	IN
37681	3107	48	arithmetic	arithmetic	JJ
37681	3107	49	.	.	.
37681	3108	1	A	a	DT
37681	3108	2	little	little	JJ
37681	3108	3	problem	problem	NN
37681	3108	4	that	that	WDT
37681	3108	5	always	always	RB
37681	3108	6	has	have	VBZ
37681	3108	7	some	some	DT
37681	3108	8	interest	interest	NN
37681	3108	9	for	for	IN
37681	3108	10	pupils	pupil	NNS
37681	3108	11	is	be	VBZ
37681	3108	12	one	one	CD
37681	3108	13	that	that	WDT
37681	3108	14	Napoleon	Napoleon	NNP
37681	3108	15	is	be	VBZ
37681	3108	16	said	say	VBN
37681	3108	17	to	to	TO
37681	3108	18	have	have	VB
37681	3108	19	suggested	suggest	VBN
37681	3108	20	to	to	IN
37681	3108	21	his	-PRON-	PRP$
37681	3108	22	staff	staff	NN
37681	3108	23	on	on	IN
37681	3108	24	his	-PRON-	PRP$
37681	3108	25	voyage	voyage	NN
37681	3108	26	to	to	IN
37681	3108	27	Egypt	Egypt	NNP
37681	3108	28	:	:	:
37681	3108	29	To	to	TO
37681	3108	30	divide	divide	VB
37681	3108	31	a	a	DT
37681	3108	32	circle	circle	NN
37681	3108	33	into	into	IN
37681	3108	34	four	four	CD
37681	3108	35	equal	equal	JJ
37681	3108	36	parts	part	NNS
37681	3108	37	by	by	IN
37681	3108	38	the	the	DT
37681	3108	39	use	use	NN
37681	3108	40	of	of	IN
37681	3108	41	circles	circle	NNS
37681	3108	42	alone	alone	JJ
37681	3108	43	.	.	.
37681	3109	1	[	[	-LRB-
37681	3109	2	Illustration	illustration	NN
37681	3109	3	]	]	-RRB-
37681	3109	4	Here	here	RB
37681	3109	5	the	the	DT
37681	3109	6	circles	circle	NNS
37681	3109	7	_	_	NNP
37681	3109	8	B	B	NNP
37681	3109	9	_	_	NNP
37681	3109	10	are	be	VBP
37681	3109	11	tangent	tangent	JJ
37681	3109	12	to	to	IN
37681	3109	13	the	the	DT
37681	3109	14	circle	circle	NN
37681	3109	15	_	_	NNP
37681	3109	16	A	A	NNP
37681	3109	17	_	_	NNP
37681	3109	18	at	at	IN
37681	3109	19	the	the	DT
37681	3109	20	points	point	NNS
37681	3109	21	of	of	IN
37681	3109	22	division	division	NN
37681	3109	23	.	.	.
37681	3110	1	Furthermore	furthermore	RB
37681	3110	2	,	,	,
37681	3110	3	considering	consider	VBG
37681	3110	4	areas	area	NNS
37681	3110	5	,	,	,
37681	3110	6	and	and	CC
37681	3110	7	taking	take	VBG
37681	3110	8	_	_	NNP
37681	3110	9	r	r	NNP
37681	3110	10	_	_	NNP
37681	3110	11	as	as	IN
37681	3110	12	the	the	DT
37681	3110	13	radius	radius	NN
37681	3110	14	of	of	IN
37681	3110	15	_	_	NNP
37681	3110	16	A	A	NNP
37681	3110	17	_	_	NNP
37681	3110	18	,	,	,
37681	3110	19	we	-PRON-	PRP
37681	3110	20	have	have	VBP
37681	3110	21	_	_	NNP
37681	3110	22	A	A	NNP
37681	3110	23	_	_	NNP
37681	3110	24	=	=	NFP
37681	3110	25	[	[	-LRB-
37681	3110	26	pi]_r_^2	pi]_r_^2	NNP
37681	3110	27	,	,	,
37681	3110	28	and	and	CC
37681	3110	29	_	_	NNP
37681	3110	30	B	B	NNP
37681	3110	31	_	_	NNP
37681	3110	32	=	=	NFP
37681	3110	33	[	[	-LRB-
37681	3110	34	pi](_r_/2)^2	pi](_r_/2)^2	ADD
37681	3110	35	.	.	.
37681	3111	1	Hence	hence	RB
37681	3111	2	_	_	NNP
37681	3111	3	B	B	NNP
37681	3111	4	_	_	NNP
37681	3111	5	=	=	SYM
37681	3111	6	1/4_A	1/4_a	CD
37681	3111	7	_	_	NNP
37681	3111	8	,	,	,
37681	3111	9	or	or	CC
37681	3111	10	the	the	DT
37681	3111	11	sum	sum	NN
37681	3111	12	of	of	IN
37681	3111	13	the	the	DT
37681	3111	14	areas	area	NNS
37681	3111	15	of	of	IN
37681	3111	16	the	the	DT
37681	3111	17	four	four	CD
37681	3111	18	circles	circle	NNS
37681	3111	19	_	_	NNP
37681	3111	20	B	B	NNP
37681	3111	21	_	_	NNP
37681	3111	22	equals	equal	VBZ
37681	3111	23	the	the	DT
37681	3111	24	area	area	NN
37681	3111	25	of	of	IN
37681	3111	26	_	_	NNP
37681	3111	27	A	A	NNP
37681	3111	28	_	_	NNP
37681	3111	29	.	.	.
37681	3112	1	Hence	hence	RB
37681	3112	2	the	the	DT
37681	3112	3	four	four	CD
37681	3112	4	_	_	NNP
37681	3112	5	D'_s	D'_s	NNP
37681	3112	6	must	must	MD
37681	3112	7	equal	equal	VB
37681	3112	8	the	the	DT
37681	3112	9	four	four	CD
37681	3112	10	_	_	NNP
37681	3112	11	C'_s	C'_s	NNP
37681	3112	12	,	,	,
37681	3112	13	and	and	CC
37681	3112	14	_	_	NNP
37681	3112	15	D	D	NNP
37681	3112	16	_	_	NNP
37681	3112	17	=	=	SYM
37681	3112	18	_	_	NNP
37681	3112	19	C	C	NNP
37681	3112	20	_	_	NNP
37681	3112	21	.	.	.
37681	3113	1	The	the	DT
37681	3113	2	rest	rest	NN
37681	3113	3	of	of	IN
37681	3113	4	the	the	DT
37681	3113	5	argument	argument	NN
37681	3113	6	is	be	VBZ
37681	3113	7	evident	evident	JJ
37681	3113	8	.	.	.
37681	3114	1	The	the	DT
37681	3114	2	problem	problem	NN
37681	3114	3	has	have	VBZ
37681	3114	4	some	some	DT
37681	3114	5	interest	interest	NN
37681	3114	6	to	to	IN
37681	3114	7	pupils	pupil	NNS
37681	3114	8	aside	aside	RB
37681	3114	9	from	from	IN
37681	3114	10	the	the	DT
37681	3114	11	original	original	JJ
37681	3114	12	question	question	NN
37681	3114	13	suggested	suggest	VBN
37681	3114	14	by	by	IN
37681	3114	15	Napoleon	Napoleon	NNP
37681	3114	16	.	.	.
37681	3115	1	At	at	IN
37681	3115	2	the	the	DT
37681	3115	3	close	close	NN
37681	3115	4	of	of	IN
37681	3115	5	plane	plane	NN
37681	3115	6	geometry	geometry	NN
37681	3115	7	teachers	teacher	NNS
37681	3115	8	may	may	MD
37681	3115	9	find	find	VB
37681	3115	10	it	-PRON-	PRP
37681	3115	11	helpful	helpful	JJ
37681	3115	12	to	to	TO
37681	3115	13	have	have	VB
37681	3115	14	the	the	DT
37681	3115	15	class	class	NN
37681	3115	16	make	make	VB
37681	3115	17	a	a	DT
37681	3115	18	list	list	NN
37681	3115	19	of	of	IN
37681	3115	20	the	the	DT
37681	3115	21	propositions	proposition	NNS
37681	3115	22	that	that	WDT
37681	3115	23	are	be	VBP
37681	3115	24	actually	actually	RB
37681	3115	25	used	use	VBN
37681	3115	26	in	in	IN
37681	3115	27	proving	prove	VBG
37681	3115	28	other	other	JJ
37681	3115	29	propositions	proposition	NNS
37681	3115	30	,	,	,
37681	3115	31	and	and	CC
37681	3115	32	to	to	TO
37681	3115	33	have	have	VB
37681	3115	34	it	-PRON-	PRP
37681	3115	35	appear	appear	VB
37681	3115	36	what	what	WP
37681	3115	37	ones	one	NNS
37681	3115	38	are	be	VBP
37681	3115	39	proved	prove	VBN
37681	3115	40	by	by	IN
37681	3115	41	them	-PRON-	PRP
37681	3115	42	.	.	.
37681	3116	1	This	this	DT
37681	3116	2	forms	form	VBZ
37681	3116	3	a	a	DT
37681	3116	4	kind	kind	NN
37681	3116	5	of	of	IN
37681	3116	6	genealogical	genealogical	JJ
37681	3116	7	tree	tree	NN
37681	3116	8	that	that	WDT
37681	3116	9	serves	serve	VBZ
37681	3116	10	to	to	TO
37681	3116	11	fix	fix	VB
37681	3116	12	the	the	DT
37681	3116	13	parent	parent	NN
37681	3116	14	propositions	proposition	NNS
37681	3116	15	in	in	IN
37681	3116	16	mind	mind	NN
37681	3116	17	.	.	.
37681	3117	1	Such	such	PDT
37681	3117	2	a	a	DT
37681	3117	3	work	work	NN
37681	3117	4	may	may	MD
37681	3117	5	also	also	RB
37681	3117	6	be	be	VB
37681	3117	7	carried	carry	VBN
37681	3117	8	on	on	RP
37681	3117	9	at	at	IN
37681	3117	10	the	the	DT
37681	3117	11	close	close	NN
37681	3117	12	of	of	IN
37681	3117	13	each	each	DT
37681	3117	14	book	book	NN
37681	3117	15	,	,	,
37681	3117	16	if	if	IN
37681	3117	17	desired	desire	VBN
37681	3117	18	.	.	.
37681	3118	1	It	-PRON-	PRP
37681	3118	2	should	should	MD
37681	3118	3	be	be	VB
37681	3118	4	understood	understand	VBN
37681	3118	5	,	,	,
37681	3118	6	however	however	RB
37681	3118	7	,	,	,
37681	3118	8	that	that	IN
37681	3118	9	certain	certain	JJ
37681	3118	10	propositions	proposition	NNS
37681	3118	11	are	be	VBP
37681	3118	12	used	use	VBN
37681	3118	13	in	in	IN
37681	3118	14	the	the	DT
37681	3118	15	exercises	exercise	NNS
37681	3118	16	,	,	,
37681	3118	17	even	even	RB
37681	3118	18	though	though	IN
37681	3118	19	they	-PRON-	PRP
37681	3118	20	are	be	VBP
37681	3118	21	not	not	RB
37681	3118	22	referred	refer	VBN
37681	3118	23	to	to	IN
37681	3118	24	in	in	IN
37681	3118	25	subsequent	subsequent	JJ
37681	3118	26	propositions	proposition	NNS
37681	3118	27	,	,	,
37681	3118	28	so	so	IN
37681	3118	29	that	that	IN
37681	3118	30	their	-PRON-	PRP$
37681	3118	31	omission	omission	NN
37681	3118	32	must	must	MD
37681	3118	33	not	not	RB
37681	3118	34	be	be	VB
37681	3118	35	construed	construe	VBN
37681	3118	36	to	to	TO
37681	3118	37	mean	mean	VB
37681	3118	38	that	that	IN
37681	3118	39	they	-PRON-	PRP
37681	3118	40	are	be	VBP
37681	3118	41	not	not	RB
37681	3118	42	important	important	JJ
37681	3118	43	.	.	.
37681	3119	1	An	an	DT
37681	3119	2	exercise	exercise	NN
37681	3119	3	of	of	IN
37681	3119	4	distinctly	distinctly	RB
37681	3119	5	less	less	JJR
37681	3119	6	value	value	NN
37681	3119	7	is	be	VBZ
37681	3119	8	the	the	DT
37681	3119	9	classification	classification	NN
37681	3119	10	of	of	IN
37681	3119	11	the	the	DT
37681	3119	12	definitions	definition	NNS
37681	3119	13	.	.	.
37681	3120	1	For	for	IN
37681	3120	2	example	example	NN
37681	3120	3	,	,	,
37681	3120	4	the	the	DT
37681	3120	5	classification	classification	NN
37681	3120	6	of	of	IN
37681	3120	7	polygons	polygon	NNS
37681	3120	8	or	or	CC
37681	3120	9	of	of	IN
37681	3120	10	quadrilaterals	quadrilateral	NNS
37681	3120	11	,	,	,
37681	3120	12	once	once	RB
37681	3120	13	so	so	RB
37681	3120	14	popular	popular	JJ
37681	3120	15	in	in	IN
37681	3120	16	textbook	textbook	NN
37681	3120	17	making	making	NN
37681	3120	18	,	,	,
37681	3120	19	has	have	VBZ
37681	3120	20	generally	generally	RB
37681	3120	21	been	be	VBN
37681	3120	22	abandoned	abandon	VBN
37681	3120	23	as	as	IN
37681	3120	24	tending	tend	VBG
37681	3120	25	to	to	TO
37681	3120	26	create	create	VB
37681	3120	27	or	or	CC
37681	3120	28	perpetuate	perpetuate	VB
37681	3120	29	unnecessary	unnecessary	JJ
37681	3120	30	terms	term	NNS
37681	3120	31	.	.	.
37681	3121	1	Such	such	JJ
37681	3121	2	work	work	NN
37681	3121	3	is	be	VBZ
37681	3121	4	therefore	therefore	RB
37681	3121	5	not	not	RB
37681	3121	6	recommended	recommend	VBN
37681	3121	7	.	.	.
37681	3122	1	FOOTNOTES	footnote	NNS
37681	3122	2	:	:	:
37681	3122	3	[	[	-LRB-
37681	3122	4	83	83	CD
37681	3122	5	]	]	-RRB-
37681	3122	6	Bosanquet	Bosanquet	NNP
37681	3122	7	and	and	CC
37681	3122	8	Sayre	Sayre	NNP
37681	3122	9	,	,	,
37681	3122	10	"	"	``
37681	3122	11	The	the	DT
37681	3122	12	Babylonian	babylonian	JJ
37681	3122	13	Astronomy	Astronomy	NNP
37681	3122	14	,	,	,
37681	3122	15	"	"	''
37681	3122	16	_	_	NNP
37681	3122	17	Monthly	Monthly	NNP
37681	3122	18	Notices	Notices	NNP
37681	3122	19	of	of	IN
37681	3122	20	the	the	DT
37681	3122	21	Royal	Royal	NNP
37681	3122	22	Asiatic	Asiatic	NNP
37681	3122	23	Society	Society	NNP
37681	3122	24	_	_	NNP
37681	3122	25	,	,	,
37681	3122	26	Vol	Vol	NNP
37681	3122	27	.	.	.
37681	3123	1	XL	XL	NNP
37681	3123	2	,	,	,
37681	3123	3	p.	p.	NN
37681	3123	4	108	108	CD
37681	3123	5	.	.	.
37681	3124	1	[	[	-LRB-
37681	3124	2	84	84	CD
37681	3124	3	]	]	-RRB-
37681	3124	4	This	this	DT
37681	3124	5	and	and	CC
37681	3124	6	the	the	DT
37681	3124	7	three	three	CD
37681	3124	8	illustrations	illustration	NNS
37681	3124	9	following	follow	VBG
37681	3124	10	are	be	VBP
37681	3124	11	from	from	IN
37681	3124	12	Kolb	Kolb	NNP
37681	3124	13	,	,	,
37681	3124	14	loc	loc	NNP
37681	3124	15	.	.	.
37681	3125	1	cit	cit	NNP
37681	3125	2	.	.	.
37681	3126	1	[	[	-LRB-
37681	3126	2	85	85	CD
37681	3126	3	]	]	-RRB-
37681	3126	4	This	this	DT
37681	3126	5	was	be	VBD
37681	3126	6	in	in	IN
37681	3126	7	five	five	CD
37681	3126	8	colors	color	NNS
37681	3126	9	of	of	IN
37681	3126	10	marble	marble	NN
37681	3126	11	.	.	.
37681	3127	1	[	[	-LRB-
37681	3127	2	86	86	CD
37681	3127	3	]	]	-RRB-
37681	3127	4	The	the	DT
37681	3127	5	proof	proof	NN
37681	3127	6	is	be	VBZ
37681	3127	7	too	too	RB
37681	3127	8	involved	involved	JJ
37681	3127	9	to	to	TO
37681	3127	10	be	be	VB
37681	3127	11	given	give	VBN
37681	3127	12	here	here	RB
37681	3127	13	.	.	.
37681	3128	1	The	the	DT
37681	3128	2	writer	writer	NN
37681	3128	3	has	have	VBZ
37681	3128	4	set	set	VBN
37681	3128	5	it	-PRON-	PRP
37681	3128	6	forth	forth	RB
37681	3128	7	in	in	IN
37681	3128	8	a	a	DT
37681	3128	9	chapter	chapter	NN
37681	3128	10	on	on	IN
37681	3128	11	the	the	DT
37681	3128	12	transcendency	transcendency	NN
37681	3128	13	of	of	IN
37681	3128	14	[	[	-LRB-
37681	3128	15	pi	pi	NN
37681	3128	16	]	]	-RRB-
37681	3128	17	in	in	IN
37681	3128	18	a	a	DT
37681	3128	19	work	work	NN
37681	3128	20	soon	soon	RB
37681	3128	21	to	to	TO
37681	3128	22	be	be	VB
37681	3128	23	published	publish	VBN
37681	3128	24	by	by	IN
37681	3128	25	Professor	Professor	NNP
37681	3128	26	Young	Young	NNP
37681	3128	27	of	of	IN
37681	3128	28	The	the	DT
37681	3128	29	University	University	NNP
37681	3128	30	of	of	IN
37681	3128	31	Chicago	Chicago	NNP
37681	3128	32	.	.	.
37681	3129	1	CHAPTER	chapter	NN
37681	3129	2	XIX	XIX	NNP
37681	3129	3	THE	the	DT
37681	3129	4	LEADING	lead	VBG
37681	3129	5	PROPOSITIONS	proposition	NNS
37681	3129	6	OF	of	IN
37681	3129	7	BOOK	book	NN
37681	3129	8	VI	VI	NNP
37681	3129	9	There	there	EX
37681	3129	10	have	have	VBP
37681	3129	11	been	be	VBN
37681	3129	12	numerous	numerous	JJ
37681	3129	13	suggestions	suggestion	NNS
37681	3129	14	with	with	IN
37681	3129	15	respect	respect	NN
37681	3129	16	to	to	IN
37681	3129	17	solid	solid	JJ
37681	3129	18	geometry	geometry	NN
37681	3129	19	,	,	,
37681	3129	20	to	to	IN
37681	3129	21	the	the	DT
37681	3129	22	effect	effect	NN
37681	3129	23	that	that	IN
37681	3129	24	it	-PRON-	PRP
37681	3129	25	should	should	MD
37681	3129	26	be	be	VB
37681	3129	27	more	more	RBR
37681	3129	28	closely	closely	RB
37681	3129	29	connected	connect	VBN
37681	3129	30	with	with	IN
37681	3129	31	plane	plane	NN
37681	3129	32	geometry	geometry	NN
37681	3129	33	.	.	.
37681	3130	1	The	the	DT
37681	3130	2	attempt	attempt	NN
37681	3130	3	has	have	VBZ
37681	3130	4	been	be	VBN
37681	3130	5	made	make	VBN
37681	3130	6	,	,	,
37681	3130	7	notably	notably	RB
37681	3130	8	by	by	IN
37681	3130	9	Méray	Méray	NNP
37681	3130	10	in	in	IN
37681	3130	11	France	France	NNP
37681	3130	12	and	and	CC
37681	3130	13	de	de	NNP
37681	3130	14	Paolis	Paolis	NNP
37681	3130	15	in	in	IN
37681	3130	16	Italy	Italy	NNP
37681	3130	17	,	,	,
37681	3130	18	to	to	TO
37681	3130	19	treat	treat	VB
37681	3130	20	the	the	DT
37681	3130	21	corresponding	correspond	VBG
37681	3130	22	propositions	proposition	NNS
37681	3130	23	of	of	IN
37681	3130	24	plane	plane	NN
37681	3130	25	and	and	CC
37681	3130	26	solid	solid	JJ
37681	3130	27	geometry	geometry	NN
37681	3130	28	together	together	RB
37681	3130	29	;	;	:
37681	3130	30	as	as	IN
37681	3130	31	,	,	,
37681	3130	32	for	for	IN
37681	3130	33	example	example	NN
37681	3130	34	,	,	,
37681	3130	35	those	those	DT
37681	3130	36	relating	relate	VBG
37681	3130	37	to	to	IN
37681	3130	38	parallelograms	parallelogram	NNS
37681	3130	39	and	and	CC
37681	3130	40	parallelepipeds	parallelepiped	NNS
37681	3130	41	,	,	,
37681	3130	42	and	and	CC
37681	3130	43	those	those	DT
37681	3130	44	relating	relate	VBG
37681	3130	45	to	to	IN
37681	3130	46	plane	plane	NN
37681	3130	47	and	and	CC
37681	3130	48	spherical	spherical	JJ
37681	3130	49	triangles	triangle	NNS
37681	3130	50	.	.	.
37681	3131	1	Whatever	whatever	WDT
37681	3131	2	the	the	DT
37681	3131	3	merits	merit	NNS
37681	3131	4	of	of	IN
37681	3131	5	this	this	DT
37681	3131	6	plan	plan	NN
37681	3131	7	,	,	,
37681	3131	8	it	-PRON-	PRP
37681	3131	9	is	be	VBZ
37681	3131	10	not	not	RB
37681	3131	11	feasible	feasible	JJ
37681	3131	12	in	in	IN
37681	3131	13	America	America	NNP
37681	3131	14	at	at	IN
37681	3131	15	present	present	NN
37681	3131	16	,	,	,
37681	3131	17	partly	partly	RB
37681	3131	18	because	because	IN
37681	3131	19	of	of	IN
37681	3131	20	the	the	DT
37681	3131	21	nature	nature	NN
37681	3131	22	of	of	IN
37681	3131	23	the	the	DT
37681	3131	24	college	college	NN
37681	3131	25	-	-	HYPH
37681	3131	26	entrance	entrance	NN
37681	3131	27	requirements	requirement	NNS
37681	3131	28	.	.	.
37681	3132	1	While	while	IN
37681	3132	2	it	-PRON-	PRP
37681	3132	3	is	be	VBZ
37681	3132	4	true	true	JJ
37681	3132	5	that	that	IN
37681	3132	6	to	to	IN
37681	3132	7	a	a	DT
37681	3132	8	boy	boy	NN
37681	3132	9	or	or	CC
37681	3132	10	girl	girl	VB
37681	3132	11	a	a	DT
37681	3132	12	solid	solid	JJ
37681	3132	13	is	be	VBZ
37681	3132	14	more	more	RBR
37681	3132	15	concrete	concrete	JJ
37681	3132	16	than	than	IN
37681	3132	17	a	a	DT
37681	3132	18	plane	plane	NN
37681	3132	19	,	,	,
37681	3132	20	it	-PRON-	PRP
37681	3132	21	is	be	VBZ
37681	3132	22	not	not	RB
37681	3132	23	true	true	JJ
37681	3132	24	that	that	IN
37681	3132	25	a	a	DT
37681	3132	26	geometric	geometric	JJ
37681	3132	27	solid	solid	JJ
37681	3132	28	is	be	VBZ
37681	3132	29	more	more	RBR
37681	3132	30	concrete	concrete	JJ
37681	3132	31	than	than	IN
37681	3132	32	a	a	DT
37681	3132	33	geometric	geometric	JJ
37681	3132	34	plane	plane	NN
37681	3132	35	.	.	.
37681	3133	1	Just	just	RB
37681	3133	2	as	as	IN
37681	3133	3	the	the	DT
37681	3133	4	world	world	NN
37681	3133	5	developed	develop	VBD
37681	3133	6	its	-PRON-	PRP$
37681	3133	7	solid	solid	JJ
37681	3133	8	geometry	geometry	NN
37681	3133	9	,	,	,
37681	3133	10	as	as	IN
37681	3133	11	a	a	DT
37681	3133	12	science	science	NN
37681	3133	13	,	,	,
37681	3133	14	long	long	RB
37681	3133	15	after	after	IN
37681	3133	16	it	-PRON-	PRP
37681	3133	17	had	have	VBD
37681	3133	18	developed	develop	VBN
37681	3133	19	its	-PRON-	PRP$
37681	3133	20	plane	plane	NN
37681	3133	21	geometry	geometry	NN
37681	3133	22	,	,	,
37681	3133	23	so	so	CC
37681	3133	24	the	the	DT
37681	3133	25	human	human	JJ
37681	3133	26	mind	mind	NN
37681	3133	27	grasps	grasp	VBZ
37681	3133	28	the	the	DT
37681	3133	29	ideas	idea	NNS
37681	3133	30	of	of	IN
37681	3133	31	plane	plane	NN
37681	3133	32	figures	figure	NNS
37681	3133	33	earlier	early	RBR
37681	3133	34	than	than	IN
37681	3133	35	those	those	DT
37681	3133	36	of	of	IN
37681	3133	37	the	the	DT
37681	3133	38	geometric	geometric	JJ
37681	3133	39	solid	solid	JJ
37681	3133	40	.	.	.
37681	3134	1	There	there	EX
37681	3134	2	is	be	VBZ
37681	3134	3	,	,	,
37681	3134	4	however	however	RB
37681	3134	5	,	,	,
37681	3134	6	every	every	DT
37681	3134	7	reason	reason	NN
37681	3134	8	for	for	IN
37681	3134	9	referring	refer	VBG
37681	3134	10	to	to	IN
37681	3134	11	the	the	DT
37681	3134	12	corresponding	corresponding	JJ
37681	3134	13	proposition	proposition	NN
37681	3134	14	of	of	IN
37681	3134	15	plane	plane	NN
37681	3134	16	geometry	geometry	NN
37681	3134	17	when	when	WRB
37681	3134	18	any	any	DT
37681	3134	19	given	give	VBN
37681	3134	20	proposition	proposition	NN
37681	3134	21	of	of	IN
37681	3134	22	solid	solid	JJ
37681	3134	23	geometry	geometry	NN
37681	3134	24	is	be	VBZ
37681	3134	25	under	under	IN
37681	3134	26	consideration	consideration	NN
37681	3134	27	,	,	,
37681	3134	28	and	and	CC
37681	3134	29	frequent	frequent	JJ
37681	3134	30	references	reference	NNS
37681	3134	31	of	of	IN
37681	3134	32	this	this	DT
37681	3134	33	kind	kind	NN
37681	3134	34	will	will	MD
37681	3134	35	be	be	VB
37681	3134	36	made	make	VBN
37681	3134	37	in	in	IN
37681	3134	38	speaking	speaking	NN
37681	3134	39	of	of	IN
37681	3134	40	the	the	DT
37681	3134	41	propositions	proposition	NNS
37681	3134	42	in	in	IN
37681	3134	43	this	this	DT
37681	3134	44	and	and	CC
37681	3134	45	the	the	DT
37681	3134	46	two	two	CD
37681	3134	47	succeeding	succeed	VBG
37681	3134	48	chapters	chapter	NNS
37681	3134	49	.	.	.
37681	3135	1	Such	such	JJ
37681	3135	2	reference	reference	NN
37681	3135	3	has	have	VBZ
37681	3135	4	value	value	NN
37681	3135	5	in	in	IN
37681	3135	6	the	the	DT
37681	3135	7	apperception	apperception	NN
37681	3135	8	of	of	IN
37681	3135	9	the	the	DT
37681	3135	10	various	various	JJ
37681	3135	11	laws	law	NNS
37681	3135	12	of	of	IN
37681	3135	13	solid	solid	JJ
37681	3135	14	geometry	geometry	NN
37681	3135	15	,	,	,
37681	3135	16	and	and	CC
37681	3135	17	it	-PRON-	PRP
37681	3135	18	also	also	RB
37681	3135	19	adds	add	VBZ
37681	3135	20	an	an	DT
37681	3135	21	interest	interest	NN
37681	3135	22	to	to	IN
37681	3135	23	the	the	DT
37681	3135	24	subject	subject	NN
37681	3135	25	and	and	CC
37681	3135	26	creates	create	VBZ
37681	3135	27	some	some	DT
37681	3135	28	approach	approach	NN
37681	3135	29	to	to	IN
37681	3135	30	power	power	NN
37681	3135	31	in	in	IN
37681	3135	32	the	the	DT
37681	3135	33	discovery	discovery	NN
37681	3135	34	of	of	IN
37681	3135	35	new	new	JJ
37681	3135	36	facts	fact	NNS
37681	3135	37	in	in	IN
37681	3135	38	relation	relation	NN
37681	3135	39	to	to	IN
37681	3135	40	figures	figure	NNS
37681	3135	41	of	of	IN
37681	3135	42	three	three	CD
37681	3135	43	dimensions	dimension	NNS
37681	3135	44	.	.	.
37681	3136	1	The	the	DT
37681	3136	2	introduction	introduction	NN
37681	3136	3	to	to	IN
37681	3136	4	solid	solid	JJ
37681	3136	5	geometry	geometry	NN
37681	3136	6	should	should	MD
37681	3136	7	be	be	VB
37681	3136	8	made	make	VBN
37681	3136	9	slowly	slowly	RB
37681	3136	10	.	.	.
37681	3137	1	The	the	DT
37681	3137	2	pupil	pupil	NN
37681	3137	3	has	have	VBZ
37681	3137	4	been	be	VBN
37681	3137	5	accustomed	accustom	VBN
37681	3137	6	to	to	IN
37681	3137	7	seeing	see	VBG
37681	3137	8	only	only	JJ
37681	3137	9	plane	plane	NN
37681	3137	10	figures	figure	NNS
37681	3137	11	,	,	,
37681	3137	12	and	and	CC
37681	3137	13	therefore	therefore	RB
37681	3137	14	the	the	DT
37681	3137	15	drawing	drawing	NN
37681	3137	16	of	of	IN
37681	3137	17	a	a	DT
37681	3137	18	solid	solid	JJ
37681	3137	19	figure	figure	NN
37681	3137	20	in	in	IN
37681	3137	21	the	the	DT
37681	3137	22	flat	flat	NN
37681	3137	23	is	be	VBZ
37681	3137	24	confusing	confusing	JJ
37681	3137	25	.	.	.
37681	3138	1	The	the	DT
37681	3138	2	best	good	JJS
37681	3138	3	way	way	NN
37681	3138	4	for	for	IN
37681	3138	5	the	the	DT
37681	3138	6	teacher	teacher	NN
37681	3138	7	to	to	TO
37681	3138	8	anticipate	anticipate	VB
37681	3138	9	this	this	DT
37681	3138	10	difficulty	difficulty	NN
37681	3138	11	is	be	VBZ
37681	3138	12	to	to	TO
37681	3138	13	have	have	VB
37681	3138	14	a	a	DT
37681	3138	15	few	few	JJ
37681	3138	16	pieces	piece	NNS
37681	3138	17	of	of	IN
37681	3138	18	cardboard	cardboard	NN
37681	3138	19	,	,	,
37681	3138	20	a	a	DT
37681	3138	21	few	few	JJ
37681	3138	22	knitting	knit	VBG
37681	3138	23	needles	needle	NNS
37681	3138	24	filed	file	VBN
37681	3138	25	to	to	IN
37681	3138	26	sharp	sharp	JJ
37681	3138	27	points	point	NNS
37681	3138	28	,	,	,
37681	3138	29	a	a	DT
37681	3138	30	pine	pine	JJ
37681	3138	31	board	board	NN
37681	3138	32	about	about	IN
37681	3138	33	a	a	DT
37681	3138	34	foot	foot	NN
37681	3138	35	square	square	NN
37681	3138	36	,	,	,
37681	3138	37	and	and	CC
37681	3138	38	some	some	DT
37681	3138	39	small	small	JJ
37681	3138	40	corks	cork	NNS
37681	3138	41	.	.	.
37681	3139	1	With	with	IN
37681	3139	2	the	the	DT
37681	3139	3	cardboard	cardboard	NN
37681	3139	4	he	-PRON-	PRP
37681	3139	5	can	can	MD
37681	3139	6	illustrate	illustrate	VB
37681	3139	7	planes	plane	NNS
37681	3139	8	,	,	,
37681	3139	9	whether	whether	IN
37681	3139	10	alone	alone	RB
37681	3139	11	,	,	,
37681	3139	12	intersecting	intersect	VBG
37681	3139	13	obliquely	obliquely	RB
37681	3139	14	or	or	CC
37681	3139	15	at	at	IN
37681	3139	16	right	right	JJ
37681	3139	17	angles	angle	NNS
37681	3139	18	,	,	,
37681	3139	19	or	or	CC
37681	3139	20	parallel	parallel	NN
37681	3139	21	,	,	,
37681	3139	22	and	and	CC
37681	3139	23	he	-PRON-	PRP
37681	3139	24	can	can	MD
37681	3139	25	easily	easily	RB
37681	3139	26	illustrate	illustrate	VB
37681	3139	27	the	the	DT
37681	3139	28	figures	figure	NNS
37681	3139	29	given	give	VBN
37681	3139	30	in	in	IN
37681	3139	31	the	the	DT
37681	3139	32	textbook	textbook	NN
37681	3139	33	in	in	IN
37681	3139	34	use	use	NN
37681	3139	35	.	.	.
37681	3140	1	There	there	EX
37681	3140	2	are	be	VBP
37681	3140	3	models	model	NNS
37681	3140	4	of	of	IN
37681	3140	5	this	this	DT
37681	3140	6	kind	kind	NN
37681	3140	7	for	for	IN
37681	3140	8	sale	sale	NN
37681	3140	9	,	,	,
37681	3140	10	but	but	CC
37681	3140	11	the	the	DT
37681	3140	12	simple	simple	JJ
37681	3140	13	ones	one	NNS
37681	3140	14	made	make	VBN
37681	3140	15	in	in	IN
37681	3140	16	a	a	DT
37681	3140	17	few	few	JJ
37681	3140	18	seconds	second	NNS
37681	3140	19	by	by	IN
37681	3140	20	the	the	DT
37681	3140	21	teacher	teacher	NN
37681	3140	22	or	or	CC
37681	3140	23	the	the	DT
37681	3140	24	pupil	pupil	NN
37681	3140	25	have	have	VBP
37681	3140	26	much	much	RB
37681	3140	27	more	more	JJR
37681	3140	28	meaning	meaning	NN
37681	3140	29	.	.	.
37681	3141	1	The	the	DT
37681	3141	2	knitting	knitting	NN
37681	3141	3	needles	needle	NNS
37681	3141	4	may	may	MD
37681	3141	5	be	be	VB
37681	3141	6	stuck	stick	VBN
37681	3141	7	in	in	IN
37681	3141	8	the	the	DT
37681	3141	9	board	board	NN
37681	3141	10	to	to	TO
37681	3141	11	illustrate	illustrate	VB
37681	3141	12	perpendicular	perpendicular	JJ
37681	3141	13	or	or	CC
37681	3141	14	oblique	oblique	JJ
37681	3141	15	lines	line	NNS
37681	3141	16	,	,	,
37681	3141	17	and	and	CC
37681	3141	18	if	if	IN
37681	3141	19	two	two	CD
37681	3141	20	or	or	CC
37681	3141	21	more	more	JJR
37681	3141	22	are	be	VBP
37681	3141	23	to	to	TO
37681	3141	24	meet	meet	VB
37681	3141	25	in	in	IN
37681	3141	26	a	a	DT
37681	3141	27	point	point	NN
37681	3141	28	,	,	,
37681	3141	29	they	-PRON-	PRP
37681	3141	30	may	may	MD
37681	3141	31	be	be	VB
37681	3141	32	held	hold	VBN
37681	3141	33	together	together	RB
37681	3141	34	by	by	IN
37681	3141	35	sticking	stick	VBG
37681	3141	36	them	-PRON-	PRP
37681	3141	37	in	in	IN
37681	3141	38	one	one	CD
37681	3141	39	of	of	IN
37681	3141	40	the	the	DT
37681	3141	41	small	small	JJ
37681	3141	42	corks	cork	NNS
37681	3141	43	.	.	.
37681	3142	1	Such	such	JJ
37681	3142	2	homely	homely	JJ
37681	3142	3	apparatus	apparatus	NN
37681	3142	4	,	,	,
37681	3142	5	costing	cost	VBG
37681	3142	6	almost	almost	RB
37681	3142	7	nothing	nothing	NN
37681	3142	8	,	,	,
37681	3142	9	to	to	TO
37681	3142	10	be	be	VB
37681	3142	11	put	put	VBN
37681	3142	12	together	together	RB
37681	3142	13	in	in	IN
37681	3142	14	class	class	NN
37681	3142	15	,	,	,
37681	3142	16	seems	seem	VBZ
37681	3142	17	much	much	RB
37681	3142	18	more	more	RBR
37681	3142	19	real	real	JJ
37681	3142	20	and	and	CC
37681	3142	21	is	be	VBZ
37681	3142	22	much	much	RB
37681	3142	23	more	more	RBR
37681	3142	24	satisfactory	satisfactory	JJ
37681	3142	25	than	than	IN
37681	3142	26	the	the	DT
37681	3142	27	German	german	JJ
37681	3142	28	models	model	NNS
37681	3142	29	.	.	.
37681	3143	1	[	[	-LRB-
37681	3143	2	87	87	CD
37681	3143	3	]	]	-RRB-
37681	3143	4	An	an	DT
37681	3143	5	extensive	extensive	JJ
37681	3143	6	use	use	NN
37681	3143	7	of	of	IN
37681	3143	8	models	model	NNS
37681	3143	9	is	be	VBZ
37681	3143	10	,	,	,
37681	3143	11	however	however	RB
37681	3143	12	,	,	,
37681	3143	13	unwise	unwise	JJ
37681	3143	14	.	.	.
37681	3144	1	The	the	DT
37681	3144	2	pupil	pupil	NN
37681	3144	3	must	must	MD
37681	3144	4	learn	learn	VB
37681	3144	5	very	very	RB
37681	3144	6	early	early	JJ
37681	3144	7	how	how	WRB
37681	3144	8	to	to	TO
37681	3144	9	visualize	visualize	VB
37681	3144	10	a	a	DT
37681	3144	11	solid	solid	JJ
37681	3144	12	from	from	IN
37681	3144	13	the	the	DT
37681	3144	14	flat	flat	JJ
37681	3144	15	outline	outline	NN
37681	3144	16	picture	picture	NN
37681	3144	17	,	,	,
37681	3144	18	just	just	RB
37681	3144	19	as	as	IN
37681	3144	20	a	a	DT
37681	3144	21	builder	builder	NN
37681	3144	22	or	or	CC
37681	3144	23	a	a	DT
37681	3144	24	mechanic	mechanic	NN
37681	3144	25	learns	learn	VBZ
37681	3144	26	to	to	TO
37681	3144	27	read	read	VB
37681	3144	28	his	-PRON-	PRP$
37681	3144	29	working	work	VBG
37681	3144	30	drawings	drawing	NNS
37681	3144	31	.	.	.
37681	3145	1	To	to	TO
37681	3145	2	have	have	VB
37681	3145	3	a	a	DT
37681	3145	4	model	model	NN
37681	3145	5	for	for	IN
37681	3145	6	each	each	DT
37681	3145	7	proposition	proposition	NN
37681	3145	8	,	,	,
37681	3145	9	or	or	CC
37681	3145	10	even	even	RB
37681	3145	11	to	to	TO
37681	3145	12	have	have	VB
37681	3145	13	a	a	DT
37681	3145	14	photograph	photograph	NN
37681	3145	15	or	or	CC
37681	3145	16	a	a	DT
37681	3145	17	stereoscopic	stereoscopic	JJ
37681	3145	18	picture	picture	NN
37681	3145	19	,	,	,
37681	3145	20	is	be	VBZ
37681	3145	21	a	a	DT
37681	3145	22	very	very	RB
37681	3145	23	poor	poor	JJ
37681	3145	24	educational	educational	JJ
37681	3145	25	policy	policy	NN
37681	3145	26	.	.	.
37681	3146	1	A	a	DT
37681	3146	2	textbook	textbook	NN
37681	3146	3	may	may	MD
37681	3146	4	properly	properly	RB
37681	3146	5	illustrate	illustrate	VB
37681	3146	6	a	a	DT
37681	3146	7	few	few	JJ
37681	3146	8	propositions	proposition	NNS
37681	3146	9	by	by	IN
37681	3146	10	photographic	photographic	JJ
37681	3146	11	aids	aid	NNS
37681	3146	12	,	,	,
37681	3146	13	but	but	CC
37681	3146	14	after	after	IN
37681	3146	15	that	that	DT
37681	3146	16	the	the	DT
37681	3146	17	pupil	pupil	NN
37681	3146	18	should	should	MD
37681	3146	19	use	use	VB
37681	3146	20	the	the	DT
37681	3146	21	kind	kind	NN
37681	3146	22	of	of	IN
37681	3146	23	figures	figure	NNS
37681	3146	24	that	that	WDT
37681	3146	25	he	-PRON-	PRP
37681	3146	26	must	must	MD
37681	3146	27	meet	meet	VB
37681	3146	28	in	in	IN
37681	3146	29	his	-PRON-	PRP$
37681	3146	30	mathematical	mathematical	JJ
37681	3146	31	work	work	NN
37681	3146	32	.	.	.
37681	3147	1	A	a	DT
37681	3147	2	child	child	NN
37681	3147	3	should	should	MD
37681	3147	4	not	not	RB
37681	3147	5	be	be	VB
37681	3147	6	kept	keep	VBN
37681	3147	7	in	in	IN
37681	3147	8	a	a	DT
37681	3147	9	perambulator	perambulator	NN
37681	3147	10	all	all	PDT
37681	3147	11	his	-PRON-	PRP$
37681	3147	12	life,--he	life,--he	NN
37681	3147	13	must	must	MD
37681	3147	14	learn	learn	VB
37681	3147	15	to	to	TO
37681	3147	16	walk	walk	VB
37681	3147	17	if	if	IN
37681	3147	18	he	-PRON-	PRP
37681	3147	19	is	be	VBZ
37681	3147	20	to	to	TO
37681	3147	21	be	be	VB
37681	3147	22	strong	strong	JJ
37681	3147	23	and	and	CC
37681	3147	24	grow	grow	VB
37681	3147	25	to	to	IN
37681	3147	26	maturity	maturity	NN
37681	3147	27	;	;	:
37681	3147	28	and	and	CC
37681	3147	29	it	-PRON-	PRP
37681	3147	30	is	be	VBZ
37681	3147	31	so	so	RB
37681	3147	32	with	with	IN
37681	3147	33	a	a	DT
37681	3147	34	pupil	pupil	NN
37681	3147	35	in	in	IN
37681	3147	36	the	the	DT
37681	3147	37	use	use	NN
37681	3147	38	of	of	IN
37681	3147	39	models	model	NNS
37681	3147	40	in	in	IN
37681	3147	41	solid	solid	JJ
37681	3147	42	geometry	geometry	NN
37681	3147	43	.	.	.
37681	3148	1	[	[	-LRB-
37681	3148	2	88	88	CD
37681	3148	3	]	]	-RRB-
37681	3148	4	The	the	DT
37681	3148	5	case	case	NN
37681	3148	6	is	be	VBZ
37681	3148	7	somewhat	somewhat	RB
37681	3148	8	similar	similar	JJ
37681	3148	9	with	with	IN
37681	3148	10	respect	respect	NN
37681	3148	11	to	to	IN
37681	3148	12	colored	colored	JJ
37681	3148	13	crayons	crayon	NNS
37681	3148	14	.	.	.
37681	3149	1	They	-PRON-	PRP
37681	3149	2	have	have	VBP
37681	3149	3	their	-PRON-	PRP$
37681	3149	4	value	value	NN
37681	3149	5	and	and	CC
37681	3149	6	their	-PRON-	PRP$
37681	3149	7	proper	proper	JJ
37681	3149	8	place	place	NN
37681	3149	9	,	,	,
37681	3149	10	but	but	CC
37681	3149	11	they	-PRON-	PRP
37681	3149	12	also	also	RB
37681	3149	13	have	have	VBP
37681	3149	14	their	-PRON-	PRP$
37681	3149	15	strict	strict	JJ
37681	3149	16	limitations	limitation	NNS
37681	3149	17	.	.	.
37681	3150	1	It	-PRON-	PRP
37681	3150	2	is	be	VBZ
37681	3150	3	difficult	difficult	JJ
37681	3150	4	to	to	TO
37681	3150	5	keep	keep	VB
37681	3150	6	their	-PRON-	PRP$
37681	3150	7	use	use	NN
37681	3150	8	within	within	IN
37681	3150	9	bounds	bound	NNS
37681	3150	10	;	;	:
37681	3150	11	pupils	pupil	NNS
37681	3150	12	come	come	VBP
37681	3150	13	to	to	TO
37681	3150	14	use	use	VB
37681	3150	15	them	-PRON-	PRP
37681	3150	16	to	to	TO
37681	3150	17	make	make	VB
37681	3150	18	pleasing	pleasing	JJ
37681	3150	19	pictures	picture	NNS
37681	3150	20	,	,	,
37681	3150	21	and	and	CC
37681	3150	22	teachers	teacher	NNS
37681	3150	23	unconsciously	unconsciously	RB
37681	3150	24	fall	fall	VBP
37681	3150	25	into	into	IN
37681	3150	26	the	the	DT
37681	3150	27	same	same	JJ
37681	3150	28	habit	habit	NN
37681	3150	29	.	.	.
37681	3151	1	The	the	DT
37681	3151	2	value	value	NN
37681	3151	3	of	of	IN
37681	3151	4	colored	colored	JJ
37681	3151	5	crayons	crayon	NNS
37681	3151	6	is	be	VBZ
37681	3151	7	two	two	CD
37681	3151	8	-	-	HYPH
37681	3151	9	fold	fold	RB
37681	3151	10	:	:	:
37681	3151	11	(	(	-LRB-
37681	3151	12	1	1	LS
37681	3151	13	)	)	-RRB-
37681	3151	14	they	-PRON-	PRP
37681	3151	15	sometimes	sometimes	RB
37681	3151	16	make	make	VBP
37681	3151	17	two	two	CD
37681	3151	18	planes	plane	NNS
37681	3151	19	stand	stand	VB
37681	3151	20	out	out	RP
37681	3151	21	more	more	RBR
37681	3151	22	clearly	clearly	RB
37681	3151	23	,	,	,
37681	3151	24	or	or	CC
37681	3151	25	they	-PRON-	PRP
37681	3151	26	serve	serve	VBP
37681	3151	27	to	to	TO
37681	3151	28	differentiate	differentiate	VB
37681	3151	29	some	some	DT
37681	3151	30	line	line	NN
37681	3151	31	that	that	WDT
37681	3151	32	is	be	VBZ
37681	3151	33	under	under	IN
37681	3151	34	consideration	consideration	NN
37681	3151	35	from	from	IN
37681	3151	36	others	other	NNS
37681	3151	37	that	that	WDT
37681	3151	38	are	be	VBP
37681	3151	39	not	not	RB
37681	3151	40	;	;	:
37681	3151	41	(	(	-LRB-
37681	3151	42	2	2	LS
37681	3151	43	)	)	-RRB-
37681	3151	44	they	-PRON-	PRP
37681	3151	45	enable	enable	VBP
37681	3151	46	a	a	DT
37681	3151	47	class	class	NN
37681	3151	48	to	to	TO
37681	3151	49	follow	follow	VB
37681	3151	50	a	a	DT
37681	3151	51	demonstration	demonstration	NN
37681	3151	52	more	more	RBR
37681	3151	53	easily	easily	RB
37681	3151	54	by	by	IN
37681	3151	55	hearing	hear	VBG
37681	3151	56	of	of	IN
37681	3151	57	"	"	``
37681	3151	58	the	the	DT
37681	3151	59	red	red	JJ
37681	3151	60	plane	plane	NN
37681	3151	61	perpendicular	perpendicular	JJ
37681	3151	62	to	to	IN
37681	3151	63	the	the	DT
37681	3151	64	blue	blue	JJ
37681	3151	65	one	one	NN
37681	3151	66	,	,	,
37681	3151	67	"	"	''
37681	3151	68	instead	instead	RB
37681	3151	69	of	of	IN
37681	3151	70	"	"	``
37681	3151	71	the	the	DT
37681	3151	72	plane	plane	NN
37681	3151	73	_	_	NNP
37681	3151	74	MN	MN	NNP
37681	3151	75	_	_	NNP
37681	3151	76	perpendicular	perpendicular	NN
37681	3151	77	to	to	IN
37681	3151	78	the	the	DT
37681	3151	79	plane	plane	NN
37681	3151	80	_	_	NNP
37681	3151	81	PQ	PQ	NNP
37681	3151	82	_	_	NNP
37681	3151	83	.	.	.
37681	3151	84	"	"	''
37681	3152	1	But	but	CC
37681	3152	2	it	-PRON-	PRP
37681	3152	3	should	should	MD
37681	3152	4	always	always	RB
37681	3152	5	be	be	VB
37681	3152	6	borne	bear	VBN
37681	3152	7	in	in	IN
37681	3152	8	mind	mind	NN
37681	3152	9	that	that	IN
37681	3152	10	in	in	IN
37681	3152	11	practical	practical	JJ
37681	3152	12	work	work	NN
37681	3152	13	we	-PRON-	PRP
37681	3152	14	do	do	VBP
37681	3152	15	not	not	RB
37681	3152	16	have	have	VB
37681	3152	17	colored	color	VBN
37681	3152	18	ink	ink	NN
37681	3152	19	or	or	CC
37681	3152	20	colored	colored	JJ
37681	3152	21	pencils	pencil	NNS
37681	3152	22	commonly	commonly	RB
37681	3152	23	at	at	IN
37681	3152	24	hand	hand	NN
37681	3152	25	,	,	,
37681	3152	26	nor	nor	CC
37681	3152	27	do	do	VBP
37681	3152	28	we	-PRON-	PRP
37681	3152	29	generally	generally	RB
37681	3152	30	have	have	VB
37681	3152	31	colored	color	VBN
37681	3152	32	crayons	crayon	NNS
37681	3152	33	.	.	.
37681	3153	1	Pupils	pupil	NNS
37681	3153	2	should	should	MD
37681	3153	3	therefore	therefore	RB
37681	3153	4	become	become	VB
37681	3153	5	accustomed	accustomed	JJ
37681	3153	6	to	to	IN
37681	3153	7	the	the	DT
37681	3153	8	pencil	pencil	NN
37681	3153	9	and	and	CC
37681	3153	10	the	the	DT
37681	3153	11	white	white	JJ
37681	3153	12	crayon	crayon	NN
37681	3153	13	as	as	IN
37681	3153	14	the	the	DT
37681	3153	15	regulation	regulation	NN
37681	3153	16	tools	tool	NNS
37681	3153	17	,	,	,
37681	3153	18	and	and	CC
37681	3153	19	in	in	IN
37681	3153	20	general	general	JJ
37681	3153	21	they	-PRON-	PRP
37681	3153	22	should	should	MD
37681	3153	23	use	use	VB
37681	3153	24	them	-PRON-	PRP
37681	3153	25	.	.	.
37681	3154	1	The	the	DT
37681	3154	2	figures	figure	NNS
37681	3154	3	may	may	MD
37681	3154	4	not	not	RB
37681	3154	5	be	be	VB
37681	3154	6	as	as	RB
37681	3154	7	striking	striking	JJ
37681	3154	8	,	,	,
37681	3154	9	but	but	CC
37681	3154	10	they	-PRON-	PRP
37681	3154	11	are	be	VBP
37681	3154	12	more	more	RBR
37681	3154	13	quickly	quickly	RB
37681	3154	14	made	make	VBN
37681	3154	15	and	and	CC
37681	3154	16	they	-PRON-	PRP
37681	3154	17	are	be	VBP
37681	3154	18	more	more	RBR
37681	3154	19	practical	practical	JJ
37681	3154	20	.	.	.
37681	3155	1	The	the	DT
37681	3155	2	definition	definition	NN
37681	3155	3	of	of	IN
37681	3155	4	"	"	``
37681	3155	5	plane	plane	NN
37681	3155	6	"	"	''
37681	3155	7	has	have	VBZ
37681	3155	8	already	already	RB
37681	3155	9	been	be	VBN
37681	3155	10	discussed	discuss	VBN
37681	3155	11	in	in	IN
37681	3155	12	Chapter	Chapter	NNP
37681	3155	13	XII	XII	NNP
37681	3155	14	,	,	,
37681	3155	15	and	and	CC
37681	3155	16	the	the	DT
37681	3155	17	other	other	JJ
37681	3155	18	definitions	definition	NNS
37681	3155	19	of	of	IN
37681	3155	20	Book	Book	NNP
37681	3155	21	VI	VI	NNP
37681	3155	22	are	be	VBP
37681	3155	23	not	not	RB
37681	3155	24	of	of	IN
37681	3155	25	enough	enough	JJ
37681	3155	26	interest	interest	NN
37681	3155	27	to	to	TO
37681	3155	28	call	call	VB
37681	3155	29	for	for	IN
37681	3155	30	special	special	JJ
37681	3155	31	remark	remark	NN
37681	3155	32	.	.	.
37681	3156	1	The	the	DT
37681	3156	2	axioms	axiom	NNS
37681	3156	3	are	be	VBP
37681	3156	4	the	the	DT
37681	3156	5	same	same	JJ
37681	3156	6	as	as	IN
37681	3156	7	in	in	IN
37681	3156	8	plane	plane	NN
37681	3156	9	geometry	geometry	NN
37681	3156	10	,	,	,
37681	3156	11	but	but	CC
37681	3156	12	there	there	EX
37681	3156	13	is	be	VBZ
37681	3156	14	at	at	RB
37681	3156	15	least	least	RBS
37681	3156	16	one	one	CD
37681	3156	17	postulate	postulate	NN
37681	3156	18	that	that	WDT
37681	3156	19	needs	need	VBZ
37681	3156	20	to	to	TO
37681	3156	21	be	be	VB
37681	3156	22	added	add	VBN
37681	3156	23	,	,	,
37681	3156	24	although	although	IN
37681	3156	25	it	-PRON-	PRP
37681	3156	26	would	would	MD
37681	3156	27	be	be	VB
37681	3156	28	possible	possible	JJ
37681	3156	29	to	to	TO
37681	3156	30	state	state	VB
37681	3156	31	various	various	JJ
37681	3156	32	analogues	analogue	NNS
37681	3156	33	of	of	IN
37681	3156	34	the	the	DT
37681	3156	35	postulates	postulate	NNS
37681	3156	36	of	of	IN
37681	3156	37	plane	plane	NN
37681	3156	38	geometry	geometry	NN
37681	3156	39	if	if	IN
37681	3156	40	we	-PRON-	PRP
37681	3156	41	cared	care	VBD
37681	3156	42	unnecessarily	unnecessarily	RB
37681	3156	43	to	to	TO
37681	3156	44	enlarge	enlarge	VB
37681	3156	45	the	the	DT
37681	3156	46	number	number	NN
37681	3156	47	.	.	.
37681	3157	1	The	the	DT
37681	3157	2	most	most	RBS
37681	3157	3	important	important	JJ
37681	3157	4	postulate	postulate	NN
37681	3157	5	of	of	IN
37681	3157	6	solid	solid	JJ
37681	3157	7	geometry	geometry	NN
37681	3157	8	is	be	VBZ
37681	3157	9	as	as	IN
37681	3157	10	follows	follow	VBZ
37681	3157	11	:	:	:
37681	3157	12	_	_	NNP
37681	3157	13	One	one	CD
37681	3157	14	plane	plane	NN
37681	3157	15	,	,	,
37681	3157	16	and	and	CC
37681	3157	17	only	only	RB
37681	3157	18	one	one	CD
37681	3157	19	,	,	,
37681	3157	20	can	can	MD
37681	3157	21	be	be	VB
37681	3157	22	passed	pass	VBN
37681	3157	23	through	through	IN
37681	3157	24	two	two	CD
37681	3157	25	intersecting	intersect	VBG
37681	3157	26	straight	straight	JJ
37681	3157	27	lines	line	NNS
37681	3157	28	.	.	.
37681	3157	29	_	_	NNP
37681	3157	30	This	this	DT
37681	3157	31	is	be	VBZ
37681	3157	32	easily	easily	RB
37681	3157	33	illustrated	illustrate	VBN
37681	3157	34	,	,	,
37681	3157	35	as	as	IN
37681	3157	36	in	in	IN
37681	3157	37	most	most	JJS
37681	3157	38	textbooks	textbook	NNS
37681	3157	39	,	,	,
37681	3157	40	as	as	IN
37681	3157	41	also	also	RB
37681	3157	42	are	be	VBP
37681	3157	43	three	three	CD
37681	3157	44	important	important	JJ
37681	3157	45	corollaries	corollary	NNS
37681	3157	46	derived	derive	VBN
37681	3157	47	from	from	IN
37681	3157	48	it	-PRON-	PRP
37681	3157	49	:	:	:
37681	3157	50	1	1	CD
37681	3157	51	.	.	.
37681	3158	1	_	_	NNP
37681	3158	2	A	a	DT
37681	3158	3	straight	straight	JJ
37681	3158	4	line	line	NN
37681	3158	5	and	and	CC
37681	3158	6	a	a	DT
37681	3158	7	point	point	NN
37681	3158	8	not	not	RB
37681	3158	9	in	in	IN
37681	3158	10	the	the	DT
37681	3158	11	line	line	NN
37681	3158	12	determine	determine	VB
37681	3158	13	a	a	DT
37681	3158	14	plane	plane	NN
37681	3158	15	.	.	.
37681	3158	16	_	_	NNP
37681	3158	17	Of	of	RB
37681	3158	18	course	course	RB
37681	3158	19	this	this	DT
37681	3158	20	may	may	MD
37681	3158	21	be	be	VB
37681	3158	22	made	make	VBN
37681	3158	23	the	the	DT
37681	3158	24	postulate	postulate	NN
37681	3158	25	,	,	,
37681	3158	26	as	as	IN
37681	3158	27	may	may	MD
37681	3158	28	also	also	RB
37681	3158	29	the	the	DT
37681	3158	30	next	next	JJ
37681	3158	31	one	one	NN
37681	3158	32	,	,	,
37681	3158	33	the	the	DT
37681	3158	34	postulate	postulate	NN
37681	3158	35	being	be	VBG
37681	3158	36	placed	place	VBN
37681	3158	37	among	among	IN
37681	3158	38	the	the	DT
37681	3158	39	corollaries	corollary	NNS
37681	3158	40	,	,	,
37681	3158	41	but	but	CC
37681	3158	42	the	the	DT
37681	3158	43	arrangement	arrangement	NN
37681	3158	44	here	here	RB
37681	3158	45	adopted	adopt	VBN
37681	3158	46	is	be	VBZ
37681	3158	47	probably	probably	RB
37681	3158	48	the	the	DT
37681	3158	49	most	most	RBS
37681	3158	50	satisfactory	satisfactory	JJ
37681	3158	51	for	for	IN
37681	3158	52	educational	educational	JJ
37681	3158	53	purposes	purpose	NNS
37681	3158	54	.	.	.
37681	3159	1	2	2	LS
37681	3159	2	.	.	.
37681	3160	1	_	_	NNP
37681	3160	2	Three	three	CD
37681	3160	3	points	point	NNS
37681	3160	4	not	not	RB
37681	3160	5	in	in	IN
37681	3160	6	a	a	DT
37681	3160	7	straight	straight	JJ
37681	3160	8	line	line	NN
37681	3160	9	determine	determine	VBP
37681	3160	10	a	a	DT
37681	3160	11	plane	plane	NN
37681	3160	12	.	.	.
37681	3160	13	_	_	NNP
37681	3160	14	The	the	DT
37681	3160	15	common	common	JJ
37681	3160	16	question	question	NN
37681	3160	17	as	as	IN
37681	3160	18	to	to	IN
37681	3160	19	why	why	WRB
37681	3160	20	a	a	DT
37681	3160	21	three	three	CD
37681	3160	22	-	-	HYPH
37681	3160	23	legged	legged	JJ
37681	3160	24	stool	stool	NN
37681	3160	25	stands	stand	VBZ
37681	3160	26	firmly	firmly	RB
37681	3160	27	,	,	,
37681	3160	28	while	while	IN
37681	3160	29	a	a	DT
37681	3160	30	four	four	CD
37681	3160	31	-	-	HYPH
37681	3160	32	legged	legged	JJ
37681	3160	33	table	table	NN
37681	3160	34	often	often	RB
37681	3160	35	does	do	VBZ
37681	3160	36	not	not	RB
37681	3160	37	,	,	,
37681	3160	38	will	will	MD
37681	3160	39	add	add	VB
37681	3160	40	some	some	DT
37681	3160	41	interest	interest	NN
37681	3160	42	at	at	IN
37681	3160	43	this	this	DT
37681	3160	44	point	point	NN
37681	3160	45	.	.	.
37681	3161	1	3	3	LS
37681	3161	2	.	.	.
37681	3162	1	_	_	NNP
37681	3162	2	Two	two	CD
37681	3162	3	parallel	parallel	JJ
37681	3162	4	lines	line	NNS
37681	3162	5	determine	determine	VBP
37681	3162	6	a	a	DT
37681	3162	7	plane	plane	NN
37681	3162	8	.	.	.
37681	3162	9	_	_	NNP
37681	3162	10	This	this	DT
37681	3162	11	requires	require	VBZ
37681	3162	12	a	a	DT
37681	3162	13	slight	slight	JJ
37681	3162	14	but	but	CC
37681	3162	15	informal	informal	JJ
37681	3162	16	proof	proof	NN
37681	3162	17	to	to	TO
37681	3162	18	show	show	VB
37681	3162	19	that	that	IN
37681	3162	20	it	-PRON-	PRP
37681	3162	21	properly	properly	RB
37681	3162	22	follows	follow	VBZ
37681	3162	23	as	as	IN
37681	3162	24	a	a	DT
37681	3162	25	corollary	corollary	NN
37681	3162	26	from	from	IN
37681	3162	27	the	the	DT
37681	3162	28	postulate	postulate	NN
37681	3162	29	,	,	,
37681	3162	30	but	but	CC
37681	3162	31	a	a	DT
37681	3162	32	single	single	JJ
37681	3162	33	sentence	sentence	NN
37681	3162	34	suffices	suffice	VBZ
37681	3162	35	.	.	.
37681	3163	1	While	while	IN
37681	3163	2	studying	study	VBG
37681	3163	3	this	this	DT
37681	3163	4	book	book	NN
37681	3163	5	questions	question	NNS
37681	3163	6	of	of	IN
37681	3163	7	the	the	DT
37681	3163	8	following	follow	VBG
37681	3163	9	nature	nature	NN
37681	3163	10	may	may	MD
37681	3163	11	arise	arise	VB
37681	3163	12	with	with	IN
37681	3163	13	an	an	DT
37681	3163	14	advanced	advanced	JJ
37681	3163	15	class	class	NN
37681	3163	16	,	,	,
37681	3163	17	or	or	CC
37681	3163	18	may	may	MD
37681	3163	19	be	be	VB
37681	3163	20	suggested	suggest	VBN
37681	3163	21	to	to	IN
37681	3163	22	those	those	DT
37681	3163	23	who	who	WP
37681	3163	24	have	have	VBP
37681	3163	25	had	have	VBN
37681	3163	26	higher	high	JJR
37681	3163	27	algebra	algebra	NN
37681	3163	28	:	:	:
37681	3163	29	How	how	WRB
37681	3163	30	many	many	JJ
37681	3163	31	straight	straight	JJ
37681	3163	32	lines	line	NNS
37681	3163	33	are	be	VBP
37681	3163	34	in	in	IN
37681	3163	35	general	general	JJ
37681	3163	36	(	(	-LRB-
37681	3163	37	that	that	RB
37681	3163	38	is	is	RB
37681	3163	39	,	,	,
37681	3163	40	at	at	IN
37681	3163	41	the	the	DT
37681	3163	42	most	most	RBS
37681	3163	43	)	)	-RRB-
37681	3163	44	determined	determine	VBN
37681	3163	45	by	by	IN
37681	3163	46	_	_	NNP
37681	3163	47	n	n	CC
37681	3163	48	_	_	NNP
37681	3163	49	points	point	NNS
37681	3163	50	in	in	IN
37681	3163	51	space	space	NN
37681	3163	52	?	?	.
37681	3164	1	Two	two	CD
37681	3164	2	points	point	NNS
37681	3164	3	determine	determine	VBP
37681	3164	4	1	1	CD
37681	3164	5	line	line	NN
37681	3164	6	,	,	,
37681	3164	7	a	a	DT
37681	3164	8	third	third	JJ
37681	3164	9	point	point	NN
37681	3164	10	adds	add	VBZ
37681	3164	11	(	(	-LRB-
37681	3164	12	in	in	IN
37681	3164	13	general	general	JJ
37681	3164	14	,	,	,
37681	3164	15	in	in	IN
37681	3164	16	all	all	PDT
37681	3164	17	these	these	DT
37681	3164	18	cases	case	NNS
37681	3164	19	)	)	-RRB-
37681	3164	20	2	2	CD
37681	3164	21	more	more	JJR
37681	3164	22	,	,	,
37681	3164	23	a	a	DT
37681	3164	24	fourth	fourth	JJ
37681	3164	25	point	point	NN
37681	3164	26	adds	add	VBZ
37681	3164	27	3	3	CD
37681	3164	28	more	more	JJR
37681	3164	29	,	,	,
37681	3164	30	and	and	CC
37681	3164	31	an	an	DT
37681	3164	32	_	_	NNP
37681	3164	33	n_th	n_th	NNP
37681	3164	34	point	point	NN
37681	3164	35	_	_	NNP
37681	3164	36	n	n	CC
37681	3164	37	_	_	NNP
37681	3164	38	-	-	HYPH
37681	3164	39	1	1	CD
37681	3164	40	more	more	JJR
37681	3164	41	.	.	.
37681	3165	1	Hence	hence	RB
37681	3165	2	the	the	DT
37681	3165	3	maximum	maximum	NN
37681	3165	4	is	be	VBZ
37681	3165	5	1	1	CD
37681	3165	6	+	+	SYM
37681	3165	7	2	2	CD
37681	3165	8	+	+	SYM
37681	3165	9	3	3	CD
37681	3165	10	+	+	SYM
37681	3165	11	...	...	NFP
37681	3165	12	+	+	SYM
37681	3165	13	(	(	-LRB-
37681	3165	14	_	_	NNP
37681	3165	15	n	n	CC
37681	3165	16	_	_	NNP
37681	3165	17	-	-	HYPH
37681	3165	18	1	1	NNP
37681	3165	19	)	)	-RRB-
37681	3165	20	,	,	,
37681	3165	21	or	or	CC
37681	3165	22	_	_	NNP
37681	3165	23	n_(_n_-1)/2	n_(_n_-1)/2	NNP
37681	3165	24	,	,	,
37681	3165	25	which	which	WDT
37681	3165	26	the	the	DT
37681	3165	27	pupil	pupil	NN
37681	3165	28	will	will	MD
37681	3165	29	understand	understand	VB
37681	3165	30	if	if	IN
37681	3165	31	he	-PRON-	PRP
37681	3165	32	has	have	VBZ
37681	3165	33	studied	study	VBN
37681	3165	34	arithmetical	arithmetical	JJ
37681	3165	35	progression	progression	NN
37681	3165	36	.	.	.
37681	3166	1	The	the	DT
37681	3166	2	maximum	maximum	JJ
37681	3166	3	number	number	NN
37681	3166	4	of	of	IN
37681	3166	5	intersection	intersection	NN
37681	3166	6	points	point	NNS
37681	3166	7	of	of	IN
37681	3166	8	_	_	NNP
37681	3166	9	n	n	CC
37681	3166	10	_	_	NNP
37681	3166	11	straight	straight	JJ
37681	3166	12	lines	line	NNS
37681	3166	13	in	in	IN
37681	3166	14	the	the	DT
37681	3166	15	same	same	JJ
37681	3166	16	plane	plane	NN
37681	3166	17	is	be	VBZ
37681	3166	18	also	also	RB
37681	3166	19	_	_	NNP
37681	3166	20	n_(_n	n_(_n	NNP
37681	3166	21	_	_	NNP
37681	3166	22	-	-	HYPH
37681	3166	23	1)/2	1)/2	NNP
37681	3166	24	.	.	.
37681	3167	1	How	how	WRB
37681	3167	2	many	many	JJ
37681	3167	3	straight	straight	JJ
37681	3167	4	lines	line	NNS
37681	3167	5	are	be	VBP
37681	3167	6	in	in	IN
37681	3167	7	general	general	JJ
37681	3167	8	determined	determine	VBN
37681	3167	9	by	by	IN
37681	3167	10	_	_	NNP
37681	3167	11	n	n	CC
37681	3167	12	_	_	NNP
37681	3167	13	planes	plane	NNS
37681	3167	14	?	?	.
37681	3168	1	The	the	DT
37681	3168	2	answer	answer	NN
37681	3168	3	is	be	VBZ
37681	3168	4	the	the	DT
37681	3168	5	same	same	JJ
37681	3168	6	,	,	,
37681	3168	7	_	_	NNP
37681	3168	8	n_(_n	n_(_n	NNP
37681	3168	9	_	_	NNP
37681	3168	10	-	-	HYPH
37681	3168	11	1)/2	1)/2	NNP
37681	3168	12	.	.	.
37681	3169	1	How	how	WRB
37681	3169	2	many	many	JJ
37681	3169	3	planes	plane	NNS
37681	3169	4	are	be	VBP
37681	3169	5	in	in	IN
37681	3169	6	general	general	JJ
37681	3169	7	determined	determine	VBN
37681	3169	8	by	by	IN
37681	3169	9	_	_	NNP
37681	3169	10	n	n	CC
37681	3169	11	_	_	NNP
37681	3169	12	points	point	NNS
37681	3169	13	in	in	IN
37681	3169	14	space	space	NN
37681	3169	15	?	?	.
37681	3170	1	Here	here	RB
37681	3170	2	the	the	DT
37681	3170	3	answer	answer	NN
37681	3170	4	is	be	VBZ
37681	3170	5	1	1	CD
37681	3170	6	+	+	SYM
37681	3170	7	3	3	CD
37681	3170	8	+	+	SYM
37681	3170	9	6	6	CD
37681	3170	10	+	+	SYM
37681	3170	11	10	10	CD
37681	3170	12	+	+	SYM
37681	3170	13	...	...	NFP
37681	3170	14	+	+	SYM
37681	3170	15	(	(	-LRB-
37681	3170	16	_	_	NNP
37681	3170	17	n	n	CC
37681	3170	18	_	_	NNP
37681	3170	19	-	-	HYPH
37681	3170	20	2)(_n	2)(_n	CD
37681	3170	21	_	_	NNP
37681	3170	22	-	-	HYPH
37681	3170	23	1)/2	1)/2	CD
37681	3170	24	,	,	,
37681	3170	25	or	or	CC
37681	3170	26	_	_	NNP
37681	3170	27	n_(_n	n_(_n	NNP
37681	3170	28	_	_	NNP
37681	3170	29	-	-	HYPH
37681	3170	30	1)(_n	1)(_n	CD
37681	3170	31	_	_	NNP
37681	3170	32	-	-	HYPH
37681	3170	33	2)/(1	2)/(1	NNP
37681	3170	34	×	×	NNS
37681	3170	35	2	2	CD
37681	3170	36	×	×	CD
37681	3170	37	3	3	CD
37681	3170	38	)	)	-RRB-
37681	3170	39	.	.	.
37681	3171	1	The	the	DT
37681	3171	2	same	same	JJ
37681	3171	3	number	number	NN
37681	3171	4	of	of	IN
37681	3171	5	points	point	NNS
37681	3171	6	is	be	VBZ
37681	3171	7	determined	determine	VBN
37681	3171	8	by	by	IN
37681	3171	9	_	_	NNP
37681	3171	10	n	n	CC
37681	3171	11	_	_	NNP
37681	3171	12	planes	plane	NNS
37681	3171	13	.	.	.
37681	3172	1	THEOREM	THEOREM	NNP
37681	3172	2	.	.	.
37681	3173	1	_	_	XX
37681	3173	2	If	if	IN
37681	3173	3	two	two	CD
37681	3173	4	planes	plane	NNS
37681	3173	5	cut	cut	VBD
37681	3173	6	each	each	DT
37681	3173	7	other	other	JJ
37681	3173	8	,	,	,
37681	3173	9	their	-PRON-	PRP$
37681	3173	10	intersection	intersection	NN
37681	3173	11	is	be	VBZ
37681	3173	12	a	a	DT
37681	3173	13	straight	straight	JJ
37681	3173	14	line	line	NN
37681	3173	15	.	.	.
37681	3173	16	_	_	NNP
37681	3173	17	Among	among	IN
37681	3173	18	the	the	DT
37681	3173	19	simple	simple	JJ
37681	3173	20	illustrations	illustration	NNS
37681	3173	21	are	be	VBP
37681	3173	22	the	the	DT
37681	3173	23	back	back	JJ
37681	3173	24	edges	edge	NNS
37681	3173	25	of	of	IN
37681	3173	26	the	the	DT
37681	3173	27	pages	page	NNS
37681	3173	28	of	of	IN
37681	3173	29	a	a	DT
37681	3173	30	book	book	NN
37681	3173	31	,	,	,
37681	3173	32	the	the	DT
37681	3173	33	corners	corner	NNS
37681	3173	34	of	of	IN
37681	3173	35	the	the	DT
37681	3173	36	room	room	NN
37681	3173	37	,	,	,
37681	3173	38	and	and	CC
37681	3173	39	the	the	DT
37681	3173	40	simple	simple	JJ
37681	3173	41	test	test	NN
37681	3173	42	as	as	IN
37681	3173	43	to	to	IN
37681	3173	44	whether	whether	IN
37681	3173	45	the	the	DT
37681	3173	46	edge	edge	NN
37681	3173	47	of	of	IN
37681	3173	48	a	a	DT
37681	3173	49	card	card	NN
37681	3173	50	is	be	VBZ
37681	3173	51	straight	straight	RB
37681	3173	52	by	by	IN
37681	3173	53	testing	test	VBG
37681	3173	54	it	-PRON-	PRP
37681	3173	55	on	on	IN
37681	3173	56	a	a	DT
37681	3173	57	plane	plane	NN
37681	3173	58	.	.	.
37681	3174	1	It	-PRON-	PRP
37681	3174	2	is	be	VBZ
37681	3174	3	well	well	JJ
37681	3174	4	to	to	TO
37681	3174	5	call	call	VB
37681	3174	6	attention	attention	NN
37681	3174	7	to	to	IN
37681	3174	8	the	the	DT
37681	3174	9	fact	fact	NN
37681	3174	10	that	that	IN
37681	3174	11	if	if	IN
37681	3174	12	two	two	CD
37681	3174	13	intersecting	intersect	VBG
37681	3174	14	straight	straight	JJ
37681	3174	15	lines	line	NNS
37681	3174	16	move	move	VBP
37681	3174	17	parallel	parallel	RB
37681	3174	18	to	to	IN
37681	3174	19	their	-PRON-	PRP$
37681	3174	20	original	original	JJ
37681	3174	21	position	position	NN
37681	3174	22	,	,	,
37681	3174	23	and	and	CC
37681	3174	24	so	so	IN
37681	3174	25	that	that	IN
37681	3174	26	their	-PRON-	PRP$
37681	3174	27	intersection	intersection	NN
37681	3174	28	rests	rest	VBZ
37681	3174	29	on	on	IN
37681	3174	30	a	a	DT
37681	3174	31	straight	straight	JJ
37681	3174	32	line	line	NN
37681	3174	33	not	not	RB
37681	3174	34	in	in	IN
37681	3174	35	the	the	DT
37681	3174	36	plane	plane	NN
37681	3174	37	of	of	IN
37681	3174	38	those	those	DT
37681	3174	39	lines	line	NNS
37681	3174	40	,	,	,
37681	3174	41	the	the	DT
37681	3174	42	figure	figure	NN
37681	3174	43	generated	generate	VBN
37681	3174	44	will	will	MD
37681	3174	45	be	be	VB
37681	3174	46	that	that	DT
37681	3174	47	of	of	IN
37681	3174	48	this	this	DT
37681	3174	49	proposition	proposition	NN
37681	3174	50	.	.	.
37681	3175	1	In	in	IN
37681	3175	2	general	general	JJ
37681	3175	3	,	,	,
37681	3175	4	if	if	IN
37681	3175	5	we	-PRON-	PRP
37681	3175	6	cut	cut	VBD
37681	3175	7	through	through	IN
37681	3175	8	any	any	DT
37681	3175	9	figure	figure	NN
37681	3175	10	of	of	IN
37681	3175	11	solid	solid	JJ
37681	3175	12	geometry	geometry	NN
37681	3175	13	in	in	IN
37681	3175	14	some	some	DT
37681	3175	15	particular	particular	JJ
37681	3175	16	way	way	NN
37681	3175	17	,	,	,
37681	3175	18	we	-PRON-	PRP
37681	3175	19	are	be	VBP
37681	3175	20	liable	liable	JJ
37681	3175	21	to	to	TO
37681	3175	22	get	get	VB
37681	3175	23	the	the	DT
37681	3175	24	figure	figure	NN
37681	3175	25	of	of	IN
37681	3175	26	a	a	DT
37681	3175	27	proposition	proposition	NN
37681	3175	28	in	in	IN
37681	3175	29	plane	plane	NN
37681	3175	30	geometry	geometry	NN
37681	3175	31	,	,	,
37681	3175	32	as	as	IN
37681	3175	33	will	will	MD
37681	3175	34	frequently	frequently	RB
37681	3175	35	be	be	VB
37681	3175	36	seen	see	VBN
37681	3175	37	.	.	.
37681	3176	1	THEOREM	THEOREM	NNP
37681	3176	2	.	.	.
37681	3177	1	_	_	XX
37681	3177	2	If	if	IN
37681	3177	3	a	a	DT
37681	3177	4	straight	straight	JJ
37681	3177	5	line	line	NN
37681	3177	6	is	be	VBZ
37681	3177	7	perpendicular	perpendicular	JJ
37681	3177	8	to	to	IN
37681	3177	9	each	each	DT
37681	3177	10	of	of	IN
37681	3177	11	two	two	CD
37681	3177	12	other	other	JJ
37681	3177	13	straight	straight	JJ
37681	3177	14	lines	line	NNS
37681	3177	15	at	at	IN
37681	3177	16	their	-PRON-	PRP$
37681	3177	17	point	point	NN
37681	3177	18	of	of	IN
37681	3177	19	intersection	intersection	NN
37681	3177	20	,	,	,
37681	3177	21	it	-PRON-	PRP
37681	3177	22	is	be	VBZ
37681	3177	23	perpendicular	perpendicular	JJ
37681	3177	24	to	to	IN
37681	3177	25	the	the	DT
37681	3177	26	plane	plane	NN
37681	3177	27	of	of	IN
37681	3177	28	the	the	DT
37681	3177	29	two	two	CD
37681	3177	30	lines	line	NNS
37681	3177	31	.	.	.
37681	3177	32	_	_	XX
37681	3177	33	If	if	IN
37681	3177	34	students	student	NNS
37681	3177	35	have	have	VBP
37681	3177	36	trouble	trouble	NN
37681	3177	37	in	in	IN
37681	3177	38	visualizing	visualize	VBG
37681	3177	39	the	the	DT
37681	3177	40	figure	figure	NN
37681	3177	41	in	in	IN
37681	3177	42	three	three	CD
37681	3177	43	dimensions	dimension	NNS
37681	3177	44	,	,	,
37681	3177	45	some	some	DT
37681	3177	46	knitting	knit	VBG
37681	3177	47	needles	needle	NNS
37681	3177	48	through	through	IN
37681	3177	49	a	a	DT
37681	3177	50	piece	piece	NN
37681	3177	51	of	of	IN
37681	3177	52	cardboard	cardboard	NN
37681	3177	53	will	will	MD
37681	3177	54	make	make	VB
37681	3177	55	it	-PRON-	PRP
37681	3177	56	clear	clear	JJ
37681	3177	57	.	.	.
37681	3178	1	Teachers	teacher	NNS
37681	3178	2	should	should	MD
37681	3178	3	call	call	VB
37681	3178	4	attention	attention	NN
37681	3178	5	to	to	IN
37681	3178	6	the	the	DT
37681	3178	7	simple	simple	JJ
37681	3178	8	device	device	NN
37681	3178	9	for	for	IN
37681	3178	10	determining	determine	VBG
37681	3178	11	if	if	IN
37681	3178	12	a	a	DT
37681	3178	13	rod	rod	NN
37681	3178	14	is	be	VBZ
37681	3178	15	perpendicular	perpendicular	JJ
37681	3178	16	to	to	IN
37681	3178	17	a	a	DT
37681	3178	18	board	board	NN
37681	3178	19	(	(	-LRB-
37681	3178	20	or	or	CC
37681	3178	21	a	a	DT
37681	3178	22	pipe	pipe	NN
37681	3178	23	to	to	IN
37681	3178	24	a	a	DT
37681	3178	25	floor	floor	NN
37681	3178	26	,	,	,
37681	3178	27	ceiling	ceiling	NN
37681	3178	28	,	,	,
37681	3178	29	or	or	CC
37681	3178	30	wall	wall	NN
37681	3178	31	)	)	-RRB-
37681	3178	32	,	,	,
37681	3178	33	by	by	IN
37681	3178	34	testing	test	VBG
37681	3178	35	it	-PRON-	PRP
37681	3178	36	twice	twice	RB
37681	3178	37	,	,	,
37681	3178	38	only	only	RB
37681	3178	39	,	,	,
37681	3178	40	with	with	IN
37681	3178	41	a	a	DT
37681	3178	42	carpenter	carpenter	NN
37681	3178	43	's	's	POS
37681	3178	44	square	square	NN
37681	3178	45	.	.	.
37681	3179	1	Similarly	similarly	RB
37681	3179	2	,	,	,
37681	3179	3	it	-PRON-	PRP
37681	3179	4	may	may	MD
37681	3179	5	be	be	VB
37681	3179	6	asked	ask	VBN
37681	3179	7	of	of	IN
37681	3179	8	a	a	DT
37681	3179	9	class	class	NN
37681	3179	10	,	,	,
37681	3179	11	How	how	WRB
37681	3179	12	shall	shall	MD
37681	3179	13	we	-PRON-	PRP
37681	3179	14	test	test	VB
37681	3179	15	to	to	TO
37681	3179	16	see	see	VB
37681	3179	17	if	if	IN
37681	3179	18	the	the	DT
37681	3179	19	corner	corner	NN
37681	3179	20	(	(	-LRB-
37681	3179	21	line	line	NN
37681	3179	22	)	)	-RRB-
37681	3179	23	of	of	IN
37681	3179	24	a	a	DT
37681	3179	25	room	room	NN
37681	3179	26	is	be	VBZ
37681	3179	27	perpendicular	perpendicular	JJ
37681	3179	28	to	to	IN
37681	3179	29	the	the	DT
37681	3179	30	floor	floor	NN
37681	3179	31	,	,	,
37681	3179	32	or	or	CC
37681	3179	33	if	if	IN
37681	3179	34	the	the	DT
37681	3179	35	edge	edge	NN
37681	3179	36	of	of	IN
37681	3179	37	a	a	DT
37681	3179	38	box	box	NN
37681	3179	39	is	be	VBZ
37681	3179	40	perpendicular	perpendicular	JJ
37681	3179	41	to	to	IN
37681	3179	42	one	one	CD
37681	3179	43	of	of	IN
37681	3179	44	the	the	DT
37681	3179	45	sides	side	NNS
37681	3179	46	?	?	.
37681	3180	1	In	in	IN
37681	3180	2	some	some	DT
37681	3180	3	elementary	elementary	JJ
37681	3180	4	and	and	CC
37681	3180	5	in	in	IN
37681	3180	6	most	most	RBS
37681	3180	7	higher	high	JJR
37681	3180	8	geometries	geometry	NNS
37681	3180	9	the	the	DT
37681	3180	10	perpendicular	perpendicular	NN
37681	3180	11	is	be	VBZ
37681	3180	12	called	call	VBN
37681	3180	13	a	a	DT
37681	3180	14	_	_	NNP
37681	3180	15	normal	normal	JJ
37681	3180	16	_	_	NNP
37681	3180	17	to	to	IN
37681	3180	18	the	the	DT
37681	3180	19	plane	plane	NN
37681	3180	20	.	.	.
37681	3181	1	THEOREM	THEOREM	NNP
37681	3181	2	.	.	.
37681	3182	1	_	_	NNP
37681	3182	2	All	all	PDT
37681	3182	3	the	the	DT
37681	3182	4	perpendiculars	perpendicular	NNS
37681	3182	5	that	that	WDT
37681	3182	6	can	can	MD
37681	3182	7	be	be	VB
37681	3182	8	drawn	draw	VBN
37681	3182	9	to	to	IN
37681	3182	10	a	a	DT
37681	3182	11	straight	straight	JJ
37681	3182	12	line	line	NN
37681	3182	13	at	at	IN
37681	3182	14	a	a	DT
37681	3182	15	given	give	VBN
37681	3182	16	point	point	NN
37681	3182	17	lie	lie	NN
37681	3182	18	in	in	IN
37681	3182	19	a	a	DT
37681	3182	20	plane	plane	NN
37681	3182	21	which	which	WDT
37681	3182	22	is	be	VBZ
37681	3182	23	perpendicular	perpendicular	JJ
37681	3182	24	to	to	IN
37681	3182	25	the	the	DT
37681	3182	26	line	line	NN
37681	3182	27	at	at	IN
37681	3182	28	the	the	DT
37681	3182	29	given	give	VBN
37681	3182	30	point	point	NN
37681	3182	31	.	.	.
37681	3182	32	_	_	NNP
37681	3182	33	Thus	thus	RB
37681	3182	34	the	the	DT
37681	3182	35	hands	hand	NNS
37681	3182	36	of	of	IN
37681	3182	37	a	a	DT
37681	3182	38	clock	clock	NN
37681	3182	39	pass	pass	NN
37681	3182	40	through	through	IN
37681	3182	41	a	a	DT
37681	3182	42	plane	plane	NN
37681	3182	43	as	as	IN
37681	3182	44	the	the	DT
37681	3182	45	hands	hand	NNS
37681	3182	46	revolve	revolve	VBP
37681	3182	47	,	,	,
37681	3182	48	if	if	IN
37681	3182	49	they	-PRON-	PRP
37681	3182	50	are	be	VBP
37681	3182	51	,	,	,
37681	3182	52	as	as	IN
37681	3182	53	is	be	VBZ
37681	3182	54	usual	usual	JJ
37681	3182	55	,	,	,
37681	3182	56	perpendicular	perpendicular	JJ
37681	3182	57	to	to	IN
37681	3182	58	the	the	DT
37681	3182	59	axis	axis	NN
37681	3182	60	;	;	:
37681	3182	61	and	and	CC
37681	3182	62	the	the	DT
37681	3182	63	same	same	JJ
37681	3182	64	is	be	VBZ
37681	3182	65	true	true	JJ
37681	3182	66	of	of	IN
37681	3182	67	the	the	DT
37681	3182	68	spokes	spoke	NNS
37681	3182	69	of	of	IN
37681	3182	70	a	a	DT
37681	3182	71	wheel	wheel	NN
37681	3182	72	,	,	,
37681	3182	73	and	and	CC
37681	3182	74	of	of	IN
37681	3182	75	a	a	DT
37681	3182	76	string	string	NN
37681	3182	77	with	with	IN
37681	3182	78	a	a	DT
37681	3182	79	stone	stone	NN
37681	3182	80	attached	attach	VBN
37681	3182	81	,	,	,
37681	3182	82	swung	swing	VBN
37681	3182	83	as	as	RB
37681	3182	84	rapidly	rapidly	RB
37681	3182	85	as	as	IN
37681	3182	86	possible	possible	JJ
37681	3182	87	about	about	IN
37681	3182	88	a	a	DT
37681	3182	89	boy	boy	NN
37681	3182	90	's	's	POS
37681	3182	91	arm	arm	NN
37681	3182	92	as	as	IN
37681	3182	93	an	an	DT
37681	3182	94	axis	axis	NN
37681	3182	95	.	.	.
37681	3183	1	A	a	DT
37681	3183	2	clock	clock	NN
37681	3183	3	pendulum	pendulum	NN
37681	3183	4	too	too	RB
37681	3183	5	swings	swing	NNS
37681	3183	6	in	in	IN
37681	3183	7	a	a	DT
37681	3183	8	plane	plane	NN
37681	3183	9	,	,	,
37681	3183	10	as	as	IN
37681	3183	11	does	do	VBZ
37681	3183	12	the	the	DT
37681	3183	13	lever	lever	NN
37681	3183	14	in	in	IN
37681	3183	15	a	a	DT
37681	3183	16	pair	pair	NN
37681	3183	17	of	of	IN
37681	3183	18	scales	scale	NNS
37681	3183	19	.	.	.
37681	3184	1	THEOREM	THEOREM	NNP
37681	3184	2	.	.	.
37681	3185	1	_	_	NNP
37681	3185	2	Through	through	IN
37681	3185	3	a	a	DT
37681	3185	4	given	give	VBN
37681	3185	5	point	point	NN
37681	3185	6	within	within	IN
37681	3185	7	or	or	CC
37681	3185	8	without	without	IN
37681	3185	9	a	a	DT
37681	3185	10	plane	plane	NN
37681	3185	11	there	there	EX
37681	3185	12	can	can	MD
37681	3185	13	be	be	VB
37681	3185	14	one	one	CD
37681	3185	15	perpendicular	perpendicular	JJ
37681	3185	16	to	to	IN
37681	3185	17	a	a	DT
37681	3185	18	given	give	VBN
37681	3185	19	plane	plane	NN
37681	3185	20	,	,	,
37681	3185	21	and	and	CC
37681	3185	22	only	only	RB
37681	3185	23	one	one	CD
37681	3185	24	.	.	.
37681	3185	25	_	_	NNP
37681	3185	26	This	this	DT
37681	3185	27	theorem	theorem	NN
37681	3185	28	is	be	VBZ
37681	3185	29	better	well	RBR
37681	3185	30	stated	state	VBN
37681	3185	31	to	to	IN
37681	3185	32	a	a	DT
37681	3185	33	class	class	NN
37681	3185	34	as	as	IN
37681	3185	35	two	two	CD
37681	3185	36	theorems	theorem	NNS
37681	3185	37	.	.	.
37681	3186	1	Thus	thus	RB
37681	3186	2	a	a	DT
37681	3186	3	plumb	plumb	JJ
37681	3186	4	line	line	NN
37681	3186	5	hanging	hang	VBG
37681	3186	6	from	from	IN
37681	3186	7	a	a	DT
37681	3186	8	point	point	NN
37681	3186	9	in	in	IN
37681	3186	10	the	the	DT
37681	3186	11	ceiling	ceiling	NN
37681	3186	12	,	,	,
37681	3186	13	without	without	IN
37681	3186	14	swinging	swinge	VBG
37681	3186	15	,	,	,
37681	3186	16	determines	determine	VBZ
37681	3186	17	one	one	CD
37681	3186	18	definite	definite	JJ
37681	3186	19	point	point	NN
37681	3186	20	in	in	IN
37681	3186	21	the	the	DT
37681	3186	22	floor	floor	NN
37681	3186	23	;	;	:
37681	3186	24	and	and	CC
37681	3186	25	,	,	,
37681	3186	26	conversely	conversely	RB
37681	3186	27	,	,	,
37681	3186	28	if	if	IN
37681	3186	29	it	-PRON-	PRP
37681	3186	30	touches	touch	VBZ
37681	3186	31	a	a	DT
37681	3186	32	given	give	VBN
37681	3186	33	point	point	NN
37681	3186	34	in	in	IN
37681	3186	35	the	the	DT
37681	3186	36	floor	floor	NN
37681	3186	37	,	,	,
37681	3186	38	it	-PRON-	PRP
37681	3186	39	must	must	MD
37681	3186	40	hang	hang	VB
37681	3186	41	from	from	IN
37681	3186	42	one	one	CD
37681	3186	43	definite	definite	JJ
37681	3186	44	point	point	NN
37681	3186	45	in	in	IN
37681	3186	46	the	the	DT
37681	3186	47	ceiling	ceiling	NN
37681	3186	48	.	.	.
37681	3187	1	It	-PRON-	PRP
37681	3187	2	should	should	MD
37681	3187	3	be	be	VB
37681	3187	4	noticed	notice	VBN
37681	3187	5	that	that	IN
37681	3187	6	if	if	IN
37681	3187	7	we	-PRON-	PRP
37681	3187	8	cut	cut	VBD
37681	3187	9	through	through	IN
37681	3187	10	this	this	DT
37681	3187	11	figure	figure	NN
37681	3187	12	,	,	,
37681	3187	13	on	on	IN
37681	3187	14	the	the	DT
37681	3187	15	perpendicular	perpendicular	JJ
37681	3187	16	line	line	NN
37681	3187	17	,	,	,
37681	3187	18	we	-PRON-	PRP
37681	3187	19	shall	shall	MD
37681	3187	20	have	have	VB
37681	3187	21	the	the	DT
37681	3187	22	figure	figure	NN
37681	3187	23	of	of	IN
37681	3187	24	the	the	DT
37681	3187	25	corresponding	corresponding	JJ
37681	3187	26	proposition	proposition	NN
37681	3187	27	in	in	IN
37681	3187	28	plane	plane	NN
37681	3187	29	geometry	geometry	NN
37681	3187	30	,	,	,
37681	3187	31	namely	namely	RB
37681	3187	32	,	,	,
37681	3187	33	that	that	IN
37681	3187	34	there	there	EX
37681	3187	35	can	can	MD
37681	3187	36	be	be	VB
37681	3187	37	,	,	,
37681	3187	38	under	under	IN
37681	3187	39	similar	similar	JJ
37681	3187	40	circumstances	circumstance	NNS
37681	3187	41	,	,	,
37681	3187	42	only	only	RB
37681	3187	43	one	one	CD
37681	3187	44	perpendicular	perpendicular	NN
37681	3187	45	to	to	IN
37681	3187	46	a	a	DT
37681	3187	47	line	line	NN
37681	3187	48	.	.	.
