bigram

This is a table of type bigram and their frequencies. Use it to search & browse the list to learn more about your study carrel.

bigram	frequency
straight line	125
plane geometry	71
perpetual motion	68
solid geometry	51
straight lines	49
elementary geometry	44
right angles	39
two sides	34
tells us	32
right angle	28
de morgan	28
right triangle	27
new york	27
two lines	24
one another	22
fourth dimension	22
years ago	21
one side	21
given line	21
let us	20
square inch	19
regular polygons	19
two points	19
two right	19
two triangles	18
leading propositions	18
set forth	18
basal propositions	18
one hundred	17
pythagorean theorem	17
two straight	17
equilateral triangle	17
equal angles	16
high school	16
two angles	16
well known	15
book iii	15
will find	14
given point	14
three dimensions	14
present time	13
parallel lines	13
book ii	13
book iv	13
sir william	13
isosceles triangle	13
two parallel	13
per cent	12
illustration illustration	12
may also	12
eighteenth century	12
plumb line	12
higher mathematics	12
equal parts	12
first century	12
one time	11
already stated	11
equal circles	11
line ab	11
one line	11
similar triangles	11
pure geometry	11
two circles	10
similar figures	10
two propositions	10
one foot	10
included angle	10
middle ages	10
regular polygon	10
three sides	10
united states	10
triangle abc	10
equal sides	10
square root	10
fifth century	9
practical geometry	9
universal medicine	9
sir kenelm	9
thousand years	9
may properly	9
straight angle	9
nineteenth century	9
two intersecting	9
seventeenth century	9
proposition relating	9
special case	9
large number	9
equal respectively	9
every one	9
analytic geometry	9
many times	9
great deal	9
elementary mathematics	9
liquid air	9
whole bible	9
book vi	9
educational policy	9
little later	8
decimal places	8
conic sections	8
acute angle	8
vertical angles	8
capillary attraction	8
reductio ad	8
considerable number	8
human mind	8
two thousand	8
proclus tells	8
first folio	8
corresponding proposition	8
central angles	8
regular hexagon	8
easily proved	8
regular inscribed	8
external point	8
ad absurdum	8
two planes	8
angles equal	8
proposition may	7
three times	7
polyhedral angle	7
given circle	7
special cases	7
third side	7
new sense	7
circle may	7
exterior angle	7
opposite sides	7
french mathematician	7
american textbooks	7
outdoor work	7
first book	7
hundred years	7
two parts	7
geometry will	7
even though	7
sixteenth century	7
high schools	7
usually given	7
given angle	7
will make	7
preceding proposition	7
universal solvent	7
easily made	7
given points	7
two given	7
practical applications	7
three points	7
one point	7
rectilinear figures	7
motion machine	7
simple exercises	7
intercepted arcs	6
lateral area	6
logical sequence	6
mean proportional	6
will also	6
dihedral angle	6
employing circles	6
line joining	6
feet long	6
gothic designs	6
make geometry	6
book vii	6
two dimensions	6
four propositions	6
modern times	6
line perpendicular	6
one third	6
interesting application	6
short time	6
teacher may	6
plane surface	6
enables us	6
fixed point	6
geometric design	6
broken line	6
studying geometry	6
practical purposes	6
five regular	6
thousandth part	6
will generate	6
various kinds	6
will show	6
golden section	6
demonstrative geometry	6
teachers will	6
call attention	6
will fall	6
perpetual lamps	6
great french	6
first great	6
three hundred	6
right triangles	6
bounding line	6
interesting exercise	6
interior angles	6
attention called	6
vertical angle	6
first sight	6
parallel ruler	6
third century	6
may well	6
may use	6
plane angle	6
straight angles	6
designs employing	6
pupil will	5
given straight	5
space inclosed	5
given cube	5
without breadth	5
will continue	5
greater distance	5
lines drawn	5
first place	5
included side	5
opposite side	5
without proof	5
present day	5
euclid gave	5
gothic windows	5
regular polyhedrons	5
eight times	5
michael scott	5
century ago	5
fractional places	5
modern textbooks	5
practical application	5
one proposition	5
first three	5
professor de	5
one inch	5
second part	5
better understood	5
keeley motor	5
may take	5
plane figures	5
plane perpendicular	5
kenelm digby	5
folio shakespeare	5
parallel planes	5
