id sid tid token lemma pos A47139 1 1 An an DT A47139 1 2 essay essay NN A47139 1 3 for for IN A47139 1 4 the the DT A47139 1 5 discovery discovery NN A47139 1 6 of of IN A47139 1 7 some some DT A47139 1 8 new new JJ A47139 1 9 geometrical geometrical JJ A47139 1 10 problems problem NNS A47139 1 11 ( ( -LRB- A47139 1 12 judged judge VBN A47139 1 13 by by IN A47139 1 14 some some DT A47139 1 15 learned learn VBN A47139 1 16 men man NNS A47139 1 17 , , , A47139 1 18 impracticable impracticable JJ A47139 1 19 ) ) -RRB- A47139 1 20 concerning concern VBG A47139 1 21 angular angular JJ A47139 1 22 sections section NNS A47139 1 23 , , , A47139 1 24 beginning begin VBG A47139 1 25 with with IN A47139 1 26 the the DT A47139 1 27 geometrical geometrical JJ A47139 1 28 trisection trisection NN A47139 1 29 of of IN A47139 1 30 any any DT A47139 1 31 right right JJ A47139 1 32 lined line VBN A47139 1 33 angle angle NN A47139 1 34 , , , A47139 1 35 by by IN A47139 1 36 plain plain JJ A47139 1 37 geometry geometry NN A47139 1 38 of of IN A47139 1 39 right right JJ A47139 1 40 lines line NNS A47139 1 41 and and CC A47139 1 42 arches arch NNS A47139 1 43 of of IN A47139 1 44 circles circle NNS A47139 1 45 , , , A47139 1 46 with with IN A47139 1 47 rule rule NN A47139 1 48 and and CC A47139 1 49 compass compass VB A47139 1 50 only only RB A47139 1 51 , , , A47139 1 52 with with IN A47139 1 53 out out IN A47139 1 54 all all DT A47139 1 55 conick conick NN A47139 1 56 sections section NNS A47139 1 57 , , , A47139 1 58 and and CC A47139 1 59 cubick cubick NN A47139 1 60 æquations æquation NNS A47139 1 61 . . . A47139 2 1 Whether whether IN A47139 2 2 the the DT A47139 2 3 following follow VBG A47139 2 4 praxis praxis NN A47139 2 5 , , , A47139 2 6 and and CC A47139 2 7 apparent apparent JJ A47139 2 8 demonstration demonstration NN A47139 2 9 thereof thereof RB A47139 2 10 doth doth NNP A47139 2 11 not not RB A47139 2 12 only only RB A47139 2 13 make make VBP A47139 2 14 it -PRON- PRP A47139 2 15 practicable practicable JJ A47139 2 16 , , , A47139 2 17 but but CC A47139 2 18 easie easie VB A47139 2 19 to to IN A47139 2 20 the the DT A47139 2 21 understanding understanding NN A47139 2 22 of of IN A47139 2 23 a a DT A47139 2 24 tiro tiro NN A47139 2 25 , , , A47139 2 26 who who WP A47139 2 27 but but CC A47139 2 28 understands understand VBZ A47139 2 29 a a DT A47139 2 30 little little JJ A47139 2 31 in in IN A47139 2 32 true true JJ A47139 2 33 geometrical geometrical JJ A47139 2 34 learning learning NN A47139 2 35 . . . A47139 3 1 Which which WDT A47139 3 2 layeth layeth VBD A47139 3 3 a a DT A47139 3 4 foundation foundation NN A47139 3 5 of of IN A47139 3 6 a a DT A47139 3 7 plain plain JJ A47139 3 8 method method NN A47139 3 9 how how WRB A47139 3 10 to to TO A47139 3 11 sect sect VB A47139 3 12 any any DT A47139 3 13 angle angle NN A47139 3 14 into into IN A47139 3 15 any any DT A47139 3 16 other other JJ A47139 3 17 number number NN A47139 3 18 of of IN A47139 3 19 parts part NNS A47139 3 20 required require VBN A47139 3 21 , , , A47139 3 22 even even RB A47139 3 23 as as IN A47139 3 24 4 4 CD A47139 3 25 . . . A47139 4 1 6 6 CD A47139 4 2 . . . A47139 5 1 8 8 LS A47139 5 2 . . . A47139 6 1 10 10 CD A47139 6 2 ; ; : A47139 6 3 or or CC A47139 6 4 uneven uneven RB A47139 6 5 , , , A47139 6 6 as as IN A47139 6 7 5 5 CD A47139 6 8 . . . A47139 7 1 7 7 LS A47139 7 2 . . . A47139 8 1 9 9 CD A47139 8 2 . . . A47139 9 1 11 11 CD A47139 9 2 . . . A47139 10 1 & & CC A47139 10 2 c. c. NNP A47139 10 3 As as IN A47139 10 4 also also RB A47139 10 5 to to TO A47139 10 6 divide divide VB A47139 10 7 a a DT A47139 10 8 circle circle NN A47139 10 9 into into IN A47139 10 10 any any DT A47139 10 11 number number NN A47139 10 12 even even RB A47139 10 13 , , , A47139 10 14 or or CC A47139 10 15 uneven uneven JJ A47139 10 16 of of IN A47139 10 17 equal equal JJ A47139 10 18 parts part NNS A47139 10 19 . . . A47139 11 1 All all DT A47139 11 2 which which WDT A47139 11 3 have have VBP A47139 11 4 great great JJ A47139 11 5 uses use NNS A47139 11 6 in in IN A47139 11 7 the the DT A47139 11 8 improvement improvement NN A47139 11 9 of of IN A47139 11 10 the the DT A47139 11 11 mathematical mathematical JJ A47139 11 12 sciences science NNS A47139 11 13 , , , A47139 11 14 some some DT A47139 11 15 of of IN A47139 11 16 which which WDT A47139 11 17 are be VBP A47139 11 18 here here RB A47139 11 19 specified specify VBN A47139 11 20 . . . A47139 12 1 Proposed propose VBN A47139 12 2 and and CC A47139 12 3 submitted submit VBN A47139 12 4 to to IN A47139 12 5 the the DT A47139 12 6 impartial impartial JJ A47139 12 7 tryal tryal NN A47139 12 8 and and CC A47139 12 9 examination examination NN A47139 12 10 of of IN A47139 12 11 the the DT A47139 12 12 right right JJ A47139 12 13 reason reason NN A47139 12 14 of of IN A47139 12 15 such such JJ A47139 12 16 artises artise NNS A47139 12 17 , , , A47139 12 18 to to IN A47139 12 19 whose whose WP$ A47139 12 20 hands hand NNS A47139 12 21 it -PRON- PRP A47139 12 22 may may MD A47139 12 23 come come VB A47139 12 24 . . . A47139 13 1 By by IN A47139 13 2 G.K. G.K. NNP A47139 13 3 Keith Keith NNP A47139 13 4 , , , A47139 13 5 George George NNP A47139 13 6 , , , A47139 13 7 1639?-1716 1639?-1716 CD A47139 13 8 . . . A47139 14 1 1697 1697 CD A47139 14 2 Approx Approx NNP A47139 14 3 . . . A47139 15 1 27 27 CD A47139 15 2 KB kb NN A47139 15 3 of of IN A47139 15 4 XML xml NN A47139 15 5 - - HYPH A47139 15 6 encoded encode VBN A47139 15 7 text text NN A47139 15 8 transcribed transcribed NNP A47139 15 9 from from IN A47139 15 10 11 11 CD A47139 15 11 1-bit 1-bit CD A47139 15 12 group group NN A47139 15 13 - - HYPH A47139 15 14 IV IV NNP A47139 15 15 TIFF TIFF NNP A47139 15 16 page page NN A47139 15 17 images image NNS A47139 15 18 . . . A47139 16 1 Text Text NNP A47139 16 2 Creation Creation NNP A47139 16 3 Partnership Partnership NNP A47139 16 4 , , , A47139 16 5 Ann Ann NNP A47139 16 6 Arbor Arbor NNP A47139 16 7 , , , A47139 16 8 MI MI NNP A47139 16 9 ; ; : A47139 16 10 Oxford Oxford NNP A47139 16 11 ( ( -LRB- A47139 16 12 UK UK NNP A47139 16 13 ) ) -RRB- A47139 16 14 : : : A47139 16 15 2005 2005 CD A47139 16 16 - - SYM A47139 16 17 12 12 CD A47139 16 18 ( ( -LRB- A47139 16 19 EEBO EEBO NNP A47139 16 20 - - HYPH A47139 16 21 TCP TCP NNP A47139 16 22 Phase Phase NNP A47139 16 23 1 1 CD A47139 16 24 ) ) -RRB- A47139 16 25 . . . A47139 17 1 A47139 A47139 NNP A47139 17 2 Wing Wing NNP A47139 17 3 K160 K160 NNP A47139 17 4 ESTC ESTC NNP A47139 17 5 R221663 R221663 NNP A47139 17 6 99832942 99832942 CD A47139 17 7 99832942 99832942 CD A47139 17 8 37417 37417 CD A47139 17 9 This this DT A47139 17 10 keyboarded keyboarded JJ A47139 17 11 and and CC A47139 17 12 encoded encode VBD A47139 17 13 edition edition NN A47139 17 14 of of IN A47139 17 15 the the DT A47139 17 16 work work NN A47139 17 17 described describe VBN A47139 17 18 above above RB A47139 17 19 is be VBZ A47139 17 20 co co VBN A47139 17 21 - - VBN A47139 17 22 owned own VBN A47139 17 23 by by IN A47139 17 24 the the DT A47139 17 25 institutions institution NNS A47139 17 26 providing provide VBG A47139 17 27 financial financial JJ A47139 17 28 support support NN A47139 17 29 to to IN A47139 17 30 the the DT A47139 17 31 Early early JJ A47139 17 32 English English NNP A47139 17 33 Books Books NNPS A47139 17 34 Online Online NNP A47139 17 35 Text Text NNP A47139 17 36 Creation Creation NNP A47139 17 37 Partnership Partnership NNP A47139 17 38 . . . A47139 18 1 This this DT A47139 18 2 Phase Phase NNP A47139 18 3 I -PRON- PRP A47139 18 4 text text NN A47139 18 5 is be VBZ A47139 18 6 available available JJ A47139 18 7 for for IN A47139 18 8 reuse reuse NN A47139 18 9 , , , A47139 18 10 according accord VBG A47139 18 11 to to IN A47139 18 12 the the DT A47139 18 13 terms term NNS A47139 18 14 of of IN A47139 18 15 Creative Creative NNP A47139 18 16 Commons Commons NNPS A47139 18 17 0 0 CD A47139 18 18 1.0 1.0 CD A47139 18 19 Universal Universal NNP A47139 18 20 . . . A47139 19 1 The the DT A47139 19 2 text text NN A47139 19 3 can can MD A47139 19 4 be be VB A47139 19 5 copied copy VBN A47139 19 6 , , , A47139 19 7 modified modify VBN A47139 19 8 , , , A47139 19 9 distributed distribute VBN A47139 19 10 and and CC A47139 19 11 performed perform VBN A47139 19 12 , , , A47139 19 13 even even RB A47139 19 14 for for IN A47139 19 15 commercial commercial JJ A47139 19 16 purposes purpose NNS A47139 19 17 , , , A47139 19 18 all all DT A47139 19 19 without without IN A47139 19 20 asking ask VBG A47139 19 21 permission permission NN A47139 19 22 . . . A47139 20 1 Early early JJ A47139 20 2 English english JJ A47139 20 3 books book NNS A47139 20 4 online online RB A47139 20 5 . . . A47139 21 1 ( ( -LRB- A47139 21 2 EEBO eebo NN A47139 21 3 - - HYPH A47139 21 4 TCP TCP NNP A47139 21 5 ; ; : A47139 21 6 phase phase NN A47139 21 7 1 1 CD A47139 21 8 , , , A47139 21 9 no no UH A47139 21 10 . . . A47139 22 1 A47139 A47139 NNP A47139 22 2 ) ) -RRB- A47139 22 3 Transcribed Transcribed NNP A47139 22 4 from from IN A47139 22 5 : : : A47139 22 6 ( ( -LRB- A47139 22 7 Early early JJ A47139 22 8 English english JJ A47139 22 9 Books book NNS A47139 22 10 Online online RB A47139 22 11 ; ; , A47139 22 12 image image NN A47139 22 13 set set NN A47139 22 14 37417 37417 CD A47139 22 15 ) ) -RRB- A47139 22 16 Images image NNS A47139 22 17 scanned scan VBN A47139 22 18 from from IN A47139 22 19 microfilm microfilm NN A47139 22 20 : : : A47139 22 21 ( ( -LRB- A47139 22 22 Early early JJ A47139 22 23 English english JJ A47139 22 24 books book NNS A47139 22 25 , , , A47139 22 26 1641 1641 CD A47139 22 27 - - SYM A47139 22 28 1700 1700 CD A47139 22 29 ; ; : A47139 22 30 2188:04 2188:04 LS A47139 22 31 ) ) -RRB- A47139 22 32 An an DT A47139 22 33 essay essay NN A47139 22 34 for for IN A47139 22 35 the the DT A47139 22 36 discovery discovery NN A47139 22 37 of of IN A47139 22 38 some some DT A47139 22 39 new new JJ A47139 22 40 geometrical geometrical JJ A47139 22 41 problems problem NNS A47139 22 42 ( ( -LRB- A47139 22 43 judged judge VBN A47139 22 44 by by IN A47139 22 45 some some DT A47139 22 46 learned learn VBN A47139 22 47 men man NNS A47139 22 48 , , , A47139 22 49 impracticable impracticable JJ A47139 22 50 ) ) -RRB- A47139 22 51 concerning concern VBG A47139 22 52 angular angular JJ A47139 22 53 sections section NNS A47139 22 54 , , , A47139 22 55 beginning begin VBG A47139 22 56 with with IN A47139 22 57 the the DT A47139 22 58 geometrical geometrical JJ A47139 22 59 trisection trisection NN A47139 22 60 of of IN A47139 22 61 any any DT A47139 22 62 right right JJ A47139 22 63 lined line VBN A47139 22 64 angle angle NN A47139 22 65 , , , A47139 22 66 by by IN A47139 22 67 plain plain JJ A47139 22 68 geometry geometry NN A47139 22 69 of of IN A47139 22 70 right right JJ A47139 22 71 lines line NNS A47139 22 72 and and CC A47139 22 73 arches arch NNS A47139 22 74 of of IN A47139 22 75 circles circle NNS A47139 22 76 , , , A47139 22 77 with with IN A47139 22 78 rule rule NN A47139 22 79 and and CC A47139 22 80 compass compass VB A47139 22 81 only only RB A47139 22 82 , , , A47139 22 83 with with IN A47139 22 84 out out IN A47139 22 85 all all DT A47139 22 86 conick conick NN A47139 22 87 sections section NNS A47139 22 88 , , , A47139 22 89 and and CC A47139 22 90 cubick cubick NN A47139 22 91 æquations æquation NNS A47139 22 92 . . . A47139 23 1 Whether whether IN A47139 23 2 the the DT A47139 23 3 following follow VBG A47139 23 4 praxis praxis NN A47139 23 5 , , , A47139 23 6 and and CC A47139 23 7 apparent apparent JJ A47139 23 8 demonstration demonstration NN A47139 23 9 thereof thereof RB A47139 23 10 doth doth NNP A47139 23 11 not not RB A47139 23 12 only only RB A47139 23 13 make make VBP A47139 23 14 it -PRON- PRP A47139 23 15 practicable practicable JJ A47139 23 16 , , , A47139 23 17 but but CC A47139 23 18 easie easie VB A47139 23 19 to to IN A47139 23 20 the the DT A47139 23 21 understanding understanding NN A47139 23 22 of of IN A47139 23 23 a a DT A47139 23 24 tiro tiro NN A47139 23 25 , , , A47139 23 26 who who WP A47139 23 27 but but CC A47139 23 28 understands understand VBZ A47139 23 29 a a DT A47139 23 30 little little JJ A47139 23 31 in in IN A47139 23 32 true true JJ A47139 23 33 geometrical geometrical JJ A47139 23 34 learning learning NN A47139 23 35 . . . A47139 24 1 Which which WDT A47139 24 2 layeth layeth VBD A47139 24 3 a a DT A47139 24 4 foundation foundation NN A47139 24 5 of of IN A47139 24 6 a a DT A47139 24 7 plain plain JJ A47139 24 8 method method NN A47139 24 9 how how WRB A47139 24 10 to to TO A47139 24 11 sect sect VB A47139 24 12 any any DT A47139 24 13 angle angle NN A47139 24 14 into into IN A47139 24 15 any any DT A47139 24 16 other other JJ A47139 24 17 number number NN A47139 24 18 of of IN A47139 24 19 parts part NNS A47139 24 20 required require VBN A47139 24 21 , , , A47139 24 22 even even RB A47139 24 23 as as IN A47139 24 24 4 4 CD A47139 24 25 . . . A47139 25 1 6 6 CD A47139 25 2 . . . A47139 26 1 8 8 LS A47139 26 2 . . . A47139 27 1 10 10 CD A47139 27 2 ; ; : A47139 27 3 or or CC A47139 27 4 uneven uneven RB A47139 27 5 , , , A47139 27 6 as as IN A47139 27 7 5 5 CD A47139 27 8 . . . A47139 28 1 7 7 LS A47139 28 2 . . . A47139 29 1 9 9 CD A47139 29 2 . . . A47139 30 1 11 11 CD A47139 30 2 . . . A47139 31 1 & & CC A47139 31 2 c. c. NNP A47139 31 3 As as IN A47139 31 4 also also RB A47139 31 5 to to TO A47139 31 6 divide divide VB A47139 31 7 a a DT A47139 31 8 circle circle NN A47139 31 9 into into IN A47139 31 10 any any DT A47139 31 11 number number NN A47139 31 12 even even RB A47139 31 13 , , , A47139 31 14 or or CC A47139 31 15 uneven uneven JJ A47139 31 16 of of IN A47139 31 17 equal equal JJ A47139 31 18 parts part NNS A47139 31 19 . . . A47139 32 1 All all DT A47139 32 2 which which WDT A47139 32 3 have have VBP A47139 32 4 great great JJ A47139 32 5 uses use NNS A47139 32 6 in in IN A47139 32 7 the the DT A47139 32 8 improvement improvement NN A47139 32 9 of of IN A47139 32 10 the the DT A47139 32 11 mathematical mathematical JJ A47139 32 12 sciences science NNS A47139 32 13 , , , A47139 32 14 some some DT A47139 32 15 of of IN A47139 32 16 which which WDT A47139 32 17 are be VBP A47139 32 18 here here RB A47139 32 19 specified specify VBN A47139 32 20 . . . A47139 33 1 Proposed propose VBN A47139 33 2 and and CC A47139 33 3 submitted submit VBN A47139 33 4 to to IN A47139 33 5 the the DT A47139 33 6 impartial impartial JJ A47139 33 7 tryal tryal NN A47139 33 8 and and CC A47139 33 9 examination examination NN A47139 33 10 of of IN A47139 33 11 the the DT A47139 33 12 right right JJ A47139 33 13 reason reason NN A47139 33 14 of of IN A47139 33 15 such such JJ A47139 33 16 artises artise NNS A47139 33 17 , , , A47139 33 18 to to IN A47139 33 19 whose whose WP$ A47139 33 20 hands hand NNS A47139 33 21 it -PRON- PRP A47139 33 22 may may MD A47139 33 23 come come VB A47139 33 24 . . . A47139 34 1 By by IN A47139 34 2 G.K. G.K. NNP A47139 34 3 Keith Keith NNP A47139 34 4 , , , A47139 34 5 George George NNP A47139 34 6 , , , A47139 34 7 1639?-1716 1639?-1716 CD A47139 34 8 . . . A47139 35 1 12 12 CD A47139 35 2 p. p. NN A47139 35 3 , , , A47139 35 4 [ [ -LRB- A47139 35 5 4 4 CD A47139 35 6 ] ] -RRB- A47139 35 7 leaves leave NNS A47139 35 8 of of IN A47139 35 9 plates plate NNS A47139 35 10 : : : A47139 35 11 ill ill NNP A47139 35 12 . . . A47139 35 13 printed printed NNP A47139 35 14 1697 1697 CD A47139 35 15 . . . A47139 36 1 And and CC A47139 36 2 to to TO A47139 36 3 be be VB A47139 36 4 sold sell VBN A47139 36 5 by by IN A47139 36 6 the the DT A47139 36 7 author author NN A47139 36 8 , , , A47139 36 9 at at IN A47139 36 10 his -PRON- PRP$ A47139 36 11 house house NN A47139 36 12 in in IN A47139 36 13 Pudding Pudding NNP A47139 36 14 - - HYPH A47139 36 15 Lane Lane NNP A47139 36 16 , , , A47139 36 17 at at IN A47139 36 18 the the DT A47139 36 19 sign sign NN A47139 36 20 of of IN A47139 36 21 he -PRON- PRP A47139 36 22 [ [ -LRB- A47139 36 23 sic sic NN A47139 36 24 ] ] -RRB- A47139 36 25 Golden Golden NNP A47139 36 26 - - HYPH A47139 36 27 Ball Ball NNP A47139 36 28 , , , A47139 36 29 near near IN A47139 36 30 the the DT A47139 36 31 Monument Monument NNP A47139 36 32 ; ; : A47139 36 33 and and CC A47139 36 34 by by IN A47139 36 35 B. B. NNP A47139 36 36 Aylmer Aylmer NNP A47139 36 37 at at IN A47139 36 38 the the DT A47139 36 39 Three Three NNP A47139 36 40 Pigeons Pigeons NNPS A47139 36 41 over over RB A47139 36 42 against against IN A47139 36 43 the the DT A47139 36 44 Royal Royal NNP A47139 36 45 - - HYPH A47139 36 46 Exchange Exchange NNP A47139 36 47 , , , A47139 36 48 London London NNP A47139 36 49 : : : A47139 36 50 [ [ -LRB- A47139 36 51 1697 1697 CD A47139 36 52 ] ] -RRB- A47139 36 53 G.K. G.K. NNP A47139 36 54 = = SYM A47139 36 55 George George NNP A47139 36 56 Keith Keith NNP A47139 36 57 . . . A47139 37 1 Reproduction reproduction NN A47139 37 2 of of IN A47139 37 3 the the DT A47139 37 4 original original NN A47139 37 5 in in IN A47139 37 6 Dr. Dr. NNP A47139 37 7 Williams Williams NNP A47139 37 8 ' ' POS A47139 37 9 Library Library NNP A47139 37 10 , , , A47139 37 11 London London NNP A47139 37 12 . . . A47139 38 1 Created create VBN A47139 38 2 by by IN A47139 38 3 converting convert VBG A47139 38 4 TCP TCP NNP A47139 38 5 files file NNS A47139 38 6 to to IN A47139 38 7 TEI TEI NNP A47139 38 8 P5 P5 NNP A47139 38 9 using use VBG A47139 38 10 tcp2tei.xsl tcp2tei.xsl NN A47139 38 11 , , , A47139 38 12 TEI TEI NNP A47139 38 13 @ @ CC A47139 38 14 Oxford Oxford NNP A47139 38 15 . . . A47139 39 1 Re Re NNS A47139 39 2 - - VBN A47139 39 3 processed process VBN A47139 39 4 by by IN A47139 39 5 University University NNP A47139 39 6 of of IN A47139 39 7 Nebraska Nebraska NNP A47139 39 8 - - HYPH A47139 39 9 Lincoln Lincoln NNP A47139 39 10 and and CC A47139 39 11 Northwestern Northwestern NNP A47139 39 12 , , , A47139 39 13 with with IN A47139 39 14 changes change NNS A47139 39 15 to to TO A47139 39 16 facilitate facilitate VB A47139 39 17 morpho morpho NN A47139 39 18 - - HYPH A47139 39 19 syntactic syntactic JJ A47139 39 20 tagging tagging NN A47139 39 21 . . . A47139 40 1 Gap Gap NNP A47139 40 2 elements element NNS A47139 40 3 of of IN A47139 40 4 known know VBN A47139 40 5 extent extent NN A47139 40 6 have have VBP A47139 40 7 been be VBN A47139 40 8 transformed transform VBN A47139 40 9 into into IN A47139 40 10 placeholder placeholder NN A47139 40 11 characters character NNS A47139 40 12 or or CC A47139 40 13 elements element NNS A47139 40 14 to to TO A47139 40 15 simplify simplify VB A47139 40 16 the the DT A47139 40 17 filling filling NN A47139 40 18 in in RP A47139 40 19 of of IN A47139 40 20 gaps gap NNS A47139 40 21 by by IN A47139 40 22 user user NN A47139 40 23 contributors contributor NNS A47139 40 24 . . . A47139 41 1 EEBO EEBO NNP A47139 41 2 - - HYPH A47139 41 3 TCP TCP NNP A47139 41 4 is be VBZ A47139 41 5 a a DT A47139 41 6 partnership partnership NN A47139 41 7 between between IN A47139 41 8 the the DT A47139 41 9 Universities Universities NNPS A47139 41 10 of of IN A47139 41 11 Michigan Michigan NNP A47139 41 12 and and CC A47139 41 13 Oxford Oxford NNP A47139 41 14 and and CC A47139 41 15 the the DT A47139 41 16 publisher publisher NN A47139 41 17 ProQuest ProQuest NNP A47139 41 18 to to TO A47139 41 19 create create VB A47139 41 20 accurately accurately RB A47139 41 21 transcribed transcribe VBN A47139 41 22 and and CC A47139 41 23 encoded encode VBN A47139 41 24 texts text NNS A47139 41 25 based base VBN A47139 41 26 on on IN A47139 41 27 the the DT A47139 41 28 image image NN A47139 41 29 sets set NNS A47139 41 30 published publish VBN A47139 41 31 by by IN A47139 41 32 ProQuest ProQuest NNP A47139 41 33 via via IN A47139 41 34 their -PRON- PRP$ A47139 41 35 Early early JJ A47139 41 36 English english JJ A47139 41 37 Books book NNS A47139 41 38 Online Online NNP A47139 41 39 ( ( -LRB- A47139 41 40 EEBO EEBO NNP A47139 41 41 ) ) -RRB- A47139 41 42 database database NN A47139 41 43 ( ( -LRB- A47139 41 44 http://eebo.chadwyck.com http://eebo.chadwyck.com ADD A47139 41 45 ) ) -RRB- A47139 41 46 . . . A47139 42 1 The the DT A47139 42 2 general general JJ A47139 42 3 aim aim NN A47139 42 4 of of IN A47139 42 5 EEBO eebo NN A47139 42 6 - - HYPH A47139 42 7 TCP TCP NNP A47139 42 8 is be VBZ A47139 42 9 to to TO A47139 42 10 encode encode VB A47139 42 11 one one CD A47139 42 12 copy copy NN A47139 42 13 ( ( -LRB- A47139 42 14 usually usually RB A47139 42 15 the the DT A47139 42 16 first first JJ A47139 42 17 edition edition NN A47139 42 18 ) ) -RRB- A47139 42 19 of of IN A47139 42 20 every every DT A47139 42 21 monographic monographic JJ A47139 42 22 English English NNP A47139 42 23 - - HYPH A47139 42 24 language language NN A47139 42 25 title title NN A47139 42 26 published publish VBN A47139 42 27 between between IN A47139 42 28 1473 1473 CD A47139 42 29 and and CC A47139 42 30 1700 1700 CD A47139 42 31 available available JJ A47139 42 32 in in IN A47139 42 33 EEBO EEBO NNP A47139 42 34 . . . A47139 43 1 EEBO EEBO NNP A47139 43 2 - - HYPH A47139 43 3 TCP TCP NNP A47139 43 4 aimed aim VBN A47139 43 5 to to TO A47139 43 6 produce produce VB A47139 43 7 large large JJ A47139 43 8 quantities quantity NNS A47139 43 9 of of IN A47139 43 10 textual textual JJ A47139 43 11 data datum NNS A47139 43 12 within within IN A47139 43 13 the the DT A47139 43 14 usual usual JJ A47139 43 15 project project NN A47139 43 16 restraints restraint NNS A47139 43 17 of of IN A47139 43 18 time time NN A47139 43 19 and and CC A47139 43 20 funding funding NN A47139 43 21 , , , A47139 43 22 and and CC A47139 43 23 therefore therefore RB A47139 43 24 chose choose VBD A47139 43 25 to to TO A47139 43 26 create create VB A47139 43 27 diplomatic diplomatic JJ A47139 43 28 transcriptions transcription NNS A47139 43 29 ( ( -LRB- A47139 43 30 as as IN A47139 43 31 opposed oppose VBN A47139 43 32 to to IN A47139 43 33 critical critical JJ A47139 43 34 editions edition NNS A47139 43 35 ) ) -RRB- A47139 43 36 with with