This is a table of type quadgram and their frequencies. Use it to search & browse the list to learn more about your study carrel.
quadgram | frequency |
---|---|
the sum of the | 42 |
in the case of | 32 |
is equal to the | 26 |
the area of a | 26 |
the area of the | 24 |
it is well to | 22 |
sum of the angles | 22 |
on the other hand | 21 |
for the purpose of | 18 |
at the same time | 17 |
the case of the | 17 |
the leading propositions of | 16 |
in the same way | 16 |
the volume of a | 16 |
seems to have been | 16 |
the teaching of geometry | 15 |
is one of the | 15 |
the use of the | 15 |
leading propositions of book | 14 |
the mensuration of the | 14 |
of the angles of | 14 |
a straight line is | 14 |
to the fact that | 14 |
the nature of the | 14 |
the fact that the | 14 |
it is possible to | 14 |
in connection with the | 13 |
in the form of | 13 |
area of a circle | 13 |
in regard to the | 13 |
the volume of the | 13 |
by the use of | 12 |
to the product of | 12 |
by means of a | 12 |
equal to the product | 12 |
the construction of the | 12 |
one of the most | 12 |
it is easy to | 12 |
at the close of | 12 |
at the beginning of | 12 |
it is interesting to | 12 |
that a straight line | 12 |
plane and solid geometry | 11 |
angles of a triangle | 11 |
it is evident that | 11 |
by means of the | 11 |
on the part of | 11 |
equal to one another | 11 |
the study of the | 11 |
is said to have | 11 |
the diameter of the | 11 |
the length of the | 11 |
the product of the | 11 |
the product of its | 11 |
it is probable that | 10 |
is perpendicular to the | 10 |
from the standpoint of | 10 |
it is better to | 10 |
the number of sides | 9 |
the number of propositions | 9 |
of the fact that | 9 |
the square on the | 9 |
as shown in the | 9 |
the included angle of | 9 |
straight line is the | 9 |
of a square inch | 9 |
of the one are | 9 |
at the present time | 9 |
in the same plane | 9 |
so as to make | 9 |
that the area of | 9 |
the center of the | 9 |
that there is no | 9 |
the locus of a | 9 |
included angle of the | 9 |
to square the circle | 9 |
the case of a | 9 |
the size of the | 8 |
the form of a | 8 |
and the included angle | 8 |
area of the circle | 8 |
the value of pi | 8 |
sides and the included | 8 |
to a given line | 8 |
of a triangle are | 8 |
on the other side | 8 |
the one are equal | 8 |
to a class to | 8 |
is from the greek | 8 |
have been made to | 8 |
are equal respectively to | 8 |
the side of the | 8 |
of its base by | 8 |
the sides of a | 8 |
by the help of | 8 |
the other two sides | 8 |
locus of a point | 8 |
sides of a triangle | 8 |
the angles of a | 8 |
is greater than the | 8 |
but it is not | 8 |
the circumference of a | 8 |
proposition relating to the | 8 |
the edge of a | 8 |
its base by its | 8 |
triangles are congruent if | 8 |
as a matter of | 8 |
two sides and the | 8 |
and this is the | 8 |
two triangles are congruent | 8 |
base by its altitude | 8 |
in the use of | 8 |
product of its base | 8 |
the side of a | 8 |
one are equal respectively | 8 |
to have been the | 8 |
the square root of | 7 |
in such a way | 7 |
it is true that | 7 |
one of the best | 7 |
to find the area | 7 |
square on the hypotenuse | 7 |
of a fourth dimension | 7 |
angle of the other | 7 |
angle of the one | 7 |
proclus tells us that | 7 |
proposition of plane geometry | 7 |
in the way of | 7 |
it is necessary to | 7 |
what is meant by | 7 |
of the teaching of | 7 |
circumference of a circle | 7 |
of a straight line | 7 |
find the area of | 7 |
mensuration of the circle | 7 |
it will be found | 7 |
the conservation of energy | 7 |
to the sum of | 7 |
in spite of the | 7 |
of a triangle is | 7 |
so far as to | 7 |
the height of the | 7 |
of a right triangle | 7 |
attempts have been made | 7 |
two sides of a | 7 |
is seen in the | 7 |
in a straight line | 7 |
is from the latin | 7 |
the value of the | 7 |
the bottom of the | 7 |
for the sake of | 7 |
of the same kind | 7 |
the use of a | 6 |
from the fact that | 6 |
the weight of the | 6 |
the discovery of the | 6 |
the foot of the | 6 |