37681	3188	1	THEOREM	THEOREM	NNP
37681	3188	2	.	.	.
37681	3189	1	_	_	NNP
37681	3189	2	Oblique	Oblique	NNP
37681	3189	3	lines	line	NNS
37681	3189	4	drawn	draw	VBN
37681	3189	5	from	from	IN
37681	3189	6	a	a	DT
37681	3189	7	point	point	NN
37681	3189	8	to	to	IN
37681	3189	9	a	a	DT
37681	3189	10	plane	plane	NN
37681	3189	11	,	,	,
37681	3189	12	meeting	meet	VBG
37681	3189	13	the	the	DT
37681	3189	14	plane	plane	NN
37681	3189	15	at	at	IN
37681	3189	16	equal	equal	JJ
37681	3189	17	distances	distance	NNS
37681	3189	18	from	from	IN
37681	3189	19	the	the	DT
37681	3189	20	foot	foot	NN
37681	3189	21	of	of	IN
37681	3189	22	the	the	DT
37681	3189	23	perpendicular	perpendicular	NN
37681	3189	24	,	,	,
37681	3189	25	are	be	VBP
37681	3189	26	equal	equal	JJ
37681	3189	27	,	,	,
37681	3189	28	etc	etc	FW
37681	3189	29	.	.	.
37681	3189	30	_	_	NNP
37681	3189	31	There	there	EX
37681	3189	32	is	be	VBZ
37681	3189	33	no	no	DT
37681	3189	34	objection	objection	NN
37681	3189	35	to	to	IN
37681	3189	36	speaking	speak	VBG
37681	3189	37	of	of	IN
37681	3189	38	a	a	DT
37681	3189	39	right	right	JJ
37681	3189	40	circular	circular	JJ
37681	3189	41	cone	cone	NN
37681	3189	42	in	in	IN
37681	3189	43	connection	connection	NN
37681	3189	44	with	with	IN
37681	3189	45	this	this	DT
37681	3189	46	proposition	proposition	NN
37681	3189	47	,	,	,
37681	3189	48	and	and	CC
37681	3189	49	saying	say	VBG
37681	3189	50	that	that	IN
37681	3189	51	the	the	DT
37681	3189	52	slant	slant	NN
37681	3189	53	height	height	NN
37681	3189	54	is	be	VBZ
37681	3189	55	thus	thus	RB
37681	3189	56	proved	prove	VBN
37681	3189	57	to	to	TO
37681	3189	58	be	be	VB
37681	3189	59	constant	constant	JJ
37681	3189	60	.	.	.
37681	3190	1	The	the	DT
37681	3190	2	usual	usual	JJ
37681	3190	3	corollary	corollary	NN
37681	3190	4	,	,	,
37681	3190	5	that	that	IN
37681	3190	6	if	if	IN
37681	3190	7	the	the	DT
37681	3190	8	obliques	oblique	NNS
37681	3190	9	are	be	VBP
37681	3190	10	equal	equal	JJ
37681	3190	11	they	-PRON-	PRP
37681	3190	12	meet	meet	VBP
37681	3190	13	the	the	DT
37681	3190	14	plane	plane	NN
37681	3190	15	in	in	IN
37681	3190	16	a	a	DT
37681	3190	17	circle	circle	NN
37681	3190	18	,	,	,
37681	3190	19	offers	offer	VBZ
37681	3190	20	a	a	DT
37681	3190	21	new	new	JJ
37681	3190	22	plan	plan	NN
37681	3190	23	of	of	IN
37681	3190	24	drawing	draw	VBG
37681	3190	25	a	a	DT
37681	3190	26	circle	circle	NN
37681	3190	27	.	.	.
37681	3191	1	A	a	DT
37681	3191	2	plumb	plumb	JJ
37681	3191	3	line	line	NN
37681	3191	4	that	that	WDT
37681	3191	5	is	be	VBZ
37681	3191	6	a	a	DT
37681	3191	7	little	little	JJ
37681	3191	8	too	too	RB
37681	3191	9	long	long	JJ
37681	3191	10	to	to	TO
37681	3191	11	reach	reach	VB
37681	3191	12	the	the	DT
37681	3191	13	floor	floor	NN
37681	3191	14	will	will	MD
37681	3191	15	,	,	,
37681	3191	16	if	if	IN
37681	3191	17	swung	swing	VBN
37681	3191	18	so	so	IN
37681	3191	19	as	as	IN
37681	3191	20	just	just	RB
37681	3191	21	to	to	TO
37681	3191	22	touch	touch	VB
37681	3191	23	the	the	DT
37681	3191	24	floor	floor	NN
37681	3191	25	,	,	,
37681	3191	26	describe	describe	VB
37681	3191	27	a	a	DT
37681	3191	28	circle	circle	NN
37681	3191	29	.	.	.
37681	3192	1	A	a	DT
37681	3192	2	10-foot	10-foot	CD
37681	3192	3	pole	pole	NN
37681	3192	4	standing	standing	NN
37681	3192	5	in	in	IN
37681	3192	6	a	a	DT
37681	3192	7	9-foot	9-foot	CD
37681	3192	8	room	room	NN
37681	3192	9	will	will	MD
37681	3192	10	,	,	,
37681	3192	11	if	if	IN
37681	3192	12	it	-PRON-	PRP
37681	3192	13	moves	move	VBZ
37681	3192	14	so	so	IN
37681	3192	15	as	as	IN
37681	3192	16	to	to	TO
37681	3192	17	touch	touch	VB
37681	3192	18	constantly	constantly	RB
37681	3192	19	a	a	DT
37681	3192	20	fixed	fix	VBN
37681	3192	21	point	point	NN
37681	3192	22	on	on	IN
37681	3192	23	either	either	CC
37681	3192	24	the	the	DT
37681	3192	25	floor	floor	NN
37681	3192	26	or	or	CC
37681	3192	27	the	the	DT
37681	3192	28	ceiling	ceiling	NN
37681	3192	29	,	,	,
37681	3192	30	describe	describe	VB
37681	3192	31	a	a	DT
37681	3192	32	circle	circle	NN
37681	3192	33	on	on	IN
37681	3192	34	the	the	DT
37681	3192	35	ceiling	ceiling	NN
37681	3192	36	or	or	CC
37681	3192	37	floor	floor	NN
37681	3192	38	respectively	respectively	RB
37681	3192	39	.	.	.
37681	3193	1	One	one	CD
37681	3193	2	of	of	IN
37681	3193	3	the	the	DT
37681	3193	4	corollaries	corollary	NNS
37681	3193	5	states	state	VBZ
37681	3193	6	that	that	IN
37681	3193	7	the	the	DT
37681	3193	8	locus	locus	NN
37681	3193	9	of	of	IN
37681	3193	10	points	point	NNS
37681	3193	11	in	in	IN
37681	3193	12	space	space	NN
37681	3193	13	equidistant	equidistant	NN
37681	3193	14	from	from	IN
37681	3193	15	the	the	DT
37681	3193	16	extremities	extremity	NNS
37681	3193	17	of	of	IN
37681	3193	18	a	a	DT
37681	3193	19	straight	straight	JJ
37681	3193	20	line	line	NN
37681	3193	21	is	be	VBZ
37681	3193	22	the	the	DT
37681	3193	23	plane	plane	NN
37681	3193	24	perpendicular	perpendicular	JJ
37681	3193	25	to	to	IN
37681	3193	26	this	this	DT
37681	3193	27	line	line	NN
37681	3193	28	at	at	IN
37681	3193	29	its	-PRON-	PRP$
37681	3193	30	middle	middle	JJ
37681	3193	31	point	point	NN
37681	3193	32	.	.	.
37681	3194	1	This	this	DT
37681	3194	2	has	have	VBZ
37681	3194	3	been	be	VBN
37681	3194	4	taken	take	VBN
37681	3194	5	by	by	IN
37681	3194	6	some	some	DT
37681	3194	7	writers	writer	NNS
37681	3194	8	as	as	IN
37681	3194	9	the	the	DT
37681	3194	10	definition	definition	NN
37681	3194	11	of	of	IN
37681	3194	12	a	a	DT
37681	3194	13	plane	plane	NN
37681	3194	14	,	,	,
37681	3194	15	but	but	CC
37681	3194	16	it	-PRON-	PRP
37681	3194	17	is	be	VBZ
37681	3194	18	too	too	RB
37681	3194	19	abstract	abstract	JJ
37681	3194	20	to	to	TO
37681	3194	21	be	be	VB
37681	3194	22	usable	usable	JJ
37681	3194	23	.	.	.
37681	3195	1	It	-PRON-	PRP
37681	3195	2	is	be	VBZ
37681	3195	3	advisable	advisable	JJ
37681	3195	4	to	to	TO
37681	3195	5	cut	cut	VB
37681	3195	6	through	through	IN
37681	3195	7	the	the	DT
37681	3195	8	figure	figure	NN
37681	3195	9	along	along	IN
37681	3195	10	the	the	DT
37681	3195	11	given	give	VBN
37681	3195	12	straight	straight	JJ
37681	3195	13	line	line	NN
37681	3195	14	,	,	,
37681	3195	15	and	and	CC
37681	3195	16	see	see	VB
37681	3195	17	that	that	IN
37681	3195	18	we	-PRON-	PRP
37681	3195	19	come	come	VBP
37681	3195	20	back	back	RB
37681	3195	21	to	to	IN
37681	3195	22	the	the	DT
37681	3195	23	corresponding	corresponding	JJ
37681	3195	24	proposition	proposition	NN
37681	3195	25	in	in	IN
37681	3195	26	plane	plane	NN
37681	3195	27	geometry	geometry	NN
37681	3195	28	.	.	.
37681	3196	1	A	a	DT
37681	3196	2	good	good	JJ
37681	3196	3	many	many	JJ
37681	3196	4	ships	ship	NNS
37681	3196	5	have	have	VBP
37681	3196	6	been	be	VBN
37681	3196	7	saved	save	VBN
37681	3196	8	from	from	IN
37681	3196	9	being	be	VBG
37681	3196	10	wrecked	wreck	VBN
37681	3196	11	by	by	IN
37681	3196	12	the	the	DT
37681	3196	13	principle	principle	NN
37681	3196	14	involved	involve	VBN
37681	3196	15	in	in	IN
37681	3196	16	this	this	DT
37681	3196	17	proposition	proposition	NN
37681	3196	18	.	.	.
37681	3197	1	[	[	-LRB-
37681	3197	2	Illustration	illustration	NN
37681	3197	3	]	]	-RRB-
37681	3197	4	If	if	IN
37681	3197	5	a	a	DT
37681	3197	6	dangerous	dangerous	JJ
37681	3197	7	shoal	shoal	NN
37681	3197	8	_	_	NNP
37681	3197	9	A	A	NNP
37681	3197	10	_	_	NNP
37681	3197	11	is	be	VBZ
37681	3197	12	near	near	IN
37681	3197	13	a	a	DT
37681	3197	14	headland	headland	NN
37681	3197	15	_	_	NNP
37681	3197	16	H	H	NNP
37681	3197	17	_	_	NNP
37681	3197	18	,	,	,
37681	3197	19	the	the	DT
37681	3197	20	angle	angle	NN
37681	3197	21	_	_	NNP
37681	3197	22	HAX	HAX	NNP
37681	3197	23	_	_	NNP
37681	3197	24	is	be	VBZ
37681	3197	25	measured	measure	VBN
37681	3197	26	and	and	CC
37681	3197	27	is	be	VBZ
37681	3197	28	put	put	VBN
37681	3197	29	down	down	RP
37681	3197	30	upon	upon	IN
37681	3197	31	the	the	DT
37681	3197	32	charts	chart	NNS
37681	3197	33	as	as	IN
37681	3197	34	the	the	DT
37681	3197	35	"	"	``
37681	3197	36	vertical	vertical	JJ
37681	3197	37	danger	danger	NN
37681	3197	38	angle	angle	NN
37681	3197	39	.	.	.
37681	3197	40	"	"	''
37681	3198	1	Ships	ship	NNS
37681	3198	2	coming	come	VBG
37681	3198	3	near	near	IN
37681	3198	4	the	the	DT
37681	3198	5	headland	headland	NN
37681	3198	6	are	be	VBP
37681	3198	7	careful	careful	JJ
37681	3198	8	to	to	TO
37681	3198	9	keep	keep	VB
37681	3198	10	far	far	RB
37681	3198	11	enough	enough	RB
37681	3198	12	away	away	RB
37681	3198	13	,	,	,
37681	3198	14	say	say	VBP
37681	3198	15	at	at	IN
37681	3198	16	_	_	NNP
37681	3198	17	S	S	NNP
37681	3198	18	_	_	NNP
37681	3198	19	,	,	,
37681	3198	20	so	so	IN
37681	3198	21	that	that	IN
37681	3198	22	the	the	DT
37681	3198	23	angle	angle	NN
37681	3198	24	_	_	NNP
37681	3198	25	HSX	HSX	NNP
37681	3198	26	_	_	NNP
37681	3198	27	shall	shall	MD
37681	3198	28	be	be	VB
37681	3198	29	less	less	JJR
37681	3198	30	than	than	IN
37681	3198	31	this	this	DT
37681	3198	32	danger	danger	NN
37681	3198	33	angle	angle	NN
37681	3198	34	.	.	.
37681	3199	1	They	-PRON-	PRP
37681	3199	2	are	be	VBP
37681	3199	3	then	then	RB
37681	3199	4	sure	sure	JJ
37681	3199	5	that	that	IN
37681	3199	6	they	-PRON-	PRP
37681	3199	7	will	will	MD
37681	3199	8	avoid	avoid	VB
37681	3199	9	the	the	DT
37681	3199	10	dangerous	dangerous	JJ
37681	3199	11	shoal	shoal	NN
37681	3199	12	.	.	.
37681	3200	1	Related	related	JJ
37681	3200	2	to	to	IN
37681	3200	3	this	this	DT
37681	3200	4	proposition	proposition	NN
37681	3200	5	is	be	VBZ
37681	3200	6	the	the	DT
37681	3200	7	problem	problem	NN
37681	3200	8	of	of	IN
37681	3200	9	supporting	support	VBG
37681	3200	10	a	a	DT
37681	3200	11	tall	tall	JJ
37681	3200	12	iron	iron	NN
37681	3200	13	smokestack	smokestack	NN
37681	3200	14	by	by	IN
37681	3200	15	wire	wire	NN
37681	3200	16	stays	stay	NNS
37681	3200	17	.	.	.
37681	3201	1	Evidently	evidently	RB
37681	3201	2	three	three	CD
37681	3201	3	stays	stay	NNS
37681	3201	4	are	be	VBP
37681	3201	5	needed	need	VBN
37681	3201	6	,	,	,
37681	3201	7	and	and	CC
37681	3201	8	they	-PRON-	PRP
37681	3201	9	are	be	VBP
37681	3201	10	preferably	preferably	RB
37681	3201	11	placed	place	VBN
37681	3201	12	at	at	IN
37681	3201	13	the	the	DT
37681	3201	14	vertices	vertex	NNS
37681	3201	15	of	of	IN
37681	3201	16	an	an	DT
37681	3201	17	equilateral	equilateral	JJ
37681	3201	18	triangle	triangle	NN
37681	3201	19	,	,	,
37681	3201	20	the	the	DT
37681	3201	21	smokestack	smokestack	NN
37681	3201	22	being	be	VBG
37681	3201	23	in	in	IN
37681	3201	24	the	the	DT
37681	3201	25	center	center	NN
37681	3201	26	.	.	.
37681	3202	1	The	the	DT
37681	3202	2	practical	practical	JJ
37681	3202	3	problem	problem	NN
37681	3202	4	may	may	MD
37681	3202	5	be	be	VB
37681	3202	6	given	give	VBN
37681	3202	7	of	of	IN
37681	3202	8	locating	locate	VBG
37681	3202	9	the	the	DT
37681	3202	10	vertices	vertex	NNS
37681	3202	11	of	of	IN
37681	3202	12	the	the	DT
37681	3202	13	triangle	triangle	NN
37681	3202	14	and	and	CC
37681	3202	15	of	of	IN
37681	3202	16	finding	find	VBG
37681	3202	17	the	the	DT
37681	3202	18	length	length	NN
37681	3202	19	of	of	IN
37681	3202	20	each	each	DT
37681	3202	21	stay	stay	NN
37681	3202	22	.	.	.
37681	3203	1	THEOREM	THEOREM	NNP
37681	3203	2	.	.	.
37681	3204	1	_	_	NNP
37681	3204	2	Two	two	CD
37681	3204	3	straight	straight	JJ
37681	3204	4	lines	line	NNS
37681	3204	5	perpendicular	perpendicular	JJ
37681	3204	6	to	to	IN
37681	3204	7	the	the	DT
37681	3204	8	same	same	JJ
37681	3204	9	plane	plane	NN
37681	3204	10	are	be	VBP
37681	3204	11	parallel	parallel	JJ
37681	3204	12	.	.	.
37681	3204	13	_	_	NNP
37681	3204	14	Here	here	RB
37681	3204	15	again	again	RB
37681	3204	16	we	-PRON-	PRP
37681	3204	17	may	may	MD
37681	3204	18	cut	cut	VB
37681	3204	19	through	through	IN
37681	3204	20	the	the	DT
37681	3204	21	figure	figure	NN
37681	3204	22	by	by	IN
37681	3204	23	the	the	DT
37681	3204	24	plane	plane	NN
37681	3204	25	of	of	IN
37681	3204	26	the	the	DT
37681	3204	27	two	two	CD
37681	3204	28	parallels	parallel	NNS
37681	3204	29	,	,	,
37681	3204	30	and	and	CC
37681	3204	31	we	-PRON-	PRP
37681	3204	32	get	get	VBP
37681	3204	33	the	the	DT
37681	3204	34	figure	figure	NN
37681	3204	35	of	of	IN
37681	3204	36	plane	plane	NN
37681	3204	37	geometry	geometry	NN
37681	3204	38	relating	relate	VBG
37681	3204	39	to	to	IN
37681	3204	40	lines	line	NNS
37681	3204	41	that	that	WDT
37681	3204	42	are	be	VBP
37681	3204	43	perpendicular	perpendicular	JJ
37681	3204	44	to	to	IN
37681	3204	45	the	the	DT
37681	3204	46	same	same	JJ
37681	3204	47	line	line	NN
37681	3204	48	.	.	.
37681	3205	1	The	the	DT
37681	3205	2	proposition	proposition	NN
37681	3205	3	shows	show	VBZ
37681	3205	4	that	that	IN
37681	3205	5	the	the	DT
37681	3205	6	opposite	opposite	JJ
37681	3205	7	corners	corner	NNS
37681	3205	8	of	of	IN
37681	3205	9	a	a	DT
37681	3205	10	room	room	NN
37681	3205	11	are	be	VBP
37681	3205	12	parallel	parallel	JJ
37681	3205	13	,	,	,
37681	3205	14	and	and	CC
37681	3205	15	that	that	IN
37681	3205	16	therefore	therefore	RB
37681	3205	17	they	-PRON-	PRP
37681	3205	18	lie	lie	VBP
37681	3205	19	in	in	IN
37681	3205	20	the	the	DT
37681	3205	21	same	same	JJ
37681	3205	22	plane	plane	NN
37681	3205	23	,	,	,
37681	3205	24	or	or	CC
37681	3205	25	are	be	VBP
37681	3205	26	_	_	NNP
37681	3205	27	coplanar	coplanar	JJ
37681	3205	28	_	_	NNP
37681	3205	29	,	,	,
37681	3205	30	as	as	IN
37681	3205	31	is	be	VBZ
37681	3205	32	said	say	VBN
37681	3205	33	in	in	IN
37681	3205	34	higher	high	JJR
37681	3205	35	geometry	geometry	NN
37681	3205	36	.	.	.
37681	3206	1	It	-PRON-	PRP
37681	3206	2	is	be	VBZ
37681	3206	3	interesting	interesting	JJ
37681	3206	4	to	to	IN
37681	3206	5	a	a	DT
37681	3206	6	class	class	NN
37681	3206	7	to	to	TO
37681	3206	8	have	have	VB
37681	3206	9	attention	attention	NN
37681	3206	10	called	call	VBN
37681	3206	11	to	to	IN
37681	3206	12	the	the	DT
37681	3206	13	corollary	corollary	NN
37681	3206	14	that	that	IN
37681	3206	15	if	if	IN
37681	3206	16	two	two	CD
37681	3206	17	straight	straight	JJ
37681	3206	18	lines	line	NNS
37681	3206	19	are	be	VBP
37681	3206	20	parallel	parallel	JJ
37681	3206	21	to	to	IN
37681	3206	22	a	a	DT
37681	3206	23	third	third	JJ
37681	3206	24	straight	straight	JJ
37681	3206	25	line	line	NN
37681	3206	26	,	,	,
37681	3206	27	they	-PRON-	PRP
37681	3206	28	are	be	VBP
37681	3206	29	parallel	parallel	JJ
37681	3206	30	to	to	IN
37681	3206	31	each	each	DT
37681	3206	32	other	other	JJ
37681	3206	33	;	;	:
37681	3206	34	and	and	CC
37681	3206	35	to	to	TO
37681	3206	36	have	have	VB
37681	3206	37	the	the	DT
37681	3206	38	question	question	NN
37681	3206	39	asked	ask	VBN
37681	3206	40	why	why	WRB
37681	3206	41	it	-PRON-	PRP
37681	3206	42	is	be	VBZ
37681	3206	43	necessary	necessary	JJ
37681	3206	44	to	to	TO
37681	3206	45	prove	prove	VB
37681	3206	46	this	this	DT
37681	3206	47	when	when	WRB
37681	3206	48	the	the	DT
37681	3206	49	same	same	JJ
37681	3206	50	thing	thing	NN
37681	3206	51	was	be	VBD
37681	3206	52	proved	prove	VBN
37681	3206	53	in	in	IN
37681	3206	54	plane	plane	NN
37681	3206	55	geometry	geometry	NN
37681	3206	56	.	.	.
37681	3207	1	In	in	IN
37681	3207	2	case	case	NN
37681	3207	3	the	the	DT
37681	3207	4	reason	reason	NN
37681	3207	5	is	be	VBZ
37681	3207	6	not	not	RB
37681	3207	7	clear	clear	JJ
37681	3207	8	,	,	,
37681	3207	9	let	let	VB
37681	3207	10	some	some	DT
37681	3207	11	student	student	NN
37681	3207	12	try	try	VB
37681	3207	13	to	to	TO
37681	3207	14	apply	apply	VB
37681	3207	15	the	the	DT
37681	3207	16	proof	proof	NN
37681	3207	17	used	use	VBN
37681	3207	18	in	in	IN
37681	3207	19	plane	plane	NN
37681	3207	20	geometry	geometry	NN
37681	3207	21	.	.	.
37681	3208	1	THEOREM	THEOREM	NNP
37681	3208	2	.	.	.
37681	3209	1	_	_	NNP
37681	3209	2	Two	Two	NNP
37681	3209	3	planes	plane	NNS
37681	3209	4	perpendicular	perpendicular	JJ
37681	3209	5	to	to	IN
37681	3209	6	the	the	DT
37681	3209	7	same	same	JJ
37681	3209	8	straight	straight	JJ
37681	3209	9	line	line	NN
37681	3209	10	are	be	VBP
37681	3209	11	parallel	parallel	JJ
37681	3209	12	.	.	.
37681	3209	13	_	_	NNP
37681	3209	14	Besides	besides	IN
37681	3209	15	calling	call	VBG
37681	3209	16	attention	attention	NN
37681	3209	17	to	to	IN
37681	3209	18	the	the	DT
37681	3209	19	corresponding	corresponding	JJ
37681	3209	20	proposition	proposition	NN
37681	3209	21	of	of	IN
37681	3209	22	plane	plane	NN
37681	3209	23	geometry	geometry	NN
37681	3209	24	,	,	,
37681	3209	25	it	-PRON-	PRP
37681	3209	26	is	be	VBZ
37681	3209	27	well	well	RB
37681	3209	28	now	now	RB
37681	3209	29	to	to	TO
37681	3209	30	speak	speak	VB
37681	3209	31	of	of	IN
37681	3209	32	the	the	DT
37681	3209	33	fact	fact	NN
37681	3209	34	that	that	IN
37681	3209	35	in	in	IN
37681	3209	36	propositions	proposition	NNS
37681	3209	37	involving	involve	VBG
37681	3209	38	planes	plane	NNS
37681	3209	39	and	and	CC
37681	3209	40	lines	line	NNS
37681	3209	41	we	-PRON-	PRP
37681	3209	42	may	may	MD
37681	3209	43	often	often	RB
37681	3209	44	interchange	interchange	VB
37681	3209	45	these	these	DT
37681	3209	46	words	word	NNS
37681	3209	47	.	.	.
37681	3210	1	For	for	IN
37681	3210	2	example	example	NN
37681	3210	3	,	,	,
37681	3210	4	using	use	VBG
37681	3210	5	"	"	``
37681	3210	6	line	line	NN
37681	3210	7	"	"	''
37681	3210	8	for	for	IN
37681	3210	9	"	"	``
37681	3210	10	straight	straight	JJ
37681	3210	11	line	line	NN
37681	3210	12	,	,	,
37681	3210	13	"	"	''
37681	3210	14	for	for	IN
37681	3210	15	brevity	brevity	NN
37681	3210	16	,	,	,
37681	3210	17	we	-PRON-	PRP
37681	3210	18	have	have	VBP
37681	3210	19	:	:	:
37681	3210	20	One	one	CD
37681	3210	21	_	_	NNP
37681	3210	22	line	line	NN
37681	3210	23	_	_	NNP
37681	3210	24	does	do	VBZ
37681	3210	25	not	not	RB
37681	3210	26	determine	determine	VB
37681	3210	27	One	one	CD
37681	3210	28	_	_	NNP
37681	3210	29	plane	plane	NN
37681	3210	30	_	_	NNP
37681	3210	31	does	do	VBZ
37681	3210	32	not	not	RB
37681	3210	33	determine	determine	VB
37681	3210	34	a	a	DT
37681	3210	35	_	_	NNP
37681	3210	36	plane	plane	NN
37681	3210	37	_	_	NNP
37681	3210	38	.	.	.
37681	3211	1	a	a	DT
37681	3211	2	_	_	NNP
37681	3211	3	line	line	NN
37681	3211	4	_	_	NNP
37681	3211	5	.	.	.
37681	3212	1	Two	two	CD
37681	3212	2	intersecting	intersect	VBG
37681	3212	3	_	_	NNP
37681	3212	4	lines	line	NNS
37681	3212	5	_	_	NNP
37681	3212	6	Two	Two	NNP
37681	3212	7	intersecting	intersect	VBG
37681	3212	8	_	_	NNP
37681	3212	9	planes	plane	NNS
37681	3212	10	_	_	NNP
37681	3212	11	determine	determine	NN
37681	3212	12	determine	determine	VBP
37681	3212	13	a	a	DT
37681	3212	14	_	_	NNP
37681	3212	15	plane	plane	NN
37681	3212	16	_	_	NNP
37681	3212	17	.	.	.
37681	3213	1	a	a	DT
37681	3213	2	_	_	NNP
37681	3213	3	line	line	NN
37681	3213	4	_	_	NNP
37681	3213	5	.	.	.
37681	3214	1	Two	two	CD
37681	3214	2	_	_	NNP
37681	3214	3	lines	line	NNS
37681	3214	4	_	_	NNP
37681	3214	5	perpendicular	perpendicular	JJ
37681	3214	6	to	to	IN
37681	3214	7	Two	two	CD
37681	3214	8	_	_	NNP
37681	3214	9	planes	plane	NNS
37681	3214	10	_	_	NNP
37681	3214	11	perpendicular	perpendicular	NN
37681	3214	12	to	to	IN
37681	3214	13	a	a	DT
37681	3214	14	_	_	NNP
37681	3214	15	plane	plane	NN
37681	3214	16	_	_	NNP
37681	3214	17	are	be	VBP
37681	3214	18	parallel	parallel	JJ
37681	3214	19	.	.	.
37681	3215	1	a	a	DT
37681	3215	2	_	_	NNP
37681	3215	3	line	line	NN
37681	3215	4	_	_	NNP
37681	3215	5	are	be	VBP
37681	3215	6	parallel	parallel	JJ
37681	3215	7	.	.	.
37681	3216	1	If	if	IN
37681	3216	2	one	one	CD
37681	3216	3	of	of	IN
37681	3216	4	two	two	CD
37681	3216	5	parallel	parallel	NN
37681	3216	6	_	_	NNP
37681	3216	7	lines	line	NNS
37681	3216	8	_	_	XX
37681	3216	9	If	if	IN
37681	3216	10	one	one	CD
37681	3216	11	of	of	IN
37681	3216	12	two	two	CD
37681	3216	13	parallel	parallel	NN
37681	3216	14	_	_	NNP
37681	3216	15	planes	plane	NNS
37681	3216	16	_	_	NNP
37681	3216	17	is	be	VBZ
37681	3216	18	perpendicular	perpendicular	JJ
37681	3216	19	to	to	IN
37681	3216	20	a	a	DT
37681	3216	21	_	_	NNP
37681	3216	22	plane	plane	NN
37681	3216	23	_	_	NNP
37681	3216	24	,	,	,
37681	3216	25	the	the	DT
37681	3216	26	is	be	VBZ
37681	3216	27	perpendicular	perpendicular	JJ
37681	3216	28	to	to	IN
37681	3216	29	a	a	DT
37681	3216	30	_	_	NNP
37681	3216	31	line	line	NN
37681	3216	32	_	_	NNP
37681	3216	33	,	,	,
37681	3216	34	the	the	DT
37681	3216	35	other	other	JJ
37681	3216	36	is	be	VBZ
37681	3216	37	also	also	RB
37681	3216	38	perpendicular	perpendicular	JJ
37681	3216	39	to	to	IN
37681	3216	40	other	other	JJ
37681	3216	41	is	be	VBZ
37681	3216	42	also	also	RB
37681	3216	43	perpendicular	perpendicular	JJ
37681	3216	44	to	to	IN
37681	3216	45	the	the	DT
37681	3216	46	_	_	NNP
37681	3216	47	plane	plane	NN
37681	3216	48	_	_	NNP
37681	3216	49	.	.	.
37681	3217	1	the	the	DT
37681	3217	2	_	_	NNP
37681	3217	3	line	line	NN
37681	3217	4	_	_	NNP
37681	3217	5	.	.	.
37681	3218	1	If	if	IN
37681	3218	2	two	two	CD
37681	3218	3	_	_	NNP
37681	3218	4	lines	line	NNS
37681	3218	5	_	_	NNP
37681	3218	6	are	be	VBP
37681	3218	7	parallel	parallel	JJ
37681	3218	8	,	,	,
37681	3218	9	every	every	DT
37681	3218	10	If	if	IN
37681	3218	11	two	two	CD
37681	3218	12	_	_	NNP
37681	3218	13	planes	plane	NNS
37681	3218	14	_	_	NNP
37681	3218	15	are	be	VBP
37681	3218	16	parallel	parallel	JJ
37681	3218	17	,	,	,
37681	3218	18	_	_	NNP
37681	3218	19	plane	plane	NN
37681	3218	20	_	_	NNP
37681	3218	21	containing	contain	VBG
37681	3218	22	one	one	CD
37681	3218	23	of	of	IN
37681	3218	24	the	the	DT
37681	3218	25	every	every	DT
37681	3218	26	_	_	NNP
37681	3218	27	line	line	NN
37681	3218	28	_	_	NNP
37681	3218	29	in	in	IN
37681	3218	30	one	one	CD
37681	3218	31	of	of	IN
37681	3218	32	the	the	DT
37681	3218	33	_	_	NNP
37681	3218	34	planes	plane	NNS
37681	3218	35	_	_	NNP
37681	3218	36	_	_	NNP
37681	3218	37	lines	line	NNS
37681	3218	38	_	_	NNP
37681	3218	39	is	be	VBZ
37681	3218	40	parallel	parallel	NN
37681	3218	41	to	to	IN
37681	3218	42	the	the	DT
37681	3218	43	other	other	JJ
37681	3218	44	is	be	VBZ
37681	3218	45	parallel	parallel	JJ
37681	3218	46	to	to	IN
37681	3218	47	the	the	DT
37681	3218	48	other	other	JJ
37681	3218	49	_	_	NNP
37681	3218	50	plane	plane	NN
37681	3218	51	_	_	NNP
37681	3218	52	.	.	.
37681	3219	1	_	_	NNP
37681	3219	2	line	line	NN
37681	3219	3	_	_	NNP
37681	3219	4	.	.	.
37681	3220	1	THEOREM	THEOREM	NNP
37681	3220	2	.	.	.
37681	3221	1	_	_	NNP
37681	3221	2	The	the	DT
37681	3221	3	intersections	intersection	NNS
37681	3221	4	of	of	IN
37681	3221	5	two	two	CD
37681	3221	6	parallel	parallel	JJ
37681	3221	7	planes	plane	NNS
37681	3221	8	by	by	IN
37681	3221	9	a	a	DT
37681	3221	10	third	third	JJ
37681	3221	11	plane	plane	NN
37681	3221	12	are	be	VBP
37681	3221	13	parallel	parallel	JJ
37681	3221	14	lines	line	NNS
37681	3221	15	.	.	.
37681	3221	16	_	_	NNP
37681	3221	17	Thus	thus	RB
37681	3221	18	one	one	CD
37681	3221	19	of	of	IN
37681	3221	20	the	the	DT
37681	3221	21	edges	edge	NNS
37681	3221	22	of	of	IN
37681	3221	23	a	a	DT
37681	3221	24	box	box	NN
37681	3221	25	is	be	VBZ
37681	3221	26	parallel	parallel	JJ
37681	3221	27	to	to	IN
37681	3221	28	the	the	DT
37681	3221	29	next	next	JJ
37681	3221	30	succeeding	succeed	VBG
37681	3221	31	edge	edge	NN
37681	3221	32	if	if	IN
37681	3221	33	the	the	DT
37681	3221	34	opposite	opposite	JJ
37681	3221	35	faces	face	NNS
37681	3221	36	are	be	VBP
37681	3221	37	parallel	parallel	JJ
37681	3221	38	,	,	,
37681	3221	39	and	and	CC
37681	3221	40	in	in	IN
37681	3221	41	sawing	saw	VBG
37681	3221	42	diagonally	diagonally	RB
37681	3221	43	through	through	IN
37681	3221	44	an	an	DT
37681	3221	45	ordinary	ordinary	JJ
37681	3221	46	board	board	NN
37681	3221	47	(	(	-LRB-
37681	3221	48	with	with	IN
37681	3221	49	rectangular	rectangular	NNP
37681	3221	50	cross	cross	NNP
37681	3221	51	section	section	NN
37681	3221	52	)	)	-RRB-
37681	3221	53	the	the	DT
37681	3221	54	section	section	NN
37681	3221	55	is	be	VBZ
37681	3221	56	a	a	DT
37681	3221	57	parallelogram	parallelogram	NN
37681	3221	58	.	.	.
37681	3222	1	THEOREM	THEOREM	NNP
37681	3222	2	.	.	.
37681	3223	1	_	_	NNP
37681	3223	2	A	a	DT
37681	3223	3	straight	straight	JJ
37681	3223	4	line	line	NN
37681	3223	5	perpendicular	perpendicular	JJ
37681	3223	6	to	to	IN
37681	3223	7	one	one	CD
37681	3223	8	of	of	IN
37681	3223	9	two	two	CD
37681	3223	10	parallel	parallel	JJ
37681	3223	11	planes	plane	NNS
37681	3223	12	is	be	VBZ
37681	3223	13	perpendicular	perpendicular	JJ
37681	3223	14	to	to	IN
37681	3223	15	the	the	DT
37681	3223	16	other	other	JJ
37681	3223	17	also	also	RB
37681	3223	18	.	.	.
37681	3223	19	_	_	NNP
37681	3223	20	Notice	Notice	NNP
37681	3223	21	(	(	-LRB-
37681	3223	22	1	1	LS
37681	3223	23	)	)	-RRB-
37681	3223	24	the	the	DT
37681	3223	25	corresponding	corresponding	JJ
37681	3223	26	proposition	proposition	NN
37681	3223	27	in	in	IN
37681	3223	28	plane	plane	NN
37681	3223	29	geometry	geometry	NN
37681	3223	30	;	;	:
37681	3223	31	(	(	-LRB-
37681	3223	32	2	2	LS
37681	3223	33	)	)	-RRB-
37681	3223	34	the	the	DT
37681	3223	35	proposition	proposition	NN
37681	3223	36	that	that	WDT
37681	3223	37	results	result	VBZ
37681	3223	38	from	from	IN
37681	3223	39	interchanging	interchange	VBG
37681	3223	40	"	"	``
37681	3223	41	plane	plane	NN
37681	3223	42	"	"	''
37681	3223	43	and	and	CC
37681	3223	44	(	(	-LRB-
37681	3223	45	straight	straight	JJ
37681	3223	46	)	)	-RRB-
37681	3223	47	"	"	``
37681	3223	48	line	line	NN
37681	3223	49	.	.	.
37681	3223	50	"	"	''
37681	3224	1	THEOREM	THEOREM	NNP
37681	3224	2	.	.	.
37681	3225	1	_	_	XX
37681	3225	2	If	if	IN
37681	3225	3	two	two	CD
37681	3225	4	intersecting	intersect	VBG
37681	3225	5	straight	straight	JJ
37681	3225	6	lines	line	NNS
37681	3225	7	are	be	VBP
37681	3225	8	each	each	DT
37681	3225	9	parallel	parallel	JJ
37681	3225	10	to	to	IN
37681	3225	11	a	a	DT
37681	3225	12	plane	plane	NN
37681	3225	13	,	,	,
37681	3225	14	the	the	DT
37681	3225	15	plane	plane	NN
37681	3225	16	of	of	IN
37681	3225	17	these	these	DT
37681	3225	18	lines	line	NNS
37681	3225	19	is	be	VBZ
37681	3225	20	parallel	parallel	JJ
37681	3225	21	to	to	IN
37681	3225	22	that	that	DT
37681	3225	23	plane	plane	NN
37681	3225	24	.	.	.
37681	3225	25	_	_	NNP
37681	3225	26	Interchanging	Interchanging	NNP
37681	3225	27	"	"	``
37681	3225	28	plane	plane	NN
37681	3225	29	"	"	''
37681	3225	30	and	and	CC
37681	3225	31	(	(	-LRB-
37681	3225	32	straight	straight	JJ
37681	3225	33	)	)	-RRB-
37681	3225	34	"	"	``
37681	3225	35	line	line	NN
37681	3225	36	,	,	,
37681	3225	37	"	"	''
37681	3225	38	we	-PRON-	PRP
37681	3225	39	have	have	VBP
37681	3225	40	:	:	:
37681	3225	41	If	if	IN
37681	3225	42	two	two	CD
37681	3225	43	intersecting	intersect	VBG
37681	3225	44	_	_	NNP
37681	3225	45	planes	plane	NNS
37681	3225	46	_	_	NNP
37681	3225	47	are	be	VBP
37681	3225	48	each	each	DT
37681	3225	49	parallel	parallel	JJ
37681	3225	50	to	to	IN
37681	3225	51	a	a	DT
37681	3225	52	_	_	NNP
37681	3225	53	line	line	NN
37681	3225	54	_	_	NNP
37681	3225	55	,	,	,
37681	3225	56	the	the	DT
37681	3225	57	_	_	NNP
37681	3225	58	line	line	NN
37681	3225	59	_	_	NNP
37681	3225	60	of	of	IN
37681	3225	61	(	(	-LRB-
37681	3225	62	intersection	intersection	NN
37681	3225	63	of	of	IN
37681	3225	64	)	)	-RRB-
37681	3225	65	these	these	DT
37681	3225	66	_	_	NNP
37681	3225	67	planes	plane	NNS
37681	3225	68	_	_	NNP
37681	3225	69	is	be	VBZ
37681	3225	70	parallel	parallel	JJ
37681	3225	71	to	to	IN
37681	3225	72	that	that	DT
37681	3225	73	_	_	NNP
37681	3225	74	line	line	NN
37681	3225	75	_	_	NNP
37681	3225	76	.	.	.
37681	3226	1	Is	be	VBZ
37681	3226	2	this	this	DT
37681	3226	3	true	true	JJ
37681	3226	4	?	?	.
37681	3227	1	THEOREM	THEOREM	NNP
37681	3227	2	.	.	.
37681	3228	1	_	_	XX
37681	3228	2	If	if	IN
37681	3228	3	two	two	CD
37681	3228	4	angles	angle	NNS
37681	3228	5	not	not	RB
37681	3228	6	in	in	IN
37681	3228	7	the	the	DT
37681	3228	8	same	same	JJ
37681	3228	9	plane	plane	NN
37681	3228	10	have	have	VBP
37681	3228	11	their	-PRON-	PRP$
37681	3228	12	sides	side	NNS
37681	3228	13	respectively	respectively	RB
37681	3228	14	parallel	parallel	JJ
37681	3228	15	and	and	CC
37681	3228	16	lying	lie	VBG
37681	3228	17	on	on	IN
37681	3228	18	the	the	DT
37681	3228	19	same	same	JJ
37681	3228	20	side	side	NN
37681	3228	21	of	of	IN
37681	3228	22	the	the	DT
37681	3228	23	straight	straight	JJ
37681	3228	24	line	line	NN
37681	3228	25	joining	join	VBG
37681	3228	26	their	-PRON-	PRP$
37681	3228	27	vertices	vertex	NNS
37681	3228	28	,	,	,
37681	3228	29	they	-PRON-	PRP
37681	3228	30	are	be	VBP
37681	3228	31	equal	equal	JJ
37681	3228	32	and	and	CC
37681	3228	33	their	-PRON-	PRP$
37681	3228	34	planes	plane	NNS
37681	3228	35	are	be	VBP
37681	3228	36	parallel	parallel	JJ
37681	3228	37	.	.	.
37681	3228	38	_	_	NNP
37681	3228	39	Questions	Questions	NNPS
37681	3228	40	like	like	IN
37681	3228	41	the	the	DT
37681	3228	42	following	follow	VBG
37681	3228	43	may	may	MD
37681	3228	44	be	be	VB
37681	3228	45	asked	ask	VBN
37681	3228	46	in	in	IN
37681	3228	47	connection	connection	NN
37681	3228	48	with	with	IN
37681	3228	49	the	the	DT
37681	3228	50	proposition	proposition	NN
37681	3228	51	:	:	:
37681	3228	52	What	what	WP
37681	3228	53	is	be	VBZ
37681	3228	54	the	the	DT
37681	3228	55	corresponding	corresponding	JJ
37681	3228	56	proposition	proposition	NN
37681	3228	57	in	in	IN
37681	3228	58	plane	plane	NN
37681	3228	59	geometry	geometry	NN
37681	3228	60	?	?	.
37681	3229	1	Why	why	WRB
37681	3229	2	do	do	VBP
37681	3229	3	we	-PRON-	PRP
37681	3229	4	need	need	VB
37681	3229	5	another	another	DT
37681	3229	6	proof	proof	NN
37681	3229	7	here	here	RB
37681	3229	8	?	?	.
37681	3230	1	Try	try	VB
37681	3230	2	the	the	DT
37681	3230	3	plane	plane	NN
37681	3230	4	-	-	HYPH
37681	3230	5	geometry	geometry	NN
37681	3230	6	proof	proof	NN
37681	3230	7	here	here	RB
37681	3230	8	.	.	.
37681	3231	1	THEOREM	THEOREM	NNP
37681	3231	2	.	.	.
37681	3232	1	_	_	XX
37681	3232	2	If	if	IN
37681	3232	3	two	two	CD
37681	3232	4	straight	straight	JJ
37681	3232	5	lines	line	NNS
37681	3232	6	are	be	VBP
37681	3232	7	cut	cut	VBN
37681	3232	8	by	by	IN
37681	3232	9	three	three	CD
37681	3232	10	parallel	parallel	JJ
37681	3232	11	planes	plane	NNS
37681	3232	12	,	,	,
37681	3232	13	their	-PRON-	PRP$
37681	3232	14	corresponding	corresponding	JJ
37681	3232	15	segments	segment	NNS
37681	3232	16	are	be	VBP
37681	3232	17	proportional	proportional	JJ
37681	3232	18	.	.	.
37681	3232	19	_	_	NNP
37681	3232	20	Here	here	RB
37681	3232	21	,	,	,
37681	3232	22	again	again	RB
37681	3232	23	,	,	,
37681	3232	24	it	-PRON-	PRP
37681	3232	25	is	be	VBZ
37681	3232	26	desirable	desirable	JJ
37681	3232	27	to	to	TO
37681	3232	28	ask	ask	VB
37681	3232	29	for	for	IN
37681	3232	30	the	the	DT
37681	3232	31	corresponding	corresponding	JJ
37681	3232	32	proposition	proposition	NN
37681	3232	33	of	of	IN
37681	3232	34	plane	plane	NN
37681	3232	35	geometry	geometry	NN
37681	3232	36	,	,	,
37681	3232	37	and	and	CC
37681	3232	38	to	to	TO
37681	3232	39	ask	ask	VB
37681	3232	40	why	why	WRB
37681	3232	41	the	the	DT
37681	3232	42	proof	proof	NN
37681	3232	43	of	of	IN
37681	3232	44	that	that	DT
37681	3232	45	proposition	proposition	NN
37681	3232	46	will	will	MD
37681	3232	47	not	not	RB
37681	3232	48	suffice	suffice	VB
37681	3232	49	for	for	IN
37681	3232	50	this	this	DT
37681	3232	51	one	one	NN
37681	3232	52	.	.	.
37681	3233	1	The	the	DT
37681	3233	2	usual	usual	JJ
37681	3233	3	figure	figure	NN
37681	3233	4	may	may	MD
37681	3233	5	be	be	VB
37681	3233	6	varied	vary	VBN
37681	3233	7	in	in	IN
37681	3233	8	an	an	DT
37681	3233	9	interesting	interesting	JJ
37681	3233	10	manner	manner	NN
37681	3233	11	by	by	IN
37681	3233	12	having	have	VBG
37681	3233	13	the	the	DT
37681	3233	14	two	two	CD
37681	3233	15	lines	line	NNS
37681	3233	16	meet	meet	VBP
37681	3233	17	on	on	IN
37681	3233	18	one	one	CD
37681	3233	19	of	of	IN
37681	3233	20	the	the	DT
37681	3233	21	planes	plane	NNS
37681	3233	22	,	,	,
37681	3233	23	or	or	CC
37681	3233	24	outside	outside	IN
37681	3233	25	the	the	DT
37681	3233	26	planes	plane	NNS
37681	3233	27	,	,	,
37681	3233	28	or	or	CC
37681	3233	29	by	by	IN
37681	3233	30	having	have	VBG
37681	3233	31	them	-PRON-	PRP
37681	3233	32	parallel	parallel	JJ
37681	3233	33	,	,	,
37681	3233	34	in	in	IN
37681	3233	35	which	which	WDT
37681	3233	36	cases	case	NNS
37681	3233	37	the	the	DT
37681	3233	38	proof	proof	NN
37681	3233	39	of	of	IN
37681	3233	40	the	the	DT
37681	3233	41	plane	plane	NN
37681	3233	42	-	-	HYPH
37681	3233	43	geometry	geometry	NN
37681	3233	44	proposition	proposition	NN
37681	3233	45	holds	hold	VBZ
37681	3233	46	here	here	RB
37681	3233	47	.	.	.
37681	3234	1	This	this	DT
37681	3234	2	proposition	proposition	NN
37681	3234	3	is	be	VBZ
37681	3234	4	not	not	RB
37681	3234	5	of	of	IN
37681	3234	6	great	great	JJ
37681	3234	7	importance	importance	NN
37681	3234	8	from	from	IN
37681	3234	9	the	the	DT
37681	3234	10	practical	practical	JJ
37681	3234	11	standpoint	standpoint	NN
37681	3234	12	,	,	,
37681	3234	13	and	and	CC
37681	3234	14	it	-PRON-	PRP
37681	3234	15	is	be	VBZ
37681	3234	16	omitted	omit	VBN
37681	3234	17	from	from	IN
37681	3234	18	some	some	DT
37681	3234	19	of	of	IN
37681	3234	20	the	the	DT
37681	3234	21	standard	standard	JJ
37681	3234	22	syllabi	syllabi	NN
37681	3234	23	at	at	IN
37681	3234	24	present	present	NN
37681	3234	25	,	,	,
37681	3234	26	although	although	IN
37681	3234	27	included	include	VBN
37681	3234	28	in	in	IN
37681	3234	29	certain	certain	JJ
37681	3234	30	others	other	NNS
37681	3234	31	.	.	.
37681	3235	1	It	-PRON-	PRP
37681	3235	2	is	be	VBZ
37681	3235	3	easy	easy	JJ
37681	3235	4	,	,	,
37681	3235	5	however	however	RB
37681	3235	6	,	,	,
37681	3235	7	to	to	TO
37681	3235	8	frame	frame	VB
37681	3235	9	some	some	DT
37681	3235	10	interesting	interesting	JJ
37681	3235	11	questions	question	NNS
37681	3235	12	depending	depend	VBG
37681	3235	13	upon	upon	IN
37681	3235	14	it	-PRON-	PRP
37681	3235	15	for	for	IN
37681	3235	16	their	-PRON-	PRP$
37681	3235	17	answers	answer	NNS
37681	3235	18	,	,	,
37681	3235	19	such	such	JJ
37681	3235	20	as	as	IN
37681	3235	21	the	the	DT
37681	3235	22	following	following	NN
37681	3235	23	:	:	:
37681	3235	24	In	in	IN
37681	3235	25	a	a	DT
37681	3235	26	gymnasium	gymnasium	NN
37681	3235	27	swimming	swimming	NN
37681	3235	28	tank	tank	NN
37681	3235	29	the	the	DT
37681	3235	30	water	water	NN
37681	3235	31	is	be	VBZ
37681	3235	32	4	4	CD
37681	3235	33	feet	foot	NNS
37681	3235	34	deep	deep	JJ
37681	3235	35	and	and	CC
37681	3235	36	the	the	DT
37681	3235	37	ceiling	ceiling	NN
37681	3235	38	is	be	VBZ
37681	3235	39	8	8	CD
37681	3235	40	feet	foot	NNS
37681	3235	41	above	above	IN
37681	3235	42	the	the	DT
37681	3235	43	surface	surface	NN
37681	3235	44	of	of	IN
37681	3235	45	the	the	DT
37681	3235	46	water	water	NN
37681	3235	47	.	.	.
37681	3236	1	A	a	DT
37681	3236	2	pole	pole	NN
37681	3236	3	15	15	CD
37681	3236	4	feet	foot	NNS
37681	3236	5	long	long	JJ
37681	3236	6	touches	touch	VBZ
37681	3236	7	the	the	DT
37681	3236	8	ceiling	ceiling	NN
37681	3236	9	and	and	CC
37681	3236	10	the	the	DT
37681	3236	11	bottom	bottom	NN
37681	3236	12	of	of	IN
37681	3236	13	the	the	DT
37681	3236	14	tank	tank	NN
37681	3236	15	.	.	.
37681	3237	1	Required	require	VBN
37681	3237	2	to	to	TO
37681	3237	3	know	know	VB
37681	3237	4	what	what	WP
37681	3237	5	length	length	NN
37681	3237	6	of	of	IN
37681	3237	7	the	the	DT
37681	3237	8	pole	pole	NN
37681	3237	9	is	be	VBZ
37681	3237	10	in	in	IN
37681	3237	11	the	the	DT
37681	3237	12	water	water	NN
37681	3237	13	.	.	.
37681	3238	1	At	at	IN
37681	3238	2	this	this	DT
37681	3238	3	point	point	NN
37681	3238	4	in	in	IN
37681	3238	5	Book	Book	NNP
37681	3238	6	VI	VI	NNP
37681	3238	7	it	-PRON-	PRP
37681	3238	8	is	be	VBZ
37681	3238	9	customary	customary	JJ
37681	3238	10	to	to	TO
37681	3238	11	introduce	introduce	VB
37681	3238	12	the	the	DT
37681	3238	13	dihedral	dihedral	JJ
37681	3238	14	angle	angle	NN
37681	3238	15	.	.	.
37681	3239	1	The	the	DT
37681	3239	2	word	word	NN
37681	3239	3	"	"	``
37681	3239	4	dihedral	dihedral	NN
37681	3239	5	"	"	''
37681	3239	6	is	be	VBZ
37681	3239	7	from	from	IN
37681	3239	8	the	the	DT
37681	3239	9	Greek	Greek	NNP
37681	3239	10	,	,	,
37681	3239	11	_	_	NNP
37681	3239	12	di-	di-	XX
37681	3239	13	_	_	NNP
37681	3239	14	meaning	mean	VBG
37681	3239	15	"	"	``
37681	3239	16	two	two	CD
37681	3239	17	,	,	,
37681	3239	18	"	"	''
37681	3239	19	and	and	CC
37681	3239	20	_	_	NNP
37681	3239	21	hedra	hedra	NNP
37681	3239	22	_	_	NNP
37681	3239	23	meaning	mean	VBG
37681	3239	24	"	"	``
37681	3239	25	seat	seat	NN
37681	3239	26	.	.	.
37681	3239	27	"	"	''
37681	3240	1	We	-PRON-	PRP
37681	3240	2	have	have	VBP
37681	3240	3	the	the	DT
37681	3240	4	root	root	NN
37681	3240	5	_	_	NNP
37681	3240	6	hedra	hedra	NNP
37681	3240	7	_	_	NNP
37681	3240	8	also	also	RB
37681	3240	9	in	in	IN
37681	3240	10	"	"	``
37681	3240	11	trihedral	trihedral	JJ
37681	3240	12	"	"	''
37681	3240	13	(	(	-LRB-
37681	3240	14	three	three	CD
37681	3240	15	-	-	HYPH
37681	3240	16	seated	seated	JJ
37681	3240	17	)	)	-RRB-
37681	3240	18	,	,	,
37681	3240	19	"	"	``
37681	3240	20	polyhedral	polyhedral	JJ
37681	3240	21	"	"	''
37681	3240	22	(	(	-LRB-
37681	3240	23	many	many	JJ
37681	3240	24	-	-	HYPH
37681	3240	25	seated	seated	JJ
37681	3240	26	)	)	-RRB-
37681	3240	27	,	,	,
37681	3240	28	and	and	CC
37681	3240	29	"	"	``
37681	3240	30	cathedral	cathedral	JJ
37681	3240	31	"	"	''
37681	3240	32	(	(	-LRB-
37681	3240	33	a	a	DT
37681	3240	34	church	church	NN
37681	3240	35	having	have	VBG
37681	3240	36	a	a	DT
37681	3240	37	bishop	bishop	NN
37681	3240	38	's	's	POS
37681	3240	39	seat	seat	NN
37681	3240	40	)	)	-RRB-
37681	3240	41	.	.	.
37681	3241	1	The	the	DT
37681	3241	2	word	word	NN
37681	3241	3	is	be	VBZ
37681	3241	4	also	also	RB
37681	3241	5	,	,	,
37681	3241	6	but	but	CC
37681	3241	7	less	less	RBR
37681	3241	8	properly	properly	RB
37681	3241	9	,	,	,
37681	3241	10	spelled	spell	VBN
37681	3241	11	without	without	IN
37681	3241	12	the	the	DT
37681	3241	13	_	_	NNP
37681	3241	14	h	h	NNP
37681	3241	15	_	_	NNP
37681	3241	16	,	,	,
37681	3241	17	"	"	``
37681	3241	18	diedral	diedral	JJ
37681	3241	19	,	,	,
37681	3241	20	"	"	''
37681	3241	21	a	a	DT
37681	3241	22	spelling	spelling	NN
37681	3241	23	not	not	RB
37681	3241	24	favored	favor	VBN
37681	3241	25	by	by	IN
37681	3241	26	modern	modern	JJ
37681	3241	27	usage	usage	NN
37681	3241	28	.	.	.
37681	3242	1	It	-PRON-	PRP
37681	3242	2	is	be	VBZ
37681	3242	3	not	not	RB
37681	3242	4	necessary	necessary	JJ
37681	3242	5	to	to	TO
37681	3242	6	dwell	dwell	VB
37681	3242	7	at	at	IN
37681	3242	8	length	length	NN
37681	3242	9	upon	upon	IN
37681	3242	10	the	the	DT
37681	3242	11	dihedral	dihedral	JJ
37681	3242	12	angle	angle	NN
37681	3242	13	,	,	,
37681	3242	14	except	except	IN
37681	3242	15	to	to	TO
37681	3242	16	show	show	VB
37681	3242	17	the	the	DT
37681	3242	18	analogy	analogy	NN
37681	3242	19	between	between	IN
37681	3242	20	it	-PRON-	PRP
37681	3242	21	and	and	CC
37681	3242	22	the	the	DT
37681	3242	23	plane	plane	NN
37681	3242	24	angle	angle	NN
37681	3242	25	.	.	.
37681	3243	1	A	a	DT
37681	3243	2	few	few	JJ
37681	3243	3	illustrations	illustration	NNS
37681	3243	4	,	,	,
37681	3243	5	as	as	IN
37681	3243	6	of	of	IN
37681	3243	7	an	an	DT
37681	3243	8	open	open	JJ
37681	3243	9	book	book	NN
37681	3243	10	,	,	,
37681	3243	11	the	the	DT
37681	3243	12	wall	wall	NN
37681	3243	13	and	and	CC
37681	3243	14	floor	floor	NN
37681	3243	15	of	of	IN
37681	3243	16	a	a	DT
37681	3243	17	room	room	NN
37681	3243	18	,	,	,
37681	3243	19	and	and	CC
37681	3243	20	a	a	DT
37681	3243	21	swinging	swinge	VBG
37681	3243	22	door	door	NN
37681	3243	23	,	,	,
37681	3243	24	serve	serve	VB
37681	3243	25	to	to	TO
37681	3243	26	make	make	VB
37681	3243	27	the	the	DT
37681	3243	28	concept	concept	NN
37681	3243	29	clear	clear	JJ
37681	3243	30	,	,	,
37681	3243	31	while	while	IN
37681	3243	32	a	a	DT
37681	3243	33	plane	plane	NN
37681	3243	34	at	at	IN
37681	3243	35	right	right	JJ
37681	3243	36	angles	angle	NNS
37681	3243	37	to	to	IN
37681	3243	38	the	the	DT
37681	3243	39	edge	edge	NN
37681	3243	40	shows	show	VBZ
37681	3243	41	the	the	DT
37681	3243	42	measuring	measure	VBG
37681	3243	43	plane	plane	NN
37681	3243	44	angle	angle	NN
37681	3243	45	.	.	.
37681	3244	1	So	so	RB
37681	3244	2	manifest	manifest	NN
37681	3244	3	is	be	VBZ
37681	3244	4	this	this	DT
37681	3244	5	relationship	relationship	NN
37681	3244	6	between	between	IN
37681	3244	7	the	the	DT
37681	3244	8	dihedral	dihedral	JJ
37681	3244	9	angle	angle	NN
37681	3244	10	and	and	CC
37681	3244	11	its	-PRON-	PRP$
37681	3244	12	measuring	measure	VBG
37681	3244	13	plane	plane	NN
37681	3244	14	angle	angle	NN
37681	3244	15	that	that	WDT
37681	3244	16	some	some	DT
37681	3244	17	teachers	teacher	NNS
37681	3244	18	omit	omit	VBP
37681	3244	19	the	the	DT
37681	3244	20	proposition	proposition	NN
37681	3244	21	that	that	IN
37681	3244	22	two	two	CD
37681	3244	23	dihedral	dihedral	JJ
37681	3244	24	angles	angle	NNS
37681	3244	25	have	have	VBP
37681	3244	26	the	the	DT
37681	3244	27	same	same	JJ
37681	3244	28	ratio	ratio	NN
37681	3244	29	as	as	IN
37681	3244	30	their	-PRON-	PRP$
37681	3244	31	plane	plane	NN
37681	3244	32	angles	angle	NNS
37681	3244	33	.	.	.
37681	3245	1	THEOREM	THEOREM	NNP
37681	3245	2	.	.	.
37681	3246	1	_	_	XX
37681	3246	2	If	if	IN
37681	3246	3	two	two	CD
37681	3246	4	planes	plane	NNS
37681	3246	5	are	be	VBP
37681	3246	6	perpendicular	perpendicular	JJ
37681	3246	7	to	to	IN
37681	3246	8	each	each	DT
37681	3246	9	other	other	JJ
37681	3246	10	,	,	,
37681	3246	11	a	a	DT
37681	3246	12	straight	straight	JJ
37681	3246	13	line	line	NN
37681	3246	14	drawn	draw	VBN
37681	3246	15	in	in	IN
37681	3246	16	one	one	CD
37681	3246	17	of	of	IN
37681	3246	18	them	-PRON-	PRP
37681	3246	19	perpendicular	perpendicular	VBP
37681	3246	20	to	to	IN
37681	3246	21	their	-PRON-	PRP$
37681	3246	22	intersection	intersection	NN
37681	3246	23	is	be	VBZ
37681	3246	24	perpendicular	perpendicular	JJ
37681	3246	25	to	to	IN
37681	3246	26	the	the	DT
37681	3246	27	other	other	JJ
37681	3246	28	.	.	.
37681	3246	29	_	_	NNP
37681	3246	30	This	this	DT
37681	3246	31	and	and	CC
37681	3246	32	the	the	DT
37681	3246	33	related	related	JJ
37681	3246	34	propositions	proposition	NNS
37681	3246	35	allow	allow	VBP
37681	3246	36	of	of	IN
37681	3246	37	numerous	numerous	JJ
37681	3246	38	illustrations	illustration	NNS
37681	3246	39	taken	take	VBN
37681	3246	40	from	from	IN
37681	3246	41	the	the	DT
37681	3246	42	schoolroom	schoolroom	NN
37681	3246	43	,	,	,
37681	3246	44	as	as	IN
37681	3246	45	of	of	IN
37681	3246	46	door	door	NN
37681	3246	47	edges	edge	NNS
37681	3246	48	being	be	VBG
37681	3246	49	perpendicular	perpendicular	JJ
37681	3246	50	to	to	IN
37681	3246	51	the	the	DT
37681	3246	52	floor	floor	NN
37681	3246	53	.	.	.
37681	3247	1	The	the	DT
37681	3247	2	pretended	pretended	JJ
37681	3247	3	applications	application	NNS
37681	3247	4	of	of	IN
37681	3247	5	these	these	DT
37681	3247	6	propositions	proposition	NNS
37681	3247	7	are	be	VBP
37681	3247	8	usually	usually	RB
37681	3247	9	fictitious	fictitious	JJ
37681	3247	10	,	,	,
37681	3247	11	and	and	CC
37681	3247	12	the	the	DT
37681	3247	13	propositions	proposition	NNS
37681	3247	14	are	be	VBP
37681	3247	15	of	of	IN
37681	3247	16	value	value	NN
37681	3247	17	chiefly	chiefly	RB
37681	3247	18	for	for	IN
37681	3247	19	their	-PRON-	PRP$
37681	3247	20	own	own	JJ
37681	3247	21	interest	interest	NN
37681	3247	22	and	and	CC
37681	3247	23	because	because	IN
37681	3247	24	they	-PRON-	PRP
37681	3247	25	are	be	VBP
37681	3247	26	needed	need	VBN
37681	3247	27	in	in	IN
37681	3247	28	subsequent	subsequent	JJ
37681	3247	29	proofs	proof	NNS
37681	3247	30	.	.	.
37681	3248	1	THEOREM	THEOREM	NNP
37681	3248	2	.	.	.
37681	3249	1	_	_	NNP
37681	3249	2	The	the	DT
37681	3249	3	locus	locus	NN
37681	3249	4	of	of	IN
37681	3249	5	a	a	DT
37681	3249	6	point	point	NN
37681	3249	7	equidistant	equidistant	NN
37681	3249	8	from	from	IN
37681	3249	9	the	the	DT
37681	3249	10	faces	face	NNS
37681	3249	11	of	of	IN
37681	3249	12	a	a	DT
37681	3249	13	dihedral	dihedral	JJ
37681	3249	14	angle	angle	NN
37681	3249	15	is	be	VBZ
37681	3249	16	the	the	DT
37681	3249	17	plane	plane	NN
37681	3249	18	bisecting	bisect	VBG
37681	3249	19	the	the	DT
37681	3249	20	angle	angle	NN
37681	3249	21	.	.	.
37681	3249	22	_	_	NNP
37681	3249	23	By	by	IN
37681	3249	24	changing	change	VBG
37681	3249	25	"	"	``
37681	3249	26	plane	plane	NN
37681	3249	27	"	"	''
37681	3249	28	to	to	TO
37681	3249	29	"	"	``
37681	3249	30	line	line	NN
37681	3249	31	,	,	,
37681	3249	32	"	"	''
37681	3249	33	and	and	CC
37681	3249	34	by	by	IN
37681	3249	35	making	make	VBG
37681	3249	36	other	other	JJ
37681	3249	37	obvious	obvious	JJ
37681	3249	38	changes	change	NNS
37681	3249	39	to	to	TO
37681	3249	40	correspond	correspond	VB
37681	3249	41	,	,	,
37681	3249	42	this	this	DT
37681	3249	43	reduces	reduce	VBZ
37681	3249	44	to	to	IN
37681	3249	45	the	the	DT
37681	3249	46	analogous	analogous	JJ
37681	3249	47	proposition	proposition	NN
37681	3249	48	of	of	IN
37681	3249	49	plane	plane	NN
37681	3249	50	geometry	geometry	NN
37681	3249	51	.	.	.
37681	3250	1	The	the	DT
37681	3250	2	figure	figure	NN
37681	3250	3	formed	form	VBN
37681	3250	4	by	by	IN
37681	3250	5	the	the	DT
37681	3250	6	plane	plane	NN
37681	3250	7	perpendicular	perpendicular	JJ
37681	3250	8	to	to	IN
37681	3250	9	the	the	DT
37681	3250	10	edge	edge	NN
37681	3250	11	is	be	VBZ
37681	3250	12	also	also	RB
37681	3250	13	the	the	DT
37681	3250	14	figure	figure	NN
37681	3250	15	of	of	IN
37681	3250	16	that	that	DT
37681	3250	17	analogous	analogous	JJ
37681	3250	18	proposition	proposition	NN
37681	3250	19	.	.	.
37681	3251	1	This	this	DT
37681	3251	2	at	at	IN
37681	3251	3	once	once	RB
37681	3251	4	suggests	suggest	VBZ
37681	3251	5	that	that	IN
37681	3251	6	there	there	EX
37681	3251	7	are	be	VBP
37681	3251	8	two	two	CD
37681	3251	9	planes	plane	NNS
37681	3251	10	in	in	IN
37681	3251	11	the	the	DT
37681	3251	12	locus	locus	NN
37681	3251	13	,	,	,
37681	3251	14	provided	provide	VBD
37681	3251	15	the	the	DT
37681	3251	16	planes	plane	NNS
37681	3251	17	of	of	IN
37681	3251	18	the	the	DT
37681	3251	19	dihedral	dihedral	JJ
37681	3251	20	angle	angle	NN
37681	3251	21	are	be	VBP
37681	3251	22	taken	take	VBN
37681	3251	23	as	as	IN
37681	3251	24	indefinite	indefinite	JJ
37681	3251	25	in	in	IN
37681	3251	26	extent	extent	NN
37681	3251	27	,	,	,
37681	3251	28	and	and	CC
37681	3251	29	that	that	IN
37681	3251	30	these	these	DT
37681	3251	31	planes	plane	NNS
37681	3251	32	are	be	VBP
37681	3251	33	perpendicular	perpendicular	JJ
37681	3251	34	to	to	IN
37681	3251	35	each	each	DT
37681	3251	36	other	other	JJ
37681	3251	37	.	.	.
37681	3252	1	It	-PRON-	PRP
37681	3252	2	may	may	MD
37681	3252	3	interest	interest	VB
37681	3252	4	some	some	DT
37681	3252	5	of	of	IN
37681	3252	6	the	the	DT
37681	3252	7	pupils	pupil	NNS
37681	3252	8	to	to	TO
37681	3252	9	draw	draw	VB
37681	3252	10	this	this	DT
37681	3252	11	general	general	JJ
37681	3252	12	figure	figure	NN
37681	3252	13	,	,	,
37681	3252	14	analogous	analogous	JJ
37681	3252	15	to	to	IN
37681	3252	16	the	the	DT
37681	3252	17	one	one	CD
37681	3252	18	in	in	IN
37681	3252	19	plane	plane	NN
37681	3252	20	geometry	geometry	NN
37681	3252	21	.	.	.
37681	3253	1	THEOREM	THEOREM	NNP
37681	3253	2	.	.	.
37681	3254	1	_	_	NNP
37681	3254	2	The	the	DT
37681	3254	3	projection	projection	NN
37681	3254	4	of	of	IN
37681	3254	5	a	a	DT
37681	3254	6	straight	straight	JJ
37681	3254	7	line	line	NN
37681	3254	8	not	not	RB
37681	3254	9	perpendicular	perpendicular	JJ
37681	3254	10	to	to	IN
37681	3254	11	a	a	DT
37681	3254	12	plane	plane	NN
37681	3254	13	upon	upon	IN
37681	3254	14	that	that	DT
37681	3254	15	plane	plane	NN
37681	3254	16	is	be	VBZ
37681	3254	17	a	a	DT
37681	3254	18	straight	straight	JJ
37681	3254	19	line	line	NN
37681	3254	20	.	.	.
37681	3254	21	_	_	NNP
37681	3254	22	In	in	IN
37681	3254	23	higher	high	JJR
37681	3254	24	mathematics	mathematic	NNS
37681	3254	25	it	-PRON-	PRP
37681	3254	26	would	would	MD
37681	3254	27	simply	simply	RB
37681	3254	28	be	be	VB
37681	3254	29	said	say	VBN
37681	3254	30	that	that	IN
37681	3254	31	the	the	DT
37681	3254	32	projection	projection	NN
37681	3254	33	is	be	VBZ
37681	3254	34	a	a	DT
37681	3254	35	straight	straight	JJ
37681	3254	36	line	line	NN
37681	3254	37	,	,	,
37681	3254	38	the	the	DT
37681	3254	39	special	special	JJ
37681	3254	40	case	case	NN
37681	3254	41	of	of	IN
37681	3254	42	the	the	DT
37681	3254	43	projection	projection	NN
37681	3254	44	of	of	IN
37681	3254	45	a	a	DT
37681	3254	46	perpendicular	perpendicular	JJ
37681	3254	47	being	be	VBG
37681	3254	48	considered	consider	VBN
37681	3254	49	as	as	IN
37681	3254	50	a	a	DT
37681	3254	51	line	line	NN
37681	3254	52	-	-	HYPH
37681	3254	53	segment	segment	NN
37681	3254	54	of	of	IN
37681	3254	55	zero	zero	CD
37681	3254	56	length	length	NN
37681	3254	57	.	.	.
37681	3255	1	There	there	EX
37681	3255	2	is	be	VBZ
37681	3255	3	no	no	DT
37681	3255	4	advantage	advantage	NN
37681	3255	5	,	,	,
37681	3255	6	however	however	RB
37681	3255	7	,	,	,
37681	3255	8	of	of	IN
37681	3255	9	bringing	bring	VBG
37681	3255	10	in	in	RP
37681	3255	11	zero	zero	CD
37681	3255	12	and	and	CC
37681	3255	13	infinity	infinity	NN
37681	3255	14	in	in	IN
37681	3255	15	the	the	DT
37681	3255	16	course	course	NN
37681	3255	17	in	in	IN
37681	3255	18	elementary	elementary	JJ
37681	3255	19	geometry	geometry	NN
37681	3255	20	.	.	.
37681	3256	1	The	the	DT
37681	3256	2	legitimate	legitimate	JJ
37681	3256	3	reason	reason	NN
37681	3256	4	for	for	IN
37681	3256	5	the	the	DT
37681	3256	6	modern	modern	JJ
37681	3256	7	use	use	NN
37681	3256	8	of	of	IN
37681	3256	9	these	these	DT
37681	3256	10	terms	term	NNS
37681	3256	11	is	be	VBZ
37681	3256	12	seldom	seldom	RB
37681	3256	13	understood	understand	VBN
37681	3256	14	by	by	IN
37681	3256	15	beginners	beginner	NNS
37681	3256	16	.	.	.
37681	3257	1	This	this	DT
37681	3257	2	subject	subject	NN
37681	3257	3	of	of	IN
37681	3257	4	projection	projection	NN
37681	3257	5	(	(	-LRB-
37681	3257	6	Latin	Latin	NNP
37681	3257	7	_	_	NNP
37681	3257	8	pro-	pro-	NN
37681	3257	9	_	_	NNP
37681	3257	10	,	,	,
37681	3257	11	"	"	``
37681	3257	12	forth	forth	RB
37681	3257	13	,	,	,
37681	3257	14	"	"	''
37681	3257	15	and	and	CC
37681	3257	16	_	_	NNP
37681	3257	17	jacere	jacere	NNP
37681	3257	18	_	_	NNP
37681	3257	19	,	,	,
37681	3257	20	"	"	``
37681	3257	21	to	to	TO
37681	3257	22	throw	throw	VB
37681	3257	23	"	"	''
37681	3257	24	)	)	-RRB-
37681	3257	25	is	be	VBZ
37681	3257	26	extensively	extensively	RB
37681	3257	27	used	use	VBN
37681	3257	28	in	in	IN
37681	3257	29	modern	modern	JJ
37681	3257	30	mathematics	mathematic	NNS
37681	3257	31	and	and	CC
37681	3257	32	also	also	RB
37681	3257	33	in	in	IN
37681	3257	34	the	the	DT
37681	3257	35	elementary	elementary	JJ
37681	3257	36	work	work	NN
37681	3257	37	of	of	IN
37681	3257	38	the	the	DT
37681	3257	39	draftsman	draftsman	NN
37681	3257	40	,	,	,
37681	3257	41	and	and	CC
37681	3257	42	it	-PRON-	PRP
37681	3257	43	will	will	MD
37681	3257	44	be	be	VB
37681	3257	45	referred	refer	VBN
37681	3257	46	to	to	IN
37681	3257	47	a	a	DT
37681	3257	48	little	little	JJ
37681	3257	49	later	later	RBR
37681	3257	50	.	.	.
37681	3258	1	At	at	IN
37681	3258	2	this	this	DT
37681	3258	3	time	time	NN
37681	3258	4	,	,	,
37681	3258	5	however	however	RB
37681	3258	6	,	,	,
37681	3258	7	it	-PRON-	PRP
37681	3258	8	is	be	VBZ
37681	3258	9	well	well	JJ
37681	3258	10	to	to	TO
37681	3258	11	call	call	VB
37681	3258	12	attention	attention	NN
37681	3258	13	to	to	IN
37681	3258	14	the	the	DT
37681	3258	15	fact	fact	NN
37681	3258	16	that	that	IN
37681	3258	17	the	the	DT
37681	3258	18	projection	projection	NN
37681	3258	19	of	of	IN
37681	3258	20	a	a	DT
37681	3258	21	straight	straight	JJ
37681	3258	22	line	line	NN
37681	3258	23	on	on	IN
37681	3258	24	a	a	DT
37681	3258	25	plane	plane	NN
37681	3258	26	is	be	VBZ
37681	3258	27	a	a	DT
37681	3258	28	straight	straight	JJ
37681	3258	29	line	line	NN
37681	3258	30	or	or	CC
37681	3258	31	a	a	DT
37681	3258	32	point	point	NN
37681	3258	33	;	;	:
37681	3258	34	the	the	DT
37681	3258	35	projection	projection	NN
37681	3258	36	of	of	IN
37681	3258	37	a	a	DT
37681	3258	38	curve	curve	NN
37681	3258	39	may	may	MD
37681	3258	40	be	be	VB
37681	3258	41	a	a	DT
37681	3258	42	curve	curve	NN
37681	3258	43	or	or	CC
37681	3258	44	it	-PRON-	PRP
37681	3258	45	may	may	MD
37681	3258	46	be	be	VB
37681	3258	47	straight	straight	JJ
37681	3258	48	;	;	:
37681	3258	49	the	the	DT
37681	3258	50	projection	projection	NN
37681	3258	51	of	of	IN
37681	3258	52	a	a	DT
37681	3258	53	point	point	NN
37681	3258	54	is	be	VBZ
37681	3258	55	a	a	DT
37681	3258	56	point	point	NN
37681	3258	57	;	;	:
37681	3258	58	and	and	CC
37681	3258	59	the	the	DT
37681	3258	60	projection	projection	NN
37681	3258	61	of	of	IN
37681	3258	62	a	a	DT
37681	3258	63	plane	plane	NN
37681	3258	64	(	(	-LRB-
37681	3258	65	which	which	WDT
37681	3258	66	is	be	VBZ
37681	3258	67	easily	easily	RB
37681	3258	68	understood	understand	VBN
37681	3258	69	without	without	IN
37681	3258	70	defining	define	VBG
37681	3258	71	it	-PRON-	PRP
37681	3258	72	)	)	-RRB-
37681	3258	73	may	may	MD
37681	3258	74	be	be	VB
37681	3258	75	a	a	DT
37681	3258	76	surface	surface	NN
37681	3258	77	or	or	CC
37681	3258	78	it	-PRON-	PRP
37681	3258	79	may	may	MD
37681	3258	80	be	be	VB
37681	3258	81	a	a	DT
37681	3258	82	straight	straight	JJ
37681	3258	83	line	line	NN
37681	3258	84	.	.	.
37681	3259	1	An	an	DT
37681	3259	2	artisan	artisan	NNP
37681	3259	3	represents	represent	VBZ
37681	3259	4	a	a	DT
37681	3259	5	solid	solid	JJ
37681	3259	6	by	by	IN
37681	3259	7	drawing	draw	VBG
37681	3259	8	its	-PRON-	PRP$
37681	3259	9	projection	projection	NN
37681	3259	10	upon	upon	IN
37681	3259	11	two	two	CD
37681	3259	12	planes	plane	NNS
37681	3259	13	at	at	IN
37681	3259	14	right	right	JJ
37681	3259	15	angles	angle	NNS
37681	3259	16	to	to	IN
37681	3259	17	each	each	DT
37681	3259	18	other	other	JJ
37681	3259	19	,	,	,
37681	3259	20	and	and	CC
37681	3259	21	a	a	DT
37681	3259	22	map	map	NN
37681	3259	23	maker	maker	NN
37681	3259	24	(	(	-LRB-
37681	3259	25	cartographer	cartographer	NN
37681	3259	26	)	)	-RRB-
37681	3259	27	represents	represent	VBZ
37681	3259	28	the	the	DT
37681	3259	29	surface	surface	NN
37681	3259	30	of	of	IN
37681	3259	31	the	the	DT
37681	3259	32	earth	earth	NN
37681	3259	33	by	by	IN
37681	3259	34	projecting	project	VBG
37681	3259	35	it	-PRON-	PRP
37681	3259	36	upon	upon	IN
37681	3259	37	a	a	DT
37681	3259	38	plane	plane	NN
37681	3259	39	.	.	.
37681	3260	1	A	a	DT
37681	3260	2	photograph	photograph	NN
37681	3260	3	of	of	IN
37681	3260	4	the	the	DT
37681	3260	5	class	class	NN
37681	3260	6	is	be	VBZ
37681	3260	7	merely	merely	RB
37681	3260	8	the	the	DT
37681	3260	9	projection	projection	NN
37681	3260	10	of	of	IN
37681	3260	11	the	the	DT
37681	3260	12	class	class	NN
37681	3260	13	upon	upon	IN
37681	3260	14	a	a	DT
37681	3260	15	photographic	photographic	JJ
37681	3260	16	plate	plate	NN
37681	3260	17	(	(	-LRB-
37681	3260	18	plane	plane	NN
37681	3260	19	)	)	-RRB-
37681	3260	20	,	,	,
37681	3260	21	and	and	CC
37681	3260	22	when	when	WRB
37681	3260	23	we	-PRON-	PRP
37681	3260	24	draw	draw	VBP
37681	3260	25	a	a	DT
37681	3260	26	figure	figure	NN
37681	3260	27	in	in	IN
37681	3260	28	solid	solid	JJ
37681	3260	29	geometry	geometry	NN
37681	3260	30	,	,	,
37681	3260	31	we	-PRON-	PRP
37681	3260	32	merely	merely	RB
37681	3260	33	project	project	VBP
37681	3260	34	the	the	DT
37681	3260	35	solid	solid	JJ
37681	3260	36	upon	upon	IN
37681	3260	37	the	the	DT
37681	3260	38	plane	plane	NN
37681	3260	39	of	of	IN
37681	3260	40	the	the	DT
37681	3260	41	paper	paper	NN
37681	3260	42	.	.	.
37681	3261	1	There	there	EX
37681	3261	2	are	be	VBP
37681	3261	3	other	other	JJ
37681	3261	4	projections	projection	NNS
37681	3261	5	than	than	IN
37681	3261	6	those	those	DT
37681	3261	7	formed	form	VBN
37681	3261	8	by	by	IN
37681	3261	9	lines	line	NNS
37681	3261	10	that	that	WDT
37681	3261	11	are	be	VBP
37681	3261	12	perpendicular	perpendicular	JJ
37681	3261	13	to	to	IN
37681	3261	14	the	the	DT
37681	3261	15	plane	plane	NN
37681	3261	16	.	.	.
37681	3262	1	The	the	DT
37681	3262	2	lines	line	NNS
37681	3262	3	may	may	MD
37681	3262	4	be	be	VB
37681	3262	5	oblique	oblique	JJ
37681	3262	6	to	to	IN
37681	3262	7	the	the	DT
37681	3262	8	plane	plane	NN
37681	3262	9	,	,	,
37681	3262	10	and	and	CC
37681	3262	11	this	this	DT
37681	3262	12	is	be	VBZ
37681	3262	13	the	the	DT
37681	3262	14	case	case	NN
37681	3262	15	with	with	IN
37681	3262	16	most	most	JJS
37681	3262	17	projections	projection	NNS
37681	3262	18	.	.	.
37681	3263	1	A	a	DT
37681	3263	2	photograph	photograph	NN
37681	3263	3	,	,	,
37681	3263	4	for	for	IN
37681	3263	5	example	example	NN
37681	3263	6	,	,	,
37681	3263	7	is	be	VBZ
37681	3263	8	not	not	RB
37681	3263	9	formed	form	VBN
37681	3263	10	by	by	IN
37681	3263	11	lines	line	NNS
37681	3263	12	perpendicular	perpendicular	JJ
37681	3263	13	to	to	IN
37681	3263	14	a	a	DT
37681	3263	15	plane	plane	NN
37681	3263	16	,	,	,
37681	3263	17	for	for	IN
37681	3263	18	they	-PRON-	PRP
37681	3263	19	all	all	DT
37681	3263	20	converge	converge	VBP
37681	3263	21	in	in	IN
37681	3263	22	the	the	DT
37681	3263	23	camera	camera	NN
37681	3263	24	.	.	.
37681	3264	1	If	if	IN
37681	3264	2	the	the	DT
37681	3264	3	lines	line	NNS
37681	3264	4	of	of	IN
37681	3264	5	projection	projection	NN
37681	3264	6	are	be	VBP
37681	3264	7	all	all	RB
37681	3264	8	perpendicular	perpendicular	JJ
37681	3264	9	to	to	IN
37681	3264	10	the	the	DT
37681	3264	11	plane	plane	NN
37681	3264	12	,	,	,
37681	3264	13	the	the	DT
37681	3264	14	projection	projection	NN
37681	3264	15	is	be	VBZ
37681	3264	16	said	say	VBN
37681	3264	17	to	to	TO
37681	3264	18	be	be	VB
37681	3264	19	orthographic	orthographic	JJ
37681	3264	20	,	,	,
37681	3264	21	from	from	IN
37681	3264	22	the	the	DT
37681	3264	23	Greek	Greek	NNP
37681	3264	24	_	_	NNP
37681	3264	25	ortho-	ortho-	NN
37681	3264	26	_	_	NNP
37681	3264	27	(	(	-LRB-
37681	3264	28	straight	straight	RB
37681	3264	29	)	)	-RRB-
37681	3264	30	and	and	CC
37681	3264	31	_	_	NNP
37681	3264	32	graphein	graphein	NNP
37681	3264	33	_	_	NNP
37681	3264	34	(	(	-LRB-
37681	3264	35	to	to	TO
37681	3264	36	draw	draw	VB
37681	3264	37	)	)	-RRB-
37681	3264	38	.	.	.
37681	3265	1	A	a	DT
37681	3265	2	good	good	JJ
37681	3265	3	example	example	NN
37681	3265	4	of	of	IN
37681	3265	5	orthographic	orthographic	JJ
37681	3265	6	projection	projection	NN
37681	3265	7	may	may	MD
37681	3265	8	be	be	VB
37681	3265	9	seen	see	VBN
37681	3265	10	in	in	IN
37681	3265	11	the	the	DT
37681	3265	12	shadow	shadow	NN
37681	3265	13	cast	cast	VBN
37681	3265	14	by	by	IN
37681	3265	15	an	an	DT
37681	3265	16	object	object	NN
37681	3265	17	upon	upon	IN
37681	3265	18	a	a	DT
37681	3265	19	piece	piece	NN
37681	3265	20	of	of	IN
37681	3265	21	paper	paper	NN
37681	3265	22	that	that	WDT
37681	3265	23	is	be	VBZ
37681	3265	24	held	hold	VBN
37681	3265	25	perpendicular	perpendicular	JJ
37681	3265	26	to	to	IN
37681	3265	27	the	the	DT
37681	3265	28	sun	sun	NN
37681	3265	29	's	's	POS
37681	3265	30	rays	ray	NNS
37681	3265	31	.	.	.
37681	3266	1	A	a	DT
37681	3266	2	good	good	JJ
37681	3266	3	example	example	NN
37681	3266	4	of	of	IN
37681	3266	5	oblique	oblique	JJ
37681	3266	6	projection	projection	NN
37681	3266	7	is	be	VBZ
37681	3266	8	a	a	DT
37681	3266	9	shadow	shadow	NN
37681	3266	10	on	on	IN
37681	3266	11	the	the	DT
37681	3266	12	floor	floor	NN
37681	3266	13	of	of	IN
37681	3266	14	the	the	DT
37681	3266	15	schoolroom	schoolroom	NN
37681	3266	16	.	.	.
37681	3267	1	THEOREM	THEOREM	NNP
37681	3267	2	.	.	.
37681	3268	1	_	_	NNP
37681	3268	2	Between	between	IN
37681	3268	3	two	two	CD
37681	3268	4	straight	straight	JJ
37681	3268	5	lines	line	NNS
37681	3268	6	not	not	RB
37681	3268	7	in	in	IN
37681	3268	8	the	the	DT
37681	3268	9	same	same	JJ
37681	3268	10	plane	plane	NN
37681	3268	11	there	there	EX
37681	3268	12	can	can	MD
37681	3268	13	be	be	VB
37681	3268	14	one	one	CD
37681	3268	15	common	common	JJ
37681	3268	16	perpendicular	perpendicular	NN
37681	3268	17	,	,	,
37681	3268	18	and	and	CC
37681	3268	19	only	only	RB
37681	3268	20	one	one	CD
37681	3268	21	.	.	.
37681	3268	22	_	_	NNP
37681	3268	23	The	the	DT
37681	3268	24	usual	usual	JJ
37681	3268	25	corollary	corollary	JJ
37681	3268	26	states	state	NNS
37681	3268	27	that	that	IN
37681	3268	28	this	this	DT
37681	3268	29	perpendicular	perpendicular	NN
37681	3268	30	is	be	VBZ
37681	3268	31	the	the	DT
37681	3268	32	shortest	short	JJS
37681	3268	33	line	line	NN
37681	3268	34	joining	join	VBG
37681	3268	35	them	-PRON-	PRP
37681	3268	36	.	.	.
37681	3269	1	It	-PRON-	PRP
37681	3269	2	is	be	VBZ
37681	3269	3	interesting	interesting	JJ
37681	3269	4	to	to	TO
37681	3269	5	compare	compare	VB
37681	3269	6	this	this	DT
37681	3269	7	with	with	IN
37681	3269	8	the	the	DT
37681	3269	9	case	case	NN
37681	3269	10	of	of	IN
37681	3269	11	two	two	CD
37681	3269	12	lines	line	NNS
37681	3269	13	in	in	IN
37681	3269	14	the	the	DT
37681	3269	15	same	same	JJ
37681	3269	16	plane	plane	NN
37681	3269	17	.	.	.
37681	3270	1	If	if	IN
37681	3270	2	they	-PRON-	PRP
37681	3270	3	are	be	VBP
37681	3270	4	parallel	parallel	JJ
37681	3270	5	,	,	,
37681	3270	6	there	there	EX
37681	3270	7	may	may	MD
37681	3270	8	be	be	VB
37681	3270	9	any	any	DT
37681	3270	10	number	number	NN
37681	3270	11	of	of	IN
37681	3270	12	common	common	JJ
37681	3270	13	perpendiculars	perpendicular	NNS
37681	3270	14	.	.	.
37681	3271	1	If	if	IN
37681	3271	2	they	-PRON-	PRP
37681	3271	3	intersect	intersect	VBP
37681	3271	4	,	,	,
37681	3271	5	there	there	EX
37681	3271	6	is	be	VBZ
37681	3271	7	still	still	RB
37681	3271	8	a	a	DT
37681	3271	9	common	common	JJ
37681	3271	10	perpendicular	perpendicular	NN
37681	3271	11	,	,	,
37681	3271	12	but	but	CC
37681	3271	13	this	this	DT
37681	3271	14	can	can	MD
37681	3271	15	hardly	hardly	RB
37681	3271	16	be	be	VB
37681	3271	17	said	say	VBN
37681	3271	18	to	to	TO
37681	3271	19	be	be	VB
37681	3271	20	between	between	IN
37681	3271	21	them	-PRON-	PRP
37681	3271	22	,	,	,
37681	3271	23	except	except	IN
37681	3271	24	for	for	IN
37681	3271	25	its	-PRON-	PRP$
37681	3271	26	zero	zero	CD
37681	3271	27	segment	segment	NN
37681	3271	28	.	.	.
37681	3272	1	There	there	EX
37681	3272	2	are	be	VBP
37681	3272	3	many	many	JJ
37681	3272	4	simple	simple	JJ
37681	3272	5	illustrations	illustration	NNS
37681	3272	6	of	of	IN
37681	3272	7	this	this	DT
37681	3272	8	case	case	NN
37681	3272	9	.	.	.
37681	3273	1	For	for	IN
37681	3273	2	example	example	NN
37681	3273	3	,	,	,
37681	3273	4	what	what	WP
37681	3273	5	is	be	VBZ
37681	3273	6	the	the	DT
37681	3273	7	shortest	short	JJS
37681	3273	8	line	line	NN
37681	3273	9	between	between	IN
37681	3273	10	any	any	DT
37681	3273	11	given	give	VBN
37681	3273	12	edge	edge	NN
37681	3273	13	of	of	IN
37681	3273	14	the	the	DT
37681	3273	15	ceiling	ceiling	NN
37681	3273	16	and	and	CC
37681	3273	17	the	the	DT
37681	3273	18	various	various	JJ
37681	3273	19	edges	edge	NNS
37681	3273	20	of	of	IN
37681	3273	21	the	the	DT
37681	3273	22	floor	floor	NN
37681	3273	23	of	of	IN
37681	3273	24	the	the	DT
37681	3273	25	schoolroom	schoolroom	NN
37681	3273	26	?	?	.
37681	3274	1	If	if	IN
37681	3274	2	two	two	CD
37681	3274	3	galleries	gallery	NNS
37681	3274	4	in	in	IN
37681	3274	5	a	a	DT
37681	3274	6	mine	mine	NN
37681	3274	7	are	be	VBP
37681	3274	8	to	to	TO
37681	3274	9	be	be	VB
37681	3274	10	connected	connect	VBN
37681	3274	11	by	by	IN
37681	3274	12	an	an	DT
37681	3274	13	air	air	NN
37681	3274	14	shaft	shaft	NN
37681	3274	15	,	,	,
37681	3274	16	how	how	WRB
37681	3274	17	shall	shall	MD
37681	3274	18	it	-PRON-	PRP
37681	3274	19	be	be	VB
37681	3274	20	planned	plan	VBN
37681	3274	21	so	so	IN
37681	3274	22	as	as	IN
37681	3274	23	to	to	TO
37681	3274	24	save	save	VB
37681	3274	25	labor	labor	NN
37681	3274	26	?	?	.
37681	3275	1	Make	make	VB
37681	3275	2	a	a	DT
37681	3275	3	drawing	drawing	NN
37681	3275	4	of	of	IN
37681	3275	5	the	the	DT
37681	3275	6	plan	plan	NN
37681	3275	7	.	.	.
37681	3276	1	At	at	IN
37681	3276	2	this	this	DT
37681	3276	3	point	point	NN
37681	3276	4	the	the	DT
37681	3276	5	polyhedral	polyhedral	JJ
37681	3276	6	angle	angle	NN
37681	3276	7	is	be	VBZ
37681	3276	8	introduced	introduce	VBN
37681	3276	9	.	.	.
37681	3277	1	The	the	DT
37681	3277	2	word	word	NN
37681	3277	3	is	be	VBZ
37681	3277	4	from	from	IN
37681	3277	5	the	the	DT
37681	3277	6	Greek	Greek	NNP
37681	3277	7	_	_	NNP
37681	3277	8	polys	polys	NN
37681	3277	9	_	_	NNP
37681	3277	10	(	(	-LRB-
37681	3277	11	many	many	JJ
37681	3277	12	)	)	-RRB-
37681	3277	13	and	and	CC
37681	3277	14	_	_	NNP
37681	3277	15	hedra	hedra	NNP
37681	3277	16	_	_	NNP
37681	3277	17	(	(	-LRB-
37681	3277	18	seat	seat	NN
37681	3277	19	)	)	-RRB-
37681	3277	20	.	.	.