IN A47139 43 37 light light JJ A47139 43 38 - - HYPH A47139 43 39 touch touch NN A47139 43 40 , , , A47139 43 41 mainly mainly RB A47139 43 42 structural structural JJ A47139 43 43 encoding encoding NN A47139 43 44 based base VBN A47139 43 45 on on IN A47139 43 46 the the DT A47139 43 47 Text Text NNP A47139 43 48 Encoding Encoding NNP A47139 43 49 Initiative Initiative NNP A47139 43 50 ( ( -LRB- A47139 43 51 http://www.tei-c.org http://www.tei-c.org NFP A47139 43 52 ) ) -RRB- A47139 43 53 . . . A47139 44 1 The the DT A47139 44 2 EEBO EEBO NNP A47139 44 3 - - HYPH A47139 44 4 TCP TCP NNP A47139 44 5 project project NN A47139 44 6 was be VBD A47139 44 7 divided divide VBN A47139 44 8 into into IN A47139 44 9 two two CD A47139 44 10 phases phase NNS A47139 44 11 . . . A47139 45 1 The the DT A47139 45 2 25,363 25,363 CD A47139 45 3 texts text NNS A47139 45 4 created create VBN A47139 45 5 during during IN A47139 45 6 Phase Phase NNP A47139 45 7 1 1 CD A47139 45 8 of of IN A47139 45 9 the the DT A47139 45 10 project project NN A47139 45 11 have have VBP A47139 45 12 been be VBN A47139 45 13 released release VBN A47139 45 14 into into IN A47139 45 15 the the DT A47139 45 16 public public JJ A47139 45 17 domain domain NN A47139 45 18 as as IN A47139 45 19 of of IN A47139 45 20 1 1 CD A47139 45 21 January January NNP A47139 45 22 2015 2015 CD A47139 45 23 . . . A47139 46 1 Anyone anyone NN A47139 46 2 can can MD A47139 46 3 now now RB A47139 46 4 take take VB A47139 46 5 and and CC A47139 46 6 use use VB A47139 46 7 these these DT A47139 46 8 texts text NNS A47139 46 9 for for IN A47139 46 10 their -PRON- PRP$ A47139 46 11 own own JJ A47139 46 12 purposes purpose NNS A47139 46 13 , , , A47139 46 14 but but CC A47139 46 15 we -PRON- PRP A47139 46 16 respectfully respectfully RB A47139 46 17 request request VBP A47139 46 18 that that DT A47139 46 19 due due JJ A47139 46 20 credit credit NN A47139 46 21 and and CC A47139 46 22 attribution attribution NN A47139 46 23 is be VBZ A47139 46 24 given give VBN A47139 46 25 to to IN A47139 46 26 their -PRON- PRP$ A47139 46 27 original original JJ A47139 46 28 source source NN A47139 46 29 . . . A47139 47 1 Users user NNS A47139 47 2 should should MD A47139 47 3 be be VB A47139 47 4 aware aware JJ A47139 47 5 of of IN A47139 47 6 the the DT A47139 47 7 process process NN A47139 47 8 of of IN A47139 47 9 creating create VBG A47139 47 10 the the DT A47139 47 11 TCP TCP NNP A47139 47 12 texts text NNS A47139 47 13 , , , A47139 47 14 and and CC A47139 47 15 therefore therefore RB A47139 47 16 of of IN A47139 47 17 any any DT A47139 47 18 assumptions assumption NNS A47139 47 19 that that WDT A47139 47 20 can can MD A47139 47 21 be be VB A47139 47 22 made make VBN A47139 47 23 about about IN A47139 47 24 the the DT A47139 47 25 data datum NNS A47139 47 26 . . . A47139 48 1 Text text NN A47139 48 2 selection selection NN A47139 48 3 was be VBD A47139 48 4 based base VBN A47139 48 5 on on IN A47139 48 6 the the DT A47139 48 7 New New NNP A47139 48 8 Cambridge Cambridge NNP A47139 48 9 Bibliography Bibliography NNP A47139 48 10 of of IN A47139 48 11 English English NNP A47139 48 12 Literature Literature NNP A47139 48 13 ( ( -LRB- A47139 48 14 NCBEL NCBEL NNP A47139 48 15 ) ) -RRB- A47139 48 16 . . . A47139 49 1 If if IN A47139 49 2 an an DT A47139 49 3 author author NN A47139 49 4 ( ( -LRB- A47139 49 5 or or CC A47139 49 6 for for IN A47139 49 7 an an DT A47139 49 8 anonymous anonymous JJ A47139 49 9 work work NN A47139 49 10 , , , A47139 49 11 the the DT A47139 49 12 title title NN A47139 49 13 ) ) -RRB- A47139 49 14 appears appear VBZ A47139 49 15 in in IN A47139 49 16 NCBEL NCBEL NNP A47139 49 17 , , , A47139 49 18 then then RB A47139 49 19 their -PRON- PRP$ A47139 49 20 works work NNS A47139 49 21 are be VBP A47139 49 22 eligible eligible JJ A47139 49 23 for for IN A47139 49 24 inclusion inclusion NN A47139 49 25 . . . A47139 50 1 Selection selection NN A47139 50 2 was be VBD A47139 50 3 intended intend VBN A47139 50 4 to to TO A47139 50 5 range range VB A47139 50 6 over over RP A47139 50 7 a a DT A47139 50 8 wide wide JJ A47139 50 9 variety variety NN A47139 50 10 of of IN A47139 50 11 subject subject JJ A47139 50 12 areas area NNS A47139 50 13 , , , A47139 50 14 to to TO A47139 50 15 reflect reflect VB A47139 50 16 the the DT A47139 50 17 true true JJ A47139 50 18 nature nature NN A47139 50 19 of of IN A47139 50 20 the the DT A47139 50 21 print print NN A47139 50 22 record record NN A47139 50 23 of of IN A47139 50 24 the the DT A47139 50 25 period period NN A47139 50 26 . . . A47139 51 1 In in IN A47139 51 2 general general JJ A47139 51 3 , , , A47139 51 4 first first JJ A47139 51 5 editions edition NNS A47139 51 6 of of IN A47139 51 7 a a DT A47139 51 8 works work NNS A47139 51 9 in in IN A47139 51 10 English English NNP A47139 51 11 were be VBD A47139 51 12 prioritized prioritize VBN A47139 51 13 , , , A47139 51 14 although although IN A47139 51 15 there there EX A47139 51 16 are be VBP A47139 51 17 a a DT A47139 51 18 number number NN A47139 51 19 of of IN A47139 51 20 works work NNS A47139 51 21 in in IN A47139 51 22 other other JJ A47139 51 23 languages language NNS A47139 51 24 , , , A47139 51 25 notably notably RB A47139 51 26 Latin Latin NNP A47139 51 27 and and CC A47139 51 28 Welsh Welsh NNP A47139 51 29 , , , A47139 51 30 included include VBD A47139 51 31 and and CC A47139 51 32 sometimes sometimes RB A47139 51 33 a a DT A47139 51 34 second second JJ A47139 51 35 or or CC A47139 51 36 later later JJ A47139 51 37 edition edition NN A47139 51 38 of of IN A47139 51 39 a a DT A47139 51 40 work work NN A47139 51 41 was be VBD A47139 51 42 chosen choose VBN A47139 51 43 if if IN A47139 51 44 there there EX A47139 51 45 was be VBD A47139 51 46 a a DT A47139 51 47 compelling compelling JJ A47139 51 48 reason reason NN A47139 51 49 to to TO A47139 51 50 do do VB A47139 51 51 so so RB A47139 51 52 . . . A47139 52 1 Image image NN A47139 52 2 sets set NNS A47139 52 3 were be VBD A47139 52 4 sent send VBN A47139 52 5 to to IN A47139 52 6 external external JJ A47139 52 7 keying keying NN A47139 52 8 companies company NNS A47139 52 9 for for IN A47139 52 10 transcription transcription NN A47139 52 11 and and CC A47139 52 12 basic basic JJ A47139 52 13 encoding encoding NN A47139 52 14 . . . A47139 53 1 Quality quality JJ A47139 53 2 assurance assurance NN A47139 53 3 was be VBD A47139 53 4 then then RB A47139 53 5 carried carry VBN A47139 53 6 out out RP A47139 53 7 by by IN A47139 53 8 editorial editorial JJ A47139 53 9 teams team NNS A47139 53 10 in in IN A47139 53 11 Oxford Oxford NNP A47139 53 12 and and CC A47139 53 13 Michigan Michigan NNP A47139 53 14 . . . A47139 54 1 5 5 CD A47139 54 2 % % NN A47139 54 3 ( ( -LRB- A47139 54 4 or or CC A47139 54 5 5 5 CD A47139 54 6 pages page NNS A47139 54 7 , , , A47139 54 8 whichever whichever WDT A47139 54 9 is be VBZ A47139 54 10 the the DT A47139 54 11 greater great JJR A47139 54 12 ) ) -RRB- A47139 54 13 of of IN A47139 54 14 each each DT A47139 54 15 text text NN A47139 54 16 was be VBD A47139 54 17 proofread proofread NN A47139 54 18 for for IN A47139 54 19 accuracy accuracy NN A47139 54 20 and and CC A47139 54 21 those those DT A47139 54 22 which which WDT A47139 54 23 did do VBD A47139 54 24 not not RB A47139 54 25 meet meet VB A47139 54 26 QA qa NN A47139 54 27 standards standard NNS A47139 54 28 were be VBD A47139 54 29 returned return VBN A47139 54 30 to to IN A47139 54 31 the the DT A47139 54 32 keyers keyer NNS A47139 54 33 to to TO A47139 54 34 be be VB A47139 54 35 redone redone NN A47139 54 36 . . . A47139 55 1 After after IN A47139 55 2 proofreading proofreading NN A47139 55 3 , , , A47139 55 4 the the DT A47139 55 5 encoding encoding NN A47139 55 6 was be VBD A47139 55 7 enhanced enhance VBN A47139 55 8 and/or and/or CC A47139 55 9 corrected correct VBD A47139 55 10 and and CC A47139 55 11 characters character NNS A47139 55 12 marked mark VBN A47139 55 13 as as IN A47139 55 14 illegible illegible JJ A47139 55 15 were be VBD A47139 55 16 corrected correct VBN A47139 55 17 where where WRB A47139 55 18 possible possible JJ A47139 55 19 up up IN A47139 55 20 to to IN A47139 55 21 a a DT A47139 55 22 limit limit NN A47139 55 23 of of IN A47139 55 24 100 100 CD A47139 55 25 instances instance NNS A47139 55 26 per per IN A47139 55 27 text text NN A47139 55 28 . . . A47139 56 1 Any any DT A47139 56 2 remaining remain VBG A47139 56 3 illegibles illegible NNS A47139 56 4 were be VBD A47139 56 5 encoded encode VBN A47139 56 6 as as IN A47139 56 7 < < XX A47139 56 8 gap gap NN A47139 56 9 > > XX A47139 56 10 s s XX A47139 56 11 . . . A47139 57 1 Understanding understand VBG A47139 57 2 these these DT A47139 57 3 processes process NNS A47139 57 4 should should MD A47139 57 5 make make VB A47139 57 6 clear clear JJ A47139 57 7 that that IN A47139 57 8 , , , A47139 57 9 while while IN A47139 57 10 the the DT A47139 57 11 overall overall JJ A47139 57 12 quality quality NN A47139 57 13 of of IN A47139 57 14 TCP TCP NNP A47139 57 15 data datum NNS A47139 57 16 is be VBZ A47139 57 17 very very RB A47139 57 18 good good JJ A47139 57 19 , , , A47139 57 20 some some DT A47139 57 21 errors error NNS A47139 57 22 will will MD A47139 57 23 remain remain VB A47139 57 24 and and CC A47139 57 25 some some DT A47139 57 26 readable readable JJ A47139 57 27 characters character NNS A47139 57 28 will will MD A47139 57 29 be be VB A47139 57 30 marked mark VBN A47139 57 31 as as IN A47139 57 32 illegible illegible JJ A47139 57 33 . . . A47139 58 1 Users user NNS A47139 58 2 should should MD A47139 58 3 bear bear VB A47139 58 4 in in IN A47139 58 5 mind mind NN A47139 58 6 that that IN A47139 58 7 in in IN A47139 58 8 all all DT A47139 58 9 likelihood likelihood NN A47139 58 10 such such JJ A47139 58 11 instances instance NNS A47139 58 12 will will MD A47139 58 13 never never RB A47139 58 14 have have VB A47139 58 15 been be VBN A47139 58 16 looked look VBN A47139 58 17 at at IN A47139 58 18 by by IN A47139 58 19 a a DT A47139 58 20 TCP TCP NNP A47139 58 21 editor editor NN A47139 58 22 . . . A47139 59 1 The the DT A47139 59 2 texts text NNS A47139 59 3 were be VBD A47139 59 4 encoded encode VBN A47139 59 5 and and CC A47139 59 6 linked link VBN A47139 59 7 to to IN A47139 59 8 page page NN A47139 59 9 images image NNS A47139 59 10 in in IN A47139 59 11 accordance accordance NN A47139 59 12 with with IN A47139 59 13 level level NN A47139 59 14 4 4 CD A47139 59 15 of of IN A47139 59 16 the the DT A47139 59 17 TEI TEI NNP A47139 59 18 in in IN A47139 59 19 Libraries Libraries NNP A47139 59 20 guidelines guideline NNS A47139 59 21 . . . A47139 60 1 Copies copy NNS A47139 60 2 of of IN A47139 60 3 the the DT A47139 60 4 texts text NNS A47139 60 5 have have VBP A47139 60 6 been be VBN A47139 60 7 issued issue VBN A47139 60 8 variously variously RB A47139 60 9 as as IN A47139 60 10 SGML SGML NNP A47139 60 11 ( ( -LRB- A47139 60 12 TCP TCP NNP A47139 60 13 schema schema NN A47139 60 14 ; ; : A47139 60 15 ASCII ASCII NNP A47139 60 16 text text NN A47139 60 17 with with IN A47139 60 18 mnemonic mnemonic NNP A47139 60 19 sdata sdata NNP A47139 60 20 character character NNP A47139 60 21 entities entity NNS A47139 60 22 ) ) -RRB- A47139 60 23 ; ; : A47139 60 24 displayable displayable JJ A47139 60 25 XML xml NN A47139 60 26 ( ( -LRB- A47139 60 27 TCP TCP NNP A47139 60 28 schema schema NN A47139 60 29 ; ; : A47139 60 30 characters character NNS A47139 60 31 represented represent VBD A47139 60 32 either either CC A47139 60 33 as as IN A47139 60 34 UTF-8 UTF-8 NNP A47139 60 35 Unicode Unicode NNP A47139 60 36 or or CC A47139 60 37 text text NN A47139 60 38 strings string NNS A47139 60 39 within within IN A47139 60 40 braces brace NNS A47139 60 41 ) ) -RRB- A47139 60 42 ; ; : A47139 60 43 or or CC A47139 60 44 lossless lossless JJ A47139 60 45 XML xml NN A47139 60 46 ( ( -LRB- A47139 60 47 TEI TEI NNP A47139 60 48 P5 P5 NNP A47139 60 49 , , , A47139 60 50 characters character NNS A47139 60 51 represented represent VBD A47139 60 52 either either CC A47139 60 53 as as IN A47139 60 54 UTF-8 UTF-8 NNP A47139 60 55 Unicode Unicode NNP A47139 60 56 or or CC A47139 60 57 TEI TEI NNP A47139 60 58 g g NN A47139 60 59 elements element NNS A47139 60 60 ) ) -RRB- A47139 60 61 . . . A47139 61 1 Keying keying NN A47139 61 2 and and CC A47139 61 3 markup markup NN A47139 61 4 guidelines guideline NNS A47139 61 5 are be VBP A47139 61 6 available available JJ A47139 61 7 at at IN A47139 61 8 the the DT A47139 61 9 Text Text NNP A47139 61 10 Creation Creation NNP A47139 61 11 Partnership Partnership NNP A47139 61 12 web web NN A47139 61 13 site site NN A47139 61 14 . . . A47139 62 1 eng eng NNP A47139 62 2 Geometry Geometry NNP A47139 62 3 -- -- : A47139 62 4 Early early RB A47139 62 5 works work NNS A47139 62 6 to to IN A47139 62 7 1800 1800 CD A47139 62 8 . . . A47139 63 1 2005 2005 CD A47139 63 2 - - SYM A47139 63 3 05 05 CD A47139 63 4 TCP TCP NNP A47139 63 5 Assigned assign VBN A47139 63 6 for for IN A47139 63 7 keying keying NN A47139 63 8 and and CC A47139 63 9 markup markup NNP A47139 63 10 2005 2005 CD A47139 63 11 - - SYM A47139 63 12 06 06 CD A47139 63 13 Aptara Aptara NNP A47139 63 14 Keyed Keyed NNP A47139 63 15 and and CC A47139 63 16 coded code VBN A47139 63 17 from from IN A47139 63 18 ProQuest ProQuest NNP A47139 63 19 page page NN A47139 63 20 images image NNS A47139 63 21 2005 2005 CD A47139 63 22 - - SYM A47139 63 23 07 07 CD A47139 63 24 Mona Mona NNP A47139 63 25 Logarbo Logarbo NNP A47139 63 26 Sampled Sampled NNP A47139 63 27 and and CC A47139 63 28 proofread proofread JJ A47139 63 29 2005 2005 CD A47139 63 30 - - SYM A47139 63 31 07 07 CD A47139 63 32 Mona Mona NNP A47139 63 33 Logarbo Logarbo NNP A47139 63 34 Text Text NNP A47139 63 35 and and CC A47139 63 36 markup markup NN A47139 63 37 reviewed review VBD A47139 63 38 and and CC A47139 63 39 edited edit VBD A47139 63 40 2005 2005 CD A47139 63 41 - - SYM A47139 63 42 10 10 CD A47139 63 43 pfs pfs NN A47139 63 44 Batch Batch NNP A47139 63 45 review review NN A47139 63 46 ( ( -LRB- A47139 63 47 QC QC NNP A47139 63 48 ) ) -RRB- A47139 63 49 and and CC A47139 63 50 XML xml NN A47139 63 51 conversion conversion NN A47139 63 52 AN an DT A47139 63 53 ESSAY ESSAY NNP A47139 63 54 For for IN A47139 63 55 the the DT A47139 63 56 Discovery Discovery NNP A47139 63 57 of of IN A47139 63 58 Some some DT A47139 63 59 NEW NEW NNP A47139 63 60 Geometrical Geometrical NNP A47139 63 61 Problems Problems NNPS A47139 63 62 , , , A47139 63 63 ( ( -LRB- A47139 63 64 Judged judge VBN A47139 63 65 by by IN A47139 63 66 some some DT A47139 63 67 Learned learned JJ A47139 63 68 Men Men NNPS A47139 63 69 , , , A47139 63 70 Impracticable Impracticable NNP A47139 63 71 ) ) -RRB- A47139 63 72 Concerning concern VBG A47139 63 73 ANGULAR angular NN A47139 63 74 SECTIONS section NNS A47139 63 75 , , , A47139 63 76 Beginning begin VBG A47139 63 77 with with IN A47139 63 78 the the DT A47139 63 79 GEOMETRICAL GEOMETRICAL NNP A47139 63 80 TRISECTION TRISECTION NNP A47139 63 81 of of IN A47139 63 82 any any DT A47139 63 83 Right Right NNP A47139 63 84 Lined Lined NNP A47139 63 85 Angle Angle NNP A47139 63 86 , , , A47139 63 87 by by IN A47139 63 88 Plain Plain NNP A47139 63 89 Geometry Geometry NNP A47139 63 90 of of IN A47139 63 91 Right Right NNP A47139 63 92 Lines Lines NNPS A47139 63 93 and and CC A47139 63 94 Arches Arches NNPS A47139 63 95 of of IN A47139 63 96 Circles Circles NNP A47139 63 97 , , , A47139 63 98 With with IN A47139 63 99 RVLE RVLE NNP A47139 63 100 and and CC A47139 63 101 COMPASS COMPASS NNP A47139 63 102 only only RB A47139 63 103 , , , A47139 63 104 without without IN A47139 63 105 all all DT A47139 63 106 Conick Conick NNP A47139 63 107 Sections Sections NNPS A47139 63 108 , , , A47139 63 109 and and CC A47139 63 110 Cubick Cubick NNP A47139 63 111 Aequations Aequations NNPS A47139 63 112 . . . A47139 64 1 Whether whether IN A47139 64 2 the the DT A47139 64 3 following follow VBG A47139 64 4 Praxis Praxis NNP A47139 64 5 , , , A47139 64 6 and and CC A47139 64 7 apparent apparent JJ A47139 64 8 demonstration demonstration NN A47139 64 9 thereof thereof RB A47139 64 10 doth doth NNP A47139 64 11 not not RB A47139 64 12 only only RB A47139 64 13 make make VBP A47139 64 14 it -PRON- PRP A47139 64 15 Practicable practicable JJ A47139 64 16 , , , A47139 64 17 but but CC A47139 64 18 easie easie VB A47139 64 19 to to IN A47139 64 20 the the DT A47139 64 21 Understanding understanding NN A47139 64 22 of of IN A47139 64 23 a a DT A47139 64 24 Tiro Tiro NNP A47139 64 25 , , , A47139 64 26 who who WP A47139 64 27 but but CC A47139 64 28 understands understand VBZ A47139 64 29 a a DT A47139 64 30 little little JJ A47139 64 31 in in IN A47139 64 32 true true JJ A47139 64 33 Geometrical Geometrical NNP A47139 64 34 Learning Learning NNP A47139 64 35 . . . A47139 65 1 Which which WDT A47139 65 2 layeth layeth VBD A47139 65 3 a a DT A47139 65 4 Foundation Foundation NNP A47139 65 5 of of IN A47139 65 6 a a DT A47139 65 7 Plain Plain NNP A47139 65 8 Method Method NNP A47139 65 9 how how WRB A47139 65 10 to to IN A47139 65 11 Sect Sect NNP A47139 65 12 any any DT A47139 65 13 Angle Angle NNP A47139 65 14 into into IN A47139 65 15 any any DT A47139 65 16 other other JJ A47139 65 17 Number number NN A47139 65 18 of of IN A47139 65 19 Parts Parts NNPS A47139 65 20 required require VBN A47139 65 21 , , , A47139 65 22 Even even RB A47139 65 23 as as IN A47139 65 24 4 4 CD A47139 65 25 . . . A47139 66 1 6 6 CD A47139 66 2 . . . A47139 67 1 8 8 LS A47139 67 2 . . . A47139 68 1 10 10 CD A47139 68 2 ; ; : A47139 68 3 or or CC A47139 68 4 Vneven Vneven NNP A47139 68 5 , , , A47139 68 6 as as IN A47139 68 7 5 5 CD A47139 68 8 . . . A47139 69 1 7 7 LS A47139 69 2 . . . A47139 70 1 9 9 CD A47139 70 2 . . . A47139 71 1 11 11 CD A47139 71 2 . . . A47139 72 1 & & CC A47139 72 2 c. c. NNP A47139 72 3 As as IN A47139 72 4 also also RB A47139 72 5 to to TO A47139 72 6 divide divide VB A47139 72 7 a a DT A47139 72 8 Circle Circle NNP A47139 72 9 into into IN A47139 72 10 any any DT A47139 72 11 number number NN A47139 72 12 Even even RB A47139 72 13 , , , A47139 72 14 or or CC A47139 72 15 Vneven Vneven NNP A47139 72 16 of of IN A47139 72 17 equal equal JJ A47139 72 18 parts part NNS A47139 72 19 . . . A47139 73 1 All all DT A47139 73 2 which which WDT A47139 73 3 have have VBP A47139 73 4 great great JJ A47139 73 5 Uses use NNS A47139 73 6 in in IN A47139 73 7 the the DT A47139 73 8 Improvement improvement NN A47139 73 9 of of IN A47139 73 10 the the DT A47139 73 11 Mathematical Mathematical NNP A47139 73 12 Sciences Sciences NNPS A47139 73 13 , , , A47139 73 14 some some DT A47139 73 15 of of IN A47139 73 16 which which WDT A47139 73 17 are be VBP A47139 73 18 here here RB A47139 73 19 specified specify VBN A47139 73 20 . . . A47139 74 1 Proposed propose VBN A47139 74 2 and and CC A47139 74 3 Submitted submit VBN A47139 74 4 to to IN A47139 74 5 the the DT A47139 74 6 Impartial Impartial NNP A47139 74 7 Tryal Tryal NNP A47139 74 8 and and CC A47139 74 9 Examination Examination NNP A47139 74 10 of of IN A47139 74 11 the the DT A47139 74 12 Right Right NNP A47139 74 13 Reason Reason NNP A47139 74 14 of of IN A47139 74 15 such such JJ A47139 74 16 Artists Artists NNPS A47139 74 17 , , , A47139 74 18 to to IN A47139 74 19 whose whose WP$ A47139 74 20 Hands hand NNS A47139 74 21 it -PRON- PRP A47139 74 22 may may MD A47139 74 23 come come VB A47139 74 24 . . . A47139 75 1 By by IN A47139 75 2 G. G. NNP A47139 75 3 K. K. NNP A47139 75 4 London London NNP A47139 75 5 , , , A47139 75 6 Printed Printed NNP A47139 75 7 1697 1697 CD A47139 75 8 . . . A47139 76 1 And and CC A47139 76 2 to to TO A47139 76 3 be be VB A47139 76 4 Sold sell VBN A47139 76 5 by by IN A47139 76 6 the the DT A47139 76 7 Author author NN A47139 76 8 , , , A47139 76 9 at at IN A47139 76 10 his -PRON- PRP$ A47139 76 11 House House NNP A47139 76 12 in in IN A47139 76 13 Pudding Pudding NNP A47139 76 14 - - HYPH A47139 76 15 Lane Lane NNP A47139 76 16 , , , A47139 76 17 at at IN A47139 76 18 the the DT A47139 76 19 Sign Sign NNP A47139 76 20 of of IN A47139 76 21 he -PRON- PRP A47139 76 22 Golden Golden NNP A47139 76 23 - - HYPH A47139 76 24 Ball Ball NNP A47139 76 25 , , , A47139 76 26 near near IN A47139 76 27 the the DT A47139 76 28 Monument Monument NNP A47139 76 29 ; ; : A47139 76 30 And and CC A47139 76 31 by by IN A47139 76 32 B. B. NNP A47139 76 33 Aylmer Aylmer NNP A47139 76 34 at at IN A47139 76 35 the the DT A47139 76 36 Three Three NNP A47139 76 37 Pigeons Pigeons NNPS A47139 76 38 over over RB A47139 76 39 against against IN A47139 76 40 the the DT A47139 76 41 Royal Royal NNP A47139 76 42 - - HYPH A47139 76 43 Exchange Exchange NNP A47139 76 44 . . . A47139 77 1 Some some DT A47139 77 2 New New NNP A47139 77 3 Geometrical Geometrical NNP A47139 77 4 Problems Problems NNPS A47139 77 5 , , , A47139 77 6 & & CC A47139 77 7 c. c. NNP A47139 77 8 ALthough although IN A47139 77 9 the the DT A47139 77 10 Trisection Trisection NNP A47139 77 11 of of IN A47139 77 12 a a DT A47139 77 13 right right NN A47139 77 14 lined line VBN A47139 77 15 Angle Angle NNP A47139 77 16 and and CC A47139 77 17 also also RB A47139 77 18 its -PRON- PRP$ A47139 77 19 Section section NN A47139 77 20 into into IN A47139 77 21 any any DT A47139 77 22 parts part NNS A47139 77 23 required require VBN A47139 77 24 , , , A47139 77 25 to to IN A47139 77 26 a a DT A47139 77 27 true true JJ A47139 77 28 Mathematical mathematical JJ A47139 77 29 exactness exactness NN A47139 77 30 , , , A47139 77 31 is be VBZ A47139 77 32 denyed denyed JJ A47139 77 33 to to TO A47139 77 34 be be VB A47139 77 35 practicable practicable JJ A47139 77 36 by by IN A47139 77 37 plain plain JJ A47139 77 38 Geometry Geometry NNP A47139 77 39 ( ( -LRB- A47139 77 40 of of IN A47139 77 41 right right JJ A47139 77 42 Lines Lines NNPS A47139 77 43 and and CC A47139 77 44 Arches Arches NNPS A47139 77 45 of of IN A47139 77 46 Circles Circles NNP A47139 77 47 , , , A47139 77 48 with with IN A47139 77 49 Rule Rule NNP