of the conservation of | 6 |
are equal to one | 6 |
a straight line and | 6 |
from time to time | 6 |
finding the area of | 6 |
duplication of the cube | 6 |
l b l c | 6 |
the history of the | 6 |
of the sides of | 6 |
is to be proved | 6 |
are congruent if two | 6 |
we could find the | 6 |
it is well known | 6 |
attention to the fact | 6 |
nair i z i | 6 |
on one side of | 6 |
interesting to a class | 6 |
in terms of the | 6 |
transmutation of the metals | 6 |
two sides of the | 6 |
this is one of | 6 |
the first book of | 6 |
such a way as | 6 |
gothic designs employing circles | 6 |
of the eighteenth century | 6 |
proposition in plane geometry | 6 |
at right angles to | 6 |
the projection of a | 6 |
of the nature of | 6 |
a considerable number of | 6 |
the powder of sympathy | 6 |
is supposed to be | 6 |
the elixir of life | 6 |
a piece of paper | 6 |
of the seventeenth century | 6 |
the beginning of the | 6 |
that it is the | 6 |
equal to the sum | 6 |
it would be possible | 6 |
of algebra and geometry | 6 |
to speak of the | 6 |
if a straight line | 6 |
of a circle is | 6 |
foot of the perpendicular | 6 |
it would not be | 6 |
a large number of | 6 |
in the fifth century | 6 |
the circumference of the | 6 |
for the reason that | 6 |
a great deal of | 6 |
designs employing circles and | 6 |
measured by half the | 6 |
the surface of a | 6 |
line is the shortest | 6 |
the locus of points | 6 |
it should also be | 6 |
as a center and | 6 |
have been the first | 6 |
the close of the | 6 |
it will be noticed | 6 |
it will be seen | 6 |
the same circle or | 6 |
over and over again | 6 |
value of the ratio | 6 |
a way as to | 6 |
equal respectively to two | 6 |
the case of two | 6 |
come down to us | 6 |
be found in the | 5 |
than that of the | 5 |
it is to be | 5 |
in the united states | 5 |
in the first place | 5 |
two angles and the | 5 |
should be noticed that | 5 |
perpendicular to the plane | 5 |
the trisection of an | 5 |
been the first to | 5 |
the part of the | 5 |
that it was the | 5 |
of an inch in | 5 |
is known as the | 5 |
a circle may be | 5 |
in the same order | 5 |
have the same ratio | 5 |
in one of the | 5 |
are to each other | 5 |
be noticed that euclid | 5 |
at the end of | 5 |
to two right angles | 5 |
the end of the | 5 |
as far as possible | 5 |
can easily be made | 5 |
sum of the squares | 5 |
to the area of | 5 |
will be noticed that | 5 |
of squaring the circle | 5 |
to each other as | 5 |
as in the case | 5 |
the extremities of a | 5 |
equal to two right | 5 |
wrote a commentary on | 5 |
propositions of plane geometry | 5 |
on account of its | 5 |
will be that of | 5 |
tells us that the | 5 |
of the nineteenth century | 5 |
is an interesting exercise | 5 |
the duplication of the | 5 |
the surface of the | 5 |
the mean proportional between | 5 |
is well known that | 5 |
the size of a | 5 |
the plane of the | 5 |
path between two points | 5 |
it is not a | 5 |
can be drawn to | 5 |
the squares on the | 5 |
cut by a transversal | 5 |
half the sum of | 5 |
the ratio of the | 5 |
total for plane geometry | 5 |
in connection with this | 5 |
equal to half the | 5 |
the solution of this | 5 |
and the included side | 5 |
in the hope that | 5 |
trisection of an angle | 5 |
the experience of the | 5 |
teaching of elementary mathematics | 5 |
to the nature of | 5 |
circumference of the circle | 5 |
construction of the regular | 5 |
for the purposes of | 5 |
would be possible to | 5 |
the segments of the | 5 |
of a regular inscribed | 5 |
the transmutation of the | 5 |
the construction of a | 5 |
it should be noticed | 5 |
perpendicular to a line | 5 |
perpendicular to a plane | 5 |
the best of the | 5 |
a right angle is | 5 |
the shortest path between | 5 |
is the shortest path | 5 |
extreme and mean ratio | 5 |
of the sixteenth century | 5 |
to a given circle | 5 |
mean proportional between the | 5 |
that it is impossible | 5 |
that there is a | 5 |
to the use of | 5 |
in the middle ages | 5 |
of the area of | 5 |
and it is not | 5 |
the lateral area of | 5 |
angles and the included | 5 |
and it is well | 5 |