37681	3278	1	Students	student	NNS
37681	3278	2	have	have	VBP
37681	3278	3	more	more	JJR
37681	3278	4	difficulty	difficulty	NN
37681	3278	5	in	in	IN
37681	3278	6	grasping	grasp	VBG
37681	3278	7	the	the	DT
37681	3278	8	meaning	meaning	NN
37681	3278	9	of	of	IN
37681	3278	10	the	the	DT
37681	3278	11	size	size	NN
37681	3278	12	of	of	IN
37681	3278	13	a	a	DT
37681	3278	14	polyhedral	polyhedral	JJ
37681	3278	15	angle	angle	NN
37681	3278	16	than	than	IN
37681	3278	17	is	be	VBZ
37681	3278	18	the	the	DT
37681	3278	19	case	case	NN
37681	3278	20	with	with	IN
37681	3278	21	dihedral	dihedral	JJ
37681	3278	22	and	and	CC
37681	3278	23	plane	plane	NN
37681	3278	24	angles	angle	NNS
37681	3278	25	.	.	.
37681	3279	1	For	for	IN
37681	3279	2	this	this	DT
37681	3279	3	reason	reason	NN
37681	3279	4	it	-PRON-	PRP
37681	3279	5	is	be	VBZ
37681	3279	6	not	not	RB
37681	3279	7	good	good	JJ
37681	3279	8	policy	policy	NN
37681	3279	9	to	to	TO
37681	3279	10	dwell	dwell	VB
37681	3279	11	much	much	JJ
37681	3279	12	upon	upon	IN
37681	3279	13	this	this	DT
37681	3279	14	subject	subject	NN
37681	3279	15	unless	unless	IN
37681	3279	16	the	the	DT
37681	3279	17	question	question	NN
37681	3279	18	arises	arise	VBZ
37681	3279	19	,	,	,
37681	3279	20	since	since	IN
37681	3279	21	it	-PRON-	PRP
37681	3279	22	is	be	VBZ
37681	3279	23	better	well	RBR
37681	3279	24	understood	understand	VBN
37681	3279	25	when	when	WRB
37681	3279	26	the	the	DT
37681	3279	27	relation	relation	NN
37681	3279	28	of	of	IN
37681	3279	29	the	the	DT
37681	3279	30	polyhedral	polyhedral	JJ
37681	3279	31	angle	angle	NN
37681	3279	32	and	and	CC
37681	3279	33	the	the	DT
37681	3279	34	spherical	spherical	JJ
37681	3279	35	polygon	polygon	NN
37681	3279	36	is	be	VBZ
37681	3279	37	met	meet	VBN
37681	3279	38	.	.	.
37681	3280	1	Teachers	teacher	NNS
37681	3280	2	will	will	MD
37681	3280	3	naturally	naturally	RB
37681	3280	4	see	see	VB
37681	3280	5	that	that	DT
37681	3280	6	just	just	RB
37681	3280	7	as	as	IN
37681	3280	8	we	-PRON-	PRP
37681	3280	9	may	may	MD
37681	3280	10	measure	measure	VB
37681	3280	11	the	the	DT
37681	3280	12	plane	plane	NN
37681	3280	13	angle	angle	NN
37681	3280	14	by	by	IN
37681	3280	15	taking	take	VBG
37681	3280	16	the	the	DT
37681	3280	17	ratio	ratio	NN
37681	3280	18	of	of	IN
37681	3280	19	an	an	DT
37681	3280	20	arc	arc	NN
37681	3280	21	to	to	IN
37681	3280	22	the	the	DT
37681	3280	23	whole	whole	JJ
37681	3280	24	circle	circle	NN
37681	3280	25	,	,	,
37681	3280	26	and	and	CC
37681	3280	27	of	of	IN
37681	3280	28	a	a	DT
37681	3280	29	dihedral	dihedral	JJ
37681	3280	30	angle	angle	NN
37681	3280	31	by	by	IN
37681	3280	32	taking	take	VBG
37681	3280	33	the	the	DT
37681	3280	34	ratio	ratio	NN
37681	3280	35	of	of	IN
37681	3280	36	that	that	DT
37681	3280	37	part	part	NN
37681	3280	38	of	of	IN
37681	3280	39	the	the	DT
37681	3280	40	cylindric	cylindric	JJ
37681	3280	41	surface	surface	NN
37681	3280	42	that	that	WDT
37681	3280	43	is	be	VBZ
37681	3280	44	cut	cut	VBN
37681	3280	45	out	out	RP
37681	3280	46	by	by	IN
37681	3280	47	the	the	DT
37681	3280	48	planes	plane	NNS
37681	3280	49	to	to	IN
37681	3280	50	the	the	DT
37681	3280	51	whole	whole	JJ
37681	3280	52	surface	surface	NN
37681	3280	53	,	,	,
37681	3280	54	so	so	IN
37681	3280	55	we	-PRON-	PRP
37681	3280	56	may	may	MD
37681	3280	57	measure	measure	VB
37681	3280	58	a	a	DT
37681	3280	59	polyhedral	polyhedral	JJ
37681	3280	60	angle	angle	NN
37681	3280	61	by	by	IN
37681	3280	62	taking	take	VBG
37681	3280	63	the	the	DT
37681	3280	64	ratio	ratio	NN
37681	3280	65	of	of	IN
37681	3280	66	the	the	DT
37681	3280	67	spherical	spherical	JJ
37681	3280	68	polygon	polygon	NN
37681	3280	69	to	to	IN
37681	3280	70	the	the	DT
37681	3280	71	whole	whole	JJ
37681	3280	72	spherical	spherical	JJ
37681	3280	73	surface	surface	NN
37681	3280	74	.	.	.
37681	3281	1	It	-PRON-	PRP
37681	3281	2	should	should	MD
37681	3281	3	also	also	RB
37681	3281	4	be	be	VB
37681	3281	5	observed	observe	VBN
37681	3281	6	that	that	DT
37681	3281	7	just	just	RB
37681	3281	8	as	as	IN
37681	3281	9	we	-PRON-	PRP
37681	3281	10	may	may	MD
37681	3281	11	have	have	VB
37681	3281	12	cross	cross	JJ
37681	3281	13	polygons	polygon	NNS
37681	3281	14	in	in	IN
37681	3281	15	a	a	DT
37681	3281	16	plane	plane	NN
37681	3281	17	,	,	,
37681	3281	18	so	so	IN
37681	3281	19	we	-PRON-	PRP
37681	3281	20	may	may	MD
37681	3281	21	have	have	VB
37681	3281	22	spherical	spherical	JJ
37681	3281	23	polygons	polygon	NNS
37681	3281	24	that	that	WDT
37681	3281	25	are	be	VBP
37681	3281	26	similarly	similarly	RB
37681	3281	27	tangled	tangle	VBN
37681	3281	28	,	,	,
37681	3281	29	and	and	CC
37681	3281	30	that	that	IN
37681	3281	31	to	to	IN
37681	3281	32	these	these	DT
37681	3281	33	will	will	MD
37681	3281	34	correspond	correspond	VB
37681	3281	35	polyhedral	polyhedral	JJ
37681	3281	36	angles	angle	NNS
37681	3281	37	that	that	WDT
37681	3281	38	are	be	VBP
37681	3281	39	also	also	RB
37681	3281	40	cross	cros	VBN
37681	3281	41	,	,	,
37681	3281	42	their	-PRON-	PRP$
37681	3281	43	representation	representation	NN
37681	3281	44	by	by	IN
37681	3281	45	drawings	drawing	NNS
37681	3281	46	being	be	VBG
37681	3281	47	too	too	RB
37681	3281	48	complicated	complicated	JJ
37681	3281	49	for	for	IN
37681	3281	50	class	class	NN
37681	3281	51	use	use	NN
37681	3281	52	.	.	.
37681	3282	1	The	the	DT
37681	3282	2	idea	idea	NN
37681	3282	3	of	of	IN
37681	3282	4	symmetric	symmetric	JJ
37681	3282	5	solids	solid	NNS
37681	3282	6	may	may	MD
37681	3282	7	be	be	VB
37681	3282	8	illustrated	illustrate	VBN
37681	3282	9	by	by	IN
37681	3282	10	a	a	DT
37681	3282	11	pair	pair	NN
37681	3282	12	of	of	IN
37681	3282	13	gloves	glove	NNS
37681	3282	14	,	,	,
37681	3282	15	all	all	DT
37681	3282	16	their	-PRON-	PRP$
37681	3282	17	parts	part	NNS
37681	3282	18	being	be	VBG
37681	3282	19	mutually	mutually	RB
37681	3282	20	equal	equal	JJ
37681	3282	21	but	but	CC
37681	3282	22	arranged	arrange	VBN
37681	3282	23	in	in	IN
37681	3282	24	opposite	opposite	JJ
37681	3282	25	order	order	NN
37681	3282	26	.	.	.
37681	3283	1	Our	-PRON-	PRP$
37681	3283	2	hands	hand	NNS
37681	3283	3	,	,	,
37681	3283	4	feet	foot	NNS
37681	3283	5	,	,	,
37681	3283	6	and	and	CC
37681	3283	7	ears	ear	NNS
37681	3283	8	afford	afford	VBP
37681	3283	9	other	other	JJ
37681	3283	10	illustrations	illustration	NNS
37681	3283	11	of	of	IN
37681	3283	12	symmetric	symmetric	JJ
37681	3283	13	solids	solid	NNS
37681	3283	14	.	.	.
37681	3284	1	THEOREM	THEOREM	NNP
37681	3284	2	.	.	.
37681	3285	1	_	_	NNP
37681	3285	2	The	the	DT
37681	3285	3	sum	sum	NN
37681	3285	4	of	of	IN
37681	3285	5	the	the	DT
37681	3285	6	face	face	NN
37681	3285	7	angles	angle	NNS
37681	3285	8	of	of	IN
37681	3285	9	any	any	DT
37681	3285	10	convex	convex	NNP
37681	3285	11	polyhedral	polyhedral	JJ
37681	3285	12	angle	angle	NN
37681	3285	13	is	be	VBZ
37681	3285	14	less	less	JJR
37681	3285	15	than	than	IN
37681	3285	16	four	four	CD
37681	3285	17	right	right	JJ
37681	3285	18	angles	angle	NNS
37681	3285	19	.	.	.
37681	3285	20	_	_	NNP
37681	3285	21	There	there	EX
37681	3285	22	are	be	VBP
37681	3285	23	several	several	JJ
37681	3285	24	interesting	interesting	JJ
37681	3285	25	points	point	NNS
37681	3285	26	of	of	IN
37681	3285	27	discussion	discussion	NN
37681	3285	28	in	in	IN
37681	3285	29	connection	connection	NN
37681	3285	30	with	with	IN
37681	3285	31	this	this	DT
37681	3285	32	proposition	proposition	NN
37681	3285	33	.	.	.
37681	3286	1	For	for	IN
37681	3286	2	example	example	NN
37681	3286	3	,	,	,
37681	3286	4	suppose	suppose	VB
37681	3286	5	the	the	DT
37681	3286	6	vertex	vertex	NN
37681	3286	7	_	_	NNP
37681	3286	8	V	V	NNP
37681	3286	9	_	_	NNP
37681	3286	10	to	to	TO
37681	3286	11	approach	approach	VB
37681	3286	12	the	the	DT
37681	3286	13	plane	plane	NN
37681	3286	14	that	that	WDT
37681	3286	15	cuts	cut	VBZ
37681	3286	16	the	the	DT
37681	3286	17	edges	edge	NNS
37681	3286	18	in	in	IN
37681	3286	19	_	_	NNP
37681	3286	20	A	A	NNP
37681	3286	21	_	_	NNP
37681	3286	22	,	,	,
37681	3286	23	_	_	NNP
37681	3286	24	B	B	NNP
37681	3286	25	_	_	NNP
37681	3286	26	,	,	,
37681	3286	27	_	_	NNP
37681	3286	28	C	C	NNP
37681	3286	29	_	_	NNP
37681	3286	30	,	,	,
37681	3286	31	_	_	NNP
37681	3286	32	D	D	NNP
37681	3286	33	_	_	NNP
37681	3286	34	,	,	,
37681	3286	35	...	...	NFP
37681	3286	36	,	,	,
37681	3286	37	the	the	DT
37681	3286	38	edges	edge	NNS
37681	3286	39	continuing	continue	VBG
37681	3286	40	to	to	TO
37681	3286	41	pass	pass	VB
37681	3286	42	through	through	RP
37681	3286	43	these	these	DT
37681	3286	44	as	as	IN
37681	3286	45	fixed	fix	VBN
37681	3286	46	points	point	NNS
37681	3286	47	.	.	.
37681	3287	1	The	the	DT
37681	3287	2	sum	sum	NN
37681	3287	3	of	of	IN
37681	3287	4	the	the	DT
37681	3287	5	angles	angle	NNS
37681	3287	6	about	about	IN
37681	3287	7	_	_	NNP
37681	3287	8	V	V	NNP
37681	3287	9	_	_	NNP
37681	3287	10	approaches	approach	VBZ
37681	3287	11	what	what	WDT
37681	3287	12	limit	limit	NN
37681	3287	13	?	?	.
37681	3288	1	On	on	IN
37681	3288	2	the	the	DT
37681	3288	3	other	other	JJ
37681	3288	4	hand	hand	NN
37681	3288	5	,	,	,
37681	3288	6	suppose	suppose	VB
37681	3288	7	_	_	NNP
37681	3288	8	V	V	NNP
37681	3288	9	_	_	NNP
37681	3288	10	recedes	recede	VBZ
37681	3288	11	indefinitely	indefinitely	RB
37681	3288	12	;	;	:
37681	3288	13	then	then	RB
37681	3288	14	the	the	DT
37681	3288	15	sum	sum	NN
37681	3288	16	approaches	approach	VBZ
37681	3288	17	what	what	WDT
37681	3288	18	limit	limit	NN
37681	3288	19	?	?	.
37681	3289	1	Then	then	RB
37681	3289	2	what	what	WP
37681	3289	3	are	be	VBP
37681	3289	4	the	the	DT
37681	3289	5	two	two	CD
37681	3289	6	limits	limit	NNS
37681	3289	7	of	of	IN
37681	3289	8	this	this	DT
37681	3289	9	sum	sum	NN
37681	3289	10	?	?	.
37681	3290	1	Suppose	suppose	VB
37681	3290	2	the	the	DT
37681	3290	3	polyhedral	polyhedral	JJ
37681	3290	4	angle	angle	NN
37681	3290	5	were	be	VBD
37681	3290	6	concave	concave	NNP
37681	3290	7	,	,	,
37681	3290	8	why	why	WRB
37681	3290	9	would	would	MD
37681	3290	10	the	the	DT
37681	3290	11	proof	proof	NN
37681	3290	12	not	not	RB
37681	3290	13	hold	hold	VB
37681	3290	14	?	?	.
37681	3291	1	FOOTNOTES	footnote	NNS
37681	3291	2	:	:	:
37681	3291	3	[	[	-LRB-
37681	3291	4	87	87	CD
37681	3291	5	]	]	-RRB-
37681	3291	6	These	these	DT
37681	3291	7	may	may	MD
37681	3291	8	be	be	VB
37681	3291	9	purchased	purchase	VBN
37681	3291	10	through	through	IN
37681	3291	11	the	the	DT
37681	3291	12	Leipziger	Leipziger	NNP
37681	3291	13	Lehrmittelanstalt	Lehrmittelanstalt	NNP
37681	3291	14	,	,	,
37681	3291	15	Leipzig	Leipzig	NNP
37681	3291	16	,	,	,
37681	3291	17	Germany	Germany	NNP
37681	3291	18	,	,	,
37681	3291	19	which	which	WDT
37681	3291	20	will	will	MD
37681	3291	21	send	send	VB
37681	3291	22	catalogues	catalogue	NNS
37681	3291	23	to	to	IN
37681	3291	24	intending	intend	VBG
37681	3291	25	buyers	buyer	NNS
37681	3291	26	.	.	.
37681	3292	1	[	[	-LRB-
37681	3292	2	88	88	CD
37681	3292	3	]	]	-RRB-
37681	3292	4	An	an	DT
37681	3292	5	excellent	excellent	JJ
37681	3292	6	set	set	NN
37681	3292	7	of	of	IN
37681	3292	8	stereoscopic	stereoscopic	JJ
37681	3292	9	views	view	NNS
37681	3292	10	of	of	IN
37681	3292	11	the	the	DT
37681	3292	12	figures	figure	NNS
37681	3292	13	of	of	IN
37681	3292	14	solid	solid	JJ
37681	3292	15	geometry	geometry	NN
37681	3292	16	,	,	,
37681	3292	17	prepared	prepare	VBN
37681	3292	18	by	by	IN
37681	3292	19	E.	E.	NNP
37681	3292	20	M.	M.	NNP
37681	3292	21	Langley	Langley	NNP
37681	3292	22	of	of	IN
37681	3292	23	Bedford	Bedford	NNP
37681	3292	24	,	,	,
37681	3292	25	England	England	NNP
37681	3292	26	,	,	,
37681	3292	27	is	be	VBZ
37681	3292	28	published	publish	VBN
37681	3292	29	by	by	IN
37681	3292	30	Underwood	Underwood	NNP
37681	3292	31	&	&	CC
37681	3292	32	Underwood	Underwood	NNP
37681	3292	33	,	,	,
37681	3292	34	New	New	NNP
37681	3292	35	York	York	NNP
37681	3292	36	.	.	.
37681	3293	1	Such	such	PDT
37681	3293	2	a	a	DT
37681	3293	3	set	set	NN
37681	3293	4	may	may	MD
37681	3293	5	properly	properly	RB
37681	3293	6	have	have	VB
37681	3293	7	place	place	NN
37681	3293	8	in	in	IN
37681	3293	9	a	a	DT
37681	3293	10	school	school	NN
37681	3293	11	library	library	NN
37681	3293	12	or	or	CC
37681	3293	13	in	in	IN
37681	3293	14	a	a	DT
37681	3293	15	classroom	classroom	NN
37681	3293	16	in	in	IN
37681	3293	17	geometry	geometry	NN
37681	3293	18	,	,	,
37681	3293	19	to	to	TO
37681	3293	20	be	be	VB
37681	3293	21	used	use	VBN
37681	3293	22	when	when	WRB
37681	3293	23	it	-PRON-	PRP
37681	3293	24	seems	seem	VBZ
37681	3293	25	advantageous	advantageous	JJ
37681	3293	26	.	.	.
37681	3294	1	CHAPTER	chapter	NN
37681	3294	2	XX	XX	NNP
37681	3294	3	THE	the	DT
37681	3294	4	LEADING	lead	VBG
37681	3294	5	PROPOSITIONS	proposition	NNS
37681	3294	6	OF	of	IN
37681	3294	7	BOOK	BOOK	NNP
37681	3294	8	VII	VII	NNP
37681	3294	9	Book	Book	NNP
37681	3294	10	VII	VII	NNP
37681	3294	11	relates	relate	VBZ
37681	3294	12	to	to	IN
37681	3294	13	polyhedrons	polyhedron	NNS
37681	3294	14	,	,	,
37681	3294	15	cylinders	cylinder	NNS
37681	3294	16	,	,	,
37681	3294	17	and	and	CC
37681	3294	18	cones	cone	NNS
37681	3294	19	.	.	.
37681	3295	1	It	-PRON-	PRP
37681	3295	2	opens	open	VBZ
37681	3295	3	with	with	IN
37681	3295	4	the	the	DT
37681	3295	5	necessary	necessary	JJ
37681	3295	6	definitions	definition	NNS
37681	3295	7	relating	relate	VBG
37681	3295	8	to	to	IN
37681	3295	9	polyhedrons	polyhedron	NNS
37681	3295	10	,	,	,
37681	3295	11	the	the	DT
37681	3295	12	etymology	etymology	NN
37681	3295	13	of	of	IN
37681	3295	14	the	the	DT
37681	3295	15	terms	term	NNS
37681	3295	16	often	often	RB
37681	3295	17	proving	prove	VBG
37681	3295	18	interesting	interesting	JJ
37681	3295	19	and	and	CC
37681	3295	20	valuable	valuable	JJ
37681	3295	21	when	when	WRB
37681	3295	22	brought	bring	VBN
37681	3295	23	into	into	IN
37681	3295	24	the	the	DT
37681	3295	25	work	work	NN
37681	3295	26	incidentally	incidentally	RB
37681	3295	27	by	by	IN
37681	3295	28	the	the	DT
37681	3295	29	teacher	teacher	NN
37681	3295	30	.	.	.
37681	3296	1	"	"	``
37681	3296	2	Polyhedron	Polyhedron	NNP
37681	3296	3	"	"	''
37681	3296	4	is	be	VBZ
37681	3296	5	from	from	IN
37681	3296	6	the	the	DT
37681	3296	7	Greek	Greek	NNP
37681	3296	8	_	_	NNP
37681	3296	9	polys	polys	NN
37681	3296	10	_	_	NNP
37681	3296	11	(	(	-LRB-
37681	3296	12	many	many	JJ
37681	3296	13	)	)	-RRB-
37681	3296	14	and	and	CC
37681	3296	15	_	_	NNP
37681	3296	16	hedra	hedra	NNP
37681	3296	17	_	_	NNP
37681	3296	18	(	(	-LRB-
37681	3296	19	seat	seat	NN
37681	3296	20	)	)	-RRB-
37681	3296	21	.	.	.
37681	3297	1	The	the	DT
37681	3297	2	Greek	greek	JJ
37681	3297	3	plural	plural	NN
37681	3297	4	,	,	,
37681	3297	5	_	_	NNP
37681	3297	6	polyhedra	polyhedron	NNS
37681	3297	7	_	_	NNP
37681	3297	8	,	,	,
37681	3297	9	is	be	VBZ
37681	3297	10	used	use	VBN
37681	3297	11	in	in	IN
37681	3297	12	early	early	JJ
37681	3297	13	English	english	JJ
37681	3297	14	works	work	NNS
37681	3297	15	,	,	,
37681	3297	16	but	but	CC
37681	3297	17	"	"	``
37681	3297	18	polyhedrons	polyhedron	NNS
37681	3297	19	"	"	''
37681	3297	20	is	be	VBZ
37681	3297	21	the	the	DT
37681	3297	22	form	form	NN
37681	3297	23	now	now	RB
37681	3297	24	more	more	RBR
37681	3297	25	commonly	commonly	RB
37681	3297	26	seen	see	VBN
37681	3297	27	in	in	IN
37681	3297	28	America	America	NNP
37681	3297	29	.	.	.
37681	3298	1	"	"	``
37681	3298	2	Prism	prism	NN
37681	3298	3	"	"	''
37681	3298	4	is	be	VBZ
37681	3298	5	from	from	IN
37681	3298	6	the	the	DT
37681	3298	7	Greek	Greek	NNP
37681	3298	8	_	_	NNP
37681	3298	9	prisma	prisma	NN
37681	3298	10	_	_	NNP
37681	3298	11	(	(	-LRB-
37681	3298	12	something	something	NN
37681	3298	13	sawed	saw	VBN
37681	3298	14	,	,	,
37681	3298	15	like	like	IN
37681	3298	16	a	a	DT
37681	3298	17	piece	piece	NN
37681	3298	18	of	of	IN
37681	3298	19	wood	wood	NN
37681	3298	20	sawed	saw	VBN
37681	3298	21	from	from	IN
37681	3298	22	a	a	DT
37681	3298	23	beam	beam	NN
37681	3298	24	)	)	-RRB-
37681	3298	25	.	.	.
37681	3299	1	"	"	``
37681	3299	2	Lateral	lateral	JJ
37681	3299	3	"	"	''
37681	3299	4	is	be	VBZ
37681	3299	5	from	from	IN
37681	3299	6	the	the	DT
37681	3299	7	Latin	Latin	NNP
37681	3299	8	_	_	NNP
37681	3299	9	latus	latus	NN
37681	3299	10	_	_	NNP
37681	3299	11	(	(	-LRB-
37681	3299	12	side	side	NN
37681	3299	13	)	)	-RRB-
37681	3299	14	.	.	.
37681	3300	1	"	"	``
37681	3300	2	Parallelepiped	Parallelepiped	NNP
37681	3300	3	"	"	''
37681	3300	4	is	be	VBZ
37681	3300	5	from	from	IN
37681	3300	6	the	the	DT
37681	3300	7	Greek	Greek	NNP
37681	3300	8	_	_	NNP
37681	3300	9	parallelos	parallelos	NNP
37681	3300	10	_	_	NNP
37681	3300	11	(	(	-LRB-
37681	3300	12	parallel	parallel	NN
37681	3300	13	)	)	-RRB-
37681	3300	14	and	and	CC
37681	3300	15	_	_	NNP
37681	3300	16	epipedon	epipedon	NNP
37681	3300	17	_	_	NNP
37681	3300	18	(	(	-LRB-
37681	3300	19	a	a	DT
37681	3300	20	plane	plane	NN
37681	3300	21	surface	surface	NN
37681	3300	22	)	)	-RRB-
37681	3300	23	,	,	,
37681	3300	24	from	from	IN
37681	3300	25	_	_	NNP
37681	3300	26	epi	epi	NNP
37681	3300	27	_	_	NNP
37681	3300	28	(	(	-LRB-
37681	3300	29	on	on	RB
37681	3300	30	)	)	-RRB-
37681	3300	31	and	and	CC
37681	3300	32	_	_	NNP
37681	3300	33	pedon	pedon	NNP
37681	3300	34	_	_	NNP
37681	3300	35	(	(	-LRB-
37681	3300	36	ground	ground	NN
37681	3300	37	)	)	-RRB-
37681	3300	38	.	.	.
37681	3301	1	By	by	IN
37681	3301	2	analogy	analogy	NN
37681	3301	3	to	to	IN
37681	3301	4	"	"	``
37681	3301	5	parallelogram	parallelogram	VB
37681	3301	6	"	"	''
37681	3301	7	the	the	DT
37681	3301	8	word	word	NN
37681	3301	9	is	be	VBZ
37681	3301	10	often	often	RB
37681	3301	11	spelled	spell	VBN
37681	3301	12	"	"	''
37681	3301	13	parallelopiped	parallelopipe	VBN
37681	3301	14	,	,	,
37681	3301	15	"	"	''
37681	3301	16	but	but	CC
37681	3301	17	the	the	DT
37681	3301	18	best	good	JJS
37681	3301	19	mathematical	mathematical	JJ
37681	3301	20	works	work	NNS
37681	3301	21	now	now	RB
37681	3301	22	adopt	adopt	VBP
37681	3301	23	the	the	DT
37681	3301	24	etymological	etymological	JJ
37681	3301	25	spelling	spelling	NN
37681	3301	26	above	above	IN
37681	3301	27	given	give	VBN
37681	3301	28	.	.	.
37681	3302	1	"	"	``
37681	3302	2	Truncate	Truncate	NNP
37681	3302	3	"	"	''
37681	3302	4	is	be	VBZ
37681	3302	5	from	from	IN
37681	3302	6	the	the	DT
37681	3302	7	Latin	Latin	NNP
37681	3302	8	_	_	NNP
37681	3302	9	truncare	truncare	NN
37681	3302	10	_	_	NNP
37681	3302	11	(	(	-LRB-
37681	3302	12	to	to	TO
37681	3302	13	cut	cut	VB
37681	3302	14	off	off	RP
37681	3302	15	)	)	-RRB-
37681	3302	16	.	.	.
37681	3303	1	A	a	DT
37681	3303	2	few	few	JJ
37681	3303	3	of	of	IN
37681	3303	4	the	the	DT
37681	3303	5	leading	lead	VBG
37681	3303	6	propositions	proposition	NNS
37681	3303	7	are	be	VBP
37681	3303	8	now	now	RB
37681	3303	9	considered	consider	VBN
37681	3303	10	.	.	.
37681	3304	1	THEOREM	THEOREM	NNP
37681	3304	2	.	.	.
37681	3305	1	_	_	NNP
37681	3305	2	The	the	DT
37681	3305	3	lateral	lateral	JJ
37681	3305	4	area	area	NN
37681	3305	5	of	of	IN
37681	3305	6	a	a	DT
37681	3305	7	prism	prism	NN
37681	3305	8	is	be	VBZ
37681	3305	9	equal	equal	JJ
37681	3305	10	to	to	IN
37681	3305	11	the	the	DT
37681	3305	12	product	product	NN
37681	3305	13	of	of	IN
37681	3305	14	a	a	DT
37681	3305	15	lateral	lateral	JJ
37681	3305	16	edge	edge	NN
37681	3305	17	by	by	IN
37681	3305	18	the	the	DT
37681	3305	19	perimeter	perimeter	NN
37681	3305	20	of	of	IN
37681	3305	21	the	the	DT
37681	3305	22	right	right	JJ
37681	3305	23	section	section	NN
37681	3305	24	.	.	.
37681	3305	25	_	_	NNP
37681	3305	26	It	-PRON-	PRP
37681	3305	27	should	should	MD
37681	3305	28	be	be	VB
37681	3305	29	noted	note	VBN
37681	3305	30	that	that	IN
37681	3305	31	although	although	IN
37681	3305	32	some	some	DT
37681	3305	33	syllabi	syllabi	NN
37681	3305	34	do	do	VBP
37681	3305	35	not	not	RB
37681	3305	36	give	give	VB
37681	3305	37	the	the	DT
37681	3305	38	proposition	proposition	NN
37681	3305	39	that	that	IN
37681	3305	40	parallel	parallel	JJ
37681	3305	41	sections	section	NNS
37681	3305	42	are	be	VBP
37681	3305	43	congruent	congruent	JJ
37681	3305	44	,	,	,
37681	3305	45	this	this	DT
37681	3305	46	is	be	VBZ
37681	3305	47	necessary	necessary	JJ
37681	3305	48	for	for	IN
37681	3305	49	this	this	DT
37681	3305	50	proposition	proposition	NN
37681	3305	51	,	,	,
37681	3305	52	because	because	IN
37681	3305	53	it	-PRON-	PRP
37681	3305	54	shows	show	VBZ
37681	3305	55	that	that	IN
37681	3305	56	the	the	DT
37681	3305	57	right	right	JJ
37681	3305	58	sections	section	NNS
37681	3305	59	are	be	VBP
37681	3305	60	all	all	RB
37681	3305	61	congruent	congruent	JJ
37681	3305	62	and	and	CC
37681	3305	63	hence	hence	RB
37681	3305	64	that	that	IN
37681	3305	65	any	any	DT
37681	3305	66	one	one	CD
37681	3305	67	of	of	IN
37681	3305	68	them	-PRON-	PRP
37681	3305	69	may	may	MD
37681	3305	70	be	be	VB
37681	3305	71	taken	take	VBN
37681	3305	72	.	.	.
37681	3306	1	It	-PRON-	PRP
37681	3306	2	is	be	VBZ
37681	3306	3	,	,	,
37681	3306	4	of	of	IN
37681	3306	5	course	course	NN
37681	3306	6	,	,	,
37681	3306	7	possible	possible	JJ
37681	3306	8	to	to	TO
37681	3306	9	construct	construct	VB
37681	3306	10	a	a	DT
37681	3306	11	prism	prism	NN
37681	3306	12	so	so	RB
37681	3306	13	oblique	oblique	JJ
37681	3306	14	and	and	CC
37681	3306	15	so	so	RB
37681	3306	16	low	low	JJ
37681	3306	17	that	that	IN
37681	3306	18	a	a	DT
37681	3306	19	right	right	JJ
37681	3306	20	section	section	NN
37681	3306	21	,	,	,
37681	3306	22	that	that	RB
37681	3306	23	is	is	RB
37681	3306	24	,	,	,
37681	3306	25	a	a	DT
37681	3306	26	section	section	NN
37681	3306	27	cutting	cut	VBG
37681	3306	28	all	all	PDT
37681	3306	29	the	the	DT
37681	3306	30	lateral	lateral	JJ
37681	3306	31	edges	edge	NNS
37681	3306	32	at	at	IN
37681	3306	33	right	right	JJ
37681	3306	34	angles	angle	NNS
37681	3306	35	,	,	,
37681	3306	36	is	be	VBZ
37681	3306	37	impossible	impossible	JJ
37681	3306	38	.	.	.
37681	3307	1	In	in	IN
37681	3307	2	this	this	DT
37681	3307	3	case	case	NN
37681	3307	4	the	the	DT
37681	3307	5	lateral	lateral	JJ
37681	3307	6	faces	face	NNS
37681	3307	7	must	must	MD
37681	3307	8	be	be	VB
37681	3307	9	extended	extend	VBN
37681	3307	10	,	,	,
37681	3307	11	thus	thus	RB
37681	3307	12	forming	form	VBG
37681	3307	13	what	what	WP
37681	3307	14	is	be	VBZ
37681	3307	15	called	call	VBN
37681	3307	16	a	a	DT
37681	3307	17	_	_	NNP
37681	3307	18	prismatic	prismatic	JJ
37681	3307	19	space	space	NN
37681	3307	20	_	_	NNP
37681	3307	21	.	.	.
37681	3308	1	This	this	DT
37681	3308	2	term	term	NN
37681	3308	3	may	may	MD
37681	3308	4	or	or	CC
37681	3308	5	may	may	MD
37681	3308	6	not	not	RB
37681	3308	7	be	be	VB
37681	3308	8	introduced	introduce	VBN
37681	3308	9	,	,	,
37681	3308	10	depending	depend	VBG
37681	3308	11	upon	upon	IN
37681	3308	12	the	the	DT
37681	3308	13	nature	nature	NN
37681	3308	14	of	of	IN
37681	3308	15	the	the	DT
37681	3308	16	class	class	NN
37681	3308	17	.	.	.
37681	3309	1	This	this	DT
37681	3309	2	proposition	proposition	NN
37681	3309	3	is	be	VBZ
37681	3309	4	one	one	CD
37681	3309	5	of	of	IN
37681	3309	6	the	the	DT
37681	3309	7	most	most	RBS
37681	3309	8	important	important	JJ
37681	3309	9	in	in	IN
37681	3309	10	Book	Book	NNP
37681	3309	11	VII	vii	NN
37681	3309	12	,	,	,
37681	3309	13	because	because	IN
37681	3309	14	it	-PRON-	PRP
37681	3309	15	is	be	VBZ
37681	3309	16	the	the	DT
37681	3309	17	basis	basis	NN
37681	3309	18	of	of	IN
37681	3309	19	the	the	DT
37681	3309	20	mensuration	mensuration	NN
37681	3309	21	of	of	IN
37681	3309	22	the	the	DT
37681	3309	23	cylinder	cylinder	NN
37681	3309	24	as	as	RB
37681	3309	25	well	well	RB
37681	3309	26	as	as	IN
37681	3309	27	the	the	DT
37681	3309	28	prism	prism	NN
37681	3309	29	.	.	.
37681	3310	1	Practical	practical	JJ
37681	3310	2	applications	application	NNS
37681	3310	3	are	be	VBP
37681	3310	4	easily	easily	RB
37681	3310	5	suggested	suggest	VBN
37681	3310	6	in	in	IN
37681	3310	7	connection	connection	NN
37681	3310	8	with	with	IN
37681	3310	9	beams	beam	NNS
37681	3310	10	,	,	,
37681	3310	11	corridors	corridor	NNS
37681	3310	12	,	,	,
37681	3310	13	and	and	CC
37681	3310	14	prismatic	prismatic	JJ
37681	3310	15	columns	column	NNS
37681	3310	16	,	,	,
37681	3310	17	such	such	JJ
37681	3310	18	as	as	IN
37681	3310	19	are	be	VBP
37681	3310	20	often	often	RB
37681	3310	21	seen	see	VBN
37681	3310	22	in	in	IN
37681	3310	23	school	school	NN
37681	3310	24	buildings	building	NNS
37681	3310	25	.	.	.
37681	3311	1	Most	Most	JJS
37681	3311	2	geometries	geometry	NNS
37681	3311	3	supply	supply	VBP
37681	3311	4	sufficient	sufficient	JJ
37681	3311	5	material	material	NN
37681	3311	6	in	in	IN
37681	3311	7	this	this	DT
37681	3311	8	line	line	NN
37681	3311	9	,	,	,
37681	3311	10	however	however	RB
37681	3311	11	.	.	.
37681	3312	1	THEOREM	THEOREM	NNP
37681	3312	2	.	.	.
37681	3313	1	_	_	NNP
37681	3313	2	An	an	DT
37681	3313	3	oblique	oblique	JJ
37681	3313	4	prism	prism	NN
37681	3313	5	is	be	VBZ
37681	3313	6	equivalent	equivalent	JJ
37681	3313	7	to	to	IN
37681	3313	8	a	a	DT
37681	3313	9	right	right	JJ
37681	3313	10	prism	prism	NN
37681	3313	11	whose	whose	WP$
37681	3313	12	base	base	NN
37681	3313	13	is	be	VBZ
37681	3313	14	equal	equal	JJ
37681	3313	15	to	to	IN
37681	3313	16	a	a	DT
37681	3313	17	right	right	JJ
37681	3313	18	section	section	NN
37681	3313	19	of	of	IN
37681	3313	20	the	the	DT
37681	3313	21	oblique	oblique	JJ
37681	3313	22	prism	prism	NN
37681	3313	23	,	,	,
37681	3313	24	and	and	CC
37681	3313	25	whose	whose	WP$
37681	3313	26	altitude	altitude	NN
37681	3313	27	is	be	VBZ
37681	3313	28	equal	equal	JJ
37681	3313	29	to	to	IN
37681	3313	30	a	a	DT
37681	3313	31	lateral	lateral	JJ
37681	3313	32	edge	edge	NN
37681	3313	33	of	of	IN
37681	3313	34	the	the	DT
37681	3313	35	oblique	oblique	JJ
37681	3313	36	prism	prism	NN
37681	3313	37	.	.	.
37681	3313	38	_	_	NNP
37681	3313	39	This	this	DT
37681	3313	40	is	be	VBZ
37681	3313	41	a	a	DT
37681	3313	42	fundamental	fundamental	JJ
37681	3313	43	theorem	theorem	NN
37681	3313	44	leading	lead	VBG
37681	3313	45	up	up	IN
37681	3313	46	to	to	IN
37681	3313	47	the	the	DT
37681	3313	48	mensuration	mensuration	NN
37681	3313	49	of	of	IN
37681	3313	50	the	the	DT
37681	3313	51	prism	prism	NN
37681	3313	52	.	.	.
37681	3314	1	Attention	attention	NN
37681	3314	2	should	should	MD
37681	3314	3	be	be	VB
37681	3314	4	called	call	VBN
37681	3314	5	to	to	IN
37681	3314	6	the	the	DT
37681	3314	7	analogous	analogous	JJ
37681	3314	8	proposition	proposition	NN
37681	3314	9	in	in	IN
37681	3314	10	plane	plane	NN
37681	3314	11	geometry	geometry	NN
37681	3314	12	relating	relate	VBG
37681	3314	13	to	to	IN
37681	3314	14	the	the	DT
37681	3314	15	area	area	NN
37681	3314	16	of	of	IN
37681	3314	17	the	the	DT
37681	3314	18	parallelogram	parallelogram	NN
37681	3314	19	and	and	CC
37681	3314	20	rectangle	rectangle	NN
37681	3314	21	,	,	,
37681	3314	22	and	and	CC
37681	3314	23	to	to	IN
37681	3314	24	the	the	DT
37681	3314	25	fact	fact	NN
37681	3314	26	that	that	IN
37681	3314	27	if	if	IN
37681	3314	28	we	-PRON-	PRP
37681	3314	29	cut	cut	VBD
37681	3314	30	through	through	IN
37681	3314	31	the	the	DT
37681	3314	32	solid	solid	JJ
37681	3314	33	figure	figure	NN
37681	3314	34	by	by	IN
37681	3314	35	a	a	DT
37681	3314	36	plane	plane	NN
37681	3314	37	parallel	parallel	NN
37681	3314	38	to	to	IN
37681	3314	39	one	one	CD
37681	3314	40	of	of	IN
37681	3314	41	the	the	DT
37681	3314	42	lateral	lateral	JJ
37681	3314	43	edges	edge	NNS
37681	3314	44	,	,	,
37681	3314	45	the	the	DT
37681	3314	46	resulting	result	VBG
37681	3314	47	figure	figure	NN
37681	3314	48	will	will	MD
37681	3314	49	be	be	VB
37681	3314	50	that	that	DT
37681	3314	51	of	of	IN
37681	3314	52	the	the	DT
37681	3314	53	proposition	proposition	NN
37681	3314	54	mentioned	mention	VBD
37681	3314	55	.	.	.
37681	3315	1	As	as	IN
37681	3315	2	in	in	IN
37681	3315	3	the	the	DT
37681	3315	4	preceding	precede	VBG
37681	3315	5	proposition	proposition	NN
37681	3315	6	,	,	,
37681	3315	7	so	so	CC
37681	3315	8	in	in	IN
37681	3315	9	this	this	DT
37681	3315	10	case	case	NN
37681	3315	11	,	,	,
37681	3315	12	there	there	EX
37681	3315	13	may	may	MD
37681	3315	14	be	be	VB
37681	3315	15	a	a	DT
37681	3315	16	question	question	NN
37681	3315	17	raised	raise	VBN
37681	3315	18	that	that	WDT
37681	3315	19	will	will	MD
37681	3315	20	make	make	VB
37681	3315	21	it	-PRON-	PRP
37681	3315	22	helpful	helpful	JJ
37681	3315	23	to	to	TO
37681	3315	24	introduce	introduce	VB
37681	3315	25	the	the	DT
37681	3315	26	idea	idea	NN
37681	3315	27	of	of	IN
37681	3315	28	prismatic	prismatic	JJ
37681	3315	29	space	space	NN
37681	3315	30	.	.	.
37681	3316	1	THEOREM	THEOREM	NNP
37681	3316	2	.	.	.
37681	3317	1	_	_	NNP
37681	3317	2	The	the	DT
37681	3317	3	opposite	opposite	JJ
37681	3317	4	lateral	lateral	JJ
37681	3317	5	faces	face	NNS
37681	3317	6	of	of	IN
37681	3317	7	a	a	DT
37681	3317	8	parallelepiped	parallelepipe	VBN
37681	3317	9	are	be	VBP
37681	3317	10	congruent	congruent	JJ
37681	3317	11	and	and	CC
37681	3317	12	parallel	parallel	JJ
37681	3317	13	.	.	.
37681	3317	14	_	_	NNP
37681	3317	15	It	-PRON-	PRP
37681	3317	16	is	be	VBZ
37681	3317	17	desirable	desirable	JJ
37681	3317	18	to	to	TO
37681	3317	19	refer	refer	VB
37681	3317	20	to	to	IN
37681	3317	21	the	the	DT
37681	3317	22	corresponding	corresponding	JJ
37681	3317	23	case	case	NN
37681	3317	24	in	in	IN
37681	3317	25	plane	plane	NN
37681	3317	26	geometry	geometry	NN
37681	3317	27	,	,	,
37681	3317	28	and	and	CC
37681	3317	29	to	to	TO
37681	3317	30	note	note	VB
37681	3317	31	again	again	RB
37681	3317	32	that	that	IN
37681	3317	33	the	the	DT
37681	3317	34	figure	figure	NN
37681	3317	35	is	be	VBZ
37681	3317	36	obtained	obtain	VBN
37681	3317	37	by	by	IN
37681	3317	38	passing	pass	VBG
37681	3317	39	a	a	DT
37681	3317	40	plane	plane	NN
37681	3317	41	through	through	IN
37681	3317	42	the	the	DT
37681	3317	43	parallelepiped	parallelepipe	VBN
37681	3317	44	parallel	parallel	NN
37681	3317	45	to	to	IN
37681	3317	46	a	a	DT
37681	3317	47	lateral	lateral	JJ
37681	3317	48	edge	edge	NN
37681	3317	49	.	.	.
37681	3318	1	The	the	DT
37681	3318	2	same	same	JJ
37681	3318	3	may	may	MD
37681	3318	4	be	be	VB
37681	3318	5	said	say	VBN
37681	3318	6	for	for	IN
37681	3318	7	the	the	DT
37681	3318	8	proposition	proposition	NN
37681	3318	9	about	about	IN
37681	3318	10	the	the	DT
37681	3318	11	diagonal	diagonal	JJ
37681	3318	12	plane	plane	NN
37681	3318	13	of	of	IN
37681	3318	14	a	a	DT
37681	3318	15	parallelepiped	parallelepiped	NN
37681	3318	16	.	.	.
37681	3319	1	These	these	DT
37681	3319	2	two	two	CD
37681	3319	3	propositions	proposition	NNS
37681	3319	4	are	be	VBP
37681	3319	5	fundamental	fundamental	JJ
37681	3319	6	in	in	IN
37681	3319	7	the	the	DT
37681	3319	8	mensuration	mensuration	NN
37681	3319	9	of	of	IN
37681	3319	10	the	the	DT
37681	3319	11	prism	prism	NN
37681	3319	12	.	.	.
37681	3320	1	THEOREM	THEOREM	NNP
37681	3320	2	.	.	.
37681	3321	1	_	_	NNP
37681	3321	2	Two	two	CD
37681	3321	3	rectangular	rectangular	JJ
37681	3321	4	parallelepipeds	parallelepiped	NNS
37681	3321	5	are	be	VBP
37681	3321	6	to	to	IN
37681	3321	7	each	each	DT
37681	3321	8	other	other	JJ
37681	3321	9	as	as	IN
37681	3321	10	the	the	DT
37681	3321	11	products	product	NNS
37681	3321	12	of	of	IN
37681	3321	13	their	-PRON-	PRP$
37681	3321	14	three	three	CD
37681	3321	15	dimensions	dimension	NNS
37681	3321	16	.	.	.
37681	3321	17	_	_	NNP
37681	3321	18	This	this	DT
37681	3321	19	leads	lead	VBZ
37681	3321	20	at	at	IN
37681	3321	21	once	once	RB
37681	3321	22	to	to	IN
37681	3321	23	the	the	DT
37681	3321	24	corollary	corollary	NN
37681	3321	25	that	that	IN
37681	3321	26	the	the	DT
37681	3321	27	volume	volume	NN
37681	3321	28	of	of	IN
37681	3321	29	a	a	DT
37681	3321	30	rectangular	rectangular	JJ
37681	3321	31	parallelepiped	parallelepipe	VBD
37681	3321	32	equals	equal	VBZ
37681	3321	33	the	the	DT
37681	3321	34	product	product	NN
37681	3321	35	of	of	IN
37681	3321	36	its	-PRON-	PRP$
37681	3321	37	three	three	CD
37681	3321	38	dimensions	dimension	NNS
37681	3321	39	,	,	,
37681	3321	40	the	the	DT
37681	3321	41	fundamental	fundamental	JJ
37681	3321	42	law	law	NN
37681	3321	43	in	in	IN
37681	3321	44	the	the	DT
37681	3321	45	mensuration	mensuration	NN
37681	3321	46	of	of	IN
37681	3321	47	all	all	DT
37681	3321	48	solids	solid	NNS
37681	3321	49	.	.	.
37681	3322	1	It	-PRON-	PRP
37681	3322	2	is	be	VBZ
37681	3322	3	preceded	precede	VBN
37681	3322	4	by	by	IN
37681	3322	5	the	the	DT
37681	3322	6	proposition	proposition	NN
37681	3322	7	asserting	assert	VBG
37681	3322	8	that	that	IN
37681	3322	9	rectangular	rectangular	JJ
37681	3322	10	parallelepipeds	parallelepiped	NNS
37681	3322	11	having	have	VBG
37681	3322	12	congruent	congruent	JJ
37681	3322	13	bases	basis	NNS
37681	3322	14	are	be	VBP
37681	3322	15	proportional	proportional	JJ
37681	3322	16	to	to	IN
37681	3322	17	their	-PRON-	PRP$
37681	3322	18	altitudes	altitude	NNS
37681	3322	19	.	.	.
37681	3323	1	This	this	DT
37681	3323	2	includes	include	VBZ
37681	3323	3	the	the	DT
37681	3323	4	incommensurable	incommensurable	JJ
37681	3323	5	case	case	NN
37681	3323	6	,	,	,
37681	3323	7	but	but	CC
37681	3323	8	this	this	DT
37681	3323	9	case	case	NN
37681	3323	10	may	may	MD
37681	3323	11	be	be	VB
37681	3323	12	omitted	omit	VBN
37681	3323	13	.	.	.
37681	3324	1	The	the	DT
37681	3324	2	number	number	NN
37681	3324	3	of	of	IN
37681	3324	4	simple	simple	JJ
37681	3324	5	applications	application	NNS
37681	3324	6	of	of	IN
37681	3324	7	this	this	DT
37681	3324	8	proposition	proposition	NN
37681	3324	9	is	be	VBZ
37681	3324	10	practically	practically	RB
37681	3324	11	unlimited	unlimited	JJ
37681	3324	12	.	.	.
37681	3325	1	In	in	IN
37681	3325	2	all	all	DT
37681	3325	3	such	such	JJ
37681	3325	4	cases	case	NNS
37681	3325	5	it	-PRON-	PRP
37681	3325	6	is	be	VBZ
37681	3325	7	advisable	advisable	JJ
37681	3325	8	to	to	TO
37681	3325	9	take	take	VB
37681	3325	10	a	a	DT
37681	3325	11	considerable	considerable	JJ
37681	3325	12	number	number	NN
37681	3325	13	of	of	IN
37681	3325	14	numerical	numerical	JJ
37681	3325	15	exercises	exercise	NNS
37681	3325	16	in	in	IN
37681	3325	17	order	order	NN
37681	3325	18	to	to	TO
37681	3325	19	fix	fix	VB
37681	3325	20	in	in	IN
37681	3325	21	mind	mind	NN
37681	3325	22	the	the	DT
37681	3325	23	real	real	JJ
37681	3325	24	nature	nature	NN
37681	3325	25	of	of	IN
37681	3325	26	the	the	DT
37681	3325	27	proposition	proposition	NN
37681	3325	28	.	.	.
37681	3326	1	Any	any	DT
37681	3326	2	good	good	JJ
37681	3326	3	geometry	geometry	NN
37681	3326	4	furnishes	furnish	VBZ
37681	3326	5	a	a	DT
37681	3326	6	certain	certain	JJ
37681	3326	7	number	number	NN
37681	3326	8	of	of	IN
37681	3326	9	these	these	DT
37681	3326	10	exercises	exercise	NNS
37681	3326	11	.	.	.
37681	3327	1	The	the	DT
37681	3327	2	following	follow	VBG
37681	3327	3	is	be	VBZ
37681	3327	4	an	an	DT
37681	3327	5	interesting	interesting	JJ
37681	3327	6	property	property	NN
37681	3327	7	of	of	IN
37681	3327	8	the	the	DT
37681	3327	9	rectangular	rectangular	JJ
37681	3327	10	parallelepiped	parallelepipe	VBD
37681	3327	11	,	,	,
37681	3327	12	often	often	RB
37681	3327	13	called	call	VBD
37681	3327	14	the	the	DT
37681	3327	15	rectangular	rectangular	JJ
37681	3327	16	solid	solid	RB
37681	3327	17	:	:	:
37681	3327	18	If	if	IN
37681	3327	19	the	the	DT
37681	3327	20	edges	edge	NNS
37681	3327	21	are	be	VBP
37681	3327	22	_	_	NNP
37681	3327	23	a	a	DT
37681	3327	24	_	_	NNP
37681	3327	25	,	,	,
37681	3327	26	_	_	NNP
37681	3327	27	b	b	NNP
37681	3327	28	_	_	NNP
37681	3327	29	,	,	,
37681	3327	30	and	and	CC
37681	3327	31	_	_	NNP
37681	3327	32	c	c	NNP
37681	3327	33	_	_	NNP
37681	3327	34	,	,	,
37681	3327	35	and	and	CC
37681	3327	36	the	the	DT
37681	3327	37	diagonal	diagonal	JJ
37681	3327	38	is	be	VBZ
37681	3327	39	_	_	NNP
37681	3327	40	d	d	NNP
37681	3327	41	_	_	NNP
37681	3327	42	,	,	,
37681	3327	43	then	then	RB
37681	3327	44	(	(	-LRB-
37681	3327	45	_	_	NNP
37681	3327	46	a_/_d_)^2	a_/_d_)^2	NNP
37681	3327	47	+	+	NFP
37681	3327	48	(	(	-LRB-
37681	3327	49	_	_	NNP
37681	3327	50	b_/_d_)^2	b_/_d_)^2	NNP
37681	3327	51	+	+	NFP
37681	3327	52	(	(	-LRB-
37681	3327	53	_	_	NNP
37681	3327	54	c_/_d_)^2	c_/_d_)^2	NNP
37681	3327	55	=	=	SYM
37681	3327	56	1	1	CD
37681	3327	57	.	.	.
37681	3328	1	This	this	DT
37681	3328	2	property	property	NN
37681	3328	3	is	be	VBZ
37681	3328	4	easily	easily	RB
37681	3328	5	proved	prove	VBN
37681	3328	6	by	by	IN
37681	3328	7	the	the	DT
37681	3328	8	Pythagorean	Pythagorean	NNP
37681	3328	9	Theorem	Theorem	NNP
37681	3328	10	,	,	,
37681	3328	11	for	for	IN
37681	3328	12	_	_	NNP
37681	3328	13	d_^2	d_^2	NNP
37681	3328	14	=	=	SYM
37681	3328	15	_	_	NNP
37681	3328	16	a_^2	a_^2	NNP
37681	3328	17	+	+	SYM
37681	3328	18	_	_	NNP
37681	3328	19	b_^2	b_^2	NNP
37681	3328	20	+	+	NNP
37681	3328	21	_	_	NNP
37681	3328	22	c_^2	c_^2	NNP
37681	3328	23	,	,	,
37681	3328	24	whence	whence	NN
37681	3328	25	(	(	-LRB-
37681	3328	26	_	_	NNP
37681	3328	27	a_^2	a_^2	NNP
37681	3328	28	+	+	SYM
37681	3328	29	_	_	NNP
37681	3328	30	b_^2	b_^2	NNP
37681	3328	31	+	+	NNP
37681	3328	32	_	_	NNP
37681	3328	33	c_^2	c_^2	NNP
37681	3328	34	)	)	-RRB-
37681	3328	35	/	/	NFP
37681	3328	36	_	_	NNP
37681	3328	37	d_^2	d_^2	NNP
37681	3328	38	=	=	SYM
37681	3328	39	1	1	CD
37681	3328	40	.	.	.
37681	3329	1	In	in	IN
37681	3329	2	case	case	NN
37681	3329	3	_	_	NNP
37681	3329	4	c	c	NNP
37681	3329	5	_	_	NNP
37681	3329	6	=	=	SYM
37681	3329	7	0	0	NFP
37681	3329	8	,	,	,
37681	3329	9	this	this	DT
37681	3329	10	reduces	reduce	VBZ
37681	3329	11	to	to	IN
37681	3329	12	the	the	DT
37681	3329	13	Pythagorean	Pythagorean	NNP
37681	3329	14	Theorem	Theorem	NNP
37681	3329	15	.	.	.
37681	3330	1	The	the	DT
37681	3330	2	property	property	NN
37681	3330	3	is	be	VBZ
37681	3330	4	the	the	DT
37681	3330	5	fundamental	fundamental	JJ
37681	3330	6	one	one	CD
37681	3330	7	of	of	IN
37681	3330	8	solid	solid	JJ
37681	3330	9	analytic	analytic	JJ
37681	3330	10	geometry	geometry	NN
37681	3330	11	.	.	.
37681	3331	1	THEOREM	THEOREM	NNP
37681	3331	2	.	.	.
37681	3332	1	_	_	NNP
37681	3332	2	The	the	DT
37681	3332	3	volume	volume	NN
37681	3332	4	of	of	IN
37681	3332	5	any	any	DT
37681	3332	6	parallelepiped	parallelepiped	NN
37681	3332	7	is	be	VBZ
37681	3332	8	equal	equal	JJ
37681	3332	9	to	to	IN
37681	3332	10	the	the	DT
37681	3332	11	product	product	NN
37681	3332	12	of	of	IN
37681	3332	13	its	-PRON-	PRP$
37681	3332	14	base	base	NN
37681	3332	15	by	by	IN
37681	3332	16	its	-PRON-	PRP$
37681	3332	17	altitude	altitude	NN
37681	3332	18	.	.	.
37681	3332	19	_	_	NNP
37681	3332	20	This	this	DT
37681	3332	21	is	be	VBZ
37681	3332	22	one	one	CD
37681	3332	23	of	of	IN
37681	3332	24	the	the	DT
37681	3332	25	few	few	JJ
37681	3332	26	propositions	proposition	NNS
37681	3332	27	in	in	IN
37681	3332	28	Book	Book	NNP
37681	3332	29	VII	VII	NNP
37681	3332	30	where	where	WRB
37681	3332	31	a	a	DT
37681	3332	32	model	model	NN
37681	3332	33	is	be	VBZ
37681	3332	34	of	of	IN
37681	3332	35	any	any	DT
37681	3332	36	advantage	advantage	NN
37681	3332	37	.	.	.
37681	3333	1	It	-PRON-	PRP
37681	3333	2	is	be	VBZ
37681	3333	3	easy	easy	JJ
37681	3333	4	to	to	TO
37681	3333	5	make	make	VB
37681	3333	6	one	one	NN
37681	3333	7	out	out	IN
37681	3333	8	of	of	IN
37681	3333	9	pasteboard	pasteboard	NN
37681	3333	10	,	,	,
37681	3333	11	or	or	CC
37681	3333	12	to	to	TO
37681	3333	13	cut	cut	VB
37681	3333	14	one	one	CD
37681	3333	15	from	from	IN
37681	3333	16	wood	wood	NN
37681	3333	17	.	.	.
37681	3334	1	If	if	IN
37681	3334	2	a	a	DT
37681	3334	3	wooden	wooden	JJ
37681	3334	4	one	one	NN
37681	3334	5	is	be	VBZ
37681	3334	6	made	make	VBN
37681	3334	7	,	,	,
37681	3334	8	it	-PRON-	PRP
37681	3334	9	is	be	VBZ
37681	3334	10	advisable	advisable	JJ
37681	3334	11	to	to	TO
37681	3334	12	take	take	VB
37681	3334	13	an	an	DT
37681	3334	14	oblique	oblique	JJ
37681	3334	15	parallelepiped	parallelepiped	NN
37681	3334	16	and	and	CC
37681	3334	17	,	,	,
37681	3334	18	by	by	IN
37681	3334	19	properly	properly	RB
37681	3334	20	sawing	saw	VBG
37681	3334	21	it	-PRON-	PRP
37681	3334	22	,	,	,
37681	3334	23	to	to	TO
37681	3334	24	transform	transform	VB
37681	3334	25	it	-PRON-	PRP
37681	3334	26	into	into	IN
37681	3334	27	a	a	DT
37681	3334	28	rectangular	rectangular	JJ
37681	3334	29	one	one	NN
37681	3334	30	instead	instead	RB
37681	3334	31	of	of	IN
37681	3334	32	using	use	VBG
37681	3334	33	three	three	CD
37681	3334	34	different	different	JJ
37681	3334	35	solids	solid	NNS
37681	3334	36	.	.	.
37681	3335	1	On	on	IN
37681	3335	2	account	account	NN
37681	3335	3	of	of	IN
37681	3335	4	its	-PRON-	PRP$
37681	3335	5	awkward	awkward	JJ
37681	3335	6	form	form	NN
37681	3335	7	,	,	,
37681	3335	8	this	this	DT
37681	3335	9	figure	figure	NN
37681	3335	10	is	be	VBZ
37681	3335	11	sometimes	sometimes	RB
37681	3335	12	called	call	VBN
37681	3335	13	the	the	DT
37681	3335	14	Devil	Devil	NNP
37681	3335	15	's	's	POS
37681	3335	16	Coffin	Coffin	NNP
37681	3335	17	,	,	,
37681	3335	18	but	but	CC
37681	3335	19	it	-PRON-	PRP
37681	3335	20	is	be	VBZ
37681	3335	21	a	a	DT
37681	3335	22	name	name	NN
37681	3335	23	that	that	IN
37681	3335	24	it	-PRON-	PRP
37681	3335	25	would	would	MD
37681	3335	26	be	be	VB
37681	3335	27	well	well	JJ
37681	3335	28	not	not	RB
37681	3335	29	to	to	TO
37681	3335	30	perpetuate	perpetuate	VB
37681	3335	31	.	.	.
37681	3336	1	THEOREM	THEOREM	NNP
37681	3336	2	.	.	.
37681	3337	1	_	_	NNP
37681	3337	2	The	the	DT
37681	3337	3	volume	volume	NN
37681	3337	4	of	of	IN
37681	3337	5	any	any	DT
37681	3337	6	prism	prism	NN
37681	3337	7	is	be	VBZ
37681	3337	8	equal	equal	JJ
37681	3337	9	to	to	IN
37681	3337	10	the	the	DT
37681	3337	11	product	product	NN
37681	3337	12	of	of	IN
37681	3337	13	its	-PRON-	PRP$
37681	3337	14	base	base	NN
37681	3337	15	by	by	IN
37681	3337	16	its	-PRON-	PRP$
37681	3337	17	altitude	altitude	NN
37681	3337	18	.	.	.
37681	3337	19	_	_	NNP
37681	3337	20	This	this	DT
37681	3337	21	is	be	VBZ
37681	3337	22	also	also	RB
37681	3337	23	one	one	CD
37681	3337	24	of	of	IN
37681	3337	25	the	the	DT
37681	3337	26	basal	basal	NN
37681	3337	27	propositions	proposition	NNS
37681	3337	28	of	of	IN
37681	3337	29	solid	solid	JJ
37681	3337	30	geometry	geometry	NN
37681	3337	31	,	,	,
37681	3337	32	and	and	CC
37681	3337	33	it	-PRON-	PRP
37681	3337	34	has	have	VBZ
37681	3337	35	many	many	JJ
37681	3337	36	applications	application	NNS
37681	3337	37	in	in	IN
37681	3337	38	practical	practical	JJ
37681	3337	39	mensuration	mensuration	NN
37681	3337	40	.	.	.
37681	3338	1	A	a	DT
37681	3338	2	first	first	JJ
37681	3338	3	-	-	HYPH
37681	3338	4	class	class	NN
37681	3338	5	textbook	textbook	NN
37681	3338	6	will	will	MD
37681	3338	7	give	give	VB
37681	3338	8	a	a	DT
37681	3338	9	sufficient	sufficient	JJ
37681	3338	10	list	list	NN
37681	3338	11	of	of	IN
37681	3338	12	problems	problem	NNS
37681	3338	13	involving	involve	VBG
37681	3338	14	numerical	numerical	JJ
37681	3338	15	measurement	measurement	NN
37681	3338	16	,	,	,
37681	3338	17	to	to	TO
37681	3338	18	fix	fix	VB
37681	3338	19	the	the	DT
37681	3338	20	law	law	NN
37681	3338	21	in	in	IN
37681	3338	22	mind	mind	NN
37681	3338	23	.	.	.
37681	3339	1	For	for	IN
37681	3339	2	outdoor	outdoor	JJ
37681	3339	3	work	work	NN
37681	3339	4	,	,	,
37681	3339	5	involving	involve	VBG
37681	3339	6	measurements	measurement	NNS
37681	3339	7	near	near	IN
37681	3339	8	the	the	DT
37681	3339	9	school	school	NN
37681	3339	10	or	or	CC
37681	3339	11	within	within	IN
37681	3339	12	the	the	DT
37681	3339	13	knowledge	knowledge	NN
37681	3339	14	of	of	IN
37681	3339	15	the	the	DT
37681	3339	16	pupils	pupil	NNS
37681	3339	17	,	,	,
37681	3339	18	the	the	DT
37681	3339	19	following	follow	VBG
37681	3339	20	problem	problem	NN
37681	3339	21	is	be	VBZ
37681	3339	22	a	a	DT
37681	3339	23	type	type	NN
37681	3339	24	:	:	:
37681	3339	25	[	[	-LRB-
37681	3339	26	Illustration	illustration	NN
37681	3339	27	]	]	-RRB-
37681	3339	28	If	if	IN
37681	3339	29	this	this	DT
37681	3339	30	represents	represent	VBZ
37681	3339	31	the	the	DT
37681	3339	32	cross	cross	NN
37681	3339	33	section	section	NN
37681	3339	34	of	of	IN
37681	3339	35	a	a	DT
37681	3339	36	railway	railway	NN
37681	3339	37	embankment	embankment	NN
37681	3339	38	that	that	WDT
37681	3339	39	is	be	VBZ
37681	3339	40	_	_	NNP
37681	3339	41	l	l	NNP
37681	3339	42	_	_	NNP
37681	3339	43	feet	foot	NNS
37681	3339	44	long	long	JJ
37681	3339	45	,	,	,
37681	3339	46	_	_	NNP
37681	3339	47	h	h	NNP
37681	3339	48	_	_	NNP
37681	3339	49	feet	foot	NNS
37681	3339	50	high	high	JJ
37681	3339	51	,	,	,
37681	3339	52	_	_	NNP
37681	3339	53	b	b	NNP
37681	3339	54	_	_	NNP
37681	3339	55	feet	foot	NNS
37681	3339	56	wide	wide	JJ
37681	3339	57	at	at	IN
37681	3339	58	the	the	DT
37681	3339	59	bottom	bottom	NN
37681	3339	60	,	,	,
37681	3339	61	and	and	CC
37681	3339	62	_	_	NNP
37681	3339	63	b	b	NNP
37681	3339	64	'	'	``
37681	3339	65	_	_	NNP
37681	3339	66	feet	foot	NNS
37681	3339	67	wide	wide	JJ
37681	3339	68	at	at	IN
37681	3339	69	the	the	DT
37681	3339	70	top	top	NN
37681	3339	71	,	,	,
37681	3339	72	find	find	VB
37681	3339	73	the	the	DT
37681	3339	74	number	number	NN
37681	3339	75	of	of	IN
37681	3339	76	cubic	cubic	JJ
37681	3339	77	feet	foot	NNS
37681	3339	78	in	in	IN
37681	3339	79	the	the	DT
37681	3339	80	embankment	embankment	NN
37681	3339	81	.	.	.
37681	3340	1	Find	find	VB
37681	3340	2	the	the	DT
37681	3340	3	volume	volume	NN
37681	3340	4	if	if	IN
37681	3340	5	_	_	NNP
37681	3340	6	l	l	NNP
37681	3340	7	_	_	NNP
37681	3340	8	=	=	SYM
37681	3340	9	300	300	CD
37681	3340	10	,	,	,
37681	3340	11	_	_	NNP
37681	3340	12	h	h	NNP
37681	3340	13	_	_	NNP
37681	3340	14	=	=	SYM
37681	3340	15	8	8	CD
37681	3340	16	,	,	,
37681	3340	17	_	_	NNP
37681	3340	18	b	b	NNP
37681	3340	19	_	_	NNP
37681	3340	20	=	=	SYM
37681	3340	21	60	60	CD
37681	3340	22	,	,	,
37681	3340	23	and	and	CC
37681	3340	24	_	_	NNP
37681	3340	25	b	b	NNP
37681	3340	26	'	'	''
37681	3340	27	_	_	NNP
37681	3340	28	=	=	SYM
37681	3340	29	28	28	CD
37681	3340	30	.	.	.
37681	3341	1	The	the	DT
37681	3341	2	mensuration	mensuration	NN
37681	3341	3	of	of	IN
37681	3341	4	the	the	DT
37681	3341	5	volume	volume	NN
37681	3341	6	of	of	IN
37681	3341	7	the	the	DT
37681	3341	8	prism	prism	NN
37681	3341	9	,	,	,
37681	3341	10	including	include	VBG
37681	3341	11	the	the	DT
37681	3341	12	rectangular	rectangular	JJ
37681	3341	13	parallelepiped	parallelepiped	NNP
37681	3341	14	and	and	CC
37681	3341	15	cube	cube	NNP
37681	3341	16	,	,	,
37681	3341	17	was	be	VBD
37681	3341	18	known	know	VBN
37681	3341	19	to	to	IN
37681	3341	20	the	the	DT
37681	3341	21	ancients	ancient	NNS
37681	3341	22	.	.	.
37681	3342	1	Euclid	Euclid	NNP
37681	3342	2	was	be	VBD
37681	3342	3	not	not	RB
37681	3342	4	concerned	concern	VBN
37681	3342	5	with	with	IN
37681	3342	6	practical	practical	JJ
37681	3342	7	measurement	measurement	NN
37681	3342	8	,	,	,
37681	3342	9	so	so	IN
37681	3342	10	that	that	IN
37681	3342	11	none	none	NN
37681	3342	12	of	of	IN
37681	3342	13	this	this	DT
37681	3342	14	part	part	NN
37681	3342	15	of	of	IN
37681	3342	16	geometry	geometry	NN
37681	3342	17	appears	appear	VBZ
37681	3342	18	in	in	IN
37681	3342	19	his	-PRON-	PRP$
37681	3342	20	"	"	``
37681	3342	21	Elements	Elements	NNPS
37681	3342	22	.	.	.
37681	3342	23	"	"	''
37681	3343	1	We	-PRON-	PRP
37681	3343	2	find	find	VBP
37681	3343	3	,	,	,
37681	3343	4	however	however	RB
37681	3343	5	,	,	,
37681	3343	6	in	in	IN
37681	3343	7	the	the	DT
37681	3343	8	papyrus	papyrus	NN
37681	3343	9	of	of	IN
37681	3343	10	Ahmes	Ahmes	NNP
37681	3343	11	,	,	,
37681	3343	12	directions	direction	NNS
37681	3343	13	for	for	IN
37681	3343	14	the	the	DT
37681	3343	15	measuring	measuring	NN
37681	3343	16	of	of	IN
37681	3343	17	bins	bin	NNS
37681	3343	18	,	,	,
37681	3343	19	and	and	CC
37681	3343	20	the	the	DT
37681	3343	21	Egyptian	egyptian	JJ
37681	3343	22	builders	builder	NNS
37681	3343	23	,	,	,
37681	3343	24	long	long	RB
37681	3343	25	before	before	IN
37681	3343	26	his	-PRON-	PRP$
37681	3343	27	time	time	NN
37681	3343	28	,	,	,
37681	3343	29	must	must	MD
37681	3343	30	have	have	VB
37681	3343	31	known	know	VBN
37681	3343	32	the	the	DT
37681	3343	33	mensuration	mensuration	NN
37681	3343	34	of	of	IN
37681	3343	35	the	the	DT
37681	3343	36	rectangular	rectangular	JJ
37681	3343	37	parallelepiped	parallelepiped	NNP
37681	3343	38	.	.	.
37681	3344	1	Among	among	IN
37681	3344	2	the	the	DT
37681	3344	3	Hindus	Hindus	NNPS
37681	3344	4	,	,	,
37681	3344	5	long	long	RB
37681	3344	6	before	before	IN
37681	3344	7	the	the	DT
37681	3344	8	Christian	christian	JJ
37681	3344	9	era	era	NN
37681	3344	10	,	,	,
37681	3344	11	rules	rule	NNS
37681	3344	12	were	be	VBD
37681	3344	13	known	know	VBN
37681	3344	14	for	for	IN
37681	3344	15	the	the	DT
37681	3344	16	construction	construction	NN
37681	3344	17	of	of	IN
37681	3344	18	altars	altar	NNS
37681	3344	19	,	,	,
37681	3344	20	and	and	CC
37681	3344	21	among	among	IN
37681	3344	22	the	the	DT
37681	3344	23	Greeks	Greeks	NNPS
37681	3344	24	the	the	DT
37681	3344	25	problem	problem	NN
37681	3344	26	of	of	IN
37681	3344	27	constructing	construct	VBG
37681	3344	28	a	a	DT
37681	3344	29	cube	cube	NN
37681	3344	30	with	with	IN
37681	3344	31	twice	twice	PDT
37681	3344	32	the	the	DT
37681	3344	33	volume	volume	NN
37681	3344	34	of	of	IN
37681	3344	35	a	a	DT
37681	3344	36	given	give	VBN
37681	3344	37	cube	cube	NN
37681	3344	38	(	(	-LRB-
37681	3344	39	the	the	DT
37681	3344	40	"	"	``
37681	3344	41	duplication	duplication	NN
37681	3344	42	of	of	IN
37681	3344	43	the	the	DT
37681	3344	44	cube	cube	NNP
37681	3344	45	"	"	''
37681	3344	46	)	)	-RRB-
37681	3344	47	was	be	VBD
37681	3344	48	attacked	attack	VBN
37681	3344	49	by	by	IN
37681	3344	50	many	many	JJ
37681	3344	51	mathematicians	mathematician	NNS
37681	3344	52	.	.	.
37681	3345	1	The	the	DT
37681	3345	2	solution	solution	NN
37681	3345	3	of	of	IN
37681	3345	4	this	this	DT
37681	3345	5	problem	problem	NN
37681	3345	6	is	be	VBZ
37681	3345	7	impossible	impossible	JJ
37681	3345	8	by	by	IN
37681	3345	9	elementary	elementary	JJ
37681	3345	10	geometry	geometry	NN
37681	3345	11	.	.	.
37681	3346	1	If	if	IN
37681	3346	2	_	_	NNP
37681	3346	3	e	e	NNP
37681	3346	4	_	_	NNP
37681	3346	5	equals	equal	VBZ
37681	3346	6	the	the	DT
37681	3346	7	edge	edge	NN
37681	3346	8	of	of	IN
37681	3346	9	the	the	DT
37681	3346	10	given	give	VBN
37681	3346	11	cube	cube	NN
37681	3346	12	,	,	,
37681	3346	13	then	then	RB
37681	3346	14	_	_	NNP
37681	3346	15	e_^3	e_^3	NNP
37681	3346	16	is	be	VBZ
37681	3346	17	its	-PRON-	PRP$
37681	3346	18	volume	volume	NN
37681	3346	19	and	and	CC
37681	3346	20	2_e_^3	2_e_^3	NN
37681	3346	21	is	be	VBZ
37681	3346	22	the	the	DT
37681	3346	23	volume	volume	NN
37681	3346	24	of	of	IN
37681	3346	25	the	the	DT
37681	3346	26	required	require	VBN
37681	3346	27	cube	cube	NN
37681	3346	28	.	.	.
37681	3347	1	Therefore	therefore	RB
37681	3347	2	the	the	DT
37681	3347	3	edge	edge	NN
37681	3347	4	of	of	IN
37681	3347	5	the	the	DT
37681	3347	6	required	require	VBN
37681	3347	7	cube	cube	NN
37681	3347	8	is	be	VBZ
37681	3347	9	_	_	NNP
37681	3347	10	e_[3root]2	e_[3root]2	NNP
37681	3347	11	.	.	.
37681	3348	1	Now	now	RB
37681	3348	2	if	if	IN
37681	3348	3	_	_	NNP
37681	3348	4	e	e	NNP
37681	3348	5	_	_	NNP
37681	3348	6	is	be	VBZ
37681	3348	7	given	give	VBN
37681	3348	8	,	,	,
37681	3348	9	it	-PRON-	PRP
37681	3348	10	is	be	VBZ
37681	3348	11	not	not	RB
37681	3348	12	possible	possible	JJ
37681	3348	13	with	with	IN
37681	3348	14	the	the	DT
37681	3348	15	straightedge	straightedge	NN
37681	3348	16	and	and	CC
37681	3348	17	compasses	compass	NNS
37681	3348	18	to	to	TO
37681	3348	19	construct	construct	VB
37681	3348	20	a	a	DT
37681	3348	21	line	line	NN
37681	3348	22	equal	equal	JJ
37681	3348	23	to	to	IN
37681	3348	24	_	_	NNP
37681	3348	25	e_[3root]2	e_[3root]2	NNP
37681	3348	26	,	,	,
37681	3348	27	although	although	IN
37681	3348	28	it	-PRON-	PRP
37681	3348	29	is	be	VBZ
37681	3348	30	easy	easy	JJ
37681	3348	31	to	to	TO
37681	3348	32	construct	construct	VB
37681	3348	33	one	one	NN
37681	3348	34	equal	equal	JJ
37681	3348	35	to	to	IN
37681	3348	36	_	_	NNP
37681	3348	37	e_[sqrt]2	e_[sqrt]2	NNP
37681	3348	38	.	.	.
37681	3349	1	The	the	DT
37681	3349	2	study	study	NN
37681	3349	3	of	of	IN
37681	3349	4	the	the	DT
37681	3349	5	pyramid	pyramid	NN
37681	3349	6	begins	begin	VBZ
37681	3349	7	at	at	IN
37681	3349	8	this	this	DT
37681	3349	9	point	point	NN
37681	3349	10	.	.	.
37681	3350	1	In	in	IN
37681	3350	2	practical	practical	JJ
37681	3350	3	measurement	measurement	NN
37681	3350	4	we	-PRON-	PRP
37681	3350	5	usually	usually	RB
37681	3350	6	meet	meet	VBP
37681	3350	7	the	the	DT
37681	3350	8	regular	regular	JJ
37681	3350	9	pyramid	pyramid	NN
37681	3350	10	.	.	.
37681	3351	1	It	-PRON-	PRP
37681	3351	2	is	be	VBZ
37681	3351	3	,	,	,
37681	3351	4	however	however	RB
37681	3351	5	,	,	,
37681	3351	6	a	a	DT
37681	3351	7	simple	simple	JJ
37681	3351	8	matter	matter	NN
37681	3351	9	to	to	TO
37681	3351	10	consider	consider	VB
37681	3351	11	the	the	DT
37681	3351	12	oblique	oblique	JJ
37681	3351	13	pyramid	pyramid	NN
37681	3351	14	as	as	RB
37681	3351	15	well	well	RB
37681	3351	16	,	,	,
37681	3351	17	and	and	CC
37681	3351	18	in	in	IN
37681	3351	19	measuring	measure	VBG
37681	3351	20	volumes	volume	NNS
37681	3351	21	we	-PRON-	PRP
37681	3351	22	sometimes	sometimes	RB
37681	3351	23	find	find	VBP
37681	3351	24	these	these	DT
37681	3351	25	forms	form	NNS
37681	3351	26	.	.	.
37681	3352	1	THEOREM	THEOREM	NNP
37681	3352	2	.	.	.
37681	3353	1	_	_	NNP
37681	3353	2	The	the	DT
37681	3353	3	lateral	lateral	JJ
37681	3353	4	area	area	NN
37681	3353	5	of	of	IN
37681	3353	6	a	a	DT
37681	3353	7	regular	regular	JJ
37681	3353	8	pyramid	pyramid	NN
37681	3353	9	is	be	VBZ
37681	3353	10	equal	equal	JJ
37681	3353	11	to	to	IN
37681	3353	12	half	half	PDT
37681	3353	13	the	the	DT
37681	3353	14	product	product	NN
37681	3353	15	of	of	IN
37681	3353	16	its	-PRON-	PRP$
37681	3353	17	slant	slant	NN
37681	3353	18	height	height	NN
37681	3353	19	by	by	IN
37681	3353	20	the	the	DT
37681	3353	21	perimeter	perimeter	NN
37681	3353	22	of	of	IN
37681	3353	23	its	-PRON-	PRP$
37681	3353	24	base	base	NN
37681	3353	25	.	.	.
37681	3353	26	_	_	NNP
37681	3353	27	This	this	DT
37681	3353	28	leads	lead	VBZ
37681	3353	29	to	to	IN
37681	3353	30	the	the	DT
37681	3353	31	corollary	corollary	NN
37681	3353	32	concerning	concern	VBG
37681	3353	33	the	the	DT
37681	3353	34	lateral	lateral	JJ
37681	3353	35	area	area	NN
37681	3353	36	of	of	IN
37681	3353	37	the	the	DT
37681	3353	38	frustum	frustum	NN
37681	3353	39	of	of	IN
37681	3353	40	a	a	DT
37681	3353	41	regular	regular	JJ
37681	3353	42	pyramid	pyramid	NN
37681	3353	43	.	.	.
37681	3354	1	It	-PRON-	PRP
37681	3354	2	should	should	MD
37681	3354	3	be	be	VB
37681	3354	4	noticed	notice	VBN
37681	3354	5	that	that	IN
37681	3354	6	the	the	DT
37681	3354	7	regular	regular	JJ
37681	3354	8	pyramid	pyramid	NN
37681	3354	9	may	may	MD
37681	3354	10	be	be	VB
37681	3354	11	considered	consider	VBN
37681	3354	12	as	as	IN
37681	3354	13	a	a	DT
37681	3354	14	frustum	frustum	NN
37681	3354	15	with	with	IN
37681	3354	16	the	the	DT
37681	3354	17	upper	upper	JJ
37681	3354	18	base	base	NN
37681	3354	19	zero	zero	CD
37681	3354	20	,	,	,
37681	3354	21	and	and	CC
37681	3354	22	the	the	DT
37681	3354	23	proposition	proposition	NN
37681	3354	24	as	as	IN
37681	3354	25	a	a	DT
37681	3354	26	special	special	JJ
37681	3354	27	case	case	NN
37681	3354	28	under	under	IN
37681	3354	29	the	the	DT
37681	3354	30	corollary	corollary	NN
37681	3354	31	.	.	.
37681	3355	1	It	-PRON-	PRP
37681	3355	2	is	be	VBZ
37681	3355	3	also	also	RB
37681	3355	4	possible	possible	JJ
37681	3355	5	,	,	,
37681	3355	6	if	if	IN
37681	3355	7	we	-PRON-	PRP
37681	3355	8	choose	choose	VBP
37681	3355	9	,	,	,
37681	3355	10	to	to	TO
37681	3355	11	let	let	VB
37681	3355	12	the	the	DT
37681	3355	13	upper	upper	JJ
37681	3355	14	base	base	NN
37681	3355	15	of	of	IN
37681	3355	16	the	the	DT
37681	3355	17	frustum	frustum	NN
37681	3355	18	pass	pass	VB
37681	3355	19	through	through	IN
37681	3355	20	the	the	DT
37681	3355	21	vertex	vertex	NN
37681	3355	22	and	and	CC
37681	3355	23	cut	cut	VBD
37681	3355	24	the	the	DT
37681	3355	25	lateral	lateral	JJ
37681	3355	26	edges	edge	NNS
37681	3355	27	above	above	IN
37681	3355	28	that	that	DT
37681	3355	29	point	point	NN
37681	3355	30	,	,	,
37681	3355	31	although	although	IN
37681	3355	32	this	this	DT
37681	3355	33	is	be	VBZ
37681	3355	34	too	too	RB
37681	3355	35	complicated	complicated	JJ
37681	3355	36	for	for	IN
37681	3355	37	most	most	JJS
37681	3355	38	pupils	pupil	NNS
37681	3355	39	.	.	.
37681	3356	1	If	if	IN
37681	3356	2	this	this	DT
37681	3356	3	case	case	NN
37681	3356	4	is	be	VBZ
37681	3356	5	considered	consider	VBN
37681	3356	6	,	,	,
37681	3356	7	it	-PRON-	PRP
37681	3356	8	is	be	VBZ
37681	3356	9	well	well	JJ
37681	3356	10	to	to	TO
37681	3356	11	bring	bring	VB
37681	3356	12	in	in	RP
37681	3356	13	the	the	DT
37681	3356	14	general	general	JJ
37681	3356	15	idea	idea	NN
37681	3356	16	of	of	IN
37681	3356	17	_	_	NNP
37681	3356	18	pyramidal	pyramidal	NN
37681	3356	19	space	space	NN
37681	3356	20	_	_	NNP
37681	3356	21	,	,	,
37681	3356	22	the	the	DT
37681	3356	23	infinite	infinite	JJ
37681	3356	24	space	space	NN
37681	3356	25	bounded	bound	VBN
37681	3356	26	on	on	IN
37681	3356	27	several	several	JJ
37681	3356	28	sides	side	NNS
37681	3356	29	by	by	IN
37681	3356	30	the	the	DT
37681	3356	31	lateral	lateral	JJ
37681	3356	32	faces	face	NNS
37681	3356	33	,	,	,
37681	3356	34	of	of	IN
37681	3356	35	the	the	DT
37681	3356	36	pyramid	pyramid	NN
37681	3356	37	.	.	.
37681	3357	1	This	this	DT
37681	3357	2	pyramidal	pyramidal	NN
37681	3357	3	space	space	NN
37681	3357	4	is	be	VBZ
37681	3357	5	double	double	JJ
37681	3357	6	,	,	,
37681	3357	7	extending	extend	VBG
37681	3357	8	on	on	IN
37681	3357	9	two	two	CD
37681	3357	10	sides	side	NNS
37681	3357	11	of	of	IN
37681	3357	12	the	the	DT
37681	3357	13	vertex	vertex	NN
37681	3357	14	.	.	.
37681	3358	1	THEOREM	THEOREM	NNP
37681	3358	2	.	.	.
37681	3359	1	_	_	XX
37681	3359	2	If	if	IN
37681	3359	3	a	a	DT
37681	3359	4	pyramid	pyramid	NN
37681	3359	5	is	be	VBZ
37681	3359	6	cut	cut	VBN
37681	3359	7	by	by	IN
37681	3359	8	a	a	DT
37681	3359	9	plane	plane	NN
37681	3359	10	parallel	parallel	NN
37681	3359	11	to	to	IN
37681	3359	12	the	the	DT
37681	3359	13	base	base	NN
37681	3359	14	:	:	:
37681	3359	15	_	_	NNP
37681	3359	16	1	1	CD
37681	3359	17	.	.	.
37681	3360	1	_	_	NNP
37681	3360	2	The	the	DT
37681	3360	3	edges	edge	NNS
37681	3360	4	and	and	CC
37681	3360	5	altitude	altitude	NN
37681	3360	6	are	be	VBP
37681	3360	7	divided	divide	VBN
37681	3360	8	proportionally	proportionally	RB
37681	3360	9	.	.	.
37681	3360	10	_	_	NNP
37681	3360	11	2	2	CD
37681	3360	12	.	.	.
37681	3361	1	_	_	NNP
37681	3361	2	The	the	DT
37681	3361	3	section	section	NN
37681	3361	4	is	be	VBZ
37681	3361	5	a	a	DT
37681	3361	6	polygon	polygon	NN
37681	3361	7	similar	similar	JJ
37681	3361	8	to	to	IN
37681	3361	9	the	the	DT
37681	3361	10	base	base	NN
37681	3361	11	.	.	.
37681	3361	12	_	_	NNP
37681	3361	13	To	to	TO
37681	3361	14	get	get	VB
37681	3361	15	the	the	DT
37681	3361	16	analogous	analogous	JJ
37681	3361	17	proposition	proposition	NN
37681	3361	18	of	of	IN
37681	3361	19	plane	plane	NN
37681	3361	20	geometry	geometry	NN
37681	3361	21	,	,	,
37681	3361	22	pass	pass	VB
37681	3361	23	a	a	DT
37681	3361	24	plane	plane	NN
37681	3361	25	through	through	IN
37681	3361	26	the	the	DT
37681	3361	27	vertex	vertex	NN
37681	3361	28	so	so	IN
37681	3361	29	as	as	IN
37681	3361	30	to	to	TO
37681	3361	31	cut	cut	VB
37681	3361	32	the	the	DT
37681	3361	33	base	base	NN
37681	3361	34	.	.	.
37681	3362	1	We	-PRON-	PRP
37681	3362	2	shall	shall	MD
37681	3362	3	then	then	RB
37681	3362	4	have	have	VB
37681	3362	5	the	the	DT
37681	3362	6	sides	side	NNS
37681	3362	7	and	and	CC
37681	3362	8	altitude	altitude	NN
37681	3362	9	of	of	IN
37681	3362	10	the	the	DT
37681	3362	11	triangle	triangle	NN
37681	3362	12	divided	divide	VBN
37681	3362	13	proportionally	proportionally	RB
37681	3362	14	,	,	,
37681	3362	15	and	and	CC
37681	3362	16	of	of	IN
37681	3362	17	course	course	NN
37681	3362	18	the	the	DT
37681	3362	19	section	section	NN
37681	3362	20	will	will	MD
37681	3362	21	merely	merely	RB
37681	3362	22	be	be	VB
37681	3362	23	a	a	DT
37681	3362	24	line	line	NN
37681	3362	25	-	-	HYPH
37681	3362	26	segment	segment	NN
37681	3362	27	,	,	,
37681	3362	28	and	and	CC
37681	3362	29	therefore	therefore	RB
37681	3362	30	it	-PRON-	PRP
37681	3362	31	is	be	VBZ
37681	3362	32	similar	similar	JJ
37681	3362	33	to	to	IN
37681	3362	34	the	the	DT
37681	3362	35	base	base	NN
37681	3362	36	line	line	NN
37681	3362	37	.	.	.
37681	3363	1	The	the	DT
37681	3363	2	cutting	cut	VBG
37681	3363	3	plane	plane	NN
37681	3363	4	may	may	MD
37681	3363	5	pass	pass	VB
37681	3363	6	through	through	IN
37681	3363	7	the	the	DT
37681	3363	8	vertex	vertex	NN
37681	3363	9	,	,	,
37681	3363	10	or	or	CC
37681	3363	11	it	-PRON-	PRP
37681	3363	12	may	may	MD
37681	3363	13	cut	cut	VB
37681	3363	14	the	the	DT
37681	3363	15	pyramidal	pyramidal	JJ
37681	3363	16	space	space	NN
37681	3363	17	above	above	IN
37681	3363	18	the	the	DT
37681	3363	19	vertex	vertex	NN
37681	3363	20	.	.	.
37681	3364	1	In	in	IN
37681	3364	2	either	either	DT
37681	3364	3	case	case	NN
37681	3364	4	the	the	DT
37681	3364	5	proof	proof	NN
37681	3364	6	is	be	VBZ
37681	3364	7	essentially	essentially	RB
37681	3364	8	the	the	DT
37681	3364	9	same	same	JJ
37681	3364	10	.	.	.
37681	3365	1	THEOREM	THEOREM	NNP
37681	3365	2	.	.	.
37681	3366	1	_	_	NNP
37681	3366	2	The	the	DT
37681	3366	3	volume	volume	NN
37681	3366	4	of	of	IN
37681	3366	5	a	a	DT
37681	3366	6	triangular	triangular	JJ
37681	3366	7	pyramid	pyramid	NN
37681	3366	8	is	be	VBZ
37681	3366	9	equal	equal	JJ
37681	3366	10	to	to	IN
37681	3366	11	one	one	CD
37681	3366	12	third	third	NN
37681	3366	13	of	of	IN
37681	3366	14	the	the	DT
37681	3366	15	product	product	NN
37681	3366	16	of	of	IN
37681	3366	17	its	-PRON-	PRP$
37681	3366	18	base	base	NN
37681	3366	19	by	by	IN
37681	3366	20	its	-PRON-	PRP$
37681	3366	21	altitude	altitude	NN
37681	3366	22	,	,	,
37681	3366	23	and	and	CC
37681	3366	24	this	this	DT
37681	3366	25	is	be	VBZ
37681	3366	26	also	also	RB
37681	3366	27	true	true	JJ
37681	3366	28	of	of	IN
37681	3366	29	any	any	DT
37681	3366	30	pyramid	pyramid	NN
37681	3366	31	.	.	.
37681	3366	32	_	_	NNP
37681	3366	33	This	this	DT
37681	3366	34	is	be	VBZ
37681	3366	35	stated	state	VBN
37681	3366	36	as	as	IN
37681	3366	37	two	two	CD
37681	3366	38	theorems	theorem	NNS
37681	3366	39	in	in	IN
37681	3366	40	all	all	DT
37681	3366	41	textbooks	textbook	NNS
37681	3366	42	,	,	,
37681	3366	43	and	and	CC
37681	3366	44	properly	properly	RB
37681	3366	45	so	so	RB
37681	3366	46	.	.	.
37681	3367	1	It	-PRON-	PRP
37681	3367	2	is	be	VBZ
37681	3367	3	explained	explain	VBN
37681	3367	4	to	to	IN
37681	3367	5	children	child	NNS
37681	3367	6	who	who	WP
37681	3367	7	are	be	VBP
37681	3367	8	studying	study	VBG
37681	3367	9	arithmetic	arithmetic	JJ
37681	3367	10	by	by	IN
37681	3367	11	means	mean	NNS
37681	3367	12	of	of	IN
37681	3367	13	a	a	DT
37681	3367	14	hollow	hollow	JJ
37681	3367	15	pyramid	pyramid	NN
37681	3367	16	and	and	CC
37681	3367	17	a	a	DT
37681	3367	18	hollow	hollow	JJ
37681	3367	19	prism	prism	NN
37681	3367	20	of	of	IN
37681	3367	21	equal	equal	JJ
37681	3367	22	base	base	NN
37681	3367	23	and	and	CC
37681	3367	24	equal	equal	JJ
37681	3367	25	altitude	altitude	NN
37681	3367	26	.	.	.
37681	3368	1	The	the	DT
37681	3368	2	pyramid	pyramid	NN
37681	3368	3	is	be	VBZ
37681	3368	4	filled	fill	VBN
37681	3368	5	with	with	IN
37681	3368	6	sand	sand	NN
37681	3368	7	or	or	CC
37681	3368	8	grain	grain	NN
37681	3368	9	,	,	,
37681	3368	10	and	and	CC
37681	3368	11	the	the	DT
37681	3368	12	contents	content	NNS
37681	3368	13	is	be	VBZ
37681	3368	14	poured	pour	VBN
37681	3368	15	into	into	IN
37681	3368	16	the	the	DT
37681	3368	17	prism	prism	NN
37681	3368	18	.	.	.
37681	3369	1	This	this	DT
37681	3369	2	is	be	VBZ
37681	3369	3	repeated	repeat	VBN
37681	3369	4	,	,	,
37681	3369	5	and	and	CC
37681	3369	6	again	again	RB
37681	3369	7	repeated	repeat	VBN
37681	3369	8	,	,	,
37681	3369	9	showing	show	VBG
37681	3369	10	that	that	IN
37681	3369	11	the	the	DT
37681	3369	12	volume	volume	NN
37681	3369	13	of	of	IN
37681	3369	14	the	the	DT
37681	3369	15	prism	prism	NN
37681	3369	16	is	be	VBZ
37681	3369	17	three	three	CD
37681	3369	18	times	time	NNS
37681	3369	19	the	the	DT
37681	3369	20	volume	volume	NN
37681	3369	21	of	of	IN
37681	3369	22	the	the	DT
37681	3369	23	pyramid	pyramid	NN
37681	3369	24	.	.	.