A47139 77 50 and and CC A47139 77 51 Compass Compass NNP A47139 77 52 only only RB A47139 77 53 , , , A47139 77 54 without without IN A47139 77 55 all all DT A47139 77 56 Conick Conick NNP A47139 77 57 Sections Sections NNPS A47139 77 58 , , , A47139 77 59 and and CC A47139 77 60 Algebra Algebra NNP A47139 77 61 Equations Equations NNP A47139 77 62 ) ) -RRB- A47139 77 63 by by IN A47139 77 64 some some DT A47139 77 65 learned learn VBN A47139 77 66 Artists artist NNS A47139 77 67 ; ; : A47139 77 68 yet yet CC A47139 77 69 others other NNS A47139 77 70 as as IN A47139 77 71 learned learn VBN A47139 77 72 are be VBP A47139 77 73 not not RB A47139 77 74 so so RB A47139 77 75 positive positive JJ A47139 77 76 , , , A47139 77 77 but but CC A47139 77 78 acknowledge acknowledge VB A47139 77 79 the the DT A47139 77 80 Practise practise NN A47139 77 81 of of IN A47139 77 82 it -PRON- PRP A47139 77 83 is be VBZ A47139 77 84 not not RB A47139 77 85 as as RB A47139 77 86 yet yet RB A47139 77 87 discovered discover VBN A47139 77 88 , , , A47139 77 89 among among IN A47139 77 90 whom whom WP A47139 77 91 is be VBZ A47139 77 92 the the DT A47139 77 93 learned learned JJ A47139 77 94 Is be VBZ A47139 77 95 . . . A47139 78 1 Barrow Barrow NNP A47139 78 2 , , , A47139 78 3 who who WP A47139 78 4 hath hath VBP A47139 78 5 writ writ NNP A47139 78 6 thus thus RB A47139 78 7 , , , A47139 78 8 in in IN A47139 78 9 Corol Corol NNP A47139 78 10 . . . A47139 79 1 ad ad NN A47139 79 2 . . . A47139 80 1 9 9 CD A47139 80 2 . . . A47139 81 1 1 1 LS A47139 81 2 . . . A47139 81 3 elem elem NNP A47139 81 4 . . . A47139 82 1 Eucl eucl VB A47139 82 2 . . . A47139 83 1 Methodus Methodus NNP A47139 83 2 vero vero NN A47139 83 3 regula regula NN A47139 83 4 & & CC A47139 83 5 Circino Circino NNP A47139 83 6 angulos angulo NNS A47139 83 7 secandi secandi NN A47139 83 8 in in IN A47139 83 9 aequales aequales NNP A47139 83 10 quotcunque quotcunque NNP A47139 83 11 hactenus hactenus NNP A47139 83 12 Geometras Geometras NNP A47139 83 13 latuit latuit NN A47139 83 14 . . . A47139 84 1 and and CC A47139 84 2 in in IN A47139 84 3 Schol Schol NNP A47139 84 4 . . . A47139 85 1 ad ad NN A47139 85 2 16 16 CD A47139 85 3 . . . A47139 86 1 4 4 LS A47139 86 2 . . . A47139 87 1 Elem Elem NNP A47139 87 2 . . . A47139 88 1 Coeterum Coeterum NNP A47139 88 2 divisio divisio JJ A47139 88 3 circumferentiae circumferentiae NN A47139 88 4 in in IN A47139 88 5 partes partes NNP A47139 88 6 datas datas NNP A47139 88 7 etiamnum etiamnum NNP A47139 88 8 desideratur desideratur NNP A47139 88 9 . . . A47139 89 1 The the DT A47139 89 2 Praxis Praxis NNP A47139 89 3 of of IN A47139 89 4 the the DT A47139 89 5 Trisection Trisection NNP A47139 89 6 of of IN A47139 89 7 any any DT A47139 89 8 given give VBN A47139 89 9 Angle Angle NNP A47139 89 10 . . . A47139 90 1 1 1 LS A47139 90 2 . . . A47139 91 1 Divide divide VB A47139 91 2 the the DT A47139 91 3 Cord Cord NNP A47139 91 4 BC BC NNP A47139 91 5 into into IN A47139 91 6 3 3 CD A47139 91 7 equal equal JJ A47139 91 8 Parts part NNS A47139 91 9 , , , A47139 91 10 as as IN A47139 91 11 BE BE NNP A47139 91 12 = = SYM A47139 91 13 EE EE NNP A47139 91 14 = = SYM A47139 91 15 EC EC NNP A47139 91 16 by by IN A47139 91 17 10 10 CD A47139 91 18 . . . A47139 92 1 6 6 LS A47139 92 2 . . . A47139 92 3 elem elem NNP A47139 92 4 . . . A47139 93 1 Euclid euclid JJ A47139 93 2 . . . A47139 94 1 and and CC A47139 94 2 draw draw VB A47139 94 3 the the DT A47139 94 4 2 2 CD A47139 94 5 Perpendiculars perpendicular NNS A47139 94 6 EF EF NNP A47139 94 7 . . . A47139 95 1 EF EF NNP A47139 95 2 . . . A47139 96 1 2 2 LS A47139 96 2 . . . A47139 97 1 With with IN A47139 97 2 the the DT A47139 97 3 extent extent NN A47139 97 4 of of IN A47139 97 5 ⅓ ⅓ NNP A47139 97 6 of of IN A47139 97 7 the the DT A47139 97 8 Cord Cord NNP A47139 97 9 as as IN A47139 97 10 EC EC NNP A47139 97 11 measure measure NN A47139 97 12 on on IN A47139 97 13 the the DT A47139 97 14 Arch Arch NNP A47139 97 15 from from IN A47139 97 16 C c NN A47139 97 17 to to IN A47139 97 18 G g NN A47139 97 19 , , , A47139 97 20 and and CC A47139 97 21 draw draw VB A47139 97 22 the the DT A47139 97 23 Line Line NNP A47139 97 24 or or CC A47139 97 25 Cord Cord NNP A47139 97 26 GC GC NNP A47139 97 27 = = SYM A47139 97 28 EC EC NNP A47139 97 29 . . . A47139 98 1 3 3 LS A47139 98 2 . . . A47139 99 1 With with IN A47139 99 2 another another DT A47139 99 3 Radius Radius NNP A47139 99 4 less less JJR A47139 99 5 than than IN A47139 99 6 AC AC NNP A47139 99 7 , , , A47139 99 8 viz viz NN A47139 99 9 . . . A47139 100 1 AK AK NNP A47139 100 2 draw draw VBP A47139 100 3 a a DT A47139 100 4 second second JJ A47139 100 5 arch arch NN A47139 100 6 as as IN A47139 100 7 KL KL NNP A47139 100 8 , , , A47139 100 9 until until IN A47139 100 10 it -PRON- PRP A47139 100 11 cut cut VBD A47139 100 12 the the DT A47139 100 13 perpendicular perpendicular JJ A47139 100 14 EF EF NNP A47139 100 15 , , , A47139 100 16 and and CC A47139 100 17 let let VB A47139 100 18 the the DT A47139 100 19 Radius Radius NNP A47139 100 20 AK AK NNP A47139 100 21 be be VB A47139 100 22 so so RB A47139 100 23 long long RB A47139 100 24 , , , A47139 100 25 that that IN A47139 100 26 the the DT A47139 100 27 extent extent NN A47139 100 28 of of IN A47139 100 29 the the DT A47139 100 30 Cord Cord NNP A47139 100 31 betwixt betwixt JJ A47139 100 32 K k NN A47139 100 33 and and CC A47139 100 34 L L NNP A47139 100 35 be be VB A47139 100 36 somewhat somewhat RB A47139 100 37 longer long JJR A47139 100 38 than than IN A47139 100 39 EC EC NNP A47139 100 40 , , , A47139 100 41 and and CC A47139 100 42 with with IN A47139 100 43 the the DT A47139 100 44 same same JJ A47139 100 45 extent extent NN A47139 100 46 EC EC NNP A47139 100 47 measure measure NN A47139 100 48 on on IN A47139 100 49 this this DT A47139 100 50 second second JJ A47139 100 51 arch arch JJ A47139 100 52 KR KR NNP A47139 100 53 = = SYM A47139 100 54 EC EC NNP A47139 100 55 . . . A47139 101 1 4 4 LS A47139 101 2 . . . A47139 102 1 From from IN A47139 102 2 G g NN A47139 102 3 to to IN A47139 102 4 R r NN A47139 102 5 draw draw VB A47139 102 6 a a DT A47139 102 7 straight straight JJ A47139 102 8 Line Line NNP A47139 102 9 by by IN A47139 102 10 post post NN A47139 102 11 1 1 CD A47139 102 12 . . . A47139 103 1 1 1 LS A47139 103 2 . . . A47139 103 3 elem elem NNP A47139 103 4 . . . A47139 104 1 and and CC A47139 104 2 produce produce VB A47139 104 3 the the DT A47139 104 4 same same JJ A47139 104 5 by by IN A47139 104 6 post post NNP A47139 104 7 2 2 CD A47139 104 8 . . . A47139 104 9 until until IN A47139 104 10 it -PRON- PRP A47139 104 11 cut cut VBD A47139 104 12 the the DT A47139 104 13 Perpendiculars perpendicular NNS A47139 104 14 at at IN A47139 104 15 I I NNP A47139 104 16 and and CC A47139 104 17 O. O. NNP A47139 105 1 5 5 CD A47139 105 2 . . . A47139 106 1 Draw draw VB A47139 106 2 the the DT A47139 106 3 straight straight JJ A47139 106 4 lines line NNS A47139 106 5 AI AI NNP A47139 106 6 and and CC A47139 106 7 AO AO NNP A47139 106 8 , , , A47139 106 9 and and CC A47139 106 10 extend extend VB A47139 106 11 them -PRON- PRP A47139 106 12 to to IN A47139 106 13 H h NN A47139 106 14 on on IN A47139 106 15 both both DT A47139 106 16 sides side NNS A47139 106 17 , , , A47139 106 18 so so IN A47139 106 19 that that IN A47139 106 20 the the DT A47139 106 21 one one CD A47139 106 22 line line NN A47139 106 23 shall shall MD A47139 106 24 be be VB A47139 106 25 AIH aih NN A47139 106 26 , , , A47139 106 27 and and CC A47139 106 28 the the DT A47139 106 29 other other JJ A47139 106 30 AOH AOH NNP A47139 106 31 , , , A47139 106 32 which which WDT A47139 106 33 two two CD A47139 106 34 Lines line NNS A47139 106 35 shall shall MD A47139 106 36 sect sect VB A47139 106 37 the the DT A47139 106 38 given give VBN A47139 106 39 angle angle NN A47139 106 40 BAC BAC NNP A47139 106 41 into into IN A47139 106 42 three three CD A47139 106 43 parts part NNS A47139 106 44 or or CC A47139 106 45 angles angle NNS A47139 106 46 , , , A47139 106 47 viz viz NN A47139 106 48 . . . A47139 107 1 BAH BAH NNP A47139 107 2 , , , A47139 107 3 HAH HAH NNP A47139 107 4 , , , A47139 107 5 HAC HAC NNP A47139 107 6 . . . A47139 108 1 The the DT A47139 108 2 Question question NN A47139 108 3 , , , A47139 108 4 or or CC A47139 108 5 Problem problem NN A47139 108 6 to to TO A47139 108 7 be be VB A47139 108 8 resolved resolve VBN A47139 108 9 is be VBZ A47139 108 10 , , , A47139 108 11 whether whether IN A47139 108 12 these these DT A47139 108 13 three three CD A47139 108 14 angles angle NNS A47139 108 15 are be VBP A47139 108 16 not not RB A47139 108 17 equal equal JJ A47139 108 18 , , , A47139 108 19 and and CC A47139 108 20 consequently consequently RB A47139 108 21 that that IN A47139 108 22 the the DT A47139 108 23 angle angle NN A47139 108 24 BAC BAC NNP A47139 108 25 is be VBZ A47139 108 26 trisected trisect VBN A47139 108 27 into into IN A47139 108 28 equal equal JJ A47139 108 29 angles angle NNS A47139 108 30 . . . A47139 109 1 The the DT A47139 109 2 apparent apparent JJ A47139 109 3 demonstration demonstration NN A47139 109 4 that that WDT A47139 109 5 is be VBZ A47139 109 6 here here RB A47139 109 7 proposed propose VBN A47139 109 8 to to TO A47139 109 9 prove prove VB A47139 109 10 it -PRON- PRP A47139 109 11 , , , A47139 109 12 followeth followeth NNP A47139 109 13 . . . A47139 110 1 In in IN A47139 110 2 order order NN A47139 110 3 to to IN A47139 110 4 the the DT A47139 110 5 apparent apparent JJ A47139 110 6 following following JJ A47139 110 7 demonstration demonstration NN A47139 110 8 , , , A47139 110 9 by by IN A47139 110 10 way way NN A47139 110 11 of of IN A47139 110 12 Preparation Preparation NNP A47139 110 13 , , , A47139 110 14 1 1 CD A47139 110 15 . . . A47139 111 1 Draw draw VB A47139 111 2 the the DT A47139 111 3 line line NN A47139 111 4 OI OI NNP A47139 111 5 , , , A47139 111 6 which which WDT A47139 111 7 shall shall MD A47139 111 8 be be VB A47139 111 9 parallel parallel JJ A47139 111 10 to to IN A47139 111 11 EE ee NN A47139 111 12 by by IN A47139 111 13 28 28 CD A47139 111 14 . . . A47139 112 1 1 1 LS A47139 112 2 . . . A47139 112 3 elem elem NNP A47139 112 4 . . . A47139 113 1 and and CC A47139 113 2 extend extend VB A47139 113 3 it -PRON- PRP A47139 113 4 on on IN A47139 113 5 both both DT A47139 113 6 sides side NNS A47139 113 7 , , , A47139 113 8 from from IN A47139 113 9 I -PRON- PRP A47139 113 10 to to IN A47139 113 11 N n NN A47139 113 12 on on IN A47139 113 13 the the DT A47139 113 14 one one CD A47139 113 15 side side NN A47139 113 16 , , , A47139 113 17 and and CC A47139 113 18 from from IN A47139 113 19 O o NN A47139 113 20 to to IN A47139 113 21 N n NN A47139 113 22 on on IN A47139 113 23 the the DT A47139 113 24 other other JJ A47139 113 25 , , , A47139 113 26 making make VBG A47139 113 27 IN IN NNP A47139 113 28 = = SYM A47139 113 29 ON ON NNP A47139 113 30 = = SYM A47139 113 31 EC EC NNP A47139 113 32 = = SYM A47139 113 33 OI OI NNP A47139 113 34 . . . A47139 114 1 2 2 LS A47139 114 2 . . . A47139 115 1 With with IN A47139 115 2 Radius Radius NNP A47139 115 3 IN IN NNP A47139 115 4 , , , A47139 115 5 and and CC A47139 115 6 ON ON NNP A47139 115 7 , , , A47139 115 8 describe describe VB A47139 115 9 the the DT A47139 115 10 arches arch NNS A47139 115 11 on on IN A47139 115 12 both both DT A47139 115 13 sides side NNS A47139 115 14 NM NM NNP A47139 115 15 until until IN A47139 115 16 these these DT A47139 115 17 arches arch NNS A47139 115 18 cut cut VBP A47139 115 19 the the DT A47139 115 20 lines line NNS A47139 115 21 AC AC NNP A47139 115 22 and and CC A47139 115 23 AB AB NNP A47139 115 24 , , , A47139 115 25 so so RB A47139 115 26 shall shall MD A47139 115 27 the the DT A47139 115 28 lines line NNS A47139 115 29 or or CC A47139 115 30 cords cord NNS A47139 115 31 drawn draw VBN A47139 115 32 betwixt betwixt NNP A47139 115 33 I I NNP A47139 115 34 and and CC A47139 115 35 M M NNP A47139 115 36 and and CC A47139 115 37 O O NNP A47139 115 38 and and CC A47139 115 39 M M NNP A47139 115 40 , , , A47139 115 41 viz viz NN A47139 115 42 . . . A47139 116 1 IM IM NNP A47139 116 2 and and CC A47139 116 3 OM OM NNP A47139 116 4 = = SYM A47139 116 5 EC EC NNP A47139 116 6 . . . A47139 117 1 3 3 LS A47139 117 2 . . . A47139 118 1 Make make VB A47139 118 2 the the DT A47139 118 3 angle angle NN A47139 118 4 IMP IMP NNP A47139 118 5 = = SYM A47139 118 6 angle angle NN A47139 118 7 MIN MIN NNP A47139 118 8 by by IN A47139 118 9 23 23 CD A47139 118 10 . . . A47139 119 1 1 1 LS A47139 119 2 . . . A47139 119 3 elem elem NNP A47139 119 4 . . . A47139 120 1 and and CC A47139 120 2 OMP OMP NNP A47139 120 3 = = SYM A47139 120 4 MON MON NNP A47139 120 5 , , , A47139 120 6 and and CC A47139 120 7 extend extend VB A47139 120 8 the the DT A47139 120 9 line line NN A47139 120 10 MP MP NNP A47139 120 11 , , , A47139 120 12 until until IN A47139 120 13 it -PRON- PRP A47139 120 14 cut cut VBD A47139 120 15 the the DT A47139 120 16 line line NN A47139 120 17 AI ai NN A47139 120 18 at at IN A47139 120 19 P p NN A47139 120 20 , , , A47139 120 21 and and CC A47139 120 22 AO AO NNP A47139 120 23 at at IN A47139 120 24 P. P. NNP A47139 120 25 4 4 CD A47139 120 26 . . . A47139 121 1 Draw draw VB A47139 121 2 the the DT A47139 121 3 line line NN A47139 121 4 OP op NN A47139 121 5 parallel parallel NN A47139 121 6 to to IN A47139 121 7 IM IM NNP A47139 121 8 , , , A47139 121 9 until until IN A47139 121 10 it -PRON- PRP A47139 121 11 cut cut VBD A47139 121 12 MP MP NNP A47139 121 13 , , , A47139 121 14 whence whence NN A47139 121 15 the the DT A47139 121 16 perfect perfect JJ A47139 121 17 Rhombus Rhombus NNP A47139 121 18 OMPI OMPI NNP A47139 121 19 shall shall MD A47139 121 20 be be VB A47139 121 21 formed form VBN A47139 121 22 , , , A47139 121 23 having have VBG A47139 121 24 the the DT A47139 121 25 opposit opposit JJ A47139 121 26 side side NN A47139 121 27 ; ; : A47139 121 28 paralel paralel NNS A47139 121 29 and and CC A47139 121 30 equal equal JJ A47139 121 31 , , , A47139 121 32 for for IN A47139 121 33 PM pm NN A47139 121 34 by by IN A47139 121 35 construction construction NN A47139 121 36 is be VBZ A47139 121 37 parallel parallel JJ A47139 121 38 with with IN A47139 121 39 OI OI NNP A47139 121 40 , , , A47139 121 41 and and CC A47139 121 42 OP op NN A47139 121 43 with with IN A47139 121 44 IM IM NNP A47139 121 45 and and CC A47139 121 46 that that IN A47139 121 47 the the DT A47139 121 48 Line Line NNP A47139 121 49 OP OP NNP A47139 121 50 drawn draw VBD A47139 121 51 parallel parallel RB A47139 121 52 to to IN A47139 121 53 IM IM NNP A47139 121 54 can can MD A47139 121 55 cut cut VB A47139 121 56 the the DT A47139 121 57 Line Line NNP A47139 121 58 PM pm NN A47139 121 59 no no UH A47139 121 60 where where WRB A47139 121 61 but but CC A47139 121 62 at at IN A47139 121 63 P p NN A47139 121 64 on on IN A47139 121 65 the the DT A47139 121 66 line line NN A47139 121 67 AI AI NNP A47139 121 68 is be VBZ A47139 121 69 proved prove VBN A47139 121 70 thus thus RB A47139 121 71 . . . A47139 122 1 Suppose suppose VB A47139 122 2 it -PRON- PRP A47139 122 3 cut cut VBD A47139 122 4 the the DT A47139 122 5 line line NN A47139 122 6 PM pm NN A47139 122 7 any any RB A47139 122 8 where where WRB A47139 122 9 else else RB A47139 122 10 , , , A47139 122 11 than than IN A47139 122 12 on on IN A47139 122 13 the the DT A47139 122 14 line line NN A47139 122 15 AI AI NNP A47139 122 16 on on IN A47139 122 17 either either DT A47139 122 18 side side NN A47139 122 19 , , , A47139 122 20 it -PRON- PRP A47139 122 21 should should MD A47139 122 22 make make VB A47139 122 23 PM PM NNP A47139 122 24 either either CC A47139 122 25 longer long RBR A47139 122 26 or or CC A47139 122 27 shorter short JJR A47139 122 28 than than IN A47139 122 29 its -PRON- PRP$ A47139 122 30 opposit opposit JJ A47139 122 31 side side NN A47139 122 32 ( ( -LRB- A47139 122 33 for for IN A47139 122 34 the the DT A47139 122 35 arch arch JJ A47139 122 36 drawn draw VBN A47139 122 37 by by IN A47139 122 38 the the DT A47139 122 39 radius radius NN A47139 122 40 MI MI NNP A47139 122 41 , , , A47139 122 42 and and CC A47139 122 43 cutting cut VBG A47139 122 44 the the DT A47139 122 45 line line NN A47139 122 46 AI ai NN A47139 122 47 at at IN A47139 122 48 P p NN A47139 122 49 proveth proveth JJ A47139 122 50 MP MP NNP A47139 122 51 = = SYM A47139 122 52 MI MI NNP A47139 122 53 by by IN A47139 122 54 def def NN A47139 122 55 . . . A47139 123 1 15 15 CD A47139 123 2 . . . A47139 124 1 1 1 LS A47139 124 2 . . . A47139 124 3 elem elem NNP A47139 124 4 . . . A47139 124 5 ) ) -RRB- A47139 125 1 as as IN A47139 125 2 also also RB A47139 125 3 OP OP NNP A47139 125 4 should should MD A47139 125 5 be be VB A47139 125 6 longer long RBR A47139 125 7 or or CC A47139 125 8 shorter short JJR A47139 125 9 than than IN A47139 125 10 IM IM NNP A47139 125 11 , , , A47139 125 12 ( ( -LRB- A47139 125 13 as as IN A47139 125 14 the the DT A47139 125 15 like like JJ A47139 125 16 arch arch NN A47139 125 17 conceived conceive VBD A47139 125 18 to to TO A47139 125 19 be be VB A47139 125 20 drawn draw VBN A47139 125 21 by by IN A47139 125 22 radius radius NN A47139 125 23 OI OI NNP A47139 125 24 , , , A47139 125 25 and and CC A47139 125 26 cutting cut VBG A47139 125 27 AI AI NNP A47139 125 28 at at IN A47139 125 29 P p NN A47139 125 30 , , , A47139 125 31 proveth proveth JJ A47139 125 32 OI oi NN A47139 125 33 = = SYM A47139 125 34 OP op NN A47139 125 35 by by IN A47139 125 36 the the DT A47139 125 37 same same JJ A47139 125 38 , , , A47139 125 39 def def JJ A47139 125 40 . . . A47139 126 1 15 15 CD A47139 126 2 . . . A47139 127 1 1 1 LS A47139 127 2 . . . A47139 127 3 elem elem NNP A47139 127 4 . . . A47139 127 5 ) ) -RRB- A47139 128 1 but but CC A47139 128 2 both both PDT A47139 128 3 these these DT A47139 128 4 Consequences consequence NNS A47139 128 5 are be VBP A47139 128 6 absurd absurd JJ A47139 128 7 , , , A47139 128 8 making make VBG A47139 128 9 the the DT A47139 128 10 opposit opposit JJ A47139 128 11 sides side NNS A47139 128 12 of of IN A47139 128 13 a a DT A47139 128 14 Paralellogram Paralellogram NNP A47139 128 15 to to TO A47139 128 16 be be VB A47139 128 17 unequal unequal JJ A47139 128 18 , , , A47139 128 19 contrary contrary JJ A47139 128 20 to to IN A47139 128 21 34 34 CD A47139 128 22 . . . A47139 129 1 1 1 LS A47139 129 2 . . . A47139 129 3 elem elem NNP A47139 129 4 . . . A47139 130 1 Because because IN A47139 130 2 the the DT A47139 130 3 Figure Figure NNP A47139 130 4 OPMI OPMI NNP A47139 130 5 is be VBZ A47139 130 6 proved prove VBN A47139 130 7 to to TO A47139 130 8 be be VB A47139 130 9 a a DT A47139 130 10 perfect perfect JJ A47139 130 11 Rhombus Rhombus NNP A47139 130 12 , , , A47139 130 13 having have VBG A47139 130 14 all all PDT A47139 130 15 the the DT A47139 130 16 sides side NNS A47139 130 17 equal equal JJ A47139 130 18 , , , A47139 130 19 whereof whereof IN A47139 130 20 the the DT A47139 130 21 line line NN A47139 130 22 PI PI NNP A47139 130 23 is be VBZ A47139 130 24 the the DT A47139 130 25 diagonal diagonal JJ A47139 130 26 , , , A47139 130 27 ( ( -LRB- A47139 130 28 it -PRON- PRP A47139 130 29 being be VBG A47139 130 30 proved prove VBN A47139 130 31 that that IN A47139 130 32 OP op NN A47139 130 33 and and CC A47139 130 34 PM pm NN A47139 130 35 terminate terminate VBP A47139 130 36 on on IN A47139 130 37 AI AI NNP A47139 130 38 ) ) -RRB- A47139 130 39 therefore therefore RB A47139 130 40 the the DT A47139 130 41 angle angle NN A47139 130 42 OIP OIP NNP A47139 130 43 ( ( -LRB- A47139 130 44 = = SYM A47139 130 45 OIA OIA NNP A47139 130 46 ) ) -RRB- A47139 130 47 = = SYM A47139 130 48 PIM PIM NNP A47139 130 49 = = NFP A47139 130 50 ( ( -LRB- A47139 130 51 AIM AIM NNP A47139 130 52 ) ) -RRB- A47139 130 53 by by IN A47139 130 54 8 8 CD A47139 130 55 . . . A47139 130 56 and and CC A47139 130 57 4 4 CD A47139 130 58 . . . A47139 131 1 1 1 LS A47139 131 2 . . . A47139 131 3 elem elem NNP A47139 131 4 . . . A47139 132 1 Lastly lastly RB A47139 132 2 , , , A47139 132 3 these these DT A47139 132 4 two two CD A47139 132 5 Triangles Triangles NNPS A47139 132 6 OAI OAI NNP A47139 132 7 and and CC A47139 132 8 IAM IAM NNP A47139 132 9 shall shall MD A47139 132 10 be be VB A47139 132 11 according accord VBG A47139 132 12 to to IN A47139 132 13 the the DT A47139 132 14 4th 4th NN A47139 132 15 . . . A47139 133 1 prop prop NNP A47139 133 2 . . . A47139 134 1 1 1 LS A47139 134 2 . . . A47139 134 3 elem elem NNP A47139 134 4 . . . A47139 135 1 and and CC A47139 135 2 so so RB A47139 135 3 shall shall MD A47139 135 4 OAI OAI NNP A47139 135 5 and and CC A47139 135 6 OAM OAM NNP A47139 135 7 , , , A47139 135 8 for for IN A47139 135 9 OI OI NNP A47139 135 10 = = SYM A47139 135 11 IM IM NNP A47139 135 12 as as IN A47139 135 13 above above IN A47139 135 14 proved prove VBN A47139 135 15 , , , A47139 135 16 and and CC A47139 135 17 AI AI NNP A47139 135 18 is be VBZ A47139 135 19 common common JJ A47139 135 20 to to IN A47139 135 21 both both DT A47139 135 22 , , , A47139 135 23 and and CC A47139 135 24 the the DT A47139 135 25 Angle Angle NNP A47139 135 26 OIA OIA NNP A47139 135 27 = = SYM A47139 135 28 AIM AIM NNP A47139 135 29 as as IN A47139 135 30 is be VBZ A47139 135 31 above above RB A47139 135 32 proved prove VBN A47139 135 33 , , , A47139 135 34 therefore therefore RB A47139 135 35 by by IN A47139 135 36 4 4 CD A47139 135 37 . . . A47139 136 1 1 1 LS A47139 136 2 . . . A47139 136 3 elem elem NNP A47139 136 4 . . . A47139 137 1 AM AM NNP A47139 137 2 = = SYM A47139 137 3 AO AO NNP A47139 137 4 = = SYM A47139 137 5 AI AI NNP A47139 137 6 , , , A47139 137 7 and and CC A47139 137 8 consequently consequently RB A47139 137 9 by by IN A47139 137 10 8 8 CD A47139 137 11 . . . A47139 138 1 1 1 LS A47139 138 2 . . . A47139 138 3 the the DT A47139 138 4 angles angle NNS A47139 138 5 IAM IAM NNP A47139 138 6 = = SYM A47139 138 7 OAI OAI NNP A47139 138 8 = = SYM A47139 138 9 OAM OAM NNP A47139 138 10 , , , A47139 138 11 therefore therefore