simple matter	5
analogous proposition	5
much attention	5
ratio accepted	5
partial converse	5
shortest path	5
two theorems	5
enable us	5
hundred thirty	5
intercept equal	5
must equal	5
circumscribed polygons	5
angle formed	5
small number	5
make use	5
pupils will	5
put forth	5
take away	5
generally known	5
mean ratio	5
twelfth century	5
will now	5
textbook writers	5
exterior angles	5
school grounds	5
lines perpendicular	5
modern mathematics	5
inscribed polygon	5
irreducible minimum	5
prayer written	5
best known	5
along two	5
congruent triangles	5
upper base	5
thing defined	5
three propositions	5
new lesson	5
paper protractor	5
many years	5
british museum	5
ball will	4
many interesting	4
one perpendicular	4
angled triangle	4
one way	4
natural history	4
modern form	4
early times	4
may think	4
proclus speaks	4
line equal	4
must make	4
danger angle	4
one square	4
rhind papyrus	4
water will	4
natural philosophy	4
working model	4
spherical triangles	4
several years	4
common tangents	4
circles equal	4
one plane	4
required length	4
de luc	4
two similar	4
will equal	4
perpetuum mobile	4
either directly	4
first part	4
illustration suppose	4
one may	4
ancient geometry	4
rectangular parallelepiped	4
van ceulen	4
also used	4
seven follies	4
arab writers	4
far beyond	4
working drawings	4
best way	4
modern science	4
intersecting lines	4
royal road	4
regular pentagon	4
four dimensions	4
essential features	4
recent years	4
greater side	4
line parallel	4
every case	4
teaching geometry	4
two perpendiculars	4
line drawn	4
greek mathematics	4
far enough	4
least one	4
five minutes	4
easily seen	4
book viii	4
board problem	4
knitting needles	4
pythagorean numbers	4
subject matter	4
equal arcs	4
latin translation	4
required subject	4
similar polygons	4
secondary schools	4
columbia college	4
large part	4
recent times	4
easily found	4
numerical values	4
euclid stated	4
will prove	4
right section	4
may seem	4
shortest line	4
points determine	4
greek letter	4
oblique lines	4
cross section	4
adjacent angles	4
without violating	4
certain propositions	4
accepted ratio	4
space without	4
good deal	4
three angles	4
now consider	4
corresponding sides	4
special attention	4
figure formed	4
arithmetical puzzles	4
great circle	4
mathematical recreations	4
plane parallel	4
considerable amount	4
ab bc	4
see page	4
important part	4
whose base	4
reward offered	4
right circular	4
certain point	4
ap pb	4
arabic numerals	4
ahmes papyrus	4
inscribed angle	4
one twenty	4
minute writing	4
spherical polygon	4
cold water	4
will probably	4
american high	4
school course	4
archimedean screw	4
railway carriage	4
thirteenth century	4
perpendicular bisectors	4
every teacher	4
first proposition	4
incommensurable case	4
may find	4
three equal	4
another type	4
rubber bands	4
two arcs	4
pons asinorum	4
point equidistant	4
exactly equal	4
cutting plane	4
walk along	4
sides equal	4
will contain	4
easily shown	4
angle becomes	4
lies evenly	4
work entitled	4
morgan says	4
principle involved	4
will lie	4
will give	4
advanced students	4
regular pyramid	4
geometry must	4
generally accepted	4
taught mathematics	4
four triangles	4
squared paper	4
might well	4
somewhat similar	4
shall geometry	4
patent office	4
usually made	4
page shows	4
nail problem	4
class may	4
us suppose	4
circular cone	4
good educational	3
practical work	3
slant height	3
lines without	3
another case	3
four right	3
fairly well	3
simple device	3
ten fractional	3
easily understood	3
fine arts	3
put forward	3
feet high	3
fully demonstrated	3
given distance	3
greek greek	3
lines containing	3
small budget	3
cross polygons	3
great importance	3
may interest	3
must necessarily	3
figure rigid	3
re et	3
time may	3
motion seekers	3
obtuse angle	3
three inches	3
congruent figures	3
geometric magnitudes	3
motion machines	3
scientific impossibilities	3
combined mathematics	3
two spheres	3
true ratio	3
problem becomes	3
concept clear	3
arithmetical problems	3
will suffice	3
wise men	3
ordinary mind	3
professor ball	3
intersecting straight	3
regular propositions	3
left hand	3
lincoln cathedral	3
sixth century	3
second chapter	3
result will	3
geometrical lines	3
angle less	3
first one	3