37681	3370	1	It	-PRON-	PRP
37681	3370	2	sometimes	sometimes	RB
37681	3370	3	varies	vary	VBZ
37681	3370	4	the	the	DT
37681	3370	5	work	work	NN
37681	3370	6	to	to	TO
37681	3370	7	show	show	VB
37681	3370	8	this	this	DT
37681	3370	9	to	to	IN
37681	3370	10	a	a	DT
37681	3370	11	class	class	NN
37681	3370	12	in	in	IN
37681	3370	13	geometry	geometry	NN
37681	3370	14	.	.	.
37681	3371	1	This	this	DT
37681	3371	2	proposition	proposition	NN
37681	3371	3	was	be	VBD
37681	3371	4	first	first	RB
37681	3371	5	proved	prove	VBN
37681	3371	6	,	,	,
37681	3371	7	so	so	RB
37681	3371	8	Archimedes	Archimedes	NNP
37681	3371	9	asserts	assert	VBZ
37681	3371	10	,	,	,
37681	3371	11	by	by	IN
37681	3371	12	Eudoxus	Eudoxus	NNP
37681	3371	13	of	of	IN
37681	3371	14	Cnidus	Cnidus	NNP
37681	3371	15	,	,	,
37681	3371	16	famous	famous	JJ
37681	3371	17	as	as	IN
37681	3371	18	an	an	DT
37681	3371	19	astronomer	astronomer	NN
37681	3371	20	,	,	,
37681	3371	21	geometer	geometer	NN
37681	3371	22	,	,	,
37681	3371	23	physician	physician	NN
37681	3371	24	,	,	,
37681	3371	25	and	and	CC
37681	3371	26	lawgiver	lawgiver	NNP
37681	3371	27	,	,	,
37681	3371	28	born	bear	VBN
37681	3371	29	in	in	IN
37681	3371	30	humble	humble	JJ
37681	3371	31	circumstances	circumstance	NNS
37681	3371	32	about	about	IN
37681	3371	33	407	407	CD
37681	3371	34	B.C.	B.C.	NNS
37681	3372	1	He	-PRON-	PRP
37681	3372	2	studied	study	VBD
37681	3372	3	at	at	IN
37681	3372	4	Athens	Athens	NNP
37681	3372	5	and	and	CC
37681	3372	6	in	in	IN
37681	3372	7	Egypt	Egypt	NNP
37681	3372	8	,	,	,
37681	3372	9	and	and	CC
37681	3372	10	founded	found	VBD
37681	3372	11	a	a	DT
37681	3372	12	famous	famous	JJ
37681	3372	13	school	school	NN
37681	3372	14	of	of	IN
37681	3372	15	geometry	geometry	NN
37681	3372	16	at	at	IN
37681	3372	17	Cyzicus	Cyzicus	NNP
37681	3372	18	.	.	.
37681	3373	1	His	-PRON-	PRP$
37681	3373	2	discovery	discovery	NN
37681	3373	3	also	also	RB
37681	3373	4	extended	extend	VBD
37681	3373	5	to	to	IN
37681	3373	6	the	the	DT
37681	3373	7	volume	volume	NN
37681	3373	8	of	of	IN
37681	3373	9	the	the	DT
37681	3373	10	cone	cone	NN
37681	3373	11	,	,	,
37681	3373	12	and	and	CC
37681	3373	13	it	-PRON-	PRP
37681	3373	14	was	be	VBD
37681	3373	15	his	-PRON-	PRP$
37681	3373	16	work	work	NN
37681	3373	17	that	that	WDT
37681	3373	18	gave	give	VBD
37681	3373	19	the	the	DT
37681	3373	20	beginning	beginning	NN
37681	3373	21	to	to	IN
37681	3373	22	the	the	DT
37681	3373	23	science	science	NN
37681	3373	24	of	of	IN
37681	3373	25	stereometry	stereometry	NN
37681	3373	26	,	,	,
37681	3373	27	the	the	DT
37681	3373	28	mensuration	mensuration	NN
37681	3373	29	part	part	NN
37681	3373	30	of	of	IN
37681	3373	31	solid	solid	JJ
37681	3373	32	geometry	geometry	NN
37681	3373	33	.	.	.
37681	3374	1	THEOREM	THEOREM	NNP
37681	3374	2	.	.	.
37681	3375	1	_	_	NNP
37681	3375	2	The	the	DT
37681	3375	3	volume	volume	NN
37681	3375	4	of	of	IN
37681	3375	5	the	the	DT
37681	3375	6	frustum	frustum	NN
37681	3375	7	of	of	IN
37681	3375	8	any	any	DT
37681	3375	9	pyramid	pyramid	NN
37681	3375	10	is	be	VBZ
37681	3375	11	equal	equal	JJ
37681	3375	12	to	to	IN
37681	3375	13	the	the	DT
37681	3375	14	sum	sum	NN
37681	3375	15	of	of	IN
37681	3375	16	the	the	DT
37681	3375	17	volumes	volume	NNS
37681	3375	18	of	of	IN
37681	3375	19	three	three	CD
37681	3375	20	pyramids	pyramid	NNS
37681	3375	21	whose	whose	WP$
37681	3375	22	common	common	JJ
37681	3375	23	altitude	altitude	NN
37681	3375	24	is	be	VBZ
37681	3375	25	the	the	DT
37681	3375	26	altitude	altitude	NN
37681	3375	27	of	of	IN
37681	3375	28	the	the	DT
37681	3375	29	frustum	frustum	NN
37681	3375	30	,	,	,
37681	3375	31	and	and	CC
37681	3375	32	whose	whose	WP$
37681	3375	33	bases	basis	NNS
37681	3375	34	are	be	VBP
37681	3375	35	the	the	DT
37681	3375	36	lower	low	JJR
37681	3375	37	base	base	NN
37681	3375	38	,	,	,
37681	3375	39	the	the	DT
37681	3375	40	upper	upper	JJ
37681	3375	41	base	base	NN
37681	3375	42	,	,	,
37681	3375	43	and	and	CC
37681	3375	44	the	the	DT
37681	3375	45	mean	mean	NN
37681	3375	46	proportional	proportional	JJ
37681	3375	47	between	between	IN
37681	3375	48	the	the	DT
37681	3375	49	bases	basis	NNS
37681	3375	50	of	of	IN
37681	3375	51	the	the	DT
37681	3375	52	frustum	frustum	NN
37681	3375	53	.	.	.
37681	3375	54	_	_	NNP
37681	3375	55	Attention	attention	NN
37681	3375	56	should	should	MD
37681	3375	57	be	be	VB
37681	3375	58	called	call	VBN
37681	3375	59	to	to	IN
37681	3375	60	the	the	DT
37681	3375	61	fact	fact	NN
37681	3375	62	that	that	IN
37681	3375	63	this	this	DT
37681	3375	64	formula	formula	NN
37681	3375	65	_	_	NNP
37681	3375	66	v	v	NNP
37681	3375	67	_	_	NNP
37681	3375	68	=	=	SYM
37681	3375	69	1/3	1/3	CD
37681	3375	70	_	_	NNP
37681	3375	71	a_(_b	a_(_b	NNP
37681	3375	72	_	_	NNP
37681	3375	73	+	+	SYM
37681	3375	74	_	_	NNP
37681	3375	75	b	b	NNP
37681	3375	76	'	'	``
37681	3375	77	_	_	NN
37681	3375	78	+	+	CC
37681	3375	79	[	[	-LRB-
37681	3375	80	sqrt](_bb	sqrt](_bb	NNP
37681	3375	81	'	'	``
37681	3375	82	_	_	NNP
37681	3375	83	)	)	-RRB-
37681	3375	84	)	)	-RRB-
37681	3375	85	applies	apply	VBZ
37681	3375	86	to	to	IN
37681	3375	87	the	the	DT
37681	3375	88	pyramid	pyramid	NN
37681	3375	89	by	by	IN
37681	3375	90	letting	let	VBG
37681	3375	91	_	_	NNP
37681	3375	92	b	b	NNP
37681	3375	93	'	'	``
37681	3375	94	_	_	NNP
37681	3375	95	=	=	SYM
37681	3375	96	0	0	CD
37681	3375	97	,	,	,
37681	3375	98	to	to	IN
37681	3375	99	the	the	DT
37681	3375	100	prism	prism	NN
37681	3375	101	by	by	IN
37681	3375	102	letting	let	VBG
37681	3375	103	_	_	NNP
37681	3375	104	b	b	NNP
37681	3375	105	_	_	NNP
37681	3375	106	=	=	SYM
37681	3375	107	_	_	NNP
37681	3375	108	b	b	NNP
37681	3375	109	'	'	``
37681	3375	110	_	_	NNP
37681	3375	111	,	,	,
37681	3375	112	and	and	CC
37681	3375	113	also	also	RB
37681	3375	114	to	to	IN
37681	3375	115	the	the	DT
37681	3375	116	parallelepiped	parallelepiped	NNP
37681	3375	117	and	and	CC
37681	3375	118	cube	cube	NN
37681	3375	119	,	,	,
37681	3375	120	these	these	DT
37681	3375	121	being	be	VBG
37681	3375	122	special	special	JJ
37681	3375	123	forms	form	NNS
37681	3375	124	of	of	IN
37681	3375	125	the	the	DT
37681	3375	126	prism	prism	NN
37681	3375	127	.	.	.
37681	3376	1	This	this	DT
37681	3376	2	formula	formula	NN
37681	3376	3	is	be	VBZ
37681	3376	4	,	,	,
37681	3376	5	therefore	therefore	RB
37681	3376	6	,	,	,
37681	3376	7	a	a	DT
37681	3376	8	very	very	RB
37681	3376	9	general	general	JJ
37681	3376	10	one	one	NN
37681	3376	11	,	,	,
37681	3376	12	relating	relate	VBG
37681	3376	13	to	to	IN
37681	3376	14	all	all	PDT
37681	3376	15	the	the	DT
37681	3376	16	polyhedrons	polyhedron	NNS
37681	3376	17	that	that	WDT
37681	3376	18	are	be	VBP
37681	3376	19	commonly	commonly	RB
37681	3376	20	met	meet	VBN
37681	3376	21	in	in	IN
37681	3376	22	mensuration	mensuration	NN
37681	3376	23	.	.	.
37681	3377	1	THEOREM	THEOREM	NNP
37681	3377	2	.	.	.
37681	3378	1	_	_	NNP
37681	3378	2	There	there	EX
37681	3378	3	can	can	MD
37681	3378	4	not	not	RB
37681	3378	5	be	be	VB
37681	3378	6	more	more	JJR
37681	3378	7	than	than	IN
37681	3378	8	five	five	CD
37681	3378	9	regular	regular	JJ
37681	3378	10	convex	convex	NNS
37681	3378	11	polyhedrons	polyhedron	NNS
37681	3378	12	.	.	.
37681	3378	13	_	_	NNP
37681	3378	14	Eudemus	Eudemus	NNP
37681	3378	15	of	of	IN
37681	3378	16	Rhodes	Rhodes	NNP
37681	3378	17	,	,	,
37681	3378	18	one	one	CD
37681	3378	19	of	of	IN
37681	3378	20	the	the	DT
37681	3378	21	principal	principal	JJ
37681	3378	22	pupils	pupil	NNS
37681	3378	23	of	of	IN
37681	3378	24	Aristotle	Aristotle	NNP
37681	3378	25	,	,	,
37681	3378	26	in	in	IN
37681	3378	27	his	-PRON-	PRP$
37681	3378	28	history	history	NN
37681	3378	29	of	of	IN
37681	3378	30	geometry	geometry	NN
37681	3378	31	of	of	IN
37681	3378	32	which	which	WDT
37681	3378	33	Proclus	Proclus	NNP
37681	3378	34	preserves	preserve	VBZ
37681	3378	35	some	some	DT
37681	3378	36	fragments	fragment	NNS
37681	3378	37	,	,	,
37681	3378	38	tells	tell	VBZ
37681	3378	39	us	-PRON-	PRP
37681	3378	40	that	that	IN
37681	3378	41	Pythagoras	Pythagoras	NNP
37681	3378	42	discovered	discover	VBD
37681	3378	43	the	the	DT
37681	3378	44	construction	construction	NN
37681	3378	45	of	of	IN
37681	3378	46	the	the	DT
37681	3378	47	"	"	``
37681	3378	48	mundane	mundane	JJ
37681	3378	49	figures	figure	NNS
37681	3378	50	,	,	,
37681	3378	51	"	"	''
37681	3378	52	meaning	mean	VBG
37681	3378	53	the	the	DT
37681	3378	54	five	five	CD
37681	3378	55	regular	regular	JJ
37681	3378	56	polyhedrons	polyhedron	NNS
37681	3378	57	.	.	.
37681	3379	1	Iamblichus	Iamblichus	NNP
37681	3379	2	speaks	speak	VBZ
37681	3379	3	of	of	IN
37681	3379	4	the	the	DT
37681	3379	5	discovery	discovery	NN
37681	3379	6	of	of	IN
37681	3379	7	the	the	DT
37681	3379	8	dodecahedron	dodecahedron	NN
37681	3379	9	in	in	IN
37681	3379	10	these	these	DT
37681	3379	11	words	word	NNS
37681	3379	12	:	:	:
37681	3379	13	As	as	IN
37681	3379	14	to	to	IN
37681	3379	15	Hippasus	Hippasus	NNP
37681	3379	16	,	,	,
37681	3379	17	who	who	WP
37681	3379	18	was	be	VBD
37681	3379	19	a	a	DT
37681	3379	20	Pythagorean	Pythagorean	NNP
37681	3379	21	,	,	,
37681	3379	22	they	-PRON-	PRP
37681	3379	23	say	say	VBP
37681	3379	24	that	that	IN
37681	3379	25	he	-PRON-	PRP
37681	3379	26	perished	perish	VBD
37681	3379	27	in	in	IN
37681	3379	28	the	the	DT
37681	3379	29	sea	sea	NN
37681	3379	30	on	on	IN
37681	3379	31	account	account	NN
37681	3379	32	of	of	IN
37681	3379	33	his	-PRON-	PRP$
37681	3379	34	impiety	impiety	NN
37681	3379	35	,	,	,
37681	3379	36	inasmuch	inasmuch	JJ
37681	3379	37	as	as	IN
37681	3379	38	he	-PRON-	PRP
37681	3379	39	boasted	boast	VBD
37681	3379	40	that	that	IN
37681	3379	41	he	-PRON-	PRP
37681	3379	42	first	first	RB
37681	3379	43	divulged	divulge	VBD
37681	3379	44	the	the	DT
37681	3379	45	knowledge	knowledge	NN
37681	3379	46	of	of	IN
37681	3379	47	the	the	DT
37681	3379	48	sphere	sphere	NN
37681	3379	49	with	with	IN
37681	3379	50	the	the	DT
37681	3379	51	twelve	twelve	CD
37681	3379	52	pentagons	pentagon	NNS
37681	3379	53	.	.	.
37681	3380	1	Hippasus	Hippasus	NNP
37681	3380	2	assumed	assume	VBD
37681	3380	3	the	the	DT
37681	3380	4	glory	glory	NN
37681	3380	5	of	of	IN
37681	3380	6	the	the	DT
37681	3380	7	discovery	discovery	NN
37681	3380	8	to	to	IN
37681	3380	9	himself	-PRON-	PRP
37681	3380	10	,	,	,
37681	3380	11	whereas	whereas	IN
37681	3380	12	everything	everything	NN
37681	3380	13	belongs	belong	VBZ
37681	3380	14	to	to	IN
37681	3380	15	Him	-PRON-	PRP
37681	3380	16	,	,	,
37681	3380	17	for	for	IN
37681	3380	18	thus	thus	RB
37681	3380	19	they	-PRON-	PRP
37681	3380	20	designate	designate	VBP
37681	3380	21	Pythagoras	Pythagoras	NNP
37681	3380	22	,	,	,
37681	3380	23	and	and	CC
37681	3380	24	do	do	VBP
37681	3380	25	not	not	RB
37681	3380	26	call	call	VB
37681	3380	27	Him	-PRON-	PRP
37681	3380	28	by	by	IN
37681	3380	29	name	name	NN
37681	3380	30	.	.	.
37681	3381	1	Iamblichus	Iamblichus	NNP
37681	3381	2	here	here	RB
37681	3381	3	refers	refer	VBZ
37681	3381	4	to	to	IN
37681	3381	5	the	the	DT
37681	3381	6	dodecahedron	dodecahedron	NN
37681	3381	7	inscribed	inscribe	VBN
37681	3381	8	in	in	IN
37681	3381	9	the	the	DT
37681	3381	10	sphere	sphere	NN
37681	3381	11	.	.	.
37681	3382	1	The	the	DT
37681	3382	2	Pythagoreans	Pythagoreans	NNPS
37681	3382	3	looked	look	VBD
37681	3382	4	upon	upon	IN
37681	3382	5	these	these	DT
37681	3382	6	five	five	CD
37681	3382	7	solids	solid	NNS
37681	3382	8	as	as	IN
37681	3382	9	fundamental	fundamental	JJ
37681	3382	10	forms	form	NNS
37681	3382	11	in	in	IN
37681	3382	12	the	the	DT
37681	3382	13	structure	structure	NN
37681	3382	14	of	of	IN
37681	3382	15	the	the	DT
37681	3382	16	universe	universe	NN
37681	3382	17	.	.	.
37681	3383	1	In	in	IN
37681	3383	2	particular	particular	JJ
37681	3383	3	Plato	Plato	NNP
37681	3383	4	tells	tell	VBZ
37681	3383	5	us	-PRON-	PRP
37681	3383	6	that	that	IN
37681	3383	7	they	-PRON-	PRP
37681	3383	8	asserted	assert	VBD
37681	3383	9	that	that	IN
37681	3383	10	the	the	DT
37681	3383	11	four	four	CD
37681	3383	12	elements	element	NNS
37681	3383	13	of	of	IN
37681	3383	14	the	the	DT
37681	3383	15	real	real	JJ
37681	3383	16	world	world	NN
37681	3383	17	were	be	VBD
37681	3383	18	the	the	DT
37681	3383	19	tetrahedron	tetrahedron	JJ
37681	3383	20	,	,	,
37681	3383	21	octahedron	octahedron	NNP
37681	3383	22	,	,	,
37681	3383	23	icosahedron	icosahedron	NNP
37681	3383	24	,	,	,
37681	3383	25	and	and	CC
37681	3383	26	cube	cube	NN
37681	3383	27	,	,	,
37681	3383	28	and	and	CC
37681	3383	29	Plutarch	Plutarch	NNP
37681	3383	30	ascribes	ascribe	VBZ
37681	3383	31	this	this	DT
37681	3383	32	doctrine	doctrine	NN
37681	3383	33	to	to	IN
37681	3383	34	Pythagoras	Pythagoras	NNP
37681	3383	35	himself	-PRON-	PRP
37681	3383	36	.	.	.
37681	3384	1	Philolaus	Philolaus	NNP
37681	3384	2	,	,	,
37681	3384	3	who	who	WP
37681	3384	4	lived	live	VBD
37681	3384	5	in	in	IN
37681	3384	6	the	the	DT
37681	3384	7	fifth	fifth	JJ
37681	3384	8	century	century	NN
37681	3384	9	B.C.	B.C.	NNP
37681	3384	10	,	,	,
37681	3384	11	held	hold	VBD
37681	3384	12	that	that	IN
37681	3384	13	the	the	DT
37681	3384	14	elementary	elementary	JJ
37681	3384	15	nature	nature	NN
37681	3384	16	of	of	IN
37681	3384	17	bodies	body	NNS
37681	3384	18	depended	depend	VBD
37681	3384	19	on	on	IN
37681	3384	20	their	-PRON-	PRP$
37681	3384	21	form	form	NN
37681	3384	22	.	.	.
37681	3385	1	The	the	DT
37681	3385	2	tetrahedron	tetrahedron	NN
37681	3385	3	was	be	VBD
37681	3385	4	assigned	assign	VBN
37681	3385	5	to	to	IN
37681	3385	6	fire	fire	NN
37681	3385	7	,	,	,
37681	3385	8	the	the	DT
37681	3385	9	octahedron	octahedron	NN
37681	3385	10	to	to	IN
37681	3385	11	air	air	NN
37681	3385	12	,	,	,
37681	3385	13	the	the	DT
37681	3385	14	icosahedron	icosahedron	NN
37681	3385	15	to	to	IN
37681	3385	16	water	water	NN
37681	3385	17	,	,	,
37681	3385	18	and	and	CC
37681	3385	19	the	the	DT
37681	3385	20	cube	cube	NN
37681	3385	21	to	to	IN
37681	3385	22	earth	earth	NN
37681	3385	23	,	,	,
37681	3385	24	it	-PRON-	PRP
37681	3385	25	being	be	VBG
37681	3385	26	asserted	assert	VBN
37681	3385	27	that	that	IN
37681	3385	28	the	the	DT
37681	3385	29	smallest	small	JJS
37681	3385	30	constituent	constituent	JJ
37681	3385	31	part	part	NN
37681	3385	32	of	of	IN
37681	3385	33	each	each	DT
37681	3385	34	of	of	IN
37681	3385	35	these	these	DT
37681	3385	36	substances	substance	NNS
37681	3385	37	had	have	VBD
37681	3385	38	the	the	DT
37681	3385	39	form	form	NN
37681	3385	40	here	here	RB
37681	3385	41	assigned	assign	VBN
37681	3385	42	to	to	IN
37681	3385	43	it	-PRON-	PRP
37681	3385	44	.	.	.
37681	3386	1	Although	although	IN
37681	3386	2	Eudemus	Eudemus	NNP
37681	3386	3	attributes	attribute	VBZ
37681	3386	4	all	all	DT
37681	3386	5	five	five	CD
37681	3386	6	to	to	IN
37681	3386	7	Pythagoras	Pythagoras	NNP
37681	3386	8	,	,	,
37681	3386	9	it	-PRON-	PRP
37681	3386	10	is	be	VBZ
37681	3386	11	certain	certain	JJ
37681	3386	12	that	that	IN
37681	3386	13	the	the	DT
37681	3386	14	tetrahedron	tetrahedron	NN
37681	3386	15	,	,	,
37681	3386	16	cube	cube	NN
37681	3386	17	,	,	,
37681	3386	18	and	and	CC
37681	3386	19	octahedron	octahedron	NNP
37681	3386	20	were	be	VBD
37681	3386	21	known	know	VBN
37681	3386	22	to	to	IN
37681	3386	23	the	the	DT
37681	3386	24	Egyptians	Egyptians	NNPS
37681	3386	25	,	,	,
37681	3386	26	since	since	IN
37681	3386	27	they	-PRON-	PRP
37681	3386	28	appear	appear	VBP
37681	3386	29	in	in	IN
37681	3386	30	their	-PRON-	PRP$
37681	3386	31	architectural	architectural	JJ
37681	3386	32	decorations	decoration	NNS
37681	3386	33	.	.	.
37681	3387	1	These	these	DT
37681	3387	2	solids	solid	NNS
37681	3387	3	were	be	VBD
37681	3387	4	studied	study	VBN
37681	3387	5	so	so	RB
37681	3387	6	extensively	extensively	RB
37681	3387	7	in	in	IN
37681	3387	8	the	the	DT
37681	3387	9	school	school	NN
37681	3387	10	of	of	IN
37681	3387	11	Plato	Plato	NNP
37681	3387	12	that	that	IN
37681	3387	13	Proclus	Proclus	NNP
37681	3387	14	also	also	RB
37681	3387	15	speaks	speak	VBZ
37681	3387	16	of	of	IN
37681	3387	17	them	-PRON-	PRP
37681	3387	18	as	as	IN
37681	3387	19	the	the	DT
37681	3387	20	Platonic	platonic	JJ
37681	3387	21	bodies	body	NNS
37681	3387	22	,	,	,
37681	3387	23	saying	say	VBG
37681	3387	24	that	that	IN
37681	3387	25	Euclid	Euclid	NNP
37681	3387	26	"	"	''
37681	3387	27	proposed	propose	VBD
37681	3387	28	to	to	IN
37681	3387	29	himself	-PRON-	PRP
37681	3387	30	the	the	DT
37681	3387	31	construction	construction	NN
37681	3387	32	of	of	IN
37681	3387	33	the	the	DT
37681	3387	34	so	so	RB
37681	3387	35	-	-	HYPH
37681	3387	36	called	call	VBN
37681	3387	37	Platonic	platonic	JJ
37681	3387	38	bodies	body	NNS
37681	3387	39	as	as	IN
37681	3387	40	the	the	DT
37681	3387	41	final	final	JJ
37681	3387	42	aim	aim	NN
37681	3387	43	of	of	IN
37681	3387	44	his	-PRON-	PRP$
37681	3387	45	arrangement	arrangement	NN
37681	3387	46	of	of	IN
37681	3387	47	the	the	DT
37681	3387	48	'	'	``
37681	3387	49	Elements	Elements	NNPS
37681	3387	50	.	.	.
37681	3387	51	'	'	''
37681	3387	52	"	"	''
37681	3388	1	Aristæus	Aristæus	NNP
37681	3388	2	,	,	,
37681	3388	3	probably	probably	RB
37681	3388	4	a	a	DT
37681	3388	5	little	little	JJ
37681	3388	6	older	old	JJR
37681	3388	7	than	than	IN
37681	3388	8	Euclid	Euclid	NNP
37681	3388	9	,	,	,
37681	3388	10	wrote	write	VBD
37681	3388	11	a	a	DT
37681	3388	12	book	book	NN
37681	3388	13	upon	upon	IN
37681	3388	14	these	these	DT
37681	3388	15	solids	solid	NNS
37681	3388	16	.	.	.
37681	3389	1	As	as	IN
37681	3389	2	an	an	DT
37681	3389	3	interesting	interesting	JJ
37681	3389	4	amplification	amplification	NN
37681	3389	5	of	of	IN
37681	3389	6	this	this	DT
37681	3389	7	proposition	proposition	NN
37681	3389	8	,	,	,
37681	3389	9	the	the	DT
37681	3389	10	centers	center	NNS
37681	3389	11	of	of	IN
37681	3389	12	the	the	DT
37681	3389	13	faces	face	NNS
37681	3389	14	(	(	-LRB-
37681	3389	15	squares	square	NNS
37681	3389	16	)	)	-RRB-
37681	3389	17	of	of	IN
37681	3389	18	a	a	DT
37681	3389	19	cube	cube	NN
37681	3389	20	may	may	MD
37681	3389	21	be	be	VB
37681	3389	22	connected	connect	VBN
37681	3389	23	,	,	,
37681	3389	24	an	an	DT
37681	3389	25	inscribed	inscribed	JJ
37681	3389	26	octahedron	octahedron	NN
37681	3389	27	being	be	VBG
37681	3389	28	thereby	thereby	RB
37681	3389	29	formed	form	VBN
37681	3389	30	.	.	.
37681	3390	1	Furthermore	furthermore	RB
37681	3390	2	,	,	,
37681	3390	3	if	if	IN
37681	3390	4	the	the	DT
37681	3390	5	vertices	vertex	NNS
37681	3390	6	of	of	IN
37681	3390	7	the	the	DT
37681	3390	8	cube	cube	NN
37681	3390	9	are	be	VBP
37681	3390	10	_	_	NNP
37681	3390	11	A	A	NNP
37681	3390	12	_	_	NNP
37681	3390	13	,	,	,
37681	3390	14	_	_	NNP
37681	3390	15	B	B	NNP
37681	3390	16	_	_	NNP
37681	3390	17	,	,	,
37681	3390	18	_	_	NNP
37681	3390	19	C	C	NNP
37681	3390	20	_	_	NNP
37681	3390	21	,	,	,
37681	3390	22	_	_	NNP
37681	3390	23	D	D	NNP
37681	3390	24	_	_	NNP
37681	3390	25	,	,	,
37681	3390	26	_	_	NNP
37681	3390	27	A	A	NNP
37681	3390	28	'	'	''
37681	3390	29	_	_	NNP
37681	3390	30	,	,	,
37681	3390	31	_	_	NNP
37681	3390	32	B	B	NNP
37681	3390	33	'	'	''
37681	3390	34	_	_	NNP
37681	3390	35	,	,	,
37681	3390	36	_	_	NNP
37681	3390	37	C	C	NNP
37681	3390	38	'	'	''
37681	3390	39	_	_	NNP
37681	3390	40	,	,	,
37681	3390	41	_	_	NNP
37681	3390	42	D	D	NNP
37681	3390	43	'	'	''
37681	3390	44	_	_	NNP
37681	3390	45	,	,	,
37681	3390	46	then	then	RB
37681	3390	47	by	by	IN
37681	3390	48	drawing	draw	VBG
37681	3390	49	_	_	NNP
37681	3390	50	AC	AC	NNP
37681	3390	51	_	_	NNP
37681	3390	52	,	,	,
37681	3390	53	_	_	NNP
37681	3390	54	CD	CD	NNP
37681	3390	55	'	'	POS
37681	3390	56	_	_	NNP
37681	3390	57	,	,	,
37681	3390	58	_	_	NNP
37681	3390	59	D'A	D'A	NNP
37681	3390	60	_	_	NNP
37681	3390	61	,	,	,
37681	3390	62	_	_	NNP
37681	3390	63	D'B	D'B	NNP
37681	3390	64	'	'	''
37681	3390	65	_	_	NNP
37681	3390	66	,	,	,
37681	3390	67	_	_	NNP
37681	3390	68	B'A	B'A	NNP
37681	3390	69	_	_	NNP
37681	3390	70	,	,	,
37681	3390	71	and	and	CC
37681	3390	72	_	_	NNP
37681	3390	73	B'C	B'C	NNP
37681	3390	74	_	_	NNP
37681	3390	75	,	,	,
37681	3390	76	a	a	DT
37681	3390	77	regular	regular	JJ
37681	3390	78	tetrahedron	tetrahedron	NN
37681	3390	79	will	will	MD
37681	3390	80	be	be	VB
37681	3390	81	formed	form	VBN
37681	3390	82	.	.	.
37681	3391	1	Since	since	IN
37681	3391	2	the	the	DT
37681	3391	3	construction	construction	NN
37681	3391	4	of	of	IN
37681	3391	5	the	the	DT
37681	3391	6	cube	cube	NN
37681	3391	7	is	be	VBZ
37681	3391	8	a	a	DT
37681	3391	9	simple	simple	JJ
37681	3391	10	matter	matter	NN
37681	3391	11	,	,	,
37681	3391	12	this	this	DT
37681	3391	13	shows	show	VBZ
37681	3391	14	how	how	WRB
37681	3391	15	three	three	CD
37681	3391	16	of	of	IN
37681	3391	17	the	the	DT
37681	3391	18	five	five	CD
37681	3391	19	regular	regular	JJ
37681	3391	20	solids	solid	NNS
37681	3391	21	may	may	MD
37681	3391	22	be	be	VB
37681	3391	23	constructed	construct	VBN
37681	3391	24	.	.	.
37681	3392	1	The	the	DT
37681	3392	2	actual	actual	JJ
37681	3392	3	construction	construction	NN
37681	3392	4	of	of	IN
37681	3392	5	the	the	DT
37681	3392	6	solids	solid	NNS
37681	3392	7	is	be	VBZ
37681	3392	8	not	not	RB
37681	3392	9	suited	suit	VBN
37681	3392	10	to	to	IN
37681	3392	11	elementary	elementary	JJ
37681	3392	12	geometry	geometry	NN
37681	3392	13	.	.	.
37681	3393	1	[	[	-LRB-
37681	3393	2	89	89	CD
37681	3393	3	]	]	-RRB-
37681	3393	4	It	-PRON-	PRP
37681	3393	5	is	be	VBZ
37681	3393	6	not	not	RB
37681	3393	7	difficult	difficult	JJ
37681	3393	8	for	for	IN
37681	3393	9	a	a	DT
37681	3393	10	class	class	NN
37681	3393	11	to	to	TO
37681	3393	12	find	find	VB
37681	3393	13	the	the	DT
37681	3393	14	relative	relative	JJ
37681	3393	15	areas	area	NNS
37681	3393	16	of	of	IN
37681	3393	17	the	the	DT
37681	3393	18	cube	cube	NNP
37681	3393	19	and	and	CC
37681	3393	20	the	the	DT
37681	3393	21	inscribed	inscribed	JJ
37681	3393	22	tetrahedron	tetrahedron	JJ
37681	3393	23	and	and	CC
37681	3393	24	octahedron	octahedron	NNP
37681	3393	25	.	.	.
37681	3394	1	If	if	IN
37681	3394	2	_	_	NNP
37681	3394	3	s	s	NNP
37681	3394	4	_	_	NNP
37681	3394	5	is	be	VBZ
37681	3394	6	the	the	DT
37681	3394	7	side	side	NN
37681	3394	8	of	of	IN
37681	3394	9	the	the	DT
37681	3394	10	cube	cube	NN
37681	3394	11	,	,	,
37681	3394	12	these	these	DT
37681	3394	13	areas	area	NNS
37681	3394	14	are	be	VBP
37681	3394	15	6_s_^2	6_s_^2	CD
37681	3394	16	,	,	,
37681	3394	17	(	(	-LRB-
37681	3394	18	1/2)_s_^2[sqrt]3	1/2)_s_^2[sqrt]3	CD
37681	3394	19	,	,	,
37681	3394	20	and	and	CC
37681	3394	21	_	_	NNP
37681	3394	22	s_^2[sqrt]3	s_^2[sqrt]3	NN
37681	3394	23	;	;	:
37681	3394	24	that	that	RB
37681	3394	25	is	is	RB
37681	3394	26	,	,	,
37681	3394	27	the	the	DT
37681	3394	28	area	area	NN
37681	3394	29	of	of	IN
37681	3394	30	the	the	DT
37681	3394	31	octahedron	octahedron	NN
37681	3394	32	is	be	VBZ
37681	3394	33	twice	twice	PDT
37681	3394	34	that	that	DT
37681	3394	35	of	of	IN
37681	3394	36	the	the	DT
37681	3394	37	tetrahedron	tetrahedron	NN
37681	3394	38	inscribed	inscribe	VBN
37681	3394	39	in	in	IN
37681	3394	40	the	the	DT
37681	3394	41	cube	cube	NN
37681	3394	42	.	.	.
37681	3395	1	Somewhat	somewhat	RB
37681	3395	2	related	related	JJ
37681	3395	3	to	to	IN
37681	3395	4	the	the	DT
37681	3395	5	preceding	precede	VBG
37681	3395	6	paragraph	paragraph	NN
37681	3395	7	is	be	VBZ
37681	3395	8	the	the	DT
37681	3395	9	fact	fact	NN
37681	3395	10	that	that	IN
37681	3395	11	the	the	DT
37681	3395	12	edges	edge	NNS
37681	3395	13	of	of	IN
37681	3395	14	the	the	DT
37681	3395	15	five	five	CD
37681	3395	16	regular	regular	JJ
37681	3395	17	solids	solid	NNS
37681	3395	18	are	be	VBP
37681	3395	19	incommensurable	incommensurable	JJ
37681	3395	20	with	with	IN
37681	3395	21	the	the	DT
37681	3395	22	radius	radius	NN
37681	3395	23	of	of	IN
37681	3395	24	the	the	DT
37681	3395	25	circumscribed	circumscribed	NNP
37681	3395	26	sphere	sphere	NN
37681	3395	27	.	.	.
37681	3396	1	This	this	DT
37681	3396	2	fact	fact	NN
37681	3396	3	seems	seem	VBZ
37681	3396	4	to	to	TO
37681	3396	5	have	have	VB
37681	3396	6	been	be	VBN
37681	3396	7	known	know	VBN
37681	3396	8	to	to	IN
37681	3396	9	the	the	DT
37681	3396	10	Greeks	Greeks	NNPS
37681	3396	11	,	,	,
37681	3396	12	perhaps	perhaps	RB
37681	3396	13	to	to	IN
37681	3396	14	Theætetus	Theætetus	NNP
37681	3396	15	(	(	-LRB-
37681	3396	16	_	_	NNP
37681	3396	17	ca	ca	NNP
37681	3396	18	.	.	.
37681	3396	19	_	_	NNP
37681	3396	20	400	400	CD
37681	3396	21	B.C.	B.C.	NNP
37681	3396	22	)	)	-RRB-
37681	3397	1	and	and	CC
37681	3397	2	Aristæus	Aristæus	NNP
37681	3397	3	(	(	-LRB-
37681	3397	4	_	_	NNP
37681	3397	5	ca	ca	NNP
37681	3397	6	.	.	.
37681	3397	7	_	_	NNP
37681	3397	8	300	300	CD
37681	3397	9	B.C.	B.C.	NNP
37681	3398	1	)	)	-RRB-
37681	3398	2	,	,	,
37681	3398	3	both	both	DT
37681	3398	4	of	of	IN
37681	3398	5	whom	whom	WP
37681	3398	6	wrote	write	VBD
37681	3398	7	on	on	IN
37681	3398	8	incommensurables	incommensurable	NNS
37681	3398	9	.	.	.
37681	3399	1	Just	just	RB
37681	3399	2	as	as	IN
37681	3399	3	we	-PRON-	PRP
37681	3399	4	may	may	MD
37681	3399	5	produce	produce	VB
37681	3399	6	the	the	DT
37681	3399	7	sides	side	NNS
37681	3399	8	of	of	IN
37681	3399	9	a	a	DT
37681	3399	10	regular	regular	JJ
37681	3399	11	polygon	polygon	NN
37681	3399	12	and	and	CC
37681	3399	13	form	form	VB
37681	3399	14	a	a	DT
37681	3399	15	regular	regular	JJ
37681	3399	16	cross	cross	NN
37681	3399	17	polygon	polygon	NN
37681	3399	18	or	or	CC
37681	3399	19	stellar	stellar	JJ
37681	3399	20	polygon	polygon	NN
37681	3399	21	,	,	,
37681	3399	22	so	so	IN
37681	3399	23	we	-PRON-	PRP
37681	3399	24	may	may	MD
37681	3399	25	have	have	VB
37681	3399	26	stellar	stellar	JJ
37681	3399	27	polyhedrons	polyhedron	NNS
37681	3399	28	.	.	.
37681	3400	1	Kepler	Kepler	NNP
37681	3400	2	,	,	,
37681	3400	3	the	the	DT
37681	3400	4	great	great	JJ
37681	3400	5	astronomer	astronomer	NN
37681	3400	6	,	,	,
37681	3400	7	constructed	construct	VBD
37681	3400	8	some	some	DT
37681	3400	9	of	of	IN
37681	3400	10	these	these	DT
37681	3400	11	solids	solid	NNS
37681	3400	12	in	in	IN
37681	3400	13	1619	1619	CD
37681	3400	14	,	,	,
37681	3400	15	and	and	CC
37681	3400	16	Poinsot	Poinsot	NNP
37681	3400	17	,	,	,
37681	3400	18	a	a	DT
37681	3400	19	French	french	JJ
37681	3400	20	mathematician	mathematician	NN
37681	3400	21	,	,	,
37681	3400	22	carried	carry	VBD
37681	3400	23	the	the	DT
37681	3400	24	constructions	construction	NNS
37681	3400	25	so	so	RB
37681	3400	26	far	far	RB
37681	3400	27	in	in	IN
37681	3400	28	1801	1801	CD
37681	3400	29	that	that	IN
37681	3400	30	several	several	JJ
37681	3400	31	of	of	IN
37681	3400	32	these	these	DT
37681	3400	33	stellar	stellar	JJ
37681	3400	34	polyhedrons	polyhedron	NNS
37681	3400	35	are	be	VBP
37681	3400	36	known	know	VBN
37681	3400	37	as	as	IN
37681	3400	38	Poinsot	Poinsot	NNP
37681	3400	39	solids	solid	NNS
37681	3400	40	.	.	.
37681	3401	1	There	there	EX
37681	3401	2	is	be	VBZ
37681	3401	3	a	a	DT
37681	3401	4	very	very	RB
37681	3401	5	extensive	extensive	JJ
37681	3401	6	literature	literature	NN
37681	3401	7	upon	upon	IN
37681	3401	8	this	this	DT
37681	3401	9	subject	subject	NN
37681	3401	10	.	.	.
37681	3402	1	The	the	DT
37681	3402	2	following	follow	VBG
37681	3402	3	table	table	NN
37681	3402	4	may	may	MD
37681	3402	5	be	be	VB
37681	3402	6	of	of	IN
37681	3402	7	some	some	DT
37681	3402	8	service	service	NN
37681	3402	9	in	in	IN
37681	3402	10	assigning	assigning	NN
37681	3402	11	problems	problem	NNS
37681	3402	12	in	in	IN
37681	3402	13	mensuration	mensuration	NN
37681	3402	14	in	in	IN
37681	3402	15	connection	connection	NN
37681	3402	16	with	with	IN
37681	3402	17	the	the	DT
37681	3402	18	regular	regular	JJ
37681	3402	19	polyhedrons	polyhedron	NNS
37681	3402	20	,	,	,
37681	3402	21	although	although	IN
37681	3402	22	some	some	DT
37681	3402	23	of	of	IN
37681	3402	24	the	the	DT
37681	3402	25	formulas	formula	NNS
37681	3402	26	are	be	VBP
37681	3402	27	too	too	RB
37681	3402	28	difficult	difficult	JJ
37681	3402	29	for	for	IN
37681	3402	30	beginners	beginner	NNS
37681	3402	31	to	to	TO
37681	3402	32	prove	prove	VB
37681	3402	33	.	.	.
37681	3403	1	In	in	IN
37681	3403	2	the	the	DT
37681	3403	3	table	table	NN
37681	3403	4	_	_	NNP
37681	3403	5	e	e	NNP
37681	3403	6	_	_	NNP
37681	3403	7	=	=	SYM
37681	3403	8	edge	edge	NN
37681	3403	9	of	of	IN
37681	3403	10	the	the	DT
37681	3403	11	polyhedron	polyhedron	NN
37681	3403	12	,	,	,
37681	3403	13	_	_	NNP
37681	3403	14	r	r	NNP
37681	3403	15	_	_	NNP
37681	3403	16	=	=	SYM
37681	3403	17	radius	radius	NN
37681	3403	18	of	of	IN
37681	3403	19	circumscribed	circumscribed	NNP
37681	3403	20	sphere	sphere	NNP
37681	3403	21	,	,	,
37681	3403	22	_	_	NNP
37681	3403	23	r	r	NNP
37681	3403	24	'	'	''
37681	3403	25	_	_	NNP
37681	3403	26	=	=	SYM
37681	3403	27	radius	radius	NN
37681	3403	28	of	of	IN
37681	3403	29	inscribed	inscribed	JJ
37681	3403	30	sphere	sphere	NN
37681	3403	31	,	,	,
37681	3403	32	_	_	NNP
37681	3403	33	a	a	DT
37681	3403	34	_	_	NNP
37681	3403	35	=	=	SYM
37681	3403	36	total	total	JJ
37681	3403	37	area	area	NN
37681	3403	38	,	,	,
37681	3403	39	_	_	NNP
37681	3403	40	v	v	NNP
37681	3403	41	_	_	NNP
37681	3403	42	=	=	SYM
37681	3403	43	volume	volume	NN
37681	3403	44	.	.	.
37681	3404	1	=	=	NFP
37681	3404	2	=	=	NFP
37681	3404	3	=	=	SYM
37681	3404	4	=	=	SYM
37681	3404	5	=	=	SYM
37681	3404	6	=	=	SYM
37681	3404	7	=	=	SYM
37681	3404	8	=	=	SYM
37681	3404	9	=	=	SYM
37681	3404	10	=	=	SYM
37681	3404	11	=	=	SYM
37681	3404	12	=	=	SYM
37681	3404	13	=	=	SYM
37681	3404	14	=	=	SYM
37681	3404	15	=	=	SYM
37681	3404	16	=	=	SYM
37681	3404	17	=	=	SYM
37681	3404	18	=	=	SYM
37681	3404	19	=	=	SYM
37681	3404	20	=	=	SYM
37681	3404	21	=	=	SYM
37681	3404	22	=	=	SYM
37681	3404	23	=	=	SYM
37681	3404	24	=	=	SYM
37681	3404	25	=	=	SYM
37681	3404	26	=	=	SYM
37681	3404	27	=	=	SYM
37681	3404	28	=	=	SYM
37681	3404	29	=	=	SYM
37681	3404	30	=	=	SYM
37681	3404	31	=	=	SYM
37681	3404	32	=	=	SYM
37681	3404	33	=	=	SYM
37681	3404	34	=	=	SYM
37681	3404	35	=	=	SYM
37681	3404	36	=	=	SYM
37681	3404	37	=	=	SYM
37681	3404	38	=	=	SYM
37681	3404	39	=	=	SYM
37681	3404	40	=	=	SYM
37681	3404	41	=	=	SYM
37681	3404	42	=	=	SYM
37681	3404	43	=	=	SYM
37681	3404	44	=	=	SYM
37681	3404	45	=	=	SYM
37681	3404	46	=	=	SYM
37681	3404	47	=	=	SYM
37681	3404	48	=	=	SYM
37681	3404	49	=	=	SYM
37681	3404	50	=	=	SYM
37681	3404	51	=	=	SYM
37681	3404	52	=	=	SYM
37681	3404	53	=	=	SYM
37681	3404	54	=	=	SYM
37681	3404	55	=	=	SYM
37681	3404	56	=	=	SYM
37681	3404	57	=	=	NFP
37681	3404	58	=	=	NFP
37681	3404	59	NUMBER	NUMBER	NNP
37681	3404	60	|	|	NNP
37681	3404	61	|	|	CD
37681	3404	62	|	|	CD
37681	3404	63	OF	of	IN
37681	3404	64	FACES|	FACES|	NNP
37681	3404	65	4	4	CD
37681	3404	66	|	|	CD
37681	3404	67	6	6	CD
37681	3404	68	|	|	CD
37681	3404	69	8	8	CD
37681	3404	70	--------+-----------------+--------------+----------------	--------+-----------------+--------------+----------------	NFP
37681	3404	71	_	_	NNP
37681	3404	72	r	r	NNP
37681	3404	73	_	_	NNP
37681	3404	74	|	|	NNP
37681	3404	75	_	_	NNP
37681	3404	76	e_[sqrt](3/8	e_[sqrt](3/8	NN
37681	3404	77	)	)	-RRB-
37681	3404	78	|(_e_/2)[sqrt]3|	|(_e_/2)[sqrt]3|	RB
37681	3404	79	_	_	NNP
37681	3404	80	e_[sqrt](1/2	e_[sqrt](1/2	NNP
37681	3404	81	)	)	-RRB-
37681	3404	82	|	|	NNP
37681	3404	83	|	|	NNP
37681	3404	84	|	|	NNP
37681	3404	85	_	_	NNP
37681	3404	86	r	r	NN
37681	3404	87	'	'	''
37681	3404	88	_	_	NNP
37681	3404	89	|	|	NNP
37681	3404	90	_	_	NNP
37681	3404	91	e_[sqrt](1/24	e_[sqrt](1/24	NNP
37681	3404	92	)	)	-RRB-
37681	3404	93	|	|	NNP
37681	3404	94	_	_	NNP
37681	3404	95	e_/2	e_/2	NNP
37681	3404	96	|	|	NNP
37681	3404	97	_	_	NNP
37681	3404	98	e_[sqrt](1/6	e_[sqrt](1/6	NNP
37681	3404	99	)	)	-RRB-
37681	3404	100	|	|	NNP
37681	3404	101	|	|	CD
37681	3404	102	|	|	NNP
37681	3404	103	_	_	NNP
37681	3404	104	a	a	DT
37681	3404	105	_	_	NNP
37681	3404	106	|	|	NNP
37681	3404	107	_	_	NNP
37681	3404	108	e_^2[sqrt]3	e_^2[sqrt]3	JJ
37681	3404	109	|	|	CD
37681	3404	110	6_e_^2	6_e_^2	CD
37681	3404	111	|	|	CD
37681	3404	112	2_e_^2[sqrt]3	2_e_^2[sqrt]3	CD
37681	3404	113	|	|	CD
37681	3404	114	|	|	CD
37681	3404	115	|	|	NNP
37681	3404	116	_	_	NNP
37681	3404	117	v	v	NNP
37681	3404	118	_	_	NNP
37681	3404	119	|(_e_^3/12)[sqrt]2|	|(_e_^3/12)[sqrt]2|	NNP
37681	3404	120	_	_	NNP
37681	3404	121	e_^3	e_^3	NNP
37681	3404	122	|(_e_^3/3)[sqrt]2	|(_e_^3/3)[sqrt]2	NNP
37681	3404	123	----------------------------------------------------------	----------------------------------------------------------	NFP
37681	3404	124	=	=	SYM
37681	3404	125	=	=	SYM
37681	3404	126	=	=	SYM
37681	3404	127	=	=	SYM
37681	3404	128	=	=	SYM
37681	3404	129	=	=	SYM
37681	3404	130	=	=	SYM
37681	3404	131	=	=	SYM
37681	3404	132	=	=	SYM
37681	3404	133	=	=	SYM
37681	3404	134	=	=	SYM
37681	3404	135	=	=	SYM
37681	3404	136	=	=	SYM
37681	3404	137	=	=	SYM
37681	3404	138	=	=	SYM
37681	3404	139	=	=	SYM
37681	3404	140	=	=	SYM
37681	3404	141	=	=	SYM
37681	3404	142	=	=	SYM
37681	3404	143	=	=	SYM
37681	3404	144	=	=	SYM
37681	3404	145	=	=	SYM
37681	3404	146	=	=	SYM
37681	3404	147	=	=	SYM
37681	3404	148	=	=	SYM
37681	3404	149	=	=	SYM
37681	3404	150	=	=	SYM
37681	3404	151	=	=	SYM
37681	3404	152	=	=	SYM
37681	3404	153	=	=	SYM
37681	3404	154	=	=	SYM
37681	3404	155	=	=	SYM
37681	3404	156	=	=	SYM
37681	3404	157	=	=	SYM
37681	3404	158	=	=	SYM
37681	3404	159	=	=	SYM
37681	3404	160	=	=	SYM
37681	3404	161	=	=	SYM
37681	3404	162	=	=	SYM
37681	3404	163	=	=	SYM
37681	3404	164	=	=	SYM
37681	3404	165	=	=	SYM
37681	3404	166	=	=	SYM
37681	3404	167	=	=	SYM
37681	3404	168	=	=	SYM
37681	3404	169	=	=	SYM
37681	3404	170	=	=	SYM
37681	3404	171	=	=	SYM
37681	3404	172	=	=	SYM
37681	3404	173	=	=	SYM
37681	3404	174	=	=	SYM
37681	3404	175	=	=	SYM
37681	3404	176	=	=	SYM
37681	3404	177	=	=	SYM
37681	3404	178	=	=	SYM
37681	3404	179	=	=	SYM
37681	3404	180	=	=	SYM
37681	3404	181	=	=	SYM
37681	3404	182	=	=	SYM
37681	3404	183	=	=	SYM
37681	3404	184	=	=	SYM
37681	3404	185	=	=	SYM
37681	3404	186	=	=	SYM
37681	3404	187	=	=	SYM
37681	3404	188	=	=	SYM
37681	3404	189	=	=	SYM
37681	3404	190	=	=	SYM
37681	3404	191	=	=	SYM
37681	3404	192	=	=	SYM
37681	3404	193	=	=	SYM
37681	3404	194	=	=	NFP
37681	3404	195	=	=	NFP
37681	3404	196	NUMBER	NUMBER	NNP
37681	3404	197	|	|	CD
37681	3404	198	|	|	CD
37681	3404	199	OF	of	IN
37681	3404	200	FACES|	FACES|	NNP
37681	3404	201	12	12	CD
37681	3404	202	|	|	CD
37681	3404	203	20	20	CD
37681	3404	204	--------+----------------------------------+----------------------------	--------+----------------------------------+----------------------------	CD
37681	3404	205	_	_	NNP
37681	3404	206	r	r	NNP
37681	3404	207	_	_	NNP
37681	3404	208	|(_e_/4)[sqrt]3([sqrt]5	|(_e_/4)[sqrt]3([sqrt]5	NNP
37681	3404	209	+	+	CC
37681	3404	210	1	1	CD
37681	3404	211	)	)	-RRB-
37681	3404	212	|_e_[sqrt]((5	|_e_[sqrt]((5	NN
37681	3404	213	+	+	NFP
37681	3404	214	[	[	-LRB-
37681	3404	215	sqrt]5)/8	sqrt]5)/8	NNP
37681	3404	216	)	)	-RRB-
37681	3404	217	|	|	NNP
37681	3404	218	|	|	NNP
37681	3404	219	_	_	NNP
37681	3404	220	r	r	NNP
37681	3404	221	'	'	''
37681	3404	222	_	_	NNP
37681	3404	223	|(_e_/2)[sqrt]((25	|(_e_/2)[sqrt]((25	NNP
37681	3404	224	+	+	CC
37681	3404	225	11[sqrt]5)/10)|(_e_[sqrt]3)/12([sqrt]5	11[sqrt]5)/10)|(_e_[sqrt]3)/12([sqrt]5	CD
37681	3404	226	+	+	SYM
37681	3404	227	3	3	CD
37681	3404	228	)	)	-RRB-
37681	3404	229	|	|	NNP
37681	3404	230	|	|	NNP
37681	3404	231	_	_	NNP
37681	3404	232	a	a	DT
37681	3404	233	_	_	NNP
37681	3404	234	|3_e_^2[sqrt](5(5	|3_e_^2[sqrt](5(5	NNP
37681	3404	235	+	+	CC
37681	3404	236	2[sqrt]5	2[sqrt]5	CD
37681	3404	237	)	)	-RRB-
37681	3404	238	)	)	-RRB-
37681	3404	239	|	|	NNP
37681	3404	240	(	(	-LRB-
37681	3404	241	5_e_^2)[sqrt]3	5_e_^2)[sqrt]3	CD
37681	3404	242	|	|	NNP
37681	3404	243	|	|	NNP
37681	3404	244	_	_	NNP
37681	3404	245	v	v	NNP
37681	3404	246	_	_	NNP
37681	3404	247	|((_e_^3)/4)(15	|((_e_^3)/4)(15	NNS
37681	3404	248	+	+	SYM
37681	3404	249	7[sqrt]5	7[sqrt]5	CD
37681	3404	250	)	)	-RRB-
37681	3404	251	|((5_e_^3)/12)([sqrt]5	|((5_e_^3)/12)([sqrt]5	IN
37681	3404	252	+	+	DT
37681	3404	253	3	3	CD
37681	3404	254	)	)	-RRB-
37681	3404	255	------------------------------------------------------------------------	------------------------------------------------------------------------	NFP
37681	3404	256	Some	some	DT
37681	3404	257	interest	interest	NN
37681	3404	258	is	be	VBZ
37681	3404	259	added	add	VBN
37681	3404	260	to	to	IN
37681	3404	261	the	the	DT
37681	3404	262	study	study	NN
37681	3404	263	of	of	IN
37681	3404	264	polyhedrons	polyhedron	NNS
37681	3404	265	by	by	IN
37681	3404	266	calling	call	VBG
37681	3404	267	attention	attention	NN
37681	3404	268	to	to	IN
37681	3404	269	their	-PRON-	PRP$
37681	3404	270	occurrence	occurrence	NN
37681	3404	271	in	in	IN
37681	3404	272	nature	nature	NN
37681	3404	273	,	,	,
37681	3404	274	in	in	IN
37681	3404	275	the	the	DT
37681	3404	276	form	form	NN
37681	3404	277	of	of	IN
37681	3404	278	crystals	crystal	NNS
37681	3404	279	.	.	.
37681	3405	1	The	the	DT
37681	3405	2	computation	computation	NN
37681	3405	3	of	of	IN
37681	3405	4	the	the	DT
37681	3405	5	surfaces	surface	NNS
37681	3405	6	and	and	CC
37681	3405	7	volumes	volume	NNS
37681	3405	8	of	of	IN
37681	3405	9	these	these	DT
37681	3405	10	forms	form	NNS
37681	3405	11	offers	offer	VBZ
37681	3405	12	an	an	DT
37681	3405	13	opportunity	opportunity	NN
37681	3405	14	for	for	IN
37681	3405	15	applying	apply	VBG
37681	3405	16	the	the	DT
37681	3405	17	rules	rule	NNS
37681	3405	18	of	of	IN
37681	3405	19	mensuration	mensuration	NN
37681	3405	20	,	,	,
37681	3405	21	and	and	CC
37681	3405	22	the	the	DT
37681	3405	23	construction	construction	NN
37681	3405	24	of	of	IN
37681	3405	25	the	the	DT
37681	3405	26	solids	solid	NNS
37681	3405	27	by	by	IN
37681	3405	28	paper	paper	NN
37681	3405	29	folding	folding	NN
37681	3405	30	or	or	CC
37681	3405	31	by	by	IN
37681	3405	32	the	the	DT
37681	3405	33	cutting	cutting	NN
37681	3405	34	of	of	IN
37681	3405	35	crayon	crayon	NN
37681	3405	36	or	or	CC
37681	3405	37	some	some	DT
37681	3405	38	other	other	JJ
37681	3405	39	substance	substance	NN
37681	3405	40	often	often	RB
37681	3405	41	arouses	arouse	VBZ
37681	3405	42	a	a	DT
37681	3405	43	considerable	considerable	JJ
37681	3405	44	interest	interest	NN
37681	3405	45	.	.	.
37681	3406	1	The	the	DT
37681	3406	2	following	follow	VBG
37681	3406	3	are	be	VBP
37681	3406	4	forms	form	NNS
37681	3406	5	of	of	IN
37681	3406	6	crystals	crystal	NNS
37681	3406	7	that	that	WDT
37681	3406	8	are	be	VBP
37681	3406	9	occasionally	occasionally	RB
37681	3406	10	found	find	VBN
37681	3406	11	:	:	:
37681	3406	12	[	[	-LRB-
37681	3406	13	Illustration	illustration	NN
37681	3406	14	]	]	-RRB-
37681	3406	15	They	-PRON-	PRP
37681	3406	16	show	show	VBP
37681	3406	17	how	how	WRB
37681	3406	18	the	the	DT
37681	3406	19	cube	cube	NN
37681	3406	20	is	be	VBZ
37681	3406	21	modified	modify	VBN
37681	3406	22	by	by	IN
37681	3406	23	having	have	VBG
37681	3406	24	its	-PRON-	PRP$
37681	3406	25	corners	corner	NNS
37681	3406	26	cut	cut	VBN
37681	3406	27	off	off	RP
37681	3406	28	.	.	.
37681	3407	1	A	a	DT
37681	3407	2	cube	cube	NN
37681	3407	3	may	may	MD
37681	3407	4	be	be	VB
37681	3407	5	inscribed	inscribe	VBN
37681	3407	6	in	in	IN
37681	3407	7	an	an	DT
37681	3407	8	octahedron	octahedron	NN
37681	3407	9	,	,	,
37681	3407	10	its	-PRON-	PRP$
37681	3407	11	vertices	vertex	NNS
37681	3407	12	being	be	VBG
37681	3407	13	at	at	IN
37681	3407	14	the	the	DT
37681	3407	15	centers	center	NNS
37681	3407	16	of	of	IN
37681	3407	17	the	the	DT
37681	3407	18	faces	face	NNS
37681	3407	19	of	of	IN
37681	3407	20	the	the	DT
37681	3407	21	octahedron	octahedron	NN
37681	3407	22	.	.	.
37681	3408	1	If	if	IN
37681	3408	2	we	-PRON-	PRP
37681	3408	3	think	think	VBP
37681	3408	4	of	of	IN
37681	3408	5	the	the	DT
37681	3408	6	cube	cube	NN
37681	3408	7	as	as	IN
37681	3408	8	expanding	expand	VBG
37681	3408	9	,	,	,
37681	3408	10	the	the	DT
37681	3408	11	faces	face	NNS
37681	3408	12	of	of	IN
37681	3408	13	the	the	DT
37681	3408	14	octahedron	octahedron	NN
37681	3408	15	will	will	MD
37681	3408	16	cut	cut	VB
37681	3408	17	off	off	RP
37681	3408	18	the	the	DT
37681	3408	19	corners	corner	NNS
37681	3408	20	of	of	IN
37681	3408	21	the	the	DT
37681	3408	22	cube	cube	NN
37681	3408	23	as	as	IN
37681	3408	24	seen	see	VBN
37681	3408	25	in	in	IN
37681	3408	26	the	the	DT
37681	3408	27	first	first	JJ
37681	3408	28	figure	figure	NN
37681	3408	29	,	,	,
37681	3408	30	leaving	leave	VBG
37681	3408	31	the	the	DT
37681	3408	32	cube	cube	NN
37681	3408	33	as	as	IN
37681	3408	34	shown	show	VBN
37681	3408	35	in	in	IN
37681	3408	36	the	the	DT
37681	3408	37	second	second	JJ
37681	3408	38	figure	figure	NN
37681	3408	39	.	.	.
37681	3409	1	If	if	IN
37681	3409	2	the	the	DT
37681	3409	3	corners	corner	NNS
37681	3409	4	are	be	VBP
37681	3409	5	cut	cut	VBN
37681	3409	6	off	off	RP
37681	3409	7	still	still	RB
37681	3409	8	more	more	JJR
37681	3409	9	,	,	,
37681	3409	10	we	-PRON-	PRP
37681	3409	11	have	have	VBP
37681	3409	12	the	the	DT
37681	3409	13	third	third	JJ
37681	3409	14	figure	figure	NN
37681	3409	15	.	.	.
37681	3410	1	Similarly	similarly	RB
37681	3410	2	,	,	,
37681	3410	3	an	an	DT
37681	3410	4	octahedron	octahedron	NN
37681	3410	5	may	may	MD
37681	3410	6	be	be	VB
37681	3410	7	inscribed	inscribe	VBN
37681	3410	8	in	in	IN
37681	3410	9	a	a	DT
37681	3410	10	cube	cube	NN
37681	3410	11	,	,	,
37681	3410	12	and	and	CC
37681	3410	13	by	by	IN
37681	3410	14	letting	let	VBG
37681	3410	15	it	-PRON-	PRP
37681	3410	16	expand	expand	VB
37681	3410	17	a	a	DT
37681	3410	18	little	little	JJ
37681	3410	19	,	,	,
37681	3410	20	the	the	DT
37681	3410	21	faces	face	NNS
37681	3410	22	of	of	IN
37681	3410	23	the	the	DT
37681	3410	24	cube	cube	NN
37681	3410	25	will	will	MD
37681	3410	26	cut	cut	VB
37681	3410	27	off	off	RP
37681	3410	28	the	the	DT
37681	3410	29	corners	corner	NNS
37681	3410	30	of	of	IN
37681	3410	31	the	the	DT
37681	3410	32	octahedron	octahedron	NN
37681	3410	33	.	.	.
37681	3411	1	This	this	DT
37681	3411	2	is	be	VBZ
37681	3411	3	seen	see	VBN
37681	3411	4	in	in	IN
37681	3411	5	the	the	DT
37681	3411	6	following	following	JJ
37681	3411	7	figures	figure	NNS
37681	3411	8	:	:	:
37681	3411	9	[	[	-LRB-
37681	3411	10	Illustration	illustration	NN
37681	3411	11	]	]	-RRB-
37681	3411	12	This	this	DT
37681	3411	13	is	be	VBZ
37681	3411	14	a	a	DT
37681	3411	15	form	form	NN
37681	3411	16	that	that	WDT
37681	3411	17	is	be	VBZ
37681	3411	18	found	find	VBN
37681	3411	19	in	in	IN
37681	3411	20	crystals	crystal	NNS
37681	3411	21	,	,	,
37681	3411	22	and	and	CC
37681	3411	23	the	the	DT
37681	3411	24	computation	computation	NN
37681	3411	25	of	of	IN
37681	3411	26	the	the	DT
37681	3411	27	surface	surface	NN
37681	3411	28	and	and	CC
37681	3411	29	volume	volume	NN
37681	3411	30	is	be	VBZ
37681	3411	31	an	an	DT
37681	3411	32	interesting	interesting	JJ
37681	3411	33	exercise	exercise	NN
37681	3411	34	.	.	.
37681	3412	1	The	the	DT
37681	3412	2	quartz	quartz	NN
37681	3412	3	crystal	crystal	NN
37681	3412	4	,	,	,
37681	3412	5	an	an	DT
37681	3412	6	hexagonal	hexagonal	JJ
37681	3412	7	pyramid	pyramid	NN
37681	3412	8	on	on	IN
37681	3412	9	an	an	DT
37681	3412	10	hexagonal	hexagonal	JJ
37681	3412	11	prism	prism	NN
37681	3412	12	,	,	,
37681	3412	13	is	be	VBZ
37681	3412	14	found	find	VBN
37681	3412	15	in	in	IN
37681	3412	16	many	many	JJ
37681	3412	17	parts	part	NNS
37681	3412	18	of	of	IN
37681	3412	19	the	the	DT
37681	3412	20	country	country	NN
37681	3412	21	,	,	,
37681	3412	22	or	or	CC
37681	3412	23	is	be	VBZ
37681	3412	24	to	to	TO
37681	3412	25	be	be	VB
37681	3412	26	seen	see	VBN
37681	3412	27	in	in	IN
37681	3412	28	the	the	DT
37681	3412	29	school	school	NN
37681	3412	30	museum	museum	NN
37681	3412	31	,	,	,
37681	3412	32	and	and	CC
37681	3412	33	this	this	DT
37681	3412	34	also	also	RB
37681	3412	35	forms	form	VBZ
37681	3412	36	an	an	DT
37681	3412	37	interesting	interesting	JJ
37681	3412	38	object	object	NN
37681	3412	39	of	of	IN
37681	3412	40	study	study	NN
37681	3412	41	in	in	IN
37681	3412	42	this	this	DT
37681	3412	43	connection	connection	NN
37681	3412	44	.	.	.
37681	3413	1	The	the	DT
37681	3413	2	properties	property	NNS
37681	3413	3	of	of	IN
37681	3413	4	the	the	DT
37681	3413	5	cylinder	cylinder	NN
37681	3413	6	are	be	VBP
37681	3413	7	next	next	RB
37681	3413	8	studied	study	VBN
37681	3413	9	.	.	.
37681	3414	1	The	the	DT
37681	3414	2	word	word	NN
37681	3414	3	is	be	VBZ
37681	3414	4	from	from	IN
37681	3414	5	the	the	DT
37681	3414	6	Greek	Greek	NNP
37681	3414	7	_	_	NNP
37681	3414	8	kylindros	kylindros	NNP
37681	3414	9	_	_	NNP
37681	3414	10	,	,	,
37681	3414	11	from	from	IN
37681	3414	12	_	_	NNP
37681	3414	13	kyliein	kyliein	NNP
37681	3414	14	_	_	NNP
37681	3414	15	(	(	-LRB-
37681	3414	16	to	to	TO
37681	3414	17	roll	roll	VB
37681	3414	18	)	)	-RRB-
37681	3414	19	.	.	.
37681	3415	1	In	in	IN
37681	3415	2	ancient	ancient	JJ
37681	3415	3	mathematics	mathematic	NNS
37681	3415	4	circular	circular	JJ
37681	3415	5	cylinders	cylinder	NNS
37681	3415	6	were	be	VBD
37681	3415	7	the	the	DT
37681	3415	8	only	only	JJ
37681	3415	9	ones	one	NNS
37681	3415	10	studied	study	VBN
37681	3415	11	,	,	,
37681	3415	12	but	but	CC
37681	3415	13	since	since	IN
37681	3415	14	some	some	DT
37681	3415	15	of	of	IN
37681	3415	16	the	the	DT
37681	3415	17	properties	property	NNS
37681	3415	18	are	be	VBP
37681	3415	19	as	as	RB
37681	3415	20	easily	easily	RB
37681	3415	21	proved	prove	VBN
37681	3415	22	for	for	IN
37681	3415	23	the	the	DT
37681	3415	24	case	case	NN
37681	3415	25	of	of	IN
37681	3415	26	a	a	DT
37681	3415	27	noncircular	noncircular	JJ
37681	3415	28	directrix	directrix	NN
37681	3415	29	,	,	,
37681	3415	30	it	-PRON-	PRP
37681	3415	31	is	be	VBZ
37681	3415	32	not	not	RB
37681	3415	33	now	now	RB
37681	3415	34	customary	customary	JJ
37681	3415	35	to	to	TO
37681	3415	36	limit	limit	VB
37681	3415	37	them	-PRON-	PRP
37681	3415	38	in	in	IN
37681	3415	39	this	this	DT
37681	3415	40	way	way	NN
37681	3415	41	.	.	.
37681	3416	1	It	-PRON-	PRP
37681	3416	2	is	be	VBZ
37681	3416	3	convenient	convenient	JJ
37681	3416	4	to	to	TO
37681	3416	5	begin	begin	VB
37681	3416	6	by	by	IN
37681	3416	7	a	a	DT
37681	3416	8	study	study	NN
37681	3416	9	of	of	IN
37681	3416	10	the	the	DT
37681	3416	11	cylindric	cylindric	JJ
37681	3416	12	surface	surface	NN
37681	3416	13	,	,	,
37681	3416	14	and	and	CC
37681	3416	15	a	a	DT
37681	3416	16	piece	piece	NN
37681	3416	17	of	of	IN
37681	3416	18	paper	paper	NN
37681	3416	19	may	may	MD
37681	3416	20	be	be	VB
37681	3416	21	curved	curve	VBN
37681	3416	22	or	or	CC
37681	3416	23	rolled	roll	VBN
37681	3416	24	up	up	RP
37681	3416	25	to	to	TO
37681	3416	26	illustrate	illustrate	VB
37681	3416	27	this	this	DT
37681	3416	28	concept	concept	NN
37681	3416	29	.	.	.
37681	3417	1	If	if	IN
37681	3417	2	the	the	DT
37681	3417	3	paper	paper	NN
37681	3417	4	is	be	VBZ
37681	3417	5	brought	bring	VBN
37681	3417	6	around	around	RP
37681	3417	7	so	so	IN
37681	3417	8	that	that	IN
37681	3417	9	the	the	DT
37681	3417	10	edges	edge	NNS
37681	3417	11	meet	meet	VBP
37681	3417	12	,	,	,
37681	3417	13	whatever	whatever	WDT
37681	3417	14	curve	curve	NN
37681	3417	15	may	may	MD
37681	3417	16	form	form	VB
37681	3417	17	a	a	DT
37681	3417	18	cross	cross	NN
37681	3417	19	section	section	NN
37681	3417	20	the	the	DT
37681	3417	21	surface	surface	NN
37681	3417	22	is	be	VBZ
37681	3417	23	said	say	VBN
37681	3417	24	to	to	TO
37681	3417	25	inclose	inclose	VB
37681	3417	26	a	a	DT
37681	3417	27	_	_	NNP
37681	3417	28	cylindric	cylindric	JJ
37681	3417	29	space	space	NN
37681	3417	30	_	_	NNP
37681	3417	31	.	.	.
37681	3418	1	This	this	DT
37681	3418	2	concept	concept	NN
37681	3418	3	is	be	VBZ
37681	3418	4	sometimes	sometimes	RB
37681	3418	5	convenient	convenient	JJ
37681	3418	6	,	,	,
37681	3418	7	but	but	CC
37681	3418	8	it	-PRON-	PRP
37681	3418	9	need	nee	MD
37681	3418	10	be	be	VB
37681	3418	11	introduced	introduce	VBN
37681	3418	12	only	only	RB
37681	3418	13	as	as	IN
37681	3418	14	necessity	necessity	NN
37681	3418	15	for	for	IN
37681	3418	16	using	use	VBG
37681	3418	17	it	-PRON-	PRP
37681	3418	18	arises	arise	VBZ
37681	3418	19	.	.	.
37681	3419	1	The	the	DT
37681	3419	2	other	other	JJ
37681	3419	3	definitions	definition	NNS
37681	3419	4	concerning	concern	VBG
37681	3419	5	the	the	DT
37681	3419	6	cylinder	cylinder	NN
37681	3419	7	are	be	VBP
37681	3419	8	so	so	RB
37681	3419	9	simple	simple	JJ
37681	3419	10	as	as	IN
37681	3419	11	to	to	TO
37681	3419	12	require	require	VB
37681	3419	13	no	no	DT
37681	3419	14	comment	comment	NN
37681	3419	15	.	.	.
37681	3420	1	The	the	DT
37681	3420	2	mensuration	mensuration	NN
37681	3420	3	of	of	IN
37681	3420	4	the	the	DT
37681	3420	5	volume	volume	NN
37681	3420	6	of	of	IN
37681	3420	7	a	a	DT
37681	3420	8	cylinder	cylinder	NN
37681	3420	9	depends	depend	VBZ
37681	3420	10	upon	upon	IN
37681	3420	11	the	the	DT
37681	3420	12	assumption	assumption	NN
37681	3420	13	that	that	IN
37681	3420	14	the	the	DT
37681	3420	15	cylinder	cylinder	NN
37681	3420	16	is	be	VBZ
37681	3420	17	the	the	DT
37681	3420	18	limit	limit	NN
37681	3420	19	of	of	IN
37681	3420	20	a	a	DT
37681	3420	21	certain	certain	JJ
37681	3420	22	inscribed	inscribe	VBN
37681	3420	23	or	or	CC
37681	3420	24	circumscribed	circumscribe	VBN
37681	3420	25	prism	prism	NN
37681	3420	26	as	as	IN
37681	3420	27	the	the	DT
37681	3420	28	number	number	NN
37681	3420	29	of	of	IN
37681	3420	30	sides	side	NNS
37681	3420	31	of	of	IN
37681	3420	32	the	the	DT
37681	3420	33	base	base	NN
37681	3420	34	is	be	VBZ
37681	3420	35	indefinitely	indefinitely	RB
37681	3420	36	increased	increase	VBN
37681	3420	37	.	.	.
37681	3421	1	It	-PRON-	PRP
37681	3421	2	is	be	VBZ
37681	3421	3	possible	possible	JJ
37681	3421	4	to	to	TO
37681	3421	5	give	give	VB
37681	3421	6	a	a	DT
37681	3421	7	fairly	fairly	RB
37681	3421	8	satisfactory	satisfactory	JJ
37681	3421	9	and	and	CC
37681	3421	10	simple	simple	JJ
37681	3421	11	proof	proof	NN
37681	3421	12	of	of	IN
37681	3421	13	this	this	DT
37681	3421	14	fact	fact	NN
37681	3421	15	,	,	,
37681	3421	16	but	but	CC
37681	3421	17	for	for	IN
37681	3421	18	pupils	pupil	NNS
37681	3421	19	of	of	IN
37681	3421	20	the	the	DT
37681	3421	21	age	age	NN
37681	3421	22	of	of	IN
37681	3421	23	beginners	beginner	NNS
37681	3421	24	in	in	IN
37681	3421	25	geometry	geometry	NN
37681	3421	26	in	in	IN
37681	3421	27	America	America	NNP
37681	3421	28	it	-PRON-	PRP
37681	3421	29	is	be	VBZ
37681	3421	30	better	well	JJR
37681	3421	31	to	to	TO
37681	3421	32	make	make	VB
37681	3421	33	the	the	DT
37681	3421	34	assumption	assumption	NN
37681	3421	35	outright	outright	RB
37681	3421	36	.	.	.
37681	3422	1	This	this	DT
37681	3422	2	is	be	VBZ
37681	3422	3	one	one	CD
37681	3422	4	of	of	IN
37681	3422	5	several	several	JJ
37681	3422	6	cases	case	NNS
37681	3422	7	in	in	IN
37681	3422	8	geometry	geometry	NN
37681	3422	9	where	where	WRB
37681	3422	10	a	a	DT
37681	3422	11	proof	proof	NN
37681	3422	12	is	be	VBZ
37681	3422	13	less	less	RBR
37681	3422	14	convincing	convincing	JJ
37681	3422	15	than	than	IN
37681	3422	16	the	the	DT
37681	3422	17	assumed	assumed	JJ
37681	3422	18	statement	statement	NN
37681	3422	19	.	.	.
37681	3423	1	THEOREM	THEOREM	NNP
37681	3423	2	.	.	.
37681	3424	1	_	_	NNP
37681	3424	2	The	the	DT
37681	3424	3	lateral	lateral	JJ
37681	3424	4	area	area	NN
37681	3424	5	of	of	IN
37681	3424	6	a	a	DT
37681	3424	7	circular	circular	JJ
37681	3424	8	cylinder	cylinder	NN
37681	3424	9	is	be	VBZ
37681	3424	10	equal	equal	JJ
37681	3424	11	to	to	IN
37681	3424	12	the	the	DT
37681	3424	13	product	product	NN
37681	3424	14	of	of	IN
37681	3424	15	the	the	DT
37681	3424	16	perimeter	perimeter	NN
37681	3424	17	of	of	IN
37681	3424	18	a	a	DT
37681	3424	19	right	right	JJ
37681	3424	20	section	section	NN
37681	3424	21	of	of	IN
37681	3424	22	the	the	DT
37681	3424	23	cylinder	cylinder	NN
37681	3424	24	by	by	IN
37681	3424	25	an	an	DT
37681	3424	26	element	element	NN
37681	3424	27	.	.	.
37681	3424	28	_	_	NNP
37681	3424	29	For	for	IN
37681	3424	30	practical	practical	JJ
37681	3424	31	purposes	purpose	NNS
37681	3424	32	the	the	DT
37681	3424	33	cylinder	cylinder	NN
37681	3424	34	of	of	IN
37681	3424	35	revolution	revolution	NN
37681	3424	36	(	(	-LRB-
37681	3424	37	right	right	JJ
37681	3424	38	circular	circular	JJ
37681	3424	39	cylinder	cylinder	NN
37681	3424	40	)	)	-RRB-
37681	3424	41	is	be	VBZ
37681	3424	42	the	the	DT
37681	3424	43	one	one	CD
37681	3424	44	most	most	RBS
37681	3424	45	frequently	frequently	RB
37681	3424	46	used	use	VBN
37681	3424	47	,	,	,
37681	3424	48	and	and	CC
37681	3424	49	the	the	DT
37681	3424	50	important	important	JJ
37681	3424	51	formula	formula	NN
37681	3424	52	is	be	VBZ
37681	3424	53	therefore	therefore	RB
37681	3424	54	_	_	NNP
37681	3424	55	l	l	NNP
37681	3424	56	_	_	NNP
37681	3424	57	=	=	SYM
37681	3424	58	2[pi]_rh	2[pi]_rh	CD
37681	3424	59	_	_	NNP
37681	3424	60	where	where	WRB
37681	3424	61	_	_	NNP
37681	3424	62	l	l	NNP
37681	3424	63	_	_	NNP
37681	3424	64	=	=	NFP
37681	3424	65	the	the	DT
37681	3424	66	lateral	lateral	JJ
37681	3424	67	area	area	NN
37681	3424	68	,	,	,
37681	3424	69	_	_	NNP
37681	3424	70	r	r	NNP
37681	3424	71	_	_	NNP
37681	3424	72	=	=	SYM
37681	3424	73	the	the	DT
37681	3424	74	radius	radius	NN
37681	3424	75	,	,	,
37681	3424	76	and	and	CC
37681	3424	77	_	_	NNP
37681	3424	78	h	h	NNP
37681	3424	79	_	_	NNP
37681	3424	80	=	=	NFP
37681	3424	81	the	the	DT
37681	3424	82	altitude	altitude	NN
37681	3424	83	.	.	.
37681	3425	1	Applications	application	NNS
37681	3425	2	of	of	IN
37681	3425	3	this	this	DT
37681	3425	4	formula	formula	NN
37681	3425	5	are	be	VBP
37681	3425	6	easily	easily	RB
37681	3425	7	found	find	VBN
37681	3425	8	.	.	.
37681	3426	1	THEOREM	THEOREM	NNP
37681	3426	2	.	.	.
37681	3427	1	_	_	NNP
37681	3427	2	The	the	DT
37681	3427	3	volume	volume	NN
37681	3427	4	of	of	IN
37681	3427	5	a	a	DT
37681	3427	6	circular	circular	JJ
37681	3427	7	cylinder	cylinder	NN
37681	3427	8	is	be	VBZ
37681	3427	9	equal	equal	JJ
37681	3427	10	to	to	IN
37681	3427	11	the	the	DT
37681	3427	12	product	product	NN
37681	3427	13	of	of	IN
37681	3427	14	its	-PRON-	PRP$
37681	3427	15	base	base	NN
37681	3427	16	by	by	IN
37681	3427	17	its	-PRON-	PRP$
37681	3427	18	altitude	altitude	NN
37681	3427	19	.	.	.
37681	3427	20	_	_	NNP
37681	3427	21	Here	here	RB
37681	3427	22	again	again	RB
37681	3427	23	the	the	DT
37681	3427	24	important	important	JJ
37681	3427	25	case	case	NN
37681	3427	26	is	be	VBZ
37681	3427	27	that	that	DT
37681	3427	28	of	of	IN
37681	3427	29	the	the	DT
37681	3427	30	cylinder	cylinder	NN
37681	3427	31	of	of	IN
37681	3427	32	revolution	revolution	NN
37681	3427	33	,	,	,
37681	3427	34	where	where	WRB
37681	3427	35	_	_	NNP
37681	3427	36	v	v	NNP
37681	3427	37	_	_	NNP
37681	3427	38	=	=	NFP
37681	3427	39	[	[	-LRB-
37681	3427	40	pi]_r_^2_h	pi]_r_^2_h	CD
37681	3427	41	_	_	NNP
37681	3427	42	.	.	.
37681	3428	1	The	the	DT
37681	3428	2	number	number	NN
37681	3428	3	of	of	IN
37681	3428	4	applications	application	NNS
37681	3428	5	of	of	IN
37681	3428	6	this	this	DT
37681	3428	7	proposition	proposition	NN
37681	3428	8	is	be	VBZ
37681	3428	9	,	,	,
37681	3428	10	of	of	IN
37681	3428	11	course	course	NN
37681	3428	12	,	,	,
37681	3428	13	very	very	RB
37681	3428	14	great	great	JJ
37681	3428	15	.	.	.
37681	3429	1	In	in	IN
37681	3429	2	architecture	architecture	NN
37681	3429	3	and	and	CC
37681	3429	4	in	in	IN
37681	3429	5	mechanics	mechanic	NNS
37681	3429	6	the	the	DT
37681	3429	7	cylinder	cylinder	NN
37681	3429	8	is	be	VBZ
37681	3429	9	constantly	constantly	RB
37681	3429	10	seen	see	VBN
37681	3429	11	,	,	,
37681	3429	12	and	and	CC
37681	3429	13	the	the	DT
37681	3429	14	mensuration	mensuration	NN
37681	3429	15	of	of	IN
37681	3429	16	the	the	DT
37681	3429	17	surface	surface	NN
37681	3429	18	and	and	CC
37681	3429	19	the	the	DT
37681	3429	20	volume	volume	NN
37681	3429	21	is	be	VBZ
37681	3429	22	important	important	JJ
37681	3429	23	.	.	.
37681	3430	1	A	a	DT
37681	3430	2	single	single	JJ
37681	3430	3	illustration	illustration	NN
37681	3430	4	of	of	IN
37681	3430	5	this	this	DT
37681	3430	6	type	type	NN
37681	3430	7	of	of	IN
37681	3430	8	problem	problem	NN
37681	3430	9	will	will	MD
37681	3430	10	suffice	suffice	VB
37681	3430	11	.	.	.
37681	3431	1	A	a	DT
37681	3431	2	machinist	machinist	NN
37681	3431	3	is	be	VBZ
37681	3431	4	making	make	VBG
37681	3431	5	a	a	DT
37681	3431	6	crank	crank	NN
37681	3431	7	pin	pin	NN
37681	3431	8	(	(	-LRB-
37681	3431	9	a	a	DT
37681	3431	10	kind	kind	NN
37681	3431	11	of	of	IN
37681	3431	12	bolt	bolt	NN
37681	3431	13	)	)	-RRB-
37681	3431	14	for	for	IN
37681	3431	15	an	an	DT
37681	3431	16	engine	engine	NN
37681	3431	17	,	,	,
37681	3431	18	according	accord	VBG
37681	3431	19	to	to	IN
37681	3431	20	this	this	DT
37681	3431	21	drawing	drawing	NN
37681	3431	22	.	.	.
37681	3432	1	He	-PRON-	PRP
37681	3432	2	considers	consider	VBZ
37681	3432	3	it	-PRON-	PRP
37681	3432	4	as	as	IN
37681	3432	5	weighing	weigh	VBG
37681	3432	6	the	the	DT
37681	3432	7	same	same	JJ
37681	3432	8	as	as	IN
37681	3432	9	three	three	CD
37681	3432	10	steel	steel	NN
37681	3432	11	cylinders	cylinder	NNS
37681	3432	12	having	have	VBG
37681	3432	13	the	the	DT
37681	3432	14	diameters	diameter	NNS
37681	3432	15	and	and	CC
37681	3432	16	lengths	length	NNS
37681	3432	17	in	in	IN
37681	3432	18	inches	inch	NNS
37681	3432	19	as	as	IN
37681	3432	20	here	here	RB
37681	3432	21	shown	show	VBN
37681	3432	22	,	,	,
37681	3432	23	where	where	WRB
37681	3432	24	7	7	CD
37681	3432	25	3/4	3/4	CD
37681	3432	26	"	"	''
37681	3432	27	means	mean	VBZ
37681	3432	28	7	7	CD
37681	3432	29	3/4	3/4	CD
37681	3432	30	inches	inch	NNS
37681	3432	31	.	.	.
37681	3433	1	He	-PRON-	PRP
37681	3433	2	has	have	VBZ
37681	3433	3	this	this	DT
37681	3433	4	formula	formula	NN
37681	3433	5	for	for	IN
37681	3433	6	the	the	DT
37681	3433	7	weight	weight	NN
37681	3433	8	(	(	-LRB-
37681	3433	9	_	_	NNP
37681	3433	10	w	w	NNP
37681	3433	11	_	_	NNP
37681	3433	12	)	)	-RRB-
37681	3433	13	of	of	IN
37681	3433	14	a	a	DT
37681	3433	15	steel	steel	NN
37681	3433	16	cylinder	cylinder	NN
37681	3433	17	where	where	WRB
37681	3433	18	_	_	NNP
37681	3433	19	d	d	NNP
37681	3433	20	_	_	NNP
37681	3433	21	is	be	VBZ
37681	3433	22	the	the	DT
37681	3433	23	diameter	diameter	NN
37681	3433	24	and	and	CC
37681	3433	25	_	_	NNP
37681	3433	26	l	l	NNP
37681	3433	27	_	_	NNP
37681	3433	28	is	be	VBZ
37681	3433	29	the	the	DT
37681	3433	30	length	length	NN
37681	3433	31	:	:	:
37681	3433	32	_	_	NNP
37681	3433	33	w	w	NNP
37681	3433	34	_	_	NNP
37681	3433	35	=	=	SYM
37681	3433	36	0.07[pi]_d_^2_l	0.07[pi]_d_^2_l	.
37681	3433	37	_	_	NNP
37681	3433	38	.	.	.
37681	3434	1	Taking	take	VBG
37681	3434	2	[	[	-LRB-
37681	3434	3	pi	pi	NN
37681	3434	4	]	]	-RRB-
37681	3434	5	=	=	NFP
37681	3434	6	3	3	CD
37681	3434	7	1/7	1/7	CD
37681	3434	8	,	,	,
37681	3434	9	find	find	VB
37681	3434	10	the	the	DT
37681	3434	11	weight	weight	NN
37681	3434	12	of	of	IN
37681	3434	13	the	the	DT
37681	3434	14	pin	pin	NN
37681	3434	15	.	.	.
37681	3435	1	The	the	DT
37681	3435	2	most	most	RBS
37681	3435	3	elaborate	elaborate	JJ
37681	3435	4	study	study	NN
37681	3435	5	of	of	IN
37681	3435	6	the	the	DT
37681	3435	7	cylinder	cylinder	NN
37681	3435	8	,	,	,
37681	3435	9	cone	cone	NN
37681	3435	10	,	,	,
37681	3435	11	and	and	CC
37681	3435	12	sphere	sphere	NNP
37681	3435	13	(	(	-LRB-
37681	3435	14	the	the	DT
37681	3435	15	"	"	``
37681	3435	16	three	three	CD
37681	3435	17	round	round	JJ
37681	3435	18	bodies	body	NNS
37681	3435	19	"	"	''
37681	3435	20	)	)	-RRB-
37681	3435	21	in	in	IN
37681	3435	22	the	the	DT
37681	3435	23	Greek	greek	JJ
37681	3435	24	literature	literature	NN
37681	3435	25	is	be	VBZ
37681	3435	26	that	that	DT
37681	3435	27	of	of	IN
37681	3435	28	Archimedes	Archimedes	NNPS
37681	3435	29	of	of	IN
37681	3435	30	Syracuse	Syracuse	NNP
37681	3435	31	(	(	-LRB-
37681	3435	32	on	on	IN
37681	3435	33	the	the	DT
37681	3435	34	island	island	NN
37681	3435	35	of	of	IN
37681	3435	36	Sicily	Sicily	NNP
37681	3435	37	)	)	-RRB-
37681	3435	38	,	,	,
37681	3435	39	who	who	WP
37681	3435	40	lived	live	VBD
37681	3435	41	in	in	IN
37681	3435	42	the	the	DT
37681	3435	43	third	third	JJ
37681	3435	44	century	century	NN
37681	3435	45	B.C.	B.C.	NNP
37681	3436	1	Archimedes	archimedes	RB
37681	3436	2	tells	tell	VBZ
37681	3436	3	us	-PRON-	PRP
37681	3436	4	,	,	,
37681	3436	5	however	however	RB
37681	3436	6	,	,	,
37681	3436	7	that	that	IN
37681	3436	8	Eudoxus	Eudoxus	NNP
37681	3436	9	(	(	-LRB-
37681	3436	10	born	bear	VBN
37681	3436	11	_	_	NNP
37681	3436	12	ca	ca	NNP
37681	3436	13	.	.	.
37681	3436	14	_	_	NNP
37681	3436	15	407	407	CD
37681	3436	16	B.C.	B.C.	NNP
37681	3436	17	)	)	-RRB-
37681	3437	1	discovered	discover	VBN
37681	3437	2	that	that	IN
37681	3437	3	any	any	DT
37681	3437	4	cone	cone	NN
37681	3437	5	is	be	VBZ
37681	3437	6	one	one	CD
37681	3437	7	third	third	NN
37681	3437	8	of	of	IN
37681	3437	9	a	a	DT
37681	3437	10	cylinder	cylinder	NN
37681	3437	11	of	of	IN
37681	3437	12	the	the	DT
37681	3437	13	same	same	JJ
37681	3437	14	base	base	NN
37681	3437	15	and	and	CC
37681	3437	16	the	the	DT
37681	3437	17	same	same	JJ
37681	3437	18	altitude	altitude	NN
37681	3437	19	.	.	.
37681	3438	1	Tradition	tradition	NN
37681	3438	2	says	say	VBZ
37681	3438	3	that	that	IN
37681	3438	4	Archimedes	Archimedes	NNP
37681	3438	5	requested	request	VBD
37681	3438	6	that	that	IN
37681	3438	7	a	a	DT
37681	3438	8	sphere	sphere	NN
37681	3438	9	and	and	CC
37681	3438	10	a	a	DT
37681	3438	11	cylinder	cylinder	NN
37681	3438	12	be	be	VB
37681	3438	13	carved	carve	VBN
37681	3438	14	upon	upon	IN
37681	3438	15	his	-PRON-	PRP$
37681	3438	16	tomb	tomb	NN
37681	3438	17	,	,	,
37681	3438	18	and	and	CC
37681	3438	19	that	that	IN
37681	3438	20	this	this	DT
37681	3438	21	was	be	VBD
37681	3438	22	done	do	VBN
37681	3438	23	.	.	.
37681	3439	1	Cicero	Cicero	NNP
37681	3439	2	relates	relate	VBZ
37681	3439	3	that	that	IN
37681	3439	4	he	-PRON-	PRP
37681	3439	5	discovered	discover	VBD
37681	3439	6	the	the	DT
37681	3439	7	tomb	tomb	NN
37681	3439	8	by	by	IN
37681	3439	9	means	mean	NNS
37681	3439	10	of	of	IN
37681	3439	11	these	these	DT
37681	3439	12	symbols	symbol	NNS
37681	3439	13	.	.	.
37681	3440	1	The	the	DT
37681	3440	2	tomb	tomb	NN
37681	3440	3	now	now	RB
37681	3440	4	shown	show	VBN
37681	3440	5	to	to	IN
37681	3440	6	visitors	visitor	NNS
37681	3440	7	in	in	IN
37681	3440	8	ancient	ancient	JJ
37681	3440	9	Syracuse	Syracuse	NNP
37681	3440	10	as	as	IN
37681	3440	11	that	that	DT
37681	3440	12	of	of	IN
37681	3440	13	Archimedes	archimede	NNS
37681	3440	14	can	can	MD
37681	3440	15	not	not	RB
37681	3440	16	be	be	VB
37681	3440	17	his	-PRON-	PRP$
37681	3440	18	,	,	,
37681	3440	19	for	for	IN
37681	3440	20	it	-PRON-	PRP
37681	3440	21	bears	bear	VBZ
37681	3440	22	no	no	DT
37681	3440	23	such	such	JJ
37681	3440	24	figures	figure	NNS
37681	3440	25	,	,	,
37681	3440	26	and	and	CC
37681	3440	27	is	be	VBZ
37681	3440	28	not	not	RB
37681	3440	29	"	"	``
37681	3440	30	outside	outside	IN
37681	3440	31	the	the	DT
37681	3440	32	gate	gate	NN
37681	3440	33	of	of	IN
37681	3440	34	Agrigentum	Agrigentum	NNP
37681	3440	35	,	,	,
37681	3440	36	"	"	''
37681	3440	37	as	as	IN
37681	3440	38	Cicero	Cicero	NNP
37681	3440	39	describes	describe	VBZ
37681	3440	40	.	.	.
37681	3441	1	The	the	DT
37681	3441	2	cone	cone	NN
37681	3441	3	is	be	VBZ
37681	3441	4	now	now	RB
37681	3441	5	introduced	introduce	VBN
37681	3441	6	.	.	.