is measured by half | 5 |
shortest path between two | 5 |
will be found that | 5 |
the teaching of mathematics | 5 |
of the same size | 5 |
it is helpful to | 5 |
gives an account of | 5 |
is that which has | 5 |
of an isosceles triangle | 5 |
the sum of two | 5 |
and it will be | 5 |
will be seen that | 5 |
study of the subject | 5 |
on the teaching of | 4 |
between axiom and postulate | 4 |
in the eighteenth century | 4 |
or in equal circles | 4 |
similar to the one | 4 |
of geometry in the | 4 |
of a regular polygon | 4 |
to call attention to | 4 |
triangle that has one | 4 |
corresponding proposition in plane | 4 |
circle or in equal | 4 |
points of the compass | 4 |
inscribed and circumscribed polygons | 4 |
right angles are equal | 4 |
of a given cube | 4 |
a line perpendicular to | 4 |
and the elixir of | 4 |
is a straight line | 4 |
perpendicular to the same | 4 |
and one of the | 4 |
a triangle that has | 4 |
which have been made | 4 |
of which the side | 4 |
the circle and the | 4 |
not seem to be | 4 |
circle may be described | 4 |
as the extremity of | 4 |
in any of the | 4 |
it has been suggested | 4 |
with respect to the | 4 |
in the same circle | 4 |
from a to b | 4 |
but we do not | 4 |
angle of the triangle | 4 |
the law of converse | 4 |
same circle or in | 4 |
this proposition is the | 4 |
let us suppose that | 4 |
of plane and solid | 4 |
the study of geometry | 4 |
the area of an | 4 |
congruent if two sides | 4 |
the proposition relating to | 4 |
one side of a | 4 |
conception of a fourth | 4 |
the straightedge and compasses | 4 |
these two propositions are | 4 |
archimedes and his fulcrum | 4 |
the angles of all | 4 |
determine a straight line | 4 |
of which it is | 4 |
to be found in | 4 |
is the mean proportional | 4 |
shown in the engraving | 4 |
in the british museum | 4 |
a perpendicular to a | 4 |
it is impossible to | 4 |
and half an egg | 4 |
is the limit of | 4 |
than a right angle | 4 |
it is difficult to | 4 |
the same is true | 4 |
of this proposition is | 4 |
in equal circles equal | 4 |
of the mensuration of | 4 |
of a perpetual motion | 4 |
a quarter of a | 4 |
is equal to half | 4 |
to the study of | 4 |
the first of these | 4 |
but at the same | 4 |
angles a right angle | 4 |
is that of the | 4 |
of the other two | 4 |
has been suggested that | 4 |
and that it is | 4 |
three sides of the | 4 |
the circle is the | 4 |
the motion of the | 4 |
the hope that the | 4 |
a given straight line | 4 |
the meaning of the | 4 |
is interesting to a | 4 |
it is easily proved | 4 |
that is to say | 4 |
reduce the number of | 4 |
the fixation of mercury | 4 |
on the side of | 4 |
volume of a given | 4 |
the points of the | 4 |
twice the volume of | 4 |
seen in the case | 4 |
the three sides of | 4 |
has one of its | 4 |
be drawn to a | 4 |
a simple matter to | 4 |
is the basis of | 4 |
if two sides and | 4 |
that which has its | 4 |
law of the conservation | 4 |
triangle is equal to | 4 |
the position of the | 4 |
the proposition about the | 4 |
a few of the | 4 |
a good deal of | 4 |
a copy of the | 4 |
half an egg more | 4 |
it is said that | 4 |
it is customary to | 4 |
of the value of | 4 |
a circle is a | 4 |
with the study of | 4 |
the corresponding proposition in | 4 |
in the mensuration of | 4 |
corresponding proposition of plane | 4 |
that it is not | 4 |
the properties of the | 4 |
sides of a right | 4 |
is that which is | 4 |
the definition of a | 4 |
of the basal propositions | 4 |
one of two parallel | 4 |
an account of a | 4 |
by means of which | 4 |
regular polygons of n | 4 |
the fact that a | 4 |
for the construction of | 4 |
are cut by a | 4 |
first book of euclid | 4 |
in the works of | 4 |
a commentary on euclid | 4 |
area of a triangle | 4 |
parallel to a given | 4 |
be made to coincide | 4 |
is perp to x | 4 |
divided into three equal | 4 |
the reductio ad absurdum | 4 |
product of the segments | 4 |
on a square inch | 4 |
in any triangle the | 4 |
the attention of the | 4 |
the law of the | 4 |
lateral area of a | 4 |
from an external point | 4 |