will see	3
perpetual lamp	3
may cut	3
circumference exactly	3
fifteen hundred	3
already given	3
space may	3
direction ab	3
two tangents	3
small squares	3
lateral edges	3
ionic school	3
fundamental principles	3
certain amount	3
shall now	3
eight years	3
ordinary paper	3
applied geometry	3
eugene smith	3
brought forward	3
just mentioned	3
present value	3
hermes trismegistus	3
overbalancing wheels	3
line may	3
angle may	3
relatively unimportant	3
convenient point	3
new senses	3
oblique prism	3
numerical measures	3
chapter xvi	3
american teachers	3
let fall	3
may better	3
natural sciences	3
morgan gives	3
usually followed	3
may form	3
rara arithmetica	3
sufficiently accurate	3
isosceles triangles	3
et praxi	3
large one	3
ab ac	3
two streets	3
york city	3
called attention	3
may now	3
teachers may	3
bible might	3
machine will	3
geometric converse	3
later writers	3
chapter xv	3
common sense	3
printing press	3
late dr	3
side ab	3
double progression	3
sympathetic powder	3
important formula	3
burning lamps	3
great majority	3
tenth century	3
great body	3
lie along	3
equal altitudes	3
sand dunes	3
every line	3
something besides	3
english writer	3
various subjects	3
figure drawn	3
hot water	3
per second	3
ancient theory	3
praxi geometrica	3
sound educational	3
figure contained	3
roman surveyors	3
study literature	3
school will	3
one equal	3
six books	3
may say	3
following illustration	3
normal mind	3
one cent	3
commensurable case	3
two different	3
last one	3
full appreciation	3
good teacher	3
regular cross	3
pythagoras discovered	3
lateral faces	3
famous problem	3
triangles abc	3
whose altitude	3
general proof	3
ancient times	3
radical axis	3
one per	3
david eugene	3
similar kind	3
one thing	3
must learn	3
right hand	3
lateral edge	3
without deformation	3
important propositions	3
hydrostatic paradox	3
every proposition	3
point may	3
common one	3
early writers	3
mathematical society	3
spherical surfaces	3
pupils may	3
greater angle	3
great accuracy	3
church schools	3
ac cb	3
given later	3
gold dollar	3
textbook writer	3
horizontal lines	3
four times	3
inch pipe	3
greek geometry	3
now began	3
one concerning	3
one case	3
student may	3
derive pleasure	3
miles per	3
angle acb	3
work may	3
de la	3
right eye	3
van helmont	3
pyramidal space	3
following simple	3
two thirds	3
greek writers	3
book work	3
modern symbols	3
angles opposite	3
asia minor	3
circle will	3
measurement will	3
figure may	3
ludolph van	3
gothic window	3
along ab	3
whole subject	3
much time	3
original work	3
well worth	3
quadrant used	3
geometric algebra	3
fractional place	3
following figure	3
many practical	3
around us	3
equally well	3
general proposition	3
famous mathematician	3
seven wise	3
illustration another	3
will cut	3
just given	3
essential part	3
several attempts	3
remaining angle	3
de paolis	3
figures book	3
much better	3
proportion book	3
simple illustrations	3
inclined planes	3
one will	3
easily explained	3
teacher will	3
old alchemists	3
central angle	3
beginning geometry	3
equal straight	3
ac bc	3
triangle whose	3
american mathematical	3
twentieth globe	3
let abc	3
strictly speaking	3
two parallels	3
sides opposite	3
second figure	3
steam pressure	3
numerical value	3
hundred sixty	3
moving railway	3
mutually equal	3
de re	3
general case	3
absolute value	3
base ab	3
mechanical drawing	3
every point	3
mathematical work	3
absolutely necessary	3
angle equal	3
trilateral figures	3
without using	3
proposition concerning	3
given triangle	3
given external	3
sphere may	3
form part	3
becomes negative	3
one hand	3
whole surface	3
lower end	3
protractor may	3
may therefore	3
makes one	3
square roots	3
last century	3
average pupil	3
commonly used	3
shall see	3
might easily	3
often given	3
modern writers	3
spherical triangle	3
less time	3
used instead	3
two chords	3
und die	3
constant motion	3
will appear	3
generally recognized	3
proposition asserts	3
educational standpoint	3
similar sets	3
real problem	3
already mentioned	3
turned round	3
diameter bisects	3
geometrical quadrature	3
geometric forms	3
proved propositions	3
southern italy	3
genuine application	3
curved surface	3
practical mechanics	3
following curious	3