37681	3442	1	A	a	DT
37681	3442	2	conic	conic	JJ
37681	3442	3	surface	surface	NN
37681	3442	4	is	be	VBZ
37681	3442	5	easily	easily	RB
37681	3442	6	illustrated	illustrate	VBN
37681	3442	7	to	to	IN
37681	3442	8	a	a	DT
37681	3442	9	class	class	NN
37681	3442	10	by	by	IN
37681	3442	11	taking	take	VBG
37681	3442	12	a	a	DT
37681	3442	13	piece	piece	NN
37681	3442	14	of	of	IN
37681	3442	15	paper	paper	NN
37681	3442	16	and	and	CC
37681	3442	17	rolling	roll	VBG
37681	3442	18	it	-PRON-	PRP
37681	3442	19	up	up	RP
37681	3442	20	into	into	IN
37681	3442	21	a	a	DT
37681	3442	22	cornucopia	cornucopia	NN
37681	3442	23	,	,	,
37681	3442	24	the	the	DT
37681	3442	25	space	space	NN
37681	3442	26	inclosed	inclose	VBD
37681	3442	27	being	be	VBG
37681	3442	28	a	a	DT
37681	3442	29	_	_	NNP
37681	3442	30	conic	conic	JJ
37681	3442	31	space	space	NN
37681	3442	32	_	_	NNP
37681	3442	33	,	,	,
37681	3442	34	a	a	DT
37681	3442	35	term	term	NN
37681	3442	36	that	that	WDT
37681	3442	37	is	be	VBZ
37681	3442	38	sometimes	sometimes	RB
37681	3442	39	convenient	convenient	JJ
37681	3442	40	.	.	.
37681	3443	1	The	the	DT
37681	3443	2	generation	generation	NN
37681	3443	3	of	of	IN
37681	3443	4	a	a	DT
37681	3443	5	conic	conic	JJ
37681	3443	6	surface	surface	NN
37681	3443	7	may	may	MD
37681	3443	8	be	be	VB
37681	3443	9	shown	show	VBN
37681	3443	10	by	by	IN
37681	3443	11	taking	take	VBG
37681	3443	12	a	a	DT
37681	3443	13	blackboard	blackboard	NN
37681	3443	14	pointer	pointer	NN
37681	3443	15	and	and	CC
37681	3443	16	swinging	swinge	VBG
37681	3443	17	it	-PRON-	PRP
37681	3443	18	around	around	RB
37681	3443	19	by	by	IN
37681	3443	20	its	-PRON-	PRP$
37681	3443	21	tip	tip	NN
37681	3443	22	so	so	IN
37681	3443	23	that	that	IN
37681	3443	24	the	the	DT
37681	3443	25	other	other	JJ
37681	3443	26	end	end	NN
37681	3443	27	moves	move	NNS
37681	3443	28	in	in	IN
37681	3443	29	a	a	DT
37681	3443	30	curve	curve	NN
37681	3443	31	.	.	.
37681	3444	1	If	if	IN
37681	3444	2	we	-PRON-	PRP
37681	3444	3	consider	consider	VBP
37681	3444	4	a	a	DT
37681	3444	5	straight	straight	JJ
37681	3444	6	line	line	NN
37681	3444	7	as	as	IN
37681	3444	8	the	the	DT
37681	3444	9	limit	limit	NN
37681	3444	10	of	of	IN
37681	3444	11	a	a	DT
37681	3444	12	curve	curve	NN
37681	3444	13	,	,	,
37681	3444	14	then	then	RB
37681	3444	15	the	the	DT
37681	3444	16	pointer	pointer	NN
37681	3444	17	may	may	MD
37681	3444	18	swing	swing	VB
37681	3444	19	in	in	IN
37681	3444	20	a	a	DT
37681	3444	21	plane	plane	NN
37681	3444	22	,	,	,
37681	3444	23	and	and	CC
37681	3444	24	so	so	RB
37681	3444	25	a	a	DT
37681	3444	26	plane	plane	NN
37681	3444	27	is	be	VBZ
37681	3444	28	the	the	DT
37681	3444	29	limit	limit	NN
37681	3444	30	of	of	IN
37681	3444	31	a	a	DT
37681	3444	32	conic	conic	JJ
37681	3444	33	surface	surface	NN
37681	3444	34	.	.	.
37681	3445	1	If	if	IN
37681	3445	2	we	-PRON-	PRP
37681	3445	3	swing	swing	VBP
37681	3445	4	the	the	DT
37681	3445	5	pointer	pointer	NN
37681	3445	6	about	about	IN
37681	3445	7	a	a	DT
37681	3445	8	point	point	NN
37681	3445	9	in	in	IN
37681	3445	10	the	the	DT
37681	3445	11	middle	middle	NN
37681	3445	12	,	,	,
37681	3445	13	we	-PRON-	PRP
37681	3445	14	shall	shall	MD
37681	3445	15	generate	generate	VB
37681	3445	16	the	the	DT
37681	3445	17	two	two	CD
37681	3445	18	nappes	nappe	NNS
37681	3445	19	of	of	IN
37681	3445	20	the	the	DT
37681	3445	21	cone	cone	NN
37681	3445	22	,	,	,
37681	3445	23	the	the	DT
37681	3445	24	conic	conic	JJ
37681	3445	25	space	space	NN
37681	3445	26	now	now	RB
37681	3445	27	being	be	VBG
37681	3445	28	double	double	JJ
37681	3445	29	.	.	.
37681	3446	1	In	in	IN
37681	3446	2	practice	practice	NN
37681	3446	3	the	the	DT
37681	3446	4	right	right	JJ
37681	3446	5	circular	circular	JJ
37681	3446	6	cone	cone	NN
37681	3446	7	,	,	,
37681	3446	8	or	or	CC
37681	3446	9	cone	cone	NN
37681	3446	10	of	of	IN
37681	3446	11	revolution	revolution	NN
37681	3446	12	,	,	,
37681	3446	13	is	be	VBZ
37681	3446	14	the	the	DT
37681	3446	15	important	important	JJ
37681	3446	16	type	type	NN
37681	3446	17	,	,	,
37681	3446	18	and	and	CC
37681	3446	19	special	special	JJ
37681	3446	20	attention	attention	NN
37681	3446	21	should	should	MD
37681	3446	22	be	be	VB
37681	3446	23	given	give	VBN
37681	3446	24	to	to	IN
37681	3446	25	this	this	DT
37681	3446	26	form	form	NN
37681	3446	27	.	.	.
37681	3447	1	THEOREM	THEOREM	NNP
37681	3447	2	.	.	.
37681	3448	1	_	_	NNP
37681	3448	2	Every	every	DT
37681	3448	3	section	section	NN
37681	3448	4	of	of	IN
37681	3448	5	a	a	DT
37681	3448	6	cone	cone	NN
37681	3448	7	made	make	VBN
37681	3448	8	by	by	IN
37681	3448	9	a	a	DT
37681	3448	10	plane	plane	NN
37681	3448	11	passing	pass	VBG
37681	3448	12	through	through	IN
37681	3448	13	its	-PRON-	PRP$
37681	3448	14	vertex	vertex	NN
37681	3448	15	is	be	VBZ
37681	3448	16	a	a	DT
37681	3448	17	triangle	triangle	NN
37681	3448	18	.	.	.
37681	3448	19	_	_	NNP
37681	3448	20	At	at	IN
37681	3448	21	this	this	DT
37681	3448	22	time	time	NN
37681	3448	23	,	,	,
37681	3448	24	or	or	CC
37681	3448	25	in	in	IN
37681	3448	26	speaking	speaking	NN
37681	3448	27	of	of	IN
37681	3448	28	the	the	DT
37681	3448	29	preliminary	preliminary	JJ
37681	3448	30	definitions	definition	NNS
37681	3448	31	,	,	,
37681	3448	32	reference	reference	NN
37681	3448	33	should	should	MD
37681	3448	34	be	be	VB
37681	3448	35	made	make	VBN
37681	3448	36	to	to	IN
37681	3448	37	the	the	DT
37681	3448	38	conic	conic	JJ
37681	3448	39	sections	section	NNS
37681	3448	40	.	.	.
37681	3449	1	Of	of	IN
37681	3449	2	these	these	DT
37681	3449	3	there	there	EX
37681	3449	4	are	be	VBP
37681	3449	5	three	three	CD
37681	3449	6	great	great	JJ
37681	3449	7	types	type	NNS
37681	3449	8	:	:	:
37681	3449	9	(	(	-LRB-
37681	3449	10	1	1	LS
37681	3449	11	)	)	-RRB-
37681	3449	12	the	the	DT
37681	3449	13	ellipse	ellipse	NN
37681	3449	14	,	,	,
37681	3449	15	where	where	WRB
37681	3449	16	the	the	DT
37681	3449	17	cutting	cut	VBG
37681	3449	18	plane	plane	NN
37681	3449	19	intersects	intersect	VBZ
37681	3449	20	all	all	PDT
37681	3449	21	the	the	DT
37681	3449	22	elements	element	NNS
37681	3449	23	on	on	IN
37681	3449	24	one	one	CD
37681	3449	25	side	side	NN
37681	3449	26	of	of	IN
37681	3449	27	the	the	DT
37681	3449	28	vertex	vertex	NN
37681	3449	29	;	;	:
37681	3449	30	a	a	DT
37681	3449	31	circle	circle	NN
37681	3449	32	is	be	VBZ
37681	3449	33	a	a	DT
37681	3449	34	special	special	JJ
37681	3449	35	form	form	NN
37681	3449	36	of	of	IN
37681	3449	37	the	the	DT
37681	3449	38	ellipse	ellipse	NN
37681	3449	39	;	;	:
37681	3449	40	(	(	-LRB-
37681	3449	41	2	2	LS
37681	3449	42	)	)	-RRB-
37681	3449	43	the	the	DT
37681	3449	44	parabola	parabola	NN
37681	3449	45	,	,	,
37681	3449	46	where	where	WRB
37681	3449	47	the	the	DT
37681	3449	48	plane	plane	NN
37681	3449	49	is	be	VBZ
37681	3449	50	parallel	parallel	JJ
37681	3449	51	to	to	IN
37681	3449	52	an	an	DT
37681	3449	53	element	element	NN
37681	3449	54	;	;	:
37681	3449	55	(	(	-LRB-
37681	3449	56	3	3	LS
37681	3449	57	)	)	-RRB-
37681	3449	58	the	the	DT
37681	3449	59	hyperbola	hyperbola	NN
37681	3449	60	,	,	,
37681	3449	61	where	where	WRB
37681	3449	62	the	the	DT
37681	3449	63	plane	plane	NN
37681	3449	64	cuts	cut	VBZ
37681	3449	65	some	some	DT
37681	3449	66	of	of	IN
37681	3449	67	the	the	DT
37681	3449	68	elements	element	NNS
37681	3449	69	on	on	IN
37681	3449	70	one	one	CD
37681	3449	71	side	side	NN
37681	3449	72	of	of	IN
37681	3449	73	the	the	DT
37681	3449	74	vertex	vertex	NN
37681	3449	75	,	,	,
37681	3449	76	and	and	CC
37681	3449	77	the	the	DT
37681	3449	78	rest	rest	NN
37681	3449	79	on	on	IN
37681	3449	80	the	the	DT
37681	3449	81	other	other	JJ
37681	3449	82	side	side	NN
37681	3449	83	;	;	:
37681	3449	84	that	that	RB
37681	3449	85	is	is	RB
37681	3449	86	,	,	,
37681	3449	87	where	where	WRB
37681	3449	88	it	-PRON-	PRP
37681	3449	89	cuts	cut	VBZ
37681	3449	90	both	both	DT
37681	3449	91	nappes	nappe	NNS
37681	3449	92	.	.	.
37681	3450	1	It	-PRON-	PRP
37681	3450	2	is	be	VBZ
37681	3450	3	to	to	TO
37681	3450	4	be	be	VB
37681	3450	5	observed	observe	VBN
37681	3450	6	that	that	IN
37681	3450	7	the	the	DT
37681	3450	8	ellipse	ellipse	NN
37681	3450	9	may	may	MD
37681	3450	10	vary	vary	VB
37681	3450	11	greatly	greatly	RB
37681	3450	12	in	in	IN
37681	3450	13	shape	shape	NN
37681	3450	14	,	,	,
37681	3450	15	from	from	IN
37681	3450	16	a	a	DT
37681	3450	17	circle	circle	NN
37681	3450	18	to	to	IN
37681	3450	19	a	a	DT
37681	3450	20	very	very	RB
37681	3450	21	long	long	JJ
37681	3450	22	ellipse	ellipse	NN
37681	3450	23	,	,	,
37681	3450	24	as	as	IN
37681	3450	25	the	the	DT
37681	3450	26	cutting	cut	VBG
37681	3450	27	plane	plane	NN
37681	3450	28	changes	change	NNS
37681	3450	29	from	from	IN
37681	3450	30	being	be	VBG
37681	3450	31	perpendicular	perpendicular	JJ
37681	3450	32	to	to	IN
37681	3450	33	the	the	DT
37681	3450	34	axis	axis	NN
37681	3450	35	to	to	IN
37681	3450	36	being	be	VBG
37681	3450	37	nearly	nearly	RB
37681	3450	38	parallel	parallel	JJ
37681	3450	39	to	to	IN
37681	3450	40	an	an	DT
37681	3450	41	element	element	NN
37681	3450	42	.	.	.
37681	3451	1	The	the	DT
37681	3451	2	instant	instant	NN
37681	3451	3	it	-PRON-	PRP
37681	3451	4	becomes	become	VBZ
37681	3451	5	parallel	parallel	JJ
37681	3451	6	to	to	IN
37681	3451	7	an	an	DT
37681	3451	8	element	element	NN
37681	3451	9	the	the	DT
37681	3451	10	ellipse	ellipse	NN
37681	3451	11	changes	change	NNS
37681	3451	12	suddenly	suddenly	RB
37681	3451	13	to	to	IN
37681	3451	14	a	a	DT
37681	3451	15	parabola	parabola	NN
37681	3451	16	.	.	.
37681	3452	1	If	if	IN
37681	3452	2	the	the	DT
37681	3452	3	plane	plane	NN
37681	3452	4	tips	tip	VBZ
37681	3452	5	the	the	DT
37681	3452	6	slightest	slight	JJS
37681	3452	7	amount	amount	NN
37681	3452	8	more	more	JJR
37681	3452	9	,	,	,
37681	3452	10	the	the	DT
37681	3452	11	section	section	NN
37681	3452	12	becomes	become	VBZ
37681	3452	13	an	an	DT
37681	3452	14	hyperbola	hyperbola	NN
37681	3452	15	.	.	.
37681	3453	1	While	while	IN
37681	3453	2	these	these	DT
37681	3453	3	conic	conic	JJ
37681	3453	4	sections	section	NNS
37681	3453	5	are	be	VBP
37681	3453	6	not	not	RB
37681	3453	7	studied	study	VBN
37681	3453	8	in	in	IN
37681	3453	9	elementary	elementary	JJ
37681	3453	10	geometry	geometry	NN
37681	3453	11	,	,	,
37681	3453	12	the	the	DT
37681	3453	13	terms	term	NNS
37681	3453	14	should	should	MD
37681	3453	15	be	be	VB
37681	3453	16	known	know	VBN
37681	3453	17	for	for	IN
37681	3453	18	general	general	JJ
37681	3453	19	information	information	NN
37681	3453	20	,	,	,
37681	3453	21	particularly	particularly	RB
37681	3453	22	the	the	DT
37681	3453	23	ellipse	ellipse	NN
37681	3453	24	and	and	CC
37681	3453	25	parabola	parabola	NNP
37681	3453	26	.	.	.
37681	3454	1	The	the	DT
37681	3454	2	study	study	NN
37681	3454	3	of	of	IN
37681	3454	4	the	the	DT
37681	3454	5	conic	conic	JJ
37681	3454	6	sections	section	NNS
37681	3454	7	forms	form	VBZ
37681	3454	8	a	a	DT
37681	3454	9	large	large	JJ
37681	3454	10	part	part	NN
37681	3454	11	of	of	IN
37681	3454	12	the	the	DT
37681	3454	13	work	work	NN
37681	3454	14	of	of	IN
37681	3454	15	analytic	analytic	JJ
37681	3454	16	geometry	geometry	NN
37681	3454	17	,	,	,
37681	3454	18	a	a	DT
37681	3454	19	subject	subject	NN
37681	3454	20	in	in	IN
37681	3454	21	which	which	WDT
37681	3454	22	the	the	DT
37681	3454	23	figures	figure	NNS
37681	3454	24	resemble	resemble	VBP
37681	3454	25	the	the	DT
37681	3454	26	graphic	graphic	JJ
37681	3454	27	work	work	NN
37681	3454	28	in	in	IN
37681	3454	29	algebra	algebra	NN
37681	3454	30	,	,	,
37681	3454	31	this	this	DT
37681	3454	32	having	have	VBG
37681	3454	33	been	be	VBN
37681	3454	34	taken	take	VBN
37681	3454	35	from	from	IN
37681	3454	36	"	"	``
37681	3454	37	analytics	analytic	NNS
37681	3454	38	,	,	,
37681	3454	39	"	"	''
37681	3454	40	as	as	IN
37681	3454	41	the	the	DT
37681	3454	42	higher	high	JJR
37681	3454	43	subject	subject	NN
37681	3454	44	is	be	VBZ
37681	3454	45	commonly	commonly	RB
37681	3454	46	called	call	VBN
37681	3454	47	.	.	.
37681	3455	1	The	the	DT
37681	3455	2	planets	planet	NNS
37681	3455	3	move	move	VBP
37681	3455	4	about	about	IN
37681	3455	5	the	the	DT
37681	3455	6	sun	sun	NN
37681	3455	7	in	in	IN
37681	3455	8	elliptic	elliptic	JJ
37681	3455	9	orbits	orbit	NNS
37681	3455	10	,	,	,
37681	3455	11	and	and	CC
37681	3455	12	Halley	Halley	NNP
37681	3455	13	's	's	POS
37681	3455	14	comet	comet	NN
37681	3455	15	that	that	WDT
37681	3455	16	returned	return	VBD
37681	3455	17	to	to	IN
37681	3455	18	view	view	NN
37681	3455	19	in	in	IN
37681	3455	20	1909	1909	CD
37681	3455	21	-	-	SYM
37681	3455	22	1910	1910	CD
37681	3455	23	has	have	VBZ
37681	3455	24	for	for	IN
37681	3455	25	its	-PRON-	PRP$
37681	3455	26	path	path	NN
37681	3455	27	an	an	DT
37681	3455	28	enormous	enormous	JJ
37681	3455	29	ellipse	ellipse	NN
37681	3455	30	.	.	.
37681	3456	1	Most	Most	JJS
37681	3456	2	comets	comet	NNS
37681	3456	3	seem	seem	VBP
37681	3456	4	to	to	TO
37681	3456	5	move	move	VB
37681	3456	6	in	in	IN
37681	3456	7	parabolas	parabola	NNS
37681	3456	8	,	,	,
37681	3456	9	and	and	CC
37681	3456	10	a	a	DT
37681	3456	11	body	body	NN
37681	3456	12	thrown	throw	VBN
37681	3456	13	into	into	IN
37681	3456	14	the	the	DT
37681	3456	15	air	air	NN
37681	3456	16	would	would	MD
37681	3456	17	take	take	VB
37681	3456	18	a	a	DT
37681	3456	19	parabolic	parabolic	JJ
37681	3456	20	path	path	NN
37681	3456	21	if	if	IN
37681	3456	22	it	-PRON-	PRP
37681	3456	23	were	be	VBD
37681	3456	24	not	not	RB
37681	3456	25	for	for	IN
37681	3456	26	the	the	DT
37681	3456	27	resistance	resistance	NN
37681	3456	28	of	of	IN
37681	3456	29	the	the	DT
37681	3456	30	atmosphere	atmosphere	NN
37681	3456	31	.	.	.
37681	3457	1	Two	two	CD
37681	3457	2	of	of	IN
37681	3457	3	the	the	DT
37681	3457	4	sides	side	NNS
37681	3457	5	of	of	IN
37681	3457	6	the	the	DT
37681	3457	7	triangle	triangle	NN
37681	3457	8	in	in	IN
37681	3457	9	this	this	DT
37681	3457	10	proposition	proposition	NN
37681	3457	11	constitute	constitute	VBP
37681	3457	12	a	a	DT
37681	3457	13	special	special	JJ
37681	3457	14	form	form	NN
37681	3457	15	of	of	IN
37681	3457	16	the	the	DT
37681	3457	17	hyperbola	hyperbola	NN
37681	3457	18	.	.	.
37681	3458	1	The	the	DT
37681	3458	2	study	study	NN
37681	3458	3	of	of	IN
37681	3458	4	conic	conic	JJ
37681	3458	5	sections	section	NNS
37681	3458	6	was	be	VBD
37681	3458	7	brought	bring	VBN
37681	3458	8	to	to	IN
37681	3458	9	a	a	DT
37681	3458	10	high	high	JJ
37681	3458	11	state	state	NN
37681	3458	12	by	by	IN
37681	3458	13	the	the	DT
37681	3458	14	Greeks	Greeks	NNPS
37681	3458	15	.	.	.
37681	3459	1	They	-PRON-	PRP
37681	3459	2	were	be	VBD
37681	3459	3	not	not	RB
37681	3459	4	known	know	VBN
37681	3459	5	to	to	IN
37681	3459	6	the	the	DT
37681	3459	7	Pythagoreans	Pythagoreans	NNPS
37681	3459	8	,	,	,
37681	3459	9	but	but	CC
37681	3459	10	were	be	VBD
37681	3459	11	discovered	discover	VBN
37681	3459	12	by	by	IN
37681	3459	13	Menæchmus	Menæchmus	NNP
37681	3459	14	in	in	IN
37681	3459	15	the	the	DT
37681	3459	16	fourth	fourth	JJ
37681	3459	17	century	century	NN
37681	3459	18	B.C.	B.C.	NNP
37681	3460	1	This	this	DT
37681	3460	2	discovery	discovery	NN
37681	3460	3	is	be	VBZ
37681	3460	4	mentioned	mention	VBN
37681	3460	5	by	by	IN
37681	3460	6	Proclus	Proclus	NNP
37681	3460	7	,	,	,
37681	3460	8	who	who	WP
37681	3460	9	says	say	VBZ
37681	3460	10	,	,	,
37681	3460	11	"	"	``
37681	3460	12	Further	further	RB
37681	3460	13	,	,	,
37681	3460	14	as	as	IN
37681	3460	15	to	to	IN
37681	3460	16	these	these	DT
37681	3460	17	sections	section	NNS
37681	3460	18	,	,	,
37681	3460	19	the	the	DT
37681	3460	20	conics	conic	NNS
37681	3460	21	were	be	VBD
37681	3460	22	conceived	conceive	VBN
37681	3460	23	by	by	IN
37681	3460	24	Menæchmus	Menæchmus	NNP
37681	3460	25	.	.	.
37681	3460	26	"	"	''
37681	3461	1	Since	since	IN
37681	3461	2	if	if	IN
37681	3461	3	the	the	DT
37681	3461	4	cutting	cut	VBG
37681	3461	5	plane	plane	NN
37681	3461	6	is	be	VBZ
37681	3461	7	perpendicular	perpendicular	JJ
37681	3461	8	to	to	IN
37681	3461	9	the	the	DT
37681	3461	10	axis	axi	NNS
37681	3461	11	the	the	DT
37681	3461	12	section	section	NN
37681	3461	13	is	be	VBZ
37681	3461	14	a	a	DT
37681	3461	15	circle	circle	NN
37681	3461	16	,	,	,
37681	3461	17	and	and	CC
37681	3461	18	if	if	IN
37681	3461	19	oblique	oblique	NNP
37681	3461	20	it	-PRON-	PRP
37681	3461	21	is	be	VBZ
37681	3461	22	an	an	DT
37681	3461	23	ellipse	ellipse	NN
37681	3461	24	,	,	,
37681	3461	25	a	a	DT
37681	3461	26	parabola	parabola	NN
37681	3461	27	,	,	,
37681	3461	28	or	or	CC
37681	3461	29	an	an	DT
37681	3461	30	hyperbola	hyperbola	NN
37681	3461	31	,	,	,
37681	3461	32	it	-PRON-	PRP
37681	3461	33	follows	follow	VBZ
37681	3461	34	that	that	IN
37681	3461	35	if	if	IN
37681	3461	36	light	light	JJ
37681	3461	37	proceeds	proceed	VBZ
37681	3461	38	from	from	IN
37681	3461	39	a	a	DT
37681	3461	40	point	point	NN
37681	3461	41	,	,	,
37681	3461	42	the	the	DT
37681	3461	43	shadow	shadow	NN
37681	3461	44	of	of	IN
37681	3461	45	a	a	DT
37681	3461	46	circle	circle	NN
37681	3461	47	is	be	VBZ
37681	3461	48	a	a	DT
37681	3461	49	circle	circle	NN
37681	3461	50	,	,	,
37681	3461	51	an	an	DT
37681	3461	52	ellipse	ellipse	NN
37681	3461	53	,	,	,
37681	3461	54	a	a	DT
37681	3461	55	parabola	parabola	NN
37681	3461	56	,	,	,
37681	3461	57	or	or	CC
37681	3461	58	an	an	DT
37681	3461	59	hyperbola	hyperbola	NN
37681	3461	60	,	,	,
37681	3461	61	depending	depend	VBG
37681	3461	62	on	on	IN
37681	3461	63	the	the	DT
37681	3461	64	position	position	NN
37681	3461	65	of	of	IN
37681	3461	66	the	the	DT
37681	3461	67	plane	plane	NN
37681	3461	68	on	on	IN
37681	3461	69	which	which	WDT
37681	3461	70	the	the	DT
37681	3461	71	shadow	shadow	NN
37681	3461	72	falls	fall	VBZ
37681	3461	73	.	.	.
37681	3462	1	It	-PRON-	PRP
37681	3462	2	is	be	VBZ
37681	3462	3	interesting	interesting	JJ
37681	3462	4	and	and	CC
37681	3462	5	instructive	instructive	JJ
37681	3462	6	to	to	IN
37681	3462	7	a	a	DT
37681	3462	8	class	class	NN
37681	3462	9	to	to	TO
37681	3462	10	see	see	VB
37681	3462	11	these	these	DT
37681	3462	12	shadows	shadow	NNS
37681	3462	13	,	,	,
37681	3462	14	but	but	CC
37681	3462	15	of	of	IN
37681	3462	16	course	course	NN
37681	3462	17	not	not	RB
37681	3462	18	much	much	JJ
37681	3462	19	time	time	NN
37681	3462	20	can	can	MD
37681	3462	21	be	be	VB
37681	3462	22	allowed	allow	VBN
37681	3462	23	for	for	IN
37681	3462	24	such	such	JJ
37681	3462	25	work	work	NN
37681	3462	26	.	.	.
37681	3463	1	At	at	IN
37681	3463	2	this	this	DT
37681	3463	3	point	point	NN
37681	3463	4	the	the	DT
37681	3463	5	chief	chief	JJ
37681	3463	6	thing	thing	NN
37681	3463	7	is	be	VBZ
37681	3463	8	to	to	TO
37681	3463	9	have	have	VB
37681	3463	10	the	the	DT
37681	3463	11	names	name	NNS
37681	3463	12	"	"	``
37681	3463	13	ellipse	ellipse	NN
37681	3463	14	"	"	''
37681	3463	15	and	and	CC
37681	3463	16	"	"	``
37681	3463	17	parabola	parabola	NNP
37681	3463	18	,	,	,
37681	3463	19	"	"	''
37681	3463	20	so	so	RB
37681	3463	21	often	often	RB
37681	3463	22	met	meet	VBD
37681	3463	23	in	in	IN
37681	3463	24	reading	reading	NN
37681	3463	25	,	,	,
37681	3463	26	understood	understand	VBD
37681	3463	27	.	.	.
37681	3464	1	It	-PRON-	PRP
37681	3464	2	is	be	VBZ
37681	3464	3	also	also	RB
37681	3464	4	of	of	IN
37681	3464	5	interest	interest	NN
37681	3464	6	to	to	IN
37681	3464	7	pupils	pupil	NNS
37681	3464	8	to	to	TO
37681	3464	9	see	see	VB
37681	3464	10	at	at	IN
37681	3464	11	this	this	DT
37681	3464	12	time	time	NN
37681	3464	13	the	the	DT
37681	3464	14	method	method	NN
37681	3464	15	of	of	IN
37681	3464	16	drawing	draw	VBG
37681	3464	17	an	an	DT
37681	3464	18	ellipse	ellipse	NN
37681	3464	19	by	by	IN
37681	3464	20	means	mean	NNS
37681	3464	21	of	of	IN
37681	3464	22	a	a	DT
37681	3464	23	pencil	pencil	NN
37681	3464	24	stretching	stretch	VBG
37681	3464	25	a	a	DT
37681	3464	26	string	string	NN
37681	3464	27	band	band	NN
37681	3464	28	that	that	WDT
37681	3464	29	moves	move	VBZ
37681	3464	30	about	about	RB
37681	3464	31	two	two	CD
37681	3464	32	pins	pin	NNS
37681	3464	33	fastened	fasten	VBN
37681	3464	34	in	in	IN
37681	3464	35	the	the	DT
37681	3464	36	paper	paper	NN
37681	3464	37	.	.	.
37681	3465	1	This	this	DT
37681	3465	2	is	be	VBZ
37681	3465	3	a	a	DT
37681	3465	4	practical	practical	JJ
37681	3465	5	method	method	NN
37681	3465	6	,	,	,
37681	3465	7	and	and	CC
37681	3465	8	is	be	VBZ
37681	3465	9	familiar	familiar	JJ
37681	3465	10	to	to	IN
37681	3465	11	all	all	DT
37681	3465	12	teachers	teacher	NNS
37681	3465	13	who	who	WP
37681	3465	14	have	have	VBP
37681	3465	15	studied	study	VBN
37681	3465	16	analytic	analytic	JJ
37681	3465	17	geometry	geometry	NN
37681	3465	18	.	.	.
37681	3466	1	In	in	IN
37681	3466	2	designing	design	VBG
37681	3466	3	elliptic	elliptic	JJ
37681	3466	4	arches	arch	NNS
37681	3466	5	,	,	,
37681	3466	6	however	however	RB
37681	3466	7	,	,	,
37681	3466	8	three	three	CD
37681	3466	9	circular	circular	JJ
37681	3466	10	arcs	arc	NNS
37681	3466	11	are	be	VBP
37681	3466	12	often	often	RB
37681	3466	13	joined	join	VBN
37681	3466	14	,	,	,
37681	3466	15	as	as	IN
37681	3466	16	here	here	RB
37681	3466	17	shown	show	VBN
37681	3466	18	,	,	,
37681	3466	19	the	the	DT
37681	3466	20	result	result	NN
37681	3466	21	being	be	VBG
37681	3466	22	approximately	approximately	RB
37681	3466	23	an	an	DT
37681	3466	24	elliptic	elliptic	JJ
37681	3466	25	arc	arc	NN
37681	3466	26	.	.	.
37681	3467	1	[	[	-LRB-
37681	3467	2	Illustration	illustration	NN
37681	3467	3	]	]	-RRB-
37681	3467	4	Here	here	RB
37681	3467	5	_	_	IN
37681	3467	6	O	O	NNP
37681	3467	7	_	_	NNP
37681	3467	8	is	be	VBZ
37681	3467	9	the	the	DT
37681	3467	10	center	center	NN
37681	3467	11	of	of	IN
37681	3467	12	arc	arc	NNP
37681	3467	13	_	_	NNP
37681	3467	14	BC	BC	NNP
37681	3467	15	_	_	NNP
37681	3467	16	,	,	,
37681	3467	17	_	_	NNP
37681	3467	18	M	M	NNP
37681	3467	19	_	_	NNP
37681	3467	20	of	of	IN
37681	3467	21	arc	arc	NNP
37681	3467	22	_	_	NNP
37681	3467	23	AB	AB	NNP
37681	3467	24	_	_	NNP
37681	3467	25	,	,	,
37681	3467	26	and	and	CC
37681	3467	27	_	_	NNP
37681	3467	28	N	N	NNP
37681	3467	29	_	_	NNP
37681	3467	30	of	of	IN
37681	3467	31	arc	arc	NNP
37681	3467	32	_	_	NNP
37681	3467	33	CD	CD	NNP
37681	3467	34	_	_	NNP
37681	3467	35	.	.	.
37681	3468	1	Since	since	IN
37681	3468	2	_	_	NNP
37681	3468	3	XY	XY	NNP
37681	3468	4	_	_	NNP
37681	3468	5	is	be	VBZ
37681	3468	6	perpendicular	perpendicular	JJ
37681	3468	7	to	to	IN
37681	3468	8	_	_	NNP
37681	3468	9	BM	BM	NNP
37681	3468	10	_	_	NNP
37681	3468	11	and	and	CC
37681	3468	12	_	_	NNP
37681	3468	13	BO	BO	NNP
37681	3468	14	_	_	NNP
37681	3468	15	,	,	,
37681	3468	16	it	-PRON-	PRP
37681	3468	17	is	be	VBZ
37681	3468	18	tangent	tangent	NN
37681	3468	19	to	to	IN
37681	3468	20	arcs	arcs	NNP
37681	3468	21	_	_	NNP
37681	3468	22	AB	AB	NNP
37681	3468	23	_	_	NNP
37681	3468	24	and	and	CC
37681	3468	25	_	_	NNP
37681	3468	26	BC	BC	NNP
37681	3468	27	_	_	NNP
37681	3468	28	,	,	,
37681	3468	29	so	so	CC
37681	3468	30	there	there	EX
37681	3468	31	is	be	VBZ
37681	3468	32	no	no	DT
37681	3468	33	abrupt	abrupt	JJ
37681	3468	34	turning	turning	NN
37681	3468	35	at	at	IN
37681	3468	36	_	_	NNP
37681	3468	37	B	B	NNP
37681	3468	38	_	_	NNP
37681	3468	39	,	,	,
37681	3468	40	and	and	CC
37681	3468	41	similarly	similarly	RB
37681	3468	42	for	for	IN
37681	3468	43	_	_	NNP
37681	3468	44	C	C	NNP
37681	3468	45	_	_	NNP
37681	3468	46	.	.	.
37681	3469	1	[	[	-LRB-
37681	3469	2	90	90	CD
37681	3469	3	]	]	-RRB-
37681	3469	4	THEOREM	theorem	NN
37681	3469	5	.	.	.
37681	3470	1	_	_	NNP
37681	3470	2	The	the	DT
37681	3470	3	volume	volume	NN
37681	3470	4	of	of	IN
37681	3470	5	a	a	DT
37681	3470	6	circular	circular	JJ
37681	3470	7	cone	cone	NN
37681	3470	8	is	be	VBZ
37681	3470	9	equal	equal	JJ
37681	3470	10	to	to	IN
37681	3470	11	one	one	CD
37681	3470	12	third	third	NN
37681	3470	13	the	the	DT
37681	3470	14	product	product	NN
37681	3470	15	of	of	IN
37681	3470	16	its	-PRON-	PRP$
37681	3470	17	base	base	NN
37681	3470	18	by	by	IN
37681	3470	19	its	-PRON-	PRP$
37681	3470	20	altitude	altitude	NN
37681	3470	21	.	.	.
37681	3470	22	_	_	NNP
37681	3470	23	It	-PRON-	PRP
37681	3470	24	is	be	VBZ
37681	3470	25	easy	easy	JJ
37681	3470	26	to	to	TO
37681	3470	27	prove	prove	VB
37681	3470	28	this	this	DT
37681	3470	29	for	for	IN
37681	3470	30	noncircular	noncircular	JJ
37681	3470	31	cones	cone	NNS
37681	3470	32	as	as	RB
37681	3470	33	well	well	RB
37681	3470	34	,	,	,
37681	3470	35	but	but	CC
37681	3470	36	since	since	IN
37681	3470	37	they	-PRON-	PRP
37681	3470	38	are	be	VBP
37681	3470	39	not	not	RB
37681	3470	40	met	meet	VBN
37681	3470	41	commonly	commonly	RB
37681	3470	42	in	in	IN
37681	3470	43	practice	practice	NN
37681	3470	44	,	,	,
37681	3470	45	they	-PRON-	PRP
37681	3470	46	may	may	MD
37681	3470	47	be	be	VB
37681	3470	48	omitted	omit	VBN
37681	3470	49	in	in	IN
37681	3470	50	elementary	elementary	JJ
37681	3470	51	geometry	geometry	NN
37681	3470	52	.	.	.
37681	3471	1	The	the	DT
37681	3471	2	important	important	JJ
37681	3471	3	formula	formula	NN
37681	3471	4	at	at	IN
37681	3471	5	this	this	DT
37681	3471	6	time	time	NN
37681	3471	7	is	be	VBZ
37681	3471	8	_	_	NNP
37681	3471	9	v	v	NNP
37681	3471	10	_	_	NNP
37681	3471	11	=	=	SYM
37681	3471	12	1/3[pi]_r_^2_h	1/3[pi]_r_^2_h	CD
37681	3471	13	_	_	NNP
37681	3471	14	.	.	.
37681	3472	1	As	as	IN
37681	3472	2	already	already	RB
37681	3472	3	stated	state	VBN
37681	3472	4	,	,	,
37681	3472	5	this	this	DT
37681	3472	6	proposition	proposition	NN
37681	3472	7	was	be	VBD
37681	3472	8	discovered	discover	VBN
37681	3472	9	by	by	IN
37681	3472	10	Eudoxus	Eudoxus	NNP
37681	3472	11	of	of	IN
37681	3472	12	Cnidus	Cnidus	NNP
37681	3472	13	(	(	-LRB-
37681	3472	14	born	bear	VBN
37681	3472	15	_	_	NNP
37681	3472	16	ca	ca	NNP
37681	3472	17	.	.	.
37681	3472	18	_	_	NNP
37681	3472	19	407	407	CD
37681	3472	20	B.C.	B.C.	NNP
37681	3472	21	,	,	,
37681	3472	22	died	die	VBD
37681	3472	23	_	_	NNP
37681	3472	24	ca	ca	NNP
37681	3472	25	.	.	.
37681	3472	26	_	_	NNP
37681	3472	27	354	354	CD
37681	3472	28	B.C.	B.C.	NNP
37681	3473	1	)	)	-RRB-
37681	3473	2	,	,	,
37681	3473	3	a	a	DT
37681	3473	4	man	man	NN
37681	3473	5	who	who	WP
37681	3473	6	,	,	,
37681	3473	7	as	as	RB
37681	3473	8	already	already	RB
37681	3473	9	stated	state	VBN
37681	3473	10	,	,	,
37681	3473	11	was	be	VBD
37681	3473	12	born	bear	VBN
37681	3473	13	poor	poor	JJ
37681	3473	14	,	,	,
37681	3473	15	but	but	CC
37681	3473	16	who	who	WP
37681	3473	17	became	become	VBD
37681	3473	18	one	one	CD
37681	3473	19	of	of	IN
37681	3473	20	the	the	DT
37681	3473	21	most	most	RBS
37681	3473	22	illustrious	illustrious	JJ
37681	3473	23	and	and	CC
37681	3473	24	most	most	RBS
37681	3473	25	highly	highly	RB
37681	3473	26	esteemed	esteemed	JJ
37681	3473	27	of	of	IN
37681	3473	28	all	all	PDT
37681	3473	29	the	the	DT
37681	3473	30	Greeks	Greeks	NNPS
37681	3473	31	of	of	IN
37681	3473	32	his	-PRON-	PRP$
37681	3473	33	time	time	NN
37681	3473	34	.	.	.
37681	3474	1	THEOREM	THEOREM	NNP
37681	3474	2	.	.	.
37681	3475	1	_	_	NNP
37681	3475	2	The	the	DT
37681	3475	3	lateral	lateral	JJ
37681	3475	4	area	area	NN
37681	3475	5	of	of	IN
37681	3475	6	a	a	DT
37681	3475	7	frustum	frustum	NN
37681	3475	8	of	of	IN
37681	3475	9	a	a	DT
37681	3475	10	cone	cone	NN
37681	3475	11	of	of	IN
37681	3475	12	revolution	revolution	NN
37681	3475	13	is	be	VBZ
37681	3475	14	equal	equal	JJ
37681	3475	15	to	to	IN
37681	3475	16	half	half	PDT
37681	3475	17	the	the	DT
37681	3475	18	sum	sum	NN
37681	3475	19	of	of	IN
37681	3475	20	the	the	DT
37681	3475	21	circumferences	circumference	NNS
37681	3475	22	of	of	IN
37681	3475	23	its	-PRON-	PRP$
37681	3475	24	bases	basis	NNS
37681	3475	25	multiplied	multiply	VBN
37681	3475	26	by	by	IN
37681	3475	27	the	the	DT
37681	3475	28	slant	slant	NN
37681	3475	29	height	height	NN
37681	3475	30	.	.	.
37681	3475	31	_	_	NNP
37681	3475	32	An	an	DT
37681	3475	33	interesting	interesting	JJ
37681	3475	34	case	case	NN
37681	3475	35	for	for	IN
37681	3475	36	a	a	DT
37681	3475	37	class	class	NN
37681	3475	38	to	to	TO
37681	3475	39	notice	notice	VB
37681	3475	40	is	be	VBZ
37681	3475	41	that	that	IN
37681	3475	42	in	in	IN
37681	3475	43	which	which	WDT
37681	3475	44	the	the	DT
37681	3475	45	upper	upper	JJ
37681	3475	46	base	base	NN
37681	3475	47	becomes	become	VBZ
37681	3475	48	zero	zero	CD
37681	3475	49	and	and	CC
37681	3475	50	the	the	DT
37681	3475	51	frustum	frustum	NN
37681	3475	52	becomes	become	VBZ
37681	3475	53	a	a	DT
37681	3475	54	cone	cone	NN
37681	3475	55	,	,	,
37681	3475	56	the	the	DT
37681	3475	57	proposition	proposition	NN
37681	3475	58	being	be	VBG
37681	3475	59	still	still	RB
37681	3475	60	true	true	JJ
37681	3475	61	.	.	.
37681	3476	1	If	if	IN
37681	3476	2	the	the	DT
37681	3476	3	upper	upper	JJ
37681	3476	4	base	base	NN
37681	3476	5	is	be	VBZ
37681	3476	6	equal	equal	JJ
37681	3476	7	to	to	IN
37681	3476	8	the	the	DT
37681	3476	9	lower	low	JJR
37681	3476	10	base	base	NN
37681	3476	11	,	,	,
37681	3476	12	the	the	DT
37681	3476	13	frustum	frustum	NN
37681	3476	14	becomes	become	VBZ
37681	3476	15	a	a	DT
37681	3476	16	cylinder	cylinder	NN
37681	3476	17	,	,	,
37681	3476	18	and	and	CC
37681	3476	19	still	still	RB
37681	3476	20	the	the	DT
37681	3476	21	proposition	proposition	NN
37681	3476	22	remains	remain	VBZ
37681	3476	23	true	true	JJ
37681	3476	24	.	.	.
37681	3477	1	The	the	DT
37681	3477	2	proposition	proposition	NN
37681	3477	3	thus	thus	RB
37681	3477	4	offers	offer	VBZ
37681	3477	5	an	an	DT
37681	3477	6	excellent	excellent	JJ
37681	3477	7	illustration	illustration	NN
37681	3477	8	of	of	IN
37681	3477	9	the	the	DT
37681	3477	10	elementary	elementary	JJ
37681	3477	11	Principle	Principle	NNP
37681	3477	12	of	of	IN
37681	3477	13	Continuity	Continuity	NNP
37681	3477	14	.	.	.
37681	3478	1	Then	then	RB
37681	3478	2	follows	follow	VBZ
37681	3478	3	,	,	,
37681	3478	4	in	in	IN
37681	3478	5	most	most	JJS
37681	3478	6	textbooks	textbook	NNS
37681	3478	7	,	,	,
37681	3478	8	a	a	DT
37681	3478	9	theorem	theorem	NN
37681	3478	10	relating	relate	VBG
37681	3478	11	to	to	IN
37681	3478	12	the	the	DT
37681	3478	13	volume	volume	NN
37681	3478	14	of	of	IN
37681	3478	15	a	a	DT
37681	3478	16	frustum	frustum	NN
37681	3478	17	.	.	.
37681	3479	1	In	in	IN
37681	3479	2	the	the	DT
37681	3479	3	case	case	NN
37681	3479	4	of	of	IN
37681	3479	5	a	a	DT
37681	3479	6	cone	cone	NN
37681	3479	7	of	of	IN
37681	3479	8	revolution	revolution	NN
37681	3479	9	_	_	NNP
37681	3479	10	v	v	NNP
37681	3479	11	_	_	NNP
37681	3479	12	=	=	NFP
37681	3479	13	(	(	-LRB-
37681	3479	14	1/3)[pi]_h_(_r_^2	1/3)[pi]_h_(_r_^2	CD
37681	3479	15	+	+	SYM
37681	3479	16	_	_	NNP
37681	3479	17	r'_^2	r'_^2	NNP
37681	3479	18	+	+	SYM
37681	3479	19	_	_	NNP
37681	3479	20	rr	rr	NN
37681	3479	21	'	'	''
37681	3479	22	_	_	NN
37681	3479	23	)	)	-RRB-
37681	3479	24	.	.	.
37681	3480	1	Here	here	RB
37681	3480	2	if	if	IN
37681	3480	3	_	_	NNP
37681	3480	4	r	r	NNP
37681	3480	5	'	'	''
37681	3480	6	_	_	NNP
37681	3480	7	=	=	SYM
37681	3480	8	0	0	NFP
37681	3480	9	,	,	,
37681	3480	10	we	-PRON-	PRP
37681	3480	11	have	have	VBP
37681	3480	12	_	_	NNP
37681	3480	13	v	v	NNP
37681	3480	14	_	_	NNP
37681	3480	15	=	=	NFP
37681	3480	16	(	(	-LRB-
37681	3480	17	1/3)[pi]_r_^2_h	1/3)[pi]_r_^2_h	CD
37681	3480	18	_	_	NNP
37681	3480	19	,	,	,
37681	3480	20	the	the	DT
37681	3480	21	volume	volume	NN
37681	3480	22	of	of	IN
37681	3480	23	a	a	DT
37681	3480	24	cone	cone	NN
37681	3480	25	.	.	.
37681	3481	1	If	if	IN
37681	3481	2	_	_	NNP
37681	3481	3	r	r	NNP
37681	3481	4	'	'	''
37681	3481	5	_	_	NNP
37681	3481	6	=	=	SYM
37681	3481	7	_	_	NNP
37681	3481	8	r	r	NNP
37681	3481	9	_	_	NNP
37681	3481	10	,	,	,
37681	3481	11	we	-PRON-	PRP
37681	3481	12	have	have	VBP
37681	3481	13	_	_	NNP
37681	3481	14	v	v	NNP
37681	3481	15	_	_	NNP
37681	3481	16	=	=	NFP
37681	3481	17	(	(	-LRB-
37681	3481	18	1/3)[pi]_h_(_r_^2	1/3)[pi]_h_(_r_^2	CD
37681	3481	19	+	+	SYM
37681	3481	20	_	_	NNP
37681	3481	21	r_^2	r_^2	NNP
37681	3481	22	+	+	SYM
37681	3481	23	_	_	NNP
37681	3481	24	r_^2	r_^2	NNP
37681	3481	25	)	)	-RRB-
37681	3481	26	=	=	NFP
37681	3481	27	[	[	-LRB-
37681	3481	28	pi]_hr_^2	pi]_hr_^2	UH
37681	3481	29	,	,	,
37681	3481	30	the	the	DT
37681	3481	31	volume	volume	NN
37681	3481	32	of	of	IN
37681	3481	33	a	a	DT
37681	3481	34	cylinder	cylinder	NN
37681	3481	35	.	.	.
37681	3482	1	If	if	IN
37681	3482	2	one	one	PRP
37681	3482	3	needs	need	VBZ
37681	3482	4	examples	example	NNS
37681	3482	5	in	in	IN
37681	3482	6	mensuration	mensuration	NN
37681	3482	7	beyond	beyond	IN
37681	3482	8	those	those	DT
37681	3482	9	given	give	VBN
37681	3482	10	in	in	IN
37681	3482	11	a	a	DT
37681	3482	12	first	first	JJ
37681	3482	13	-	-	HYPH
37681	3482	14	class	class	NN
37681	3482	15	textbook	textbook	NN
37681	3482	16	,	,	,
37681	3482	17	they	-PRON-	PRP
37681	3482	18	are	be	VBP
37681	3482	19	easily	easily	RB
37681	3482	20	found	find	VBN
37681	3482	21	.	.	.
37681	3483	1	The	the	DT
37681	3483	2	monument	monument	NN
37681	3483	3	to	to	IN
37681	3483	4	Sir	Sir	NNP
37681	3483	5	Christopher	Christopher	NNP
37681	3483	6	Wren	Wren	NNP
37681	3483	7	,	,	,
37681	3483	8	the	the	DT
37681	3483	9	professor	professor	NN
37681	3483	10	of	of	IN
37681	3483	11	geometry	geometry	NN
37681	3483	12	in	in	IN
37681	3483	13	Cambridge	Cambridge	NNP
37681	3483	14	University	University	NNP
37681	3483	15	,	,	,
37681	3483	16	who	who	WP
37681	3483	17	became	become	VBD
37681	3483	18	the	the	DT
37681	3483	19	great	great	JJ
37681	3483	20	architect	architect	NN
37681	3483	21	of	of	IN
37681	3483	22	St.	St.	NNP
37681	3483	23	Paul	Paul	NNP
37681	3483	24	's	's	POS
37681	3483	25	Cathedral	Cathedral	NNP
37681	3483	26	in	in	IN
37681	3483	27	London	London	NNP
37681	3483	28	,	,	,
37681	3483	29	has	have	VBZ
37681	3483	30	a	a	DT
37681	3483	31	Latin	latin	JJ
37681	3483	32	inscription	inscription	NN
37681	3483	33	which	which	WDT
37681	3483	34	means	mean	VBZ
37681	3483	35	,	,	,
37681	3483	36	"	"	``
37681	3483	37	Reader	reader	NN
37681	3483	38	,	,	,
37681	3483	39	if	if	IN
37681	3483	40	you	-PRON-	PRP
37681	3483	41	would	would	MD
37681	3483	42	see	see	VB
37681	3483	43	his	-PRON-	PRP$
37681	3483	44	monument	monument	NN
37681	3483	45	,	,	,
37681	3483	46	look	look	VB
37681	3483	47	about	about	IN
37681	3483	48	you	-PRON-	PRP
37681	3483	49	.	.	.
37681	3483	50	"	"	''
37681	3484	1	So	so	CC
37681	3484	2	it	-PRON-	PRP
37681	3484	3	is	be	VBZ
37681	3484	4	with	with	IN
37681	3484	5	practical	practical	JJ
37681	3484	6	examples	example	NNS
37681	3484	7	in	in	IN
37681	3484	8	Book	Book	NNP
37681	3484	9	VII	VII	NNP
37681	3484	10	.	.	.
37681	3485	1	Appended	append	VBN
37681	3485	2	to	to	IN
37681	3485	3	this	this	DT
37681	3485	4	Book	Book	NNP
37681	3485	5	,	,	,
37681	3485	6	or	or	CC
37681	3485	7	more	more	RBR
37681	3485	8	often	often	RB
37681	3485	9	to	to	IN
37681	3485	10	the	the	DT
37681	3485	11	course	course	NN
37681	3485	12	in	in	IN
37681	3485	13	solid	solid	JJ
37681	3485	14	geometry	geometry	NN
37681	3485	15	,	,	,
37681	3485	16	is	be	VBZ
37681	3485	17	frequently	frequently	RB
37681	3485	18	found	find	VBN
37681	3485	19	a	a	DT
37681	3485	20	proposition	proposition	NN
37681	3485	21	known	know	VBN
37681	3485	22	as	as	IN
37681	3485	23	Euler	Euler	NNP
37681	3485	24	's	's	POS
37681	3485	25	Theorem	theorem	NN
37681	3485	26	.	.	.
37681	3486	1	This	this	DT
37681	3486	2	is	be	VBZ
37681	3486	3	often	often	RB
37681	3486	4	considered	consider	VBN
37681	3486	5	too	too	RB
37681	3486	6	difficult	difficult	JJ
37681	3486	7	for	for	IN
37681	3486	8	the	the	DT
37681	3486	9	average	average	JJ
37681	3486	10	pupil	pupil	NN
37681	3486	11	and	and	CC
37681	3486	12	is	be	VBZ
37681	3486	13	therefore	therefore	RB
37681	3486	14	omitted	omit	VBN
37681	3486	15	.	.	.
37681	3487	1	On	on	IN
37681	3487	2	account	account	NN
37681	3487	3	of	of	IN
37681	3487	4	its	-PRON-	PRP$
37681	3487	5	importance	importance	NN
37681	3487	6	,	,	,
37681	3487	7	however	however	RB
37681	3487	8	,	,	,
37681	3487	9	in	in	IN
37681	3487	10	the	the	DT
37681	3487	11	theory	theory	NN
37681	3487	12	of	of	IN
37681	3487	13	polyhedrons	polyhedron	NNS
37681	3487	14	,	,	,
37681	3487	15	some	some	DT
37681	3487	16	reference	reference	NN
37681	3487	17	to	to	IN
37681	3487	18	it	-PRON-	PRP
37681	3487	19	at	at	IN
37681	3487	20	this	this	DT
37681	3487	21	time	time	NN
37681	3487	22	may	may	MD
37681	3487	23	be	be	VB
37681	3487	24	helpful	helpful	JJ
37681	3487	25	to	to	IN
37681	3487	26	the	the	DT
37681	3487	27	teacher	teacher	NN
37681	3487	28	.	.	.
37681	3488	1	The	the	DT
37681	3488	2	theorem	theorem	NN
37681	3488	3	asserts	assert	VBZ
37681	3488	4	that	that	IN
37681	3488	5	in	in	IN
37681	3488	6	any	any	DT
37681	3488	7	convex	convex	NNP
37681	3488	8	polyhedron	polyhedron	NN
37681	3488	9	the	the	DT
37681	3488	10	number	number	NN
37681	3488	11	of	of	IN
37681	3488	12	edges	edge	NNS
37681	3488	13	increased	increase	VBN
37681	3488	14	by	by	IN
37681	3488	15	two	two	CD
37681	3488	16	is	be	VBZ
37681	3488	17	equal	equal	JJ
37681	3488	18	to	to	IN
37681	3488	19	the	the	DT
37681	3488	20	number	number	NN
37681	3488	21	of	of	IN
37681	3488	22	vertices	vertex	NNS
37681	3488	23	increased	increase	VBN
37681	3488	24	by	by	IN
37681	3488	25	the	the	DT
37681	3488	26	number	number	NN
37681	3488	27	of	of	IN
37681	3488	28	faces	face	NNS
37681	3488	29	.	.	.
37681	3489	1	In	in	IN
37681	3489	2	other	other	JJ
37681	3489	3	words	word	NNS
37681	3489	4	,	,	,
37681	3489	5	that	that	IN
37681	3489	6	_	_	NNP
37681	3489	7	e	e	NNP
37681	3489	8	_	_	NNP
37681	3489	9	+	+	CC
37681	3489	10	2	2	CD
37681	3489	11	=	=	SYM
37681	3489	12	_	_	NNP
37681	3489	13	v	v	NNP
37681	3489	14	_	_	NNP
37681	3489	15	+	+	NNP
37681	3489	16	_	_	NNP
37681	3489	17	f	f	NNP
37681	3489	18	_	_	NNP
37681	3489	19	.	.	.
37681	3490	1	On	on	IN
37681	3490	2	account	account	NN
37681	3490	3	of	of	IN
37681	3490	4	its	-PRON-	PRP$
37681	3490	5	importance	importance	NN
37681	3490	6	a	a	DT
37681	3490	7	proof	proof	NN
37681	3490	8	will	will	MD
37681	3490	9	be	be	VB
37681	3490	10	given	give	VBN
37681	3490	11	that	that	IN
37681	3490	12	differs	differ	NNS
37681	3490	13	from	from	IN
37681	3490	14	the	the	DT
37681	3490	15	one	one	NN
37681	3490	16	ordinarily	ordinarily	RB
37681	3490	17	found	find	VBN
37681	3490	18	in	in	IN
37681	3490	19	textbooks	textbook	NNS
37681	3490	20	.	.	.
37681	3491	1	Let	let	VB
37681	3491	2	_	_	NNP
37681	3491	3	s__{1	s__{1	NN
37681	3491	4	}	}	-RRB-
37681	3491	5	,	,	,
37681	3491	6	_	_	NNP
37681	3491	7	s__{2	s__{2	NNP
37681	3491	8	}	}	-RRB-
37681	3491	9	,	,	,
37681	3491	10	·	·	NFP
37681	3491	11	·	·	NFP
37681	3491	12	·	·	NFP
37681	3491	13	,	,	,
37681	3491	14	_	_	NNP
37681	3491	15	s__{_n	s__{_n	NNP
37681	3491	16	_	_	NNP
37681	3491	17	}	}	-RRB-
37681	3491	18	be	be	VB
37681	3491	19	the	the	DT
37681	3491	20	number	number	NN
37681	3491	21	of	of	IN
37681	3491	22	sides	side	NNS
37681	3491	23	of	of	IN
37681	3491	24	the	the	DT
37681	3491	25	various	various	JJ
37681	3491	26	faces	face	NNS
37681	3491	27	,	,	,
37681	3491	28	and	and	CC
37681	3491	29	_	_	NNP
37681	3491	30	f	f	NNP
37681	3491	31	_	_	NNP
37681	3491	32	the	the	DT
37681	3491	33	number	number	NN
37681	3491	34	of	of	IN
37681	3491	35	faces	face	NNS
37681	3491	36	.	.	.
37681	3492	1	Now	now	RB
37681	3492	2	since	since	IN
37681	3492	3	the	the	DT
37681	3492	4	sum	sum	NN
37681	3492	5	of	of	IN
37681	3492	6	the	the	DT
37681	3492	7	angles	angle	NNS
37681	3492	8	of	of	IN
37681	3492	9	a	a	DT
37681	3492	10	polygon	polygon	NN
37681	3492	11	of	of	IN
37681	3492	12	_	_	NNP
37681	3492	13	s	s	NNP
37681	3492	14	_	_	NNP
37681	3492	15	sides	side	NNS
37681	3492	16	is	be	VBZ
37681	3492	17	(	(	-LRB-
37681	3492	18	_	_	NNP
37681	3492	19	s	s	NNP
37681	3492	20	_	_	NNP
37681	3492	21	-	-	HYPH
37681	3492	22	2)180	2)180	NNP
37681	3492	23	°	°	NNS
37681	3492	24	,	,	,
37681	3492	25	therefore	therefore	RB
37681	3492	26	the	the	DT
37681	3492	27	sum	sum	NN
37681	3492	28	of	of	IN
37681	3492	29	the	the	DT
37681	3492	30	angles	angle	NNS
37681	3492	31	of	of	IN
37681	3492	32	all	all	PDT
37681	3492	33	the	the	DT
37681	3492	34	faces	face	NNS
37681	3492	35	is	be	VBZ
37681	3492	36	(	(	-LRB-
37681	3492	37	_	_	NNP
37681	3492	38	s__{1	s__{1	NNP
37681	3492	39	}	}	-RRB-
37681	3492	40	+	+	CC
37681	3492	41	_	_	NNP
37681	3492	42	s__{2	s__{2	NNP
37681	3492	43	}	}	-RRB-
37681	3492	44	+	+	CC
37681	3492	45	_	_	NNP
37681	3492	46	s__{3	s__{3	NNP
37681	3492	47	}	}	-RRB-
37681	3492	48	+	+	CC
37681	3492	49	·	·	NFP
37681	3492	50	·	·	NFP
37681	3492	51	·	·	NFP
37681	3492	52	+	+	NFP
37681	3492	53	_	_	NNP
37681	3492	54	s__{_n	s__{_n	NNP
37681	3492	55	_	_	NNP
37681	3492	56	}	}	-RRB-
37681	3492	57	-	-	HYPH
37681	3492	58	2_f_)180	2_f_)180	CD
37681	3492	59	°	°	NNS
37681	3492	60	.	.	.
37681	3493	1	But	but	CC
37681	3493	2	_	_	NNP
37681	3493	3	s__{1	s__{1	NNP
37681	3493	4	}	}	-RRB-
37681	3493	5	+	+	CC
37681	3493	6	_	_	NNP
37681	3493	7	s__{2	s__{2	NNP
37681	3493	8	}	}	-RRB-
37681	3493	9	+	+	CC
37681	3493	10	_	_	NNP
37681	3493	11	s__{3	s__{3	NNP
37681	3493	12	}	}	-RRB-
37681	3493	13	+	+	CC
37681	3493	14	·	·	NFP
37681	3493	15	·	·	NFP
37681	3493	16	·	·	NFP
37681	3493	17	+	+	NFP
37681	3493	18	_	_	NNP
37681	3493	19	s__{_n	s__{_n	NNP
37681	3493	20	_	_	NNP
37681	3493	21	}	}	-RRB-
37681	3493	22	is	be	VBZ
37681	3493	23	twice	twice	PDT
37681	3493	24	the	the	DT
37681	3493	25	number	number	NN
37681	3493	26	of	of	IN
37681	3493	27	edges	edge	NNS
37681	3493	28	,	,	,
37681	3493	29	because	because	IN
37681	3493	30	each	each	DT
37681	3493	31	edge	edge	NN
37681	3493	32	belongs	belong	VBZ
37681	3493	33	to	to	IN
37681	3493	34	two	two	CD
37681	3493	35	faces	face	NNS
37681	3493	36	.	.	.
37681	3494	1	[	[	-LRB-
37681	3494	2	therefore	therefore	RB
37681	3494	3	]	]	-RRB-
37681	3494	4	the	the	DT
37681	3494	5	sum	sum	NN
37681	3494	6	of	of	IN
37681	3494	7	the	the	DT
37681	3494	8	angles	angle	NNS
37681	3494	9	of	of	IN
37681	3494	10	all	all	PDT
37681	3494	11	the	the	DT
37681	3494	12	faces	face	NNS
37681	3494	13	is	be	VBZ
37681	3494	14	(	(	-LRB-
37681	3494	15	2_e	2_e	CD
37681	3494	16	_	_	NNP
37681	3494	17	-	-	HYPH
37681	3494	18	2_f_)180	2_f_)180	NNP
37681	3494	19	°	°	NNS
37681	3494	20	,	,	,
37681	3494	21	or	or	CC
37681	3494	22	(	(	-LRB-
37681	3494	23	_	_	NNP
37681	3494	24	e	e	NNP
37681	3494	25	_	_	NNP
37681	3494	26	-	-	HYPH
37681	3494	27	_	_	NNP
37681	3494	28	f_)360	f_)360	NN
37681	3494	29	°	°	NNS
37681	3494	30	.	.	.
37681	3495	1	Since	since	IN
37681	3495	2	the	the	DT
37681	3495	3	polyhedron	polyhedron	NN
37681	3495	4	is	be	VBZ
37681	3495	5	convex	convex	NNP
37681	3495	6	,	,	,
37681	3495	7	it	-PRON-	PRP
37681	3495	8	is	be	VBZ
37681	3495	9	possible	possible	JJ
37681	3495	10	to	to	TO
37681	3495	11	find	find	VB
37681	3495	12	some	some	DT
37681	3495	13	outside	outside	JJ
37681	3495	14	point	point	NN
37681	3495	15	of	of	IN
37681	3495	16	view	view	NN
37681	3495	17	,	,	,
37681	3495	18	_	_	NNP
37681	3495	19	P	P	NNP
37681	3495	20	_	_	NNP
37681	3495	21	,	,	,
37681	3495	22	from	from	IN
37681	3495	23	which	which	WDT
37681	3495	24	some	some	DT
37681	3495	25	face	face	NN
37681	3495	26	,	,	,
37681	3495	27	as	as	IN
37681	3495	28	_	_	NNP
37681	3495	29	ABCDE	ABCDE	NNP
37681	3495	30	_	_	NNP
37681	3495	31	,	,	,
37681	3495	32	covers	cover	VBZ
37681	3495	33	up	up	RP
37681	3495	34	the	the	DT
37681	3495	35	whole	whole	JJ
37681	3495	36	figure	figure	NN
37681	3495	37	,	,	,
37681	3495	38	as	as	IN
37681	3495	39	in	in	IN
37681	3495	40	this	this	DT
37681	3495	41	illustration	illustration	NN
37681	3495	42	.	.	.
37681	3496	1	If	if	IN
37681	3496	2	we	-PRON-	PRP
37681	3496	3	think	think	VBP
37681	3496	4	of	of	IN
37681	3496	5	all	all	PDT
37681	3496	6	the	the	DT
37681	3496	7	vertices	vertex	NNS
37681	3496	8	projected	project	VBN
37681	3496	9	on	on	IN
37681	3496	10	_	_	NNP
37681	3496	11	ABCDE	ABCDE	NNP
37681	3496	12	_	_	NNP
37681	3496	13	,	,	,
37681	3496	14	by	by	IN
37681	3496	15	lines	line	NNS
37681	3496	16	through	through	IN
37681	3496	17	_	_	NNP
37681	3496	18	P	P	NNP
37681	3496	19	_	_	NNP
37681	3496	20	,	,	,
37681	3496	21	the	the	DT
37681	3496	22	sum	sum	NN
37681	3496	23	of	of	IN
37681	3496	24	the	the	DT
37681	3496	25	angles	angle	NNS
37681	3496	26	of	of	IN
37681	3496	27	all	all	PDT
37681	3496	28	the	the	DT
37681	3496	29	faces	face	NNS
37681	3496	30	will	will	MD
37681	3496	31	be	be	VB
37681	3496	32	the	the	DT
37681	3496	33	same	same	JJ
37681	3496	34	as	as	IN
37681	3496	35	the	the	DT
37681	3496	36	sum	sum	NN
37681	3496	37	of	of	IN
37681	3496	38	the	the	DT
37681	3496	39	angles	angle	NNS
37681	3496	40	of	of	IN
37681	3496	41	all	all	DT
37681	3496	42	their	-PRON-	PRP$
37681	3496	43	projections	projection	NNS
37681	3496	44	on	on	IN
37681	3496	45	_	_	NNP
37681	3496	46	ABCDE	ABCDE	NNP
37681	3496	47	_	_	NNP
37681	3496	48	.	.	.
37681	3497	1	Calling	call	VBG
37681	3497	2	_	_	NNP
37681	3497	3	ABCDE	ABCDE	NNP
37681	3497	4	_	_	NNP
37681	3497	5	_	_	NNP
37681	3497	6	s__{1	s__{1	NNP
37681	3497	7	}	}	-RRB-
37681	3497	8	,	,	,
37681	3497	9	and	and	CC
37681	3497	10	thinking	thinking	NN
37681	3497	11	of	of	IN
37681	3497	12	the	the	DT
37681	3497	13	projections	projection	NNS
37681	3497	14	as	as	IN
37681	3497	15	traced	trace	VBN
37681	3497	16	by	by	IN
37681	3497	17	dotted	dotted	JJ
37681	3497	18	lines	line	NNS
37681	3497	19	on	on	IN
37681	3497	20	the	the	DT
37681	3497	21	opposite	opposite	JJ
37681	3497	22	side	side	NN
37681	3497	23	of	of	IN
37681	3497	24	_	_	NNP
37681	3497	25	s__{1	s__{1	NNP
37681	3497	26	}	}	-RRB-
37681	3497	27	,	,	,
37681	3497	28	this	this	DT
37681	3497	29	sum	sum	NN
37681	3497	30	is	be	VBZ
37681	3497	31	evidently	evidently	RB
37681	3497	32	equal	equal	JJ
37681	3497	33	to	to	IN
37681	3497	34	(	(	-LRB-
37681	3497	35	1	1	LS
37681	3497	36	)	)	-RRB-
37681	3497	37	the	the	DT
37681	3497	38	sum	sum	NN
37681	3497	39	of	of	IN
37681	3497	40	the	the	DT
37681	3497	41	angles	angle	NNS
37681	3497	42	in	in	IN
37681	3497	43	_	_	NNP
37681	3497	44	s__{1	s__{1	NNP
37681	3497	45	}	}	-RRB-
37681	3497	46	,	,	,
37681	3497	47	or	or	CC
37681	3497	48	(	(	-LRB-
37681	3497	49	_	_	NNP
37681	3497	50	s__{1	s__{1	NNP
37681	3497	51	}	}	-RRB-
37681	3497	52	-	-	HYPH
37681	3497	53	2	2	CD
37681	3497	54	)	)	-RRB-
37681	3497	55	180	180	CD
37681	3497	56	°	°	NNS
37681	3497	57	,	,	,
37681	3497	58	plus	plus	CC
37681	3497	59	(	(	-LRB-
37681	3497	60	2	2	LS
37681	3497	61	)	)	-RRB-
37681	3497	62	the	the	DT
37681	3497	63	sum	sum	NN
37681	3497	64	of	of	IN
37681	3497	65	the	the	DT
37681	3497	66	angles	angle	NNS
37681	3497	67	on	on	IN
37681	3497	68	the	the	DT
37681	3497	69	other	other	JJ
37681	3497	70	side	side	NN
37681	3497	71	of	of	IN
37681	3497	72	_	_	NNP
37681	3497	73	s__{1	s__{1	NNP
37681	3497	74	}	}	-RRB-
37681	3497	75	,	,	,
37681	3497	76	or	or	CC
37681	3497	77	(	(	-LRB-
37681	3497	78	_	_	NNP
37681	3497	79	s__{1	s__{1	NNP
37681	3497	80	}	}	-RRB-
37681	3497	81	-	-	:
37681	3497	82	2)180	2)180	NNP
37681	3497	83	°	°	NNS
37681	3497	84	,	,	,
37681	3497	85	plus	plus	CC
37681	3497	86	(	(	-LRB-
37681	3497	87	3	3	LS
37681	3497	88	)	)	-RRB-
37681	3497	89	the	the	DT
37681	3497	90	sum	sum	NN
37681	3497	91	of	of	IN
37681	3497	92	the	the	DT
37681	3497	93	angles	angle	NNS
37681	3497	94	about	about	IN
37681	3497	95	the	the	DT
37681	3497	96	various	various	JJ
37681	3497	97	points	point	NNS
37681	3497	98	shown	show	VBN
37681	3497	99	as	as	IN
37681	3497	100	inside	inside	RB
37681	3497	101	of	of	IN
37681	3497	102	_	_	NNP
37681	3497	103	s__{1	s__{1	NNP
37681	3497	104	}	}	-RRB-
37681	3497	105	,	,	,
37681	3497	106	of	of	IN
37681	3497	107	which	which	WDT
37681	3497	108	there	there	EX
37681	3497	109	are	be	VBP
37681	3497	110	_	_	NNP
37681	3497	111	v	v	NNP
37681	3497	112	_	_	NNP
37681	3497	113	-	-	HYPH
37681	3497	114	_	_	NNP
37681	3497	115	s__{1	s__{1	NNP
37681	3497	116	}	}	-RRB-
37681	3497	117	points	point	NNS
37681	3497	118	,	,	,
37681	3497	119	about	about	IN
37681	3497	120	each	each	DT
37681	3497	121	of	of	IN
37681	3497	122	which	which	WDT
37681	3497	123	the	the	DT
37681	3497	124	sum	sum	NN
37681	3497	125	of	of	IN
37681	3497	126	the	the	DT
37681	3497	127	angles	angle	NNS
37681	3497	128	is	be	VBZ
37681	3497	129	360	360	CD
37681	3497	130	°	°	NNS
37681	3497	131	,	,	,
37681	3497	132	making	make	VBG
37681	3497	133	(	(	-LRB-
37681	3497	134	_	_	NNP
37681	3497	135	v	v	NNP
37681	3497	136	_	_	NNP
37681	3497	137	-	-	HYPH
37681	3497	138	_	_	NNP
37681	3497	139	s__{1})360	s__{1})360	NNP
37681	3497	140	°	°	NNS
37681	3497	141	in	in	IN
37681	3497	142	all	all	DT
37681	3497	143	.	.	.
37681	3498	1	[	[	-LRB-
37681	3498	2	Illustration	illustration	NN
37681	3498	3	]	]	-RRB-
37681	3498	4	Adding	add	VBG
37681	3498	5	,	,	,
37681	3498	6	we	-PRON-	PRP
37681	3498	7	have	have	VBP
37681	3498	8	(	(	-LRB-
37681	3498	9	_	_	NNP
37681	3498	10	s__{1	s__{1	NNP
37681	3498	11	}	}	-RRB-
37681	3498	12	-	-	:
37681	3498	13	2)180	2)180	NNP
37681	3498	14	°	°	,
37681	3498	15	+	+	NFP
37681	3498	16	(	(	-LRB-
37681	3498	17	_	_	NNP
37681	3498	18	s__{1	s__{1	NNP
37681	3498	19	}	}	-RRB-
37681	3498	20	-	-	:
37681	3498	21	2)180	2)180	NNP
37681	3498	22	°	°	,
37681	3498	23	+	+	NFP
37681	3498	24	(	(	-LRB-
37681	3498	25	_	_	NNP
37681	3498	26	v	v	NNP
37681	3498	27	_	_	NNP
37681	3498	28	-	-	HYPH
37681	3498	29	_	_	NNP
37681	3498	30	s__{1})360	s__{1})360	NNP
37681	3498	31	°	°	,
37681	3498	32	=	=	NFP
37681	3498	33	[	[	-LRB-
37681	3498	34	(	(	-LRB-
37681	3498	35	_	_	NNP
37681	3498	36	s__{1	s__{1	NNP
37681	3498	37	}	}	-RRB-
37681	3498	38	-	-	HYPH
37681	3498	39	2	2	CD
37681	3498	40	)	)	-RRB-
37681	3498	41	+	+	NFP
37681	3498	42	(	(	-LRB-
37681	3498	43	_	_	NNP
37681	3498	44	v	v	NNP
37681	3498	45	_	_	NNP
37681	3498	46	-	-	HYPH
37681	3498	47	_	_	NNP
37681	3498	48	s__{1})]360	s__{1})]360	NNP
37681	3498	49	°	°	NNS
37681	3498	50	=	=	NFP
37681	3498	51	(	(	-LRB-
37681	3498	52	_	_	NNP
37681	3498	53	v	v	NNP
37681	3498	54	_	_	NNP
37681	3498	55	-	-	HYPH
37681	3498	56	2)360	2)360	NNP
37681	3498	57	°	°	NNS
37681	3498	58	.	.	.
37681	3499	1	Equating	equate	VBG
37681	3499	2	the	the	DT
37681	3499	3	two	two	CD
37681	3499	4	sums	sum	NNS
37681	3499	5	already	already	RB
37681	3499	6	found	find	VBN
37681	3499	7	,	,	,
37681	3499	8	we	-PRON-	PRP
37681	3499	9	have	have	VBP
37681	3499	10	(	(	-LRB-
37681	3499	11	_	_	NNP
37681	3499	12	e	e	NNP
37681	3499	13	_	_	NNP
37681	3499	14	-	-	HYPH
37681	3499	15	_	_	NNP
37681	3499	16	f_)360	f_)360	NN
37681	3499	17	°	°	NNS
37681	3499	18	=	=	NFP
37681	3499	19	(	(	-LRB-
37681	3499	20	_	_	NNP
37681	3499	21	v	v	NNP
37681	3499	22	_	_	NNP
37681	3499	23	-	-	HYPH
37681	3499	24	2)360	2)360	NNP
37681	3499	25	°	°	NNS
37681	3499	26	,	,	,
37681	3499	27	or	or	CC
37681	3499	28	_	_	NNP
37681	3499	29	e	e	NNP
37681	3499	30	_	_	NNP
37681	3499	31	-	-	HYPH
37681	3499	32	_	_	NNP
37681	3499	33	f	f	NNP
37681	3499	34	_	_	NNP
37681	3499	35	=	=	SYM
37681	3499	36	_	_	NNP
37681	3499	37	v	v	NNP
37681	3499	38	_	_	NNP
37681	3499	39	-	-	HYPH
37681	3499	40	2	2	NNP
37681	3499	41	,	,	,
37681	3499	42	or	or	CC
37681	3499	43	_	_	NNP
37681	3499	44	e	e	NNP
37681	3499	45	_	_	NNP
37681	3499	46	+	+	CC
37681	3499	47	2	2	CD
37681	3499	48	=	=	SYM
37681	3499	49	_	_	NNP
37681	3499	50	v	v	NNP
37681	3499	51	_	_	NNP
37681	3499	52	+	+	NNP
37681	3499	53	_	_	NNP
37681	3499	54	f	f	NNP
37681	3499	55	_	_	NNP
37681	3499	56	.	.	.
37681	3500	1	This	this	DT
37681	3500	2	proof	proof	NN
37681	3500	3	is	be	VBZ
37681	3500	4	too	too	RB
37681	3500	5	abstract	abstract	JJ
37681	3500	6	for	for	IN
37681	3500	7	most	most	JJS
37681	3500	8	pupils	pupil	NNS
37681	3500	9	in	in	IN
37681	3500	10	the	the	DT
37681	3500	11	high	high	JJ
37681	3500	12	school	school	NN
37681	3500	13	,	,	,
37681	3500	14	but	but	CC
37681	3500	15	it	-PRON-	PRP
37681	3500	16	is	be	VBZ
37681	3500	17	more	more	RBR
37681	3500	18	scientific	scientific	JJ
37681	3500	19	than	than	IN
37681	3500	20	those	those	DT
37681	3500	21	found	find	VBN
37681	3500	22	in	in	IN
37681	3500	23	any	any	DT
37681	3500	24	of	of	IN
37681	3500	25	the	the	DT
37681	3500	26	elementary	elementary	JJ
37681	3500	27	textbooks	textbook	NNS
37681	3500	28	,	,	,
37681	3500	29	and	and	CC
37681	3500	30	teachers	teacher	NNS
37681	3500	31	will	will	MD
37681	3500	32	find	find	VB
37681	3500	33	it	-PRON-	PRP
37681	3500	34	of	of	IN
37681	3500	35	service	service	NN
37681	3500	36	in	in	IN
37681	3500	37	relieving	relieve	VBG
37681	3500	38	their	-PRON-	PRP$
37681	3500	39	own	own	JJ
37681	3500	40	minds	mind	NNS
37681	3500	41	of	of	IN
37681	3500	42	any	any	DT
37681	3500	43	question	question	NN
37681	3500	44	as	as	IN
37681	3500	45	to	to	IN
37681	3500	46	the	the	DT
37681	3500	47	legitimacy	legitimacy	NN
37681	3500	48	of	of	IN
37681	3500	49	the	the	DT
37681	3500	50	theorem	theorem	NN
37681	3500	51	.	.	.
37681	3501	1	Although	although	IN
37681	3501	2	this	this	DT
37681	3501	3	proposition	proposition	NN
37681	3501	4	is	be	VBZ
37681	3501	5	generally	generally	RB
37681	3501	6	attributed	attribute	VBN
37681	3501	7	to	to	IN
37681	3501	8	Euler	Euler	NNP
37681	3501	9	,	,	,
37681	3501	10	and	and	CC
37681	3501	11	was	be	VBD
37681	3501	12	,	,	,
37681	3501	13	indeed	indeed	RB
37681	3501	14	,	,	,
37681	3501	15	rediscovered	rediscover	VBN
37681	3501	16	by	by	IN
37681	3501	17	him	-PRON-	PRP
37681	3501	18	and	and	CC
37681	3501	19	published	publish	VBN
37681	3501	20	in	in	IN
37681	3501	21	1752	1752	CD
37681	3501	22	,	,	,
37681	3501	23	it	-PRON-	PRP
37681	3501	24	was	be	VBD
37681	3501	25	known	know	VBN
37681	3501	26	to	to	IN
37681	3501	27	the	the	DT
37681	3501	28	great	great	JJ
37681	3501	29	French	french	JJ
37681	3501	30	geometer	geometer	NN
37681	3501	31	Descartes	Descartes	NNPS
37681	3501	32	,	,	,
37681	3501	33	a	a	DT
37681	3501	34	fact	fact	NN
37681	3501	35	that	that	IN
37681	3501	36	Leibnitz	Leibnitz	NNP
37681	3501	37	mentions	mention	NNS
37681	3501	38	.	.	.
37681	3502	1	[	[	-LRB-
37681	3502	2	91	91	CD
37681	3502	3	]	]	-RRB-
37681	3502	4	This	this	DT
37681	3502	5	theorem	theorem	NN
37681	3502	6	has	have	VBZ
37681	3502	7	a	a	DT
37681	3502	8	very	very	RB
37681	3502	9	practical	practical	JJ
37681	3502	10	application	application	NN
37681	3502	11	in	in	IN
37681	3502	12	the	the	DT
37681	3502	13	study	study	NN
37681	3502	14	of	of	IN
37681	3502	15	crystals	crystal	NNS
37681	3502	16	,	,	,
37681	3502	17	since	since	IN
37681	3502	18	it	-PRON-	PRP
37681	3502	19	offers	offer	VBZ
37681	3502	20	a	a	DT
37681	3502	21	convenient	convenient	JJ
37681	3502	22	check	check	NN
37681	3502	23	on	on	IN
37681	3502	24	the	the	DT
37681	3502	25	count	count	NN
37681	3502	26	of	of	IN
37681	3502	27	faces	face	NNS
37681	3502	28	,	,	,
37681	3502	29	edges	edge	NNS
37681	3502	30	,	,	,
37681	3502	31	and	and	CC
37681	3502	32	vertices	vertex	NNS
37681	3502	33	.	.	.
37681	3503	1	Some	some	DT
37681	3503	2	use	use	NN
37681	3503	3	of	of	IN
37681	3503	4	crystals	crystal	NNS
37681	3503	5	,	,	,
37681	3503	6	or	or	CC
37681	3503	7	even	even	RB
37681	3503	8	of	of	IN
37681	3503	9	polyhedrons	polyhedron	NNS
37681	3503	10	cut	cut	VBN
37681	3503	11	from	from	IN
37681	3503	12	a	a	DT
37681	3503	13	piece	piece	NN
37681	3503	14	of	of	IN
37681	3503	15	crayon	crayon	NN
37681	3503	16	,	,	,
37681	3503	17	is	be	VBZ
37681	3503	18	desirable	desirable	JJ
37681	3503	19	when	when	WRB
37681	3503	20	studying	study	VBG
37681	3503	21	Euler	Euler	NNP
37681	3503	22	's	's	POS
37681	3503	23	proposition	proposition	NN
37681	3503	24	.	.	.
37681	3504	1	The	the	DT
37681	3504	2	following	follow	VBG
37681	3504	3	illustrations	illustration	NNS
37681	3504	4	of	of	IN
37681	3504	5	common	common	JJ
37681	3504	6	forms	form	NNS
37681	3504	7	of	of	IN
37681	3504	8	crystals	crystal	NNS
37681	3504	9	may	may	MD
37681	3504	10	be	be	VB
37681	3504	11	used	use	VBN
37681	3504	12	in	in	IN
37681	3504	13	this	this	DT
37681	3504	14	connection	connection	NN
37681	3504	15	:	:	:
37681	3504	16	[	[	-LRB-
37681	3504	17	Illustration	illustration	NN
37681	3504	18	]	]	-RRB-
37681	3504	19	The	the	DT
37681	3504	20	first	first	JJ
37681	3504	21	represents	represent	VBZ
37681	3504	22	two	two	CD
37681	3504	23	truncated	truncate	VBN
37681	3504	24	pyramids	pyramid	NNS
37681	3504	25	placed	place	VBN
37681	3504	26	base	base	NN
37681	3504	27	to	to	IN
37681	3504	28	base	base	NN
37681	3504	29	.	.	.
37681	3505	1	Here	here	RB
37681	3505	2	_	_	NNP
37681	3505	3	e	e	NNP
37681	3505	4	_	_	NNP
37681	3505	5	=	=	SYM
37681	3505	6	20	20	CD
37681	3505	7	,	,	,
37681	3505	8	_	_	NNP
37681	3505	9	f	f	NNP
37681	3505	10	_	_	NNP
37681	3505	11	=	=	SYM
37681	3505	12	10	10	CD
37681	3505	13	,	,	,
37681	3505	14	_	_	NNP
37681	3505	15	v	v	NNP
37681	3505	16	_	_	NNP
37681	3505	17	=	=	SYM
37681	3505	18	12	12	CD
37681	3505	19	,	,	,
37681	3505	20	so	so	IN
37681	3505	21	that	that	IN
37681	3505	22	_	_	NNP
37681	3505	23	e	e	NNP
37681	3505	24	_	_	NNP
37681	3505	25	+	+	CC
37681	3505	26	2	2	CD
37681	3505	27	=	=	SYM
37681	3505	28	_	_	NNP
37681	3505	29	f	f	NNP
37681	3505	30	_	_	NNP
37681	3505	31	+	+	NNP
37681	3505	32	_	_	NNP
37681	3505	33	v	v	NNP
37681	3505	34	_	_	NNP
37681	3505	35	.	.	.
37681	3506	1	The	the	DT
37681	3506	2	second	second	JJ
37681	3506	3	represents	represent	VBZ
37681	3506	4	a	a	DT
37681	3506	5	crystal	crystal	NN
37681	3506	6	formed	form	VBN
37681	3506	7	by	by	IN
37681	3506	8	replacing	replace	VBG
37681	3506	9	each	each	DT
37681	3506	10	edge	edge	NN
37681	3506	11	of	of	IN
37681	3506	12	a	a	DT
37681	3506	13	cube	cube	NN
37681	3506	14	by	by	IN
37681	3506	15	a	a	DT
37681	3506	16	plane	plane	NN
37681	3506	17	,	,	,
37681	3506	18	with	with	IN
37681	3506	19	the	the	DT
37681	3506	20	result	result	NN
37681	3506	21	that	that	IN
37681	3506	22	_	_	NNP
37681	3506	23	e	e	NNP
37681	3506	24	_	_	NNP
37681	3506	25	=	=	SYM
37681	3506	26	40	40	CD
37681	3506	27	,	,	,
37681	3506	28	_	_	NNP
37681	3506	29	f	f	NNP
37681	3506	30	_	_	NNP
37681	3506	31	=	=	SYM
37681	3506	32	18	18	CD
37681	3506	33	,	,	,
37681	3506	34	and	and	CC
37681	3506	35	_	_	NNP
37681	3506	36	v	v	NNP
37681	3506	37	_	_	NNP
37681	3506	38	=	=	SYM
37681	3506	39	24	24	CD
37681	3506	40	.	.	.
37681	3507	1	The	the	DT
37681	3507	2	third	third	JJ
37681	3507	3	represents	represent	VBZ
37681	3507	4	a	a	DT
37681	3507	5	crystal	crystal	NN
37681	3507	6	formed	form	VBN
37681	3507	7	by	by	IN
37681	3507	8	replacing	replace	VBG
37681	3507	9	each	each	DT
37681	3507	10	edge	edge	NN
37681	3507	11	of	of	IN
37681	3507	12	an	an	DT
37681	3507	13	octahedron	octahedron	NN
37681	3507	14	by	by	IN
37681	3507	15	a	a	DT
37681	3507	16	plane	plane	NN
37681	3507	17	,	,	,
37681	3507	18	it	-PRON-	PRP
37681	3507	19	being	be	VBG
37681	3507	20	easy	easy	JJ
37681	3507	21	to	to	TO
37681	3507	22	see	see	VB
37681	3507	23	that	that	IN
37681	3507	24	Euler	Euler	NNP
37681	3507	25	's	's	POS
37681	3507	26	law	law	NN
37681	3507	27	still	still	RB
37681	3507	28	holds	hold	VBZ
37681	3507	29	true	true	JJ
37681	3507	30	.	.	.
37681	3508	1	FOOTNOTES	footnote	NNS
37681	3508	2	:	:	:
37681	3508	3	[	[	-LRB-
37681	3508	4	89	89	CD
37681	3508	5	]	]	-RRB-
37681	3508	6	The	the	DT
37681	3508	7	actual	actual	JJ
37681	3508	8	construction	construction	NN
37681	3508	9	of	of	IN
37681	3508	10	these	these	DT
37681	3508	11	solids	solid	NNS
37681	3508	12	is	be	VBZ
37681	3508	13	given	give	VBN
37681	3508	14	by	by	IN
37681	3508	15	Pappus	Pappus	NNP
37681	3508	16	.	.	.
37681	3509	1	See	see	VB
37681	3509	2	his	-PRON-	PRP$
37681	3509	3	"	"	``
37681	3509	4	Mathematicae	Mathematicae	NNP
37681	3509	5	Collectiones	Collectiones	NNPS
37681	3509	6	,	,	,
37681	3509	7	"	"	''
37681	3509	8	p.	p.	NN
37681	3509	9	48	48	CD
37681	3509	10	,	,	,
37681	3509	11	Bologna	Bologna	NNPS
37681	3509	12	,	,	,
37681	3509	13	1660	1660	CD
37681	3509	14	.	.	.
37681	3510	1	[	[	-LRB-
37681	3510	2	90	90	CD
37681	3510	3	]	]	-RRB-
37681	3510	4	The	the	DT
37681	3510	5	illustration	illustration	NN
37681	3510	6	is	be	VBZ
37681	3510	7	from	from	IN
37681	3510	8	Dupin	Dupin	NNP
37681	3510	9	,	,	,
37681	3510	10	loc	loc	NNP
37681	3510	11	.	.	.
37681	3511	1	cit	cit	NNP
37681	3511	2	.	.	.
37681	3512	1	[	[	-LRB-
37681	3512	2	91	91	CD
37681	3512	3	]	]	-RRB-
37681	3512	4	For	for	IN
37681	3512	5	the	the	DT
37681	3512	6	historical	historical	JJ
37681	3512	7	bibliography	bibliography	NN
37681	3512	8	consult	consult	NNP
37681	3512	9	G.	G.	NNP
37681	3512	10	Holzmüller	Holzmüller	NNP
37681	3512	11	,	,	,
37681	3512	12	_	_	NNP
37681	3512	13	Elemente	Elemente	NNP
37681	3512	14	der	der	VBP
37681	3512	15	Stereometrie	Stereometrie	NNP
37681	3512	16	_	_	NNP
37681	3512	17	,	,	,
37681	3512	18	Vol	Vol	NNP
37681	3512	19	.	.	.
37681	3513	1	I	-PRON-	PRP
37681	3513	2	,	,	,
37681	3513	3	p.	p.	NN
37681	3513	4	181	181	CD
37681	3513	5	,	,	,
37681	3513	6	Leipzig	Leipzig	NNP
37681	3513	7	,	,	,
37681	3513	8	1900	1900	CD
37681	3513	9	.	.	.
37681	3514	1	CHAPTER	chapter	NN
37681	3514	2	XXI	xxi	VBP
37681	3514	3	THE	the	DT
37681	3514	4	LEADING	lead	VBG
37681	3514	5	PROPOSITIONS	proposition	NNS
37681	3514	6	OF	of	IN
37681	3514	7	BOOK	book	NN
37681	3514	8	VIII	viii	NN
37681	3514	9	Book	book	NN
37681	3514	10	VIII	viii	VBP
37681	3514	11	treats	treat	NNS
37681	3514	12	of	of	IN
37681	3514	13	the	the	DT
37681	3514	14	sphere	sphere	NN
37681	3514	15	.	.	.
37681	3515	1	Just	just	RB
37681	3515	2	as	as	IN
37681	3515	3	the	the	DT
37681	3515	4	circle	circle	NN
37681	3515	5	may	may	MD
37681	3515	6	be	be	VB
37681	3515	7	defined	define	VBN
37681	3515	8	either	either	CC
37681	3515	9	as	as	IN
37681	3515	10	a	a	DT
37681	3515	11	plane	plane	NN
37681	3515	12	surface	surface	NN
37681	3515	13	or	or	CC
37681	3515	14	as	as	IN
37681	3515	15	the	the	DT
37681	3515	16	bounding	bound	VBG
37681	3515	17	line	line	NN
37681	3515	18	which	which	WDT
37681	3515	19	is	be	VBZ
37681	3515	20	the	the	DT
37681	3515	21	locus	locus	NN
37681	3515	22	of	of	IN
37681	3515	23	a	a	DT
37681	3515	24	point	point	NN
37681	3515	25	in	in	IN
37681	3515	26	a	a	DT
37681	3515	27	plane	plane	NN
37681	3515	28	at	at	IN
37681	3515	29	a	a	DT
37681	3515	30	given	give	VBN
37681	3515	31	distance	distance	NN
37681	3515	32	from	from	IN
37681	3515	33	a	a	DT
37681	3515	34	fixed	fix	VBN
37681	3515	35	point	point	NN
37681	3515	36	,	,	,
37681	3515	37	so	so	CC
37681	3515	38	a	a	DT
37681	3515	39	sphere	sphere	NN
37681	3515	40	may	may	MD
37681	3515	41	be	be	VB
37681	3515	42	defined	define	VBN
37681	3515	43	either	either	CC
37681	3515	44	as	as	IN
37681	3515	45	a	a	DT
37681	3515	46	solid	solid	JJ
37681	3515	47	or	or	CC
37681	3515	48	as	as	IN
37681	3515	49	the	the	DT
37681	3515	50	bounding	bound	VBG
37681	3515	51	surface	surface	NN
37681	3515	52	which	which	WDT
37681	3515	53	is	be	VBZ
37681	3515	54	the	the	DT
37681	3515	55	locus	locus	NN
37681	3515	56	of	of	IN
37681	3515	57	a	a	DT
37681	3515	58	point	point	NN
37681	3515	59	in	in	IN
37681	3515	60	space	space	NN
37681	3515	61	at	at	IN
37681	3515	62	a	a	DT
37681	3515	63	given	give	VBN
37681	3515	64	distance	distance	NN
37681	3515	65	from	from	IN
37681	3515	66	a	a	DT
37681	3515	67	fixed	fix	VBN
37681	3515	68	point	point	NN
37681	3515	69	.	.	.
37681	3516	1	In	in	IN
37681	3516	2	higher	high	JJR
37681	3516	3	mathematics	mathematic	NNS
37681	3516	4	the	the	DT
37681	3516	5	circle	circle	NN
37681	3516	6	is	be	VBZ
37681	3516	7	defined	define	VBN
37681	3516	8	as	as	IN
37681	3516	9	the	the	DT
37681	3516	10	bounding	bound	VBG
37681	3516	11	line	line	NN
37681	3516	12	and	and	CC
37681	3516	13	the	the	DT
37681	3516	14	sphere	sphere	NN
37681	3516	15	as	as	IN
37681	3516	16	the	the	DT
37681	3516	17	bounding	bound	VBG
37681	3516	18	surface	surface	NN
37681	3516	19	;	;	:
37681	3516	20	that	that	RB
37681	3516	21	is	is	RB
37681	3516	22	,	,	,
37681	3516	23	each	each	DT
37681	3516	24	is	be	VBZ
37681	3516	25	defined	define	VBN
37681	3516	26	as	as	IN
37681	3516	27	a	a	DT
37681	3516	28	locus	locus	NN
37681	3516	29	.	.	.