same is true of | 4 |
side of a square | 4 |
same time we must | 4 |
it is claimed that | 4 |
the centers of the | 4 |
this phase of the | 4 |
attention called to the | 4 |
tells us that he | 4 |
straight line and a | 4 |
the one about the | 4 |
a point equidistant from | 4 |
the same ratio as | 4 |
all right angles are | 4 |
is a right triangle | 4 |
quadrature of the circle | 4 |
be equal to the | 4 |
it is found that | 4 |
the diameter of a | 4 |
invented a perpetual motion | 4 |
volume of a sphere | 4 |
a quadrant of the | 4 |
of the diameter of | 4 |
in the hands of | 4 |
the included side of | 4 |
a matter of fact | 4 |
angle of a triangle | 4 |
included side of the | 4 |
may be found in | 4 |
be seen that the | 4 |
each other as the | 4 |
on the surface of | 4 |
illustration illustration illustration illustration | 4 |
of the circle is | 4 |
lines in the same | 4 |
experience of the world | 4 |
a regular inscribed polygon | 4 |
when we come to | 4 |
distant from the center | 4 |
of the first folio | 4 |
center and any given | 4 |
respectively to two sides | 4 |
a class to have | 4 |
equal to a given | 4 |
at a very early | 4 |
is the case in | 4 |
the bible and testament | 4 |
two straight lines are | 4 |
angles of a polygon | 4 |
have come down to | 4 |
that geometry is not | 4 |
center of the circle | 4 |
the edge of the | 4 |
that has one of | 4 |
the extremity of a | 4 |
the proofs of the | 4 |
one of its angles | 4 |
lines are cut by | 4 |
to become a millionaire | 4 |
its angles a right | 4 |
triangle that which has | 4 |
the same base and | 4 |
one of the equal | 4 |
four for the third | 4 |
of a sphere is | 4 |
of its angles a | 4 |
straight angles are equal | 4 |
the intersection of two | 4 |
the same time we | 4 |
in the fact that | 4 |
said to have been | 4 |
brought into contact with | 4 |
of the locus of | 4 |
an inch in diameter | 4 |
greater than the third | 4 |
i have endeavored to | 3 |
has the sanction of | 3 |
been known to the | 3 |
been suggested that the | 3 |
that can easily be | 3 |
of the middle ages | 3 |
a basis for the | 3 |
but the proof is | 3 |
he is said to | 3 |
the sense of touch | 3 |
the value of geometry | 3 |
applications of this proposition | 3 |
a preliminary to the | 3 |
is shown in the | 3 |
what are not the | 3 |
the language of the | 3 |
let it swing about | 3 |
in his mathematical recreations | 3 |
may be considered as | 3 |
than two right angles | 3 |
as de morgan says | 3 |
the equilateral triangle and | 3 |
some of the most | 3 |
as that of the | 3 |
bottom of the crucible | 3 |
of the school grounds | 3 |
in this connection that | 3 |
of a century ago | 3 |
distinction between axiom and | 3 |
of the american mathematical | 3 |
to about one hundred | 3 |
that pythagoras discovered the | 3 |
course in solid geometry | 3 |
the efforts of the | 3 |
do not attempt to | 3 |
to find the side | 3 |
length of the circumference | 3 |
to let fall a | 3 |
the fact that there | 3 |
the limit of a | 3 |
one cent for the | 3 |
the bisector of an | 3 |
the definition is not | 3 |
the measure of the | 3 |
line perpendicular to a | 3 |
cut off the corners | 3 |
as it is generally | 3 |
and a few of | 3 |
euclid does not use | 3 |
line is a line | 3 |
a solution of the | 3 |
of the leading propositions | 3 |
the purpose of increasing | 3 |
this is the first | 3 |
line as a radius | 3 |
reasons for studying geometry | 3 |
for the teacher to | 3 |
from the study of | 3 |
angle formed by two | 3 |
a little more than | 3 |
pyramid is equal to | 3 |
quarter of a dollar | 3 |
points determine a straight | 3 |
should be given to | 3 |
than is the case | 3 |
on the other two | 3 |
by a straight line | 3 |
it is related that | 3 |
with any given point | 3 |
in the same direction | 3 |
in a bowl of | 3 |
the compasses and ruler | 3 |
find the center of | 3 |
the faces of the | 3 |
are unequal in the | 3 |
questions like the following | 3 |
in the schools of | 3 |
the two triangles are | 3 |
that there are two | 3 |
for the measuring of | 3 |
number of sides of | 3 |