RB A47139 138 12 the the DT A47139 138 13 given give VBN A47139 138 14 angle angle NN A47139 138 15 BAC BAC NNP A47139 138 16 is be VBZ A47139 138 17 Geometrically geometrically RB A47139 138 18 trisected trisect VBN A47139 138 19 by by IN A47139 138 20 the the DT A47139 138 21 Lines Lines NNPS A47139 138 22 AO AO NNP A47139 138 23 and and CC A47139 138 24 AI AI NNP A47139 138 25 extended extend VBD A47139 138 26 to to IN A47139 138 27 H. H. NNP A47139 138 28 Q. Q. NNP A47139 138 29 E. E. NNP A47139 138 30 D. D. NNP A47139 138 31 Here here RB A47139 138 32 Note Note NNP A47139 138 33 , , , A47139 138 34 let let VB A47139 138 35 the the DT A47139 138 36 Radius radius NN A47139 138 37 be be VB A47139 138 38 ever ever RB A47139 138 39 so so RB A47139 138 40 much much RB A47139 138 41 changed change VBN A47139 138 42 betwixt betwixt NNP A47139 138 43 M M NNP A47139 138 44 and and CC A47139 138 45 C C NNP A47139 138 46 , , , A47139 138 47 taking take VBG A47139 138 48 it -PRON- PRP A47139 138 49 at at IN A47139 138 50 any any DT A47139 138 51 extent extent NN A47139 138 52 from from IN A47139 138 53 A a NN A47139 138 54 , , , A47139 138 55 and and CC A47139 138 56 let let VB A47139 138 57 ever ever RB A47139 138 58 so so RB A47139 138 59 many many JJ A47139 138 60 Concentrick Concentrick NNP A47139 138 61 Arches Arches NNPS A47139 138 62 be be VB A47139 138 63 drawn draw VBN A47139 138 64 from from IN A47139 138 65 the the DT A47139 138 66 Center Center NNP A47139 138 67 A a DT A47139 138 68 betwixt betwixt JJ A47139 138 69 IM IM NNP A47139 138 70 and and CC A47139 138 71 GC GC NNP A47139 138 72 , , , A47139 138 73 their -PRON- PRP$ A47139 138 74 Cords Cords NNP A47139 138 75 terminating terminate VBG A47139 138 76 on on IN A47139 138 77 the the DT A47139 138 78 streight streight JJ A47139 138 79 Lines Lines NNP A47139 138 80 MC MC NNP A47139 138 81 on on IN A47139 138 82 the the DT A47139 138 83 one one CD A47139 138 84 side side NN A47139 138 85 , , , A47139 138 86 and and CC A47139 138 87 IG IG NNP A47139 138 88 on on IN A47139 138 89 the the DT A47139 138 90 other other JJ A47139 138 91 shall shall MD A47139 138 92 all all DT A47139 138 93 be be VB A47139 138 94 equal equal JJ A47139 138 95 , , , A47139 138 96 one one CD A47139 138 97 to to IN A47139 138 98 another another DT A47139 138 99 , , , A47139 138 100 and and CC A47139 138 101 to to IN A47139 138 102 the the DT A47139 138 103 Cord Cord NNP A47139 138 104 GC GC NNP A47139 138 105 = = SYM A47139 138 106 ● ● . A47139 138 107 BC BC NNP A47139 138 108 . . . A47139 139 1 as as IN A47139 139 2 the the DT A47139 139 3 demonstration demonstration NN A47139 139 4 above above IN A47139 139 5 given give VBN A47139 139 6 proveth proveth NNP A47139 139 7 , , , A47139 139 8 for for IN A47139 139 9 the the DT A47139 139 10 reason reason NN A47139 139 11 that that WDT A47139 139 12 proveth proveth VBP A47139 139 13 the the DT A47139 139 14 Cords Cords NNPS A47139 139 15 of of IN A47139 139 16 any any DT A47139 139 17 3 3 CD A47139 139 18 Concentrick Concentrick NNP A47139 139 19 Arches Arches NNPS A47139 139 20 , , , A47139 139 21 terminating terminate VBG A47139 139 22 on on IN A47139 139 23 two two CD A47139 139 24 streight streight JJ A47139 139 25 Lines line NNS A47139 139 26 to to TO A47139 139 27 be be VB A47139 139 28 equal equal JJ A47139 139 29 within within IN A47139 139 30 the the DT A47139 139 31 limits limit NNS A47139 139 32 MI MI NNP A47139 139 33 and and CC A47139 139 34 GC GC NNP A47139 139 35 , , , A47139 139 36 being be VBG A47139 139 37 a a DT A47139 139 38 Trapezia Trapezia NNP A47139 139 39 , , , A47139 139 40 proveth proveth VB A47139 139 41 any any DT A47139 139 42 other other JJ A47139 139 43 3 3 CD A47139 139 44 to to TO A47139 139 45 be be VB A47139 139 46 equal equal JJ A47139 139 47 within within IN A47139 139 48 the the DT A47139 139 49 same same JJ A47139 139 50 limits limit NNS A47139 139 51 . . . A47139 140 1 But but CC A47139 140 2 if if IN A47139 140 3 we -PRON- PRP A47139 140 4 draw draw VBP A47139 140 5 any any DT A47139 140 6 Concentrick Concentrick NNP A47139 140 7 Arches Arches NNPS A47139 140 8 without without IN A47139 140 9 the the DT A47139 140 10 Trapezia Trapezia NNP A47139 140 11 IGCM igcm NN A47139 140 12 , , , A47139 140 13 as as IN A47139 140 14 with with IN A47139 140 15 a a DT A47139 140 16 less less JJR A47139 140 17 Radius radius NN A47139 140 18 , , , A47139 140 19 than than IN A47139 140 20 AM am NN A47139 140 21 , , , A47139 140 22 or or CC A47139 140 23 with with IN A47139 140 24 a a DT A47139 140 25 greater great JJR A47139 140 26 Radius Radius NNP A47139 140 27 , , , A47139 140 28 than than IN A47139 140 29 AC AC NNP A47139 140 30 , , , A47139 140 31 the the DT A47139 140 32 Case Case NNP A47139 140 33 is be VBZ A47139 140 34 altered alter VBN A47139 140 35 , , , A47139 140 36 and and CC A47139 140 37 the the DT A47139 140 38 equal equal JJ A47139 140 39 Cords Cords NNPS A47139 140 40 will will MD A47139 140 41 not not RB A47139 140 42 terminate terminate VB A47139 140 43 on on IN A47139 140 44 the the DT A47139 140 45 streight streight JJ A47139 140 46 Line Line NNP A47139 140 47 IG IG NNP A47139 140 48 , , , A47139 140 49 but but CC A47139 140 50 diviate diviate NN A47139 140 51 or or CC A47139 140 52 depart depart NN A47139 140 53 therefrom therefrom NNP A47139 140 54 , , , A47139 140 55 as as IN A47139 140 56 both both CC A47139 140 57 true true JJ A47139 140 58 Reason reason NN A47139 140 59 doth doth NN A47139 140 60 prove prove NN A47139 140 61 , , , A47139 140 62 and and CC A47139 140 63 even even RB A47139 140 64 ocular ocular IN A47139 140 65 inspection inspection NN A47139 140 66 doth doth NN A47139 140 67 shew shew NN A47139 140 68 ; ; : A47139 140 69 for for IN A47139 140 70 though though IN A47139 140 71 the the DT A47139 140 72 Eye Eye NNP A47139 140 73 is be VBZ A47139 140 74 not not RB A47139 140 75 able able JJ A47139 140 76 to to TO A47139 140 77 judge judge VB A47139 140 78 of of IN A47139 140 79 a a DT A47139 140 80 straight straight JJ A47139 140 81 Line line NN A47139 140 82 , , , A47139 140 83 yet yet CC A47139 140 84 when when WRB A47139 140 85 a a DT A47139 140 86 Line line NN A47139 140 87 is be VBZ A47139 140 88 visibly visibly RB A47139 140 89 apparent apparent JJ A47139 140 90 to to TO A47139 140 91 make make VB A47139 140 92 an an DT A47139 140 93 Angle angle NN A47139 140 94 with with IN A47139 140 95 another another DT A47139 140 96 Line line NN A47139 140 97 , , , A47139 140 98 these these DT A47139 140 99 two two CD A47139 140 100 Lines line NNS A47139 140 101 can can MD A47139 140 102 not not RB A47139 140 103 be be VB A47139 140 104 a a DT A47139 140 105 straight straight JJ A47139 140 106 Line line NN A47139 140 107 . . . A47139 141 1 I -PRON- PRP A47139 141 2 call call VBP A47139 141 3 the the DT A47139 141 4 Figure figure NN A47139 141 5 IMCG IMCG VBZ A47139 141 6 a a DT A47139 141 7 Trapezia Trapezia NNP A47139 141 8 , , , A47139 141 9 for for IN A47139 141 10 it -PRON- PRP A47139 141 11 is be VBZ A47139 141 12 not not RB A47139 141 13 any any DT A47139 141 14 Paralellogram Paralellogram NNP A47139 141 15 , , , A47139 141 16 because because IN A47139 141 17 the the DT A47139 141 18 side side NN A47139 141 19 IG IG NNP A47139 141 20 , , , A47139 141 21 is be VBZ A47139 141 22 not not RB A47139 141 23 parallel parallel JJ A47139 141 24 to to IN A47139 141 25 the the DT A47139 141 26 side side NN A47139 141 27 MC MC NNP A47139 141 28 , , , A47139 141 29 but but CC A47139 141 30 very very RB A47139 141 31 unparalel unparalel RB A47139 141 32 , , , A47139 141 33 which which WDT A47139 141 34 makes make VBZ A47139 141 35 the the DT A47139 141 36 side side NN A47139 141 37 IG IG NNP A47139 141 38 to to TO A47139 141 39 be be VB A47139 141 40 longer long JJR A47139 141 41 than than IN A47139 141 42 the the DT A47139 141 43 side side NN A47139 141 44 MC MC NNP A47139 141 45 , , , A47139 141 46 but but CC A47139 141 47 this this DT A47139 141 48 doth doth NN A47139 141 49 not not RB A47139 141 50 hinder hinder VBP A47139 141 51 that that IN A47139 141 52 all all PDT A47139 141 53 the the DT A47139 141 54 Cords Cords NNPS A47139 141 55 of of IN A47139 141 56 the the DT A47139 141 57 Concentrick Concentrick NNP A47139 141 58 Arches Arches NNPS A47139 141 59 drawn draw VBN A47139 141 60 betwixt betwixt VBP A47139 141 61 IG IG NNP A47139 141 62 and and CC A47139 141 63 MC MC NNP A47139 141 64 are be VBP A47139 141 65 equal equal JJ A47139 141 66 , , , A47139 141 67 for for IN A47139 141 68 let let VB A47139 141 69 them -PRON- PRP A47139 141 70 be be VB A47139 141 71 ever ever RB A47139 141 72 so so RB A47139 141 73 many many JJ A47139 141 74 within within IN A47139 141 75 the the DT A47139 141 76 limits limit NNS A47139 141 77 IM IM NNP A47139 141 78 and and CC A47139 141 79 GC GC NNP A47139 141 80 , , , A47139 141 81 they -PRON- PRP A47139 141 82 are be VBP A47139 141 83 all all RB A47139 141 84 equal equal JJ A47139 141 85 , , , A47139 141 86 though though IN A47139 141 87 their -PRON- PRP$ A47139 141 88 Arches arch NNS A47139 141 89 are be VBP A47139 141 90 unequal unequal JJ A47139 141 91 being be VBG A47139 141 92 from from IN A47139 141 93 a a DT A47139 141 94 differing differ VBG A47139 141 95 Radius radius NN A47139 141 96 . . . A47139 142 1 And and CC A47139 142 2 though though IN A47139 142 3 the the DT A47139 142 4 demonstration demonstration NN A47139 142 5 above above IN A47139 142 6 given give VBN A47139 142 7 may may MD A47139 142 8 seem seem VB A47139 142 9 sufficient sufficient JJ A47139 142 10 to to TO A47139 142 11 prove prove VB A47139 142 12 it -PRON- PRP A47139 142 13 , , , A47139 142 14 yet yet RB A47139 142 15 for for IN A47139 142 16 a a DT A47139 142 17 further further JJ A47139 142 18 proof proof NN A47139 142 19 , , , A47139 142 20 let let VB A47139 142 21 a a DT A47139 142 22 Line line NN A47139 142 23 be be VB A47139 142 24 drawn draw VBN A47139 142 25 , , , A47139 142 26 or or CC A47139 142 27 conceived conceive VBN A47139 142 28 to to TO A47139 142 29 be be VB A47139 142 30 drawn draw VBN A47139 142 31 ( ( -LRB- A47139 142 32 as as IN A47139 142 33 in in IN A47139 142 34 this this DT A47139 142 35 Figure figure NN A47139 142 36 it -PRON- PRP A47139 142 37 is be VBZ A47139 142 38 only only RB A47139 142 39 conceived conceive VBN A47139 142 40 ) ) -RRB- A47139 142 41 from from IN A47139 142 42 I -PRON- PRP A47139 142 43 Paralel Paralel NNP A47139 142 44 to to IN A47139 142 45 AC AC NNP A47139 142 46 , , , A47139 142 47 towards towards IN A47139 142 48 FC FC NNP A47139 142 49 and and CC A47139 142 50 beyond beyond IN A47139 142 51 it -PRON- PRP A47139 142 52 , , , A47139 142 53 all all PDT A47139 142 54 the the DT A47139 142 55 extream extream JJ A47139 142 56 Points point NNS A47139 142 57 of of IN A47139 142 58 the the DT A47139 142 59 Cords Cords NNPS A47139 142 60 of of IN A47139 142 61 the the DT A47139 142 62 Concentick Concentick NNP A47139 142 63 Arches Arches NNPS A47139 142 64 , , , A47139 142 65 above above RB A47139 142 66 mentioned mention VBN A47139 142 67 , , , A47139 142 68 terminating terminate VBG A47139 142 69 on on IN A47139 142 70 the the DT A47139 142 71 streight streight JJ A47139 142 72 line line NN A47139 142 73 IG IG NNP A47139 142 74 , , , A47139 142 75 do do VBP A47139 142 76 gradually gradually RB A47139 142 77 still still RB A47139 142 78 more more RBR A47139 142 79 and and CC A47139 142 80 more more JJR A47139 142 81 depart depart NN A47139 142 82 from from IN A47139 142 83 that that DT A47139 142 84 parallel parallel NN A47139 142 85 towards towards IN A47139 142 86 the the DT A47139 142 87 perpendicular perpendicular JJ A47139 142 88 IF if IN A47139 142 89 within within IN A47139 142 90 the the DT A47139 142 91 aforesaid aforesaid JJ A47139 142 92 limits limit NNS A47139 142 93 , , , A47139 142 94 IM IM NNP A47139 142 95 and and CC A47139 142 96 GC GC NNP A47139 142 97 , , , A47139 142 98 on on IN A47139 142 99 the the DT A47139 142 100 first first JJ A47139 142 101 Arch Arch NNP A47139 142 102 , , , A47139 142 103 which which WDT A47139 142 104 I -PRON- PRP A47139 142 105 call call VBP A47139 142 106 the the DT A47139 142 107 primitive primitive JJ A47139 142 108 Arch Arch NNP A47139 142 109 ; ; : A47139 142 110 but but CC A47139 142 111 if if IN A47139 142 112 we -PRON- PRP A47139 142 113 draw draw VBP A47139 142 114 any any DT A47139 142 115 Arch Arch NNP A47139 142 116 , , , A47139 142 117 without without IN A47139 142 118 GC GC NNP A47139 142 119 by by IN A47139 142 120 a a DT A47139 142 121 longer long JJR A47139 142 122 Radius Radius NNP A47139 142 123 than than IN A47139 142 124 AC AC NNP A47139 142 125 , , , A47139 142 126 or or CC A47139 142 127 within within IN A47139 142 128 IM IM NNP A47139 142 129 by by IN A47139 142 130 a a DT A47139 142 131 shorter short JJR A47139 142 132 Radius radius NN A47139 142 133 than than IN A47139 142 134 AM AM NNP A47139 142 135 , , , A47139 142 136 the the DT A47139 142 137 Cords Cords NNPS A47139 142 138 of of IN A47139 142 139 those those DT A47139 142 140 concentrick concentrick NN A47139 142 141 Arches arch NNS A47139 142 142 , , , A47139 142 143 if if IN A47139 142 144 equal equal JJ A47139 142 145 , , , A47139 142 146 shall shall MD A47139 142 147 deviate deviate VB A47139 142 148 from from IN A47139 142 149 the the DT A47139 142 150 streight streight JJ A47139 142 151 line line NN A47139 142 152 IG IG NNP A47139 142 153 , , , A47139 142 154 and and CC A47139 142 155 come come VB A47139 142 156 nearer nearer RB A47139 142 157 to to IN A47139 142 158 the the DT A47139 142 159 Parallel Parallel NNP A47139 142 160 above above IN A47139 142 161 mentioned mention VBN A47139 142 162 , , , A47139 142 163 but but CC A47139 142 164 that that IN A47139 142 165 within within IN A47139 142 166 the the DT A47139 142 167 Trapezia Trapezia NNP A47139 142 168 above above RB A47139 142 169 said say VBD A47139 142 170 IMCG IMCG NNP A47139 142 171 , , , A47139 142 172 the the DT A47139 142 173 equal equal JJ A47139 142 174 Cords cord NNS A47139 142 175 of of IN A47139 142 176 all all PDT A47139 142 177 these these DT A47139 142 178 Arches arch NNS A47139 142 179 shall shall MD A47139 142 180 terminate terminate VB A47139 142 181 on on IN A47139 142 182 the the DT A47139 142 183 straight straight JJ A47139 142 184 line line NN A47139 142 185 IGI IGI NNP A47139 142 186 thus thus RB A47139 142 187 further further RB A47139 142 188 prove prove NN A47139 142 189 . . . A47139 143 1 Draw draw VB A47139 143 2 , , , A47139 143 3 ( ( -LRB- A47139 143 4 or or CC A47139 143 5 conceive conceive VB A47139 143 6 as as IN A47139 143 7 drawn draw VBN A47139 143 8 in in IN A47139 143 9 this this DT A47139 143 10 Figure figure NN A47139 143 11 ) ) -RRB- A47139 143 12 a a DT A47139 143 13 straight straight JJ A47139 143 14 Line line NN A47139 143 15 from from IN A47139 143 16 C c NN A47139 143 17 to to IN A47139 143 18 H h NN A47139 143 19 parallel parallel NN A47139 143 20 to to IN A47139 143 21 IM IM NNP A47139 143 22 , , , A47139 143 23 and and CC A47139 143 24 take take VB A47139 143 25 a a DT A47139 143 26 Cord Cord NNP A47139 143 27 of of IN A47139 143 28 any any DT A47139 143 29 of of IN A47139 143 30 those those DT A47139 143 31 Concentrick Concentrick NNP A47139 143 32 Arches Arches NNPS A47139 143 33 = = SYM A47139 143 34 ⅓ ⅓ NN A47139 143 35 of of IN A47139 143 36 the the DT A47139 143 37 Cord Cord NNP A47139 143 38 BC BC NNP A47139 143 39 = = SYM A47139 143 40 IM IM NNP A47139 143 41 , , , A47139 143 42 I -PRON- PRP A47139 143 43 say say VBP A47139 143 44 it -PRON- PRP A47139 143 45 must must MD A47139 143 46 terminate terminate VB A47139 143 47 on on IN A47139 143 48 the the DT A47139 143 49 line line NN A47139 143 50 IG IG NNP A47139 143 51 , , , A47139 143 52 and and CC A47139 143 53 neither neither CC A47139 143 54 go go VB A47139 143 55 without without IN A47139 143 56 it -PRON- PRP A47139 143 57 , , , A47139 143 58 nor nor CC A47139 143 59 within within IN A47139 143 60 it -PRON- PRP A47139 143 61 , , , A47139 143 62 otherwise otherwise RB A47139 143 63 the the DT A47139 143 64 same same JJ A47139 143 65 extent extent NN A47139 143 66 cutting cut VBG A47139 143 67 the the DT A47139 143 68 paralel paralel NNS A47139 143 69 Lines line NNS A47139 143 70 , , , A47139 143 71 viz viz NN A47139 143 72 . . . A47139 144 1 the the DT A47139 144 2 one one CD A47139 144 3 parallel parallel NN A47139 144 4 to to IN A47139 144 5 MC MC NNP A47139 144 6 , , , A47139 144 7 the the DT A47139 144 8 other other JJ A47139 144 9 to to IN A47139 144 10 IM IM NNP A47139 144 11 , , , A47139 144 12 shall shall MD A47139 144 13 make make VB A47139 144 14 the the DT A47139 144 15 opposite opposite JJ A47139 144 16 sides side NNS A47139 144 17 of of IN A47139 144 18 a a DT A47139 144 19 Paralellogram Paralellogram NNP A47139 144 20 unequal unequal JJ A47139 144 21 contrary contrary NN A47139 144 22 to to IN A47139 144 23 34 34 CD A47139 144 24 . . . A47139 145 1 1 1 LS A47139 145 2 . . . A47139 145 3 elem elem NNP A47139 145 4 . . . A47139 146 1 Eucl eucl VB A47139 146 2 . . . A47139 147 1 as as IN A47139 147 2 the the DT A47139 147 3 due due JJ A47139 147 4 Cosideration cosideration NN A47139 147 5 of of IN A47139 147 6 the the DT A47139 147 7 Figure Figure NNP A47139 147 8 Will Will MD A47139 147 9 show show VB A47139 147 10 , , , A47139 147 11 and and CC A47139 147 12 the the DT A47139 147 13 part part NN A47139 147 14 equal equal JJ A47139 147 15 to to IN A47139 147 16 the the DT A47139 147 17 whole whole NN A47139 147 18 . . . A47139 148 1 I -PRON- PRP A47139 148 2 have have VBP A47139 148 3 in in IN A47139 148 4 the the DT A47139 148 5 Example Example NNP A47139 148 6 of of IN A47139 148 7 Trisection Trisection NNP A47139 148 8 used use VBD A47139 148 9 an an DT A47139 148 10 obtuse obtuse JJ A47139 148 11 Angle Angle NNP A47139 148 12 , , , A47139 148 13 because because IN A47139 148 14 it -PRON- PRP A47139 148 15 is be VBZ A47139 148 16 more more RBR A47139 148 17 commodious commodious JJ A47139 148 18 and and CC A47139 148 19 easie easie VB A47139 148 20 to to TO A47139 148 21 be be VB A47139 148 22 done do VBN A47139 148 23 by by IN A47139 148 24 Manual Manual NNP A47139 148 25 Operation Operation NNP A47139 148 26 in in IN A47139 148 27 an an DT A47139 148 28 obtuse obtuse JJ A47139 148 29 Angle Angle NNP A47139 148 30 than than IN A47139 148 31 in in IN A47139 148 32 an an DT A47139 148 33 Acute acute NN A47139 148 34 as as IN A47139 148 35 Experience Experience NNP A47139 148 36 will will MD A47139 148 37 show show VB A47139 148 38 , , , A47139 148 39 though though IN A47139 148 40 the the DT A47139 148 41 demonstration demonstration NN A47139 148 42 is be VBZ A47139 148 43 the the DT A47139 148 44 same same JJ A47139 148 45 both both DT A47139 148 46 in in IN A47139 148 47 the the DT A47139 148 48 Obtuse Obtuse NNP A47139 148 49 and and CC A47139 148 50 Acute Acute NNP A47139 148 51 . . . A47139 149 1 Nor nor CC A47139 149 2 is be VBZ A47139 149 3 it -PRON- PRP A47139 149 4 any any DT A47139 149 5 just just RB A47139 149 6 exception exception NN A47139 149 7 , , , A47139 149 8 that that IN A47139 149 9 some some DT A47139 149 10 acute acute JJ A47139 149 11 Angles angle NNS A47139 149 12 being be VBG A47139 149 13 small small JJ A47139 149 14 , , , A47139 149 15 can can MD A47139 149 16 hardly hardly RB A47139 149 17 be be VB A47139 149 18 trisected trisect VBN A47139 149 19 by by IN A47139 149 20 this this DT A47139 149 21 Method Method NNP A47139 149 22 ; ; : A47139 149 23 for for IN A47139 149 24 when when WRB A47139 149 25 Angles angle NNS A47139 149 26 are be VBP A47139 149 27 very very RB A47139 149 28 acute acute JJ A47139 149 29 , , , A47139 149 30 they -PRON- PRP A47139 149 31 can can MD A47139 149 32 hardly hardly RB A47139 149 33 be be VB A47139 149 34 bisected bisect VBN A47139 149 35 . . . A47139 150 1 But but CC A47139 150 2 the the DT A47139 150 3 proper proper JJ A47139 150 4 Remedy remedy NN A47139 150 5 for for IN A47139 150 6 both both DT A47139 150 7 is be VBZ A47139 150 8 , , , A47139 150 9 when when WRB A47139 150 10 the the DT A47139 150 11 Angle Angle NNP A47139 150 12 is be VBZ A47139 150 13 small small JJ A47139 150 14 , , , A47139 150 15 double double JJ A47139 150 16 or or CC A47139 150 17 quadruple quadruple JJ A47139 150 18 it -PRON- PRP A47139 150 19 , , , A47139 150 20 and and CC A47139 150 21 then then RB A47139 150 22 bisect bisect JJ A47139 150 23 or or CC A47139 150 24 trisect trisect JJ A47139 150 25 it -PRON- PRP A47139 150 26 , , , A47139 150 27 as as IN A47139 150 28 occasion occasion NN A47139 150 29 requires require VBZ A47139 150 30 . . . A47139 151 1 The the DT A47139 151 2 Praxis Praxis NNP A47139 151 3 of of IN A47139 151 4 the the DT A47139 151 5 Trisection Trisection NNP A47139 151 6 hath hath NN A47139 151 7 these these DT A47139 151 8 following follow VBG A47139 151 9 great great JJ A47139 151 10 Uses use NNS A47139 151 11 . . . A47139 152 1 By by IN A47139 152 2 the the DT A47139 152 3 Trisection Trisection NNP A47139 152 4 of of IN A47139 152 5 the the DT A47139 152 6 Angle Angle NNP A47139 152 7 of of IN A47139 152 8 120 120 CD A47139 152 9 degrees degree NNS A47139 152 10 we -PRON- PRP A47139 152 11 have have VBP A47139 152 12 the the DT A47139 152 13 true true JJ A47139 152 14 Mathematical Mathematical NNP A47139 152 15 Cord Cord NNP A47139 152 16 of of IN A47139 152 17 40 40 CD A47139 152 18 degrees degree NNS A47139 152 19 , , , A47139 152 20 and and CC A47139 152 21 seeing see VBG A47139 152 22 it -PRON- PRP A47139 152 23 is be VBZ A47139 152 24 demonstrated demonstrate VBN A47139 152 25 in in IN A47139 152 26 11 11 CD A47139 152 27 . . . A47139 153 1 4 4 LS A47139 153 2 . . . A47139 153 3 elem elem NNP A47139 153 4 . . . A47139 154 1 Euclid euclid JJ A47139 154 2 . . . A47139 155 1 to to TO A47139 155 2 find find VB A47139 155 3 the the DT A47139 155 4 Cord Cord NNP A47139 155 5 of of IN A47139 155 6 ⅕ ⅕ , A47139 155 7 of of IN A47139 155 8 the the DT A47139 155 9 Circle Circle NNP A47139 155 10 , , , A47139 