37681	3517	1	This	this	DT
37681	3517	2	view	view	NN
37681	3517	3	of	of	IN
37681	3517	4	the	the	DT
37681	3517	5	circle	circle	NN
37681	3517	6	as	as	IN
37681	3517	7	a	a	DT
37681	3517	8	line	line	NN
37681	3517	9	is	be	VBZ
37681	3517	10	becoming	become	VBG
37681	3517	11	quite	quite	RB
37681	3517	12	general	general	JJ
37681	3517	13	in	in	IN
37681	3517	14	elementary	elementary	JJ
37681	3517	15	geometry	geometry	NNP
37681	3517	16	,	,	,
37681	3517	17	it	-PRON-	PRP
37681	3517	18	being	be	VBG
37681	3517	19	the	the	DT
37681	3517	20	desire	desire	NN
37681	3517	21	that	that	IN
37681	3517	22	students	student	NNS
37681	3517	23	may	may	MD
37681	3517	24	not	not	RB
37681	3517	25	have	have	VB
37681	3517	26	to	to	TO
37681	3517	27	change	change	VB
37681	3517	28	definitions	definition	NNS
37681	3517	29	in	in	IN
37681	3517	30	passing	pass	VBG
37681	3517	31	from	from	IN
37681	3517	32	elementary	elementary	JJ
37681	3517	33	to	to	IN
37681	3517	34	higher	high	JJR
37681	3517	35	mathematics	mathematic	NNS
37681	3517	36	.	.	.
37681	3518	1	The	the	DT
37681	3518	2	sphere	sphere	NN
37681	3518	3	is	be	VBZ
37681	3518	4	less	less	RBR
37681	3518	5	frequently	frequently	RB
37681	3518	6	looked	look	VBN
37681	3518	7	upon	upon	IN
37681	3518	8	in	in	IN
37681	3518	9	geometry	geometry	NN
37681	3518	10	as	as	IN
37681	3518	11	a	a	DT
37681	3518	12	surface	surface	NN
37681	3518	13	,	,	,
37681	3518	14	and	and	CC
37681	3518	15	in	in	IN
37681	3518	16	popular	popular	JJ
37681	3518	17	usage	usage	NN
37681	3518	18	it	-PRON-	PRP
37681	3518	19	is	be	VBZ
37681	3518	20	always	always	RB
37681	3518	21	taken	take	VBN
37681	3518	22	as	as	IN
37681	3518	23	a	a	DT
37681	3518	24	solid	solid	NN
37681	3518	25	.	.	.
37681	3519	1	Analogous	analogous	JJ
37681	3519	2	to	to	IN
37681	3519	3	the	the	DT
37681	3519	4	postulate	postulate	NN
37681	3519	5	that	that	WDT
37681	3519	6	a	a	DT
37681	3519	7	circle	circle	NN
37681	3519	8	may	may	MD
37681	3519	9	be	be	VB
37681	3519	10	described	describe	VBN
37681	3519	11	with	with	IN
37681	3519	12	any	any	DT
37681	3519	13	given	give	VBN
37681	3519	14	point	point	NN
37681	3519	15	as	as	IN
37681	3519	16	a	a	DT
37681	3519	17	center	center	NN
37681	3519	18	and	and	CC
37681	3519	19	any	any	DT
37681	3519	20	given	give	VBN
37681	3519	21	line	line	NN
37681	3519	22	as	as	IN
37681	3519	23	a	a	DT
37681	3519	24	radius	radius	NN
37681	3519	25	,	,	,
37681	3519	26	is	be	VBZ
37681	3519	27	the	the	DT
37681	3519	28	postulate	postulate	NN
37681	3519	29	for	for	IN
37681	3519	30	constructing	construct	VBG
37681	3519	31	a	a	DT
37681	3519	32	sphere	sphere	NN
37681	3519	33	with	with	IN
37681	3519	34	any	any	DT
37681	3519	35	given	give	VBN
37681	3519	36	center	center	NN
37681	3519	37	and	and	CC
37681	3519	38	any	any	DT
37681	3519	39	given	give	VBN
37681	3519	40	radius	radius	NN
37681	3519	41	.	.	.
37681	3520	1	This	this	DT
37681	3520	2	postulate	postulate	NN
37681	3520	3	is	be	VBZ
37681	3520	4	not	not	RB
37681	3520	5	so	so	RB
37681	3520	6	essential	essential	JJ
37681	3520	7	,	,	,
37681	3520	8	however	however	RB
37681	3520	9	,	,	,
37681	3520	10	as	as	IN
37681	3520	11	the	the	DT
37681	3520	12	one	one	CD
37681	3520	13	about	about	IN
37681	3520	14	the	the	DT
37681	3520	15	circle	circle	NN
37681	3520	16	,	,	,
37681	3520	17	because	because	IN
37681	3520	18	we	-PRON-	PRP
37681	3520	19	are	be	VBP
37681	3520	20	not	not	RB
37681	3520	21	so	so	RB
37681	3520	22	concerned	concerned	JJ
37681	3520	23	with	with	IN
37681	3520	24	constructions	construction	NNS
37681	3520	25	here	here	RB
37681	3520	26	as	as	IN
37681	3520	27	we	-PRON-	PRP
37681	3520	28	are	be	VBP
37681	3520	29	in	in	IN
37681	3520	30	plane	plane	NN
37681	3520	31	geometry	geometry	NN
37681	3520	32	.	.	.
37681	3521	1	A	a	DT
37681	3521	2	good	good	JJ
37681	3521	3	opportunity	opportunity	NN
37681	3521	4	is	be	VBZ
37681	3521	5	offered	offer	VBN
37681	3521	6	for	for	IN
37681	3521	7	illustrating	illustrate	VBG
37681	3521	8	several	several	JJ
37681	3521	9	of	of	IN
37681	3521	10	the	the	DT
37681	3521	11	definitions	definition	NNS
37681	3521	12	connected	connect	VBN
37681	3521	13	with	with	IN
37681	3521	14	the	the	DT
37681	3521	15	study	study	NN
37681	3521	16	of	of	IN
37681	3521	17	the	the	DT
37681	3521	18	sphere	sphere	NN
37681	3521	19	,	,	,
37681	3521	20	such	such	JJ
37681	3521	21	as	as	IN
37681	3521	22	great	great	JJ
37681	3521	23	circle	circle	NN
37681	3521	24	,	,	,
37681	3521	25	axis	axis	NNP
37681	3521	26	,	,	,
37681	3521	27	small	small	JJ
37681	3521	28	circle	circle	NN
37681	3521	29	,	,	,
37681	3521	30	and	and	CC
37681	3521	31	pole	pole	NNP
37681	3521	32	,	,	,
37681	3521	33	by	by	IN
37681	3521	34	referring	refer	VBG
37681	3521	35	to	to	IN
37681	3521	36	geography	geography	NN
37681	3521	37	.	.	.
37681	3522	1	Indeed	indeed	RB
37681	3522	2	,	,	,
37681	3522	3	the	the	DT
37681	3522	4	first	first	JJ
37681	3522	5	three	three	CD
37681	3522	6	propositions	proposition	NNS
37681	3522	7	usually	usually	RB
37681	3522	8	given	give	VBN
37681	3522	9	in	in	IN
37681	3522	10	Book	book	NN
37681	3522	11	VIII	viii	NN
37681	3522	12	have	have	VBP
37681	3522	13	a	a	DT
37681	3522	14	direct	direct	JJ
37681	3522	15	bearing	bearing	NN
37681	3522	16	upon	upon	IN
37681	3522	17	the	the	DT
37681	3522	18	study	study	NN
37681	3522	19	of	of	IN
37681	3522	20	the	the	DT
37681	3522	21	earth	earth	NN
37681	3522	22	.	.	.
37681	3523	1	THEOREM	THEOREM	NNP
37681	3523	2	.	.	.
37681	3524	1	_	_	NNP
37681	3524	2	A	a	DT
37681	3524	3	plane	plane	NN
37681	3524	4	perpendicular	perpendicular	JJ
37681	3524	5	to	to	IN
37681	3524	6	a	a	DT
37681	3524	7	radius	radius	NN
37681	3524	8	at	at	IN
37681	3524	9	its	-PRON-	PRP$
37681	3524	10	extremity	extremity	NN
37681	3524	11	is	be	VBZ
37681	3524	12	tangent	tangent	NN
37681	3524	13	to	to	IN
37681	3524	14	the	the	DT
37681	3524	15	sphere	sphere	NN
37681	3524	16	.	.	.
37681	3524	17	_	_	NNP
37681	3524	18	The	the	DT
37681	3524	19	student	student	NN
37681	3524	20	should	should	MD
37681	3524	21	always	always	RB
37681	3524	22	have	have	VB
37681	3524	23	his	-PRON-	PRP$
37681	3524	24	attention	attention	NN
37681	3524	25	called	call	VBN
37681	3524	26	to	to	IN
37681	3524	27	the	the	DT
37681	3524	28	analogue	analogue	NN
37681	3524	29	in	in	IN
37681	3524	30	plane	plane	NN
37681	3524	31	geometry	geometry	NN
37681	3524	32	,	,	,
37681	3524	33	where	where	WRB
37681	3524	34	there	there	EX
37681	3524	35	is	be	VBZ
37681	3524	36	one	one	CD
37681	3524	37	.	.	.
37681	3525	1	If	if	IN
37681	3525	2	here	here	RB
37681	3525	3	we	-PRON-	PRP
37681	3525	4	pass	pass	VBP
37681	3525	5	a	a	DT
37681	3525	6	plane	plane	NN
37681	3525	7	through	through	IN
37681	3525	8	the	the	DT
37681	3525	9	radius	radius	NN
37681	3525	10	in	in	IN
37681	3525	11	question	question	NN
37681	3525	12	,	,	,
37681	3525	13	the	the	DT
37681	3525	14	figure	figure	NN
37681	3525	15	formed	form	VBN
37681	3525	16	on	on	IN
37681	3525	17	the	the	DT
37681	3525	18	plane	plane	NN
37681	3525	19	will	will	MD
37681	3525	20	be	be	VB
37681	3525	21	that	that	DT
37681	3525	22	of	of	IN
37681	3525	23	a	a	DT
37681	3525	24	line	line	NN
37681	3525	25	tangent	tangent	NN
37681	3525	26	to	to	IN
37681	3525	27	a	a	DT
37681	3525	28	circle	circle	NN
37681	3525	29	.	.	.
37681	3526	1	If	if	IN
37681	3526	2	we	-PRON-	PRP
37681	3526	3	revolve	revolve	VBP
37681	3526	4	this	this	DT
37681	3526	5	about	about	IN
37681	3526	6	the	the	DT
37681	3526	7	line	line	NN
37681	3526	8	of	of	IN
37681	3526	9	the	the	DT
37681	3526	10	radius	radius	NN
37681	3526	11	in	in	IN
37681	3526	12	question	question	NN
37681	3526	13	,	,	,
37681	3526	14	as	as	IN
37681	3526	15	an	an	DT
37681	3526	16	axis	axis	NN
37681	3526	17	,	,	,
37681	3526	18	the	the	DT
37681	3526	19	circle	circle	NN
37681	3526	20	will	will	MD
37681	3526	21	generate	generate	VB
37681	3526	22	the	the	DT
37681	3526	23	sphere	sphere	NN
37681	3526	24	again	again	RB
37681	3526	25	,	,	,
37681	3526	26	and	and	CC
37681	3526	27	the	the	DT
37681	3526	28	tangent	tangent	NN
37681	3526	29	line	line	NN
37681	3526	30	will	will	MD
37681	3526	31	generate	generate	VB
37681	3526	32	the	the	DT
37681	3526	33	tangent	tangent	NN
37681	3526	34	plane	plane	NN
37681	3526	35	.	.	.
37681	3527	1	THEOREM	THEOREM	NNP
37681	3527	2	.	.	.
37681	3528	1	_	_	NNP
37681	3528	2	A	a	DT
37681	3528	3	sphere	sphere	NN
37681	3528	4	may	may	MD
37681	3528	5	be	be	VB
37681	3528	6	inscribed	inscribe	VBN
37681	3528	7	in	in	IN
37681	3528	8	any	any	DT
37681	3528	9	given	give	VBN
37681	3528	10	tetrahedron	tetrahedron	NN
37681	3528	11	.	.	.
37681	3528	12	_	_	NNP
37681	3528	13	Here	here	RB
37681	3528	14	again	again	RB
37681	3528	15	we	-PRON-	PRP
37681	3528	16	may	may	MD
37681	3528	17	form	form	VB
37681	3528	18	a	a	DT
37681	3528	19	corresponding	corresponding	JJ
37681	3528	20	proposition	proposition	NN
37681	3528	21	of	of	IN
37681	3528	22	plane	plane	NN
37681	3528	23	geometry	geometry	NN
37681	3528	24	by	by	IN
37681	3528	25	passing	pass	VBG
37681	3528	26	a	a	DT
37681	3528	27	plane	plane	NN
37681	3528	28	through	through	IN
37681	3528	29	any	any	DT
37681	3528	30	three	three	CD
37681	3528	31	points	point	NNS
37681	3528	32	of	of	IN
37681	3528	33	contact	contact	NN
37681	3528	34	of	of	IN
37681	3528	35	the	the	DT
37681	3528	36	sphere	sphere	NN
37681	3528	37	and	and	CC
37681	3528	38	the	the	DT
37681	3528	39	tetrahedron	tetrahedron	NN
37681	3528	40	.	.	.
37681	3529	1	We	-PRON-	PRP
37681	3529	2	shall	shall	MD
37681	3529	3	then	then	RB
37681	3529	4	form	form	VB
37681	3529	5	the	the	DT
37681	3529	6	figure	figure	NN
37681	3529	7	of	of	IN
37681	3529	8	a	a	DT
37681	3529	9	circle	circle	NN
37681	3529	10	inscribed	inscribe	VBN
37681	3529	11	in	in	IN
37681	3529	12	a	a	DT
37681	3529	13	triangle	triangle	NN
37681	3529	14	.	.	.
37681	3530	1	And	and	CC
37681	3530	2	just	just	RB
37681	3530	3	as	as	IN
37681	3530	4	in	in	IN
37681	3530	5	the	the	DT
37681	3530	6	case	case	NN
37681	3530	7	of	of	IN
37681	3530	8	the	the	DT
37681	3530	9	triangle	triangle	NN
37681	3530	10	we	-PRON-	PRP
37681	3530	11	may	may	MD
37681	3530	12	have	have	VB
37681	3530	13	escribed	escribe	VBN
37681	3530	14	circles	circle	NNS
37681	3530	15	by	by	IN
37681	3530	16	producing	produce	VBG
37681	3530	17	the	the	DT
37681	3530	18	sides	side	NNS
37681	3530	19	,	,	,
37681	3530	20	so	so	RB
37681	3530	21	in	in	IN
37681	3530	22	the	the	DT
37681	3530	23	case	case	NN
37681	3530	24	of	of	IN
37681	3530	25	the	the	DT
37681	3530	26	tetrahedron	tetrahedron	NN
37681	3530	27	we	-PRON-	PRP
37681	3530	28	may	may	MD
37681	3530	29	have	have	VB
37681	3530	30	escribed	escribed	JJ
37681	3530	31	spheres	sphere	NNS
37681	3530	32	by	by	IN
37681	3530	33	producing	produce	VBG
37681	3530	34	the	the	DT
37681	3530	35	planes	plane	NNS
37681	3530	36	indefinitely	indefinitely	RB
37681	3530	37	and	and	CC
37681	3530	38	proceeding	proceed	VBG
37681	3530	39	in	in	IN
37681	3530	40	the	the	DT
37681	3530	41	same	same	JJ
37681	3530	42	way	way	NN
37681	3530	43	as	as	IN
37681	3530	44	for	for	IN
37681	3530	45	the	the	DT
37681	3530	46	inscribed	inscribed	JJ
37681	3530	47	sphere	sphere	NN
37681	3530	48	.	.	.
37681	3531	1	The	the	DT
37681	3531	2	figure	figure	NN
37681	3531	3	is	be	VBZ
37681	3531	4	difficult	difficult	JJ
37681	3531	5	to	to	TO
37681	3531	6	draw	draw	VB
37681	3531	7	,	,	,
37681	3531	8	but	but	CC
37681	3531	9	it	-PRON-	PRP
37681	3531	10	is	be	VBZ
37681	3531	11	not	not	RB
37681	3531	12	difficult	difficult	JJ
37681	3531	13	to	to	TO
37681	3531	14	understand	understand	VB
37681	3531	15	,	,	,
37681	3531	16	particularly	particularly	RB
37681	3531	17	if	if	IN
37681	3531	18	we	-PRON-	PRP
37681	3531	19	construct	construct	VBP
37681	3531	20	the	the	DT
37681	3531	21	tetrahedron	tetrahedron	NN
37681	3531	22	out	out	IN
37681	3531	23	of	of	IN
37681	3531	24	pasteboard	pasteboard	NN
37681	3531	25	.	.	.
37681	3532	1	THEOREM	THEOREM	NNP
37681	3532	2	.	.	.
37681	3533	1	_	_	NNP
37681	3533	2	A	a	DT
37681	3533	3	sphere	sphere	NN
37681	3533	4	may	may	MD
37681	3533	5	be	be	VB
37681	3533	6	circumscribed	circumscribe	VBN
37681	3533	7	about	about	IN
37681	3533	8	any	any	DT
37681	3533	9	given	give	VBN
37681	3533	10	tetrahedron	tetrahedron	NN
37681	3533	11	.	.	.
37681	3533	12	_	_	NNP
37681	3533	13	By	by	IN
37681	3533	14	producing	produce	VBG
37681	3533	15	one	one	CD
37681	3533	16	of	of	IN
37681	3533	17	the	the	DT
37681	3533	18	faces	face	NNS
37681	3533	19	indefinitely	indefinitely	RB
37681	3533	20	it	-PRON-	PRP
37681	3533	21	will	will	MD
37681	3533	22	cut	cut	VB
37681	3533	23	the	the	DT
37681	3533	24	sphere	sphere	NN
37681	3533	25	in	in	IN
37681	3533	26	a	a	DT
37681	3533	27	circle	circle	NN
37681	3533	28	,	,	,
37681	3533	29	and	and	CC
37681	3533	30	the	the	DT
37681	3533	31	resulting	result	VBG
37681	3533	32	figure	figure	NN
37681	3533	33	,	,	,
37681	3533	34	on	on	IN
37681	3533	35	the	the	DT
37681	3533	36	plane	plane	NN
37681	3533	37	,	,	,
37681	3533	38	will	will	MD
37681	3533	39	be	be	VB
37681	3533	40	that	that	DT
37681	3533	41	of	of	IN
37681	3533	42	the	the	DT
37681	3533	43	analogous	analogous	JJ
37681	3533	44	proposition	proposition	NN
37681	3533	45	of	of	IN
37681	3533	46	plane	plane	NN
37681	3533	47	geometry	geometry	NN
37681	3533	48	,	,	,
37681	3533	49	the	the	DT
37681	3533	50	circle	circle	NN
37681	3533	51	circumscribed	circumscribe	VBD
37681	3533	52	about	about	IN
37681	3533	53	a	a	DT
37681	3533	54	triangle	triangle	NN
37681	3533	55	.	.	.
37681	3534	1	It	-PRON-	PRP
37681	3534	2	is	be	VBZ
37681	3534	3	easily	easily	RB
37681	3534	4	proved	prove	VBN
37681	3534	5	from	from	IN
37681	3534	6	the	the	DT
37681	3534	7	proposition	proposition	NN
37681	3534	8	that	that	IN
37681	3534	9	the	the	DT
37681	3534	10	four	four	CD
37681	3534	11	perpendiculars	perpendicular	NNS
37681	3534	12	erected	erect	VBN
37681	3534	13	at	at	IN
37681	3534	14	the	the	DT
37681	3534	15	centers	center	NNS
37681	3534	16	of	of	IN
37681	3534	17	the	the	DT
37681	3534	18	faces	face	NNS
37681	3534	19	of	of	IN
37681	3534	20	a	a	DT
37681	3534	21	tetrahedron	tetrahedron	JJ
37681	3534	22	meet	meet	NN
37681	3534	23	in	in	IN
37681	3534	24	a	a	DT
37681	3534	25	point	point	NN
37681	3534	26	(	(	-LRB-
37681	3534	27	are	be	VBP
37681	3534	28	concurrent	concurrent	JJ
37681	3534	29	)	)	-RRB-
37681	3534	30	,	,	,
37681	3534	31	the	the	DT
37681	3534	32	analogue	analogue	NN
37681	3534	33	of	of	IN
37681	3534	34	the	the	DT
37681	3534	35	proposition	proposition	NN
37681	3534	36	about	about	IN
37681	3534	37	the	the	DT
37681	3534	38	perpendicular	perpendicular	JJ
37681	3534	39	bisectors	bisector	NNS
37681	3534	40	of	of	IN
37681	3534	41	the	the	DT
37681	3534	42	sides	side	NNS
37681	3534	43	of	of	IN
37681	3534	44	a	a	DT
37681	3534	45	triangle	triangle	NN
37681	3534	46	.	.	.
37681	3535	1	THEOREM	THEOREM	NNP
37681	3535	2	.	.	.
37681	3536	1	_	_	NNP
37681	3536	2	The	the	DT
37681	3536	3	intersection	intersection	NN
37681	3536	4	of	of	IN
37681	3536	5	two	two	CD
37681	3536	6	spherical	spherical	JJ
37681	3536	7	surfaces	surface	NNS
37681	3536	8	is	be	VBZ
37681	3536	9	a	a	DT
37681	3536	10	circle	circle	NN
37681	3536	11	whose	whose	WP$
37681	3536	12	plane	plane	NN
37681	3536	13	is	be	VBZ
37681	3536	14	perpendicular	perpendicular	JJ
37681	3536	15	to	to	IN
37681	3536	16	the	the	DT
37681	3536	17	line	line	NN
37681	3536	18	joining	join	VBG
37681	3536	19	the	the	DT
37681	3536	20	centers	center	NNS
37681	3536	21	of	of	IN
37681	3536	22	the	the	DT
37681	3536	23	surfaces	surface	NNS
37681	3536	24	and	and	CC
37681	3536	25	whose	whose	WP$
37681	3536	26	center	center	NN
37681	3536	27	is	be	VBZ
37681	3536	28	in	in	IN
37681	3536	29	that	that	DT
37681	3536	30	line	line	NN
37681	3536	31	.	.	.
37681	3536	32	_	_	NNP
37681	3536	33	The	the	DT
37681	3536	34	figure	figure	NN
37681	3536	35	suggests	suggest	VBZ
37681	3536	36	the	the	DT
37681	3536	37	case	case	NN
37681	3536	38	of	of	IN
37681	3536	39	two	two	CD
37681	3536	40	circles	circle	NNS
37681	3536	41	in	in	IN
37681	3536	42	plane	plane	NN
37681	3536	43	geometry	geometry	NN
37681	3536	44	.	.	.
37681	3537	1	In	in	IN
37681	3537	2	the	the	DT
37681	3537	3	case	case	NN
37681	3537	4	of	of	IN
37681	3537	5	two	two	CD
37681	3537	6	circles	circle	NNS
37681	3537	7	that	that	WDT
37681	3537	8	do	do	VBP
37681	3537	9	not	not	RB
37681	3537	10	intersect	intersect	VB
37681	3537	11	or	or	CC
37681	3537	12	touch	touch	VB
37681	3537	13	,	,	,
37681	3537	14	one	one	CD
37681	3537	15	not	not	RB
37681	3537	16	being	be	VBG
37681	3537	17	within	within	IN
37681	3537	18	the	the	DT
37681	3537	19	other	other	JJ
37681	3537	20	,	,	,
37681	3537	21	there	there	EX
37681	3537	22	are	be	VBP
37681	3537	23	four	four	CD
37681	3537	24	common	common	JJ
37681	3537	25	tangents	tangent	NNS
37681	3537	26	.	.	.
37681	3538	1	If	if	IN
37681	3538	2	the	the	DT
37681	3538	3	circles	circle	NNS
37681	3538	4	touch	touch	NN
37681	3538	5	,	,	,
37681	3538	6	two	two	CD
37681	3538	7	close	close	NN
37681	3538	8	up	up	RP
37681	3538	9	into	into	IN
37681	3538	10	one	one	CD
37681	3538	11	.	.	.
37681	3539	1	If	if	IN
37681	3539	2	one	one	CD
37681	3539	3	circle	circle	NN
37681	3539	4	is	be	VBZ
37681	3539	5	wholly	wholly	RB
37681	3539	6	within	within	IN
37681	3539	7	the	the	DT
37681	3539	8	other	other	JJ
37681	3539	9	,	,	,
37681	3539	10	this	this	DT
37681	3539	11	last	last	JJ
37681	3539	12	tangent	tangent	NN
37681	3539	13	disappears	disappear	VBZ
37681	3539	14	.	.	.
37681	3540	1	The	the	DT
37681	3540	2	same	same	JJ
37681	3540	3	thing	thing	NN
37681	3540	4	exists	exist	VBZ
37681	3540	5	in	in	IN
37681	3540	6	relation	relation	NN
37681	3540	7	to	to	IN
37681	3540	8	two	two	CD
37681	3540	9	spheres	sphere	NNS
37681	3540	10	,	,	,
37681	3540	11	and	and	CC
37681	3540	12	the	the	DT
37681	3540	13	analogous	analogous	JJ
37681	3540	14	cases	case	NNS
37681	3540	15	are	be	VBP
37681	3540	16	formed	form	VBN
37681	3540	17	by	by	IN
37681	3540	18	revolving	revolve	VBG
37681	3540	19	the	the	DT
37681	3540	20	circles	circle	NNS
37681	3540	21	and	and	CC
37681	3540	22	tangents	tangent	NNS
37681	3540	23	about	about	IN
37681	3540	24	the	the	DT
37681	3540	25	line	line	NN
37681	3540	26	through	through	IN
37681	3540	27	their	-PRON-	PRP$
37681	3540	28	centers	center	NNS
37681	3540	29	.	.	.
37681	3541	1	In	in	IN
37681	3541	2	plane	plane	NN
37681	3541	3	geometry	geometry	NN
37681	3541	4	it	-PRON-	PRP
37681	3541	5	is	be	VBZ
37681	3541	6	easily	easily	RB
37681	3541	7	proved	prove	VBN
37681	3541	8	that	that	IN
37681	3541	9	if	if	IN
37681	3541	10	two	two	CD
37681	3541	11	circles	circle	NNS
37681	3541	12	intersect	intersect	VBP
37681	3541	13	,	,	,
37681	3541	14	the	the	DT
37681	3541	15	tangents	tangent	NNS
37681	3541	16	from	from	IN
37681	3541	17	any	any	DT
37681	3541	18	point	point	NN
37681	3541	19	on	on	IN
37681	3541	20	their	-PRON-	PRP$
37681	3541	21	common	common	JJ
37681	3541	22	chord	chord	NN
37681	3541	23	produced	produce	VBN
37681	3541	24	are	be	VBP
37681	3541	25	equal	equal	JJ
37681	3541	26	.	.	.
37681	3542	1	For	for	IN
37681	3542	2	if	if	IN
37681	3542	3	the	the	DT
37681	3542	4	common	common	JJ
37681	3542	5	chord	chord	NN
37681	3542	6	is	be	VBZ
37681	3542	7	_	_	NNP
37681	3542	8	AB	AB	NNP
37681	3542	9	_	_	NNP
37681	3542	10	and	and	CC
37681	3542	11	the	the	DT
37681	3542	12	point	point	NN
37681	3542	13	_	_	NNP
37681	3542	14	P	P	NNP
37681	3542	15	_	_	NNP
37681	3542	16	is	be	VBZ
37681	3542	17	taken	take	VBN
37681	3542	18	on	on	IN
37681	3542	19	_	_	NNP
37681	3542	20	AB	AB	NNP
37681	3542	21	_	_	NNP
37681	3542	22	produced	produce	VBD
37681	3542	23	,	,	,
37681	3542	24	then	then	RB
37681	3542	25	the	the	DT
37681	3542	26	square	square	NN
37681	3542	27	on	on	IN
37681	3542	28	any	any	DT
37681	3542	29	tangent	tangent	NN
37681	3542	30	from	from	IN
37681	3542	31	_	_	NNP
37681	3542	32	P	P	NNP
37681	3542	33	_	_	NNP
37681	3542	34	is	be	VBZ
37681	3542	35	equal	equal	JJ
37681	3542	36	to	to	IN
37681	3542	37	_	_	NNP
37681	3542	38	PB	PB	NNP
37681	3542	39	_	_	NNP
37681	3542	40	×	×	NN
37681	3542	41	_	_	NNP
37681	3542	42	PA	PA	NNP
37681	3542	43	_	_	NNP
37681	3542	44	.	.	.
37681	3543	1	The	the	DT
37681	3543	2	line	line	NN
37681	3543	3	_	_	NNP
37681	3543	4	PBA	PBA	NNP
37681	3543	5	_	_	NNP
37681	3543	6	is	be	VBZ
37681	3543	7	sometimes	sometimes	RB
37681	3543	8	called	call	VBN
37681	3543	9	the	the	DT
37681	3543	10	_	_	NNP
37681	3543	11	radical	radical	JJ
37681	3543	12	axis	axis	NN
37681	3543	13	_	_	NNP
37681	3543	14	.	.	.
37681	3544	1	Similarly	similarly	RB
37681	3544	2	in	in	IN
37681	3544	3	this	this	DT
37681	3544	4	proposition	proposition	NN
37681	3544	5	concerning	concern	VBG
37681	3544	6	spheres	sphere	NNS
37681	3544	7	,	,	,
37681	3544	8	if	if	IN
37681	3544	9	from	from	IN
37681	3544	10	any	any	DT
37681	3544	11	point	point	NN
37681	3544	12	in	in	IN
37681	3544	13	the	the	DT
37681	3544	14	plane	plane	NN
37681	3544	15	of	of	IN
37681	3544	16	the	the	DT
37681	3544	17	circle	circle	NN
37681	3544	18	formed	form	VBN
37681	3544	19	by	by	IN
37681	3544	20	the	the	DT
37681	3544	21	intersection	intersection	NN
37681	3544	22	of	of	IN
37681	3544	23	the	the	DT
37681	3544	24	two	two	CD
37681	3544	25	spherical	spherical	JJ
37681	3544	26	surfaces	surface	NNS
37681	3544	27	lines	line	NNS
37681	3544	28	are	be	VBP
37681	3544	29	drawn	draw	VBN
37681	3544	30	tangent	tangent	NN
37681	3544	31	to	to	IN
37681	3544	32	either	either	CC
37681	3544	33	sphere	sphere	NN
37681	3544	34	,	,	,
37681	3544	35	these	these	DT
37681	3544	36	tangents	tangent	NNS
37681	3544	37	are	be	VBP
37681	3544	38	equal	equal	JJ
37681	3544	39	.	.	.
37681	3545	1	For	for	IN
37681	3545	2	it	-PRON-	PRP
37681	3545	3	is	be	VBZ
37681	3545	4	easily	easily	RB
37681	3545	5	proved	prove	VBN
37681	3545	6	that	that	IN
37681	3545	7	all	all	DT
37681	3545	8	tangents	tangent	NNS
37681	3545	9	to	to	IN
37681	3545	10	the	the	DT
37681	3545	11	same	same	JJ
37681	3545	12	sphere	sphere	NN
37681	3545	13	from	from	IN
37681	3545	14	an	an	DT
37681	3545	15	external	external	JJ
37681	3545	16	point	point	NN
37681	3545	17	are	be	VBP
37681	3545	18	equal	equal	JJ
37681	3545	19	,	,	,
37681	3545	20	and	and	CC
37681	3545	21	it	-PRON-	PRP
37681	3545	22	can	can	MD
37681	3545	23	be	be	VB
37681	3545	24	proved	prove	VBN
37681	3545	25	as	as	IN
37681	3545	26	in	in	IN
37681	3545	27	plane	plane	NN
37681	3545	28	geometry	geometry	NN
37681	3545	29	that	that	WDT
37681	3545	30	two	two	CD
37681	3545	31	tangents	tangent	NNS
37681	3545	32	to	to	IN
37681	3545	33	the	the	DT
37681	3545	34	two	two	CD
37681	3545	35	spheres	sphere	NNS
37681	3545	36	are	be	VBP
37681	3545	37	equal	equal	JJ
37681	3545	38	.	.	.
37681	3546	1	Among	among	IN
37681	3546	2	the	the	DT
37681	3546	3	interesting	interesting	JJ
37681	3546	4	analogies	analogy	NNS
37681	3546	5	between	between	IN
37681	3546	6	plane	plane	NN
37681	3546	7	and	and	CC
37681	3546	8	solid	solid	JJ
37681	3546	9	geometry	geometry	NN
37681	3546	10	is	be	VBZ
37681	3546	11	the	the	DT
37681	3546	12	one	one	NN
37681	3546	13	relating	relate	VBG
37681	3546	14	to	to	IN
37681	3546	15	the	the	DT
37681	3546	16	four	four	CD
37681	3546	17	common	common	JJ
37681	3546	18	tangents	tangent	NNS
37681	3546	19	to	to	IN
37681	3546	20	two	two	CD
37681	3546	21	circles	circle	NNS
37681	3546	22	.	.	.
37681	3547	1	If	if	IN
37681	3547	2	the	the	DT
37681	3547	3	figure	figure	NN
37681	3547	4	be	be	VB
37681	3547	5	revolved	revolve	VBN
37681	3547	6	about	about	IN
37681	3547	7	the	the	DT
37681	3547	8	line	line	NN
37681	3547	9	of	of	IN
37681	3547	10	centers	center	NNS
37681	3547	11	,	,	,
37681	3547	12	the	the	DT
37681	3547	13	circles	circle	NNS
37681	3547	14	generate	generate	VBP
37681	3547	15	spheres	sphere	NNS
37681	3547	16	and	and	CC
37681	3547	17	the	the	DT
37681	3547	18	tangents	tangent	NNS
37681	3547	19	generate	generate	VBP
37681	3547	20	conical	conical	JJ
37681	3547	21	surfaces	surface	NNS
37681	3547	22	.	.	.
37681	3548	1	To	to	TO
37681	3548	2	study	study	VB
37681	3548	3	this	this	DT
37681	3548	4	case	case	NN
37681	3548	5	for	for	IN
37681	3548	6	various	various	JJ
37681	3548	7	sizes	size	NNS
37681	3548	8	and	and	CC
37681	3548	9	positions	position	NNS
37681	3548	10	of	of	IN
37681	3548	11	the	the	DT
37681	3548	12	two	two	CD
37681	3548	13	spheres	sphere	NNS
37681	3548	14	is	be	VBZ
37681	3548	15	one	one	CD
37681	3548	16	of	of	IN
37681	3548	17	the	the	DT
37681	3548	18	most	most	RBS
37681	3548	19	interesting	interesting	JJ
37681	3548	20	generalizations	generalization	NNS
37681	3548	21	of	of	IN
37681	3548	22	solid	solid	JJ
37681	3548	23	geometry	geometry	NN
37681	3548	24	.	.	.
37681	3549	1	An	an	DT
37681	3549	2	application	application	NN
37681	3549	3	of	of	IN
37681	3549	4	the	the	DT
37681	3549	5	proposition	proposition	NN
37681	3549	6	is	be	VBZ
37681	3549	7	seen	see	VBN
37681	3549	8	in	in	IN
37681	3549	9	the	the	DT
37681	3549	10	case	case	NN
37681	3549	11	of	of	IN
37681	3549	12	an	an	DT
37681	3549	13	eclipse	eclipse	NN
37681	3549	14	,	,	,
37681	3549	15	where	where	WRB
37681	3549	16	the	the	DT
37681	3549	17	sphere	sphere	NN
37681	3549	18	_	_	NNP
37681	3549	19	O	O	NNP
37681	3549	20	'	'	CC
37681	3549	21	_	_	NNP
37681	3549	22	represents	represent	VBZ
37681	3549	23	the	the	DT
37681	3549	24	moon	moon	NN
37681	3549	25	,	,	,
37681	3549	26	_	_	NNP
37681	3549	27	O	O	NNP
37681	3549	28	_	_	NNP
37681	3549	29	the	the	DT
37681	3549	30	earth	earth	NN
37681	3549	31	,	,	,
37681	3549	32	and	and	CC
37681	3549	33	_	_	NNP
37681	3549	34	S	S	NNP
37681	3549	35	_	_	NNP
37681	3549	36	the	the	DT
37681	3549	37	sun	sun	NN
37681	3549	38	.	.	.
37681	3550	1	It	-PRON-	PRP
37681	3550	2	is	be	VBZ
37681	3550	3	also	also	RB
37681	3550	4	seen	see	VBN
37681	3550	5	in	in	IN
37681	3550	6	the	the	DT
37681	3550	7	case	case	NN
37681	3550	8	of	of	IN
37681	3550	9	the	the	DT
37681	3550	10	full	full	JJ
37681	3550	11	moon	moon	NN
37681	3550	12	,	,	,
37681	3550	13	when	when	WRB
37681	3550	14	_	_	NNP
37681	3550	15	S	S	NNP
37681	3550	16	_	_	NNP
37681	3550	17	is	be	VBZ
37681	3550	18	on	on	IN
37681	3550	19	the	the	DT
37681	3550	20	other	other	JJ
37681	3550	21	side	side	NN
37681	3550	22	of	of	IN
37681	3550	23	the	the	DT
37681	3550	24	earth	earth	NN
37681	3550	25	.	.	.
37681	3551	1	In	in	IN
37681	3551	2	this	this	DT
37681	3551	3	case	case	NN
37681	3551	4	the	the	DT
37681	3551	5	part	part	NN
37681	3551	6	_	_	NNP
37681	3551	7	MIN	MIN	NNP
37681	3551	8	_	_	NNP
37681	3551	9	is	be	VBZ
37681	3551	10	fully	fully	RB
37681	3551	11	illuminated	illuminate	VBN
37681	3551	12	by	by	IN
37681	3551	13	the	the	DT
37681	3551	14	moon	moon	NN
37681	3551	15	,	,	,
37681	3551	16	but	but	CC
37681	3551	17	the	the	DT
37681	3551	18	zone	zone	NN
37681	3551	19	_	_	NNP
37681	3551	20	ABNM	ABNM	NNP
37681	3551	21	_	_	NNP
37681	3551	22	is	be	VBZ
37681	3551	23	only	only	RB
37681	3551	24	partly	partly	RB
37681	3551	25	illuminated	illuminate	VBN
37681	3551	26	,	,	,
37681	3551	27	as	as	IN
37681	3551	28	the	the	DT
37681	3551	29	figure	figure	NN
37681	3551	30	shows	show	VBZ
37681	3551	31	.	.	.
37681	3552	1	[	[	-LRB-
37681	3552	2	92	92	CD
37681	3552	3	]	]	-RRB-
37681	3552	4	[	[	-LRB-
37681	3552	5	Illustration	illustration	NN
37681	3552	6	]	]	-RRB-
37681	3552	7	THEOREM	THEOREM	NNP
37681	3552	8	.	.	.
37681	3553	1	_	_	NNP
37681	3553	2	The	the	DT
37681	3553	3	sum	sum	NN
37681	3553	4	of	of	IN
37681	3553	5	the	the	DT
37681	3553	6	sides	side	NNS
37681	3553	7	of	of	IN
37681	3553	8	a	a	DT
37681	3553	9	spherical	spherical	JJ
37681	3553	10	polygon	polygon	NN
37681	3553	11	is	be	VBZ
37681	3553	12	less	less	JJR
37681	3553	13	than	than	IN
37681	3553	14	360	360	CD
37681	3553	15	°	°	NNS
37681	3553	16	.	.	.
37681	3553	17	_	_	NNP
37681	3553	18	In	in	IN
37681	3553	19	all	all	DT
37681	3553	20	such	such	JJ
37681	3553	21	cases	case	NNS
37681	3553	22	the	the	DT
37681	3553	23	relation	relation	NN
37681	3553	24	to	to	IN
37681	3553	25	the	the	DT
37681	3553	26	polyhedral	polyhedral	JJ
37681	3553	27	angle	angle	NN
37681	3553	28	should	should	MD
37681	3553	29	be	be	VB
37681	3553	30	made	make	VBN
37681	3553	31	clear	clear	JJ
37681	3553	32	.	.	.
37681	3554	1	This	this	DT
37681	3554	2	is	be	VBZ
37681	3554	3	done	do	VBN
37681	3554	4	in	in	IN
37681	3554	5	the	the	DT
37681	3554	6	proofs	proof	NNS
37681	3554	7	usually	usually	RB
37681	3554	8	given	give	VBN
37681	3554	9	in	in	IN
37681	3554	10	the	the	DT
37681	3554	11	textbooks	textbook	NNS
37681	3554	12	.	.	.
37681	3555	1	It	-PRON-	PRP
37681	3555	2	is	be	VBZ
37681	3555	3	easily	easily	RB
37681	3555	4	seen	see	VBN
37681	3555	5	that	that	IN
37681	3555	6	this	this	DT
37681	3555	7	is	be	VBZ
37681	3555	8	true	true	JJ
37681	3555	9	only	only	RB
37681	3555	10	with	with	IN
37681	3555	11	the	the	DT
37681	3555	12	limitation	limitation	NN
37681	3555	13	set	set	VBN
37681	3555	14	forth	forth	RP
37681	3555	15	in	in	IN
37681	3555	16	most	most	JJS
37681	3555	17	textbooks	textbook	NNS
37681	3555	18	,	,	,
37681	3555	19	that	that	IN
37681	3555	20	the	the	DT
37681	3555	21	spherical	spherical	JJ
37681	3555	22	polygons	polygon	NNS
37681	3555	23	considered	consider	VBN
37681	3555	24	are	be	VBP
37681	3555	25	convex	convex	NNP
37681	3555	26	.	.	.
37681	3556	1	Thus	thus	RB
37681	3556	2	we	-PRON-	PRP
37681	3556	3	might	may	MD
37681	3556	4	have	have	VB
37681	3556	5	a	a	DT
37681	3556	6	spherical	spherical	JJ
37681	3556	7	triangle	triangle	NN
37681	3556	8	that	that	WDT
37681	3556	9	is	be	VBZ
37681	3556	10	concave	concave	NNP
37681	3556	11	,	,	,
37681	3556	12	with	with	IN
37681	3556	13	its	-PRON-	PRP$
37681	3556	14	base	base	NN
37681	3556	15	359	359	CD
37681	3556	16	°	°	NNS
37681	3556	17	,	,	,
37681	3556	18	and	and	CC
37681	3556	19	its	-PRON-	PRP$
37681	3556	20	other	other	JJ
37681	3556	21	two	two	CD
37681	3556	22	sides	side	NNS
37681	3556	23	each	each	DT
37681	3556	24	90	90	CD
37681	3556	25	°	°	NNS
37681	3556	26	,	,	,
37681	3556	27	the	the	DT
37681	3556	28	sum	sum	NN
37681	3556	29	of	of	IN
37681	3556	30	the	the	DT
37681	3556	31	sides	side	NNS
37681	3556	32	being	be	VBG
37681	3556	33	539	539	CD
37681	3556	34	°	°	NNS
37681	3556	35	.	.	.
37681	3557	1	THEOREM	THEOREM	NNP
37681	3557	2	.	.	.
37681	3558	1	_	_	NNP
37681	3558	2	The	the	DT
37681	3558	3	sum	sum	NN
37681	3558	4	of	of	IN
37681	3558	5	the	the	DT
37681	3558	6	angles	angle	NNS
37681	3558	7	of	of	IN
37681	3558	8	a	a	DT
37681	3558	9	spherical	spherical	JJ
37681	3558	10	triangle	triangle	NN
37681	3558	11	is	be	VBZ
37681	3558	12	greater	great	JJR
37681	3558	13	than	than	IN
37681	3558	14	180	180	CD
37681	3558	15	°	°	NNS
37681	3558	16	and	and	CC
37681	3558	17	less	less	JJR
37681	3558	18	than	than	IN
37681	3558	19	540	540	CD
37681	3558	20	°	°	NNS
37681	3558	21	.	.	.
37681	3558	22	_	_	NNP
37681	3558	23	It	-PRON-	PRP
37681	3558	24	is	be	VBZ
37681	3558	25	for	for	IN
37681	3558	26	the	the	DT
37681	3558	27	purpose	purpose	NN
37681	3558	28	of	of	IN
37681	3558	29	proving	prove	VBG
37681	3558	30	this	this	DT
37681	3558	31	important	important	JJ
37681	3558	32	fact	fact	NN
37681	3558	33	that	that	IN
37681	3558	34	polar	polar	JJ
37681	3558	35	triangles	triangle	NNS
37681	3558	36	are	be	VBP
37681	3558	37	introduced	introduce	VBN
37681	3558	38	.	.	.
37681	3559	1	This	this	DT
37681	3559	2	proposition	proposition	NN
37681	3559	3	shows	show	VBZ
37681	3559	4	the	the	DT
37681	3559	5	relation	relation	NN
37681	3559	6	of	of	IN
37681	3559	7	the	the	DT
37681	3559	8	spherical	spherical	JJ
37681	3559	9	to	to	IN
37681	3559	10	the	the	DT
37681	3559	11	plane	plane	NN
37681	3559	12	triangle	triangle	NN
37681	3559	13	.	.	.
37681	3560	1	If	if	IN
37681	3560	2	our	-PRON-	PRP$
37681	3560	3	planes	plane	NNS
37681	3560	4	were	be	VBD
37681	3560	5	in	in	IN
37681	3560	6	reality	reality	NN
37681	3560	7	slightly	slightly	RB
37681	3560	8	curved	curve	VBN
37681	3560	9	,	,	,
37681	3560	10	being	be	VBG
37681	3560	11	small	small	JJ
37681	3560	12	portions	portion	NNS
37681	3560	13	of	of	IN
37681	3560	14	enormous	enormous	JJ
37681	3560	15	spherical	spherical	JJ
37681	3560	16	surfaces	surface	NNS
37681	3560	17	,	,	,
37681	3560	18	then	then	RB
37681	3560	19	the	the	DT
37681	3560	20	sum	sum	NN
37681	3560	21	of	of	IN
37681	3560	22	the	the	DT
37681	3560	23	angles	angle	NNS
37681	3560	24	of	of	IN
37681	3560	25	a	a	DT
37681	3560	26	triangle	triangle	NN
37681	3560	27	would	would	MD
37681	3560	28	not	not	RB
37681	3560	29	be	be	VB
37681	3560	30	exactly	exactly	RB
37681	3560	31	180	180	CD
37681	3560	32	°	°	NNS
37681	3560	33	,	,	,
37681	3560	34	but	but	CC
37681	3560	35	would	would	MD
37681	3560	36	exceed	exceed	VB
37681	3560	37	180	180	CD
37681	3560	38	°	°	NNS
37681	3560	39	by	by	IN
37681	3560	40	some	some	DT
37681	3560	41	amount	amount	NN
37681	3560	42	depending	depend	VBG
37681	3560	43	on	on	IN
37681	3560	44	the	the	DT
37681	3560	45	curvature	curvature	NN
37681	3560	46	of	of	IN
37681	3560	47	the	the	DT
37681	3560	48	surface	surface	NN
37681	3560	49	.	.	.
37681	3561	1	Just	just	RB
37681	3561	2	as	as	IN
37681	3561	3	a	a	DT
37681	3561	4	being	being	NN
37681	3561	5	may	may	MD
37681	3561	6	be	be	VB
37681	3561	7	imagined	imagine	VBN
37681	3561	8	as	as	IN
37681	3561	9	having	have	VBG
37681	3561	10	only	only	RB
37681	3561	11	two	two	CD
37681	3561	12	dimensions	dimension	NNS
37681	3561	13	,	,	,
37681	3561	14	and	and	CC
37681	3561	15	living	live	VBG
37681	3561	16	always	always	RB
37681	3561	17	on	on	IN
37681	3561	18	a	a	DT
37681	3561	19	plane	plane	NN
37681	3561	20	surface	surface	NN
37681	3561	21	(	(	-LRB-
37681	3561	22	in	in	IN
37681	3561	23	a	a	DT
37681	3561	24	space	space	NN
37681	3561	25	of	of	IN
37681	3561	26	two	two	CD
37681	3561	27	dimensions	dimension	NNS
37681	3561	28	)	)	-RRB-
37681	3561	29	,	,	,
37681	3561	30	and	and	CC
37681	3561	31	having	have	VBG
37681	3561	32	no	no	DT
37681	3561	33	conception	conception	NN
37681	3561	34	of	of	IN
37681	3561	35	a	a	DT
37681	3561	36	space	space	NN
37681	3561	37	of	of	IN
37681	3561	38	three	three	CD
37681	3561	39	dimensions	dimension	NNS
37681	3561	40	,	,	,
37681	3561	41	so	so	IN
37681	3561	42	we	-PRON-	PRP
37681	3561	43	may	may	MD
37681	3561	44	think	think	VB
37681	3561	45	of	of	IN
37681	3561	46	ourselves	-PRON-	PRP
37681	3561	47	as	as	IN
37681	3561	48	living	live	VBG
37681	3561	49	in	in	IN
37681	3561	50	a	a	DT
37681	3561	51	space	space	NN
37681	3561	52	of	of	IN
37681	3561	53	three	three	CD
37681	3561	54	dimensions	dimension	NNS
37681	3561	55	but	but	CC
37681	3561	56	surrounded	surround	VBN
37681	3561	57	by	by	IN
37681	3561	58	a	a	DT
37681	3561	59	space	space	NN
37681	3561	60	of	of	IN
37681	3561	61	four	four	CD
37681	3561	62	dimensions	dimension	NNS
37681	3561	63	.	.	.
37681	3562	1	The	the	DT
37681	3562	2	flat	flat	JJ
37681	3562	3	being	being	NN
37681	3562	4	could	could	MD
37681	3562	5	not	not	RB
37681	3562	6	point	point	VB
37681	3562	7	to	to	IN
37681	3562	8	a	a	DT
37681	3562	9	third	third	JJ
37681	3562	10	dimension	dimension	NN
37681	3562	11	because	because	IN
37681	3562	12	he	-PRON-	PRP
37681	3562	13	could	could	MD
37681	3562	14	not	not	RB
37681	3562	15	get	get	VB
37681	3562	16	out	out	IN
37681	3562	17	of	of	IN
37681	3562	18	his	-PRON-	PRP$
37681	3562	19	plane	plane	NN
37681	3562	20	,	,	,
37681	3562	21	and	and	CC
37681	3562	22	we	-PRON-	PRP
37681	3562	23	can	can	MD
37681	3562	24	not	not	RB
37681	3562	25	point	point	VB
37681	3562	26	to	to	IN
37681	3562	27	the	the	DT
37681	3562	28	fourth	fourth	JJ
37681	3562	29	dimension	dimension	NN
37681	3562	30	because	because	IN
37681	3562	31	we	-PRON-	PRP
37681	3562	32	can	can	MD
37681	3562	33	not	not	RB
37681	3562	34	get	get	VB
37681	3562	35	out	out	IN
37681	3562	36	of	of	IN
37681	3562	37	our	-PRON-	PRP$
37681	3562	38	space	space	NN
37681	3562	39	.	.	.
37681	3563	1	Now	now	RB
37681	3563	2	what	what	WP
37681	3563	3	the	the	DT
37681	3563	4	flat	flat	JJ
37681	3563	5	being	being	NN
37681	3563	6	thinks	think	VBZ
37681	3563	7	is	be	VBZ
37681	3563	8	his	-PRON-	PRP$
37681	3563	9	plane	plane	NN
37681	3563	10	may	may	MD
37681	3563	11	be	be	VB
37681	3563	12	the	the	DT
37681	3563	13	surface	surface	NN
37681	3563	14	of	of	IN
37681	3563	15	an	an	DT
37681	3563	16	enormous	enormous	JJ
37681	3563	17	sphere	sphere	NN
37681	3563	18	in	in	IN
37681	3563	19	our	-PRON-	PRP$
37681	3563	20	three	three	CD
37681	3563	21	dimensions	dimension	NNS
37681	3563	22	;	;	:
37681	3563	23	in	in	IN
37681	3563	24	other	other	JJ
37681	3563	25	words	word	NNS
37681	3563	26	,	,	,
37681	3563	27	the	the	DT
37681	3563	28	space	space	NN
37681	3563	29	he	-PRON-	PRP
37681	3563	30	lives	live	VBZ
37681	3563	31	in	in	IN
37681	3563	32	may	may	NNP
37681	3563	33	curve	curve	VB
37681	3563	34	through	through	IN
37681	3563	35	some	some	DT
37681	3563	36	higher	high	JJR
37681	3563	37	space	space	NN
37681	3563	38	without	without	IN
37681	3563	39	his	-PRON-	PRP$
37681	3563	40	being	be	VBG
37681	3563	41	conscious	conscious	JJ
37681	3563	42	of	of	IN
37681	3563	43	it	-PRON-	PRP
37681	3563	44	.	.	.
37681	3564	1	So	so	RB
37681	3564	2	our	-PRON-	PRP$
37681	3564	3	space	space	NN
37681	3564	4	may	may	MD
37681	3564	5	also	also	RB
37681	3564	6	curve	curve	VB
37681	3564	7	through	through	IN
37681	3564	8	some	some	DT
37681	3564	9	higher	high	JJR
37681	3564	10	space	space	NN
37681	3564	11	without	without	IN
37681	3564	12	our	-PRON-	PRP$
37681	3564	13	being	be	VBG
37681	3564	14	conscious	conscious	JJ
37681	3564	15	of	of	IN
37681	3564	16	it	-PRON-	PRP
37681	3564	17	.	.	.
37681	3565	1	If	if	IN
37681	3565	2	our	-PRON-	PRP$
37681	3565	3	planes	plane	NNS
37681	3565	4	have	have	VBP
37681	3565	5	really	really	RB
37681	3565	6	some	some	DT
37681	3565	7	curvature	curvature	JJ
37681	3565	8	,	,	,
37681	3565	9	then	then	RB
37681	3565	10	the	the	DT
37681	3565	11	sum	sum	NN
37681	3565	12	of	of	IN
37681	3565	13	the	the	DT
37681	3565	14	angles	angle	NNS
37681	3565	15	of	of	IN
37681	3565	16	our	-PRON-	PRP$
37681	3565	17	triangles	triangle	NNS
37681	3565	18	has	have	VBZ
37681	3565	19	a	a	DT
37681	3565	20	slight	slight	JJ
37681	3565	21	excess	excess	NN
37681	3565	22	over	over	IN
37681	3565	23	180	180	CD
37681	3565	24	°	°	NNS
37681	3565	25	.	.	.
37681	3566	1	All	all	DT
37681	3566	2	this	this	DT
37681	3566	3	is	be	VBZ
37681	3566	4	mere	mere	JJ
37681	3566	5	speculation	speculation	NN
37681	3566	6	,	,	,
37681	3566	7	but	but	CC
37681	3566	8	it	-PRON-	PRP
37681	3566	9	may	may	MD
37681	3566	10	interest	interest	VB
37681	3566	11	some	some	DT
37681	3566	12	student	student	NN
37681	3566	13	to	to	TO
37681	3566	14	know	know	VB
37681	3566	15	that	that	IN
37681	3566	16	the	the	DT
37681	3566	17	idea	idea	NN
37681	3566	18	of	of	IN
37681	3566	19	fourth	fourth	JJ
37681	3566	20	and	and	CC
37681	3566	21	higher	high	JJR
37681	3566	22	dimensions	dimension	NNS
37681	3566	23	enters	enter	VBZ
37681	3566	24	largely	largely	RB
37681	3566	25	into	into	IN
37681	3566	26	mathematical	mathematical	JJ
37681	3566	27	investigation	investigation	NN
37681	3566	28	to	to	IN
37681	3566	29	-	-	HYPH
37681	3566	30	day	day	NN
37681	3566	31	.	.	.
37681	3567	1	THEOREM	THEOREM	NNP
37681	3567	2	.	.	.
37681	3568	1	_	_	NNP
37681	3568	2	Two	two	CD
37681	3568	3	symmetric	symmetric	JJ
37681	3568	4	spherical	spherical	JJ
37681	3568	5	triangles	triangle	NNS
37681	3568	6	are	be	VBP
37681	3568	7	equivalent	equivalent	JJ
37681	3568	8	.	.	.
37681	3568	9	_	_	NNP
37681	3568	10	While	while	IN
37681	3568	11	it	-PRON-	PRP
37681	3568	12	is	be	VBZ
37681	3568	13	not	not	RB
37681	3568	14	a	a	DT
37681	3568	15	subject	subject	NN
37681	3568	16	that	that	WDT
37681	3568	17	has	have	VBZ
37681	3568	18	any	any	DT
37681	3568	19	place	place	NN
37681	3568	20	in	in	IN
37681	3568	21	a	a	DT
37681	3568	22	school	school	NN
37681	3568	23	,	,	,
37681	3568	24	save	save	VB
37681	3568	25	perhaps	perhaps	RB
37681	3568	26	for	for	IN
37681	3568	27	incidental	incidental	JJ
37681	3568	28	conversation	conversation	NN
37681	3568	29	with	with	IN
37681	3568	30	some	some	DT
37681	3568	31	group	group	NN
37681	3568	32	of	of	IN
37681	3568	33	enthusiastic	enthusiastic	JJ
37681	3568	34	students	student	NNS
37681	3568	35	,	,	,
37681	3568	36	it	-PRON-	PRP
37681	3568	37	may	may	MD
37681	3568	38	interest	interest	VB
37681	3568	39	the	the	DT
37681	3568	40	teacher	teacher	NN
37681	3568	41	to	to	TO
37681	3568	42	consider	consider	VB
37681	3568	43	this	this	DT
37681	3568	44	proposition	proposition	NN
37681	3568	45	in	in	IN
37681	3568	46	connection	connection	NN
37681	3568	47	with	with	IN
37681	3568	48	the	the	DT
37681	3568	49	fourth	fourth	JJ
37681	3568	50	dimension	dimension	NN
37681	3568	51	just	just	RB
37681	3568	52	mentioned	mention	VBN
37681	3568	53	.	.	.
37681	3569	1	Consider	consider	VB
37681	3569	2	these	these	DT
37681	3569	3	triangles	triangle	NNS
37681	3569	4	,	,	,
37681	3569	5	where	where	WRB
37681	3569	6	[	[	-LRB-
37681	3569	7	L]_A	L]_A	NNS
37681	3569	8	_	_	NNP
37681	3569	9	=	=	SYM
37681	3569	10	[	[	-LRB-
37681	3569	11	L]_A	L]_A	NNS
37681	3569	12	'	'	POS
37681	3569	13	_	_	NNP
37681	3569	14	,	,	,
37681	3569	15	_	_	NNP
37681	3569	16	AB	AB	NNP
37681	3569	17	_	_	NNP
37681	3569	18	=	=	SYM
37681	3569	19	_	_	NNP
37681	3569	20	A'B	A'B	NNP
37681	3569	21	'	'	''
37681	3569	22	_	_	NNP
37681	3569	23	,	,	,
37681	3569	24	_	_	NNP
37681	3569	25	AC	AC	NNP
37681	3569	26	_	_	NNP
37681	3569	27	=	=	SYM
37681	3569	28	_	_	NNP
37681	3569	29	A'C	a'c	RB
37681	3569	30	'	'	``
37681	3569	31	_	_	XX
37681	3569	32	.	.	.
37681	3570	1	We	-PRON-	PRP
37681	3570	2	prove	prove	VBP
37681	3570	3	them	-PRON-	PRP
37681	3570	4	congruent	congruent	JJ
37681	3570	5	by	by	IN
37681	3570	6	superposition	superposition	NN
37681	3570	7	,	,	,
37681	3570	8	turning	turn	VBG
37681	3570	9	one	one	CD
37681	3570	10	over	over	RP
37681	3570	11	and	and	CC
37681	3570	12	placing	place	VBG
37681	3570	13	it	-PRON-	PRP
37681	3570	14	upon	upon	IN
37681	3570	15	the	the	DT
37681	3570	16	other	other	JJ
37681	3570	17	.	.	.
37681	3571	1	But	but	CC
37681	3571	2	suppose	suppose	VB
37681	3571	3	we	-PRON-	PRP
37681	3571	4	were	be	VBD
37681	3571	5	beings	being	NNS
37681	3571	6	in	in	IN
37681	3571	7	Flatland	Flatland	NNP
37681	3571	8	,	,	,
37681	3571	9	beings	being	NNS
37681	3571	10	with	with	IN
37681	3571	11	only	only	RB
37681	3571	12	two	two	CD
37681	3571	13	dimensions	dimension	NNS
37681	3571	14	and	and	CC
37681	3571	15	without	without	IN
37681	3571	16	the	the	DT
37681	3571	17	power	power	NN
37681	3571	18	to	to	TO
37681	3571	19	point	point	VB
37681	3571	20	in	in	IN
37681	3571	21	any	any	DT
37681	3571	22	direction	direction	NN
37681	3571	23	except	except	IN
37681	3571	24	in	in	IN
37681	3571	25	the	the	DT
37681	3571	26	plane	plane	NN
37681	3571	27	we	-PRON-	PRP
37681	3571	28	lived	live	VBD
37681	3571	29	in	in	RB
37681	3571	30	.	.	.
37681	3572	1	We	-PRON-	PRP
37681	3572	2	should	should	MD
37681	3572	3	then	then	RB
37681	3572	4	be	be	VB
37681	3572	5	unable	unable	JJ
37681	3572	6	to	to	TO
37681	3572	7	turn	turn	VB
37681	3572	8	[	[	-LRB-
37681	3572	9	triangle]_A'B'C	triangle]_A'B'C	NNP
37681	3572	10	'	'	''
37681	3572	11	_	_	NNP
37681	3572	12	over	over	IN
37681	3572	13	so	so	IN
37681	3572	14	that	that	IN
37681	3572	15	it	-PRON-	PRP
37681	3572	16	could	could	MD
37681	3572	17	coincide	coincide	VB
37681	3572	18	with	with	IN
37681	3572	19	[	[	-LRB-
37681	3572	20	triangle]_ABC	triangle]_abc	CD
37681	3572	21	_	_	NNP
37681	3572	22	,	,	,
37681	3572	23	and	and	CC
37681	3572	24	we	-PRON-	PRP
37681	3572	25	should	should	MD
37681	3572	26	have	have	VB
37681	3572	27	to	to	TO
37681	3572	28	prove	prove	VB
37681	3572	29	these	these	DT
37681	3572	30	triangles	triangle	NNS
37681	3572	31	equivalent	equivalent	JJ
37681	3572	32	in	in	IN
37681	3572	33	some	some	DT
37681	3572	34	other	other	JJ
37681	3572	35	way	way	NN
37681	3572	36	,	,	,
37681	3572	37	probably	probably	RB
37681	3572	38	by	by	IN
37681	3572	39	dividing	divide	VBG
37681	3572	40	them	-PRON-	PRP
37681	3572	41	into	into	IN
37681	3572	42	isosceles	isoscele	NNS
37681	3572	43	triangles	triangle	NNS
37681	3572	44	that	that	WDT
37681	3572	45	could	could	MD
37681	3572	46	be	be	VB
37681	3572	47	superposed	superpose	VBN
37681	3572	48	.	.	.
37681	3573	1	[	[	-LRB-
37681	3573	2	Illustration	illustration	NN
37681	3573	3	]	]	-RRB-
37681	3573	4	[	[	-LRB-
37681	3573	5	Illustration	illustration	NN
37681	3573	6	]	]	-RRB-
37681	3573	7	Now	now	RB
37681	3573	8	it	-PRON-	PRP
37681	3573	9	is	be	VBZ
37681	3573	10	the	the	DT
37681	3573	11	same	same	JJ
37681	3573	12	thing	thing	NN
37681	3573	13	with	with	IN
37681	3573	14	symmetric	symmetric	JJ
37681	3573	15	spherical	spherical	JJ
37681	3573	16	triangles	triangle	NNS
37681	3573	17	;	;	:
37681	3573	18	we	-PRON-	PRP
37681	3573	19	can	can	MD
37681	3573	20	not	not	RB
37681	3573	21	superpose	superpose	VB
37681	3573	22	them	-PRON-	PRP
37681	3573	23	.	.	.
37681	3574	1	But	but	CC
37681	3574	2	might	may	MD
37681	3574	3	it	-PRON-	PRP
37681	3574	4	not	not	RB
37681	3574	5	be	be	VB
37681	3574	6	possible	possible	JJ
37681	3574	7	to	to	TO
37681	3574	8	do	do	VB
37681	3574	9	so	so	RB
37681	3574	10	if	if	IN
37681	3574	11	we	-PRON-	PRP
37681	3574	12	could	could	MD
37681	3574	13	turn	turn	VB
37681	3574	14	them	-PRON-	PRP
37681	3574	15	through	through	IN
37681	3574	16	the	the	DT
37681	3574	17	fourth	fourth	JJ
37681	3574	18	dimension	dimension	NN
37681	3574	19	exactly	exactly	RB
37681	3574	20	as	as	IN
37681	3574	21	we	-PRON-	PRP
37681	3574	22	turn	turn	VBP
37681	3574	23	the	the	DT
37681	3574	24	Flatlander	Flatlander	NNP
37681	3574	25	's	's	POS
37681	3574	26	triangle	triangle	NN
37681	3574	27	through	through	IN
37681	3574	28	our	-PRON-	PRP$
37681	3574	29	third	third	JJ
37681	3574	30	dimension	dimension	NN
37681	3574	31	?	?	.
37681	3575	1	It	-PRON-	PRP
37681	3575	2	is	be	VBZ
37681	3575	3	interesting	interesting	JJ
37681	3575	4	to	to	TO
37681	3575	5	think	think	VB
37681	3575	6	about	about	IN
37681	3575	7	this	this	DT
37681	3575	8	possibility	possibility	NN
37681	3575	9	even	even	RB
37681	3575	10	though	though	IN
37681	3575	11	we	-PRON-	PRP
37681	3575	12	carry	carry	VBP
37681	3575	13	it	-PRON-	PRP
37681	3575	14	no	no	RB
37681	3575	15	further	further	RB
37681	3575	16	,	,	,
37681	3575	17	and	and	CC
37681	3575	18	in	in	IN
37681	3575	19	these	these	DT
37681	3575	20	side	side	NN
37681	3575	21	lights	light	NNS
37681	3575	22	on	on	IN
37681	3575	23	mathematics	mathematic	NNS
37681	3575	24	lies	lie	VBZ
37681	3575	25	much	much	JJ
37681	3575	26	of	of	IN
37681	3575	27	the	the	DT
37681	3575	28	fascination	fascination	NN
37681	3575	29	of	of	IN
37681	3575	30	the	the	DT
37681	3575	31	subject	subject	NN
37681	3575	32	.	.	.
37681	3576	1	THEOREM	THEOREM	NNP
37681	3576	2	.	.	.
37681	3577	1	_	_	NNP
37681	3577	2	The	the	DT
37681	3577	3	shortest	short	JJS
37681	3577	4	line	line	NN
37681	3577	5	that	that	WDT
37681	3577	6	can	can	MD
37681	3577	7	be	be	VB
37681	3577	8	drawn	draw	VBN
37681	3577	9	on	on	IN
37681	3577	10	the	the	DT
37681	3577	11	surface	surface	NN
37681	3577	12	of	of	IN
37681	3577	13	a	a	DT
37681	3577	14	sphere	sphere	NN
37681	3577	15	between	between	IN
37681	3577	16	two	two	CD
37681	3577	17	points	point	NNS
37681	3577	18	is	be	VBZ
37681	3577	19	the	the	DT
37681	3577	20	minor	minor	JJ
37681	3577	21	arc	arc	NN
37681	3577	22	of	of	IN
37681	3577	23	a	a	DT
37681	3577	24	great	great	JJ
37681	3577	25	circle	circle	NN
37681	3577	26	joining	join	VBG
37681	3577	27	the	the	DT
37681	3577	28	two	two	CD
37681	3577	29	points	point	NNS
37681	3577	30	.	.	.
37681	3577	31	_	_	NNP
37681	3577	32	It	-PRON-	PRP
37681	3577	33	is	be	VBZ
37681	3577	34	always	always	RB
37681	3577	35	interesting	interesting	JJ
37681	3577	36	to	to	IN
37681	3577	37	a	a	DT
37681	3577	38	class	class	NN
37681	3577	39	to	to	TO
37681	3577	40	apply	apply	VB
37681	3577	41	this	this	DT
37681	3577	42	practically	practically	RB
37681	3577	43	.	.	.
37681	3578	1	By	by	IN
37681	3578	2	taking	take	VBG
37681	3578	3	a	a	DT
37681	3578	4	terrestrial	terrestrial	JJ
37681	3578	5	globe	globe	NN
37681	3578	6	and	and	CC
37681	3578	7	drawing	draw	VBG
37681	3578	8	a	a	DT
37681	3578	9	great	great	JJ
37681	3578	10	circle	circle	NN
37681	3578	11	between	between	IN
37681	3578	12	the	the	DT
37681	3578	13	southern	southern	JJ
37681	3578	14	point	point	NN
37681	3578	15	of	of	IN
37681	3578	16	Ireland	Ireland	NNP
37681	3578	17	and	and	CC
37681	3578	18	New	New	NNP
37681	3578	19	York	York	NNP
37681	3578	20	City	City	NNP
37681	3578	21	,	,	,
37681	3578	22	we	-PRON-	PRP
37681	3578	23	represent	represent	VBP
37681	3578	24	the	the	DT
37681	3578	25	shortest	short	JJS
37681	3578	26	route	route	NN
37681	3578	27	for	for	IN
37681	3578	28	ships	ship	NNS
37681	3578	29	crossing	cross	VBG
37681	3578	30	to	to	IN
37681	3578	31	England	England	NNP
37681	3578	32	.	.	.
37681	3579	1	Now	now	RB
37681	3579	2	if	if	IN
37681	3579	3	we	-PRON-	PRP
37681	3579	4	notice	notice	VBP
37681	3579	5	where	where	WRB
37681	3579	6	this	this	DT
37681	3579	7	great	great	JJ
37681	3579	8	-	-	HYPH
37681	3579	9	circle	circle	NN
37681	3579	10	arc	arc	NN
37681	3579	11	cuts	cut	VBZ
37681	3579	12	the	the	DT
37681	3579	13	various	various	JJ
37681	3579	14	meridians	meridian	NNS
37681	3579	15	and	and	CC
37681	3579	16	mark	mark	VB
37681	3579	17	this	this	DT
37681	3579	18	on	on	IN
37681	3579	19	an	an	DT
37681	3579	20	ordinary	ordinary	JJ
37681	3579	21	Mercator	mercator	NN
37681	3579	22	's	's	POS
37681	3579	23	projection	projection	NN
37681	3579	24	map	map	NN
37681	3579	25	,	,	,
37681	3579	26	such	such	JJ
37681	3579	27	as	as	IN
37681	3579	28	is	be	VBZ
37681	3579	29	found	find	VBN
37681	3579	30	in	in	IN
37681	3579	31	any	any	DT
37681	3579	32	schoolroom	schoolroom	NN
37681	3579	33	,	,	,
37681	3579	34	we	-PRON-	PRP
37681	3579	35	shall	shall	MD
37681	3579	36	find	find	VB
37681	3579	37	that	that	IN
37681	3579	38	the	the	DT
37681	3579	39	path	path	NN
37681	3579	40	of	of	IN
37681	3579	41	the	the	DT
37681	3579	42	ship	ship	NN
37681	3579	43	does	do	VBZ
37681	3579	44	not	not	RB
37681	3579	45	make	make	VB
37681	3579	46	a	a	DT
37681	3579	47	straight	straight	JJ
37681	3579	48	line	line	NN
37681	3579	49	.	.	.
37681	3580	1	Passengers	passenger	NNS
37681	3580	2	at	at	IN
37681	3580	3	sea	sea	NN
37681	3580	4	often	often	RB
37681	3580	5	do	do	VBP
37681	3580	6	not	not	RB
37681	3580	7	understand	understand	VB
37681	3580	8	why	why	WRB
37681	3580	9	the	the	DT
37681	3580	10	ship	ship	NN
37681	3580	11	's	's	POS
37681	3580	12	course	course	NN
37681	3580	13	on	on	IN
37681	3580	14	the	the	DT
37681	3580	15	map	map	NN
37681	3580	16	is	be	VBZ
37681	3580	17	not	not	RB
37681	3580	18	a	a	DT
37681	3580	19	straight	straight	JJ
37681	3580	20	line	line	NN
37681	3580	21	;	;	:
37681	3580	22	but	but	CC
37681	3580	23	the	the	DT
37681	3580	24	chief	chief	JJ
37681	3580	25	reason	reason	NN
37681	3580	26	is	be	VBZ
37681	3580	27	that	that	IN
37681	3580	28	the	the	DT
37681	3580	29	ship	ship	NN
37681	3580	30	is	be	VBZ
37681	3580	31	taking	take	VBG
37681	3580	32	a	a	DT
37681	3580	33	great	great	JJ
37681	3580	34	-	-	HYPH
37681	3580	35	circle	circle	NN
37681	3580	36	arc	arc	NN
37681	3580	37	,	,	,
37681	3580	38	and	and	CC
37681	3580	39	this	this	DT
37681	3580	40	is	be	VBZ
37681	3580	41	not	not	RB
37681	3580	42	,	,	,
37681	3580	43	in	in	IN
37681	3580	44	general	general	JJ
37681	3580	45	,	,	,
37681	3580	46	a	a	DT
37681	3580	47	straight	straight	JJ
37681	3580	48	line	line	NN
37681	3580	49	on	on	IN
37681	3580	50	a	a	DT
37681	3580	51	Mercator	mercator	NN
37681	3580	52	projection	projection	NN
37681	3580	53	.	.	.
37681	3581	1	The	the	DT
37681	3581	2	small	small	JJ
37681	3581	3	circles	circle	NNS
37681	3581	4	of	of	IN
37681	3581	5	latitude	latitude	NN
37681	3581	6	are	be	VBP
37681	3581	7	straight	straight	JJ
37681	3581	8	lines	line	NNS
37681	3581	9	,	,	,
37681	3581	10	and	and	CC
37681	3581	11	so	so	RB
37681	3581	12	are	be	VBP
37681	3581	13	the	the	DT
37681	3581	14	meridians	meridian	NNS
37681	3581	15	and	and	CC
37681	3581	16	the	the	DT
37681	3581	17	equator	equator	NN
37681	3581	18	,	,	,
37681	3581	19	but	but	CC
37681	3581	20	other	other	JJ
37681	3581	21	great	great	JJ
37681	3581	22	circles	circle	NNS
37681	3581	23	are	be	VBP
37681	3581	24	represented	represent	VBN
37681	3581	25	by	by	IN
37681	3581	26	curved	curved	JJ
37681	3581	27	lines	line	NNS
37681	3581	28	.	.	.
37681	3582	1	THEOREM	THEOREM	NNP
37681	3582	2	.	.	.
37681	3583	1	_	_	NNP
37681	3583	2	The	the	DT
37681	3583	3	area	area	NN
37681	3583	4	of	of	IN
37681	3583	5	the	the	DT
37681	3583	6	surface	surface	NN
37681	3583	7	of	of	IN
37681	3583	8	a	a	DT
37681	3583	9	sphere	sphere	NN
37681	3583	10	is	be	VBZ
37681	3583	11	equal	equal	JJ
37681	3583	12	to	to	IN
37681	3583	13	the	the	DT
37681	3583	14	product	product	NN
37681	3583	15	of	of	IN
37681	3583	16	its	-PRON-	PRP$
37681	3583	17	diameter	diameter	NN
37681	3583	18	by	by	IN
37681	3583	19	the	the	DT
37681	3583	20	circumference	circumference	NN
37681	3583	21	of	of	IN
37681	3583	22	a	a	DT
37681	3583	23	great	great	JJ
37681	3583	24	circle	circle	NN
37681	3583	25	.	.	.
37681	3583	26	_	_	NNP
37681	3583	27	This	this	DT
37681	3583	28	leads	lead	VBZ
37681	3583	29	to	to	IN
37681	3583	30	the	the	DT
37681	3583	31	remarkable	remarkable	JJ
37681	3583	32	formula	formula	NN
37681	3583	33	,	,	,
37681	3583	34	_	_	NNP
37681	3583	35	a	a	DT
37681	3583	36	_	_	NNP
37681	3583	37	=	=	SYM
37681	3583	38	4[pi]_r_^2	4[pi]_r_^2	CD
37681	3583	39	.	.	.
37681	3584	1	That	that	IN
37681	3584	2	the	the	DT
37681	3584	3	area	area	NN
37681	3584	4	of	of	IN
37681	3584	5	the	the	DT
37681	3584	6	sphere	sphere	NN
37681	3584	7	,	,	,
37681	3584	8	a	a	DT
37681	3584	9	curved	curved	JJ
37681	3584	10	surface	surface	NN
37681	3584	11	,	,	,
37681	3584	12	should	should	MD
37681	3584	13	exactly	exactly	RB
37681	3584	14	equal	equal	VB
37681	3584	15	the	the	DT
37681	3584	16	sum	sum	NN
37681	3584	17	of	of	IN
37681	3584	18	the	the	DT
37681	3584	19	areas	area	NNS
37681	3584	20	of	of	IN
37681	3584	21	four	four	CD
37681	3584	22	great	great	JJ
37681	3584	23	circles	circle	NNS
37681	3584	24	,	,	,
37681	3584	25	plane	plane	NN
37681	3584	26	surfaces	surface	NNS
37681	3584	27	,	,	,
37681	3584	28	is	be	VBZ
37681	3584	29	the	the	DT
37681	3584	30	remarkable	remarkable	JJ
37681	3584	31	feature	feature	NN
37681	3584	32	.	.	.
37681	3585	1	This	this	DT
37681	3585	2	was	be	VBD
37681	3585	3	one	one	CD
37681	3585	4	of	of	IN
37681	3585	5	the	the	DT
37681	3585	6	greatest	great	JJS
37681	3585	7	discoveries	discovery	NNS
37681	3585	8	of	of	IN
37681	3585	9	Archimedes	Archimedes	NNP
37681	3585	10	(	(	-LRB-
37681	3585	11	_	_	NNP
37681	3585	12	ca	ca	NNP
37681	3585	13	.	.	.
37681	3585	14	_	_	NNP
37681	3585	15	287	287	CD
37681	3585	16	-	-	SYM
37681	3585	17	212	212	CD
37681	3585	18	B.C.	B.C.	NNP
37681	3586	1	)	)	-RRB-
37681	3586	2	,	,	,
37681	3586	3	who	who	WP
37681	3586	4	gives	give	VBZ
37681	3586	5	it	-PRON-	PRP
37681	3586	6	as	as	IN
37681	3586	7	the	the	DT
37681	3586	8	thirty	thirty	CD
37681	3586	9	-	-	HYPH
37681	3586	10	fifth	fifth	JJ
37681	3586	11	proposition	proposition	NN
37681	3586	12	of	of	IN
37681	3586	13	his	-PRON-	PRP$
37681	3586	14	treatise	treatise	NN
37681	3586	15	on	on	IN
37681	3586	16	the	the	DT
37681	3586	17	"	"	``
37681	3586	18	Sphere	Sphere	NNP
37681	3586	19	and	and	CC
37681	3586	20	the	the	DT
37681	3586	21	Cylinder	cylinder	NN
37681	3586	22	,	,	,
37681	3586	23	"	"	''
37681	3586	24	and	and	CC
37681	3586	25	who	who	WP
37681	3586	26	mentions	mention	VBZ
37681	3586	27	it	-PRON-	PRP
37681	3586	28	specially	specially	RB
37681	3586	29	in	in	IN
37681	3586	30	a	a	DT
37681	3586	31	letter	letter	NN
37681	3586	32	to	to	IN
37681	3586	33	his	-PRON-	PRP$
37681	3586	34	friend	friend	NN
37681	3586	35	Dositheus	Dositheus	NNP
37681	3586	36	,	,	,
37681	3586	37	a	a	DT
37681	3586	38	mathematician	mathematician	NN
37681	3586	39	of	of	IN
37681	3586	40	some	some	DT
37681	3586	41	prominence	prominence	NN
37681	3586	42	.	.	.
37681	3587	1	Archimedes	archimede	NNS
37681	3587	2	also	also	RB
37681	3587	3	states	state	VBZ
37681	3587	4	that	that	IN
37681	3587	5	the	the	DT
37681	3587	6	surface	surface	NN
37681	3587	7	of	of	IN
37681	3587	8	a	a	DT
37681	3587	9	sphere	sphere	NN
37681	3587	10	is	be	VBZ
37681	3587	11	two	two	CD
37681	3587	12	thirds	third	NNS
37681	3587	13	that	that	DT
37681	3587	14	of	of	IN
37681	3587	15	the	the	DT
37681	3587	16	circumscribed	circumscribe	VBN
37681	3587	17	cylinder	cylinder	NN
37681	3587	18	,	,	,
37681	3587	19	or	or	CC
37681	3587	20	the	the	DT
37681	3587	21	same	same	JJ
37681	3587	22	as	as	IN
37681	3587	23	the	the	DT
37681	3587	24	curved	curved	JJ
37681	3587	25	surface	surface	NN
37681	3587	26	of	of	IN
37681	3587	27	this	this	DT
37681	3587	28	cylinder	cylinder	NN
37681	3587	29	.	.	.
37681	3588	1	This	this	DT
37681	3588	2	is	be	VBZ
37681	3588	3	evident	evident	JJ
37681	3588	4	,	,	,
37681	3588	5	since	since	IN
37681	3588	6	the	the	DT
37681	3588	7	cylindric	cylindric	JJ
37681	3588	8	surface	surface	NN
37681	3588	9	of	of	IN
37681	3588	10	the	the	DT
37681	3588	11	cylinder	cylinder	NN
37681	3588	12	is	be	VBZ
37681	3588	13	2[pi]_r	2[pi]_r	CD
37681	3588	14	_	_	NNP
37681	3588	15	×	×	NNS
37681	3588	16	2_r	2_r	CD
37681	3588	17	_	_	NNP
37681	3588	18	,	,	,
37681	3588	19	or	or	CC
37681	3588	20	4[pi]_r_^2	4[pi]_r_^2	CD
37681	3588	21	,	,	,
37681	3588	22	and	and	CC
37681	3588	23	the	the	DT
37681	3588	24	two	two	CD
37681	3588	25	bases	basis	NNS
37681	3588	26	have	have	VBP
37681	3588	27	an	an	DT
37681	3588	28	area	area	NN
37681	3588	29	[	[	-LRB-
37681	3588	30	pi]_r_^2	pi]_r_^2	NNP
37681	3588	31	+	+	CC
37681	3588	32	[	[	-LRB-
37681	3588	33	pi]_r_^2	pi]_r_^2	NNP
37681	3588	34	,	,	,
37681	3588	35	making	make	VBG
37681	3588	36	the	the	DT
37681	3588	37	total	total	JJ
37681	3588	38	area	area	NN
37681	3588	39	6[pi]_r_^2	6[pi]_r_^2	CD
37681	3588	40	.	.	.
37681	3589	1	THEOREM	THEOREM	NNP
37681	3589	2	.	.	.
37681	3590	1	_	_	NNP
37681	3590	2	The	the	DT
37681	3590	3	area	area	NN
37681	3590	4	of	of	IN
37681	3590	5	a	a	DT
37681	3590	6	spherical	spherical	JJ
37681	3590	7	triangle	triangle	NN
37681	3590	8	is	be	VBZ
37681	3590	9	equal	equal	JJ
37681	3590	10	to	to	IN
37681	3590	11	the	the	DT
37681	3590	12	area	area	NN
37681	3590	13	of	of	IN
37681	3590	14	a	a	DT
37681	3590	15	lune	lune	NN
37681	3590	16	whose	whose	WP$
37681	3590	17	angle	angle	NN
37681	3590	18	is	be	VBZ
37681	3590	19	half	half	PDT
37681	3590	20	the	the	DT
37681	3590	21	triangle	triangle	NN
37681	3590	22	's	's	POS
37681	3590	23	spherical	spherical	JJ
37681	3590	24	excess	excess	NN
37681	3590	25	.	.	.
37681	3590	26	_	_	NNP
37681	3590	27	This	this	DT
37681	3590	28	theorem	theorem	NN
37681	3590	29	,	,	,
37681	3590	30	so	so	RB
37681	3590	31	important	important	JJ
37681	3590	32	in	in	IN
37681	3590	33	finding	find	VBG
37681	3590	34	areas	area	NNS
37681	3590	35	on	on	IN
37681	3590	36	the	the	DT
37681	3590	37	earth	earth	NN
37681	3590	38	's	's	POS
37681	3590	39	surface	surface	NN
37681	3590	40	,	,	,
37681	3590	41	should	should	MD
37681	3590	42	be	be	VB
37681	3590	43	followed	follow	VBN
37681	3590	44	by	by	IN
37681	3590	45	a	a	DT
37681	3590	46	considerable	considerable	JJ
37681	3590	47	amount	amount	NN
37681	3590	48	of	of	IN
37681	3590	49	computation	computation	NN
37681	3590	50	of	of	IN
37681	3590	51	triangular	triangular	JJ
37681	3590	52	areas	area	NNS
37681	3590	53	,	,	,
37681	3590	54	else	else	RB
37681	3590	55	it	-PRON-	PRP
37681	3590	56	will	will	MD
37681	3590	57	be	be	VB
37681	3590	58	rather	rather	RB
37681	3590	59	meaningless	meaningless	JJ
37681	3590	60	.	.	.
37681	3591	1	Students	student	NNS
37681	3591	2	tend	tend	VBP
37681	3591	3	to	to	TO
37681	3591	4	memorize	memorize	VB
37681	3591	5	a	a	DT
37681	3591	6	proof	proof	NN
37681	3591	7	of	of	IN
37681	3591	8	this	this	DT
37681	3591	9	character	character	NN
37681	3591	10	,	,	,
37681	3591	11	and	and	CC
37681	3591	12	in	in	IN
37681	3591	13	order	order	NN
37681	3591	14	to	to	TO
37681	3591	15	have	have	VB
37681	3591	16	the	the	DT
37681	3591	17	proposition	proposition	NN
37681	3591	18	mean	mean	VB
37681	3591	19	what	what	WP
37681	3591	20	it	-PRON-	PRP
37681	3591	21	should	should	MD
37681	3591	22	to	to	IN
37681	3591	23	them	-PRON-	PRP
37681	3591	24	,	,	,
37681	3591	25	they	-PRON-	PRP
37681	3591	26	should	should	MD
37681	3591	27	at	at	RB
37681	3591	28	once	once	RB
37681	3591	29	apply	apply	VB
37681	3591	30	it	-PRON-	PRP
37681	3591	31	.	.	.
37681	3592	1	The	the	DT
37681	3592	2	same	same	JJ
37681	3592	3	is	be	VBZ
37681	3592	4	true	true	JJ
37681	3592	5	of	of	IN
37681	3592	6	the	the	DT
37681	3592	7	following	following	JJ
37681	3592	8	proposition	proposition	NN
37681	3592	9	on	on	IN
37681	3592	10	the	the	DT
37681	3592	11	area	area	NN
37681	3592	12	of	of	IN
37681	3592	13	a	a	DT
37681	3592	14	spherical	spherical	JJ
37681	3592	15	polygon	polygon	NN
37681	3592	16	.	.	.
37681	3593	1	It	-PRON-	PRP
37681	3593	2	is	be	VBZ
37681	3593	3	probable	probable	JJ
37681	3593	4	that	that	IN
37681	3593	5	neither	neither	DT
37681	3593	6	of	of	IN
37681	3593	7	these	these	DT
37681	3593	8	propositions	proposition	NNS
37681	3593	9	is	be	VBZ
37681	3593	10	very	very	RB
37681	3593	11	old	old	JJ
37681	3593	12	;	;	:
37681	3593	13	at	at	IN
37681	3593	14	any	any	DT
37681	3593	15	rate	rate	NN
37681	3593	16	,	,	,
37681	3593	17	they	-PRON-	PRP
37681	3593	18	do	do	VBP
37681	3593	19	not	not	RB
37681	3593	20	seem	seem	VB
37681	3593	21	to	to	TO
37681	3593	22	have	have	VB
37681	3593	23	been	be	VBN
37681	3593	24	known	know	VBN
37681	3593	25	to	to	IN
37681	3593	26	the	the	DT
37681	3593	27	writers	writer	NNS
37681	3593	28	on	on	IN
37681	3593	29	elementary	elementary	JJ
37681	3593	30	mathematics	mathematic	NNS
37681	3593	31	among	among	IN
37681	3593	32	the	the	DT
37681	3593	33	Greeks	Greeks	NNPS
37681	3593	34	.	.	.
37681	3594	1	THEOREM	THEOREM	NNP
37681	3594	2	.	.	.
37681	3595	1	_	_	NNP
37681	3595	2	The	the	DT
37681	3595	3	volume	volume	NN
37681	3595	4	of	of	IN
37681	3595	5	a	a	DT
37681	3595	6	sphere	sphere	NN
37681	3595	7	is	be	VBZ
37681	3595	8	equal	equal	JJ
37681	3595	9	to	to	IN
37681	3595	10	the	the	DT
37681	3595	11	product	product	NN
37681	3595	12	of	of	IN
37681	3595	13	the	the	DT
37681	3595	14	area	area	NN
37681	3595	15	of	of	IN
37681	3595	16	its	-PRON-	PRP$
37681	3595	17	surface	surface	NN
37681	3595	18	by	by	IN
37681	3595	19	one	one	CD
37681	3595	20	third	third	NN
37681	3595	21	of	of	IN
37681	3595	22	its	-PRON-	PRP$
37681	3595	23	radius	radius	NN
37681	3595	24	.	.	.
37681	3595	25	_	_	NNP
37681	3595	26	This	this	DT
37681	3595	27	gives	give	VBZ
37681	3595	28	the	the	DT
37681	3595	29	formula	formula	NN
37681	3595	30	_	_	NNP
37681	3595	31	v	v	NNP
37681	3595	32	_	_	NNP
37681	3595	33	=	=	NFP
37681	3595	34	(	(	-LRB-
37681	3595	35	4/3)[pi]_r_^3	4/3)[pi]_r_^3	CD
37681	3595	36	.	.	.
37681	3596	1	This	this	DT
37681	3596	2	is	be	VBZ
37681	3596	3	one	one	CD
37681	3596	4	of	of	IN
37681	3596	5	the	the	DT
37681	3596	6	greatest	great	JJS
37681	3596	7	discoveries	discovery	NNS
37681	3596	8	of	of	IN
37681	3596	9	Archimedes	archimede	NNS
37681	3596	10	.	.	.
37681	3597	1	He	-PRON-	PRP
37681	3597	2	also	also	RB
37681	3597	3	found	find	VBD
37681	3597	4	as	as	IN
37681	3597	5	a	a	DT
37681	3597	6	result	result	NN
37681	3597	7	that	that	IN
37681	3597	8	the	the	DT
37681	3597	9	volume	volume	NN
37681	3597	10	of	of	IN
37681	3597	11	a	a	DT
37681	3597	12	sphere	sphere	NN
37681	3597	13	is	be	VBZ
37681	3597	14	two	two	CD
37681	3597	15	thirds	third	NNS
37681	3597	16	the	the	DT
37681	3597	17	volume	volume	NN
37681	3597	18	of	of	IN
37681	3597	19	the	the	DT
37681	3597	20	circumscribed	circumscribe	VBN
37681	3597	21	cylinder	cylinder	NN
37681	3597	22	.	.	.
37681	3598	1	This	this	DT
37681	3598	2	is	be	VBZ
37681	3598	3	easily	easily	RB
37681	3598	4	seen	see	VBN
37681	3598	5	,	,	,
37681	3598	6	since	since	IN
37681	3598	7	the	the	DT
37681	3598	8	volume	volume	NN
37681	3598	9	of	of	IN
37681	3598	10	the	the	DT
37681	3598	11	cylinder	cylinder	NN
37681	3598	12	is	be	VBZ
37681	3598	13	[	[	-LRB-
37681	3598	14	pi]_r_^2	pi]_r_^2	NNP
37681	3598	15	×	×	NNS
37681	3598	16	2_r	2_r	CD
37681	3598	17	_	_	NNP
37681	3598	18	,	,	,
37681	3598	19	or	or	CC
37681	3598	20	2[pi]_r_^3	2[pi]_r_^3	CD
37681	3598	21	,	,	,
37681	3598	22	and	and	CC
37681	3598	23	(	(	-LRB-
37681	3598	24	4/3)[pi]_r_^3	4/3)[pi]_r_^3	CD
37681	3598	25	is	be	VBZ
37681	3598	26	2/3	2/3	CD
37681	3598	27	of	of	IN
37681	3598	28	2[pi]_r_^3	2[pi]_r_^3	CD
37681	3598	29	.	.	.
37681	3599	1	It	-PRON-	PRP
37681	3599	2	was	be	VBD
37681	3599	3	because	because	IN
37681	3599	4	of	of	IN
37681	3599	5	these	these	DT
37681	3599	6	discoveries	discovery	NNS
37681	3599	7	on	on	IN
37681	3599	8	the	the	DT
37681	3599	9	sphere	sphere	NN
37681	3599	10	and	and	CC
37681	3599	11	cylinder	cylinder	NN
37681	3599	12	that	that	WDT
37681	3599	13	Archimedes	Archimedes	NNP
37681	3599	14	wished	wish	VBD
37681	3599	15	these	these	DT
37681	3599	16	figures	figure	NNS
37681	3599	17	engraved	engrave	VBN
37681	3599	18	upon	upon	IN
37681	3599	19	his	-PRON-	PRP$
37681	3599	20	tomb	tomb	NN
37681	3599	21	,	,	,
37681	3599	22	as	as	IN
37681	3599	23	has	have	VBZ
37681	3599	24	already	already	RB
37681	3599	25	been	be	VBN
37681	3599	26	stated	state	VBN
37681	3599	27	.	.	.