that all right angles | 3 |
angle of a regular | 3 |
two angles of a | 3 |
as a preliminary to | 3 |
be divided into three | 3 |
is perpendicular to a | 3 |
to one of the | 3 |
in the american high | 3 |
same base and the | 3 |
a straight line not | 3 |
is easily shown that | 3 |
is a right angle | 3 |
paper so as to | 3 |
if two parallel lines | 3 |
so that it may | 3 |
all straight angles are | 3 |
more than is necessary | 3 |
an ordinary paper protractor | 3 |
it is a good | 3 |
are not to be | 3 |
the computation of the | 3 |
of two parallel planes | 3 |
as shown by the | 3 |
be that of the | 3 |
angles of all the | 3 |
the seven follies of | 3 |
of the triangle and | 3 |
a diameter bisects the | 3 |
terms of the radius | 3 |
the number of edges | 3 |
the same thing are | 3 |
exterior angles of a | 3 |
natural history of hell | 3 |
that can be drawn | 3 |
a triangle are concurrent | 3 |
by half the sum | 3 |
that some of the | 3 |
given in the textbook | 3 |
be found that the | 3 |
needless to say that | 3 |
the same straight line | 3 |
with most of the | 3 |
on the opposite side | 3 |
are congruent if the | 3 |
means of which he | 3 |
which has its three | 3 |
it is not difficult | 3 |
to the end of | 3 |
in area to a | 3 |
propositions in plane geometry | 3 |
it should always be | 3 |
tenths of an inch | 3 |
equals are added to | 3 |
the corresponding proposition of | 3 |
a hole in the | 3 |
off the corners of | 3 |
a regular polygon of | 3 |
that it should be | 3 |
an angle is the | 3 |
a given point in | 3 |
it is advisable to | 3 |
that which does not | 3 |
the figure is a | 3 |
the analogous proposition of | 3 |
do not seem to | 3 |
are some of the | 3 |
it is not worth | 3 |
may be described with | 3 |
from a fixed point | 3 |
the powers of the | 3 |
to run a line | 3 |
to two sides and | 3 |
a triangle is equal | 3 |
side of the other | 3 |
a certain number of | 3 |
which have the same | 3 |
diameter of a circle | 3 |
there are not wanting | 3 |
the proof of the | 3 |
is exactly in line | 3 |
if it were not | 3 |
beyond the powers of | 3 |
of the subject in | 3 |
if i can prove | 3 |
universal medicine and the | 3 |
the opening of the | 3 |
and of course the | 3 |
the first century b | 3 |
the natural history of | 3 |
equal in area to | 3 |
measurement will show that | 3 |
sense of the word | 3 |
given distance from a | 3 |
the american high school | 3 |
one side of the | 3 |
no apology for giving | 3 |
be described with any | 3 |
is one third of | 3 |
to any required length | 3 |
will be equal to | 3 |
not in the same | 3 |
the second part of | 3 |
parallel to an element | 3 |
so as to have | 3 |
about one hundred thirty | 3 |
same as that of | 3 |
we may think of | 3 |
i have no doubt | 3 |
side of the one | 3 |
as to the nature | 3 |
of the old and | 3 |
the fifth century b | 3 |
of a new sense | 3 |
nor the study of | 3 |
it is needless to | 3 |
the radius of a | 3 |
as the number of | 3 |
the search for a | 3 |
the hands of a | 3 |
to bear in mind | 3 |
area of a trapezoid | 3 |
of a similar kind | 3 |
is equal to a | 3 |
that it may be | 3 |
of the incommensurable case | 3 |
give only the ability | 3 |
of this kind of | 3 |
it may have been | 3 |
the corner at c | 3 |
area of the surface | 3 |
that the number of | 3 |
and to give a | 3 |
line is perpendicular to | 3 |
hole in the hand | 3 |
in contact with the | 3 |
a considerable amount of | 3 |
i can prove this | 3 |
on the island of | 3 |
of the segments of | 3 |
a triangle whose base | 3 |
is equal to two | 3 |
is said to be | 3 |
th of an inch | 3 |
shown in this figure | 3 |
through a given point | 3 |
the alkahest or universal | 3 |
attempts to square the | 3 |
of a class in | 3 |
protractor may be used | 3 |
to the work in | 3 |
the diameter is given | 3 |
opposite the equal sides | 3 |
of two straight lines | 3 |
form part of the | 3 |
square on a line | 3 |
of the circle and | 3 |
a sphere may be | 3 |
in the study of | 3 |
diameter of the circle | 3 |
this is done by | 3 |
bible might be written | 3 |
mathematical recreations and problems | 3 |