155 11 = = SYM A47139 155 12 72 72 CD A47139 155 13 degrees degree NNS A47139 155 14 the the DT A47139 155 15 ½ ½ NNP A47139 155 16 = = SYM A47139 155 17 36 36 CD A47139 155 18 by by IN A47139 155 19 substracting substracte VBG A47139 155 20 36d 36d NNS A47139 155 21 . . . A47139 156 1 from from IN A47139 156 2 40d 40d NNS A47139 156 3 . . . A47139 157 1 we -PRON- PRP A47139 157 2 have have VBP A47139 157 3 the the DT A47139 157 4 true true JJ A47139 157 5 Cord Cord NNP A47139 157 6 of of IN A47139 157 7 4 4 CD A47139 157 8 degrees degree NNS A47139 157 9 , , , A47139 157 10 that that WDT A47139 157 11 bisected bisect VBD A47139 157 12 gives give VBZ A47139 157 13 the the DT A47139 157 14 Cord Cord NNP A47139 157 15 of of IN A47139 157 16 2 2 CD A47139 157 17 degrees degree NNS A47139 157 18 and and CC A47139 157 19 that that IN A47139 157 20 again again RB A47139 157 21 bisected bisect VBD A47139 157 22 gives give VBZ A47139 157 23 the the DT A47139 157 24 Cord Cord NNP A47139 157 25 of of IN A47139 157 26 I -PRON- PRP A47139 157 27 degree degree VBP A47139 157 28 . . . A47139 158 1 Also also RB A47139 158 2 40 40 CD A47139 158 3 degrees degree NNS A47139 158 4 twice twice RB A47139 158 5 bisected bisect VBN A47139 158 6 gives give VBZ A47139 158 7 10 10 CD A47139 158 8 degrees degree NNS A47139 158 9 , , , A47139 158 10 and and CC A47139 158 11 that that IN A47139 158 12 again again RB A47139 158 13 bisected bisect VBD A47139 158 14 gives give VBZ A47139 158 15 5 5 CD A47139 158 16 . . . A47139 158 17 and and CC A47139 158 18 thus thus RB A47139 158 19 by by IN A47139 158 20 the the DT A47139 158 21 Trisection Trisection NNP A47139 158 22 of of IN A47139 158 23 120 120 CD A47139 158 24 or or CC A47139 158 25 60 60 CD A47139 158 26 degrees degree NNS A47139 158 27 , , , A47139 158 28 and and CC A47139 158 29 certain certain JJ A47139 158 30 other other JJ A47139 158 31 bisections bisection NNS A47139 158 32 a a DT A47139 158 33 line line NN A47139 158 34 of of IN A47139 158 35 Cords Cords NNPS A47139 158 36 truly truly RB A47139 158 37 Geometrical geometrical JJ A47139 158 38 or or CC A47139 158 39 Mathematical Mathematical NNP A47139 158 40 can can MD A47139 158 41 be be VB A47139 158 42 made make VBN A47139 158 43 by by IN A47139 158 44 plain plain JJ A47139 158 45 Geometry Geometry NNP A47139 158 46 , , , A47139 158 47 without without IN A47139 158 48 all all DT A47139 158 49 conick conick NN A47139 158 50 Sections section NNS A47139 158 51 or or CC A47139 158 52 Algebra Algebra NNP A47139 158 53 Aequations Aequations NNPS A47139 158 54 , , , A47139 158 55 and and CC A47139 158 56 tedious tedious JJ A47139 158 57 Extractions extraction NNS A47139 158 58 of of IN A47139 158 59 Roots root NNS A47139 158 60 , , , A47139 158 61 and and CC A47139 158 62 also also RB A47139 158 63 without without IN A47139 158 64 any any DT A47139 158 65 Table table NN A47139 158 66 of of IN A47139 158 67 natural natural JJ A47139 158 68 Sines Sines NNPS A47139 158 69 , , , A47139 158 70 which which WDT A47139 158 71 never never RB A47139 158 72 hitherto hitherto VBD A47139 158 73 hath hath NNP A47139 158 74 been be VBN A47139 158 75 taught teach VBN A47139 158 76 ( ( -LRB- A47139 158 77 so so RB A47139 158 78 far far RB A47139 158 79 as as IN A47139 158 80 I -PRON- PRP A47139 158 81 ever ever RB A47139 158 82 heard hear VBD A47139 158 83 or or CC A47139 158 84 read read VB A47139 158 85 ) ) -RRB- A47139 158 86 in in IN A47139 158 87 a a DT A47139 158 88 plain plain JJ A47139 158 89 method method NN A47139 158 90 , , , A47139 158 91 by by IN A47139 158 92 plain plain JJ A47139 158 93 Geometry Geometry NNP A47139 158 94 , , , A47139 158 95 so so IN A47139 158 96 as as IN A47139 158 97 to to TO A47139 158 98 be be VB A47139 158 99 made make VBN A47139 158 100 intelligible intelligible JJ A47139 158 101 to to IN A47139 158 102 any any DT A47139 158 103 Tiro Tiro NNP A47139 158 104 or or CC A47139 158 105 Young Young NNP A47139 158 106 Artist Artist NNP A47139 158 107 ; ; : A47139 158 108 and and CC A47139 158 109 yet yet RB A47139 158 110 such such PDT A47139 158 111 a a DT A47139 158 112 method method NN A47139 158 113 is be VBZ A47139 158 114 altogether altogether RB A47139 158 115 necessary necessary JJ A47139 158 116 for for IN A47139 158 117 the the DT A47139 158 118 perfection perfection NN A47139 158 119 of of IN A47139 158 120 Geometry Geometry NNP A47139 158 121 and and CC A47139 158 122 Mathematical Mathematical NNP A47139 158 123 Learning Learning NNP A47139 158 124 , , , A47139 158 125 that that IN A47139 158 126 the the DT A47139 158 127 way way NN A47139 158 128 to to TO A47139 158 129 trisect trisect VB A47139 158 130 any any DT A47139 158 131 Angle Angle NNP A47139 158 132 be be VB A47139 158 133 known know VBN A47139 158 134 by by IN A47139 158 135 plain plain JJ A47139 158 136 Geometry Geometry NNP A47139 158 137 , , , A47139 158 138 seeing see VBG A47139 158 139 many many JJ A47139 158 140 things thing NNS A47139 158 141 in in IN A47139 158 142 plain plain JJ A47139 158 143 Geometry Geometry NNP A47139 158 144 require require VBP A47139 158 145 a a DT A47139 158 146 true true JJ A47139 158 147 line line NN A47139 158 148 of of IN A47139 158 149 Cords Cords NNP A47139 158 150 , , , A47139 158 151 and and CC A47139 158 152 a a DT A47139 158 153 true true JJ A47139 158 154 line line NN A47139 158 155 of of IN A47139 158 156 Cords Cords NNPS A47139 158 157 can can MD A47139 158 158 not not RB A47139 158 159 be be VB A47139 158 160 found find VBN A47139 158 161 without without IN A47139 158 162 the the DT A47139 158 163 Trisection Trisection NNP A47139 158 164 of of IN A47139 158 165 certain certain JJ A47139 158 166 Angles Angles NNPS A47139 158 167 , , , A47139 158 168 or or CC A47139 158 169 some some DT A47139 158 170 other other JJ A47139 158 171 Section Section NNP A47139 158 172 than than IN A47139 158 173 Bisection bisection NN A47139 158 174 ; ; : A47139 158 175 and and CC A47139 158 176 to to TO A47139 158 177 refer refer VB A47139 158 178 a a DT A47139 158 179 Tiro Tiro NNP A47139 158 180 , , , A47139 158 181 or or CC A47139 158 182 Young Young NNP A47139 158 183 Scholar Scholar NNP A47139 158 184 , , , A47139 158 185 to to IN A47139 158 186 the the DT A47139 158 187 conick conick JJ A47139 158 188 Sections section NNS A47139 158 189 , , , A47139 158 190 and and CC A47139 158 191 tedious tedious JJ A47139 158 192 Algebra Algebra NNP A47139 158 193 Aequations Aequations NNPS A47139 158 194 and and CC A47139 158 195 Resolutions resolution NNS A47139 158 196 how how WRB A47139 158 197 to to TO A47139 158 198 trisect trisect VB A47139 158 199 an an DT A47139 158 200 Angle angle NN A47139 158 201 , , , A47139 158 202 or or CC A47139 158 203 understand understand VB A47139 158 204 how how WRB A47139 158 205 to to TO A47139 158 206 make make VB A47139 158 207 a a DT A47139 158 208 true true JJ A47139 158 209 Geometrical Geometrical NNP A47139 158 210 Line Line NNP A47139 158 211 of of IN A47139 158 212 Cords Cords NNP A47139 158 213 is be VBZ A47139 158 214 altogether altogether RB A47139 158 215 immethodical immethodical JJ A47139 158 216 , , , A47139 158 217 even even RB A47139 158 218 as as RB A47139 158 219 much much JJ A47139 158 220 or or CC A47139 158 221 more more JJR A47139 158 222 as as IN A47139 158 223 to to TO A47139 158 224 referr referr VB A47139 158 225 him -PRON- PRP A47139 158 226 to to IN A47139 158 227 some some DT A47139 158 228 of of IN A47139 158 229 the the DT A47139 158 230 difficultest difficultest NN A47139 158 231 Problems problem NNS A47139 158 232 in in IN A47139 158 233 Euclid Euclid NNP A47139 158 234 's 's POS A47139 158 235 Elements Elements NNPS A47139 158 236 to to TO A47139 158 237 understand understand VB A47139 158 238 the the DT A47139 158 239 demonstration demonstration NN A47139 158 240 of of IN A47139 158 241 one one CD A47139 158 242 of of IN A47139 158 243 the the DT A47139 158 244 first first JJ A47139 158 245 Propositions Propositions NNPS A47139 158 246 in in IN A47139 158 247 those those DT A47139 158 248 Elements element NNS A47139 158 249 . . . A47139 159 1 Seeing see VBG A47139 159 2 therefore therefore RB A47139 159 3 Geometry Geometry NNP A47139 159 4 as as IN A47139 159 5 it -PRON- PRP A47139 159 6 is be VBZ A47139 159 7 one one CD A47139 159 8 of of IN A47139 159 9 the the DT A47139 159 10 best good JJS A47139 159 11 natural natural JJ A47139 159 12 Sciences Sciences NNPS A47139 159 13 for for IN A47139 159 14 certainty certainty NN A47139 159 15 and and CC A47139 159 16 use use NN A47139 159 17 , , , A47139 159 18 so so RB A47139 159 19 for for IN A47139 159 20 good good JJ A47139 159 21 Method Method NNP A47139 159 22 ; ; : A47139 159 23 and and CC A47139 159 24 the the DT A47139 159 25 nature nature NN A47139 159 26 of of IN A47139 159 27 good good JJ A47139 159 28 Method Method NNP A47139 159 29 requireth requireth NN A47139 159 30 that that IN A47139 159 31 in in IN A47139 159 32 reaching reach VBG A47139 159 33 we -PRON- PRP A47139 159 34 proceed proceed VBP A47139 159 35 to to IN A47139 159 36 the the DT A47139 159 37 more more RBR A47139 159 38 unknown unknown JJ A47139 159 39 from from IN A47139 159 40 and and CC A47139 159 41 by by IN A47139 159 42 the the DT A47139 159 43 more more RBR A47139 159 44 known know VBN A47139 159 45 , , , A47139 159 46 therefore therefore RB A47139 159 47 to to TO A47139 159 48 presuppose presuppose VB A47139 159 49 the the DT A47139 159 50 knowledge knowledge NN A47139 159 51 of of IN A47139 159 52 conick conick JJ A47139 159 53 Sections section NNS A47139 159 54 to to IN A47139 159 55 the the DT A47139 159 56 knowledge knowledge NN A47139 159 57 of of IN A47139 159 58 some some DT A47139 159 59 necessary necessary JJ A47139 159 60 Problems problem NNS A47139 159 61 in in IN A47139 159 62 plain plain JJ A47139 159 63 Geometry Geometry NNP A47139 159 64 , , , A47139 159 65 is be VBZ A47139 159 66 greatly greatly RB A47139 159 67 incongruous incongruous JJ A47139 159 68 and and CC A47139 159 69 an an DT A47139 159 70 immethodical immethodical JJ A47139 159 71 Hysteron Hysteron NNP A47139 159 72 Proteron Proteron NNP A47139 159 73 , , , A47139 159 74 which which WDT A47139 159 75 this this DT A47139 159 76 new new JJ A47139 159 77 Praxis praxis JJ A47139 159 78 doth doth NN A47139 159 79 Remedy remedy NN A47139 159 80 . . . A47139 160 1 2 2 LS A47139 160 2 . . . A47139 161 1 By by IN A47139 161 2 this this DT A47139 161 3 Praxis Praxis NNP A47139 161 4 of of IN A47139 161 5 Trisection Trisection NNP A47139 161 6 a a NNP A47139 161 7 Foundation Foundation NNP A47139 161 8 of of IN A47139 161 9 Method Method NNP A47139 161 10 is be VBZ A47139 161 11 Iaid Iaid NNP A47139 161 12 to to TO A47139 161 13 sect sect VB A47139 161 14 any any DT A47139 161 15 Angle Angle NNP A47139 161 16 given give VBN A47139 161 17 into into IN A47139 161 18 any any DT A47139 161 19 other other JJ A47139 161 20 equal equal JJ A47139 161 21 parts part NNS A47139 161 22 whatsoever whatsoever RB A47139 161 23 , , , A47139 161 24 even even RB A47139 161 25 as as IN A47139 161 26 4 4 CD A47139 161 27 . . . A47139 162 1 6 6 CD A47139 162 2 . . . A47139 163 1 8 8 LS A47139 163 2 . . . A47139 164 1 10 10 CD A47139 164 2 . . . A47139 164 3 or or CC A47139 164 4 uneven uneven JJ A47139 164 5 as as IN A47139 164 6 5 5 CD A47139 164 7 . . . A47139 165 1 7 7 LS A47139 165 2 . . . A47139 166 1 9 9 CD A47139 166 2 . . . A47139 167 1 11 11 CD A47139 167 2 . . . A47139 168 1 & & CC A47139 168 2 c. c. NNP A47139 168 3 and and CC A47139 168 4 an an DT A47139 168 5 universal universal JJ A47139 168 6 Cannon Cannon NNP A47139 168 7 is be VBZ A47139 168 8 formed form VBN A47139 168 9 , , , A47139 168 10 as as IN A47139 168 11 by by IN A47139 168 12 trisection trisection NN A47139 168 13 of of IN A47139 168 14 the the DT A47139 168 15 Cord Cord NNP A47139 168 16 of of IN A47139 168 17 an an DT A47139 168 18 Angle Angle NNP A47139 168 19 , , , A47139 168 20 that that IN A47139 168 21 Angle Angle NNP A47139 168 22 is be VBZ A47139 168 23 trisected trisect VBN A47139 168 24 , , , A47139 168 25 so so RB A47139 168 26 by by IN A47139 168 27 quinquisection quinquisection NN A47139 168 28 of of IN A47139 168 29 the the DT A47139 168 30 Cord Cord NNP A47139 168 31 of of IN A47139 168 32 an an DT A47139 168 33 Angle angle NN A47139 168 34 it -PRON- PRP A47139 168 35 is be VBZ A47139 168 36 quinquisected quinquisecte VBN A47139 168 37 , , , A47139 168 38 and and CC A47139 168 39 the the DT A47139 168 40 like like JJ A47139 168 41 of of IN A47139 168 42 all all DT A47139 168 43 others other NNS A47139 168 44 . . . A47139 169 1 3 3 LS A47139 169 2 . . . A47139 170 1 By by IN A47139 170 2 the the DT A47139 170 3 like like JJ A47139 170 4 method method NN A47139 170 5 a a DT A47139 170 6 Circle Circle NNP A47139 170 7 is be VBZ A47139 170 8 divided divide VBN A47139 170 9 into into IN A47139 170 10 any any DT A47139 170 11 number number NN A47139 170 12 of of IN A47139 170 13 equal equal JJ A47139 170 14 parts part NNS A47139 170 15 even even RB A47139 170 16 or or CC A47139 170 17 uneven uneven JJ A47139 170 18 . . . A47139 171 1 4 4 LS A47139 171 2 . . . A47139 172 1 And and CC A47139 172 2 , , , A47139 172 3 by by IN A47139 172 4 the the DT A47139 172 5 like like JJ A47139 172 6 Method Method NNP A47139 172 7 , , , A47139 172 8 the the DT A47139 172 9 quantity quantity NN A47139 172 10 of of IN A47139 172 11 any any DT A47139 172 12 Right right NN A47139 172 13 - - HYPH A47139 172 14 lined line VBN A47139 172 15 Angle Angle NNP A47139 172 16 can can MD A47139 172 17 be be VB A47139 172 18 found find VBN A47139 172 19 in in IN A47139 172 20 degrees degree NNS A47139 172 21 , , , A47139 172 22 and and CC A47139 172 23 odd odd JJ A47139 172 24 Minutes Minutes NNP A47139 172 25 , , , A47139 172 26 without without IN A47139 172 27 any any DT A47139 172 28 line line NN A47139 172 29 of of IN A47139 172 30 Cords Cords NNPS A47139 172 31 by by IN A47139 172 32 a a DT A47139 172 33 line line NN A47139 172 34 of of IN A47139 172 35 equal equal JJ A47139 172 36 parts part NNS A47139 172 37 only only RB A47139 172 38 , , , A47139 172 39 as as IN A47139 172 40 the the DT A47139 172 41 diagonal diagonal JJ A47139 172 42 Scale Scale NNP A47139 172 43 of of IN A47139 172 44 Inch Inch NNP A47139 172 45 , , , A47139 172 46 or or CC A47139 172 47 half half NN A47139 172 48 Inch Inch NNP A47139 172 49 or or CC A47139 172 50 ¼ ¼ RB A47139 172 51 to to IN A47139 172 52 a a DT A47139 172 53 far far RB A47139 172 54 greater great JJR A47139 172 55 exactness exactness NN A47139 172 56 than than IN A47139 172 57 by by IN A47139 172 58 a a DT A47139 172 59 line line NN A47139 172 60 of of IN A47139 172 61 Cords Cords NNPS A47139 172 62 . . . A47139 173 1 5 5 CD A47139 173 2 . . . A47139 174 1 By by IN A47139 174 2 the the DT A47139 174 3 same same JJ A47139 174 4 , , , A47139 174 5 a a DT A47139 174 6 way way NN A47139 174 7 is be VBZ A47139 174 8 taught teach VBN A47139 174 9 how how WRB A47139 174 10 to to TO A47139 174 11 protract protract VB A47139 174 12 or or CC A47139 174 13 project project VB A47139 174 14 any any DT A47139 174 15 Angle Angle NNP A47139 174 16 , , , A47139 174 17 whose whose WP$ A47139 174 18 degrees degree NNS A47139 174 19 and and CC A47139 174 20 odd odd JJ A47139 174 21 Minutes Minutes NNPS A47139 174 22 are be VBP A47139 174 23 given give VBN A47139 174 24 . . . A47139 175 1 6 6 CD A47139 175 2 . . . A47139 176 1 Having have VBG A47139 176 2 any any DT A47139 176 3 one one CD A47139 176 4 Angle angle NN A47139 176 5 given give VBN A47139 176 6 in in IN A47139 176 7 any any DT A47139 176 8 Triangle Triangle NNP A47139 176 9 , , , A47139 176 10 and and CC A47139 176 11 the the DT A47139 176 12 Ratio ratio NN A47139 176 13 of of IN A47139 176 14 the the DT A47139 176 15 2 2 CD A47139 176 16 other other JJ A47139 176 17 Angles Angles NNPS A47139 176 18 , , , A47139 176 19 without without IN A47139 176 20 any any DT A47139 176 21 side side NN A47139 176 22 given give VBN A47139 176 23 , , , A47139 176 24 to to TO A47139 176 25 find find VB A47139 176 26 the the DT A47139 176 27 other other JJ A47139 176 28 2 2 CD A47139 176 29 Angles Angles NNPS A47139 176 30 , , , A47139 176 31 and and CC A47139 176 32 truly truly RB A47139 176 33 to to TO A47139 176 34 protract protract VB A47139 176 35 them -PRON- PRP A47139 176 36 . . . A47139 177 1 7 7 LS A47139 177 2 . . . A47139 178 1 From from IN A47139 178 2 a a DT A47139 178 3 point point NN A47139 178 4 given give VBN A47139 178 5 on on IN A47139 178 6 any any DT A47139 178 7 line line NN A47139 178 8 given give VBN A47139 178 9 to to TO A47139 178 10 raise raise VB A47139 178 11 an an DT A47139 178 12 Isosceles Isosceles NNP A47139 178 13 Triangle Triangle NNP A47139 178 14 , , , A47139 178 15 one one CD A47139 178 16 of of IN A47139 178 17 whose whose WP$ A47139 178 18 sides side NNS A47139 178 19 being be VBG A47139 178 20 produced produce VBN A47139 178 21 below below IN A47139 178 22 that that DT A47139 178 23 line line NN A47139 178 24 given give VBN A47139 178 25 shall shall MD A47139 178 26 terminate terminate VB A47139 178 27 on on IN A47139 178 28 any any DT A47139 178 29 Point Point NNP A47139 178 30 , , , A47139 178 31 given give VBN A47139 178 32 below below IN A47139 178 33 the the DT A47139 178 34 same same JJ A47139 178 35 , , , A47139 178 36 the the DT A47139 178 37 which which WDT A47139 178 38 hath hath NNP A47139 178 39 special special JJ A47139 178 40 use use NN A47139 178 41 to to TO A47139 178 42 solve solve VB A47139 178 43 some some DT A47139 178 44 new new JJ A47139 178 45 Problems problem NNS A47139 178 46 in in IN A47139 178 47 Surveying Surveying NNP A47139 178 48 , , , A47139 178 49 Geography Geography NNP A47139 178 50 , , , A47139 178 51 Architecture Architecture NNP A47139 178 52 , , , A47139 178 53 Navigation Navigation NNP A47139 178 54 . . . A47139 179 1 8 8 LS A47139 179 2 . . . A47139 180 1 As as IN A47139 180 2 this this DT A47139 180 3 method method NN A47139 180 4 of of IN A47139 180 5 Praxis Praxis NNP A47139 180 6 saveth saveth VB A47139 180 7 the the DT A47139 180 8 pains pain NNS A47139 180 9 of of IN A47139 180 10 finding find VBG A47139 180 11 out out RP A47139 180 12 Trisection Trisection NNP A47139 180 13 of of IN A47139 180 14 an an DT A47139 180 15 Angle angle NN A47139 180 16 by by IN A47139 180 17 a a DT A47139 180 18 conick conick NN A47139 180 19 Section section NN A47139 180 20 , , , A47139 180 21 and and CC A47139 180 22 Algebra Algebra NNP A47139 180 23 Aequations Aequations NNPS A47139 180 24 , , , A47139 180 25 by by IN A47139 180 26 teaching teach VBG A47139 180 27 the the DT A47139 180 28 same same JJ A47139 180 29 more more RBR A47139 180 30 easily easily RB A47139 180 31 by by IN A47139 180 32 plain plain JJ A47139 180 33 Geometry Geometry NNP A47139 180 34 , , , A47139 180 35 so so CC A47139 180 36 it -PRON- PRP A47139 180 37 is be VBZ A47139 180 38 probable probable JJ A47139 180 39 it -PRON- PRP A47139 180 40 may may MD A47139 180 41 prove prove VB A47139 180 42 of of IN A47139 180 43 great great JJ A47139 180 44 use use NN A47139 180 45 , , , A47139 180 46 both both CC A47139 180 47 in in IN A47139 180 48 conick conick JJ A47139 180 49 Sections section NNS A47139 180 50 , , , A47139 180 51 Algebra Algebra NNP A47139 180 52 Questions Questions NNPS A47139 180 53 , , , A47139 180 54 and and CC A47139 180 55 other other JJ A47139 180 56 abstruse abstruse NN A47139 180 57 Theorems Theorems NNPS A47139 180 58 to to TO A47139 180 59 improve improve VB A47139 180 60 the the DT A47139 180 61 Mathematical Mathematical NNP A47139 180 62 Sciences Sciences NNPS A47139 180 63 . . . A47139 181 1 9 9 CD A47139 181 2 . . . A47139 182 1 How how WRB A47139 182 2 to to TO A47139 182 3 find find VB A47139 182 4 the the DT A47139 182 5 natural natural JJ A47139 182 6 Cord Cord NNP A47139 182 7 , , , A47139 182 8 Sine Sine NNP A47139 182 9 , , , A47139 182 10 Tangent Tangent NNP A47139 182 11 , , , A47139 182 12 Secant secant NN A47139 182 13 of of IN A47139 182 14 any any DT A47139 182 15 Angle Angle NNP A47139 182 16 given give VBN A47139 182 17 in in IN A47139 182 18 degrees degree NNS A47139 182 19 and and CC A47139 182 20 Minutes Minutes NNPS A47139 182 21 , , , A47139 182 22 in in IN A47139 182 23 true true JJ A47139 182 24 Lines line NNS A47139 182 25 , , , A47139 182 26 more more RBR A47139 182 27 exactly exactly RB A47139 182 28 , , , A47139 182 29 than than IN A47139 182 30 by by IN A47139 182 31 any any DT A47139 182 32 common common JJ A47139 182 33 Line Line NNP A47139 182 34 of of IN A47139 182 35 Cords Cords NNPS A47139 182 36 . . . A47139 183 1 Here here RB A47139 183 2 followeth followeth VB A47139 183 3 another another DT A47139 183 4 Demonstration Demonstration NNP A47139 183 5 of of IN A47139 183 6 the the DT A47139 183 7 same same JJ A47139 183 8 Praxis Praxis NNP A47139 183 9 of of IN A47139 183 10 the the DT A47139 183 11 Trisection Trisection NNP A47139 183 12 . . . A47139 184 1 In in IN A47139 184 2 a a DT A47139 184 3 Second second JJ A47139 184 4 Figure figure NN A47139 184 5 . . . A47139 185 1 BY by IN A47139 185 2 the the DT A47139 185 3 method method NN A47139 185 4 of of IN A47139 185 5 the the DT A47139 185 6 foregoing foregoing JJ A47139 185 7 Praxis Praxis NNP A47139 185 8 , , , A47139 185 9 let let VB A47139 185 10 the the DT A47139 185 11 points point NNS A47139 185 12 I -PRON- PRP A47139 185 13 and and CC A47139 185 14 O o UH A47139 185 15 be be VB A47139 185 16 found find VBN A47139 185 17 , , , A47139 185 18 and and CC A47139 185 19 the the DT A47139 185 20 lines line NNS A47139 185 21 AI AI NNP A47139 185 22 and and CC A47139 185 23 AO AO NNP A47139 185 24 , , , A47139 185 25 which which WDT A47139 185 26 I -PRON- PRP A47139 185 27 say say VBP A47139 185 28 shall shall MD A47139 185 29 trisect trisect VB A47139 185 30 the the DT A47139 185 31 Angle Angle NNP A47139 185 32 NAK NAK NNP A47139 185 33 = = SYM A47139 185 34 BAC BAC NNP A47139 185 35 , , , A47139 185 36 Geometically geometically RB A47139 185 37 into