37681	3600	1	The	the	DT
37681	3600	2	Roman	roman	JJ
37681	3600	3	general	general	NN
37681	3600	4	Marcellus	Marcellus	NNP
37681	3600	5	conquered	conquer	VBD
37681	3600	6	Syracuse	Syracuse	NNP
37681	3600	7	in	in	IN
37681	3600	8	212	212	CD
37681	3600	9	B.C.	B.C.	NNP
37681	3600	10	,	,	,
37681	3600	11	and	and	CC
37681	3600	12	at	at	IN
37681	3600	13	the	the	DT
37681	3600	14	sack	sack	NN
37681	3600	15	of	of	IN
37681	3600	16	the	the	DT
37681	3600	17	city	city	NN
37681	3600	18	Archimedes	Archimedes	NNP
37681	3600	19	was	be	VBD
37681	3600	20	killed	kill	VBN
37681	3600	21	by	by	IN
37681	3600	22	an	an	DT
37681	3600	23	ignorant	ignorant	JJ
37681	3600	24	soldier	soldier	NN
37681	3600	25	.	.	.
37681	3601	1	Marcellus	Marcellus	NNP
37681	3601	2	carried	carry	VBD
37681	3601	3	out	out	RP
37681	3601	4	the	the	DT
37681	3601	5	wishes	wish	NNS
37681	3601	6	of	of	IN
37681	3601	7	Archimedes	archimede	NNS
37681	3601	8	with	with	IN
37681	3601	9	respect	respect	NN
37681	3601	10	to	to	IN
37681	3601	11	the	the	DT
37681	3601	12	figures	figure	NNS
37681	3601	13	on	on	IN
37681	3601	14	his	-PRON-	PRP$
37681	3601	15	tomb	tomb	NN
37681	3601	16	.	.	.
37681	3602	1	The	the	DT
37681	3602	2	volume	volume	NN
37681	3602	3	of	of	IN
37681	3602	4	a	a	DT
37681	3602	5	sphere	sphere	NN
37681	3602	6	can	can	MD
37681	3602	7	also	also	RB
37681	3602	8	be	be	VB
37681	3602	9	very	very	RB
37681	3602	10	elegantly	elegantly	RB
37681	3602	11	found	find	VBN
37681	3602	12	by	by	IN
37681	3602	13	means	mean	NNS
37681	3602	14	of	of	IN
37681	3602	15	a	a	DT
37681	3602	16	proposition	proposition	NN
37681	3602	17	known	know	VBN
37681	3602	18	as	as	IN
37681	3602	19	Cavalieri	Cavalieri	NNP
37681	3602	20	's	's	POS
37681	3602	21	Theorem	theorem	NN
37681	3602	22	.	.	.
37681	3603	1	This	this	DT
37681	3603	2	asserts	assert	VBZ
37681	3603	3	that	that	IN
37681	3603	4	if	if	IN
37681	3603	5	two	two	CD
37681	3603	6	solids	solid	NNS
37681	3603	7	lie	lie	VBP
37681	3603	8	between	between	IN
37681	3603	9	parallel	parallel	JJ
37681	3603	10	planes	plane	NNS
37681	3603	11	,	,	,
37681	3603	12	and	and	CC
37681	3603	13	are	be	VBP
37681	3603	14	such	such	JJ
37681	3603	15	that	that	IN
37681	3603	16	the	the	DT
37681	3603	17	two	two	CD
37681	3603	18	sections	section	NNS
37681	3603	19	made	make	VBN
37681	3603	20	by	by	IN
37681	3603	21	any	any	DT
37681	3603	22	plane	plane	NN
37681	3603	23	parallel	parallel	NN
37681	3603	24	to	to	IN
37681	3603	25	the	the	DT
37681	3603	26	given	give	VBN
37681	3603	27	planes	plane	NNS
37681	3603	28	are	be	VBP
37681	3603	29	equal	equal	JJ
37681	3603	30	in	in	IN
37681	3603	31	area	area	NN
37681	3603	32	,	,	,
37681	3603	33	the	the	DT
37681	3603	34	solids	solid	NNS
37681	3603	35	are	be	VBP
37681	3603	36	themselves	-PRON-	PRP
37681	3603	37	equal	equal	JJ
37681	3603	38	in	in	IN
37681	3603	39	volume	volume	NN
37681	3603	40	.	.	.
37681	3604	1	Thus	thus	RB
37681	3604	2	,	,	,
37681	3604	3	if	if	IN
37681	3604	4	these	these	DT
37681	3604	5	solids	solid	NNS
37681	3604	6	have	have	VBP
37681	3604	7	the	the	DT
37681	3604	8	same	same	JJ
37681	3604	9	altitude	altitude	NN
37681	3604	10	,	,	,
37681	3604	11	_	_	NNP
37681	3604	12	a	a	DT
37681	3604	13	_	_	NNP
37681	3604	14	,	,	,
37681	3604	15	and	and	CC
37681	3604	16	if	if	IN
37681	3604	17	_	_	NNP
37681	3604	18	S	S	NNP
37681	3604	19	_	_	NNP
37681	3604	20	and	and	CC
37681	3604	21	_	_	NNP
37681	3604	22	S	S	NNP
37681	3604	23	'	'	''
37681	3604	24	_	_	NNP
37681	3604	25	are	be	VBP
37681	3604	26	equal	equal	JJ
37681	3604	27	sections	section	NNS
37681	3604	28	made	make	VBN
37681	3604	29	by	by	IN
37681	3604	30	a	a	DT
37681	3604	31	plane	plane	NN
37681	3604	32	parallel	parallel	NN
37681	3604	33	to	to	IN
37681	3604	34	_	_	NNP
37681	3604	35	MN	MN	NNP
37681	3604	36	_	_	NNP
37681	3604	37	,	,	,
37681	3604	38	then	then	RB
37681	3604	39	the	the	DT
37681	3604	40	solids	solid	NNS
37681	3604	41	have	have	VBP
37681	3604	42	the	the	DT
37681	3604	43	same	same	JJ
37681	3604	44	volume	volume	NN
37681	3604	45	.	.	.
37681	3605	1	The	the	DT
37681	3605	2	proof	proof	NN
37681	3605	3	is	be	VBZ
37681	3605	4	simple	simple	JJ
37681	3605	5	,	,	,
37681	3605	6	since	since	IN
37681	3605	7	prisms	prism	NNS
37681	3605	8	of	of	IN
37681	3605	9	the	the	DT
37681	3605	10	same	same	JJ
37681	3605	11	altitude	altitude	NN
37681	3605	12	,	,	,
37681	3605	13	say	say	VBP
37681	3605	14	_	_	NNP
37681	3605	15	a_/_n	a_/_n	NNP
37681	3605	16	_	_	NNP
37681	3605	17	,	,	,
37681	3605	18	and	and	CC
37681	3605	19	on	on	IN
37681	3605	20	the	the	DT
37681	3605	21	bases	basis	NNS
37681	3605	22	_	_	NNP
37681	3605	23	S	S	NNP
37681	3605	24	_	_	NNP
37681	3605	25	and	and	CC
37681	3605	26	_	_	NNP
37681	3605	27	S	S	NNP
37681	3605	28	'	'	''
37681	3605	29	_	_	NNP
37681	3605	30	are	be	VBP
37681	3605	31	equivalent	equivalent	JJ
37681	3605	32	,	,	,
37681	3605	33	and	and	CC
37681	3605	34	the	the	DT
37681	3605	35	sums	sum	NNS
37681	3605	36	of	of	IN
37681	3605	37	_	_	NNP
37681	3605	38	n	n	CC
37681	3605	39	_	_	NNP
37681	3605	40	such	such	JJ
37681	3605	41	prisms	prism	NNS
37681	3605	42	are	be	VBP
37681	3605	43	the	the	DT
37681	3605	44	given	give	VBN
37681	3605	45	solids	solid	NNS
37681	3605	46	;	;	,
37681	3605	47	and	and	CC
37681	3605	48	as	as	IN
37681	3605	49	_	_	NNP
37681	3605	50	n	n	CC
37681	3605	51	_	_	NNP
37681	3605	52	increases	increase	VBZ
37681	3605	53	,	,	,
37681	3605	54	the	the	DT
37681	3605	55	sums	sum	NNS
37681	3605	56	of	of	IN
37681	3605	57	the	the	DT
37681	3605	58	prisms	prism	NNS
37681	3605	59	approach	approach	VBP
37681	3605	60	the	the	DT
37681	3605	61	solids	solid	NNS
37681	3605	62	as	as	IN
37681	3605	63	their	-PRON-	PRP$
37681	3605	64	limits	limit	NNS
37681	3605	65	;	;	:
37681	3605	66	hence	hence	RB
37681	3605	67	the	the	DT
37681	3605	68	volumes	volume	NNS
37681	3605	69	are	be	VBP
37681	3605	70	equal	equal	JJ
37681	3605	71	.	.	.
37681	3606	1	[	[	-LRB-
37681	3606	2	Illustration	illustration	NN
37681	3606	3	]	]	-RRB-
37681	3606	4	This	this	DT
37681	3606	5	proposition	proposition	NN
37681	3606	6	,	,	,
37681	3606	7	which	which	WDT
37681	3606	8	will	will	MD
37681	3606	9	now	now	RB
37681	3606	10	be	be	VB
37681	3606	11	applied	apply	VBN
37681	3606	12	to	to	IN
37681	3606	13	finding	find	VBG
37681	3606	14	the	the	DT
37681	3606	15	volume	volume	NN
37681	3606	16	of	of	IN
37681	3606	17	the	the	DT
37681	3606	18	sphere	sphere	NN
37681	3606	19	,	,	,
37681	3606	20	was	be	VBD
37681	3606	21	discovered	discover	VBN
37681	3606	22	by	by	IN
37681	3606	23	Bonaventura	Bonaventura	NNP
37681	3606	24	Cavalieri	Cavalieri	NNP
37681	3606	25	(	(	-LRB-
37681	3606	26	1591	1591	CD
37681	3606	27	or	or	CC
37681	3606	28	1598	1598	CD
37681	3606	29	-	-	SYM
37681	3606	30	1647	1647	CD
37681	3606	31	)	)	-RRB-
37681	3606	32	.	.	.
37681	3607	1	He	-PRON-	PRP
37681	3607	2	was	be	VBD
37681	3607	3	a	a	DT
37681	3607	4	Jesuit	Jesuit	NNP
37681	3607	5	professor	professor	NN
37681	3607	6	in	in	IN
37681	3607	7	the	the	DT
37681	3607	8	University	University	NNP
37681	3607	9	of	of	IN
37681	3607	10	Bologna	Bologna	NNPS
37681	3607	11	,	,	,
37681	3607	12	and	and	CC
37681	3607	13	his	-PRON-	PRP$
37681	3607	14	best	good	JJS
37681	3607	15	known	known	JJ
37681	3607	16	work	work	NN
37681	3607	17	is	be	VBZ
37681	3607	18	his	-PRON-	PRP$
37681	3607	19	"	"	``
37681	3607	20	Geometria	Geometria	NNP
37681	3607	21	Indivisilibus	Indivisilibus	NNP
37681	3607	22	,	,	,
37681	3607	23	"	"	''
37681	3607	24	which	which	WDT
37681	3607	25	he	-PRON-	PRP
37681	3607	26	wrote	write	VBD
37681	3607	27	in	in	IN
37681	3607	28	1626	1626	CD
37681	3607	29	,	,	,
37681	3607	30	at	at	IN
37681	3607	31	least	least	JJS
37681	3607	32	in	in	IN
37681	3607	33	part	part	NN
37681	3607	34	,	,	,
37681	3607	35	and	and	CC
37681	3607	36	published	publish	VBN
37681	3607	37	in	in	IN
37681	3607	38	1635	1635	CD
37681	3607	39	(	(	-LRB-
37681	3607	40	second	second	JJ
37681	3607	41	edition	edition	NN
37681	3607	42	,	,	,
37681	3607	43	1647	1647	CD
37681	3607	44	)	)	-RRB-
37681	3607	45	.	.	.
37681	3608	1	By	by	IN
37681	3608	2	means	mean	NNS
37681	3608	3	of	of	IN
37681	3608	4	the	the	DT
37681	3608	5	proposition	proposition	NN
37681	3608	6	it	-PRON-	PRP
37681	3608	7	is	be	VBZ
37681	3608	8	also	also	RB
37681	3608	9	possible	possible	JJ
37681	3608	10	to	to	TO
37681	3608	11	prove	prove	VB
37681	3608	12	several	several	JJ
37681	3608	13	other	other	JJ
37681	3608	14	theorems	theorem	NNS
37681	3608	15	,	,	,
37681	3608	16	as	as	IN
37681	3608	17	that	that	IN
37681	3608	18	the	the	DT
37681	3608	19	volumes	volume	NNS
37681	3608	20	of	of	IN
37681	3608	21	triangular	triangular	JJ
37681	3608	22	pyramids	pyramid	NNS
37681	3608	23	of	of	IN
37681	3608	24	equivalent	equivalent	JJ
37681	3608	25	bases	basis	NNS
37681	3608	26	and	and	CC
37681	3608	27	equal	equal	JJ
37681	3608	28	altitudes	altitude	NNS
37681	3608	29	are	be	VBP
37681	3608	30	equal	equal	JJ
37681	3608	31	.	.	.
37681	3609	1	[	[	-LRB-
37681	3609	2	Illustration	illustration	NN
37681	3609	3	]	]	-RRB-
37681	3609	4	To	to	TO
37681	3609	5	find	find	VB
37681	3609	6	the	the	DT
37681	3609	7	volume	volume	NN
37681	3609	8	of	of	IN
37681	3609	9	a	a	DT
37681	3609	10	sphere	sphere	NN
37681	3609	11	,	,	,
37681	3609	12	take	take	VB
37681	3609	13	the	the	DT
37681	3609	14	quadrant	quadrant	NN
37681	3609	15	_	_	NNP
37681	3609	16	OPQ	OPQ	NNP
37681	3609	17	_	_	NNP
37681	3609	18	,	,	,
37681	3609	19	in	in	IN
37681	3609	20	the	the	DT
37681	3609	21	square	square	NN
37681	3609	22	_	_	NNP
37681	3609	23	OPRQ	OPRQ	NNP
37681	3609	24	_	_	NNP
37681	3609	25	.	.	.
37681	3610	1	Then	then	RB
37681	3610	2	if	if	IN
37681	3610	3	this	this	DT
37681	3610	4	figure	figure	NN
37681	3610	5	is	be	VBZ
37681	3610	6	revolved	revolve	VBN
37681	3610	7	about	about	IN
37681	3610	8	_	_	NNP
37681	3610	9	OP	OP	NNP
37681	3610	10	_	_	NNP
37681	3610	11	,	,	,
37681	3610	12	_	_	NNP
37681	3610	13	OPQ	OPQ	NNP
37681	3610	14	_	_	NNP
37681	3610	15	will	will	MD
37681	3610	16	generate	generate	VB
37681	3610	17	a	a	DT
37681	3610	18	hemisphere	hemisphere	NN
37681	3610	19	,	,	,
37681	3610	20	_	_	NNP
37681	3610	21	OPR	OPR	NNP
37681	3610	22	_	_	NNP
37681	3610	23	will	will	MD
37681	3610	24	generate	generate	VB
37681	3610	25	a	a	DT
37681	3610	26	cone	cone	NN
37681	3610	27	of	of	IN
37681	3610	28	volume	volume	NN
37681	3610	29	(	(	-LRB-
37681	3610	30	1/3)[pi]_r_^3	1/3)[pi]_r_^3	CD
37681	3610	31	,	,	,
37681	3610	32	and	and	CC
37681	3610	33	_	_	NNP
37681	3610	34	OPRQ	OPRQ	NNP
37681	3610	35	_	_	NNP
37681	3610	36	will	will	MD
37681	3610	37	generate	generate	VB
37681	3610	38	a	a	DT
37681	3610	39	cylinder	cylinder	NN
37681	3610	40	of	of	IN
37681	3610	41	volume	volume	NN
37681	3610	42	[	[	-LRB-
37681	3610	43	pi]_r_^3	pi]_r_^3	NNP
37681	3610	44	.	.	.
37681	3611	1	Hence	hence	RB
37681	3611	2	the	the	DT
37681	3611	3	figure	figure	NN
37681	3611	4	generated	generate	VBN
37681	3611	5	by	by	IN
37681	3611	6	_	_	NNP
37681	3611	7	ORQ	ORQ	NNP
37681	3611	8	_	_	NNP
37681	3611	9	will	will	MD
37681	3611	10	have	have	VB
37681	3611	11	a	a	DT
37681	3611	12	volume	volume	NN
37681	3611	13	[	[	-LRB-
37681	3611	14	pi]_r_^3	pi]_r_^3	NNP
37681	3611	15	-	-	,
37681	3611	16	(	(	-LRB-
37681	3611	17	1/3)[pi]_r_^3	1/3)[pi]_r_^3	CD
37681	3611	18	,	,	,
37681	3611	19	or	or	CC
37681	3611	20	(	(	-LRB-
37681	3611	21	2/3)[pi]_r_^3	2/3)[pi]_r_^3	CD
37681	3611	22	,	,	,
37681	3611	23	which	which	WDT
37681	3611	24	we	-PRON-	PRP
37681	3611	25	will	will	MD
37681	3611	26	call	call	VB
37681	3611	27	_	_	NNP
37681	3611	28	x	x	NNP
37681	3611	29	_	_	NNP
37681	3611	30	.	.	.
37681	3612	1	Now	now	RB
37681	3612	2	_	_	NNP
37681	3612	3	OA	OA	NNP
37681	3612	4	_	_	NNP
37681	3612	5	=	=	SYM
37681	3612	6	_	_	NNP
37681	3612	7	AB	AB	NNP
37681	3612	8	_	_	NNP
37681	3612	9	,	,	,
37681	3612	10	and	and	CC
37681	3612	11	_	_	NNP
37681	3612	12	OC	OC	NNP
37681	3612	13	_	_	NNP
37681	3612	14	=	=	SYM
37681	3612	15	_	_	NNP
37681	3612	16	AD	AD	NNP
37681	3612	17	_	_	NNP
37681	3612	18	;	;	:
37681	3612	19	also	also	RB
37681	3612	20	(	(	-LRB-
37681	3612	21	_	_	NNP
37681	3612	22	OC_)^2	OC_)^2	NNP
37681	3612	23	-	-	,
37681	3612	24	(	(	-LRB-
37681	3612	25	_	_	NNP
37681	3612	26	OA_)^2	OA_)^2	NNP
37681	3612	27	=	=	NFP
37681	3612	28	(	(	-LRB-
37681	3612	29	_	_	NNP
37681	3612	30	AC_)^2	AC_)^2	NNP
37681	3612	31	,	,	,
37681	3612	32	so	so	IN
37681	3612	33	that	that	DT
37681	3612	34	(	(	-LRB-
37681	3612	35	_	_	NNP
37681	3612	36	AD_)^2	AD_)^2	NNP
37681	3612	37	-	-	:
37681	3612	38	(	(	-LRB-
37681	3612	39	_	_	NNP
37681	3612	40	AB_)^2	AB_)^2	NNP
37681	3612	41	=	=	FW
37681	3612	42	(	(	-LRB-
37681	3612	43	_	_	NNP
37681	3612	44	AC_)^2	AC_)^2	NNP
37681	3612	45	,	,	,
37681	3612	46	and	and	CC
37681	3612	47	[	[	-LRB-
37681	3612	48	pi](_AD_)^2	pi](_ad_)^2	CD
37681	3612	49	-	-	HYPH
37681	3612	50	[	[	-LRB-
37681	3612	51	pi](_AB_)^2	pi](_ab_)^2	NN
37681	3612	52	=	=	SYM
37681	3612	53	[	[	-LRB-
37681	3612	54	pi](_AC_)^2	pi](_ac_)^2	CD
37681	3612	55	.	.	.
37681	3613	1	But	but	CC
37681	3613	2	[	[	-LRB-
37681	3613	3	pi](_AD_)^2	pi](_ad_)^2	CD
37681	3613	4	-	-	HYPH
37681	3613	5	[	[	-LRB-
37681	3613	6	pi](_AB_)^2	pi](_ab_)^2	NN
37681	3613	7	is	be	VBZ
37681	3613	8	the	the	DT
37681	3613	9	area	area	NN
37681	3613	10	of	of	IN
37681	3613	11	the	the	DT
37681	3613	12	ring	ring	NN
37681	3613	13	generated	generate	VBN
37681	3613	14	by	by	IN
37681	3613	15	_	_	NNP
37681	3613	16	BD	BD	NNP
37681	3613	17	_	_	NNP
37681	3613	18	,	,	,
37681	3613	19	a	a	DT
37681	3613	20	section	section	NN
37681	3613	21	of	of	IN
37681	3613	22	_	_	NNP
37681	3613	23	x	x	NNP
37681	3613	24	_	_	NNP
37681	3613	25	,	,	,
37681	3613	26	and	and	CC
37681	3613	27	[	[	-LRB-
37681	3613	28	pi](_AC_)^2	pi](_ac_)^2	CD
37681	3613	29	is	be	VBZ
37681	3613	30	the	the	DT
37681	3613	31	corresponding	corresponding	JJ
37681	3613	32	section	section	NN
37681	3613	33	of	of	IN
37681	3613	34	the	the	DT
37681	3613	35	hemisphere	hemisphere	NN
37681	3613	36	.	.	.
37681	3614	1	Hence	hence	RB
37681	3614	2	,	,	,
37681	3614	3	by	by	IN
37681	3614	4	Cavalieri	Cavalieri	NNP
37681	3614	5	's	's	POS
37681	3614	6	Theorem	Theorem	NNP
37681	3614	7	,	,	,
37681	3614	8	(	(	-LRB-
37681	3614	9	2/3)[pi]_r_^3	2/3)[pi]_r_^3	CD
37681	3614	10	=	=	SYM
37681	3614	11	the	the	DT
37681	3614	12	volume	volume	NN
37681	3614	13	of	of	IN
37681	3614	14	the	the	DT
37681	3614	15	hemisphere	hemisphere	NN
37681	3614	16	.	.	.
37681	3615	1	[	[	-LRB-
37681	3615	2	therefore	therefore	RB
37681	3615	3	]	]	-RRB-
37681	3615	4	(	(	-LRB-
37681	3615	5	4/3)[pi]_r_^3	4/3)[pi]_r_^3	CD
37681	3615	6	=	=	SYM
37681	3615	7	the	the	DT
37681	3615	8	volume	volume	NN
37681	3615	9	of	of	IN
37681	3615	10	the	the	DT
37681	3615	11	sphere	sphere	NN
37681	3615	12	.	.	.
37681	3616	1	In	in	IN
37681	3616	2	connection	connection	NN
37681	3616	3	with	with	IN
37681	3616	4	the	the	DT
37681	3616	5	sphere	sphere	NN
37681	3616	6	some	some	DT
37681	3616	7	easy	easy	JJ
37681	3616	8	work	work	NN
37681	3616	9	in	in	IN
37681	3616	10	quadratics	quadratic	NNS
37681	3616	11	may	may	MD
37681	3616	12	be	be	VB
37681	3616	13	introduced	introduce	VBN
37681	3616	14	even	even	RB
37681	3616	15	if	if	IN
37681	3616	16	the	the	DT
37681	3616	17	class	class	NN
37681	3616	18	has	have	VBZ
37681	3616	19	had	have	VBN
37681	3616	20	only	only	RB
37681	3616	21	a	a	DT
37681	3616	22	year	year	NN
37681	3616	23	in	in	IN
37681	3616	24	algebra	algebra	NN
37681	3616	25	.	.	.
37681	3617	1	For	for	IN
37681	3617	2	example	example	NN
37681	3617	3	,	,	,
37681	3617	4	suppose	suppose	VB
37681	3617	5	a	a	DT
37681	3617	6	cube	cube	NN
37681	3617	7	is	be	VBZ
37681	3617	8	inscribed	inscribe	VBN
37681	3617	9	in	in	IN
37681	3617	10	a	a	DT
37681	3617	11	hemisphere	hemisphere	NN
37681	3617	12	of	of	IN
37681	3617	13	radius	radius	NN
37681	3617	14	_	_	NNP
37681	3617	15	r	r	NNP
37681	3617	16	_	_	NNP
37681	3617	17	and	and	CC
37681	3617	18	we	-PRON-	PRP
37681	3617	19	wish	wish	VBP
37681	3617	20	to	to	TO
37681	3617	21	find	find	VB
37681	3617	22	its	-PRON-	PRP$
37681	3617	23	edge	edge	NN
37681	3617	24	,	,	,
37681	3617	25	and	and	CC
37681	3617	26	thereby	thereby	RB
37681	3617	27	its	-PRON-	PRP$
37681	3617	28	surface	surface	NN
37681	3617	29	and	and	CC
37681	3617	30	its	-PRON-	PRP$
37681	3617	31	volume	volume	NN
37681	3617	32	.	.	.
37681	3618	1	If	if	IN
37681	3618	2	_	_	NNP
37681	3618	3	x	x	NNP
37681	3618	4	_	_	NNP
37681	3618	5	=	=	SYM
37681	3618	6	the	the	DT
37681	3618	7	edge	edge	NN
37681	3618	8	of	of	IN
37681	3618	9	the	the	DT
37681	3618	10	cube	cube	NN
37681	3618	11	,	,	,
37681	3618	12	the	the	DT
37681	3618	13	diagonal	diagonal	JJ
37681	3618	14	of	of	IN
37681	3618	15	the	the	DT
37681	3618	16	base	base	NN
37681	3618	17	must	must	MD
37681	3618	18	be	be	VB
37681	3618	19	_	_	NNP
37681	3618	20	x_[sqrt]2	x_[sqrt]2	NNP
37681	3618	21	,	,	,
37681	3618	22	and	and	CC
37681	3618	23	the	the	DT
37681	3618	24	projection	projection	NN
37681	3618	25	of	of	IN
37681	3618	26	_	_	NNP
37681	3618	27	r	r	NNP
37681	3618	28	_	_	NNP
37681	3618	29	(	(	-LRB-
37681	3618	30	drawn	draw	VBN
37681	3618	31	from	from	IN
37681	3618	32	the	the	DT
37681	3618	33	center	center	NN
37681	3618	34	of	of	IN
37681	3618	35	the	the	DT
37681	3618	36	base	base	NN
37681	3618	37	to	to	IN
37681	3618	38	one	one	CD
37681	3618	39	of	of	IN
37681	3618	40	the	the	DT
37681	3618	41	vertices	vertex	NNS
37681	3618	42	)	)	-RRB-
37681	3618	43	on	on	IN
37681	3618	44	the	the	DT
37681	3618	45	base	base	NN
37681	3618	46	is	be	VBZ
37681	3618	47	half	half	NN
37681	3618	48	of	of	IN
37681	3618	49	this	this	DT
37681	3618	50	diagonal	diagonal	JJ
37681	3618	51	,	,	,
37681	3618	52	or	or	CC
37681	3618	53	(	(	-LRB-
37681	3618	54	_	_	NNP
37681	3618	55	x_[sqrt]2)/2	x_[sqrt]2)/2	NNP
37681	3618	56	.	.	.
37681	3619	1	Hence	hence	RB
37681	3619	2	,	,	,
37681	3619	3	by	by	IN
37681	3619	4	the	the	DT
37681	3619	5	Pythagorean	Pythagorean	NNP
37681	3619	6	Theorem	Theorem	NNP
37681	3619	7	,	,	,
37681	3619	8	_	_	NNP
37681	3619	9	r_^2	r_^2	NNP
37681	3619	10	=	=	SYM
37681	3619	11	_	_	NNP
37681	3619	12	x_^2	x_^2	NNP
37681	3619	13	+	+	NFP
37681	3619	14	(	(	-LRB-
37681	3619	15	(	(	-LRB-
37681	3619	16	_	_	NNP
37681	3619	17	x_[sqrt]2)/2)^2	x_[sqrt]2)/2)^2	NNP
37681	3619	18	=	=	NFP
37681	3619	19	(	(	-LRB-
37681	3619	20	3/2)_x_^2	3/2)_x_^2	NNP
37681	3619	21	[	[	-LRB-
37681	3619	22	therefore	therefore	RB
37681	3619	23	]	]	-RRB-
37681	3619	24	_	_	NNP
37681	3619	25	x	x	NNP
37681	3619	26	_	_	NNP
37681	3619	27	=	=	SYM
37681	3619	28	_	_	NNP
37681	3619	29	r_[sqrt](2/3	r_[sqrt](2/3	NNP
37681	3619	30	)	)	-RRB-
37681	3619	31	,	,	,
37681	3619	32	and	and	CC
37681	3619	33	the	the	DT
37681	3619	34	total	total	JJ
37681	3619	35	surface	surface	NN
37681	3619	36	is	be	VBZ
37681	3619	37	6_x_^2	6_x_^2	JJ
37681	3619	38	=	=	SYM
37681	3619	39	4_r_^2	4_r_^2	CD
37681	3619	40	,	,	,
37681	3619	41	and	and	CC
37681	3619	42	the	the	DT
37681	3619	43	volume	volume	NN
37681	3619	44	is	be	VBZ
37681	3619	45	_	_	NNP
37681	3619	46	x_^3	x_^3	NNP
37681	3619	47	=	=	NFP
37681	3619	48	(	(	-LRB-
37681	3619	49	2/3)_r_^3[sqrt](2/3	2/3)_r_^3[sqrt](2/3	CD
37681	3619	50	)	)	-RRB-
37681	3619	51	.	.	.
37681	3620	1	FOOTNOTES	footnote	NNS
37681	3620	2	:	:	:
37681	3620	3	[	[	-LRB-
37681	3620	4	92	92	CD
37681	3620	5	]	]	-RRB-
37681	3620	6	The	the	DT
37681	3620	7	illustration	illustration	NN
37681	3620	8	is	be	VBZ
37681	3620	9	from	from	IN
37681	3620	10	Dupin	Dupin	NNP
37681	3620	11	,	,	,
37681	3620	12	loc	loc	NNP
37681	3620	13	.	.	.
37681	3621	1	cit	cit	NNP
37681	3621	2	.	.	.
37681	3622	1	L'ENVOI	l'envoi	NN
37681	3622	2	In	in	IN
37681	3622	3	the	the	DT
37681	3622	4	Valley	Valley	NNP
37681	3622	5	of	of	IN
37681	3622	6	Youth	Youth	NNP
37681	3622	7	,	,	,
37681	3622	8	through	through	IN
37681	3622	9	which	which	WDT
37681	3622	10	all	all	DT
37681	3622	11	wayfarers	wayfarer	NNS
37681	3622	12	must	must	MD
37681	3622	13	pass	pass	VB
37681	3622	14	on	on	RP
37681	3622	15	their	-PRON-	PRP$
37681	3622	16	journey	journey	NN
37681	3622	17	from	from	IN
37681	3622	18	the	the	DT
37681	3622	19	Land	Land	NNP
37681	3622	20	of	of	IN
37681	3622	21	Mystery	Mystery	NNP
37681	3622	22	to	to	IN
37681	3622	23	the	the	DT
37681	3622	24	Land	land	NN
37681	3622	25	of	of	IN
37681	3622	26	the	the	DT
37681	3622	27	Infinite	Infinite	NNP
37681	3622	28	,	,	,
37681	3622	29	there	there	EX
37681	3622	30	is	be	VBZ
37681	3622	31	a	a	DT
37681	3622	32	village	village	NN
37681	3622	33	where	where	WRB
37681	3622	34	the	the	DT
37681	3622	35	pilgrim	pilgrim	NN
37681	3622	36	rests	rest	VBZ
37681	3622	37	and	and	CC
37681	3622	38	indulges	indulge	NNS
37681	3622	39	in	in	IN
37681	3622	40	various	various	JJ
37681	3622	41	excursions	excursion	NNS
37681	3622	42	for	for	IN
37681	3622	43	which	which	WDT
37681	3622	44	the	the	DT
37681	3622	45	valley	valley	NN
37681	3622	46	is	be	VBZ
37681	3622	47	celebrated	celebrate	VBN
37681	3622	48	.	.	.
37681	3623	1	There	there	EX
37681	3623	2	also	also	RB
37681	3623	3	gather	gather	VBP
37681	3623	4	many	many	JJ
37681	3623	5	guides	guide	NNS
37681	3623	6	in	in	IN
37681	3623	7	this	this	DT
37681	3623	8	spot	spot	NN
37681	3623	9	,	,	,
37681	3623	10	some	some	DT
37681	3623	11	of	of	IN
37681	3623	12	whom	whom	WP
37681	3623	13	show	show	VBP
37681	3623	14	the	the	DT
37681	3623	15	stranger	stranger	NN
37681	3623	16	all	all	PDT
37681	3623	17	the	the	DT
37681	3623	18	various	various	JJ
37681	3623	19	points	point	NNS
37681	3623	20	of	of	IN
37681	3623	21	common	common	JJ
37681	3623	22	interest	interest	NN
37681	3623	23	,	,	,
37681	3623	24	and	and	CC
37681	3623	25	others	other	NNS
37681	3623	26	of	of	IN
37681	3623	27	whom	whom	WP
37681	3623	28	take	take	VBP
37681	3623	29	visitors	visitor	NNS
37681	3623	30	to	to	IN
37681	3623	31	special	special	JJ
37681	3623	32	points	point	NNS
37681	3623	33	from	from	IN
37681	3623	34	which	which	WDT
37681	3623	35	the	the	DT
37681	3623	36	views	view	NNS
37681	3623	37	are	be	VBP
37681	3623	38	of	of	IN
37681	3623	39	peculiar	peculiar	JJ
37681	3623	40	significance	significance	NN
37681	3623	41	.	.	.
37681	3624	1	As	as	IN
37681	3624	2	time	time	NN
37681	3624	3	has	have	VBZ
37681	3624	4	gone	go	VBN
37681	3624	5	on	on	IN
37681	3624	6	new	new	JJ
37681	3624	7	paths	path	NNS
37681	3624	8	have	have	VBP
37681	3624	9	opened	open	VBN
37681	3624	10	,	,	,
37681	3624	11	and	and	CC
37681	3624	12	new	new	JJ
37681	3624	13	resting	resting	NN
37681	3624	14	places	place	NNS
37681	3624	15	have	have	VBP
37681	3624	16	been	be	VBN
37681	3624	17	made	make	VBN
37681	3624	18	from	from	IN
37681	3624	19	which	which	WDT
37681	3624	20	these	these	DT
37681	3624	21	views	view	NNS
37681	3624	22	are	be	VBP
37681	3624	23	best	best	RB
37681	3624	24	obtained	obtain	VBN
37681	3624	25	.	.	.
37681	3625	1	Some	some	DT
37681	3625	2	of	of	IN
37681	3625	3	the	the	DT
37681	3625	4	mountain	mountain	NN
37681	3625	5	peaks	peak	NNS
37681	3625	6	have	have	VBP
37681	3625	7	been	be	VBN
37681	3625	8	neglected	neglect	VBN
37681	3625	9	in	in	IN
37681	3625	10	the	the	DT
37681	3625	11	past	past	NN
37681	3625	12	,	,	,
37681	3625	13	but	but	CC
37681	3625	14	of	of	IN
37681	3625	15	late	late	RB
37681	3625	16	they	-PRON-	PRP
37681	3625	17	too	too	RB
37681	3625	18	have	have	VBP
37681	3625	19	been	be	VBN
37681	3625	20	scaled	scale	VBN
37681	3625	21	,	,	,
37681	3625	22	and	and	CC
37681	3625	23	paths	path	NNS
37681	3625	24	have	have	VBP
37681	3625	25	been	be	VBN
37681	3625	26	hewn	hew	VBN
37681	3625	27	out	out	RP
37681	3625	28	that	that	IN
37681	3625	29	approach	approach	NN
37681	3625	30	the	the	DT
37681	3625	31	summits	summit	NNS
37681	3625	32	,	,	,
37681	3625	33	and	and	CC
37681	3625	34	many	many	JJ
37681	3625	35	pilgrims	pilgrim	NNS
37681	3625	36	ascend	ascend	VBP
37681	3625	37	them	-PRON-	PRP
37681	3625	38	and	and	CC
37681	3625	39	find	find	VB
37681	3625	40	that	that	IN
37681	3625	41	the	the	DT
37681	3625	42	result	result	NN
37681	3625	43	is	be	VBZ
37681	3625	44	abundantly	abundantly	RB
37681	3625	45	worth	worth	JJ
37681	3625	46	the	the	DT
37681	3625	47	effort	effort	NN
37681	3625	48	and	and	CC
37681	3625	49	the	the	DT
37681	3625	50	time	time	NN
37681	3625	51	.	.	.
37681	3626	1	The	the	DT
37681	3626	2	effect	effect	NN
37681	3626	3	of	of	IN
37681	3626	4	these	these	DT
37681	3626	5	several	several	JJ
37681	3626	6	improvements	improvement	NNS
37681	3626	7	has	have	VBZ
37681	3626	8	been	be	VBN
37681	3626	9	a	a	DT
37681	3626	10	natural	natural	JJ
37681	3626	11	and	and	CC
37681	3626	12	usually	usually	RB
37681	3626	13	friendly	friendly	JJ
37681	3626	14	rivalry	rivalry	NN
37681	3626	15	in	in	IN
37681	3626	16	the	the	DT
37681	3626	17	body	body	NN
37681	3626	18	of	of	IN
37681	3626	19	guides	guide	NNS
37681	3626	20	that	that	WDT
37681	3626	21	show	show	VBP
37681	3626	22	the	the	DT
37681	3626	23	way	way	NN
37681	3626	24	.	.	.
37681	3627	1	The	the	DT
37681	3627	2	mountains	mountain	NNS
37681	3627	3	have	have	VBP
37681	3627	4	not	not	RB
37681	3627	5	changed	change	VBN
37681	3627	6	,	,	,
37681	3627	7	and	and	CC
37681	3627	8	the	the	DT
37681	3627	9	views	view	NNS
37681	3627	10	are	be	VBP
37681	3627	11	what	what	WP
37681	3627	12	they	-PRON-	PRP
37681	3627	13	have	have	VBP
37681	3627	14	always	always	RB
37681	3627	15	been	be	VBN
37681	3627	16	.	.	.
37681	3628	1	But	but	CC
37681	3628	2	there	there	EX
37681	3628	3	are	be	VBP
37681	3628	4	not	not	RB
37681	3628	5	wanting	want	VBG
37681	3628	6	those	those	DT
37681	3628	7	who	who	WP
37681	3628	8	say	say	VBP
37681	3628	9	,	,	,
37681	3628	10	"	"	``
37681	3628	11	My	-PRON-	PRP$
37681	3628	12	mountain	mountain	NN
37681	3628	13	may	may	MD
37681	3628	14	not	not	RB
37681	3628	15	be	be	VB
37681	3628	16	as	as	RB
37681	3628	17	lofty	lofty	JJ
37681	3628	18	as	as	IN
37681	3628	19	yours	-PRON-	PRP
37681	3628	20	,	,	,
37681	3628	21	but	but	CC
37681	3628	22	it	-PRON-	PRP
37681	3628	23	is	be	VBZ
37681	3628	24	easier	easy	JJR
37681	3628	25	to	to	TO
37681	3628	26	ascend	ascend	VB
37681	3628	27	"	"	''
37681	3628	28	;	;	,
37681	3628	29	or	or	CC
37681	3628	30	"	"	``
37681	3628	31	There	there	EX
37681	3628	32	are	be	VBP
37681	3628	33	quarries	quarry	NNS
37681	3628	34	on	on	IN
37681	3628	35	my	-PRON-	PRP$
37681	3628	36	peak	peak	NN
37681	3628	37	,	,	,
37681	3628	38	and	and	CC
37681	3628	39	points	point	NNS
37681	3628	40	of	of	IN
37681	3628	41	view	view	NN
37681	3628	42	from	from	IN
37681	3628	43	which	which	WDT
37681	3628	44	a	a	DT
37681	3628	45	building	building	NN
37681	3628	46	may	may	MD
37681	3628	47	be	be	VB
37681	3628	48	seen	see	VBN
37681	3628	49	in	in	IN
37681	3628	50	process	process	NN
37681	3628	51	of	of	IN
37681	3628	52	erection	erection	NN
37681	3628	53	,	,	,
37681	3628	54	or	or	CC
37681	3628	55	a	a	DT
37681	3628	56	mill	mill	NN
37681	3628	57	in	in	IN
37681	3628	58	operation	operation	NN
37681	3628	59	,	,	,
37681	3628	60	or	or	CC
37681	3628	61	a	a	DT
37681	3628	62	canal	canal	NN
37681	3628	63	,	,	,
37681	3628	64	while	while	IN
37681	3628	65	your	-PRON-	PRP$
37681	3628	66	mountain	mountain	NN
37681	3628	67	shows	show	VBZ
37681	3628	68	only	only	RB
37681	3628	69	a	a	DT
37681	3628	70	stretch	stretch	NN
37681	3628	71	of	of	IN
37681	3628	72	hills	hill	NNS
37681	3628	73	and	and	CC
37681	3628	74	valleys	valley	NNS
37681	3628	75	,	,	,
37681	3628	76	and	and	CC
37681	3628	77	thus	thus	RB
37681	3628	78	you	-PRON-	PRP
37681	3628	79	will	will	MD
37681	3628	80	see	see	VB
37681	3628	81	that	that	DT
37681	3628	82	mine	mine	NN
37681	3628	83	is	be	VBZ
37681	3628	84	the	the	DT
37681	3628	85	more	more	RBR
37681	3628	86	profitable	profitable	JJ
37681	3628	87	to	to	TO
37681	3628	88	visit	visit	VB
37681	3628	89	.	.	.
37681	3628	90	"	"	''
37681	3629	1	Then	then	RB
37681	3629	2	there	there	EX
37681	3629	3	are	be	VBP
37681	3629	4	guides	guide	NNS
37681	3629	5	who	who	WP
37681	3629	6	are	be	VBP
37681	3629	7	themselves	-PRON-	PRP
37681	3629	8	often	often	RB
37681	3629	9	weak	weak	JJ
37681	3629	10	of	of	IN
37681	3629	11	limb	limb	NN
37681	3629	12	,	,	,
37681	3629	13	and	and	CC
37681	3629	14	who	who	WP
37681	3629	15	are	be	VBP
37681	3629	16	attached	attach	VBN
37681	3629	17	to	to	IN
37681	3629	18	numerous	numerous	JJ
37681	3629	19	sand	sand	NN
37681	3629	20	dunes	dune	NNS
37681	3629	21	,	,	,
37681	3629	22	and	and	CC
37681	3629	23	these	these	DT
37681	3629	24	say	say	VBP
37681	3629	25	to	to	IN
37681	3629	26	the	the	DT
37681	3629	27	weaker	weak	JJR
37681	3629	28	pilgrims	pilgrim	NNS
37681	3629	29	,	,	,
37681	3629	30	"	"	``
37681	3629	31	Why	why	WRB
37681	3629	32	tire	tire	NN
37681	3629	33	yourselves	yourself	NNS
37681	3629	34	climbing	climb	VBG
37681	3629	35	a	a	DT
37681	3629	36	rocky	rocky	JJ
37681	3629	37	mountain	mountain	NN
37681	3629	38	when	when	WRB
37681	3629	39	here	here	RB
37681	3629	40	are	be	VBP
37681	3629	41	peaks	peak	NNS
37681	3629	42	whose	whose	WP$
37681	3629	43	summits	summit	NNS
37681	3629	44	you	-PRON-	PRP
37681	3629	45	can	can	MD
37681	3629	46	reach	reach	VB
37681	3629	47	with	with	IN
37681	3629	48	ease	ease	NN
37681	3629	49	and	and	CC
37681	3629	50	from	from	IN
37681	3629	51	which	which	WDT
37681	3629	52	the	the	DT
37681	3629	53	view	view	NN
37681	3629	54	is	be	VBZ
37681	3629	55	just	just	RB
37681	3629	56	as	as	RB
37681	3629	57	good	good	JJ
37681	3629	58	as	as	IN
37681	3629	59	that	that	DT
37681	3629	60	from	from	IN
37681	3629	61	the	the	DT
37681	3629	62	most	most	RBS
37681	3629	63	famous	famous	JJ
37681	3629	64	precipice	precipice	NN
37681	3629	65	?	?	.
37681	3629	66	"	"	''
37681	3630	1	The	the	DT
37681	3630	2	result	result	NN
37681	3630	3	is	be	VBZ
37681	3630	4	not	not	RB
37681	3630	5	wholly	wholly	RB
37681	3630	6	disadvantageous	disadvantageous	JJ
37681	3630	7	,	,	,
37681	3630	8	for	for	IN
37681	3630	9	many	many	JJ
37681	3630	10	who	who	WP
37681	3630	11	pass	pass	VBP
37681	3630	12	through	through	IN
37681	3630	13	the	the	DT
37681	3630	14	valley	valley	NN
37681	3630	15	are	be	VBP
37681	3630	16	able	able	JJ
37681	3630	17	to	to	TO
37681	3630	18	approach	approach	VB
37681	3630	19	the	the	DT
37681	3630	20	summits	summit	NNS
37681	3630	21	of	of	IN
37681	3630	22	the	the	DT
37681	3630	23	sand	sand	NN
37681	3630	24	dunes	dun	VBZ
37681	3630	25	only	only	RB
37681	3630	26	,	,	,
37681	3630	27	and	and	CC
37681	3630	28	would	would	MD
37681	3630	29	make	make	VB
37681	3630	30	progress	progress	NN
37681	3630	31	with	with	IN
37681	3630	32	greatest	great	JJS
37681	3630	33	difficulty	difficulty	NN
37681	3630	34	should	should	MD
37681	3630	35	they	-PRON-	PRP
37681	3630	36	attempt	attempt	VB
37681	3630	37	to	to	TO
37681	3630	38	scale	scale	VB
37681	3630	39	a	a	DT
37681	3630	40	real	real	JJ
37681	3630	41	mountain	mountain	NN
37681	3630	42	,	,	,
37681	3630	43	although	although	IN
37681	3630	44	even	even	RB
37681	3630	45	for	for	IN
37681	3630	46	them	-PRON-	PRP
37681	3630	47	it	-PRON-	PRP
37681	3630	48	would	would	MD
37681	3630	49	be	be	VB
37681	3630	50	better	well	JJR
37681	3630	51	to	to	TO
37681	3630	52	climb	climb	VB
37681	3630	53	a	a	DT
37681	3630	54	little	little	JJ
37681	3630	55	way	way	NN
37681	3630	56	where	where	WRB
37681	3630	57	it	-PRON-	PRP
37681	3630	58	is	be	VBZ
37681	3630	59	really	really	RB
37681	3630	60	worth	worth	JJ
37681	3630	61	the	the	DT
37681	3630	62	effort	effort	NN
37681	3630	63	instead	instead	RB
37681	3630	64	of	of	IN
37681	3630	65	spending	spend	VBG
37681	3630	66	all	all	PDT
37681	3630	67	their	-PRON-	PRP$
37681	3630	68	efforts	effort	NNS
37681	3630	69	on	on	IN
37681	3630	70	the	the	DT
37681	3630	71	dunes	dune	NNS
37681	3630	72	.	.	.
37681	3631	1	Then	then	RB
37681	3631	2	,	,	,
37681	3631	3	too	too	RB
37681	3631	4	,	,	,
37681	3631	5	there	there	EX
37681	3631	6	have	have	VBP
37681	3631	7	of	of	IN
37681	3631	8	late	late	JJ
37681	3631	9	come	come	NN
37681	3631	10	guides	guide	NNS
37681	3631	11	who	who	WP
37681	3631	12	have	have	VBP
37681	3631	13	shown	show	VBN
37681	3631	14	much	much	JJ
37681	3631	15	ingenuity	ingenuity	NN
37681	3631	16	by	by	IN
37681	3631	17	digging	dig	VBG
37681	3631	18	tunnels	tunnel	NNS
37681	3631	19	into	into	IN
37681	3631	20	some	some	DT
37681	3631	21	of	of	IN
37681	3631	22	the	the	DT
37681	3631	23	greatest	great	JJS
37681	3631	24	mountains	mountain	NNS
37681	3631	25	.	.	.
37681	3632	1	These	these	DT
37681	3632	2	they	-PRON-	PRP
37681	3632	3	have	have	VBP
37681	3632	4	paved	pave	VBN
37681	3632	5	with	with	IN
37681	3632	6	smooth	smooth	JJ
37681	3632	7	concrete	concrete	NN
37681	3632	8	,	,	,
37681	3632	9	and	and	CC
37681	3632	10	have	have	VBP
37681	3632	11	arranged	arrange	VBN
37681	3632	12	for	for	IN
37681	3632	13	rubber	rubber	NN
37681	3632	14	-	-	HYPH
37681	3632	15	tired	tired	JJ
37681	3632	16	cars	car	NNS
37681	3632	17	that	that	WDT
37681	3632	18	run	run	VBP
37681	3632	19	without	without	IN
37681	3632	20	jar	jar	NN
37681	3632	21	to	to	IN
37681	3632	22	the	the	DT
37681	3632	23	heart	heart	NN
37681	3632	24	of	of	IN
37681	3632	25	some	some	DT
37681	3632	26	mountain	mountain	NN
37681	3632	27	.	.	.
37681	3633	1	Arrived	arrive	VBN
37681	3633	2	there	there	RB
37681	3633	3	the	the	DT
37681	3633	4	pilgrim	pilgrim	NN
37681	3633	5	has	have	VBZ
37681	3633	6	a	a	DT
37681	3633	7	glance	glance	NN
37681	3633	8	,	,	,
37681	3633	9	as	as	IN
37681	3633	10	the	the	DT
37681	3633	11	car	car	NN
37681	3633	12	swiftly	swiftly	RB
37681	3633	13	turns	turn	VBZ
37681	3633	14	in	in	IN
37681	3633	15	a	a	DT
37681	3633	16	blaze	blaze	NN
37681	3633	17	of	of	IN
37681	3633	18	electric	electric	JJ
37681	3633	19	light	light	NN
37681	3633	20	,	,	,
37681	3633	21	at	at	IN
37681	3633	22	a	a	DT
37681	3633	23	roughly	roughly	RB
37681	3633	24	painted	paint	VBN
37681	3633	25	panorama	panorama	NN
37681	3633	26	of	of	IN
37681	3633	27	the	the	DT
37681	3633	28	view	view	NN
37681	3633	29	from	from	IN
37681	3633	30	the	the	DT
37681	3633	31	summit	summit	NN
37681	3633	32	,	,	,
37681	3633	33	and	and	CC
37681	3633	34	he	-PRON-	PRP
37681	3633	35	is	be	VBZ
37681	3633	36	assured	assure	VBN
37681	3633	37	by	by	IN
37681	3633	38	the	the	DT
37681	3633	39	guide	guide	NN
37681	3633	40	that	that	WDT
37681	3633	41	he	-PRON-	PRP
37681	3633	42	has	have	VBZ
37681	3633	43	accomplished	accomplish	VBN
37681	3633	44	all	all	DT
37681	3633	45	that	that	WDT
37681	3633	46	he	-PRON-	PRP
37681	3633	47	would	would	MD
37681	3633	48	have	have	VB
37681	3633	49	done	do	VBN
37681	3633	50	,	,	,
37681	3633	51	had	have	VBD
37681	3633	52	he	-PRON-	PRP
37681	3633	53	laboriously	laboriously	RB
37681	3633	54	climbed	climb	VBD
37681	3633	55	the	the	DT
37681	3633	56	peak	peak	NN
37681	3633	57	itself	-PRON-	PRP
37681	3633	58	.	.	.
37681	3634	1	In	in	IN
37681	3634	2	the	the	DT
37681	3634	3	midst	midst	NN
37681	3634	4	of	of	IN
37681	3634	5	all	all	PDT
37681	3634	6	the	the	DT
37681	3634	7	advocacy	advocacy	NN
37681	3634	8	of	of	IN
37681	3634	9	sand	sand	NN
37681	3634	10	-	-	HYPH
37681	3634	11	dune	dune	NN
37681	3634	12	climbing	climbing	NN
37681	3634	13	,	,	,
37681	3634	14	and	and	CC
37681	3634	15	of	of	IN
37681	3634	16	rubber	rubber	NN
37681	3634	17	-	-	HYPH
37681	3634	18	tired	tired	JJ
37681	3634	19	cars	car	NNS
37681	3634	20	to	to	TO
37681	3634	21	see	see	VB
37681	3634	22	a	a	DT
37681	3634	23	painted	paint	VBN
37681	3634	24	view	view	NN
37681	3634	25	,	,	,
37681	3634	26	the	the	DT
37681	3634	27	great	great	JJ
37681	3634	28	body	body	NN
37681	3634	29	of	of	IN
37681	3634	30	guides	guide	NNS
37681	3634	31	still	still	RB
37681	3634	32	climb	climb	VBP
37681	3634	33	their	-PRON-	PRP$
37681	3634	34	mountains	mountain	NNS
37681	3634	35	with	with	IN
37681	3634	36	their	-PRON-	PRP$
37681	3634	37	little	little	JJ
37681	3634	38	groups	group	NNS
37681	3634	39	of	of	IN
37681	3634	40	followers	follower	NNS
37681	3634	41	,	,	,
37681	3634	42	and	and	CC
37681	3634	43	the	the	DT
37681	3634	44	vigor	vigor	NN
37681	3634	45	of	of	IN
37681	3634	46	the	the	DT
37681	3634	47	ascent	ascent	NN
37681	3634	48	and	and	CC
37681	3634	49	the	the	DT
37681	3634	50	magnificence	magnificence	NN
37681	3634	51	of	of	IN
37681	3634	52	the	the	DT
37681	3634	53	view	view	NN
37681	3634	54	still	still	RB
37681	3634	55	attract	attract	VBP
37681	3634	56	all	all	DT
37681	3634	57	who	who	WP
37681	3634	58	are	be	VBP
37681	3634	59	strong	strong	JJ
37681	3634	60	and	and	CC
37681	3634	61	earnest	earnest	JJ
37681	3634	62	,	,	,
37681	3634	63	during	during	IN
37681	3634	64	their	-PRON-	PRP$
37681	3634	65	sojourn	sojourn	NN
37681	3634	66	in	in	IN
37681	3634	67	the	the	DT
37681	3634	68	Valley	Valley	NNP
37681	3634	69	of	of	IN
37681	3634	70	Youth	Youth	NNP
37681	3634	71	.	.	.
37681	3635	1	Among	among	IN
37681	3635	2	the	the	DT
37681	3635	3	mountains	mountain	NNS
37681	3635	4	that	that	WDT
37681	3635	5	have	have	VBP
37681	3635	6	for	for	IN
37681	3635	7	ages	age	NNS
37681	3635	8	attracted	attract	VBD
37681	3635	9	the	the	DT
37681	3635	10	pilgrims	pilgrim	NNS
37681	3635	11	is	be	VBZ
37681	3635	12	Mons	Mons	NNP
37681	3635	13	Latinus	Latinus	NNP
37681	3635	14	,	,	,
37681	3635	15	usually	usually	RB
37681	3635	16	called	call	VBD
37681	3635	17	in	in	IN
37681	3635	18	the	the	DT
37681	3635	19	valley	valley	NN
37681	3635	20	by	by	IN
37681	3635	21	the	the	DT
37681	3635	22	more	more	RBR
37681	3635	23	pleasing	pleasing	JJ
37681	3635	24	name	name	NN
37681	3635	25	Latina	Latina	NNP
37681	3635	26	.	.	.
37681	3636	1	Mathematica	Mathematica	NNP
37681	3636	2	,	,	,
37681	3636	3	and	and	CC
37681	3636	4	Rhetorica	Rhetorica	NNP
37681	3636	5	,	,	,
37681	3636	6	and	and	CC
37681	3636	7	Grammatica	Grammatica	NNP
37681	3636	8	are	be	VBP
37681	3636	9	also	also	RB
37681	3636	10	among	among	IN
37681	3636	11	the	the	DT
37681	3636	12	best	well	RBS
37681	3636	13	known	know	VBN
37681	3636	14	.	.	.
37681	3637	1	A	a	DT
37681	3637	2	group	group	NN
37681	3637	3	known	know	VBN
37681	3637	4	as	as	IN
37681	3637	5	Montes	Montes	NNP
37681	3637	6	Naturales	Naturales	NNP
37681	3637	7	comprises	comprise	VBZ
37681	3637	8	Physica	Physica	NNP
37681	3637	9	,	,	,
37681	3637	10	Biologica	Biologica	NNP
37681	3637	11	,	,	,
37681	3637	12	and	and	CC
37681	3637	13	Chemica	Chemica	NNP
37681	3637	14	,	,	,
37681	3637	15	and	and	CC
37681	3637	16	one	one	CD
37681	3637	17	great	great	JJ
37681	3637	18	peak	peak	NN
37681	3637	19	with	with	IN
37681	3637	20	minor	minor	JJ
37681	3637	21	peaks	peak	NNS
37681	3637	22	about	about	IN
37681	3637	23	it	-PRON-	PRP
37681	3637	24	is	be	VBZ
37681	3637	25	called	call	VBN
37681	3637	26	by	by	IN
37681	3637	27	the	the	DT
37681	3637	28	people	people	NNS
37681	3637	29	Philosophia	Philosophia	NNP
37681	3637	30	.	.	.
37681	3638	1	There	there	EX
37681	3638	2	are	be	VBP
37681	3638	3	those	those	DT
37681	3638	4	who	who	WP
37681	3638	5	claim	claim	VBP
37681	3638	6	that	that	IN
37681	3638	7	these	these	DT
37681	3638	8	great	great	JJ
37681	3638	9	masses	masse	NNS
37681	3638	10	of	of	IN
37681	3638	11	rock	rock	NN
37681	3638	12	are	be	VBP
37681	3638	13	too	too	RB
37681	3638	14	old	old	JJ
37681	3638	15	to	to	TO
37681	3638	16	be	be	VB
37681	3638	17	climbed	climb	VBN
37681	3638	18	,	,	,
37681	3638	19	as	as	IN
37681	3638	20	if	if	IN
37681	3638	21	that	that	DT
37681	3638	22	affected	affect	VBD
37681	3638	23	the	the	DT
37681	3638	24	view	view	NN
37681	3638	25	;	;	:
37681	3638	26	while	while	IN
37681	3638	27	others	other	NNS
37681	3638	28	claim	claim	VBP
37681	3638	29	that	that	IN
37681	3638	30	the	the	DT
37681	3638	31	ascent	ascent	NN
37681	3638	32	is	be	VBZ
37681	3638	33	too	too	RB
37681	3638	34	difficult	difficult	JJ
37681	3638	35	and	and	CC
37681	3638	36	that	that	IN
37681	3638	37	all	all	DT
37681	3638	38	who	who	WP
37681	3638	39	do	do	VBP
37681	3638	40	not	not	RB
37681	3638	41	favor	favor	VB
37681	3638	42	the	the	DT
37681	3638	43	sand	sand	NN
37681	3638	44	dunes	dune	NNS
37681	3638	45	are	be	VBP
37681	3638	46	reactionary	reactionary	JJ
37681	3638	47	.	.	.
37681	3639	1	But	but	CC
37681	3639	2	this	this	DT
37681	3639	3	affects	affect	VBZ
37681	3639	4	only	only	RB
37681	3639	5	a	a	DT
37681	3639	6	few	few	JJ
37681	3639	7	who	who	WP
37681	3639	8	belong	belong	VBP
37681	3639	9	to	to	IN
37681	3639	10	the	the	DT
37681	3639	11	real	real	JJ
37681	3639	12	mountains	mountain	NNS
37681	3639	13	,	,	,
37681	3639	14	and	and	CC
37681	3639	15	the	the	DT
37681	3639	16	others	other	NNS
37681	3639	17	labor	labor	NN
37681	3639	18	diligently	diligently	RB
37681	3639	19	to	to	TO
37681	3639	20	improve	improve	VB
37681	3639	21	the	the	DT
37681	3639	22	paths	path	NNS
37681	3639	23	and	and	CC
37681	3639	24	to	to	TO
37681	3639	25	lessen	lessen	VB
37681	3639	26	unnecessary	unnecessary	JJ
37681	3639	27	toil	toil	NN
37681	3639	28	,	,	,
37681	3639	29	but	but	CC
37681	3639	30	they	-PRON-	PRP
37681	3639	31	seek	seek	VBP
37681	3639	32	not	not	RB
37681	3639	33	to	to	TO
37681	3639	34	tear	tear	VB
37681	3639	35	off	off	RP
37681	3639	36	the	the	DT
37681	3639	37	summits	summit	NNS
37681	3639	38	nor	nor	CC
37681	3639	39	do	do	VBP
37681	3639	40	they	-PRON-	PRP
37681	3639	41	attend	attend	VB
37681	3639	42	to	to	IN
37681	3639	43	the	the	DT
37681	3639	44	amusing	amusing	JJ
37681	3639	45	attempts	attempt	NNS
37681	3639	46	of	of	IN
37681	3639	47	those	those	DT
37681	3639	48	who	who	WP
37681	3639	49	sit	sit	VBP
37681	3639	50	by	by	IN
37681	3639	51	the	the	DT
37681	3639	52	hillocks	hillock	NNS
37681	3639	53	and	and	CC
37681	3639	54	throw	throw	VB
37681	3639	55	pebbles	pebble	NNS
37681	3639	56	at	at	IN
37681	3639	57	the	the	DT
37681	3639	58	rocky	rocky	JJ
37681	3639	59	sides	side	NNS
37681	3639	60	of	of	IN
37681	3639	61	the	the	DT
37681	3639	62	mountains	mountain	NNS
37681	3639	63	upon	upon	IN
37681	3639	64	which	which	WDT
37681	3639	65	they	-PRON-	PRP
37681	3639	66	work	work	VBP
37681	3639	67	.	.	.
37681	3640	1	*	*	NFP
37681	3640	2	*	*	NFP
37681	3640	3	*	*	NFP
37681	3640	4	*	*	NFP
37681	3640	5	*	*	NFP
37681	3640	6	Geometry	Geometry	NNP
37681	3640	7	is	be	VBZ
37681	3640	8	a	a	DT
37681	3640	9	mountain	mountain	NN
37681	3640	10	.	.	.
37681	3641	1	Vigor	Vigor	NNP
37681	3641	2	is	be	VBZ
37681	3641	3	needed	need	VBN
37681	3641	4	for	for	IN
37681	3641	5	its	-PRON-	PRP$
37681	3641	6	ascent	ascent	NN
37681	3641	7	.	.	.
37681	3642	1	The	the	DT
37681	3642	2	views	view	NNS
37681	3642	3	all	all	RB
37681	3642	4	along	along	IN
37681	3642	5	the	the	DT
37681	3642	6	paths	path	NNS
37681	3642	7	are	be	VBP
37681	3642	8	magnificent	magnificent	JJ
37681	3642	9	.	.	.
37681	3643	1	The	the	DT
37681	3643	2	effort	effort	NN
37681	3643	3	of	of	IN
37681	3643	4	climbing	climbing	NN
37681	3643	5	is	be	VBZ
37681	3643	6	stimulating	stimulate	VBG
37681	3643	7	.	.	.
37681	3644	1	A	a	DT
37681	3644	2	guide	guide	NN
37681	3644	3	who	who	WP
37681	3644	4	points	point	VBZ
37681	3644	5	out	out	RP
37681	3644	6	the	the	DT
37681	3644	7	beauties	beauty	NNS
37681	3644	8	,	,	,
37681	3644	9	the	the	DT
37681	3644	10	grandeur	grandeur	NN
37681	3644	11	,	,	,
37681	3644	12	and	and	CC
37681	3644	13	the	the	DT
37681	3644	14	special	special	JJ
37681	3644	15	places	place	NNS
37681	3644	16	of	of	IN
37681	3644	17	interest	interest	NN
37681	3644	18	commands	command	VBZ
37681	3644	19	the	the	DT
37681	3644	20	admiration	admiration	NN
37681	3644	21	of	of	IN
37681	3644	22	his	-PRON-	PRP$
37681	3644	23	group	group	NN
37681	3644	24	of	of	IN
37681	3644	25	pilgrims	pilgrim	NNS
37681	3644	26	.	.	.
37681	3645	1	One	one	CD
37681	3645	2	who	who	WP
37681	3645	3	fails	fail	VBZ
37681	3645	4	to	to	TO
37681	3645	5	do	do	VB
37681	3645	6	this	this	DT
37681	3645	7	,	,	,
37681	3645	8	who	who	WP
37681	3645	9	does	do	VBZ
37681	3645	10	not	not	RB
37681	3645	11	know	know	VB
37681	3645	12	the	the	DT
37681	3645	13	paths	path	NNS
37681	3645	14	,	,	,
37681	3645	15	who	who	WP
37681	3645	16	puts	put	VBZ
37681	3645	17	unnecessary	unnecessary	JJ
37681	3645	18	burdens	burden	NNS
37681	3645	19	upon	upon	IN
37681	3645	20	the	the	DT
37681	3645	21	pilgrim	pilgrim	NN
37681	3645	22	,	,	,
37681	3645	23	or	or	CC
37681	3645	24	who	who	WP
37681	3645	25	blindfolds	blindfold	VBZ
37681	3645	26	him	-PRON-	PRP
37681	3645	27	in	in	IN
37681	3645	28	his	-PRON-	PRP$
37681	3645	29	progress	progress	NN
37681	3645	30	,	,	,
37681	3645	31	is	be	VBZ
37681	3645	32	unworthy	unworthy	JJ
37681	3645	33	of	of	IN
37681	3645	34	his	-PRON-	PRP$
37681	3645	35	position	position	NN
37681	3645	36	.	.	.
37681	3646	1	The	the	DT
37681	3646	2	pretended	pretended	JJ
37681	3646	3	guide	guide	NN
37681	3646	4	who	who	WP
37681	3646	5	says	say	VBZ
37681	3646	6	that	that	IN
37681	3646	7	the	the	DT
37681	3646	8	painted	paint	VBN
37681	3646	9	panorama	panorama	NNP
37681	3646	10	,	,	,
37681	3646	11	seen	see	VBN
37681	3646	12	from	from	IN
37681	3646	13	the	the	DT
37681	3646	14	rubber	rubber	NN
37681	3646	15	-	-	HYPH
37681	3646	16	tired	tired	JJ
37681	3646	17	car	car	NN
37681	3646	18	,	,	,
37681	3646	19	is	be	VBZ
37681	3646	20	as	as	RB
37681	3646	21	good	good	JJ
37681	3646	22	as	as	IN
37681	3646	23	the	the	DT
37681	3646	24	view	view	NN
37681	3646	25	from	from	IN
37681	3646	26	the	the	DT
37681	3646	27	summit	summit	NN
37681	3646	28	is	be	VBZ
37681	3646	29	simply	simply	RB
37681	3646	30	a	a	DT
37681	3646	31	fakir	fakir	NNS
37681	3646	32	and	and	CC
37681	3646	33	is	be	VBZ
37681	3646	34	generally	generally	RB
37681	3646	35	recognized	recognize	VBN
37681	3646	36	as	as	IN
37681	3646	37	such	such	JJ
37681	3646	38	.	.	.
37681	3647	1	The	the	DT
37681	3647	2	mountain	mountain	NN
37681	3647	3	will	will	MD
37681	3647	4	stand	stand	VB
37681	3647	5	;	;	:
37681	3647	6	it	-PRON-	PRP
37681	3647	7	will	will	MD
37681	3647	8	not	not	RB
37681	3647	9	be	be	VB
37681	3647	10	used	use	VBN
37681	3647	11	as	as	IN
37681	3647	12	a	a	DT
37681	3647	13	mere	mere	JJ
37681	3647	14	commercial	commercial	JJ
37681	3647	15	quarry	quarry	NN
37681	3647	16	for	for	IN
37681	3647	17	building	build	VBG
37681	3647	18	stone	stone	NN
37681	3647	19	;	;	:
37681	3647	20	it	-PRON-	PRP
37681	3647	21	will	will	MD
37681	3647	22	not	not	RB
37681	3647	23	be	be	VB
37681	3647	24	affected	affect	VBN
37681	3647	25	by	by	IN
37681	3647	26	pellets	pellet	NNS
37681	3647	27	thrown	throw	VBN
37681	3647	28	from	from	IN
37681	3647	29	the	the	DT
37681	3647	30	little	little	JJ
37681	3647	31	hillocks	hillock	NNS
37681	3647	32	about	about	IN
37681	3647	33	;	;	:
37681	3647	34	but	but	CC
37681	3647	35	its	-PRON-	PRP$
37681	3647	36	paths	path	NNS
37681	3647	37	will	will	MD
37681	3647	38	be	be	VB
37681	3647	39	freed	free	VBN
37681	3647	40	from	from	IN
37681	3647	41	unnecessary	unnecessary	JJ
37681	3647	42	flints	flint	NNS
37681	3647	43	,	,	,
37681	3647	44	they	-PRON-	PRP
37681	3647	45	will	will	MD
37681	3647	46	be	be	VB
37681	3647	47	straightened	straighten	VBN
37681	3647	48	where	where	WRB
37681	3647	49	this	this	DT
37681	3647	50	can	can	MD
37681	3647	51	advantageously	advantageously	RB
37681	3647	52	be	be	VB
37681	3647	53	done	do	VBN
37681	3647	54	,	,	,
37681	3647	55	and	and	CC
37681	3647	56	new	new	JJ
37681	3647	57	paths	path	NNS
37681	3647	58	on	on	IN
37681	3647	59	entirely	entirely	RB
37681	3647	60	novel	novel	JJ
37681	3647	61	plans	plan	NNS
37681	3647	62	will	will	MD
37681	3647	63	be	be	VB
37681	3647	64	made	make	VBN
37681	3647	65	as	as	IN
37681	3647	66	time	time	NN
37681	3647	67	goes	go	VBZ
37681	3647	68	on	on	RP
37681	3647	69	,	,	,
37681	3647	70	but	but	CC
37681	3647	71	these	these	DT
37681	3647	72	paths	path	NNS
37681	3647	73	will	will	MD
37681	3647	74	be	be	VB
37681	3647	75	hewed	hew	VBN
37681	3647	76	out	out	IN
37681	3647	77	of	of	IN
37681	3647	78	rock	rock	NN
37681	3647	79	,	,	,
37681	3647	80	not	not	RB
37681	3647	81	made	make	VBN
37681	3647	82	out	out	IN
37681	3647	83	of	of	IN
37681	3647	84	the	the	DT
37681	3647	85	dreams	dream	NNS
37681	3647	86	of	of	IN
37681	3647	87	a	a	DT
37681	3647	88	day	day	NN
37681	3647	89	.	.	.
37681	3648	1	Every	every	DT
37681	3648	2	worthy	worthy	JJ
37681	3648	3	guide	guide	NN
37681	3648	4	will	will	MD
37681	3648	5	assist	assist	VB
37681	3648	6	in	in	IN
37681	3648	7	all	all	PDT
37681	3648	8	these	these	DT
37681	3648	9	efforts	effort	NNS
37681	3648	10	at	at	IN
37681	3648	11	betterment	betterment	NN
37681	3648	12	,	,	,
37681	3648	13	and	and	CC
37681	3648	14	will	will	MD
37681	3648	15	urge	urge	VB
37681	3648	16	the	the	DT
37681	3648	17	pilgrim	pilgrim	NN
37681	3648	18	at	at	IN
37681	3648	19	least	least	RBS
37681	3648	20	to	to	TO
37681	3648	21	ascend	ascend	VB
37681	3648	22	a	a	DT
37681	3648	23	little	little	JJ
37681	3648	24	way	way	NN
37681	3648	25	because	because	IN
37681	3648	26	of	of	IN
37681	3648	27	the	the	DT
37681	3648	28	fact	fact	NN
37681	3648	29	that	that	IN
37681	3648	30	the	the	DT
37681	3648	31	same	same	JJ
37681	3648	32	view	view	NN
37681	3648	33	can	can	MD
37681	3648	34	not	not	RB
37681	3648	35	be	be	VB
37681	3648	36	obtained	obtain	VBN
37681	3648	37	from	from	IN
37681	3648	38	other	other	JJ
37681	3648	39	peaks	peak	NNS
37681	3648	40	;	;	:
37681	3648	41	but	but	CC
37681	3648	42	he	-PRON-	PRP
37681	3648	43	will	will	MD
37681	3648	44	not	not	RB
37681	3648	45	take	take	VB
37681	3648	46	seriously	seriously	RB
37681	3648	47	the	the	DT
37681	3648	48	efforts	effort	NNS
37681	3648	49	of	of	IN
37681	3648	50	the	the	DT
37681	3648	51	fakir	fakir	NNS
37681	3648	52	,	,	,
37681	3648	53	nor	nor	CC
37681	3648	54	will	will	MD
37681	3648	55	he	-PRON-	PRP
37681	3648	56	listen	listen	VB
37681	3648	57	with	with	IN
37681	3648	58	more	more	JJR
37681	3648	59	than	than	IN
37681	3648	60	passing	pass	VBG
37681	3648	61	interest	interest	NN
37681	3648	62	to	to	IN
37681	3648	63	him	-PRON-	PRP
37681	3648	64	who	who	WP
37681	3648	65	proclaims	proclaim	VBZ
37681	3648	66	the	the	DT
37681	3648	67	sand	sand	NN
37681	3648	68	heap	heap	NN
37681	3648	69	to	to	TO
37681	3648	70	be	be	VB
37681	3648	71	a	a	DT
37681	3648	72	Matterhorn	Matterhorn	NNP
37681	3648	73	.	.	.