if we could find | 3 |
to the same line | 3 |
any given point as | 3 |
in the direction ab | 3 |
of alexander the great | 3 |
in the same ratio | 3 |
thousandth of an inch | 3 |
have twice the volume | 3 |
angle by taking the | 3 |
it is perpendicular to | 3 |
of the point as | 3 |
in the seventeenth century | 3 |
lies in the fact | 3 |
and any given line | 3 |
were known to the | 3 |
it may be said | 3 |
drawn from a point | 3 |
injected into the boiler | 3 |
a question of population | 3 |
perpendicular bisectors of the | 3 |
one of the sides | 3 |
angle is equal to | 3 |
a proposition relating to | 3 |
an important part in | 3 |
perpendicular to the line | 3 |
to inscribe a regular | 3 |
any given line as | 3 |
the number of proved | 3 |
the purposes of elementary | 3 |
given line as a | 3 |
can be drawn through | 3 |
and the construction of | 3 |
the method of analysis | 3 |
from two given points | 3 |
it is doubtful if | 3 |
before the christian era | 3 |
was supposed to be | 3 |
a class in geometry | 3 |
the same number of | 3 |
of the compasses and | 3 |
it was not until | 3 |
the object of this | 3 |
that a diameter bisects | 3 |
how to become a | 3 |
purposes of elementary geometry | 3 |
at a greater distance | 3 |
the top of the | 3 |
it might be difficult | 3 |
of the definitions of | 3 |
diameter of the earth | 3 |
one of the many | 3 |
fathom the depths of | 3 |
through a hole in | 3 |
at a given distance | 3 |
but most of them | 3 |
so it is with | 3 |
of the first century | 3 |
on a straight line | 3 |
straightedge and the compasses | 3 |
use of the compasses | 3 |
the first is the | 3 |
algebra and geometry are | 3 |
in reality it is | 3 |
conduct of a class | 3 |
in the state of | 3 |
the needs of the | 3 |
therefore the sum of | 3 |
a plane parallel to | 3 |
is the shortest line | 3 |
the line of centers | 3 |
from the educational standpoint | 3 |
the fact that if | 3 |
the nature of these | 3 |
in the high school | 3 |
would do well to | 3 |
the spirit of the | 3 |
this is not the | 3 |
the comprehension of the | 3 |
the definitions of geometry | 3 |
of the subject is | 3 |
equal respectively to the | 3 |
the same as in | 3 |
as to make the | 3 |
out of all the | 3 |
the sphere and cylinder | 3 |
given point as a | 3 |
the teaching of elementary | 3 |
is by no means | 3 |
seven wise men of | 3 |
form a conception of | 3 |
perpendicular to the base | 3 |
diameter and the circumference | 3 |
in the midst of | 3 |
the areas of two | 3 |
we should have a | 3 |
the band of sponge | 3 |
the same as that | 3 |
and some of the | 3 |
three times the diameter | 3 |
to a given angle | 3 |
two lines drawn from | 3 |
if l b l | 3 |
so as to lie | 3 |
taking the ratio of | 3 |
of a circle to | 3 |
connection with the study | 3 |
as well as the | 3 |
perpendicular to the axis | 3 |
the straight line is | 3 |
that geometry is a | 3 |
the writings of the | 3 |
an angle of a | 3 |
base and the same | 3 |
just as we may | 3 |
i can prove that | 3 |
described with any given | 3 |
is parallel to the | 3 |
one can fathom the | 3 |
to the pythagorean theorem | 3 |
then l b l | 3 |
to the mensuration of | 3 |
to form a conception | 3 |
ratio of the circumference | 3 |
the first folio shakespeare | 3 |
of the same base | 3 |
of all the faces | 3 |
same ratio as their | 3 |
for the number of | 3 |
as one of the | 3 |
of each of these | 3 |
a small budget of | 3 |
in this and the | 3 |
if we cut through | 3 |
interest to the subject | 3 |
the diagonal of a | 3 |
the seven wise men | 3 |
can be made to | 3 |
be the number of | 3 |
diagonal of a square | 3 |
and in this way | 3 |
of the inscribed and | 3 |
re et praxi geometrica | 3 |
employing circles and bisected | 3 |
be noticed that the | 3 |
by taking the ratio | 3 |
the great french philosopher | 3 |
round the corner at | 3 |
the essential features of | 3 |
from a given external | 3 |
we can find the | 3 |
as it is called | 3 |
to those who have | 3 |
to the corresponding proposition | 3 |
the propositions of geometry | 3 |
explain what is meant | 3 |