into IN A47139 185 38 three three CD A47139 185 39 equal equal JJ A47139 185 40 parts part NNS A47139 185 41 . . . A47139 186 1 In in IN A47139 186 2 order order NN A47139 186 3 to to IN A47139 186 4 the the DT A47139 186 5 demonstration demonstration NN A47139 186 6 of of IN A47139 186 7 which which WDT A47139 186 8 , , , A47139 186 9 extend extend VB A47139 186 10 the the DT A47139 186 11 line line NN A47139 186 12 AI ai NN A47139 186 13 to to IN A47139 186 14 D d NN A47139 186 15 on on IN A47139 186 16 the the DT A47139 186 17 arch arch JJ A47139 186 18 BFC BFC NNP A47139 186 19 . . . A47139 187 1 and and CC A47139 187 2 AO AO NNP A47139 187 3 to to IN A47139 187 4 X. X. NNP A47139 188 1 Again again RB A47139 188 2 , , , A47139 188 3 with with IN A47139 188 4 the the DT A47139 188 5 extent extent NN A47139 188 6 AI AI NNP A47139 188 7 on on IN A47139 188 8 the the DT A47139 188 9 center center NN A47139 188 10 I -PRON- PRP A47139 188 11 describe describe VBP A47139 188 12 the the DT A47139 188 13 circle circle NN A47139 188 14 ASHT ASHT NNP A47139 188 15 . . . A47139 189 1 and and CC A47139 189 2 with with IN A47139 189 3 the the DT A47139 189 4 same same JJ A47139 189 5 Radius Radius NNP A47139 189 6 describe describe VB A47139 189 7 the the DT A47139 189 8 arch arch JJ A47139 189 9 KLON KLON NNP A47139 189 10 . . . A47139 190 1 Again again RB A47139 190 2 , , , A47139 190 3 draw draw VB A47139 190 4 IH IH NNP A47139 190 5 parallel parallel NN A47139 190 6 to to IN A47139 190 7 AK AK NNP A47139 190 8 , , , A47139 190 9 extending extend VBG A47139 190 10 IH IH NNP A47139 190 11 to to IN A47139 190 12 the the DT A47139 190 13 Circumference Circumference NNP A47139 190 14 of of IN A47139 190 15 the the DT A47139 190 16 Circle Circle NNP A47139 190 17 ASHT ASHT NNP A47139 190 18 . . . A47139 191 1 Again again RB A47139 191 2 , , , A47139 191 3 draw draw VB A47139 191 4 AS as IN A47139 191 5 parallel parallel NN A47139 191 6 and and CC A47139 191 7 equal equal JJ A47139 191 8 to to IN A47139 191 9 OI OI NNP A47139 191 10 , , , A47139 191 11 which which WDT A47139 191 12 shall shall MD A47139 191 13 cut cut VB A47139 191 14 the the DT A47139 191 15 circle circle NN A47139 191 16 at at IN A47139 191 17 S S NNP A47139 191 18 , , , A47139 191 19 because because IN A47139 191 20 OI OI NNP A47139 191 21 = = SYM A47139 191 22 AS AS NNP A47139 191 23 cuts cut VBZ A47139 191 24 the the DT A47139 191 25 arch arch JJ A47139 191 26 KION kion NN A47139 191 27 , , , A47139 191 28 having have VBG A47139 191 29 the the DT A47139 191 30 same same JJ A47139 191 31 Radius Radius NNP A47139 191 32 . . . A47139 192 1 Again again RB A47139 192 2 , , , A47139 192 3 from from IN A47139 192 4 the the DT A47139 192 5 point point NN A47139 192 6 S s NN A47139 192 7 on on IN A47139 192 8 the the DT A47139 192 9 circumference circumference NN A47139 192 10 , , , A47139 192 11 draw draw VB A47139 192 12 the the DT A47139 192 13 line line NN A47139 192 14 SH SH NNP A47139 192 15 parallel parallel JJ A47139 192 16 to to IN A47139 192 17 AI AI NNP A47139 192 18 , , , A47139 192 19 which which WDT A47139 192 20 shall shall MD A47139 192 21 necessarily necessarily RB A47139 192 22 cut cut VB A47139 192 23 the the DT A47139 192 24 line line NN A47139 192 25 IH IH NNP A47139 192 26 on on IN A47139 192 27 the the DT A47139 192 28 circumference circumference NN A47139 192 29 at at IN A47139 192 30 the the DT A47139 192 31 point point NN A47139 192 32 H h NN A47139 192 33 , , , A47139 192 34 because because IN A47139 192 35 by by IN A47139 192 36 construction construction NN A47139 192 37 IH IH NNP A47139 192 38 is be VBZ A47139 192 39 parallel parallel JJ A47139 192 40 to to IN A47139 192 41 AK AK NNP A47139 192 42 , , , A47139 192 43 and and CC A47139 192 44 KH KH NNP A47139 192 45 to to IN A47139 192 46 AI AI NNP A47139 192 47 , , , A47139 192 48 which which WDT A47139 192 49 makes make VBZ A47139 192 50 the the DT A47139 192 51 Parallogram Parallogram NNP A47139 192 52 AKHI AKHI NNP A47139 192 53 , , , A47139 192 54 whose whose WP$ A47139 192 55 opposit opposit JJ A47139 192 56 sides side NNS A47139 192 57 are be VBP A47139 192 58 equal equal JJ A47139 192 59 , , , A47139 192 60 but but CC A47139 192 61 if if IN A47139 192 62 SH SH NNP A47139 192 63 , , , A47139 192 64 and and CC A47139 192 65 IH IH NNP A47139 192 66 did do VBD A47139 192 67 meet meet VB A47139 192 68 any any DT A47139 192 69 where where WRB A47139 192 70 else else RB A47139 192 71 than than IN A47139 192 72 on on IN A47139 192 73 the the DT A47139 192 74 circumference circumference NN A47139 192 75 , , , A47139 192 76 as as IN A47139 192 77 either either DT A47139 192 78 within within IN A47139 192 79 , , , A47139 192 80 or or CC A47139 192 81 without without IN A47139 192 82 it -PRON- PRP A47139 192 83 , , , A47139 192 84 the the DT A47139 192 85 opposit opposit JJ A47139 192 86 sides side NNS A47139 192 87 of of IN A47139 192 88 the the DT A47139 192 89 Parallogram Parallogram NNP A47139 192 90 should should MD A47139 192 91 not not RB A47139 192 92 be be VB A47139 192 93 equal equal JJ A47139 192 94 contrary contrary NN A47139 192 95 to to IN A47139 192 96 34 34 CD A47139 192 97 . . . A47139 193 1 1 1 LS A47139 193 2 . . . A47139 194 1 Eucl eucl VB A47139 194 2 . . . A47139 195 1 elem elem NNP A47139 195 2 . . . A47139 196 1 Again again RB A47139 196 2 , , , A47139 196 3 draw draw VB A47139 196 4 the the DT A47139 196 5 line line NN A47139 196 6 SI SI NNP A47139 196 7 , , , A47139 196 8 and and CC A47139 196 9 extend extend VB A47139 196 10 the the DT A47139 196 11 line line NN A47139 196 12 OI OI NNP A47139 196 13 from from IN A47139 196 14 I -PRON- PRP A47139 196 15 to to IN A47139 196 16 K k NN A47139 196 17 until until IN A47139 196 18 it -PRON- PRP A47139 196 19 cut cut VBD A47139 196 20 SH SH NNP A47139 196 21 at at IN A47139 196 22 K K NNP A47139 196 23 , , , A47139 196 24 which which WDT A47139 196 25 shall shall MD A47139 196 26 form form VB A47139 196 27 another another DT A47139 196 28 Parallogram Parallogram NNP A47139 196 29 ASKI ASKI NNP A47139 196 30 , , , A47139 196 31 which which WDT A47139 196 32 being be VBG A47139 196 33 divided divide VBN A47139 196 34 by by IN A47139 196 35 the the DT A47139 196 36 Diagonal diagonal JJ A47139 196 37 line line NN A47139 196 38 SI SI NNP A47139 196 39 , , , A47139 196 40 shall shall MD A47139 196 41 give give VB A47139 196 42 two two CD A47139 196 43 equal equal JJ A47139 196 44 Isosceies Isosceies NNPS A47139 196 45 Triangles triangle NNS A47139 196 46 AIS AIS NNP A47139 196 47 ( ( -LRB- A47139 196 48 = = SYM A47139 196 49 OAI OAI NNP A47139 196 50 ) ) -RRB- A47139 196 51 ISK ISK NNP A47139 196 52 . . . A47139 197 1 The the DT A47139 197 2 Demonstration Demonstration NNP A47139 197 3 . . . A47139 198 1 In in IN A47139 198 2 the the DT A47139 198 3 Isoceles isocele NNS A47139 198 4 triangle triangle NN A47139 198 5 ISH ISH NNP A47139 198 6 ( ( -LRB- A47139 198 7 whose whose WP$ A47139 198 8 sides side NNS A47139 198 9 IS be VBZ A47139 198 10 = = SYM A47139 198 11 IH IH NNP A47139 198 12 by by IN A47139 198 13 15 15 CD A47139 198 14 . . . A47139 198 15 def def NNP A47139 198 16 . . . A47139 199 1 1 1 LS A47139 199 2 . . . A47139 199 3 elem elem NNP A47139 199 4 . . . A47139 199 5 ) ) -RRB- A47139 200 1 the the DT A47139 200 2 angle angle NN A47139 200 3 IHS IHS NNP A47139 200 4 = = SYM A47139 200 5 ISH ISH NNP A47139 200 6 by by IN A47139 200 7 5 5 CD A47139 200 8 . . . A47139 201 1 1 1 LS A47139 201 2 . . . A47139 201 3 elem elem NNP A47139 201 4 . . . A47139 202 1 and and CC A47139 202 2 IHS IHS NNP A47139 202 3 = = SYM A47139 202 4 IAK IAK NNP A47139 202 5 by by IN A47139 202 6 8 8 CD A47139 202 7 . . . A47139 203 1 1 1 LS A47139 203 2 . . . A47139 203 3 elem elem NNP A47139 203 4 . . . A47139 204 1 therefore therefore RB A47139 204 2 IAK IAK NNP A47139 204 3 = = SYM A47139 204 4 ISH ISH NNP A47139 204 5 . . . A47139 205 1 but but CC A47139 205 2 ISH ISH NNP A47139 205 3 = = SYM A47139 205 4 AIS AIS NNP A47139 205 5 = = SYM A47139 205 6 OAI OAI NNP A47139 205 7 being be VBG A47139 205 8 alternate alternate JJ A47139 205 9 Angles angle NNS A47139 205 10 betwixt betwixt NN A47139 205 11 Parallels parallel NNS A47139 205 12 by by IN A47139 205 13 29 29 CD A47139 205 14 . . . A47139 206 1 1 1 LS A47139 206 2 . . . A47139 206 3 elem elem NNP A47139 206 4 . . . A47139 207 1 and and CC A47139 207 2 therefore therefore RB A47139 207 3 lasty lasty JJ A47139 207 4 , , , A47139 207 5 OAI OAI NNP A47139 207 6 = = SYM A47139 207 7 IAK IAK NNP A47139 207 8 , , , A47139 207 9 and and CC A47139 207 10 by by IN A47139 207 11 the the DT A47139 207 12 like like JJ A47139 207 13 method method NN A47139 207 14 OAI OAI NNP A47139 207 15 is be VBZ A47139 207 16 proved prove VBN A47139 207 17 = = -RRB- A47139 207 18 OAN oan VB A47139 207 19 drawing draw VBG A47139 207 20 the the DT A47139 207 21 like like UH A47139 207 22 parallel parallel JJ A47139 207 23 Lines line NNS A47139 207 24 on on IN A47139 207 25 the the DT A47139 207 26 other other JJ A47139 207 27 side side NN A47139 207 28 of of IN A47139 207 29 the the DT A47139 207 30 Triangle Triangle NNP A47139 207 31 OAI OAI NNP A47139 207 32 , , , A47139 207 33 and and CC A47139 207 34 therefore therefore RB A47139 207 35 the the DT A47139 207 36 angle angle NN A47139 207 37 BAC BAC NNP A47139 207 38 is be VBZ A47139 207 39 trisected trisect VBN A47139 207 40 by by IN A47139 207 41 3 3 CD A47139 207 42 equal equal JJ A47139 207 43 angles angle NNS A47139 207 44 NAO NAO NNP A47139 207 45 = = SYM A47139 207 46 OAI OAI NNP A47139 207 47 = = SYM A47139 207 48 IAK IAK NNP A47139 207 49 = = SYM A47139 207 50 BAX BAX NNP A47139 207 51 = = SYM A47139 207 52 XAD XAD NNP A47139 207 53 = = SYM A47139 207 54 DAC DAC NNP A47139 207 55 . . . A47139 208 1 Q. Q. NNP A47139 208 2 E. E. NNP A47139 208 3 D. D. NNP A47139 208 4 The the DT A47139 208 5 Praxis Praxis NNP A47139 208 6 of of IN A47139 208 7 the the DT A47139 208 8 Section Section NNP A47139 208 9 of of IN A47139 208 10 a a DT A47139 208 11 Right Right NNP A47139 208 12 Lined Lined NNP A47139 208 13 Angle Angle NNP A47139 208 14 into into IN A47139 208 15 Six six CD A47139 208 16 equal equal JJ A47139 208 17 parts part NNS A47139 208 18 . . . A47139 209 1 BEcause because IN A47139 209 2 of of IN A47139 209 3 the the DT A47139 209 4 affinity affinity NN A47139 209 5 of of IN A47139 209 6 the the DT A47139 209 7 Figure Figure NNP A47139 209 8 of of IN A47139 209 9 the the DT A47139 209 10 Trisection Trisection NNP A47139 209 11 with with IN A47139 209 12 the the DT A47139 209 13 Figure figure NN A47139 209 14 of of IN A47139 209 15 the the DT A47139 209 16 Sextisection Sextisection NNP A47139 209 17 , , , A47139 209 18 I -PRON- PRP A47139 209 19 shall shall MD A47139 209 20 begin begin VB A47139 209 21 with with IN A47139 209 22 the the DT A47139 209 23 Sextisection Sextisection NNP A47139 209 24 , , , A47139 209 25 and and CC A47139 209 26 then then RB A47139 209 27 proceed proceed VB A47139 209 28 to to IN A47139 209 29 the the DT A47139 209 30 Quinquisection Quinquisection NNP A47139 209 31 . . . A47139 210 1 In in IN A47139 210 2 the the DT A47139 210 3 3d 3d JJ A47139 210 4 figure figure NN A47139 210 5 , , , A47139 210 6 let let VB A47139 210 7 the the DT A47139 210 8 given give VBN A47139 210 9 angle angle NN A47139 210 10 be be VB A47139 210 11 BAC BAC NNP A47139 210 12 , , , A47139 210 13 as as IN A47139 210 14 above above RB A47139 210 15 , , , A47139 210 16 whose whose WP$ A47139 210 17 Cord Cord NNP A47139 210 18 is be VBZ A47139 210 19 BC BC NNP A47139 210 20 , , , A47139 210 21 and and CC A47139 210 22 its -PRON- PRP$ A47139 210 23 arch arch JJ A47139 210 24 BEFGC befgc NN A47139 210 25 . . . A47139 211 1 1 1 LS A47139 211 2 . . . A47139 212 1 Divide divide VB A47139 212 2 the the DT A47139 212 3 Cord Cord NNP A47139 212 4 BC BC NNP A47139 212 5 into into IN A47139 212 6 6 6 CD A47139 212 7 equal equal JJ A47139 212 8 parts part NNS A47139 212 9 , , , A47139 212 10 which which WDT A47139 212 11 Divisions Divisions NNPS A47139 212 12 are be VBP A47139 212 13 marked mark VBN A47139 212 14 with with IN A47139 212 15 * * NFP A47139 212 16 * * NFP A47139 212 17 * * NFP A47139 212 18 * * NFP A47139 212 19 * * NFP A47139 212 20 . . . A47139 213 1 and and CC A47139 213 2 on on IN A47139 213 3 the the DT A47139 213 4 middle middle JJ A47139 213 5 division division NN A47139 213 6 draw draw VBP A47139 213 7 the the DT A47139 213 8 line line NN A47139 213 9 ADI ADI NNP A47139 213 10 to to IN A47139 213 11 the the DT A47139 213 12 arch arch JJ A47139 213 13 BEFGC befgc NN A47139 213 14 . . . A47139 214 1 2 2 LS A47139 214 2 . . . A47139 215 1 With with IN A47139 215 2 the the DT A47139 215 3 extent extent NN A47139 215 4 of of IN A47139 215 5 one one CD A47139 215 6 of of IN A47139 215 7 the the DT A47139 215 8 Divisions Divisions NNPS A47139 215 9 , , , A47139 215 10 on on IN A47139 215 11 the the DT A47139 215 12 given give VBN A47139 215 13 arch arch JJ A47139 215 14 measure measure NN A47139 215 15 from from IN A47139 215 16 C C NNP A47139 215 17 to to IN A47139 215 18 F F NNP A47139 215 19 , , , A47139 215 20 and and CC A47139 215 21 with with IN A47139 215 22 the the DT A47139 215 23 same same JJ A47139 215 24 extent extent NN A47139 215 25 from from IN A47139 215 26 F F NNP A47139 215 27 to to IN A47139 215 28 E E NNP A47139 215 29 , , , A47139 215 30 and and CC A47139 215 31 from from IN A47139 215 32 E e NN A47139 215 33 to to IN A47139 215 34 G g NN A47139 215 35 , , , A47139 215 36 marking mark VBG A47139 215 37 the the DT A47139 215 38 points point NNS A47139 215 39 E. E. NNP A47139 215 40 F. F. NNP A47139 215 41 G. G. NNP A47139 215 42 and and CC A47139 215 43 with with IN A47139 215 44 the the DT A47139 215 45 same same JJ A47139 215 46 extent extent NN A47139 215 47 measure measure NN A47139 215 48 from from IN A47139 215 49 B b NN A47139 215 50 to to IN A47139 215 51 E e NN A47139 215 52 , , , A47139 215 53 from from IN A47139 215 54 E e NN A47139 215 55 to to IN A47139 215 56 F F NNP A47139 215 57 , , , A47139 215 58 and and CC A47139 215 59 from from IN A47139 215 60 F f NN A47139 215 61 to to IN A47139 215 62 G g VB A47139 215 63 marking mark VBG A47139 215 64 the the DT A47139 215 65 points point NNS A47139 215 66 EFG EFG NNP A47139 215 67 . . . A47139 216 1 3 3 LS A47139 216 2 . . . A47139 217 1 With with IN A47139 217 2 a a DT A47139 217 3 less less JJR A47139 217 4 Radius Radius NNP A47139 217 5 than than IN A47139 217 6 AC AC NNP A47139 217 7 as as IN A47139 217 8 AK AK NNP A47139 217 9 draw draw VBP A47139 217 10 a a DT A47139 217 11 second second JJ A47139 217 12 Arch Arch NNP A47139 217 13 as as IN A47139 217 14 KLHLK KLHLK NNP A47139 217 15 . . . A47139 218 1 which which WDT A47139 218 2 Radius Radius NNP A47139 218 3 must must MD A47139 218 4 be be VB A47139 218 5 so so RB A47139 218 6 long long JJ A47139 218 7 that that IN A47139 218 8 the the DT A47139 218 9 extent extent NN A47139 218 10 of of IN A47139 218 11 the the DT A47139 218 12 1 1 CD A47139 218 13 6th 6th NN A47139 218 14 of of IN A47139 218 15 the the DT A47139 218 16 Cord Cord NNP A47139 218 17 thrice thrice NN A47139 218 18 repeated repeat VBN A47139 218 19 , , , A47139 218 20 may may MD A47139 218 21 fall fall VB A47139 218 22 short short RB A47139 218 23 of of IN A47139 218 24 reaching reach VBG A47139 218 25 the the DT A47139 218 26 line line NN A47139 218 27 ADI ADI NNP A47139 218 28 . . . A47139 219 1 4 4 LS A47139 219 2 . . . A47139 220 1 With with IN A47139 220 2 the the DT A47139 220 3 same same JJ A47139 220 4 extent extent NN A47139 220 5 on on IN A47139 220 6 this this DT A47139 220 7 2d 2d NN A47139 220 8 . . . A47139 221 1 arch arch VB A47139 221 2 , , , A47139 221 3 measure measure NN A47139 221 4 from from IN A47139 221 5 AC AC NNP A47139 221 6 , , , A47139 221 7 and and CC A47139 221 8 from from IN A47139 221 9 AB AB NNP A47139 221 10 to to IN A47139 221 11 K K NNP A47139 221 12 , , , A47139 221 13 and and CC A47139 221 14 from from IN A47139 221 15 K K NNP A47139 221 16 to to IN A47139 221 17 L l NN A47139 221 18 , , , A47139 221 19 and and CC A47139 221 20 from from IN A47139 221 21 L l NN A47139 221 22 to to IN A47139 221 23 H h NN A47139 221 24 , , , A47139 221 25 by by IN A47139 221 26 a a DT A47139 221 27 threefold threefold JJ A47139 221 28 repitition repitition NN A47139 221 29 of of IN A47139 221 30 the the DT A47139 221 31 same same JJ A47139 221 32 extent extent NN A47139 221 33 . . . A47139 222 1 5 5 CD A47139 222 2 . . . A47139 223 1 From from IN A47139 223 2 the the DT A47139 223 3 point point NN A47139 223 4 G g NN A47139 223 5 on on IN A47139 223 6 the the DT A47139 223 7 first first JJ A47139 223 8 arch arch NN A47139 223 9 to to IN A47139 223 10 the the DT A47139 223 11 point point NN A47139 223 12 H h NN A47139 223 13 on on IN A47139 223 14 the the DT A47139 223 15 second second JJ A47139 223 16 arch arch NN A47139 223 17 , , , A47139 223 18 draw draw VB A47139 223 19 a a DT A47139 223 20 straight straight JJ A47139 223 21 line line NN A47139 223 22 , , , A47139 223 23 and and CC A47139 223 24 produce produce VB A47139 223 25 it -PRON- PRP A47139 223 26 until until IN A47139 223 27 it -PRON- PRP A47139 223 28 cut cut VBD A47139 223 29 the the DT A47139 223 30 line line NN A47139 223 31 ADI ADI NNP A47139 223 32 at at IN A47139 223 33 the the DT A47139 223 34 point point NN A47139 223 35 I. i. NN A47139 224 1 6 6 CD A47139 224 2 . . . A47139 225 1 With with IN A47139 225 2 the the DT A47139 225 3 Radius Radius NNP A47139 225 4 AI AI NNP A47139 225 5 draw draw VB A47139 225 6 a a DT A47139 225 7 3d 3d NN A47139 225 8 . . . A47139 226 1 concentrick concentrick VB A47139 226 2 Arch Arch NNP A47139 226 3 , , , A47139 226 4 betwixt betwixt VB A47139 226 5 the the DT A47139 226 6 lines line NNS A47139 226 7 AB AB NNP A47139 226 8 and and CC A47139 226 9 AC AC NNP A47139 226 10 , , , A47139 226 11 I -PRON- PRP A47139 226 12 say say VBP A47139 226 13 the the DT A47139 226 14 extent extent NN A47139 226 15 of of IN A47139 226 16 the the DT A47139 226 17 16th 16th JJ A47139 226 18 part part NN A47139 226 19 of of IN A47139 226 20 the the DT A47139 226 21 cord cord NN A47139 226 22 BC BC NNP A47139 226 23 = = SYM A47139 226 24 MC MC NNP A47139 226 25 , , , A47139 226 26 being be VBG A47139 226 27 6 6 CD A47139 226 28 times time NNS A47139 226 29 repeated repeat VBN A47139 226 30 shall shall MD A47139 226 31 cut cut VB A47139 226 32 the the DT A47139 226 33 said say VBN A47139 226 34 3d 3d NN A47139 226 35 arch arch VB A47139 226 36 into into IN A47139 226 37 six six CD A47139 226 38 Equal equal JJ A47139 226 39 parts part NNS A47139 226 40 to to IN A47139 226 41 every every DT A47139 226 42 one one CD A47139 226 43 of of IN A47139 226 44 which which WDT A47139 226 45 straight straight JJ A47139 226 46 lines line NNS A47139 226 47 drawn draw VBN A47139 226 48 from from IN A47139 226 49 the the DT A47139 226 50 Center Center NNP A47139 226 51 A A NNP A47139 226 52 , , , A47139 226 53 and and CC A47139 226 54 produced produce VBN A47139 226 55 to to IN A47139 226 56 the the DT A47139 226 57 outmost outmost JJ A47139 226 58 arch arch NN A47139 226 59 , , , A47139 226 60 shall shall MD A47139 226 61 divide divide VB A47139 226 62 the the DT A47139 226 63 given give VBN A47139 226 64 angle angle NN A47139 226 65 BAC BAC NNP A47139 226 66 into into IN A47139 226 67 six six CD A47139 226 68 equal equal JJ A47139 226 69 parts part NNS A47139 226 70 orangles orangle NNS A47139 226 71 , , , A47139 226 72 marked mark VBN A47139 226 73 with with IN A47139 226 74 1 1 CD A47139 226 75 . . . A47139 227 1 2 2 LS A47139 227 2 . . . A47139 228 1 3 3 LS A47139 228 2 . . . A47139 229 1 4 4 LS A47139 229 2 . . . A47139 230 1 5 5 CD A47139 230 2 . . . A47139 231 1 6 6 CD A47139 231 2 . . . A47139 232 1 In in IN A47139 232 2 order order NN A47139 232 3 to to IN A47139 232 4 the the DT A47139 232 5 demonstration demonstration NN A47139 232 6 of of IN A47139 232 7 the the DT A47139 232 8 Praxis Praxis NNP A47139 232 9 of of IN A47139 232 10 this this DT A47139 232 11 Section Section NNP A47139 232 12 of of IN A47139 232 13 an an DT A47139 232 14 angle angle NN A47139 232 15 into into IN A47139 232 16 6 6 CD A47139 232 17 equal equal JJ A47139 232 18 parts part NNS A47139 232 19 , , , A47139 232 20 on on IN A47139 232 21 the the DT A47139 232 22 point point NN A47139 232 23 5 5 CD A47139 232 24 , , , A47139 232 25 making make VBG A47139 232 26 it -PRON- PRP A47139 232 27 a a DT A47139 232 28 center center NN A47139 232 29 with with IN A47139 232 30 Radius Radius NNP A47139 232 31 5A 5a RB A47139 232 32 describe describe VB A47139 232 33 the the DT A47139 232 34 circle circle NN A47139 232 35 AOPQRS AOPQRS NNP A47139 232 36 . . . A47139 233 1 2 2 LS A47139 233 2 . . . A47139 234 1 From from IN A47139 234 2 the the DT A47139 234 3 point point NN A47139 234 4 5 5 CD A47139 234 5 draw draw VBP A47139 234 6 the the DT A47139 234 7 line line NN A47139 234 8 5R 5r NN A47139 234 9 parallel parallel NN A47139 234 10 to to IN A47139 234 11 AC AC NNP A47139 234 12 . . . A47139 235 1 3 3 LS A47139 235 2 . . . A47139 236 1 From from IN A47139 236 2 R r PRP A47139 236 3 draw draw VB A47139 236 4 the the DT A47139 236 5 line line NN A47139 236 6 RT RT NNP A47139 236 7 parallel parallel NN A47139 236 8 to to IN A47139 236 9 5A 5a RB A47139 236 10 4 4 CD A47139 236 11 . . . A47139 237 1 Draw draw VB A47139 237 2 the the DT A47139 237 3 line line NN A47139 237 4 AT AT NNP A47139 237 5 from from IN A47139 237 6 A A NNP A47139 237 7 to to IN A47139 237 8 T t NN A47139 237 9 5 5 CD A47139 237 10 . . . A47139 238 1 Draw draw VB A47139 238 2 the the DT A47139 238 3 line line NN A47139 238 4 T5 T5 NNP A47139 238 5 , , , A47139 238 6 and and CC A47139 238 7 draw draw VB A47139 238 8 5V 5v NN A47139 238 9 parallel parallel JJ A47139 238 10 to to IN A47139 238 11 AT AT NNP A47139 238 12 The The NNP A47139 238 13 Demonstration Demonstration NNP A47139 238 14 . . . A47139 239 1 In in IN A47139 239 2 the the DT A47139 239 3 triangle triangle NN A47139 