enthusiastic teacher	3
william ramsay	3
common chord	3
french philosopher	3
essential feature	3
cylindric surface	3
approximate value	3
certain questions	3
line must	3
define similar	3
colored crayons	3
british association	3
good plan	3
slide along	3
best one	3
one complete	3
may profitably	3
school curriculum	3
many teachers	3
naked eye	3
real purpose	3
easily followed	3
two books	3
circular cylinder	3
modern american	3
calling attention	3
certain number	3
may sometime	3
fifteen years	3
third dimension	3
questions like	3
also true	3
real geometry	3
proclus also	3
proclus called	3
one end	3
may lead	3
moving power	3
sighting along	3
thirteen books	3
conic surface	3
higher geometry	3
solids may	3
considerable space	3
go back	3
second proposition	3
famous problems	3
arc bc	3
measuring instruments	3
regular decagon	3
made much	3
practical use	3
good reason	3
christian era	3
little interest	3
whose name	3
perpendicular bisector	3
plane triangle	3
bisected angles	3
french geometer	3
sufficient condition	3
fourth century	3
diogenes laertius	3
sheet metal	3
preceding one	3
will rise	3
will add	3
point within	3
left eye	3
generally understood	3
fine writing	3
equal segments	3
every proof	3
carbonic acid	3
stellar system	3
luminous phials	3
due time	3
greek philosopher	3
harvard syllabus	3
incommensurable number	2
another hindu	2
may know	2
will come	2
story goes	2
lines intercept	2
studies geometry	2
noteworthy advance	2
heavy pasteboard	2
line whose	2
required cube	2
will furnish	2
highly esteemed	2
cutting ab	2
small valve	2
cubic feet	2
two eyes	2
better adapted	2
quite sure	2
great mathematicians	2
conic space	2
two types	2
royal society	2
simple cases	2
many parts	2
teaching world	2
analytical geometry	2
next illustration	2
arc becomes	2
propositions together	2
interesting history	2
small letters	2
whole history	2
feet wide	2
goes back	2
inclined plane	2
closely connected	2
may fall	2
strangely enough	2
three pairs	2
line bisecting	2
common base	2
roman mosaic	2
human intelligence	2
many illustrations	2
much force	2
descending side	2
even within	2
certain ones	2
following regular	2
illustration theorem	2
die geometrie	2
long run	2
apparent difference	2
la construction	2
equal chords	2
usually proved	2
true semicircle	2
evidently intended	2
prussian war	2
also well	2
lines appear	2
mystic number	2
whose date	2
last payment	2
several proofs	2
put together	2
even know	2
absolute truth	2
ancient writers	2
human interest	2
circle whose	2
power must	2
outdoor exercises	2
enthusiastic teachers	2
geometric postulate	2
king john	2
cb ab	2
spherical polygons	2
one must	2
first greek	2
curious arithmetical	2
increases indefinitely	2
intersection may	2
lies chiefly	2
equal merit	2
third wheel	2
born ca	2
present conditions	2
ablest mathematicians	2
shakespeare cyclopedia	2
college students	2
less familiar	2
usual sense	2
frustum becomes	2
one person	2
brief history	2
move round	2
foot tape	2
four definitions	2
indian prince	2
sine cosine	2
case may	2
est cuius	2
crowded curriculum	2
four hours	2
second century	2
proposition seems	2
chapter xii	2
two ways	2
little time	2
good condition	2
construction lines	2
make progress	2
useful knowledge	2
equal legs	2
present will	2
considered together	2
strength enough	2
incommensurable magnitudes	2
special form	2
shadow cast	2
basal ones	2
equal base	2
vice versa	2
just past	2
triangle may	2
will begin	2
much heavier	2
life may	2
complete circuit	2
opposite direction	2
ibn musa	2
every transversal	2
present population	2
another way	2
prevalent among	2
shadow falls	2
brought forth	2
many new	2
may become	2
written work	2
well understood	2
approximate numerical	2
ball tells	2
young man	2
easily illustrated	2
identically equal	2
geschichte der	2
schemes may	2
one equals	2
line meeting	2
statements made	2
entirely proper	2
intersecting planes	2
usually assigned	2
microscopical society	2
arab writer	2
per hour	2
one book	2
geometry may	2
mental discipline	2
also produced	2
beyond anything	2
great hindu	2
standard form	2
illustrative purposes	2
strange doctrine	2
six per	2
might look	2
shadow going	2
whenever possible	2
becomes zero	2
perfect safety	2