it will not be | 3 |
the second chapter of | 3 |
it may also be | 3 |
in the teaching of | 3 |
the number of applications | 3 |
can fathom the depths | 3 |
called to the fact | 3 |
call attention to the | 3 |
translation of the greek | 3 |
the relation of the | 3 |
than c without violating | 3 |
the perimeter of a | 3 |
to find the center | 3 |
lines containing the angle | 3 |
be used as a | 3 |
information in regard to | 3 |
equal the sum of | 3 |
construction of a perpetual | 3 |
the help of the | 3 |
perpendicular to the other | 3 |
in this chapter to | 3 |
a rule for finding | 3 |
of the intercepted arcs | 3 |
angles have the same | 3 |
of the five regular | 3 |
perpendicular to one of | 3 |
no royal road to | 3 |
a special case of | 3 |
possibility of a new | 3 |
that have been made | 3 |
the invention of printing | 3 |
squares on the other | 3 |
an angle equal to | 3 |
surface of the earth | 3 |
perpendicular to a given | 3 |
from the point of | 3 |
figure is a parallelogram | 3 |
an account of the | 3 |
the scale of the | 3 |
greater than that of | 3 |
parallel lines are cut | 3 |
to that of a | 3 |
the angle between the | 3 |
analogous proposition of plane | 3 |
line from a given | 3 |
find the side of | 3 |
are subtracted from equals | 3 |
centers of the faces | 3 |
a circle is the | 3 |
a point in the | 3 |
is also true of | 3 |
should give only the | 3 |
as seen in the | 3 |
the length of a | 3 |
the section is a | 3 |
number of simple exercises | 3 |
the perpendicular bisectors of | 3 |
that the volume of | 3 |
perpendicular to the edge | 3 |
in favor of the | 3 |
to a given straight | 3 |
a square which shall | 3 |
is easily proved that | 3 |
in all such cases | 3 |
the reason for this | 3 |
the drawing of a | 3 |
a point in a | 3 |
the height of a | 3 |
of the most important | 3 |
in the plane of | 3 |
it is not so | 3 |
be seen from the | 3 |
fact that there is | 3 |
side of a regular | 3 |
the idea of the | 3 |
that the pupil has | 3 |
the action of the | 3 |
may be made to | 3 |
the accumulation of water | 3 |
in his perpetuum mobile | 3 |
of the regular polygons | 3 |
we are justified in | 3 |
there can be no | 3 |
search for a perpetual | 3 |
that the machine will | 3 |
by a plane parallel | 3 |
square which shall be | 3 |
why geometry is studied | 3 |
are shown in the | 3 |
two parallel lines are | 3 |
the base of the | 3 |
it seems to have | 3 |
and to show that | 3 |
seven follies of science | 3 |
the diameter and the | 3 |
all the straight lines | 3 |
from a point in | 3 |
only the ability to | 3 |
equal to the radius | 3 |
a few years ago | 3 |
less than a right | 3 |
known to the ancients | 3 |
into three equal parts | 3 |
a given external point | 3 |
in the same parallels | 3 |
this can be done | 3 |
times on a square | 3 |
the five regular polyhedrons | 3 |
as to lie on | 3 |
if two straight lines | 3 |
the statement that a | 3 |
in order to have | 3 |
arc of a circle | 3 |
plane perpendicular to the | 3 |
with which we are | 3 |
proposition asserts that if | 3 |
this kind of work | 3 |
space of three dimensions | 3 |
of the theory of | 3 |
be made to move | 3 |
exactly in line with | 3 |
the square and circle | 3 |
extremity of a line | 3 |
the center of similitude | 3 |
height of the tree | 3 |
in the number of | 3 |
be equal to one | 3 |
may be inscribed in | 3 |
to show that the | 3 |
two points determine a | 3 |
but there is a | 3 |
in extreme and mean | 3 |
the corners of the | 3 |
to the pupil as | 3 |
diameter bisects the circle | 3 |
a class to see | 3 |
common tangents to two | 3 |
surface of a sphere | 3 |
for a class to | 3 |
it was thought that | 3 |
the thirteen books of | 3 |
it is easier to | 3 |
the way in which | 3 |
a certain amount of | 3 |
the perimeters of the | 3 |
of the way in | 3 |
to say that the | 3 |
the quadrant used for | 3 |
part of the work | 3 |
inscribed in a semicircle | 3 |
the limit of the | 3 |
of one per cent | 3 |
is the locus of | 3 |
a good plan to | 3 |
two right triangles are | 3 |
cos o x r | 3 |
the science of the | 3 |