239 4 T5R t5r IN A47139 239 5 being be VBG A47139 239 6 an an DT A47139 239 7 Isosceles Isosceles NNPS A47139 239 8 , , , A47139 239 9 the the DT A47139 239 10 angle angle NN A47139 239 11 5TR 5tr CD A47139 239 12 = = SYM A47139 239 13 5RT 5rt CD A47139 239 14 . . . A47139 240 1 by by IN A47139 240 2 5 5 CD A47139 240 3 . . . A47139 241 1 1 1 LS A47139 241 2 . . . A47139 241 3 elem elem NNP A47139 241 4 . . . A47139 242 1 and and CC A47139 242 2 5RT 5rt CD A47139 242 3 = = SYM A47139 242 4 ( ( -LRB- A47139 242 5 5R6 5r6 CD A47139 242 6 ) ) -RRB- A47139 242 7 5A6 5a6 RB A47139 242 8 therefore therefore RB A47139 242 9 5T6 5t6 CD A47139 242 10 = = SYM A47139 242 11 5A6 5a6 CD A47139 242 12 . . . A47139 243 1 Again again RB A47139 243 2 5 5 CD A47139 243 3 T6 t6 NN A47139 243 4 = = SYM A47139 243 5 ( ( -LRB- A47139 243 6 5TV 5tv CD A47139 243 7 ) ) -RRB- A47139 243 8 A5 a5 NN A47139 243 9 T t NN A47139 243 10 , , , A47139 243 11 and and CC A47139 243 12 A5 a5 NN A47139 243 13 T t NN A47139 243 14 = = SYM A47139 243 15 5A4 5a4 CD A47139 243 16 by by IN A47139 243 17 34.1 34.1 CD A47139 243 18 . . . A47139 244 1 and and CC A47139 244 2 therefore therefore RB A47139 244 3 lastly lastly RB A47139 244 4 5 5 CD A47139 244 5 A4 A4 NNP A47139 244 6 = = SYM A47139 244 7 5 5 CD A47139 244 8 AV av NN A47139 244 9 . . . A47139 245 1 and and CC A47139 245 2 as as IN A47139 245 3 these these DT A47139 245 4 2 2 CD A47139 245 5 angles angle NNS A47139 245 6 are be VBP A47139 245 7 proved prove VBN A47139 245 8 equal equal JJ A47139 245 9 by by IN A47139 245 10 the the DT A47139 245 11 like like JJ A47139 245 12 reasoning reasoning NN A47139 245 13 , , , A47139 245 14 all all PDT A47139 245 15 the the DT A47139 245 16 other other JJ A47139 245 17 angles angle NNS A47139 245 18 can can MD A47139 245 19 be be VB A47139 245 20 proved prove VBN A47139 245 21 equal equal JJ A47139 245 22 by by IN A47139 245 23 changing change VBG A47139 245 24 the the DT A47139 245 25 center center NN A47139 245 26 of of IN A47139 245 27 the the DT A47139 245 28 Circle Circle NNP A47139 245 29 from from IN A47139 245 30 5 5 CD A47139 245 31 to to IN A47139 245 32 4 4 CD A47139 245 33 , , , A47139 245 34 and and CC A47139 245 35 from from IN A47139 245 36 4 4 CD A47139 245 37 to to IN A47139 245 38 3 3 CD A47139 245 39 , , , A47139 245 40 and and CC A47139 245 41 from from IN A47139 245 42 3 3 CD A47139 245 43 to to IN A47139 245 44 2 2 CD A47139 245 45 , , , A47139 245 46 and and CC A47139 245 47 from from IN A47139 245 48 2 2 CD A47139 245 49 to to IN A47139 245 50 1 1 CD A47139 245 51 . . . A47139 246 1 This this DT A47139 246 2 demonstration demonstration NN A47139 246 3 having have VBG A47139 246 4 such such JJ A47139 246 5 affinity affinity NN A47139 246 6 with with IN A47139 246 7 the the DT A47139 246 8 former former JJ A47139 246 9 of of IN A47139 246 10 Trisection Trisection NNP A47139 246 11 , , , A47139 246 12 and and CC A47139 246 13 which which WDT A47139 246 14 can can MD A47139 246 15 as as RB A47139 246 16 easily easily RB A47139 246 17 be be VB A47139 246 18 demonstrated demonstrate VBN A47139 246 19 both both DT A47139 246 20 ways way NNS A47139 246 21 , , , A47139 246 22 as as IN A47139 246 23 that that DT A47139 246 24 of of IN A47139 246 25 Trisection Trisection NNP A47139 246 26 , , , A47139 246 27 I -PRON- PRP A47139 246 28 shall shall MD A47139 246 29 not not RB A47139 246 30 enlarge enlarge VB A47139 246 31 upon upon IN A47139 246 32 it -PRON- PRP A47139 246 33 , , , A47139 246 34 for for IN A47139 246 35 he -PRON- PRP A47139 246 36 who who WP A47139 246 37 understands understand VBZ A47139 246 38 and and CC A47139 246 39 assents assent VBZ A47139 246 40 to to IN A47139 246 41 the the DT A47139 246 42 verity verity NN A47139 246 43 of of IN A47139 246 44 the the DT A47139 246 45 former former JJ A47139 246 46 , , , A47139 246 47 by by IN A47139 246 48 the the DT A47139 246 49 same same JJ A47139 246 50 evidence evidence NN A47139 246 51 will will MD A47139 246 52 assent assent VB A47139 246 53 to to IN A47139 246 54 the the DT A47139 246 55 later later JJ A47139 246 56 . . . A47139 247 1 The the DT A47139 247 2 Praxis Praxis NNP A47139 247 3 of of IN A47139 247 4 the the DT A47139 247 5 Quinquisection Quinquisection NNP A47139 247 6 . . . A47139 248 1 1 1 LS A47139 248 2 . . . A47139 249 1 ACcording accord VBG A47139 249 2 to to IN A47139 249 3 the the DT A47139 249 4 former former JJ A47139 249 5 method method NN A47139 249 6 , , , A47139 249 7 divide divide VB A47139 249 8 the the DT A47139 249 9 cord cord NN A47139 249 10 of of IN A47139 249 11 the the DT A47139 249 12 given give VBN A47139 249 13 angle angle NN A47139 249 14 , , , A47139 249 15 BE be VB A47139 249 16 into into IN A47139 249 17 5 5 CD A47139 249 18 = = SYM A47139 249 19 parts part NNS A47139 249 20 . . . A47139 250 1 2 2 LS A47139 250 2 . . . A47139 251 1 On on IN A47139 251 2 the the DT A47139 251 3 middle middle JJ A47139 251 4 part part NN A47139 251 5 marked mark VBN A47139 251 6 with with IN A47139 251 7 CD cd NN A47139 251 8 , , , A47139 251 9 draw draw VB A47139 251 10 the the DT A47139 251 11 lines line NNS A47139 251 12 CH CH NNP A47139 251 13 and and CC A47139 251 14 DH DH NNP A47139 251 15 cutting cut VBG A47139 251 16 the the DT A47139 251 17 cord cord NN A47139 251 18 at at IN A47139 251 19 right right JJ A47139 251 20 angles angle NNS A47139 251 21 and and CC A47139 251 22 parallel parallel VB A47139 251 23 one one CD A47139 251 24 to to IN A47139 251 25 another another DT A47139 251 26 . . . A47139 252 1 3 3 LS A47139 252 2 . . . A47139 253 1 On on IN A47139 253 2 the the DT A47139 253 3 arch arch NN A47139 253 4 of of IN A47139 253 5 the the DT A47139 253 6 given give VBN A47139 253 7 angle angle NN A47139 253 8 BFG BFG NNP A47139 253 9 take take VBP A47139 253 10 the the DT A47139 253 11 ⅕ ⅕ ADD A47139 253 12 of of IN A47139 253 13 the the DT A47139 253 14 cord cord NN A47139 253 15 = = -RRB- A47139 253 16 CD cd NN A47139 253 17 and and CC A47139 253 18 set set VBD A47139 253 19 it -PRON- PRP A47139 253 20 from from IN A47139 253 21 E e NN A47139 253 22 to to IN A47139 253 23 F F NNP A47139 253 24 , , , A47139 253 25 and and CC A47139 253 26 from from IN A47139 253 27 F F NNP A47139 253 28 to to IN A47139 253 29 G G NNP A47139 253 30 , , , A47139 253 31 also also RB A47139 253 32 do do VBP A47139 253 33 the the DT A47139 253 34 like like NN A47139 253 35 from from IN A47139 253 36 B b NN A47139 253 37 to to IN A47139 253 38 F F NNP A47139 253 39 , , , A47139 253 40 and and CC A47139 253 41 from from IN A47139 253 42 F F NNP A47139 253 43 to to IN A47139 253 44 G. G. NNP A47139 253 45 4 4 CD A47139 253 46 . . . A47139 254 1 Draw draw VB A47139 254 2 a a DT A47139 254 3 second second JJ A47139 254 4 arch arch NN A47139 254 5 , , , A47139 254 6 with with IN A47139 254 7 a a DT A47139 254 8 less less JJR A47139 254 9 radius radius NN A47139 254 10 as as IN A47139 254 11 AK AK NNP A47139 254 12 , , , A47139 254 13 so so RB A47139 254 14 as as IN A47139 254 15 the the DT A47139 254 16 radius radius NN A47139 254 17 may may MD A47139 254 18 be be VB A47139 254 19 so so RB A47139 254 20 long long JJ A47139 254 21 that that IN A47139 254 22 the the DT A47139 254 23 extent extent NN A47139 254 24 of of IN A47139 254 25 the the DT A47139 254 26 ⅕ ⅕ '' A47139 254 27 of of IN A47139 254 28 the the DT A47139 254 29 cord cord NN A47139 254 30 twice twice RB A47139 254 31 taken take VBN A47139 254 32 on on RP A47139 254 33 that that DT A47139 254 34 second second JJ A47139 254 35 arch arch NN A47139 254 36 may may MD A47139 254 37 not not RB A47139 254 38 reach reach VB A47139 254 39 to to IN A47139 254 40 the the DT A47139 254 41 perpendicular perpendicular JJ A47139 254 42 DH DH NNP A47139 254 43 . . . A47139 255 1 5 5 CD A47139 255 2 . . . A47139 256 1 With with IN A47139 256 2 the the DT A47139 256 3 same same JJ A47139 256 4 extent extent NN A47139 256 5 twice twice RB A47139 256 6 taken take VBN A47139 256 7 , , , A47139 256 8 as as IN A47139 256 9 from from IN A47139 256 10 K K NNP A47139 256 11 to to IN A47139 256 12 * * NFP A47139 256 13 from from IN A47139 256 14 * * NN A47139 256 15 to to IN A47139 256 16 * * NFP A47139 256 17 measure measure NN A47139 256 18 on on IN A47139 256 19 the the DT A47139 256 20 second second JJ A47139 256 21 arch arch NN A47139 256 22 to to IN A47139 256 23 the the DT A47139 256 24 second second JJ A47139 256 25 * * NFP A47139 256 26 . . . A47139 257 1 6 6 CD A47139 257 2 . . . A47139 258 1 From from IN A47139 258 2 G g NN A47139 258 3 to to IN A47139 258 4 * * NFP A47139 258 5 draw draw VB A47139 258 6 a a DT A47139 258 7 straight straight JJ A47139 258 8 line line NN A47139 258 9 , , , A47139 258 10 until until IN A47139 258 11 it -PRON- PRP A47139 258 12 cut cut VBD A47139 258 13 the the DT A47139 258 14 perpendicular perpendicular JJ A47139 258 15 line line NN A47139 258 16 DH DH NNP A47139 258 17 at at IN A47139 258 18 H h NN A47139 258 19 ; ; : A47139 258 20 lastly lastly RB A47139 258 21 with with IN A47139 258 22 the the DT A47139 258 23 radius radius NN A47139 258 24 AH ah NN A47139 258 25 describe describe VBP A47139 258 26 the the DT A47139 258 27 third third JJ A47139 258 28 arch arch JJ A47139 258 29 IHHI IHHI NNS A47139 258 30 , , , A47139 258 31 and and CC A47139 258 32 draw draw VB A47139 258 33 the the DT A47139 258 34 lines line NNS A47139 258 35 AH AH NNP A47139 258 36 AH AH NNP A47139 258 37 which which WDT A47139 258 38 shall shall MD A47139 258 39 make make VB A47139 258 40 the the DT A47139 258 41 angle angle NN A47139 258 42 HAH HAH NNP A47139 258 43 = = NFP A47139 258 44 ⅕BAE ⅕bae UH A47139 258 45 . . . A47139 259 1 The the DT A47139 259 2 Demonstration Demonstration NNP A47139 259 3 of of IN A47139 259 4 this this DT A47139 259 5 , , , A47139 259 6 or or CC A47139 259 7 any any DT A47139 259 8 other other JJ A47139 259 9 Section section NN A47139 259 10 , , , A47139 259 11 being be VBG A47139 259 12 after after IN A47139 259 13 the the DT A47139 259 14 same same JJ A47139 259 15 method method NN A47139 259 16 with with IN A47139 259 17 the the DT A47139 259 18 former former JJ A47139 259 19 , , , A47139 259 20 as as IN A47139 259 21 also also RB A47139 259 22 the the DT A47139 259 23 Praxis Praxis NNP A47139 259 24 , , , A47139 259 25 it -PRON- PRP A47139 259 26 were be VBD A47139 259 27 superfluous superfluous JJ A47139 259 28 to to TO A47139 259 29 enlarge enlarge VB A47139 259 30 upon upon IN A47139 259 31 it -PRON- PRP A47139 259 32 , , , A47139 259 33 or or CC A47139 259 34 to to TO A47139 259 35 add add VB A47139 259 36 any any DT A47139 259 37 new new JJ A47139 259 38 Problems problem NNS A47139 259 39 , , , A47139 259 40 showing show VBG A47139 259 41 how how WRB A47139 259 42 to to TO A47139 259 43 sect sect VB A47139 259 44 any any DT A47139 259 45 angle angle NN A47139 259 46 into into IN A47139 259 47 any any DT A47139 259 48 other other JJ A47139 259 49 parts part NNS A47139 259 50 given give VBN A47139 259 51 , , , A47139 259 52 as as IN A47139 259 53 7 7 CD A47139 259 54 . . . A47139 260 1 8 8 LS A47139 260 2 . . . A47139 261 1 9 9 CD A47139 261 2 . . . A47139 262 1 10 10 CD A47139 262 2 . . . A47139 263 1 11 11 CD A47139 263 2 . . . A47139 264 1 & & CC A47139 264 2 c. c. NNP A47139 264 3 for for IN A47139 264 4 he -PRON- PRP A47139 264 5 who who WP A47139 264 6 understands understand VBZ A47139 264 7 by by IN A47139 264 8 the the DT A47139 264 9 foregoing foregoing JJ A47139 264 10 Method Method NNP A47139 264 11 and and CC A47139 264 12 Praxis Praxis NNP A47139 264 13 to to TO A47139 264 14 sect sect VB A47139 264 15 any any DT A47139 264 16 angle angle NN A47139 264 17 into into IN A47139 264 18 3 3 CD A47139 264 19 . . . A47139 265 1 5 5 CD A47139 265 2 . . . A47139 266 1 6 6 LS A47139 266 2 . . . A47139 266 3 as as IN A47139 266 4 is be VBZ A47139 266 5 above above RB A47139 266 6 shewed shew VBN A47139 266 7 , , , A47139 266 8 will will MD A47139 266 9 by by IN A47139 266 10 the the DT A47139 266 11 like like JJ A47139 266 12 Method Method NNP A47139 266 13 and and CC A47139 266 14 Praxis Praxis NNP A47139 266 15 be be VB A47139 266 16 able able JJ A47139 266 17 to to TO A47139 266 18 sect sect VB A47139 266 19 any any DT A47139 266 20 angle angle NN A47139 266 21 into into IN A47139 266 22 7 7 CD A47139 266 23 . . . A47139 267 1 8 8 LS A47139 267 2 . . . A47139 268 1 9 9 CD A47139 268 2 . . . A47139 269 1 10 10 CD A47139 269 2 . . . A47139 270 1 & & CC A47139 270 2 c. c. NNP A47139 270 3 equal equal JJ A47139 270 4 parts part NNS A47139 270 5 , , , A47139 270 6 and and CC A47139 270 7 also also RB A47139 270 8 to to TO A47139 270 9 demonstrate demonstrate VB A47139 270 10 the the DT A47139 270 11 same same JJ A47139 270 12 . . . A47139 271 1 Wherefore Wherefore VBN A47139 271 2 in in IN A47139 271 3 the the DT A47139 271 4 next next JJ A47139 271 5 place place NN A47139 271 6 I -PRON- PRP A47139 271 7 shall shall MD A47139 271 8 proceed proceed VB A47139 271 9 to to TO A47139 271 10 shew shew VB A47139 271 11 how how WRB A47139 271 12 a a DT A47139 271 13 Semicircle Semicircle NNP A47139 271 14 may may MD A47139 271 15 be be VB A47139 271 16 sected secte VBN A47139 271 17 into into IN A47139 271 18 any any DT A47139 271 19 number number NN A47139 271 20 of of IN A47139 271 21 equal equal JJ A47139 271 22 parts part NNS A47139 271 23 , , , A47139 271 24 even even RB A47139 271 25 as as IN A47139 271 26 4 4 CD A47139 271 27 . . . A47139 272 1 6 6 CD A47139 272 2 . . . A47139 273 1 8 8 LS A47139 273 2 . . . A47139 274 1 10 10 CD A47139 274 2 , , , A47139 274 3 & & CC A47139 274 4 c. c. NNP A47139 274 5 or or CC A47139 274 6 uneven uneven NNP A47139 274 7 , , , A47139 274 8 as as IN A47139 274 9 5 5 CD A47139 274 10 . . . A47139 275 1 7 7 LS A47139 275 2 . . . A47139 276 1 9 9 CD A47139 276 2 . . . A47139 277 1 11 11 CD A47139 277 2 . . . A47139 278 1 The the DT A47139 278 2 Praxis Praxis NNP A47139 278 3 of of IN A47139 278 4 a a DT A47139 278 5 Section Section NNP A47139 278 6 of of IN A47139 278 7 a a DT A47139 278 8 Semicircle Semicircle NNP A47139 278 9 into into IN A47139 278 10 9 9 CD A47139 278 11 equal equal JJ A47139 278 12 parts part NNS A47139 278 13 . . . A47139 279 1 LEt let VB A47139 279 2 the the DT A47139 279 3 Semicircle Semicircle NNP A47139 279 4 given give VBN A47139 279 5 be be NN A47139 279 6 BRSC BRSC NNS A47139 279 7 , , , A47139 279 8 whose whose WP$ A47139 279 9 diameter diameter NN A47139 279 10 is be VBZ A47139 279 11 BC BC NNP A47139 279 12 . . . A47139 280 1 and and CC A47139 280 2 whose whose WP$ A47139 280 3 center center NN A47139 280 4 is be VBZ A47139 280 5 A. a. NN A47139 281 1 1 1 LS A47139 281 2 . . . A47139 282 1 Divide divide VB A47139 282 2 the the DT A47139 282 3 diameter diameter NN A47139 282 4 BC BC NNP A47139 282 5 into into IN A47139 282 6 9 9 CD A47139 282 7 equal equal JJ A47139 282 8 parts part NNS A47139 282 9 . . . A47139 283 1 2 2 LS A47139 283 2 . . . A47139 284 1 From from IN A47139 284 2 the the DT A47139 284 3 center center NN A47139 284 4 A a DT A47139 284 5 set set NN A47139 284 6 off off RP A47139 284 7 AO AO NNP A47139 284 8 and and CC A47139 284 9 AN AN NNP A47139 284 10 , , , A47139 284 11 making make VBG A47139 284 12 NO no NN A47139 284 13 = = SYM A47139 284 14 1 1 CD A47139 284 15 / / SYM A47139 284 16 9 9 CD A47139 284 17 of of IN A47139 284 18 the the DT A47139 284 19 diameter diameter NN A47139 284 20 : : : A47139 284 21 and and CC A47139 284 22 draw draw VB A47139 284 23 the the DT A47139 284 24 perpendiculars perpendicular NNS A47139 284 25 NR NR NNP A47139 284 26 . . . A47139 285 1 OS OS NNP A47139 285 2 . . . A47139 286 1 3 3 LS A47139 286 2 . . . A47139 287 1 With with IN A47139 287 2 the the DT A47139 287 3 extent extent NN A47139 287 4 NO no DT A47139 287 5 measure measure NN A47139 287 6 from from IN A47139 287 7 C C NNP A47139 287 8 to to IN A47139 287 9 I -PRON- PRP A47139 287 10 , , , A47139 287 11 from from IN A47139 287 12 1 1 CD A47139 287 13 to to IN A47139 287 14 2 2 CD A47139 287 15 , , , A47139 287 16 from from IN A47139 287 17 2 2 CD A47139 287 18 to to IN A47139 287 19 three three CD A47139 287 20 , , , A47139 287 21 from from IN A47139 287 22 3 3 CD A47139 287 23 to to IN A47139 287 24 4 4 CD A47139 287 25 , , , A47139 287 26 marking mark VBG A47139 287 27 the the DT A47139 287 28 points point NNS A47139 287 29 1 1 CD A47139 287 30 . . . A47139 288 1 2 2 LS A47139 288 2 . . . A47139 289 1 3 3 LS A47139 289 2 . . . A47139 290 1 4 4 LS A47139 290 2 . . . A47139 290 3 and and CC A47139 290 4 do do VB A47139 290 5 the the DT A47139 290 6 like like NN A47139 290 7 from from IN A47139 290 8 B b NN A47139 290 9 to to IN A47139 290 10 1 1 CD A47139 290 11 . . . A47139 291 1 2 2 LS A47139 291 2 . . . A47139 292 1 3 3 LS A47139 292 2 . . . A47139 293 1 4 4 LS A47139 293 2 . . . A47139 294 1 4 4 LS A47139 294 2 . . . A47139 295 1 With with IN A47139 295 2 less less JJR A47139 295 3 radius radius NN A47139 295 4 as as IN A47139 295 5 AP AP NNP A47139 295 6 describe describe VBP A47139 295 7 the the DT A47139 295 8 Semicircle Semicircle NNP A47139 295 9 PP PP NNP A47139 295 10 , , , A47139 295 11 and and CC A47139 295 12 from from IN A47139 295 13 P p NN A47139 295 14 to to IN A47139 295 15 1 1 CD A47139 295 16 with with IN A47139 295 17 the the DT A47139 295 18 same same JJ A47139 295 19 extent extent NN A47139 295 20 on on IN A47139 295 21 that that DT A47139 295 22 2d 2d NN A47139 295 23 . . . A47139 296 1 arch arch JJ A47139 296 2 measure measure NN A47139 296 3 form form NN A47139 296 4 P p NN A47139 296 5 , , , A47139 296 6 P1 p1 NN A47139 296 7 = = SYM A47139 296 8 1 1 CD A47139 296 9 . . . A47139 297 1 2 2 CD A47139 297 2 = = SYM A47139 297 3 2 2 CD A47139 297 4 . . . A47139 298 1 3 3 CD A47139 298 2 = = SYM A47139 298 3 3 3 CD A47139 298 4 . . . A47139 299 1 4 4 LS A47139 299 2 . . . A47139 299 3 and and CC A47139 299 4 do do VB A47139 299 5 the the DT A47139 299 6 like like NN A47139 299 7 from from IN A47139 299 8 P p NN A47139 299 9 on on IN A47139 299 10 the the DT A47139 299 11 other other JJ A47139 299 12 side side NN A47139 299 13 . . . A47139 300 1 This this DT A47139 300 2 lesser less JJR A47139 300 3 Radius Radius NNP A47139 300 4 must must MD A47139 300 5 be be VB A47139 300 6 so so RB A47139 300 7 long long RB A47139 300 8 , , , A47139 300 9 that that IN A47139 300 10 the the DT A47139 300 11 extent extent NN A47139 300 12 = = : A47139 300 13 NO no DT A47139 300 14 four four CD A47139 300 15 times time NNS A47139 300 16 repeated repeat VBN A47139 300 17 do do VBP A47139 300 18 not not RB A47139 300 19 reach reach VB A47139 300 20 the the DT A47139 300 21 Perpendiculars perpendicular NNS A47139 300 22 . . . A47139 301 1 5 5 CD A47139 301 2 . . . A47139 302 1 From from IN A47139 302 2 4 4 CD A47139 302 3 to to TO A47139 302 4 4 4 CD A47139 302 5 draw draw VB A47139 302 6 a a DT A47139 302 7 straight straight JJ A47139 302 8 line line NN A47139 302 9 , , , A47139 302 10 and and CC A47139 302 11 produce produce VB A47139 302 12 it -PRON- PRP A47139 302 13 until until IN A47139 302 14 it -PRON- PRP A47139 302 15 cut cut VBD A47139 302 16 OS OS NNP A47139 302 17 at at IN A47139 302 18 4 4 CD A47139 302 19 . . . A47139 302 20 and and CC A47139 302 21 NR NR NNP A47139 302 22 at at IN A47139 302 23 9 9 CD A47139 302 24 . . . A47139 303 1 6 6 CD A47139 303 2 . . . A47139 304 1 Draw draw VB A47139 304 2 the the DT A47139 304 3 3d 3d NN A47139 304 4 arch arch JJ A47139 304 5 QQ QQ NNP A47139 304 6 with with IN A47139 304 7 radius radius NN A47139 304 8 A A NNP A47139 304 9 4 4 CD A47139 304 10 , , , A47139 304 11 and and CC A47139 304 12 draw draw VB A47139 304 13 the the DT A47139 304 14 straight straight JJ A47139 304 15 lines line NNS A47139 304 16 4 4 CD A47139 304 17 A a NN A47139 304 18 4 4 CD A47139 304 19 , , , A47139 304 20 which which WDT A47139 304 21 shall shall MD A47139 304 22 make make VB A47139 304 23 an an DT A47139 304 24 angle angle NN A47139 304 25 = = NFP A47139 304 26 a a DT A47139 304 27 9th 9th JJ A47139 304 28 part part NN A47139 304 29 of of IN A47139 304 30 the the DT A47139 304 31 semicircle semicircle NN A47139 304 32 . . . A47139 305 1 The the DT A47139 305 2 demonstration demonstration NN A47139 305 3 whereof whereof NN A47139 305 4 is be VBZ A47139 305 5 apparent apparent JJ A47139 305 6 from from IN A47139 305 7 these these DT A47139 305 8 precedent precedent NN A47139 305 9 . . . A47139 306 1 From from IN A47139 306 2 the the DT A47139 306 3 above above RB A47139 306 4 delivered deliver VBN A47139 306 5 Praxis Praxis NNP A47139 306 6 of of IN A47139 306 7 the the DT A47139 306 8 various various JJ A47139 306 9 Sections section NNS A47139 306 10 of of IN A47139 306 11 angles angle NNS A47139 306 12 , , , A47139 306 13 into into IN A47139 306 14 any any DT A47139 306 15 equal equal JJ A47139 306 16 given give VBN A47139 306 17 parts part NNS A47139 306 18 , , , A47139 306 19 I -PRON- PRP A47139 306 20 shall shall MD A47139 306 21 draw draw VB A47139 306 22 these these DT A47139 306 23 few few JJ A47139 306 24 plain plain JJ A47139 306 25 Corolaries corolarie NNS A47139 306 26 . . . A47139 307 1 1 1 LS A47139 307 2 . . . A47139 308 1 Corol Corol NNP A47139 308 2 . . . A47139 309 1 Having have VBG A47139 309 2 in in IN A47139 309 3 any any DT A47139 309 4 right right NN A47139 309 5 lined line VBN A47139 309 6 triangles triangle NNS A47139 309 7 , , , A47139 309 8 any any DT A47139 309 9 one one CD A47139 309 10 angle angle NN A47139 309 11 given give VBN A47139 309 12 , , , A47139 309 13 and and CC A47139 309 14 the the DT A47139 309 15 ratio ratio NN A47139 309 16 of of IN A47139 309 17 the the DT A47139 309 18 other other JJ A47139 309 19 2 2 CD A47139 309 20 angles angle NNS A47139 309 21 to to TO A47139 309 22 find find VB A47139 309 23 these these DT A47139 309 24 2 2 CD A47139 309 25 angles angle NNS A47139 309 26 , , , A47139 309 27 in in IN A47139 309 28 degrees degree NNS A47139 309 29 and and CC A47139 309 30 minuts minut NNS A47139 309 31 . . . A47139 310 1 e. e. NNP A47139 310 2 g. g. NNP A47139 310 3 let