equally deceptive	2
will proceed	2
devoted chiefly	2
one great	2
remarkable formula	2
another interesting	2
practically applied	2
become quite	2
men will	2
genuine applications	2
equal distances	2
adjacent angle	2
surveying must	2
gold cure	2
spherical trigonometry	2
plane may	2
way fix	2
real work	2
every reason	2
euclid proved	2
practical geometries	2
professor klein	2
four years	2
one relating	2
diameter will	2
inches long	2
finger tip	2
german philosopher	2
wooden pin	2
hindu writer	2
first years	2
second edition	2
every student	2
simple test	2
good music	2
must still	2
two general	2
textbook work	2
kind might	2
little bisulphide	2
gregoire de	2
supposed locus	2
long time	2
chapter vii	2
may however	2
simplest forms	2
carefully considered	2
higher space	2
mc nc	2
practical ends	2
seven feet	2
radical change	2
simple instrument	2
reasons already	2
meeting another	2
one due	2
high rank	2
move backward	2
cosine tangent	2
lead us	2
eight hours	2
earliest times	2
two adjacent	2
one pound	2
basal definitions	2
greek manuscripts	2
prismatic space	2
general lines	2
de st	2
geometric construction	2
second angle	2
allow pupils	2
close approximation	2
triangle equals	2
therefore ax	2
also perpendicular	2
excellent illustration	2
commonly seen	2
already attained	2
koinai ennoiai	2
figures may	2
long will	2
usual proof	2
much larger	2
usual solution	2
will go	2
never made	2
scientific treatment	2
great basal	2
first day	2
already found	2
new theory	2
will remain	2
acknowledged ability	2
interesting illustration	2
ab along	2
years later	2
will soon	2
endless chain	2
geometry wherever	2
twentieth century	2
produced indefinitely	2
educational value	2
forty days	2
create energy	2
whose minds	2
without altering	2
possible cases	2
different forms	2
entirely different	2
will differ	2
euclid also	2
following statement	2
melted mercury	2
topographical drawing	2
will feel	2
also equal	2
two quantities	2
cube may	2
motion may	2
given time	2
distance ac	2
will allow	2
solid state	2
divided harmonically	2
long since	2
geometric drawing	2
thousand pounds	2
glass slide	2
apparently seen	2
also seen	2
due south	2
similar nature	2
quantitative theory	2
motion might	2
sides respectively	2
illustration given	2
total area	2
usually taken	2
american history	2
wrote extensively	2
divided proportionally	2
general determined	2
shortest distance	2
good policy	2
elementary plane	2
numerous attempts	2
several others	2
without breaking	2
ancient sequence	2
right leg	2
historical interest	2
sir walter	2
hand spoke	2
insect engineering	2
electric light	2
took hold	2
reflex angle	2
century just	2
well afford	2
chapter vi	2
four magnitudes	2
material existence	2
two congruent	2
several times	2
circles alone	2
sir conan	2
time money	2
made great	2
several books	2
side subtends	2
trigonometric functions	2
medical museum	2
placed among	2
latter part	2
additional follies	2
proposition known	2
sides proportional	2
never find	2
one now	2
obtain results	2
judicial astrology	2
area exactly	2
six feet	2
special names	2
positive knowledge	2
explain many	2
asiatic society	2
strange fascination	2
hand side	2
general statements	2
curious effect	2
johannes campanus	2
negative course	2
modern idea	2
may happen	2
two pins	2
whole circle	2
first observed	2
definite point	2
circumference cut	2
common notions	2
exceed one	2
inclose space	2
along ac	2
tangent circles	2
des planimetrischen	2
greek word	2
compasses alone	2
one takes	2
fairly good	2
like one	2
german translation	2
will never	2
cubic foot	2
accounts given	2
mechanical means	2
will sink	2
going backward	2
swiss mathematician	2
purely mechanical	2
simple method	2
will weigh	2
practical mechanic	2
mechanical power	2
actual construction	2
john phin	2
later writer	2
containing air	2
dotted lines	2
geometric solid	2
polygons book	2
six pounds	2
list price	2
distance across	2
modern use	2
moving cause	2
thirty years	2
corresponding parts	2
problem may	2
made quite	2
negative quantities	2
single method	2
cross polygon	2
certain schools	2
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iv perpetual	2
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synthetic method	2