37681	3649	1	INDEX	INDEX	NNP
37681	3649	2	Ahmes	Ahmes	NNP
37681	3649	3	,	,	,
37681	3649	4	27	27	CD
37681	3649	5	,	,	,
37681	3649	6	254	254	CD
37681	3649	7	,	,	,
37681	3649	8	278	278	CD
37681	3649	9	,	,	,
37681	3649	10	306	306	CD
37681	3649	11	Alexandroff	Alexandroff	NNP
37681	3649	12	,	,	,
37681	3649	13	164	164	CD
37681	3649	14	Algebra	Algebra	NNP
37681	3649	15	,	,	,
37681	3649	16	37	37	CD
37681	3649	17	,	,	,
37681	3649	18	84	84	CD
37681	3649	19	Al	Al	NNP
37681	3649	20	-	-	HYPH
37681	3649	21	Khowarazmi	Khowarazmi	NNP
37681	3649	22	,	,	,
37681	3649	23	37	37	CD
37681	3649	24	Allman	Allman	NNP
37681	3649	25	,	,	,
37681	3649	26	G.	G.	NNP
37681	3649	27	J.	J.	NNP
37681	3649	28	,	,	,
37681	3649	29	29	29	CD
37681	3649	30	Almagest	Almagest	NNP
37681	3649	31	,	,	,
37681	3649	32	35	35	CD
37681	3649	33	Al	Al	NNP
37681	3649	34	-	-	HYPH
37681	3649	35	Nair[=i]z[=i	Nair[=i]z[=i	NNP
37681	3649	36	]	]	-RRB-
37681	3649	37	,	,	,
37681	3649	38	171	171	CD
37681	3649	39	,	,	,
37681	3649	40	193	193	CD
37681	3649	41	,	,	,
37681	3649	42	214	214	CD
37681	3649	43	,	,	,
37681	3649	44	264	264	CD
37681	3649	45	Al	Al	NNP
37681	3649	46	-	-	HYPH
37681	3649	47	Qif[t.][=i	Qif[t.][=i	NNP
37681	3649	48	]	]	-RRB-
37681	3649	49	,	,	,
37681	3649	50	49	49	CD
37681	3649	51	Analysis	Analysis	NNP
37681	3649	52	,	,	,
37681	3649	53	41	41	CD
37681	3649	54	,	,	,
37681	3649	55	161	161	CD
37681	3649	56	Angle	Angle	NNP
37681	3649	57	,	,	,
37681	3649	58	142	142	CD
37681	3649	59	,	,	,
37681	3649	60	155	155	CD
37681	3649	61	;	;	:
37681	3649	62	trisection	trisection	NN
37681	3649	63	of	of	IN
37681	3649	64	,	,	,
37681	3649	65	31	31	CD
37681	3649	66	,	,	,
37681	3649	67	215	215	CD
37681	3649	68	Anthonisz	Anthonisz	NNP
37681	3649	69	,	,	,
37681	3649	70	Adriaen	Adriaen	NNP
37681	3649	71	,	,	,
37681	3649	72	279	279	CD
37681	3649	73	Antiphon	Antiphon	NNP
37681	3649	74	,	,	,
37681	3649	75	31	31	CD
37681	3649	76	,	,	,
37681	3649	77	32	32	CD
37681	3649	78	,	,	,
37681	3649	79	276	276	CD
37681	3649	80	Apollodotus	Apollodotus	NNP
37681	3649	81	(	(	-LRB-
37681	3649	82	Apollodorus	Apollodorus	NNP
37681	3649	83	)	)	-RRB-
37681	3649	84	,	,	,
37681	3649	85	259	259	CD
37681	3649	86	Apollonius	Apollonius	NNP
37681	3649	87	,	,	,
37681	3649	88	34	34	CD
37681	3649	89	,	,	,
37681	3649	90	214	214	CD
37681	3649	91	,	,	,
37681	3649	92	231	231	CD
37681	3649	93	Applied	applied	JJ
37681	3649	94	problems	problem	NNS
37681	3649	95	,	,	,
37681	3649	96	75	75	CD
37681	3649	97	,	,	,
37681	3649	98	103	103	CD
37681	3649	99	,	,	,
37681	3649	100	178	178	CD
37681	3649	101	,	,	,
37681	3649	102	186	186	CD
37681	3649	103	,	,	,
37681	3649	104	192	192	CD
37681	3649	105	,	,	,
37681	3649	106	195	195	CD
37681	3649	107	,	,	,
37681	3649	108	203	203	CD
37681	3649	109	,	,	,
37681	3649	110	204	204	CD
37681	3649	111	,	,	,
37681	3649	112	209	209	CD
37681	3649	113	,	,	,
37681	3649	114	215	215	CD
37681	3649	115	,	,	,
37681	3649	116	217	217	CD
37681	3649	117	,	,	,
37681	3649	118	242	242	CD
37681	3649	119	,	,	,
37681	3649	120	267	267	CD
37681	3649	121	,	,	,
37681	3649	122	295	295	CD
37681	3649	123	,	,	,
37681	3649	124	317	317	CD
37681	3649	125	Appreciation	appreciation	NN
37681	3649	126	of	of	IN
37681	3649	127	geometry	geometry	NN
37681	3649	128	,	,	,
37681	3649	129	19	19	CD
37681	3649	130	Arab	arab	JJ
37681	3649	131	geometry	geometry	NN
37681	3649	132	,	,	,
37681	3649	133	37	37	CD
37681	3649	134	,	,	,
37681	3649	135	51	51	CD
37681	3649	136	Archimedes	archimede	NNS
37681	3649	137	,	,	,
37681	3649	138	34	34	CD
37681	3649	139	,	,	,
37681	3649	140	42	42	CD
37681	3649	141	,	,	,
37681	3649	142	48	48	CD
37681	3649	143	,	,	,
37681	3649	144	139	139	CD
37681	3649	145	,	,	,
37681	3649	146	141	141	CD
37681	3649	147	,	,	,
37681	3649	148	215	215	CD
37681	3649	149	,	,	,
37681	3649	150	276	276	CD
37681	3649	151	,	,	,
37681	3649	152	278	278	CD
37681	3649	153	,	,	,
37681	3649	154	314	314	CD
37681	3649	155	,	,	,
37681	3649	156	327	327	CD
37681	3649	157	,	,	,
37681	3649	158	328	328	CD
37681	3649	159	Aristæus	Aristæus	NNP
37681	3649	160	,	,	,
37681	3649	161	310	310	CD
37681	3649	162	Aristotle	Aristotle	NNP
37681	3649	163	,	,	,
37681	3649	164	33	33	CD
37681	3649	165	,	,	,
37681	3649	166	42	42	CD
37681	3649	167	,	,	,
37681	3649	168	134	134	CD
37681	3649	169	,	,	,
37681	3649	170	135	135	CD
37681	3649	171	,	,	,
37681	3649	172	137	137	CD
37681	3649	173	,	,	,
37681	3649	174	145	145	CD
37681	3649	175	,	,	,
37681	3649	176	154	154	CD
37681	3649	177	,	,	,
37681	3649	178	177	177	CD
37681	3649	179	,	,	,
37681	3649	180	209	209	CD
37681	3649	181	Aryabhatta	Aryabhatta	NNP
37681	3649	182	,	,	,
37681	3649	183	36	36	CD
37681	3649	184	,	,	,
37681	3649	185	279	279	CD
37681	3649	186	Associations	association	NNS
37681	3649	187	,	,	,
37681	3649	188	syllabi	syllabi	NN
37681	3649	189	of	of	IN
37681	3649	190	,	,	,
37681	3649	191	58	58	CD
37681	3649	192	,	,	,
37681	3649	193	60	60	CD
37681	3649	194	,	,	,
37681	3649	195	64	64	CD
37681	3649	196	Assumptions	assumption	NNS
37681	3649	197	,	,	,
37681	3649	198	116	116	CD
37681	3649	199	Astrolabe	Astrolabe	NNP
37681	3649	200	,	,	,
37681	3649	201	172	172	CD
37681	3649	202	Athelhard	Athelhard	NNP
37681	3649	203	of	of	IN
37681	3649	204	Bath	Bath	NNP
37681	3649	205	,	,	,
37681	3649	206	37	37	CD
37681	3649	207	,	,	,
37681	3649	208	51	51	CD
37681	3649	209	Athenæus	Athenæus	NNP
37681	3649	210	,	,	,
37681	3649	211	259	259	CD
37681	3649	212	Axioms	axiom	NNS
37681	3649	213	,	,	,
37681	3649	214	31	31	CD
37681	3649	215	,	,	,
37681	3649	216	41	41	CD
37681	3649	217	,	,	,
37681	3649	218	116	116	CD
37681	3649	219	Babylon	Babylon	NNP
37681	3649	220	,	,	,
37681	3649	221	26	26	CD
37681	3649	222	,	,	,
37681	3649	223	272	272	CD
37681	3649	224	Bartoli	Bartoli	NNP
37681	3649	225	,	,	,
37681	3649	226	10	10	CD
37681	3649	227	,	,	,
37681	3649	228	44	44	CD
37681	3649	229	,	,	,
37681	3649	230	238	238	CD
37681	3649	231	Belli	Belli	NNP
37681	3649	232	,	,	,
37681	3649	233	10	10	CD
37681	3649	234	,	,	,
37681	3649	235	44	44	CD
37681	3649	236	,	,	,
37681	3649	237	172	172	CD
37681	3649	238	Beltinus	Beltinus	NNP
37681	3649	239	,	,	,
37681	3649	240	239	239	CD
37681	3649	241	,	,	,
37681	3649	242	241	241	CD
37681	3649	243	Beltrami	Beltrami	NNP
37681	3649	244	,	,	,
37681	3649	245	127	127	CD
37681	3649	246	Bennett	Bennett	NNP
37681	3649	247	,	,	,
37681	3649	248	J.	J.	NNP
37681	3649	249	,	,	,
37681	3649	250	224	224	CD
37681	3649	251	Bernoulli	Bernoulli	NNP
37681	3649	252	,	,	,
37681	3649	253	280	280	CD
37681	3649	254	Bertrand	Bertrand	NNP
37681	3649	255	,	,	,
37681	3649	256	62	62	CD
37681	3649	257	Betz	betz	NN
37681	3649	258	,	,	,
37681	3649	259	131	131	CD
37681	3649	260	Bezout	bezout	NN
37681	3649	261	,	,	,
37681	3649	262	62	62	CD
37681	3649	263	Bhaskara	Bhaskara	NNP
37681	3649	264	,	,	,
37681	3649	265	232	232	CD
37681	3649	266	,	,	,
37681	3649	267	268	268	CD
37681	3649	268	Billings	Billings	NNPS
37681	3649	269	,	,	,
37681	3649	270	R.	R.	NNP
37681	3649	271	W.	W.	NNP
37681	3649	272	,	,	,
37681	3649	273	222	222	CD
37681	3649	274	Billingsley	Billingsley	NNP
37681	3649	275	,	,	,
37681	3649	276	52	52	CD
37681	3649	277	Bion	Bion	NNP
37681	3649	278	,	,	,
37681	3649	279	192	192	CD
37681	3649	280	,	,	,
37681	3649	281	239	239	CD
37681	3649	282	Boethius	Boethius	NNP
37681	3649	283	,	,	,
37681	3649	284	43	43	CD
37681	3649	285	,	,	,
37681	3649	286	50	50	CD
37681	3649	287	Bolyai	Bolyai	NNP
37681	3649	288	,	,	,
37681	3649	289	128	128	CD
37681	3649	290	Bonola	Bonola	NNP
37681	3649	291	,	,	,
37681	3649	292	128	128	CD
37681	3649	293	Books	book	NNS
37681	3649	294	of	of	IN
37681	3649	295	geometry	geometry	NN
37681	3649	296	,	,	,
37681	3649	297	165	165	CD
37681	3649	298	,	,	,
37681	3649	299	167	167	CD
37681	3649	300	,	,	,
37681	3649	301	201	201	CD
37681	3649	302	,	,	,
37681	3649	303	227	227	CD
37681	3649	304	,	,	,
37681	3649	305	252	252	CD
37681	3649	306	,	,	,
37681	3649	307	269	269	CD
37681	3649	308	,	,	,
37681	3649	309	289	289	CD
37681	3649	310	,	,	,
37681	3649	311	303	303	CD
37681	3649	312	,	,	,
37681	3649	313	321	321	CD
37681	3649	314	Bordas	Bordas	NNP
37681	3649	315	-	-	HYPH
37681	3649	316	Demoulin	Demoulin	NNP
37681	3649	317	,	,	,
37681	3649	318	24	24	CD
37681	3649	319	Borel	Borel	NNP
37681	3649	320	,	,	,
37681	3649	321	11	11	CD
37681	3649	322	,	,	,
37681	3649	323	67	67	CD
37681	3649	324	,	,	,
37681	3649	325	196	196	CD
37681	3649	326	Bosanquet	bosanquet	NN
37681	3649	327	,	,	,
37681	3649	328	272	272	CD
37681	3649	329	Bossut	Bossut	NNP
37681	3649	330	,	,	,
37681	3649	331	23	23	CD
37681	3649	332	Bourdon	Bourdon	NNP
37681	3649	333	,	,	,
37681	3649	334	62	62	CD
37681	3649	335	Bourlet	Bourlet	NNP
37681	3649	336	,	,	,
37681	3649	337	67	67	CD
37681	3649	338	,	,	,
37681	3649	339	165	165	CD
37681	3649	340	,	,	,
37681	3649	341	196	196	CD
37681	3649	342	Brahmagupta	Brahmagupta	NNP
37681	3649	343	,	,	,
37681	3649	344	36	36	CD
37681	3649	345	,	,	,
37681	3649	346	268	268	CD
37681	3649	347	,	,	,
37681	3649	348	279	279	CD
37681	3649	349	Bretschneider	Bretschneider	NNP
37681	3649	350	,	,	,
37681	3649	351	C.	C.	NNP
37681	3649	352	A.	A.	NNP
37681	3649	353	,	,	,
37681	3649	354	30	30	CD
37681	3649	355	Brouncker	Brouncker	NNP
37681	3649	356	,	,	,
37681	3649	357	280	280	CD
37681	3649	358	Bruce	Bruce	NNP
37681	3649	359	,	,	,
37681	3649	360	W.	W.	NNP
37681	3649	361	N.	N.	NNP
37681	3649	362	,	,	,
37681	3649	363	199	199	CD
37681	3649	364	Bryson	Bryson	NNP
37681	3649	365	,	,	,
37681	3649	366	31	31	CD
37681	3649	367	,	,	,
37681	3649	368	32	32	CD
37681	3649	369	,	,	,
37681	3649	370	276	276	CD
37681	3649	371	Cajori	Cajori	NNP
37681	3649	372	,	,	,
37681	3649	373	46	46	CD
37681	3649	374	Calandri	Calandri	NNP
37681	3649	375	,	,	,
37681	3649	376	30	30	CD
37681	3649	377	Campanus	Campanus	NNP
37681	3649	378	,	,	,
37681	3649	379	37	37	CD
37681	3649	380	,	,	,
37681	3649	381	51	51	CD
37681	3649	382	,	,	,
37681	3649	383	135	135	CD
37681	3649	384	Cantor	Cantor	NNP
37681	3649	385	,	,	,
37681	3649	386	M.	M.	NNP
37681	3649	387	,	,	,
37681	3649	388	29	29	CD
37681	3649	389	,	,	,
37681	3649	390	46	46	CD
37681	3649	391	Capella	Capella	NNP
37681	3649	392	,	,	,
37681	3649	393	50	50	CD
37681	3649	394	,	,	,
37681	3649	395	135	135	CD
37681	3649	396	Capra	Capra	NNP
37681	3649	397	,	,	,
37681	3649	398	44	44	CD
37681	3649	399	Carson	Carson	NNP
37681	3649	400	,	,	,
37681	3649	401	G.	G.	NNP
37681	3649	402	W.	W.	NNP
37681	3649	403	L.	L.	NNP
37681	3649	404	,	,	,
37681	3649	405	18	18	CD
37681	3649	406	,	,	,
37681	3649	407	96	96	CD
37681	3649	408	,	,	,
37681	3649	409	114	114	CD
37681	3649	410	Casey	Casey	NNP
37681	3649	411	,	,	,
37681	3649	412	J.	J.	NNP
37681	3649	413	,	,	,
37681	3649	414	38	38	CD
37681	3649	415	Cassiodorius	Cassiodorius	NNP
37681	3649	416	,	,	,
37681	3649	417	50	50	CD
37681	3649	418	Cataneo	Cataneo	NNP
37681	3649	419	,	,	,
37681	3649	420	10	10	CD
37681	3649	421	,	,	,
37681	3649	422	44	44	CD
37681	3649	423	Cavalieri	Cavalieri	NNP
37681	3649	424	,	,	,
37681	3649	425	136	136	CD
37681	3649	426	,	,	,
37681	3649	427	329	329	CD
37681	3649	428	Chinese	chinese	JJ
37681	3649	429	values	value	NNS
37681	3649	430	of	of	IN
37681	3649	431	[	[	-LRB-
37681	3649	432	pi	pi	NN
37681	3649	433	]	]	-RRB-
37681	3649	434	,	,	,
37681	3649	435	279	279	CD
37681	3649	436	Church	church	NN
37681	3649	437	schools	school	NNS
37681	3649	438	,	,	,
37681	3649	439	43	43	CD
37681	3649	440	Cicero	Cicero	NNP
37681	3649	441	,	,	,
37681	3649	442	34	34	CD
37681	3649	443	,	,	,
37681	3649	444	50	50	CD
37681	3649	445	,	,	,
37681	3649	446	259	259	CD
37681	3649	447	,	,	,
37681	3649	448	314	314	CD
37681	3649	449	Circle	Circle	NNP
37681	3649	450	,	,	,
37681	3649	451	145	145	CD
37681	3649	452	,	,	,
37681	3649	453	201	201	CD
37681	3649	454	,	,	,
37681	3649	455	270	270	CD
37681	3649	456	,	,	,
37681	3649	457	287	287	CD
37681	3649	458	;	;	:
37681	3649	459	squaring	square	VBG
37681	3649	460	the	the	DT
37681	3649	461	,	,	,
37681	3649	462	31	31	CD
37681	3649	463	,	,	,
37681	3649	464	32	32	CD
37681	3649	465	,	,	,
37681	3649	466	277	277	CD
37681	3649	467	Circumference	Circumference	NNP
37681	3649	468	,	,	,
37681	3649	469	145	145	CD
37681	3649	470	Cissoid	Cissoid	NNP
37681	3649	471	,	,	,
37681	3649	472	34	34	CD
37681	3649	473	Class	class	NN
37681	3649	474	in	in	IN
37681	3649	475	geometry	geometry	NN
37681	3649	476	,	,	,
37681	3649	477	108	108	CD
37681	3649	478	Clavius	Clavius	NNP
37681	3649	479	,	,	,
37681	3649	480	121	121	CD
37681	3649	481	Colleges	college	NNS
37681	3649	482	,	,	,
37681	3649	483	geometry	geometry	NN
37681	3649	484	in	in	IN
37681	3649	485	the	the	DT
37681	3649	486	,	,	,
37681	3649	487	46	46	CD
37681	3649	488	Collet	Collet	NNP
37681	3649	489	,	,	,
37681	3649	490	24	24	CD
37681	3649	491	Commensurable	commensurable	JJ
37681	3649	492	magnitudes	magnitude	NNS
37681	3649	493	,	,	,
37681	3649	494	206	206	CD
37681	3649	495	,	,	,
37681	3649	496	207	207	CD
37681	3649	497	Conchoid	Conchoid	NNP
37681	3649	498	,	,	,
37681	3649	499	34	34	CD
37681	3649	500	Condorcet	Condorcet	NNS
37681	3649	501	,	,	,
37681	3649	502	23	23	CD
37681	3649	503	Cone	cone	NN
37681	3649	504	,	,	,
37681	3649	505	315	315	CD
37681	3649	506	Congruent	congruent	JJ
37681	3649	507	,	,	,
37681	3649	508	151	151	CD
37681	3649	509	Conic	conic	JJ
37681	3649	510	sections	section	NNS
37681	3649	511	,	,	,
37681	3649	512	33	33	CD
37681	3649	513	,	,	,
37681	3649	514	315	315	CD
37681	3649	515	Continuity	Continuity	NNP
37681	3649	516	,	,	,
37681	3649	517	212	212	CD
37681	3649	518	Converse	Converse	NNP
37681	3649	519	proposition	proposition	NN
37681	3649	520	,	,	,
37681	3649	521	175	175	CD
37681	3649	522	,	,	,
37681	3649	523	190	190	CD
37681	3649	524	,	,	,
37681	3649	525	191	191	CD
37681	3649	526	Crelle	Crelle	NNP
37681	3649	527	,	,	,
37681	3649	528	142	142	CD
37681	3649	529	Cube	Cube	NNP
37681	3649	530	,	,	,
37681	3649	531	duplicating	duplicate	VBG
37681	3649	532	the	the	DT
37681	3649	533	,	,	,
37681	3649	534	32	32	CD
37681	3649	535	,	,	,
37681	3649	536	307	307	CD
37681	3649	537	Cylinder	Cylinder	NNP
37681	3649	538	,	,	,
37681	3649	539	313	313	CD
37681	3649	540	D'Alembert	D'Alembert	NNP
37681	3649	541	,	,	,
37681	3649	542	24	24	CD
37681	3649	543	,	,	,
37681	3649	544	67	67	CD
37681	3649	545	Dase	Dase	NNP
37681	3649	546	,	,	,
37681	3649	547	279	279	CD
37681	3649	548	Decagon	Decagon	NNP
37681	3649	549	,	,	,
37681	3649	550	273	273	CD
37681	3649	551	Definitions	definition	NNS
37681	3649	552	,	,	,
37681	3649	553	41	41	CD
37681	3649	554	,	,	,
37681	3649	555	132	132	CD
37681	3649	556	De	De	NNP
37681	3649	557	Judaeis	Judaeis	NNP
37681	3649	558	,	,	,
37681	3649	559	239	239	CD
37681	3649	560	,	,	,
37681	3649	561	241	241	CD
37681	3649	562	De	De	NNP
37681	3649	563	Morgan	Morgan	NNP
37681	3649	564	,	,	,
37681	3649	565	A.	A.	NNP
37681	3649	566	,	,	,
37681	3649	567	58	58	CD
37681	3649	568	De	De	NNP
37681	3649	569	Paolis	Paolis	NNP
37681	3649	570	,	,	,
37681	3649	571	67	67	CD
37681	3649	572	Descartes	Descartes	NNPS
37681	3649	573	,	,	,
37681	3649	574	38	38	CD
37681	3649	575	,	,	,
37681	3649	576	84	84	CD
37681	3649	577	,	,	,
37681	3649	578	320	320	CD
37681	3649	579	Diameter	Diameter	NNP
37681	3649	580	,	,	,
37681	3649	581	146	146	CD
37681	3649	582	Dihedral	Dihedral	NNP
37681	3649	583	,	,	,
37681	3649	584	298	298	CD
37681	3649	585	Diocles	diocle	NNS
37681	3649	586	,	,	,
37681	3649	587	34	34	CD
37681	3649	588	Diogenes	Diogenes	NNP
37681	3649	589	Laertius	Laertius	NNP
37681	3649	590	,	,	,
37681	3649	591	259	259	CD
37681	3649	592	Diorismus	Diorismus	NNP
37681	3649	593	,	,	,
37681	3649	594	41	41	CD
37681	3649	595	Direction	direction	NN
37681	3649	596	,	,	,
37681	3649	597	150	150	CD
37681	3649	598	Distance	Distance	NNP
37681	3649	599	,	,	,
37681	3649	600	154	154	CD
37681	3649	601	Doyle	Doyle	NNP
37681	3649	602	,	,	,
37681	3649	603	Conan	Conan	NNP
37681	3649	604	,	,	,
37681	3649	605	8	8	CD
37681	3649	606	Drawing	drawing	NN
37681	3649	607	,	,	,
37681	3649	608	95	95	CD
37681	3649	609	,	,	,
37681	3649	610	221	221	CD
37681	3649	611	,	,	,
37681	3649	612	281	281	CD
37681	3649	613	Duality	duality	NN
37681	3649	614	,	,	,
37681	3649	615	173	173	CD
37681	3649	616	Duhamel	Duhamel	NNP
37681	3649	617	,	,	,
37681	3649	618	164	164	CD
37681	3649	619	Dupin	Dupin	NNP
37681	3649	620	,	,	,
37681	3649	621	11	11	CD
37681	3649	622	,	,	,
37681	3649	623	217	217	CD
37681	3649	624	Duplication	Duplication	NNP
37681	3649	625	problem	problem	NN
37681	3649	626	,	,	,
37681	3649	627	32	32	CD
37681	3649	628	,	,	,
37681	3649	629	307	307	CD
37681	3649	630	Dürer	Dürer	NNP
37681	3649	631	,	,	,
37681	3649	632	10	10	CD
37681	3649	633	Educational	educational	JJ
37681	3649	634	problems	problem	NNS
37681	3649	635	,	,	,
37681	3649	636	1	1	CD
37681	3649	637	Egypt	Egypt	NNP
37681	3649	638	,	,	,
37681	3649	639	26	26	CD
37681	3649	640	,	,	,
37681	3649	641	40	40	CD
37681	3649	642	Eisenlohr	Eisenlohr	NNP
37681	3649	643	,	,	,
37681	3649	644	27	27	CD
37681	3649	645	Engel	Engel	NNP
37681	3649	646	and	and	CC
37681	3649	647	Stäckel	Stäckel	NNP
37681	3649	648	,	,	,
37681	3649	649	128	128	CD
37681	3649	650	England	England	NNP
37681	3649	651	,	,	,
37681	3649	652	14	14	CD
37681	3649	653	,	,	,
37681	3649	654	46	46	CD
37681	3649	655	,	,	,
37681	3649	656	58	58	CD
37681	3649	657	,	,	,
37681	3649	658	60	60	CD
37681	3649	659	Epicureans	Epicureans	NNPS
37681	3649	660	,	,	,
37681	3649	661	188	188	CD
37681	3649	662	Equal	equal	JJ
37681	3649	663	,	,	,
37681	3649	664	151	151	CD
37681	3649	665	,	,	,
37681	3649	666	153	153	CD
37681	3649	667	Equilateral	equilateral	JJ
37681	3649	668	,	,	,
37681	3649	669	147	147	CD
37681	3649	670	Equivalent	equivalent	JJ
37681	3649	671	,	,	,
37681	3649	672	151	151	CD
37681	3649	673	Eratosthenes	eratosthene	NNS
37681	3649	674	,	,	,
37681	3649	675	48	48	CD
37681	3649	676	Euclid	Euclid	NNP
37681	3649	677	,	,	,
37681	3649	678	33	33	CD
37681	3649	679	,	,	,
37681	3649	680	42	42	CD
37681	3649	681	,	,	,
37681	3649	682	43	43	CD
37681	3649	683	,	,	,
37681	3649	684	44	44	CD
37681	3649	685	,	,	,
37681	3649	686	119	119	CD
37681	3649	687	,	,	,
37681	3649	688	125	125	CD
37681	3649	689	,	,	,
37681	3649	690	135	135	CD
37681	3649	691	,	,	,
37681	3649	692	156	156	CD
37681	3649	693	,	,	,
37681	3649	694	165	165	CD
37681	3649	695	,	,	,
37681	3649	696	167	167	CD
37681	3649	697	ff	ff	NN
37681	3649	698	.	.	NNP
37681	3649	699	,	,	,
37681	3649	700	201	201	CD
37681	3649	701	ff	ff	NNS
37681	3649	702	.	.	NNP
37681	3649	703	,	,	,
37681	3649	704	et	et	NNP
37681	3649	705	passim	passim	NN
37681	3649	706	;	;	:
37681	3649	707	editions	edition	NNS
37681	3649	708	of	of	IN
37681	3649	709	,	,	,
37681	3649	710	47	47	CD
37681	3649	711	,	,	,
37681	3649	712	52	52	CD
37681	3649	713	;	;	:
37681	3649	714	efforts	effort	NNS
37681	3649	715	at	at	IN
37681	3649	716	improving	improve	VBG
37681	3649	717	,	,	,
37681	3649	718	57	57	CD
37681	3649	719	;	;	:
37681	3649	720	life	life	NN
37681	3649	721	of	of	IN
37681	3649	722	,	,	,
37681	3649	723	47	47	CD
37681	3649	724	;	;	:
37681	3649	725	nature	nature	NN
37681	3649	726	of	of	IN
37681	3649	727	his	-PRON-	PRP$
37681	3649	728	"	"	``
37681	3649	729	Elements	Elements	NNPS
37681	3649	730	,	,	,
37681	3649	731	"	"	''
37681	3649	732	52	52	CD
37681	3649	733	,	,	,
37681	3649	734	55	55	CD
37681	3649	735	;	;	:
37681	3649	736	opinions	opinion	NNS
37681	3649	737	of	of	IN
37681	3649	738	,	,	,
37681	3649	739	8	8	CD
37681	3649	740	Eudemus	Eudemus	NNP
37681	3649	741	,	,	,
37681	3649	742	33	33	CD
37681	3649	743	,	,	,
37681	3649	744	168	168	CD
37681	3649	745	,	,	,
37681	3649	746	171	171	CD
37681	3649	747	,	,	,
37681	3649	748	185	185	CD
37681	3649	749	,	,	,
37681	3649	750	216	216	CD
37681	3649	751	,	,	,
37681	3649	752	309	309	CD
37681	3649	753	Eudoxus	Eudoxus	NNP
37681	3649	754	,	,	,
37681	3649	755	32	32	CD
37681	3649	756	,	,	,
37681	3649	757	41	41	CD
37681	3649	758	,	,	,
37681	3649	759	48	48	CD
37681	3649	760	,	,	,
37681	3649	761	227	227	CD
37681	3649	762	,	,	,
37681	3649	763	308	308	CD
37681	3649	764	,	,	,
37681	3649	765	314	314	CD
37681	3649	766	,	,	,
37681	3649	767	317	317	CD
37681	3649	768	Euler	Euler	NNP
37681	3649	769	,	,	,
37681	3649	770	38	38	CD
37681	3649	771	,	,	,
37681	3649	772	280	280	CD
37681	3649	773	,	,	,
37681	3649	774	318	318	CD
37681	3649	775	Eutocius	Eutocius	NNP
37681	3649	776	,	,	,
37681	3649	777	184	184	CD
37681	3649	778	Exercises	exercise	NNS
37681	3649	779	,	,	,
37681	3649	780	nature	nature	NN
37681	3649	781	of	of	IN
37681	3649	782	,	,	,
37681	3649	783	74	74	CD
37681	3649	784	,	,	,
37681	3649	785	103	103	CD
37681	3649	786	;	;	:
37681	3649	787	how	how	WRB
37681	3649	788	to	to	TO
37681	3649	789	attack	attack	VB
37681	3649	790	,	,	,
37681	3649	791	160	160	CD
37681	3649	792	Exhaustions	exhaustion	NNS
37681	3649	793	,	,	,
37681	3649	794	method	method	NN
37681	3649	795	of	of	IN
37681	3649	796	,	,	,
37681	3649	797	31	31	CD
37681	3649	798	Extreme	Extreme	NNP
37681	3649	799	and	and	CC
37681	3649	800	mean	mean	JJ
37681	3649	801	ratio	ratio	NN
37681	3649	802	,	,	,
37681	3649	803	250	250	CD
37681	3649	804	Figures	figure	NNS
37681	3649	805	in	in	IN
37681	3649	806	geometry	geometry	NN
37681	3649	807	,	,	,
37681	3649	808	104	104	CD
37681	3649	809	,	,	,
37681	3649	810	107	107	CD
37681	3649	811	,	,	,
37681	3649	812	113	113	CD
37681	3649	813	Finaeus	Finaeus	NNP
37681	3649	814	,	,	,
37681	3649	815	44	44	CD
37681	3649	816	,	,	,
37681	3649	817	239	239	CD
37681	3649	818	,	,	,
37681	3649	819	240	240	CD
37681	3649	820	,	,	,
37681	3649	821	243	243	CD
37681	3649	822	Fourier	Fourier	NNP
37681	3649	823	,	,	,
37681	3649	824	142	142	CD
37681	3649	825	Fourth	fourth	JJ
37681	3649	826	dimension	dimension	NN
37681	3649	827	,	,	,
37681	3649	828	326	326	CD
37681	3649	829	Frankland	Frankland	NNP
37681	3649	830	,	,	,
37681	3649	831	56	56	CD
37681	3649	832	,	,	,
37681	3649	833	117	117	CD
37681	3649	834	,	,	,
37681	3649	835	127	127	CD
37681	3649	836	,	,	,
37681	3649	837	135	135	CD
37681	3649	838	,	,	,
37681	3649	839	159	159	CD
37681	3649	840	Fusion	fusion	NN
37681	3649	841	,	,	,
37681	3649	842	of	of	IN
37681	3649	843	algebra	algebra	NN
37681	3649	844	and	and	CC
37681	3649	845	geometry	geometry	NN
37681	3649	846	,	,	,
37681	3649	847	84	84	CD
37681	3649	848	;	;	:
37681	3649	849	of	of	IN
37681	3649	850	geometry	geometry	NN
37681	3649	851	and	and	CC
37681	3649	852	trigonometry	trigonometry	NN
37681	3649	853	,	,	,
37681	3649	854	91	91	CD
37681	3649	855	Gargioli	Gargioli	NNP
37681	3649	856	,	,	,
37681	3649	857	44	44	CD
37681	3649	858	Gauss	Gauss	NNP
37681	3649	859	,	,	,
37681	3649	860	140	140	CD
37681	3649	861	,	,	,
37681	3649	862	274	274	CD
37681	3649	863	Geminus	Geminus	NNP
37681	3649	864	,	,	,
37681	3649	865	126	126	CD
37681	3649	866	,	,	,
37681	3649	867	128	128	CD
37681	3649	868	,	,	,
37681	3649	869	149	149	CD
37681	3649	870	Geometry	Geometry	NNP
37681	3649	871	,	,	,
37681	3649	872	books	book	NNS
37681	3649	873	of	of	IN
37681	3649	874	,	,	,
37681	3649	875	165	165	CD
37681	3649	876	,	,	,
37681	3649	877	167	167	CD
37681	3649	878	,	,	,
37681	3649	879	201	201	CD
37681	3649	880	,	,	,
37681	3649	881	227	227	CD
37681	3649	882	,	,	,
37681	3649	883	252	252	CD
37681	3649	884	,	,	,
37681	3649	885	269	269	CD
37681	3649	886	,	,	,
37681	3649	887	289	289	CD
37681	3649	888	,	,	,
37681	3649	889	303	303	CD
37681	3649	890	,	,	,
37681	3649	891	321	321	CD
37681	3649	892	;	;	,
37681	3649	893	compared	compare	VBN
37681	3649	894	with	with	IN
37681	3649	895	other	other	JJ
37681	3649	896	subjects	subject	NNS
37681	3649	897	,	,	,
37681	3649	898	14	14	CD
37681	3649	899	;	;	:
37681	3649	900	introduction	introduction	NN
37681	3649	901	to	to	IN
37681	3649	902	,	,	,
37681	3649	903	93	93	CD
37681	3649	904	;	;	:
37681	3649	905	modern	modern	JJ
37681	3649	906	,	,	,
37681	3649	907	38	38	CD
37681	3649	908	;	;	:
37681	3649	909	of	of	IN
37681	3649	910	motion	motion	NN
37681	3649	911	,	,	,
37681	3649	912	68	68	CD
37681	3649	913	,	,	,
37681	3649	914	196	196	CD
37681	3649	915	;	;	:
37681	3649	916	reasons	reason	NNS
37681	3649	917	for	for	IN
37681	3649	918	teaching	teaching	NN
37681	3649	919	,	,	,
37681	3649	920	7	7	CD
37681	3649	921	,	,	,
37681	3649	922	15	15	CD
37681	3649	923	,	,	,
37681	3649	924	20	20	CD
37681	3649	925	;	;	:
37681	3649	926	related	related	JJ
37681	3649	927	to	to	IN
37681	3649	928	algebra	algebra	NN
37681	3649	929	,	,	,
37681	3649	930	84	84	CD
37681	3649	931	;	;	:
37681	3649	932	textbooks	textbook	NNS
37681	3649	933	in	in	IN
37681	3649	934	,	,	,
37681	3649	935	70	70	CD
37681	3649	936	Gerbert	Gerbert	NNP
37681	3649	937	,	,	,
37681	3649	938	43	43	CD
37681	3649	939	Gherard	Gherard	NNP
37681	3649	940	of	of	IN
37681	3649	941	Cremona	Cremona	NNP
37681	3649	942	,	,	,
37681	3649	943	37	37	CD
37681	3649	944	,	,	,
37681	3649	945	51	51	CD
37681	3649	946	Gnomon	Gnomon	NNP
37681	3649	947	,	,	,
37681	3649	948	212	212	CD
37681	3649	949	Golden	golden	JJ
37681	3649	950	section	section	NN
37681	3649	951	,	,	,
37681	3649	952	250	250	CD
37681	3649	953	Gothic	gothic	JJ
37681	3649	954	windows	window	NNS
37681	3649	955	,	,	,
37681	3649	956	75	75	CD
37681	3649	957	,	,	,
37681	3649	958	221	221	CD
37681	3649	959	ff	ff	NNP
37681	3649	960	.	.	NNP
37681	3649	961	,	,	,
37681	3649	962	274	274	CD
37681	3649	963	,	,	,
37681	3649	964	282	282	CD
37681	3649	965	Gow	Gow	NNP
37681	3649	966	,	,	,
37681	3649	967	J.	J.	NNP
37681	3649	968	,	,	,
37681	3649	969	29	29	CD
37681	3649	970	,	,	,
37681	3649	971	56	56	CD
37681	3649	972	Greece	Greece	NNP
37681	3649	973	,	,	,
37681	3649	974	28	28	CD
37681	3649	975	,	,	,
37681	3649	976	40	40	CD
37681	3649	977	Gregoire	Gregoire	NNP
37681	3649	978	de	de	NNP
37681	3649	979	St.	St.	NNP
37681	3649	980	Vincent	Vincent	NNP
37681	3649	981	,	,	,
37681	3649	982	267	267	CD
37681	3649	983	Gregory	Gregory	NNP
37681	3649	984	,	,	,
37681	3649	985	280	280	CD
37681	3649	986	Grévy	grévy	NN
37681	3649	987	,	,	,
37681	3649	988	67	67	CD
37681	3649	989	Gymnasia	Gymnasia	NNP
37681	3649	990	,	,	,
37681	3649	991	geometry	geometry	NN
37681	3649	992	in	in	IN
37681	3649	993	the	the	DT
37681	3649	994	,	,	,
37681	3649	995	45	45	CD
37681	3649	996	Hadamard	Hadamard	NNP
37681	3649	997	,	,	,
37681	3649	998	164	164	CD
37681	3649	999	Hamilton	Hamilton	NNP
37681	3649	1000	,	,	,
37681	3649	1001	W.	W.	NNP
37681	3649	1002	,	,	,
37681	3649	1003	14	14	CD
37681	3649	1004	Harmonic	harmonic	JJ
37681	3649	1005	division	division	NN
37681	3649	1006	,	,	,
37681	3649	1007	231	231	CD
37681	3649	1008	Harpedonaptae	Harpedonaptae	NNP
37681	3649	1009	,	,	,
37681	3649	1010	28	28	CD
37681	3649	1011	Harriot	Harriot	NNP
37681	3649	1012	,	,	,
37681	3649	1013	37	37	CD
37681	3649	1014	Harvard	Harvard	NNP
37681	3649	1015	syllabus	syllabus	NN
37681	3649	1016	,	,	,
37681	3649	1017	63	63	CD
37681	3649	1018	Heath	Heath	NNP
37681	3649	1019	,	,	,
37681	3649	1020	T.	T.	NNP
37681	3649	1021	L.	L.	NNP
37681	3649	1022	,	,	,
37681	3649	1023	49	49	CD
37681	3649	1024	,	,	,
37681	3649	1025	56	56	CD
37681	3649	1026	,	,	,
37681	3649	1027	119	119	CD
37681	3649	1028	,	,	,
37681	3649	1029	126	126	CD
37681	3649	1030	,	,	,
37681	3649	1031	127	127	CD
37681	3649	1032	,	,	,
37681	3649	1033	135	135	CD
37681	3649	1034	,	,	,
37681	3649	1035	149	149	CD
37681	3649	1036	,	,	,
37681	3649	1037	159	159	CD
37681	3649	1038	,	,	,
37681	3649	1039	170	170	CD
37681	3649	1040	,	,	,
37681	3649	1041	175	175	CD
37681	3649	1042	,	,	,
37681	3649	1043	228	228	CD
37681	3649	1044	,	,	,
37681	3649	1045	261	261	CD
37681	3649	1046	Hebrews	Hebrews	NNPS
37681	3649	1047	,	,	,
37681	3649	1048	26	26	CD
37681	3649	1049	Henrici	Henrici	NNP
37681	3649	1050	,	,	,
37681	3649	1051	O.	O.	NNP
37681	3649	1052	,	,	,
37681	3649	1053	11	11	CD
37681	3649	1054	,	,	,
37681	3649	1055	14	14	CD
37681	3649	1056	,	,	,
37681	3649	1057	25	25	CD
37681	3649	1058	,	,	,
37681	3649	1059	164	164	CD
37681	3649	1060	,	,	,
37681	3649	1061	196	196	CD
37681	3649	1062	Henrici	Henrici	NNP
37681	3649	1063	and	and	CC
37681	3649	1064	Treutlein	Treutlein	NNP
37681	3649	1065	,	,	,
37681	3649	1066	68	68	CD
37681	3649	1067	,	,	,
37681	3649	1068	164	164	CD
37681	3649	1069	,	,	,
37681	3649	1070	196	196	CD
37681	3649	1071	Hermite	Hermite	NNP
37681	3649	1072	,	,	,
37681	3649	1073	281	281	CD
37681	3649	1074	Herodotus	Herodotus	NNP
37681	3649	1075	,	,	,
37681	3649	1076	28	28	CD
37681	3649	1077	Heron	Heron	NNP
37681	3649	1078	,	,	,
37681	3649	1079	35	35	CD
37681	3649	1080	,	,	,
37681	3649	1081	137	137	CD
37681	3649	1082	,	,	,
37681	3649	1083	139	139	CD
37681	3649	1084	,	,	,
37681	3649	1085	141	141	CD
37681	3649	1086	,	,	,
37681	3649	1087	209	209	CD
37681	3649	1088	,	,	,
37681	3649	1089	259	259	CD
37681	3649	1090	,	,	,
37681	3649	1091	267	267	CD
37681	3649	1092	Hexagon	Hexagon	NNP
37681	3649	1093	,	,	,
37681	3649	1094	regular	regular	JJ
37681	3649	1095	,	,	,
37681	3649	1096	272	272	CD
37681	3649	1097	High	high	JJ
37681	3649	1098	schools	school	NNS
37681	3649	1099	,	,	,
37681	3649	1100	geometry	geometry	NN
37681	3649	1101	in	in	IN
37681	3649	1102	the	the	DT
37681	3649	1103	,	,	,
37681	3649	1104	45	45	CD
37681	3649	1105	Hilbert	Hilbert	NNP
37681	3649	1106	,	,	,
37681	3649	1107	119	119	CD
37681	3649	1108	,	,	,
37681	3649	1109	131	131	CD
37681	3649	1110	Hipparchus	Hipparchus	NNP
37681	3649	1111	,	,	,
37681	3649	1112	35	35	CD
37681	3649	1113	Hippasus	Hippasus	NNP
37681	3649	1114	,	,	,
37681	3649	1115	273	273	CD
37681	3649	1116	,	,	,
37681	3649	1117	309	309	CD
37681	3649	1118	Hippias	Hippias	NNP
37681	3649	1119	,	,	,
37681	3649	1120	31	31	CD
37681	3649	1121	,	,	,
37681	3649	1122	215	215	CD
37681	3649	1123	Hippocrates	hippocrate	NNS
37681	3649	1124	,	,	,
37681	3649	1125	31	31	CD
37681	3649	1126	,	,	,
37681	3649	1127	41	41	CD
37681	3649	1128	,	,	,
37681	3649	1129	281	281	CD
37681	3649	1130	History	history	NN
37681	3649	1131	of	of	IN
37681	3649	1132	geometry	geometry	NN
37681	3649	1133	,	,	,
37681	3649	1134	26	26	CD
37681	3649	1135	Hobson	Hobson	NNP
37681	3649	1136	,	,	,
37681	3649	1137	166	166	CD
37681	3649	1138	Hoffmann	Hoffmann	NNP
37681	3649	1139	,	,	,
37681	3649	1140	242	242	CD
37681	3649	1141	Holzmüller	holzmüller	NN
37681	3649	1142	,	,	,
37681	3649	1143	320	320	CD
37681	3649	1144	Hughes	Hughes	NNP
37681	3649	1145	,	,	,
37681	3649	1146	Justice	Justice	NNP
37681	3649	1147	,	,	,
37681	3649	1148	9	9	CD
37681	3649	1149	Hypatia	Hypatia	NNP
37681	3649	1150	,	,	,
37681	3649	1151	36	36	CD
37681	3649	1152	Hypsicles	hypsicle	NNS
37681	3649	1153	,	,	,
37681	3649	1154	34	34	CD
37681	3649	1155	Hypsometer	hypsometer	NN
37681	3649	1156	,	,	,
37681	3649	1157	245	245	CD
37681	3649	1158	Iamblichus	Iamblichus	NNP
37681	3649	1159	,	,	,
37681	3649	1160	273	273	CD
37681	3649	1161	,	,	,
37681	3649	1162	309	309	CD
37681	3649	1163	Illusions	Illusions	NNPS
37681	3649	1164	,	,	,
37681	3649	1165	optical	optical	JJ
37681	3649	1166	,	,	,
37681	3649	1167	100	100	CD
37681	3649	1168	Ingrami	Ingrami	NNP
37681	3649	1169	,	,	,
37681	3649	1170	128	128	CD
37681	3649	1171	Instruments	Instruments	NNPS
37681	3649	1172	,	,	,
37681	3649	1173	96	96	CD
37681	3649	1174	,	,	,
37681	3649	1175	178	178	CD
37681	3649	1176	,	,	,
37681	3649	1177	236	236	CD
37681	3649	1178	Introduction	introduction	NN
37681	3649	1179	to	to	TO
37681	3649	1180	geometry	geometry	VB
37681	3649	1181	,	,	,
37681	3649	1182	93	93	CD
37681	3649	1183	Ionic	ionic	JJ
37681	3649	1184	school	school	NN
37681	3649	1185	,	,	,
37681	3649	1186	28	28	CD
37681	3649	1187	Jackson	Jackson	NNP
37681	3649	1188	,	,	,
37681	3649	1189	C.	C.	NNP
37681	3649	1190	S.	S.	NNP
37681	3649	1191	,	,	,
37681	3649	1192	12	12	CD
37681	3649	1193	Jones	Jones	NNP
37681	3649	1194	,	,	,
37681	3649	1195	W.	W.	NNP
37681	3649	1196	,	,	,
37681	3649	1197	271	271	CD
37681	3649	1198	Junge	Junge	NNP
37681	3649	1199	,	,	,
37681	3649	1200	259	259	CD
37681	3649	1201	Karagiannides	Karagiannides	NNPS
37681	3649	1202	,	,	,
37681	3649	1203	128	128	CD
37681	3649	1204	Karpinski	Karpinski	NNP
37681	3649	1205	,	,	,
37681	3649	1206	37	37	CD
37681	3649	1207	Kaye	Kaye	NNP
37681	3649	1208	,	,	,
37681	3649	1209	G.	G.	NNP
37681	3649	1210	B.	B.	NNP
37681	3649	1211	,	,	,
37681	3649	1212	232	232	CD
37681	3649	1213	Kepler	Kepler	NNP
37681	3649	1214	,	,	,
37681	3649	1215	24	24	CD
37681	3649	1216	,	,	,
37681	3649	1217	149	149	CD
37681	3649	1218	Kingsley	Kingsley	NNP
37681	3649	1219	,	,	,
37681	3649	1220	C.	C.	NNP
37681	3649	1221	,	,	,
37681	3649	1222	36	36	CD
37681	3649	1223	Klein	Klein	NNP
37681	3649	1224	,	,	,
37681	3649	1225	F.	F.	NNP
37681	3649	1226	,	,	,
37681	3649	1227	68	68	CD
37681	3649	1228	,	,	,
37681	3649	1229	89	89	CD
37681	3649	1230	Kolb	Kolb	NNPS
37681	3649	1231	,	,	,
37681	3649	1232	222	222	CD
37681	3649	1233	Lacroix	Lacroix	NNP
37681	3649	1234	,	,	,
37681	3649	1235	24	24	CD
37681	3649	1236	,	,	,
37681	3649	1237	46	46	CD
37681	3649	1238	,	,	,
37681	3649	1239	62	62	CD
37681	3649	1240	,	,	,
37681	3649	1241	66	66	CD
37681	3649	1242	Langley	Langley	NNP
37681	3649	1243	,	,	,
37681	3649	1244	E.	E.	NNP
37681	3649	1245	M.	M.	NNP
37681	3649	1246	,	,	,
37681	3649	1247	291	291	CD
37681	3649	1248	Laplace	Laplace	NNP
37681	3649	1249	,	,	,
37681	3649	1250	101	101	CD
37681	3649	1251	Legendre	Legendre	NNP
37681	3649	1252	,	,	,
37681	3649	1253	10	10	CD
37681	3649	1254	,	,	,
37681	3649	1255	45	45	CD
37681	3649	1256	,	,	,
37681	3649	1257	62	62	CD
37681	3649	1258	,	,	,
37681	3649	1259	127	127	CD
37681	3649	1260	,	,	,
37681	3649	1261	128	128	CD
37681	3649	1262	,	,	,
37681	3649	1263	152	152	CD
37681	3649	1264	Leibnitz	Leibnitz	NNP
37681	3649	1265	,	,	,
37681	3649	1266	140	140	CD
37681	3649	1267	,	,	,
37681	3649	1268	150	150	CD
37681	3649	1269	Leon	Leon	NNP
37681	3649	1270	,	,	,
37681	3649	1271	41	41	CD
37681	3649	1272	Leonardo	Leonardo	NNP
37681	3649	1273	da	da	NNP
37681	3649	1274	Vinci	Vinci	NNP
37681	3649	1275	,	,	,
37681	3649	1276	264	264	CD
37681	3649	1277	Leonardo	Leonardo	NNP
37681	3649	1278	of	of	IN
37681	3649	1279	Pisa	Pisa	NNP
37681	3649	1280	,	,	,
37681	3649	1281	37	37	CD
37681	3649	1282	,	,	,
37681	3649	1283	43	43	CD
37681	3649	1284	,	,	,
37681	3649	1285	279	279	CD
37681	3649	1286	Lettering	lettering	NN
37681	3649	1287	figures	figure	NNS
37681	3649	1288	,	,	,
37681	3649	1289	105	105	CD
37681	3649	1290	Limits	limit	NNS
37681	3649	1291	,	,	,
37681	3649	1292	207	207	CD
37681	3649	1293	Lindemann	Lindemann	NNP
37681	3649	1294	,	,	,
37681	3649	1295	278	278	CD
37681	3649	1296	,	,	,
37681	3649	1297	281	281	CD
37681	3649	1298	Line	Line	NNP
37681	3649	1299	defined	define	VBN
37681	3649	1300	,	,	,
37681	3649	1301	137	137	CD
37681	3649	1302	Lobachevsky	Lobachevsky	NNP
37681	3649	1303	,	,	,
37681	3649	1304	128	128	CD
37681	3649	1305	Loci	Loci	NNP
37681	3649	1306	,	,	,
37681	3649	1307	163	163	CD
37681	3649	1308	,	,	,
37681	3649	1309	198	198	CD
37681	3649	1310	Locke	Locke	NNP
37681	3649	1311	,	,	,
37681	3649	1312	W.	W.	NNP
37681	3649	1313	J.	J.	NNP
37681	3649	1314	,	,	,
37681	3649	1315	13	13	CD
37681	3649	1316	Lodge	Lodge	NNP
37681	3649	1317	,	,	,
37681	3649	1318	A.	a.	NN
37681	3649	1319	,	,	,
37681	3649	1320	14	14	CD
37681	3649	1321	Logic	Logic	NNP
37681	3649	1322	,	,	,
37681	3649	1323	17	17	CD
37681	3649	1324	,	,	,
37681	3649	1325	104	104	CD
37681	3649	1326	Loomis	Loomis	NNP
37681	3649	1327	,	,	,
37681	3649	1328	164	164	CD
37681	3649	1329	Ludolph	Ludolph	NNP
37681	3649	1330	van	van	NNP
37681	3649	1331	Ceulen	Ceulen	NNP
37681	3649	1332	,	,	,
37681	3649	1333	279	279	CD
37681	3649	1334	Lycées	Lycées	NNP
37681	3649	1335	,	,	,
37681	3649	1336	geometry	geometry	NN
37681	3649	1337	in	in	RP
37681	3649	1338	,	,	,
37681	3649	1339	45	45	CD
37681	3649	1340	M'Clelland	M'Clelland	NNP
37681	3649	1341	,	,	,
37681	3649	1342	38	38	CD
37681	3649	1343	McCormack	McCormack	NNP
37681	3649	1344	,	,	,
37681	3649	1345	T.	T.	NNP
37681	3649	1346	J.	J.	NNP
37681	3649	1347	,	,	,
37681	3649	1348	11	11	CD
37681	3649	1349	Measured	measure	VBN
37681	3649	1350	by	by	IN
37681	3649	1351	,	,	,
37681	3649	1352	208	208	CD
37681	3649	1353	Memorizing	memorize	VBG
37681	3649	1354	,	,	,
37681	3649	1355	12	12	CD
37681	3649	1356	,	,	,
37681	3649	1357	79	79	CD
37681	3649	1358	Menæchmus	Menæchmus	NNP
37681	3649	1359	,	,	,
37681	3649	1360	33	33	CD
37681	3649	1361	,	,	,
37681	3649	1362	316	316	CD
37681	3649	1363	Menelaus	Menelaus	NNP
37681	3649	1364	,	,	,
37681	3649	1365	35	35	CD
37681	3649	1366	Méray	Méray	NNP
37681	3649	1367	,	,	,
37681	3649	1368	67	67	CD
37681	3649	1369	,	,	,
37681	3649	1370	68	68	CD
37681	3649	1371	,	,	,
37681	3649	1372	196	196	CD
37681	3649	1373	,	,	,
37681	3649	1374	289	289	CD
37681	3649	1375	Methods	method	NNS
37681	3649	1376	,	,	,
37681	3649	1377	41	41	CD
37681	3649	1378	,	,	,
37681	3649	1379	42	42	CD
37681	3649	1380	,	,	,
37681	3649	1381	115	115	CD
37681	3649	1382	Metius	metius	NN
37681	3649	1383	,	,	,
37681	3649	1384	279	279	CD
37681	3649	1385	Mikami	Mikami	NNP
37681	3649	1386	,	,	,
37681	3649	1387	264	264	CD
37681	3649	1388	Minchin	Minchin	NNP
37681	3649	1389	,	,	,
37681	3649	1390	14	14	CD
37681	3649	1391	Models	model	NNS
37681	3649	1392	,	,	,
37681	3649	1393	93	93	CD
37681	3649	1394	,	,	,
37681	3649	1395	290	290	CD
37681	3649	1396	Modern	modern	JJ
37681	3649	1397	geometry	geometry	NN
37681	3649	1398	,	,	,
37681	3649	1399	38	38	CD
37681	3649	1400	Mohammed	Mohammed	NNP
37681	3649	1401	ibn	ibn	NNP
37681	3649	1402	Musa	Musa	NNP
37681	3649	1403	,	,	,
37681	3649	1404	37	37	CD
37681	3649	1405	Moore	Moore	NNP
37681	3649	1406	,	,	,
37681	3649	1407	E.	E.	NNP
37681	3649	1408	H.	H.	NNP
37681	3649	1409	,	,	,
37681	3649	1410	131	131	CD
37681	3649	1411	Mosaics	Mosaics	NNPS
37681	3649	1412	,	,	,
37681	3649	1413	274	274	CD
37681	3649	1414	Müller	Müller	NNP
37681	3649	1415	,	,	,
37681	3649	1416	H.	H.	NNP
37681	3649	1417	,	,	,
37681	3649	1418	68	68	CD
37681	3649	1419	Münsterberg	Münsterberg	NNP
37681	3649	1420	,	,	,
37681	3649	1421	22	22	CD
37681	3649	1422	Napoleon	Napoleon	NNP
37681	3649	1423	,	,	,
37681	3649	1424	24	24	CD
37681	3649	1425	,	,	,
37681	3649	1426	287	287	CD
37681	3649	1427	Newton	Newton	NNP
37681	3649	1428	,	,	,
37681	3649	1429	24	24	CD
37681	3649	1430	Nicomedes	nicomede	NNS
37681	3649	1431	,	,	,
37681	3649	1432	34	34	CD
37681	3649	1433	,	,	,
37681	3649	1434	215	215	CD
37681	3649	1435	Octant	Octant	NNP
37681	3649	1436	,	,	,
37681	3649	1437	242	242	CD
37681	3649	1438	Oenopides	oenopide	NNS
37681	3649	1439	,	,	,
37681	3649	1440	31	31	CD
37681	3649	1441	,	,	,
37681	3649	1442	212	212	CD
37681	3649	1443	,	,	,
37681	3649	1444	216	216	CD
37681	3649	1445	Optical	optical	JJ
37681	3649	1446	illusions	illusion	NNS
37681	3649	1447	,	,	,
37681	3649	1448	100	100	CD
37681	3649	1449	Oughtred	oughtred	JJ
37681	3649	1450	,	,	,
37681	3649	1451	37	37	CD
37681	3649	1452	Paciuolo	Paciuolo	NNP
37681	3649	1453	,	,	,
37681	3649	1454	86	86	CD
37681	3649	1455	Pamphilius	Pamphilius	NNP
37681	3649	1456	,	,	,
37681	3649	1457	185	185	CD
37681	3649	1458	Pappus	Pappus	NNP
37681	3649	1459	,	,	,
37681	3649	1460	36	36	CD
37681	3649	1461	,	,	,
37681	3649	1462	230	230	CD
37681	3649	1463	,	,	,
37681	3649	1464	263	263	CD
37681	3649	1465	Parallelepiped	Parallelepiped	NNP
37681	3649	1466	,	,	,
37681	3649	1467	303	303	CD
37681	3649	1468	Parallels	Parallels	NNPS
37681	3649	1469	,	,	,
37681	3649	1470	149	149	CD
37681	3649	1471	,	,	,
37681	3649	1472	181	181	CD
37681	3649	1473	Parquetry	Parquetry	NNP
37681	3649	1474	,	,	,
37681	3649	1475	222	222	CD
37681	3649	1476	,	,	,
37681	3649	1477	274	274	CD
37681	3649	1478	Pascal	pascal	JJ
37681	3649	1479	,	,	,
37681	3649	1480	24	24	CD
37681	3649	1481	,	,	,
37681	3649	1482	159	159	CD
37681	3649	1483	Peletier	Peletier	NNP
37681	3649	1484	,	,	,
37681	3649	1485	169	169	CD
37681	3649	1486	Perigon	Perigon	NNP
37681	3649	1487	,	,	,
37681	3649	1488	151	151	CD
37681	3649	1489	Perry	Perry	NNP
37681	3649	1490	,	,	,
37681	3649	1491	J.	J.	NNP
37681	3649	1492	,	,	,
37681	3649	1493	13	13	CD
37681	3649	1494	,	,	,
37681	3649	1495	14	14	CD
37681	3649	1496	Petersen	Petersen	NNP
37681	3649	1497	,	,	,
37681	3649	1498	164	164	CD
37681	3649	1499	Philippus	Philippus	NNP
37681	3649	1500	of	of	IN
37681	3649	1501	Mende	Mende	NNP
37681	3649	1502	,	,	,
37681	3649	1503	32	32	CD
37681	3649	1504	,	,	,
37681	3649	1505	185	185	CD
37681	3649	1506	Philo	Philo	NNP
37681	3649	1507	,	,	,
37681	3649	1508	178	178	CD
37681	3649	1509	Philolaus	Philolaus	NNP
37681	3649	1510	,	,	,
37681	3649	1511	309	309	CD
37681	3649	1512	[	[	-LRB-
37681	3649	1513	pi	pi	NN
37681	3649	1514	]	]	-RRB-
37681	3649	1515	,	,	,
37681	3649	1516	26	26	CD
37681	3649	1517	,	,	,
37681	3649	1518	27	27	CD
37681	3649	1519	,	,	,
37681	3649	1520	34	34	CD
37681	3649	1521	,	,	,
37681	3649	1522	36	36	CD
37681	3649	1523	,	,	,
37681	3649	1524	271	271	CD
37681	3649	1525	,	,	,
37681	3649	1526	278	278	CD
37681	3649	1527	,	,	,
37681	3649	1528	280	280	CD
37681	3649	1529	Plane	plane	NN
37681	3649	1530	,	,	,
37681	3649	1531	140	140	CD
37681	3649	1532	Plato	Plato	NNP
37681	3649	1533	,	,	,
37681	3649	1534	25	25	CD
37681	3649	1535	,	,	,
37681	3649	1536	31	31	CD
37681	3649	1537	,	,	,
37681	3649	1538	41	41	CD
37681	3649	1539	,	,	,
37681	3649	1540	48	48	CD
37681	3649	1541	,	,	,
37681	3649	1542	129	129	CD
37681	3649	1543	,	,	,
37681	3649	1544	136	136	CD
37681	3649	1545	,	,	,
37681	3649	1546	137	137	CD
37681	3649	1547	,	,	,
37681	3649	1548	309	309	CD
37681	3649	1549	,	,	,
37681	3649	1550	310	310	CD
37681	3649	1551	Playfair	Playfair	NNP
37681	3649	1552	,	,	,
37681	3649	1553	128	128	CD
37681	3649	1554	Pleasure	pleasure	NN
37681	3649	1555	of	of	IN
37681	3649	1556	geometry	geometry	NN
37681	3649	1557	,	,	,
37681	3649	1558	16	16	CD
37681	3649	1559	Plimpton	Plimpton	NNP
37681	3649	1560	,	,	,
37681	3649	1561	G.	G.	NNP
37681	3649	1562	A.	A.	NNP
37681	3649	1563	,	,	,
37681	3649	1564	51	51	CD
37681	3649	1565	,	,	,
37681	3649	1566	52	52	CD
37681	3649	1567	Plutarch	Plutarch	NNP
37681	3649	1568	,	,	,
37681	3649	1569	259	259	CD
37681	3649	1570	Poinsot	Poinsot	NNP
37681	3649	1571	,	,	,
37681	3649	1572	311	311	CD
37681	3649	1573	Point	point	NN
37681	3649	1574	,	,	,
37681	3649	1575	135	135	CD
37681	3649	1576	Polygons	polygon	NNS
37681	3649	1577	,	,	,
37681	3649	1578	156	156	CD
37681	3649	1579	,	,	,
37681	3649	1580	252	252	CD
37681	3649	1581	,	,	,
37681	3649	1582	269	269	CD
37681	3649	1583	,	,	,
37681	3649	1584	274	274	CD
37681	3649	1585	Polyhedrons	polyhedron	NNS
37681	3649	1586	,	,	,
37681	3649	1587	301	301	CD
37681	3649	1588	,	,	,
37681	3649	1589	303	303	CD
37681	3649	1590	,	,	,
37681	3649	1591	310	310	CD
37681	3649	1592	Pomodoro	Pomodoro	NNP
37681	3649	1593	,	,	,
37681	3649	1594	179	179	CD
37681	3649	1595	_	_	NNP
37681	3649	1596	Pons	Pons	NNP
37681	3649	1597	asinorum	asinorum	NN
37681	3649	1598	_	_	NNP
37681	3649	1599	,	,	,
37681	3649	1600	174	174	CD
37681	3649	1601	,	,	,
37681	3649	1602	265	265	CD
37681	3649	1603	Posidonius	Posidonius	NNP
37681	3649	1604	,	,	,
37681	3649	1605	128	128	CD
37681	3649	1606	,	,	,
37681	3649	1607	149	149	CD
37681	3649	1608	Postulates	postulate	NNS
37681	3649	1609	,	,	,
37681	3649	1610	31	31	CD
37681	3649	1611	,	,	,
37681	3649	1612	41	41	CD
37681	3649	1613	,	,	,
37681	3649	1614	116	116	CD
37681	3649	1615	,	,	,
37681	3649	1616	125	125	CD
37681	3649	1617	,	,	,
37681	3649	1618	292	292	CD
37681	3649	1619	Practical	practical	JJ
37681	3649	1620	geometry	geometry	NN
37681	3649	1621	,	,	,
37681	3649	1622	3	3	CD
37681	3649	1623	,	,	,
37681	3649	1624	7	7	CD
37681	3649	1625	,	,	,
37681	3649	1626	9	9	CD
37681	3649	1627	,	,	,
37681	3649	1628	44	44	CD
37681	3649	1629	Printing	printing	NN
37681	3649	1630	,	,	,
37681	3649	1631	effect	effect	NN
37681	3649	1632	of	of	IN
37681	3649	1633	,	,	,
37681	3649	1634	44	44	CD
37681	3649	1635	Prism	prism	NN
37681	3649	1636	,	,	,
37681	3649	1637	303	303	CD
37681	3649	1638	Problems	problem	NNS
37681	3649	1639	,	,	,
37681	3649	1640	applied	apply	VBD
37681	3649	1641	,	,	,
37681	3649	1642	75	75	CD
37681	3649	1643	,	,	,
37681	3649	1644	103	103	CD
37681	3649	1645	,	,	,
37681	3649	1646	178	178	CD
37681	3649	1647	,	,	,
37681	3649	1648	186	186	CD
37681	3649	1649	,	,	,
37681	3649	1650	192	192	CD
37681	3649	1651	,	,	,
37681	3649	1652	195	195	CD
37681	3649	1653	,	,	,
37681	3649	1654	203	203	CD
37681	3649	1655	,	,	,
37681	3649	1656	204	204	CD
37681	3649	1657	,	,	,
37681	3649	1658	209	209	CD
37681	3649	1659	,	,	,
37681	3649	1660	215	215	CD
37681	3649	1661	,	,	,
37681	3649	1662	217	217	CD
37681	3649	1663	,	,	,
37681	3649	1664	242	242	CD
37681	3649	1665	,	,	,
37681	3649	1666	267	267	CD
37681	3649	1667	,	,	,
37681	3649	1668	295	295	CD
37681	3649	1669	,	,	,
37681	3649	1670	317	317	CD
37681	3649	1671	Proclus	Proclus	NNP
37681	3649	1672	,	,	,
37681	3649	1673	36	36	CD
37681	3649	1674	,	,	,
37681	3649	1675	47	47	CD
37681	3649	1676	,	,	,
37681	3649	1677	48	48	CD
37681	3649	1678	,	,	,
37681	3649	1679	52	52	CD
37681	3649	1680	,	,	,
37681	3649	1681	71	71	CD
37681	3649	1682	,	,	,
37681	3649	1683	127	127	CD
37681	3649	1684	,	,	,
37681	3649	1685	128	128	CD
37681	3649	1686	,	,	,
37681	3649	1687	136	136	CD
37681	3649	1688	,	,	,
37681	3649	1689	137	137	CD
37681	3649	1690	,	,	,
37681	3649	1691	139	139	CD
37681	3649	1692	,	,	,
37681	3649	1693	140	140	CD
37681	3649	1694	,	,	,
37681	3649	1695	149	149	CD
37681	3649	1696	,	,	,
37681	3649	1697	155	155	CD
37681	3649	1698	,	,	,
37681	3649	1699	186	186	CD
37681	3649	1700	,	,	,
37681	3649	1701	188	188	CD
37681	3649	1702	,	,	,
37681	3649	1703	197	197	CD
37681	3649	1704	,	,	,
37681	3649	1705	212	212	CD
37681	3649	1706	,	,	,
37681	3649	1707	214	214	CD
37681	3649	1708	,	,	,
37681	3649	1709	253	253	CD
37681	3649	1710	,	,	,
37681	3649	1711	258	258	CD
37681	3649	1712	,	,	,
37681	3649	1713	310	310	CD
37681	3649	1714	,	,	,
37681	3649	1715	311	311	CD
37681	3649	1716	Projections	Projections	NNPS
37681	3649	1717	,	,	,
37681	3649	1718	300	300	CD
37681	3649	1719	Proofs	Proofs	NNP
37681	3649	1720	in	in	IN
37681	3649	1721	full	full	JJ
37681	3649	1722	,	,	,
37681	3649	1723	79	79	CD
37681	3649	1724	Proportion	Proportion	NNP
37681	3649	1725	,	,	,
37681	3649	1726	32	32	CD
37681	3649	1727	,	,	,
37681	3649	1728	227	227	CD
37681	3649	1729	Psychology	psychology	NN
37681	3649	1730	,	,	,
37681	3649	1731	12	12	CD
37681	3649	1732	,	,	,
37681	3649	1733	20	20	CD
37681	3649	1734	Ptolemy	Ptolemy	NNP
37681	3649	1735	,	,	,
37681	3649	1736	C.	C.	NNP
37681	3649	1737	,	,	,
37681	3649	1738	35	35	CD
37681	3649	1739	,	,	,
37681	3649	1740	278	278	CD
37681	3649	1741	;	;	:
37681	3649	1742	king	king	NN
37681	3649	1743	,	,	,
37681	3649	1744	48	48	CD
37681	3649	1745	,	,	,
37681	3649	1746	49	49	CD
37681	3649	1747	Pyramid	Pyramid	NNP
37681	3649	1748	,	,	,
37681	3649	1749	307	307	CD
37681	3649	1750	Pythagoras	Pythagoras	NNP
37681	3649	1751	,	,	,
37681	3649	1752	29	29	CD
37681	3649	1753	,	,	,
37681	3649	1754	40	40	CD
37681	3649	1755	,	,	,
37681	3649	1756	258	258	CD
37681	3649	1757	,	,	,
37681	3649	1758	272	272	CD
37681	3649	1759	,	,	,
37681	3649	1760	273	273	CD
37681	3649	1761	,	,	,
37681	3649	1762	310	310	CD
37681	3649	1763	Pythagorean	Pythagorean	NNP
37681	3649	1764	Theorem	Theorem	NNP
37681	3649	1765	,	,	,
37681	3649	1766	28	28	CD
37681	3649	1767	,	,	,
37681	3649	1768	36	36	CD
37681	3649	1769	,	,	,
37681	3649	1770	258	258	CD
37681	3649	1771	Pythagorean	pythagorean	JJ
37681	3649	1772	numbers	number	NNS
37681	3649	1773	,	,	,
37681	3649	1774	32	32	CD
37681	3649	1775	,	,	,
37681	3649	1776	36	36	CD
37681	3649	1777	,	,	,
37681	3649	1778	263	263	CD
37681	3649	1779	,	,	,
37681	3649	1780	266	266	CD
37681	3649	1781	Pythagoreans	Pythagoreans	NNPS
37681	3649	1782	,	,	,
37681	3649	1783	136	136	CD
37681	3649	1784	,	,	,
37681	3649	1785	137	137	CD
37681	3649	1786	,	,	,
37681	3649	1787	185	185	CD
37681	3649	1788	,	,	,
37681	3649	1789	227	227	CD
37681	3649	1790	,	,	,
37681	3649	1791	269	269	CD
37681	3649	1792	,	,	,
37681	3649	1793	309	309	CD
37681	3649	1794	Quadrant	Quadrant	NNP
37681	3649	1795	,	,	,
37681	3649	1796	236	236	CD
37681	3649	1797	Quadratrix	Quadratrix	NNP
37681	3649	1798	,	,	,
37681	3649	1799	31	31	CD
37681	3649	1800	,	,	,
37681	3649	1801	215	215	CD
37681	3649	1802	Quadrilaterals	Quadrilaterals	NNPS
37681	3649	1803	,	,	,
37681	3649	1804	148	148	CD
37681	3649	1805	,	,	,
37681	3649	1806	157	157	CD
37681	3649	1807	Quadrivium	Quadrivium	NNP
37681	3649	1808	,	,	,
37681	3649	1809	42	42	CD
37681	3649	1810	Questions	question	NNS
37681	3649	1811	at	at	IN
37681	3649	1812	issue	issue	NN
37681	3649	1813	,	,	,
37681	3649	1814	3	3	CD
37681	3649	1815	Rabelais	Rabelais	NNP
37681	3649	1816	,	,	,
37681	3649	1817	24	24	CD
37681	3649	1818	Radius	Radius	NNP
37681	3649	1819	,	,	,
37681	3649	1820	153	153	CD
37681	3649	1821	Ratio	Ratio	NNP
37681	3649	1822	,	,	,
37681	3649	1823	205	205	CD
37681	3649	1824	,	,	,
37681	3649	1825	227	227	CD
37681	3649	1826	Real	real	JJ
37681	3649	1827	problem	problem	NN
37681	3649	1828	defined	define	VBN
37681	3649	1829	,	,	,
37681	3649	1830	75	75	CD
37681	3649	1831	,	,	,
37681	3649	1832	103	103	CD
37681	3649	1833	Reasons	reason	NNS
37681	3649	1834	for	for	IN
37681	3649	1835	studying	study	VBG
37681	3649	1836	geometry	geometry	NN
37681	3649	1837	,	,	,
37681	3649	1838	7	7	CD
37681	3649	1839	,	,	,
37681	3649	1840	100	100	CD
37681	3649	1841	Rebière	Rebière	NNP
37681	3649	1842	,	,	,
37681	3649	1843	25	25	CD
37681	3649	1844	Reciprocal	reciprocal	JJ
37681	3649	1845	propositions	proposition	NNS
37681	3649	1846	,	,	,
37681	3649	1847	173	173	CD
37681	3649	1848	Recitation	recitation	NN
37681	3649	1849	in	in	IN
37681	3649	1850	geometry	geometry	NN
37681	3649	1851	,	,	,
37681	3649	1852	113	113	CD
37681	3649	1853	Recorde	Recorde	NNP
37681	3649	1854	,	,	,
37681	3649	1855	37	37	CD
37681	3649	1856	Rectilinear	Rectilinear	NNP
37681	3649	1857	figures	figure	NNS
37681	3649	1858	,	,	,
37681	3649	1859	146	146	CD
37681	3649	1860	Reductio	Reductio	NNP
37681	3649	1861	ad	ad	NN
37681	3649	1862	absurdum	absurdum	NN
37681	3649	1863	,	,	,
37681	3649	1864	41	41	CD
37681	3649	1865	,	,	,
37681	3649	1866	177	177	CD
37681	3649	1867	Regular	regular	JJ
37681	3649	1868	polygons	polygon	NNS
37681	3649	1869	,	,	,
37681	3649	1870	269	269	CD
37681	3649	1871	"	"	``
37681	3649	1872	Rhind	Rhind	NNP
37681	3649	1873	Papyrus	Papyrus	NNP
37681	3649	1874	,	,	,
37681	3649	1875	"	"	''
37681	3649	1876	27	27	CD
37681	3649	1877	Rhombus	Rhombus	NNP
37681	3649	1878	and	and	CC
37681	3649	1879	rhomboid	rhomboid	NN
37681	3649	1880	,	,	,
37681	3649	1881	148	148	CD
37681	3649	1882	Riccardi	Riccardi	NNS
37681	3649	1883	,	,	,
37681	3649	1884	47	47	CD
37681	3649	1885	Richter	Richter	NNP
37681	3649	1886	,	,	,
37681	3649	1887	279	279	CD
37681	3649	1888	Roman	roman	JJ
37681	3649	1889	surveyors	surveyor	NNS
37681	3649	1890	,	,	,
37681	3649	1891	247	247	CD
37681	3649	1892	Saccheri	Saccheri	NNP
37681	3649	1893	,	,	,
37681	3649	1894	127	127	CD
37681	3649	1895	Sacrobosco	Sacrobosco	NNP
37681	3649	1896	,	,	,
37681	3649	1897	43	43	CD
37681	3649	1898	San	San	NNP
37681	3649	1899	Giovanni	Giovanni	NNP
37681	3649	1900	,	,	,
37681	3649	1901	192	192	CD
37681	3649	1902	Sauvage	sauvage	NN
37681	3649	1903	,	,	,
37681	3649	1904	164	164	CD
37681	3649	1905	Sayre	Sayre	NNP
37681	3649	1906	,	,	,
37681	3649	1907	272	272	CD
37681	3649	1908	Scalene	Scalene	NNP
37681	3649	1909	,	,	,
37681	3649	1910	147	147	CD
37681	3649	1911	Schlegel	Schlegel	NNP
37681	3649	1912	,	,	,
37681	3649	1913	68	68	CD
37681	3649	1914	Schopenhauer	Schopenhauer	NNP
37681	3649	1915	,	,	,
37681	3649	1916	121	121	CD
37681	3649	1917	,	,	,
37681	3649	1918	265	265	CD
37681	3649	1919	Schotten	Schotten	NNP
37681	3649	1920	,	,	,
37681	3649	1921	46	46	CD
37681	3649	1922	,	,	,
37681	3649	1923	135	135	CD
37681	3649	1924	,	,	,
37681	3649	1925	149	149	CD
37681	3649	1926	Sector	Sector	NNP
37681	3649	1927	,	,	,
37681	3649	1928	154	154	CD
37681	3649	1929	,	,	,
37681	3649	1930	156	156	CD
37681	3649	1931	Segment	segment	NN
37681	3649	1932	,	,	,
37681	3649	1933	154	154	CD
37681	3649	1934	Semicircle	Semicircle	NNP
37681	3649	1935	,	,	,
37681	3649	1936	146	146	CD
37681	3649	1937	Shanks	shank	NNS
37681	3649	1938	,	,	,
37681	3649	1939	279	279	CD
37681	3649	1940	Similar	similar	JJ
37681	3649	1941	figures	figure	NNS
37681	3649	1942	,	,	,
37681	3649	1943	232	232	CD
37681	3649	1944	Simon	Simon	NNP
37681	3649	1945	,	,	,
37681	3649	1946	38	38	CD
37681	3649	1947	,	,	,
37681	3649	1948	56	56	CD
37681	3649	1949	,	,	,
37681	3649	1950	135	135	CD
37681	3649	1951	Simson	Simson	NNP
37681	3649	1952	,	,	,
37681	3649	1953	142	142	CD
37681	3649	1954	Sisam	Sisam	NNP
37681	3649	1955	,	,	,
37681	3649	1956	11	11	CD
37681	3649	1957	Smith	Smith	NNP
37681	3649	1958	,	,	,
37681	3649	1959	D.	D.	NNP
37681	3649	1960	E.	E.	NNP
37681	3649	1961	,	,	,
37681	3649	1962	25	25	CD
37681	3649	1963	,	,	,
37681	3649	1964	37	37	CD
37681	3649	1965	,	,	,
37681	3649	1966	51	51	CD
37681	3649	1967	,	,	,
37681	3649	1968	52	52	CD
37681	3649	1969	,	,	,
37681	3649	1970	119	119	CD
37681	3649	1971	,	,	,
37681	3649	1972	131	131	CD
37681	3649	1973	,	,	,
37681	3649	1974	135	135	CD
37681	3649	1975	,	,	,
37681	3649	1976	159	159	CD
37681	3649	1977	Solid	solid	JJ
37681	3649	1978	geometry	geometry	NN
37681	3649	1979	,	,	,
37681	3649	1980	289	289	CD
37681	3649	1981	Speusippus	Speusippus	NNP
37681	3649	1982	,	,	,
37681	3649	1983	32	32	CD
37681	3649	1984	Sphere	Sphere	NNP
37681	3649	1985	,	,	,
37681	3649	1986	321	321	CD
37681	3649	1987	Square	Square	NNP
37681	3649	1988	on	on	IN
37681	3649	1989	a	a	DT
37681	3649	1990	line	line	NN
37681	3649	1991	,	,	,
37681	3649	1992	257	257	CD
37681	3649	1993	Squaring	square	VBG
37681	3649	1994	the	the	DT
37681	3649	1995	circle	circle	NN
37681	3649	1996	,	,	,
37681	3649	1997	31	31	CD
37681	3649	1998	,	,	,
37681	3649	1999	32	32	CD
37681	3649	2000	,	,	,
37681	3649	2001	277	277	CD
37681	3649	2002	Stäckel	Stäckel	NNP
37681	3649	2003	,	,	,
37681	3649	2004	128	128	CD
37681	3649	2005	Stamper	Stamper	NNP
37681	3649	2006	,	,	,
37681	3649	2007	46	46	CD
37681	3649	2008	,	,	,
37681	3649	2009	83	83	CD
37681	3649	2010	Stark	Stark	NNP
37681	3649	2011	,	,	,
37681	3649	2012	W.	W.	NNP
37681	3649	2013	E.	E.	NNP
37681	3649	2014	,	,	,
37681	3649	2015	172	172	CD
37681	3649	2016	,	,	,
37681	3649	2017	238	238	CD
37681	3649	2018	Stereoscopic	stereoscopic	JJ
37681	3649	2019	slides	slide	NNS
37681	3649	2020	,	,	,
37681	3649	2021	291	291	CD
37681	3649	2022	Stobæus	Stobæus	NNP
37681	3649	2023	,	,	,
37681	3649	2024	8	8	CD
37681	3649	2025	Straight	straight	JJ
37681	3649	2026	angle	angle	NN
37681	3649	2027	,	,	,
37681	3649	2028	151	151	CD
37681	3649	2029	Straight	straight	JJ
37681	3649	2030	line	line	NN
37681	3649	2031	,	,	,
37681	3649	2032	138	138	CD
37681	3649	2033	Suggested	suggest	VBN
37681	3649	2034	proofs	proof	NNS
37681	3649	2035	,	,	,
37681	3649	2036	81	81	CD
37681	3649	2037	Sulvasutras	sulvasutra	NNS
37681	3649	2038	,	,	,
37681	3649	2039	232	232	CD
37681	3649	2040	Superposition	superposition	NN
37681	3649	2041	,	,	,
37681	3649	2042	169	169	CD
37681	3649	2043	Surface	surface	NN
37681	3649	2044	,	,	,
37681	3649	2045	140	140	CD
37681	3649	2046	Swain	Swain	NNP
37681	3649	2047	,	,	,
37681	3649	2048	G.	G.	NNP
37681	3649	2049	F.	F.	NNP
37681	3649	2050	,	,	,
37681	3649	2051	13	13	CD
37681	3649	2052	Syllabi	Syllabi	NNP
37681	3649	2053	,	,	,
37681	3649	2054	58	58	CD
37681	3649	2055	,	,	,
37681	3649	2056	60	60	CD
37681	3649	2057	,	,	,
37681	3649	2058	63	63	CD
37681	3649	2059	,	,	,
37681	3649	2060	64	64	CD
37681	3649	2061	,	,	,
37681	3649	2062	66	66	CD
37681	3649	2063	,	,	,
37681	3649	2064	67	67	CD
37681	3649	2065	,	,	,
37681	3649	2066	80	80	CD
37681	3649	2067	,	,	,
37681	3649	2068	82	82	CD
37681	3649	2069	Sylvester	Sylvester	NNP
37681	3649	2070	II	II	NNP
37681	3649	2071	,	,	,
37681	3649	2072	43	43	CD
37681	3649	2073	Synthetic	synthetic	JJ
37681	3649	2074	method	method	NN
37681	3649	2075	,	,	,
37681	3649	2076	161	161	CD
37681	3649	2077	Tangent	tangent	NN
37681	3649	2078	,	,	,
37681	3649	2079	154	154	CD
37681	3649	2080	Tartaglia	Tartaglia	NNP
37681	3649	2081	,	,	,
37681	3649	2082	153	153	CD
37681	3649	2083	Tatius	Tatius	NNP
37681	3649	2084	,	,	,
37681	3649	2085	Achilles	Achilles	NNP
37681	3649	2086	,	,	,
37681	3649	2087	272	272	CD
37681	3649	2088	Teaching	teaching	NN
37681	3649	2089	geometry	geometry	NN
37681	3649	2090	,	,	,
37681	3649	2091	reasons	reason	NNS
37681	3649	2092	for	for	IN
37681	3649	2093	,	,	,
37681	3649	2094	7	7	CD
37681	3649	2095	,	,	,
37681	3649	2096	15	15	CD
37681	3649	2097	,	,	,
37681	3649	2098	20	20	CD
37681	3649	2099	;	;	:
37681	3649	2100	development	development	NN
37681	3649	2101	of	of	IN
37681	3649	2102	,	,	,
37681	3649	2103	40	40	CD
37681	3649	2104	Textbooks	textbook	NNS
37681	3649	2105	,	,	,
37681	3649	2106	32	32	CD
37681	3649	2107	,	,	,
37681	3649	2108	33	33	CD
37681	3649	2109	,	,	,
37681	3649	2110	41	41	CD
37681	3649	2111	,	,	,
37681	3649	2112	70	70	CD
37681	3649	2113	,	,	,
37681	3649	2114	80	80	CD
37681	3649	2115	,	,	,
37681	3649	2116	82	82	CD
37681	3649	2117	Thales	thale	NNS
37681	3649	2118	,	,	,
37681	3649	2119	28	28	CD
37681	3649	2120	,	,	,
37681	3649	2121	168	168	CD
37681	3649	2122	,	,	,
37681	3649	2123	171	171	CD
37681	3649	2124	,	,	,
37681	3649	2125	185	185	CD
37681	3649	2126	,	,	,
37681	3649	2127	210	210	CD
37681	3649	2128	Theætetus	Theætetus	NNP
37681	3649	2129	,	,	,
37681	3649	2130	48	48	CD
37681	3649	2131	,	,	,
37681	3649	2132	310	310	CD
37681	3649	2133	Theon	Theon	NNP
37681	3649	2134	of	of	IN
37681	3649	2135	Alexandria	Alexandria	NNP
37681	3649	2136	,	,	,
37681	3649	2137	36	36	CD
37681	3649	2138	Thibaut	Thibaut	NNP
37681	3649	2139	,	,	,
37681	3649	2140	185	185	CD
37681	3649	2141	Thoreau	Thoreau	NNP
37681	3649	2142	,	,	,
37681	3649	2143	246	246	CD
37681	3649	2144	Trapezium	Trapezium	NNP
37681	3649	2145	,	,	,
37681	3649	2146	148	148	CD
37681	3649	2147	Treutlein	Treutlein	NNP
37681	3649	2148	,	,	,
37681	3649	2149	68	68	CD
37681	3649	2150	,	,	,
37681	3649	2151	164	164	CD
37681	3649	2152	Triangle	Triangle	NNP
37681	3649	2153	,	,	,
37681	3649	2154	147	147	CD
37681	3649	2155	Trigonometry	Trigonometry	NNP
37681	3649	2156	,	,	,
37681	3649	2157	234	234	CD
37681	3649	2158	Trisection	Trisection	NNP
37681	3649	2159	problem	problem	NN
37681	3649	2160	,	,	,
37681	3649	2161	31	31	CD
37681	3649	2162	,	,	,
37681	3649	2163	215	215	CD
37681	3649	2164	Trivium	trivium	NN
37681	3649	2165	,	,	,
37681	3649	2166	42	42	CD
37681	3649	2167	Universities	university	NNS
37681	3649	2168	,	,	,
37681	3649	2169	geometry	geometry	NN
37681	3649	2170	in	in	IN
37681	3649	2171	the	the	DT
37681	3649	2172	,	,	,
37681	3649	2173	43	43	CD
37681	3649	2174	Uselessness	uselessness	NN
37681	3649	2175	of	of	IN
37681	3649	2176	mathematics	mathematic	NNS
37681	3649	2177	,	,	,
37681	3649	2178	13	13	CD
37681	3649	2179	Veblen	Veblen	NNP
37681	3649	2180	,	,	,
37681	3649	2181	131	131	CD
37681	3649	2182	,	,	,
37681	3649	2183	159	159	CD
37681	3649	2184	Vega	Vega	NNP
37681	3649	2185	,	,	,
37681	3649	2186	279	279	CD
37681	3649	2187	Veronese	Veronese	NNP
37681	3649	2188	,	,	,
37681	3649	2189	68	68	CD
37681	3649	2190	Vieta	vieta	NN
37681	3649	2191	,	,	,
37681	3649	2192	279	279	CD
37681	3649	2193	Vogt	Vogt	NNP
37681	3649	2194	,	,	,
37681	3649	2195	259	259	CD
37681	3649	2196	Wallis	Wallis	NNPS
37681	3649	2197	,	,	,
37681	3649	2198	127	127	CD
37681	3649	2199	,	,	,
37681	3649	2200	280	280	CD
37681	3649	2201	Young	Young	NNP
37681	3649	2202	,	,	,
37681	3649	2203	J.	J.	NNP
37681	3649	2204	W.	W.	NNP
37681	3649	2205	A.	A.	NNP
37681	3649	2206	,	,	,
37681	3649	2207	25	25	CD
37681	3649	2208	,	,	,
37681	3649	2209	131	131	CD
37681	3649	2210	,	,	,
37681	3649	2211	159	159	CD
37681	3649	2212	,	,	,
37681	3649	2213	277	277	CD
37681	3649	2214	Zamberti	Zamberti	NNP
37681	3649	2215	,	,	,
37681	3649	2216	52	52	CD
37681	3649	2217	Zenodorus	Zenodorus	NNP
37681	3649	2218	,	,	,
37681	3649	2219	34	34	CD
37681	3649	2220	,	,	,
37681	3649	2221	253	253	CD
37681	3649	2222	ANNOUNCEMENTS	announcement	NNS
37681	3649	2223	BOOKS	BOOKS	NNP
37681	3649	2224	FOR	for	IN
37681	3649	2225	TEACHERS	TEACHERS	NNP
37681	3649	2226	List	List	NNP
37681	3649	2227	price	price	NN
37681	3649	2228	Allen	Allen	NNP
37681	3649	2229	:	:	:
37681	3649	2230	Civics	Civics	NNP
37681	3649	2231	and	and	CC
37681	3649	2232	Health	Health	NNP
37681	3649	2233	$	$	$
37681	3649	2234	1.25	1.25	CD
37681	3649	2235	Brigham	brigham	NN
37681	3649	2236	:	:	:
37681	3649	2237	Geographic	Geographic	NNP
37681	3649	2238	Influences	Influences	NNPS
37681	3649	2239	in	in	IN
37681	3649	2240	American	American	NNP
37681	3649	2241	History	History	NNP
37681	3649	2242	1.25	1.25	CD
37681	3649	2243	Channing	Channing	NNP
37681	3649	2244	and	and	CC
37681	3649	2245	Hart	Hart	NNP
37681	3649	2246	:	:	:
37681	3649	2247	Guide	guide	VB
37681	3649	2248	to	to	IN
37681	3649	2249	the	the	DT
37681	3649	2250	Study	Study	NNP
37681	3649	2251	of	of	IN
37681	3649	2252	American	American	NNP
37681	3649	2253	History	History	NNP
37681	3649	2254	2.00	2.00	CD
37681	3649	2255	Hall	Hall	NNP
37681	3649	2256	:	:	:
37681	3649	2257	Aspects	aspect	NNS
37681	3649	2258	of	of	IN
37681	3649	2259	Child	Child	NNP
37681	3649	2260	Life	Life	NNP
37681	3649	2261	and	and	CC
37681	3649	2262	Education	Education	NNP
37681	3649	2263	1.50	1.50	CD
37681	3649	2264	Hodge	Hodge	NNP
37681	3649	2265	:	:	:
37681	3649	2266	Nature	Nature	NNP
37681	3649	2267	Study	Study	NNP
37681	3649	2268	and	and	CC
37681	3649	2269	Life	Life	NNP
37681	3649	2270	1.50	1.50	CD
37681	3649	2271	Johnson	Johnson	NNP
37681	3649	2272	:	:	:
37681	3649	2273	Education	education	NN
37681	3649	2274	by	by	IN
37681	3649	2275	Plays	Plays	NNP
37681	3649	2276	and	and	CC
37681	3649	2277	Games	Games	NNPS
37681	3649	2278	.90	.90	SYM
37681	3649	2279	Johnson	Johnson	NNP
37681	3649	2280	:	:	:
37681	3649	2281	What	what	WP
37681	3649	2282	to	to	TO
37681	3649	2283	Do	do	VB
37681	3649	2284	at	at	IN
37681	3649	2285	Recess	recess	NN
37681	3649	2286	.25	.25	.
37681	3649	2287	Kern	Kern	NNP
37681	3649	2288	:	:	:
37681	3649	2289	Among	among	IN
37681	3649	2290	Country	Country	NNP
37681	3649	2291	Schools	Schools	NNP
37681	3649	2292	1.25	1.25	CD
37681	3649	2293	Mace	mace	NN
37681	3649	2294	:	:	:
37681	3649	2295	Method	method	NN
37681	3649	2296	in	in	IN
37681	3649	2297	History	history	NN
37681	3649	2298	1.00	1.00	CD
37681	3649	2299	MacVicar	MacVicar	NNP
37681	3649	2300	:	:	:
37681	3649	2301	The	the	DT
37681	3649	2302	Principles	Principles	NNPS
37681	3649	2303	of	of	IN
37681	3649	2304	Education	Education	NNP
37681	3649	2305	.60	.60	NFP
37681	3649	2306	Moral	Moral	NNP
37681	3649	2307	Training	Training	NNP
37681	3649	2308	in	in	IN
37681	3649	2309	the	the	DT
37681	3649	2310	Public	Public	NNP
37681	3649	2311	Schools	Schools	NNP
37681	3649	2312	1.25	1.25	CD
37681	3649	2313	Prince	Prince	NNP
37681	3649	2314	:	:	:
37681	3649	2315	Courses	course	NNS
37681	3649	2316	of	of	IN
37681	3649	2317	Studies	Studies	NNPS
37681	3649	2318	and	and	CC
37681	3649	2319	Methods	Methods	NNPS
37681	3649	2320	of	of	IN
37681	3649	2321	Teaching	teaching	NN
37681	3649	2322	.75	.75	.
37681	3649	2323	Scott	Scott	NNP
37681	3649	2324	:	:	:
37681	3649	2325	Social	Social	NNP
37681	3649	2326	Education	Education	NNP
37681	3649	2327	1.25	1.25	CD
37681	3649	2328	Tompkins	tompkin	NNS
37681	3649	2329	:	:	:
37681	3649	2330	Philosophy	Philosophy	NNP
37681	3649	2331	of	of	IN
37681	3649	2332	School	School	NNP
37681	3649	2333	Management	Management	NNP
37681	3649	2334	.75	.75	CD
37681	3649	2335	Tompkins	tompkin	NNS
37681	3649	2336	:	:	:
37681	3649	2337	Philosophy	philosophy	NN
37681	3649	2338	of	of	IN
37681	3649	2339	Teaching	teaching	NN
37681	3649	2340	.75	.75	.
37681	3649	2341	Wiltse	wiltse	NN
37681	3649	2342	:	:	:
37681	3649	2343	Place	place	NN
37681	3649	2344	of	of	IN
37681	3649	2345	the	the	DT
37681	3649	2346	Story	Story	NNP
37681	3649	2347	in	in	IN
37681	3649	2348	Early	Early	NNP
37681	3649	2349	Education	Education	NNP
37681	3649	2350	,	,	,
37681	3649	2351	and	and	CC
37681	3649	2352	Other	other	JJ
37681	3649	2353	Essays	essay	NNS
37681	3649	2354	.	.	.
37681	3650	1	A	a	DT
37681	3650	2	Manual	Manual	NNP
37681	3650	3	for	for	IN
37681	3650	4	Teachers	teacher	NNS
37681	3650	5	.50	.50	NFP
37681	3650	6	FOR	for	IN
37681	3650	7	CLASS	CLASS	NNP
37681	3650	8	RECORDS	RECORDS	NNP
37681	3650	9	Comings	coming	NNS
37681	3650	10	:	:	:
37681	3650	11	Complete	complete	JJ
37681	3650	12	Record	record	NN
37681	3650	13	--	--	:
37681	3650	14	Attendance	attendance	NN
37681	3650	15	and	and	CC
37681	3650	16	Scholarship	Scholarship	NNP
37681	3650	17	Graded	Graded	NNP
37681	3650	18	-	-	HYPH
37681	3650	19	School	School	NNP
37681	3650	20	Edition	Edition	NNP
37681	3650	21	.30	.30	.
37681	3650	22	High	High	NNP
37681	3650	23	-	-	HYPH
37681	3650	24	School	School	NNP
37681	3650	25	Edition	Edition	NNP
37681	3650	26	.30	.30	.
37681	3650	27	Ginn	Ginn	NNP
37681	3650	28	and	and	CC
37681	3650	29	Company	Company	NNP
37681	3650	30	:	:	:
37681	3650	31	Teacher	teacher	NN
37681	3650	32	's	's	POS
37681	3650	33	Class	Class	NNP
37681	3650	34	Books	book	NNS
37681	3650	35	No	no	NN
37681	3650	36	.	.	.
37681	3651	1	I	-PRON-	PRP
37681	3651	2	.30	.30	.
37681	3651	3	No	no	UH
37681	3651	4	.	.	.
37681	3652	1	II	ii	CD
37681	3652	2	.40	.40	CD
37681	3652	3	Twenty	twenty	CD
37681	3652	4	Weeks	Weeks	NNPS
37681	3652	5	'	'	POS
37681	3652	6	Class	Class	NNP
37681	3652	7	Book	Book	NNP
37681	3652	8	.30	.30	NFP
37681	3652	9	CIVICS	civics	NN
37681	3652	10	AND	and	CC
37681	3652	11	HEALTH	health	NN
37681	3652	12	By	by	IN
37681	3652	13	WILLIAM	WILLIAM	NNP
37681	3652	14	H.	H.	NNP
37681	3652	15	ALLEN	ALLEN	NNP
37681	3652	16	,	,	,
37681	3652	17	Secretary	Secretary	NNP
37681	3652	18	of	of	IN
37681	3652	19	the	the	DT
37681	3652	20	Bureau	Bureau	NNP
37681	3652	21	of	of	IN
37681	3652	22	Municipal	Municipal	NNP
37681	3652	23	Research	Research	NNP
37681	3652	24	,	,	,
37681	3652	25	New	New	NNP
37681	3652	26	York	York	NNP
37681	3652	27	City	City	NNP
37681	3652	28	.	.	.
37681	3653	1	With	with	IN
37681	3653	2	an	an	DT
37681	3653	3	Introduction	introduction	NN
37681	3653	4	by	by	IN
37681	3653	5	Professor	Professor	NNP
37681	3653	6	WILLIAM	WILLIAM	NNP
37681	3653	7	T.	T.	NNP
37681	3653	8	SEDGWICK	SEDGWICK	NNP
37681	3653	9	,	,	,
37681	3653	10	Professor	Professor	NNP
37681	3653	11	of	of	IN
37681	3653	12	Biology	Biology	NNP
37681	3653	13	in	in	IN
37681	3653	14	the	the	DT
37681	3653	15	Massachusetts	Massachusetts	NNP
37681	3653	16	Institute	Institute	NNP
37681	3653	17	of	of	IN
37681	3653	18	Technology	Technology	NNP
37681	3653	19	List	List	NNP
37681	3653	20	price	price	NN
37681	3653	21	,	,	,
37681	3653	22	$	$	$
37681	3653	23	1.25	1.25	CD
37681	3653	24	_	_	NN
37681	3653	25	Adopted	adopt	VBN
37681	3653	26	by	by	IN
37681	3653	27	the	the	DT
37681	3653	28	Teachers	Teachers	NNPS
37681	3653	29	'	'	POS
37681	3653	30	Reading	Reading	NNP
37681	3653	31	Circles	Circles	NNP
37681	3653	32	of	of	IN
37681	3653	33	_	_	NNP
37681	3653	34	_	_	NNP
37681	3653	35	Maryland	Maryland	NNP
37681	3653	36	_	_	NNP
37681	3653	37	,	,	,
37681	3653	38	_	_	NNP
37681	3653	39	Kentucky	Kentucky	NNP
37681	3653	40	_	_	NNP
37681	3653	41	,	,	,
37681	3653	42	_	_	NNP
37681	3653	43	North	North	NNP
37681	3653	44	Dakota	Dakota	NNP
37681	3653	45	_	_	NNP
37681	3653	46	,	,	,
37681	3653	47	_	_	NNP
37681	3653	48	South	South	NNP
37681	3653	49	Dakota	Dakota	NNP
37681	3653	50	_	_	NNP
37681	3653	51	,	,	,
37681	3653	52	_	_	NNP
37681	3653	53	Oklahoma	Oklahoma	NNP
37681	3653	54	_	_	NNP
37681	3653	55	,	,	,
37681	3653	56	_	_	NNP
37681	3653	57	New	New	NNP
37681	3653	58	Mexico	Mexico	NNP
37681	3653	59	_	_	NNP
37681	3653	60	,	,	,
37681	3653	61	_	_	NNP
37681	3653	62	South	South	NNP
37681	3653	63	Carolina	Carolina	NNP
37681	3653	64	_	_	NNP
37681	3653	65	,	,	,
37681	3653	66	_	_	NNP
37681	3653	67	Alabama	Alabama	NNP
37681	3653	68	_	_	NNP
37681	3653	69	,	,	,
37681	3653	70	_	_	NNP
37681	3653	71	Arizona	Arizona	NNP
37681	3653	72	_	_	NNP
37681	3653	73	,	,	,
37681	3653	74	_	_	NNP
37681	3653	75	Illinois	Illinois	NNP
37681	3653	76	_	_	NNP
37681	3653	77	,	,	,
37681	3653	78	_	_	NNP
37681	3653	79	Michigan	Michigan	NNP
37681	3653	80	_	_	NNP
37681	3653	81	,	,	,
37681	3653	82	_	_	NNP
37681	3653	83	Colorado	Colorado	NNP
37681	3653	84	_	_	NNP
37681	3653	85	,	,	,
37681	3653	86	_	_	NNP
37681	3653	87	Texas	Texas	NNP
37681	3653	88	_	_	NNP
37681	3653	89	,	,	,
37681	3653	90	_	_	NNP
37681	3653	91	Virginia	Virginia	NNP
37681	3653	92	_	_	NNP
37681	3653	93	,	,	,
37681	3653	94	_	_	NNP
37681	3653	95	Iowa	Iowa	NNP
37681	3653	96	_	_	NNP
37681	3653	97	,	,	,
37681	3653	98	_	_	NNP
37681	3653	99	Arkansas	Arkansas	NNP
37681	3653	100	_	_	NNP
37681	3653	101	,	,	,
37681	3653	102	_	_	NNP
37681	3653	103	Wyoming	Wyoming	NNP
37681	3653	104	_	_	NNP
37681	3653	105	,	,	,
37681	3653	106	_	_	NNP
37681	3653	107	Missouri	Missouri	NNP
37681	3653	108	_	_	NNP
37681	3653	109	,	,	,
37681	3653	110	_	_	NNP
37681	3653	111	Indiana	Indiana	NNP
37681	3653	112	_	_	NNP
37681	3653	113	,	,	,
37681	3653	114	_	_	NNP
37681	3653	115	Nebraska	Nebraska	NNP
37681	3653	116	_	_	NNP
37681	3653	117	,	,	,
37681	3653	118	_	_	NNP
37681	3653	119	and	and	CC
37681	3653	120	Washington	Washington	NNP
37681	3653	121	_	_	NNP
37681	3653	122	*	*	NFP
37681	3653	123	*	*	NFP
37681	3653	124	*	*	NFP
37681	3653	125	*	*	NFP
37681	3653	126	*	*	NFP
37681	3653	127	For	for	IN
37681	3653	128	Dr.	Dr.	NNP
37681	3653	129	Allen	Allen	NNP
37681	3653	130	prevention	prevention	NN
37681	3653	131	is	be	VBZ
37681	3653	132	a	a	DT
37681	3653	133	text	text	NN
37681	3653	134	and	and	CC
37681	3653	135	the	the	DT
37681	3653	136	making	making	NN
37681	3653	137	of	of	IN
37681	3653	138	sound	sound	JJ
37681	3653	139	citizens	citizen	NNS
37681	3653	140	a	a	DT
37681	3653	141	sermon	sermon	NN
37681	3653	142	.	.	.
37681	3654	1	In	in	IN
37681	3654	2	"	"	``
37681	3654	3	Civics	Civics	NNPS
37681	3654	4	and	and	CC
37681	3654	5	Health	Health	NNP
37681	3654	6	"	"	''
37681	3654	7	he	-PRON-	PRP
37681	3654	8	sounds	sound	VBZ
37681	3654	9	a	a	DT
37681	3654	10	slogan	slogan	NN
37681	3654	11	which	which	WDT
37681	3654	12	should	should	MD
37681	3654	13	awaken	awaken	VB
37681	3654	14	every	every	DT
37681	3654	15	community	community	NN
37681	3654	16	in	in	IN
37681	3654	17	this	this	DT
37681	3654	18	country	country	NN
37681	3654	19	to	to	IN
37681	3654	20	its	-PRON-	PRP$
37681	3654	21	opportunities	opportunity	NNS
37681	3654	22	in	in	IN
37681	3654	23	municipal	municipal	JJ
37681	3654	24	reform	reform	NN
37681	3654	25	.	.	.
37681	3655	1	Every	every	DT
37681	3655	2	teacher	teacher	NN
37681	3655	3	who	who	WP
37681	3655	4	reads	read	VBZ
37681	3655	5	this	this	DT
37681	3655	6	book	book	NN
37681	3655	7	will	will	MD
37681	3655	8	gain	gain	VB
37681	3655	9	a	a	DT
37681	3655	10	new	new	JJ
37681	3655	11	sense	sense	NN
37681	3655	12	of	of	IN
37681	3655	13	duty	duty	NN
37681	3655	14	in	in	IN
37681	3655	15	matters	matter	NNS
37681	3655	16	of	of	IN
37681	3655	17	hygiene	hygiene	NN
37681	3655	18	and	and	CC
37681	3655	19	sanitation	sanitation	NN
37681	3655	20	.	.	.
37681	3656	1	=	=	NFP
37681	3656	2	Civics	Civics	NNP
37681	3656	3	and	and	CC
37681	3656	4	Health	Health	NNP
37681	3656	5	is	be	VBZ
37681	3656	6	enthrallingly	enthrallingly	RB
37681	3656	7	interesting	interesting	JJ
37681	3656	8	.	.	.
37681	3657	1	It	-PRON-	PRP
37681	3657	2	is	be	VBZ
37681	3657	3	humanized	humanize	VBN
37681	3657	4	sociology.=	sociology.=	JJ
37681	3657	5	Cleaning	clean	VBG
37681	3657	6	up	up	RP
37681	3657	7	children	child	NNS
37681	3657	8	by	by	IN
37681	3657	9	scientific	scientific	JJ
37681	3657	10	illumination	illumination	NN
37681	3657	11	will	will	MD
37681	3657	12	appeal	appeal	VB
37681	3657	13	to	to	IN
37681	3657	14	every	every	DT
37681	3657	15	father	father	NN
37681	3657	16	and	and	CC
37681	3657	17	mother	mother	NN
37681	3657	18	,	,	,
37681	3657	19	every	every	DT
37681	3657	20	child	child	NN
37681	3657	21	lover	lover	NN
37681	3657	22	who	who	WP
37681	3657	23	has	have	VBZ
37681	3657	24	any	any	DT
37681	3657	25	patriotism	patriotism	NN
37681	3657	26	or	or	CC
37681	3657	27	desire	desire	NN
37681	3657	28	to	to	TO
37681	3657	29	learn	learn	VB
37681	3657	30	how	how	WRB
37681	3657	31	we	-PRON-	PRP
37681	3657	32	as	as	IN
37681	3657	33	a	a	DT
37681	3657	34	people	people	NNS
37681	3657	35	are	be	VBP
37681	3657	36	to	to	TO
37681	3657	37	make	make	VB
37681	3657	38	moral	moral	JJ
37681	3657	39	-	-	HYPH
37681	3657	40	reform	reform	NN
37681	3657	41	agitations	agitation	NNS
37681	3657	42	fruitful	fruitful	JJ
37681	3657	43	through	through	IN
37681	3657	44	health	health	NN
37681	3657	45	of	of	IN
37681	3657	46	American	american	JJ
37681	3657	47	children	child	NNS
37681	3657	48	,	,	,
37681	3657	49	and	and	CC
37681	3657	50	so	so	RB
37681	3657	51	establish	establish	VB
37681	3657	52	health	health	NN
37681	3657	53	of	of	IN
37681	3657	54	national	national	JJ
37681	3657	55	life.--_Boston	life.--_Boston	NNP
37681	3657	56	Transcript	Transcript	NNP
37681	3657	57	.	.	.
37681	3657	58	_	_	NNP
37681	3657	59	This	this	DT
37681	3657	60	is	be	VBZ
37681	3657	61	one	one	CD
37681	3657	62	of	of	IN
37681	3657	63	the	the	DT
37681	3657	64	books	book	NNS
37681	3657	65	=	=	NFP
37681	3657	66	we	-PRON-	PRP
37681	3657	67	wish	wish	VBP
37681	3657	68	the	the	DT
37681	3657	69	law	law	NN
37681	3657	70	required	require	VBD
37681	3657	71	every	every	DT
37681	3657	72	citizen	citizen	NN
37681	3657	73	to	to	TO
37681	3657	74	have	have	VB
37681	3657	75	in	in	IN
37681	3657	76	his	-PRON-	PRP$
37681	3657	77	house	house	NN
37681	3657	78	and	and	CC
37681	3657	79	to	to	TO
37681	3657	80	know	know	VB
37681	3657	81	by	by	IN
37681	3657	82	heart=.	heart=.	NNP
37681	3658	1	Then	then	RB
37681	3658	2	,	,	,
37681	3658	3	indeed	indeed	RB
37681	3658	4	,	,	,
37681	3658	5	mankind	mankind	NN
37681	3658	6	would	would	MD
37681	3658	7	have	have	VB
37681	3658	8	made	make	VBN
37681	3658	9	an	an	DT
37681	3658	10	immense	immense	JJ
37681	3658	11	stride	stride	NN
37681	3658	12	forward.--_Chicago	forward.--_Chicago	NNP
37681	3658	13	Medical	Medical	NNP
37681	3658	14	Recorder	Recorder	NNP
37681	3658	15	.	.	.
37681	3658	16	_	_	NNP
37681	3658	17	=	=	NFP
37681	3658	18	The	the	DT
37681	3658	19	book	book	NN
37681	3658	20	is	be	VBZ
37681	3658	21	alive	alive	JJ
37681	3658	22	from	from	IN
37681	3658	23	cover	cover	NN
37681	3658	24	to	to	IN
37681	3658	25	cover.=	cover.=	NNP
37681	3658	26	It	-PRON-	PRP
37681	3658	27	breathes	breathe	VBZ
37681	3658	28	reform	reform	NN
37681	3658	29	but	but	CC
37681	3658	30	not	not	RB
37681	3658	31	of	of	IN
37681	3658	32	the	the	DT
37681	3658	33	platform	platform	NN
37681	3658	34	variety	variety	NN
37681	3658	35	.	.	.
37681	3659	1	It	-PRON-	PRP
37681	3659	2	abounds	abound	VBZ
37681	3659	3	in	in	IN
37681	3659	4	ugly	ugly	JJ
37681	3659	5	facts	fact	NNS
37681	3659	6	but	but	CC
37681	3659	7	superabounds	superabound	NNS
37681	3659	8	in	in	IN
37681	3659	9	the	the	DT
37681	3659	10	statement	statement	NN
37681	3659	11	of	of	IN
37681	3659	12	best	good	JJS
37681	3659	13	methods	method	NNS
37681	3659	14	of	of	IN
37681	3659	15	getting	get	VBG
37681	3659	16	rid	rid	VBN
37681	3659	17	of	of	IN
37681	3659	18	this	this	DT
37681	3659	19	ugliness	ugliness	NN
37681	3659	20	.	.	.
37681	3660	1	As	as	IN
37681	3660	2	claimed	claim	VBN
37681	3660	3	by	by	IN
37681	3660	4	the	the	DT
37681	3660	5	publishers	publisher	NNS
37681	3660	6	,	,	,
37681	3660	7	it	-PRON-	PRP
37681	3660	8	is	be	VBZ
37681	3660	9	preëminently	preëminently	RB
37681	3660	10	a	a	DT
37681	3660	11	book	book	NN
37681	3660	12	on	on	IN
37681	3660	13	"	"	``
37681	3660	14	getting	get	VBG
37681	3660	15	things	thing	NNS
37681	3660	16	done	do	VBN
37681	3660	17	.	.	.
37681	3660	18	"	"	''
37681	3661	1	--_Hygiene	--_Hygiene	NNP
37681	3661	2	and	and	CC
37681	3661	3	Physical	Physical	NNP
37681	3661	4	Education	Education	NNP
37681	3661	5	_	_	NNP
37681	3661	6	,	,	,
37681	3661	7	Springfield	Springfield	NNP
37681	3661	8	,	,	,
37681	3661	9	Mass.	Massachusetts	NNP
37681	3662	1	GINN	GINN	NNP
37681	3662	2	AND	and	CC
37681	3662	3	COMPANY	COMPANY	NNP
37681	3662	4	Publishers	Publishers	NNPS
37681	3662	5	Transcribers	Transcribers	NNP
37681	3662	6	notes	note	VBZ
37681	3662	7	On	on	IN
37681	3662	8	page	page	NN
37681	3662	9	30	30	CD
37681	3662	10	:	:	:
37681	3662	11	Pythagoras	Pythagoras	NNP
37681	3662	12	fled	flee	VBD
37681	3662	13	to	to	IN
37681	3662	14	Megapontum	Megapontum	NNP
37681	3662	15	has	have	VBZ
37681	3662	16	been	be	VBN
37681	3662	17	left	leave	VBN
37681	3662	18	as	as	IN
37681	3662	19	printed	print	VBN
37681	3662	20	,	,	,
37681	3662	21	though	though	IN
37681	3662	22	the	the	DT
37681	3662	23	author	author	NN
37681	3662	24	probably	probably	RB
37681	3662	25	meant	mean	VBD
37681	3662	26	Metapontum	Metapontum	NNP
37681	3662	27	.	.	.
37681	3663	1	On	on	IN
37681	3663	2	page	page	NN
37681	3663	3	269	269	CD
37681	3663	4	:	:	SYM
37681	3663	5	100	100	CD
37681	3663	6	B.C.	B.C.	NNS
37681	3664	1	has	have	VBZ
37681	3664	2	been	be	VBN
37681	3664	3	left	leave	VBN
37681	3664	4	as	as	IN
37681	3664	5	it	-PRON-	PRP
37681	3664	6	was	be	VBD
37681	3664	7	printed	print	VBN
37681	3664	8	,	,	,
37681	3664	9	though	though	IN
37681	3664	10	it	-PRON-	PRP
37681	3664	11	is	be	VBZ
37681	3664	12	probably	probably	RB
37681	3664	13	a	a	DT
37681	3664	14	typo	typo	NN
37681	3664	15	for	for	IN
37681	3664	16	100	100	CD
37681	3664	17	A.D.	A.D.	NNP