let VB A47139 310 4 the the DT A47139 310 5 given give VBN A47139 310 6 angle angle NN A47139 310 7 of of IN A47139 310 8 a a DT A47139 310 9 triangle triangle NN A47139 310 10 be be VB A47139 310 11 110 110 CD A47139 310 12 deg deg NN A47139 310 13 . . . A47139 311 1 and and CC A47139 311 2 the the DT A47139 311 3 ratio ratio NN A47139 311 4 of of IN A47139 311 5 the the DT A47139 311 6 other other JJ A47139 311 7 two two CD A47139 311 8 angles angle NNS A47139 311 9 be be VBP A47139 311 10 as as IN A47139 311 11 3 3 CD A47139 311 12 to to IN A47139 311 13 2 2 CD A47139 311 14 . . . A47139 312 1 Q. Q. NNP A47139 313 1 What what WP A47139 313 2 are be VBP A47139 313 3 the the DT A47139 313 4 other other JJ A47139 313 5 2 2 CD A47139 313 6 angles angle NNS A47139 313 7 . . . A47139 314 1 Ans Ans NNP A47139 314 2 . . . A47139 315 1 Take take VB A47139 315 2 the the DT A47139 315 3 complement complement NN A47139 315 4 of of IN A47139 315 5 110 110 CD A47139 315 6 to to TO A47139 315 7 180 180 CD A47139 315 8 , , , A47139 315 9 which which WDT A47139 315 10 is be VBZ A47139 315 11 70 70 CD A47139 315 12 , , , A47139 315 13 and and CC A47139 315 14 sect sect VB A47139 315 15 it -PRON- PRP A47139 315 16 into into IN A47139 315 17 5 5 CD A47139 315 18 equal equal JJ A47139 315 19 parts part NNS A47139 315 20 by by IN A47139 315 21 the the DT A47139 315 22 method method NN A47139 315 23 above above IN A47139 315 24 delivered deliver VBD A47139 315 25 , , , A47139 315 26 ⅕ ⅕ . A47139 315 27 = = NFP A47139 315 28 14 14 CD A47139 315 29 , , , A47139 315 30 this this DT A47139 315 31 multiplied multiply VBN A47139 315 32 by by IN A47139 315 33 3 3 CD A47139 315 34 gives give VBZ A47139 315 35 42 42 CD A47139 315 36 , , , A47139 315 37 and and CC A47139 315 38 by by IN A47139 315 39 2 2 CD A47139 315 40 gives give VBZ A47139 315 41 28 28 CD A47139 315 42 , , , A47139 315 43 wherefore wherefore VBD A47139 315 44 the the DT A47139 315 45 greater great JJR A47139 315 46 angle angle NN A47139 315 47 shall shall MD A47139 315 48 be be VB A47139 315 49 42 42 CD A47139 315 50 , , , A47139 315 51 and and CC A47139 315 52 the the DT A47139 315 53 less less JJR A47139 315 54 28 28 CD A47139 315 55 . . . A47139 315 56 demonstrate demonstrate VB A47139 315 57 110 110 CD A47139 315 58 + + SYM A47139 315 59 42 42 CD A47139 315 60 + + SYM A47139 315 61 28 28 CD A47139 315 62 = = SYM A47139 315 63 180 180 CD A47139 315 64 and and CC A47139 315 65 3 3 CD A47139 315 66 ∶ ∶ NNP A47139 315 67 2 2 CD A47139 315 68 ∶ ∶ NNP A47139 315 69 42 42 CD A47139 315 70 ∶ ∶ CD A47139 315 71 28 28 CD A47139 315 72 . . . A47139 316 1 2 2 LS A47139 316 2 . . . A47139 317 1 Cor Cor NNP A47139 317 2 . . . A47139 318 1 From from IN A47139 318 2 a a DT A47139 318 3 Point Point NNP A47139 318 4 given give VBN A47139 318 5 on on IN A47139 318 6 a a DT A47139 318 7 Line Line NNP A47139 318 8 given give VBN A47139 318 9 , , , A47139 318 10 to to TO A47139 318 11 erect erect VB A47139 318 12 an an DT A47139 318 13 Isosceles isosceles JJ A47139 318 14 triangle triangle NN A47139 318 15 , , , A47139 318 16 one one CD A47139 318 17 of of IN A47139 318 18 whose whose WP$ A47139 318 19 sides side NNS A47139 318 20 produced produce VBN A47139 318 21 shall shall MD A47139 318 22 come come VB A47139 318 23 to to IN A47139 318 24 a a DT A47139 318 25 point point NN A47139 318 26 given give VBN A47139 318 27 . . . A47139 319 1 ( ( -LRB- A47139 319 2 See see VB A47139 319 3 the the DT A47139 319 4 figure figure NN A47139 319 5 ) ) -RRB- A47139 319 6 let let VB A47139 319 7 the the DT A47139 319 8 point point NN A47139 319 9 given give VBN A47139 319 10 be be VB A47139 319 11 A a DT A47139 319 12 , , , A47139 319 13 the the DT A47139 319 14 line line NN A47139 319 15 given give VBN A47139 319 16 AF AF NNP A47139 319 17 , , , A47139 319 18 the the DT A47139 319 19 limited limited JJ A47139 319 20 point point NN A47139 319 21 given give VBN A47139 319 22 below below IN A47139 319 23 the the DT A47139 319 24 line line NN A47139 319 25 AF AF NNP A47139 319 26 let let VBD A47139 319 27 the the DT A47139 319 28 point point NN A47139 319 29 be be VB A47139 319 30 point point NN A47139 319 31 D. D. NNP A47139 319 32 the the DT A47139 319 33 Praxis Praxis NNP A47139 319 34 . . . A47139 320 1 1 1 LS A47139 320 2 . . . A47139 321 1 With with IN A47139 321 2 radius radius NN A47139 321 3 AD ad NN A47139 321 4 describe describe VBP A47139 321 5 the the DT A47139 321 6 semicircle semicircle NN A47139 321 7 GFDE GFDE NNP A47139 321 8 , , , A47139 321 9 so so IN A47139 321 10 that that IN A47139 321 11 GA GA NNP A47139 321 12 shall shall MD A47139 321 13 cut cut VB A47139 321 14 AF AF NNP A47139 321 15 at at IN A47139 321 16 a a DT A47139 321 17 right right JJ A47139 321 18 angle angle NN A47139 321 19 , , , A47139 321 20 and and CC A47139 321 21 AE ae RB A47139 321 22 the the DT A47139 321 23 like like JJ A47139 321 24 . . . A47139 322 1 2 2 LS A47139 322 2 . . . A47139 323 1 Draw draw VB A47139 323 2 the the DT A47139 323 3 line line NN A47139 323 4 AD ad NN A47139 323 5 , , , A47139 323 6 and and CC A47139 323 7 cut cut VB A47139 323 8 the the DT A47139 323 9 angle angle NN A47139 323 10 EAD EAD NNP A47139 323 11 into into IN A47139 323 12 3 3 CD A47139 323 13 = = SYM A47139 323 14 parts part NNS A47139 323 15 . . . A47139 324 1 3 3 LS A47139 324 2 . . . A47139 325 1 Make make VB A47139 325 2 the the DT A47139 325 3 angle angle NN A47139 325 4 GAB GAB NNP A47139 325 5 = = -RRB- A47139 325 6 ⅓ ⅓ NNP A47139 325 7 of of IN A47139 325 8 EAD EAD NNP A47139 325 9 , , , A47139 325 10 and and CC A47139 325 11 from from IN A47139 325 12 B b NN A47139 325 13 to to IN A47139 325 14 D d NN A47139 325 15 draw draw VB A47139 325 16 the the DT A47139 325 17 line line NN A47139 325 18 BD BD NNP A47139 325 19 , , , A47139 325 20 cutting cut VBG A47139 325 21 the the DT A47139 325 22 line line NN A47139 325 23 AF AF NNP A47139 325 24 at at IN A47139 325 25 C C NNP A47139 325 26 , , , A47139 325 27 the the DT A47139 325 28 triangle triangle NN A47139 325 29 ABC ABC NNP A47139 325 30 is be VBZ A47139 325 31 an an DT A47139 325 32 Isosceles Isosceles NNP A47139 325 33 , , , A47139 325 34 whose whose WP$ A47139 325 35 side side NN A47139 325 36 BC BC NNP A47139 325 37 is be VBZ A47139 325 38 produced produce VBN A47139 325 39 to to IN A47139 325 40 D. D. NNP A47139 325 41 The the DT A47139 325 42 demonstration demonstration NN A47139 325 43 is be VBZ A47139 325 44 evident evident JJ A47139 325 45 from from IN A47139 325 46 the the DT A47139 325 47 trisection trisection NN A47139 325 48 , , , A47139 325 49 and and CC A47139 325 50 it -PRON- PRP A47139 325 51 hath hath VBP A47139 325 52 singular singular JJ A47139 325 53 uses use VBZ A47139 325 54 in in IN A47139 325 55 Architecture Architecture NNP A47139 325 56 , , , A47139 325 57 and and CC A47139 325 58 affording afford VBG A47139 325 59 new new JJ A47139 325 60 Problems Problems NNPS A47139 325 61 in in IN A47139 325 62 Geography Geography NNP A47139 325 63 and and CC A47139 325 64 Navigation Navigation NNP A47139 325 65 , , , A47139 325 66 which which WDT A47139 325 67 I -PRON- PRP A47139 325 68 shall shall MD A47139 325 69 not not RB A47139 325 70 at at IN A47139 325 71 present present JJ A47139 325 72 inlarge inlarge NN A47139 325 73 upon upon IN A47139 325 74 , , , A47139 325 75 but but CC A47139 325 76 leave leave VB A47139 325 77 to to IN A47139 325 78 the the DT A47139 325 79 ingenious ingenious JJ A47139 325 80 Student Student NNP A47139 325 81 to to TO A47139 325 82 devise devise VB A47139 325 83 . . . A47139 326 1 3 3 LS A47139 326 2 . . . A47139 327 1 Corol Corol NNP A47139 327 2 . . . A47139 328 1 To to TO A47139 328 2 measure measure VB A47139 328 3 any any DT A47139 328 4 given give VBN A47139 328 5 angle angle NN A47139 328 6 in in IN A47139 328 7 degrees degree NNS A47139 328 8 and and CC A47139 328 9 odd odd JJ A47139 328 10 minuts minut NNS A47139 328 11 , , , A47139 328 12 ( ( -LRB- A47139 328 13 if if IN A47139 328 14 it -PRON- PRP A47139 328 15 have have VBP A47139 328 16 any any DT A47139 328 17 ) ) -RRB- A47139 328 18 by by IN A47139 328 19 a a DT A47139 328 20 line line NN A47139 328 21 of of IN A47139 328 22 equal equal JJ A47139 328 23 parts part NNS A47139 328 24 without without IN A47139 328 25 a a DT A47139 328 26 line line NN A47139 328 27 of of IN A47139 328 28 cords cord NNS A47139 328 29 . . . A47139 329 1 Let let VB A47139 329 2 the the DT A47139 329 3 given give VBN A47139 329 4 angle angle NN A47139 329 5 be be VB A47139 329 6 KAL KAL NNP A47139 329 7 ( ( -LRB- A47139 329 8 see see VB A47139 329 9 the the DT A47139 329 10 figure figure NN A47139 329 11 ) ) -RRB- A47139 329 12 with with IN A47139 329 13 radius radius NN A47139 329 14 AL AL NNP A47139 329 15 describe describe VB A47139 329 16 the the DT A47139 329 17 quadrant quadrant JJ A47139 329 18 LKL LKL NNP A47139 329 19 , , , A47139 329 20 and and CC A47139 329 21 on on IN A47139 329 22 that that DT A47139 329 23 arch arch NN A47139 329 24 take take VB A47139 329 25 the the DT A47139 329 26 extent extent NN A47139 329 27 of of IN A47139 329 28 the the DT A47139 329 29 cord cord NN A47139 329 30 KL KL NNP A47139 329 31 , , , A47139 329 32 and and CC A47139 329 33 set set VBD A47139 329 34 it -PRON- PRP A47139 329 35 on on IN A47139 329 36 the the DT A47139 329 37 other other JJ A47139 329 38 side side NN A47139 329 39 from from IN A47139 329 40 L l NN A47139 329 41 to to IN A47139 329 42 a a DT A47139 329 43 point point NN A47139 329 44 on on IN A47139 329 45 that that DT A47139 329 46 arch arch NN A47139 329 47 . . . A47139 330 1 Again again RB A47139 330 2 , , , A47139 330 3 take take VB A47139 330 4 the the DT A47139 330 5 cord cord NN A47139 330 6 of of IN A47139 330 7 that that DT A47139 330 8 middle middle JJ A47139 330 9 arch arch NNP A47139 330 10 betwixt betwixt VB A47139 330 11 the the DT A47139 330 12 point point NN A47139 330 13 and and CC A47139 330 14 K k NN A47139 330 15 , , , A47139 330 16 an an DT A47139 330 17 all all PDT A47139 330 18 these these DT A47139 330 19 3 3 CD A47139 330 20 cords cord NNS A47139 330 21 join join VBP A47139 330 22 them -PRON- PRP A47139 330 23 together together RB A47139 330 24 in in IN A47139 330 25 a a DT A47139 330 26 straight straight JJ A47139 330 27 line line NN A47139 330 28 , , , A47139 330 29 which which WDT A47139 330 30 make make VBP A47139 330 31 the the DT A47139 330 32 cord cord NN A47139 330 33 of of IN A47139 330 34 the the DT A47139 330 35 quadrant quadrant NN A47139 330 36 ( ( -LRB- A47139 330 37 by by IN A47139 330 38 a a DT A47139 330 39 longer long JJR A47139 330 40 radius radius NN A47139 330 41 ) ) -RRB- A47139 330 42 as as IN A47139 330 43 BC BC NNP A47139 330 44 , , , A47139 330 45 which which WDT A47139 330 46 is be VBZ A47139 330 47 easily easily RB A47139 330 48 done do VBN A47139 330 49 Geometrically geometrically RB A47139 330 50 . . . A47139 331 1 Then then RB A47139 331 2 because because IN A47139 331 3 in in IN A47139 331 4 each each DT A47139 331 5 Quadrant Quadrant NNP A47139 331 6 there there EX A47139 331 7 are be VBP A47139 331 8 5400 5400 CD A47139 331 9 minuts minut NNS A47139 331 10 , , , A47139 331 11 divide divide VB A47139 331 12 the the DT A47139 331 13 line line NN A47139 331 14 BC BC NNP A47139 331 15 by by IN A47139 331 16 the the DT A47139 331 17 Diagonal Diagonal NNP A47139 331 18 Scale Scale NNP A47139 331 19 into into IN A47139 331 20 5400 5400 CD A47139 331 21 equal equal JJ A47139 331 22 parts part NNS A47139 331 23 , , , A47139 331 24 and and CC A47139 331 25 by by IN A47139 331 26 the the DT A47139 331 27 same same JJ A47139 331 28 Diagonal Diagonal NNP A47139 331 29 Scale Scale NNP A47139 331 30 measure measure NN A47139 331 31 on on IN A47139 331 32 the the DT A47139 331 33 line line NN A47139 331 34 BC BC NNP A47139 331 35 the the DT A47139 331 36 length length NN A47139 331 37 of of IN A47139 331 38 the the DT A47139 331 39 cord cord NN A47139 331 40 of of IN A47139 331 41 KL KL NNP A47139 331 42 , , , A47139 331 43 and and CC A47139 331 44 whatever whatever WDT A47139 331 45 number number NN A47139 331 46 of of IN A47139 331 47 parts part NNS A47139 331 48 it -PRON- PRP A47139 331 49 giveth giveth VBZ A47139 331 50 , , , A47139 331 51 that that DT A47139 331 52 is be VBZ A47139 331 53 the the DT A47139 331 54 just just JJ A47139 331 55 quantity quantity NN A47139 331 56 of of IN A47139 331 57 that that DT A47139 331 58 angle angle NN A47139 331 59 in in IN A47139 331 60 minuts minut NNS A47139 331 61 , , , A47139 331 62 which which WDT A47139 331 63 divided divide VBN A47139 331 64 by by IN A47139 331 65 60 60 CD A47139 331 66 giveth giveth NNS A47139 331 67 the the DT A47139 331 68 degrees degree NNS A47139 331 69 , , , A47139 331 70 and and CC A47139 331 71 if if IN A47139 331 72 there there EX A47139 331 73 be be VBP A47139 331 74 any any DT A47139 331 75 Remainder remainder NN A47139 331 76 , , , A47139 331 77 they -PRON- PRP A47139 331 78 are be VBP A47139 331 79 the the DT A47139 331 80 odd odd JJ A47139 331 81 minuts minut NNS A47139 331 82 . . . A47139 332 1 4 4 LS A47139 332 2 . . . A47139 333 1 Corol Corol NNP A47139 333 2 . . . A47139 334 1 To to TO A47139 334 2 project project VB A47139 334 3 any any DT A47139 334 4 angle angle NN A47139 334 5 without without IN A47139 334 6 a a DT A47139 334 7 line line NN A47139 334 8 of of IN A47139 334 9 cords cord NNS A47139 334 10 , , , A47139 334 11 by by IN A47139 334 12 a a DT A47139 334 13 Diagonal diagonal JJ A47139 334 14 Line Line NNP A47139 334 15 of of IN A47139 334 16 equal equal JJ A47139 334 17 parts part NNS A47139 334 18 , , , A47139 334 19 whose whose WP$ A47139 334 20 quantity quantity NN A47139 334 21 is be VBZ A47139 334 22 given give VBN A47139 334 23 in in IN A47139 334 24 degrees degree NNS A47139 334 25 and and CC A47139 334 26 minuts minut NNS A47139 334 27 . . . A47139 335 1 Let let VB A47139 335 2 the the DT A47139 335 3 given give VBN A47139 335 4 angle angle NN A47139 335 5 to to TO A47139 335 6 be be VB A47139 335 7 projected project VBN A47139 335 8 , , , A47139 335 9 contain contain VB A47139 335 10 36 36 CD A47139 335 11 deg deg NN A47139 335 12 . . . A47139 336 1 and and CC A47139 336 2 1 1 CD A47139 336 3 min min NN A47139 336 4 . . . A47139 337 1 reduce reduce VB A47139 337 2 the the DT A47139 337 3 degrees degree NNS A47139 337 4 into into IN A47139 337 5 minuts minut NNS A47139 337 6 , , , A47139 337 7 multiplying multiply VBG A47139 337 8 36 36 CD A47139 337 9 by by IN A47139 337 10 60 60 CD A47139 337 11 , , , A47139 337 12 the the DT A47139 337 13 product product NN A47139 337 14 is be VBZ A47139 337 15 2160 2160 CD A47139 337 16 , , , A47139 337 17 to to TO A47139 337 18 which which WDT A47139 337 19 adding add VBG A47139 337 20 the the DT A47139 337 21 odd odd JJ A47139 337 22 minut minut NN A47139 337 23 , , , A47139 337 24 the the DT A47139 337 25 sum sum NN A47139 337 26 is be VBZ A47139 337 27 2161 2161 CD A47139 337 28 . . . A47139 338 1 Praxis praxi NNS A47139 338 2 . . . A47139 339 1 Take take VB A47139 339 2 off off RP A47139 339 3 from from IN A47139 339 4 the the DT A47139 339 5 cord cord NN A47139 339 6 of of IN A47139 339 7 the the DT A47139 339 8 quadrant quadrant JJ A47139 339 9 BC BC NNP A47139 339 10 2161 2161 CD A47139 339 11 from from IN A47139 339 12 C C NNP A47139 339 13 to to IN A47139 339 14 D. D. NNP A47139 339 15 on on IN A47139 339 16 the the DT A47139 339 17 point point NN A47139 339 18 D d NN A47139 339 19 erect erect NN A47139 339 20 the the DT A47139 339 21 perpendicular perpendicular JJ A47139 339 22 ED ED NNP A47139 339 23 , , , A47139 339 24 which which WDT A47139 339 25 extend extend VBP A47139 339 26 to to IN A47139 339 27 G g NN A47139 339 28 , , , A47139 339 29 with with IN A47139 339 30 the the DT A47139 339 31 extent extent NN A47139 339 32 CD cd NN A47139 339 33 measure measure NN A47139 339 34 on on IN A47139 339 35 the the DT A47139 339 36 arch arch NN A47139 339 37 of of IN A47139 339 38 the the DT A47139 339 39 quadrant quadrant NN A47139 339 40 , , , A47139 339 41 from from IN A47139 339 42 C C NNP A47139 339 43 to to IN A47139 339 44 H. H. NNP A47139 339 45 Again Again NNP A47139 339 46 , , , A47139 339 47 draw draw VB A47139 339 48 another another DT A47139 339 49 arch arch NN A47139 339 50 with with IN A47139 339 51 a a DT A47139 339 52 less less JJR A47139 339 53 radius radius NN A47139 339 54 as as IN A47139 339 55 AM AM NNP A47139 339 56 ( ( -LRB- A47139 339 57 so so IN A47139 339 58 that that IN A47139 339 59 the the DT A47139 339 60 radius radius NN A47139 339 61 be be VB A47139 339 62 so so RB A47139 339 63 long long JJ A47139 339 64 that that IN A47139 339 65 the the DT A47139 339 66 extent extent NN A47139 339 67 of of IN A47139 339 68 DC DC NNP A47139 339 69 reach reach VBP A47139 339 70 not not RB A47139 339 71 to to IN A47139 339 72 EDG EDG NNP A47139 339 73 ) ) -RRB- A47139 339 74 and and CC A47139 339 75 with with IN A47139 339 76 that that DT A47139 339 77 extent extent JJ A47139 339 78 measure measure NN A47139 339 79 from from IN A47139 339 80 M M NNP A47139 339 81 to to IN A47139 339 82 I -PRON- PRP A47139 339 83 on on IN A47139 339 84 that that DT A47139 339 85 2d 2d NN A47139 339 86 arch arch NN A47139 339 87 . . . A47139 340 1 4 4 LS A47139 340 2 . . . A47139 341 1 From from IN A47139 341 2 H h NN A47139 341 3 to to IN A47139 341 4 I -PRON- PRP A47139 341 5 draw draw VB A47139 341 6 a a DT A47139 341 7 straight straight JJ A47139 341 8 line line NN A47139 341 9 , , , A47139 341 10 and and CC A47139 341 11 produce produce VB A47139 341 12 it -PRON- PRP A47139 341 13 until until IN A47139 341 14 it -PRON- PRP A47139 341 15 cut cut VBD A47139 341 16 the the DT A47139 341 17 perpendicular perpendicular NN A47139 341 18 at at IN A47139 341 19 K. K. NNP A47139 341 20 5 5 CD A47139 341 21 . . . A47139 342 1 Draw draw VB A47139 342 2 the the DT A47139 342 3 line line NN A47139 342 4 AK AK NNP A47139 342 5 , , , A47139 342 6 which which WDT A47139 342 7 shall shall MD A47139 342 8 give give VB A47139 342 9 the the DT A47139 342 10 angle angle NN A47139 342 11 required require VBN A47139 342 12 KAL KAL NNP A47139 342 13 = = SYM A47139 342 14 FAC FAC NNP A47139 342 15 . . . A47139 343 1 the the DT A47139 343 2 demonstration demonstration NN A47139 343 3 whereof whereof NNP A47139 343 4 is be VBZ A47139 343 5 apparent apparent JJ A47139 343 6 from from IN A47139 343 7 the the DT A47139 343 8 foregoing foregoing JJ A47139 343 9 Problems problem NNS A47139 343 10 . . . A47139 344 1 If if IN A47139 344 2 any any DT A47139 344 3 discreet discreet JJ A47139 344 4 Persons Persons NNPS A47139 344 5 desire desire VBP A47139 344 6 further further JJ A47139 344 7 satisfaction satisfaction NN A47139 344 8 or or CC A47139 344 9 Information information NN A47139 344 10 about about IN A47139 344 11 these these DT A47139 344 12 New New NNP A47139 344 13 Problems Problems NNPS A47139 344 14 , , , A47139 344 15 if if IN A47139 344 16 they -PRON- PRP A47139 344 17 please please VBP A47139 344 18 to to TO A47139 344 19 call call VB A47139 344 20 at at IN A47139 344 21 my -PRON- PRP$ A47139 344 22 House House NNP A47139 344 23 , , , A47139 344 24 I -PRON- PRP A47139 344 25 shall shall MD A47139 344 26 be be VB A47139 344 27 ready ready JJ A47139 344 28 to to TO A47139 344 29 endeavour endeavour VB A47139 344 30 to to TO A47139 344 31 satisfie satisfie VB A47139 344 32 them -PRON- PRP A47139 344 33 ; ; : A47139 344 34 and and CC A47139 344 35 whereas whereas IN A47139 344 36 , , , A47139 344 37 to to IN A47139 344 38 me -PRON- PRP A47139 344 39 the the DT A47139 344 40 Method Method NNP A47139 344 41 and and CC A47139 344 42 Demonstration Demonstration NNP A47139 344 43 of of IN A47139 344 44 these these DT A47139 344 45 Matters matter NNS A47139 344 46 , , , A47139 344 47 seem seem VBP A47139 344 48 sufficiently sufficiently RB A47139 344 49 evident evident JJ A47139 344 50 , , , A47139 344 51 yet yet CC A47139 344 52 I -PRON- PRP A47139 344 53 have have VBP A47139 344 54 called call VBN A47139 344 55 the the DT A47139 344 56 whole whole JJ A47139 344 57 Praxis Praxis NNP A47139 344 58 and and CC A47139 344 59 Method Method NNP A47139 344 60 here here RB A47139 344 61 delivered deliver VBD A47139 344 62 , , , A47139 344 63 but but CC A47139 344 64 an an DT A47139 344 65 Essay Essay NNP A47139 344 66 , , , A47139 344 67 until until IN A47139 344 68 it -PRON- PRP A47139 344 69 be be VB A47139 344 70 found find VBN A47139 344 71 approved approve VBN A47139 344 72 by by IN A47139 344 73 able able JJ A47139 344 74 Artists Artists NNP A47139 344 75 , , , A47139 344 76 and and CC A47139 344 77 have have VBP A47139 344 78 proposed propose VBN A47139 344 79 it -PRON- PRP A47139 344 80 rather rather RB A47139 344 81 Problematically problematically RB A47139 344 82 than than IN A47139 344 83 Thetically Thetically NNP A47139 344 84 , , , A47139 344 85 as as IN A47139 344 86 is be VBZ A47139 344 87 usual usual JJ A47139 344 88 in in IN A47139 344 89 such such JJ A47139 344 90 cases case NNS A47139 344 91 . . . A47139 345 1 G. G. NNP A47139 345 2 Keith Keith NNP A47139 345 3 . . . A47139 346 1 ADVERTISEMENT ADVERTISEMENT NNP A47139 346 2 . . . A47139 347 1 Geometry Geometry NNP A47139 347 2 , , , A47139 347 3 Surveying Surveying NNP A47139 347 4 , , , A47139 347 5 Navigation Navigation NNP A47139 347 6 , , , A47139 347 7 Astronomy Astronomy NNP A47139 347 8 , , , A47139 347 9 Dyaling Dyaling NNP A47139 347 10 , , , A47139 347 11 and and CC A47139 347 12 other other JJ A47139 347 13 Mathematical Mathematical NNP A47139 347 14 Arts Arts NNPS A47139 347 15 are be VBP A47139 347 16 taught teach VBN A47139 347 17 by by IN A47139 347 18 G. G. NNP A47139 347 19 Keith Keith NNP A47139 347 20 at at IN A47139 347 21 his -PRON- PRP$ A47139 347 22 House House NNP A47139 347 23 in in IN A47139 347 24 Pudding Pudding NNP A47139 347 25 Lane Lane NNP A47139 347 26 , , , A47139 347 27 near near IN A47139 347 28 the the DT A47139 347 29 Monument Monument NNP A47139 347 30 - - HYPH A47139 347 31 London London NNP A47139 347 32 . . .