if it should give | 3 |
speak of the locus | 3 |
point as a center | 3 |
distance from a fixed | 3 |
the axioms and postulates | 3 |
than the sum of | 3 |
used as a compass | 3 |
interior angles are equal | 3 |
if equals are subtracted | 3 |
an arc of a | 3 |
in the drawing of | 3 |
this book is written | 3 |
history of greek mathematics | 3 |
the arrangement of the | 3 |
the textbook in geometry | 3 |
is good educational policy | 3 |
the third side of | 3 |
is now in the | 3 |
in which it is | 3 |
a good reason for | 3 |
might be difficult to | 3 |
one third of a | 3 |
right angles to the | 3 |
the meaning of a | 3 |
we come to consider | 3 |
de re et praxi | 3 |
may be seen in | 3 |
rectilinear figures book ii | 3 |
by the pythagorean theorem | 3 |
in the sense of | 3 |
large part of the | 3 |
of the squares on | 3 |
at the opening of | 3 |
it is easily shown | 3 |
propositions of solid geometry | 3 |
of the regular pentagon | 3 |
the other side of | 3 |
half the product of | 3 |
of the most interesting | 3 |
length of the diameter | 3 |
an angle formed by | 3 |
equals are subtracted from | 3 |
well to ask a | 3 |
how to find the | 3 |
the influence of the | 3 |
if equals are added | 3 |
of the surface of | 3 |
cent for the first | 3 |
an acute angle is | 3 |
of the present day | 3 |
to the needs of | 3 |
it would seem that | 3 |
from a given point | 3 |
propositions of book iii | 3 |
of a polygon of | 3 |
a plane surface is | 3 |
the american mathematical society | 3 |
from the foot of | 3 |
that they should be | 3 |
it would have been | 3 |
it may be stated | 3 |
a given distance from | 3 |
area to a given | 3 |
the perpendicular bisector of | 3 |
circles and bisected angles | 3 |
a plane through the | 3 |
the beginning of this | 3 |
and the same altitude | 3 |
third side of the | 3 |
of the equal sides | 3 |
the two straight lines | 3 |
lines drawn from a | 3 |
the machine will not | 3 |
it must not be | 3 |
the state of new | 3 |
of any of the | 3 |
the quadrature of the | 3 |
by a broken line | 3 |
an angle of the | 3 |
a center and any | 3 |
alkahest or universal solvent | 3 |
it is certain that | 3 |
state of new york | 3 |
is thus described by | 3 |
no one can fathom | 3 |
from any point on | 3 |
let fall a perpendicular | 3 |
so as to form | 3 |
purpose of increasing the | 3 |
in speaking of the | 3 |
than the third side | 3 |
we shall now consider | 3 |
in addition to the | 3 |
a circle of which | 3 |
two intersecting straight lines | 3 |
a large part of | 3 |
by the name of | 3 |
is also of interest | 2 |
of a quarter of | 2 |
easily followed by the | 2 |
a pair of compasses | 2 |
in heaven and earth | 2 |
who may care to | 2 |
which have been offered | 2 |
that we are justified | 2 |
through a pipe of | 2 |
a reasonable amount of | 2 |
this is not a | 2 |
hypatia who is the | 2 |
that might better be | 2 |
shadow may be made | 2 |
the truth of the | 2 |
and the circumference of | 2 |
on the floor of | 2 |
they have a few | 2 |
the proposition was known | 2 |
fifteen years of age | 2 |
to the mind of | 2 |
the great basal propositions | 2 |
as stated in the | 2 |
straight lines and circles | 2 |
may of course be | 2 |
pythagoras fled to megapontum | 2 |
equal to that of | 2 |
a subject in which | 2 |
all those who have | 2 |
a finite number of | 2 |
referring to the figure | 2 |
of course be understood | 2 |
line that can be | 2 |
he should be asked | 2 |
three times as long | 2 |
may be said that | 2 |
problem may be given | 2 |
so that they shall | 2 |
to the exterior angle | 2 |
be borne in mind | 2 |
price of the horse | 2 |
if the watch is | 2 |
a right triangle is | 2 |
more distant from the | 2 |
in the art of | 2 |
two books of euclid | 2 |
parallel ruler of the | 2 |
relation of algebra to | 2 |
of the thing defined | 2 |
contained by the straight | 2 |
propositions of book vii | 2 |
occupied the attention of | 2 |
this is an interesting | 2 |
for attempting to change | 2 |
as the circumference and | 2 |
number of equal parts | 2 |
standpoint of strict logic | 2 |
discussed in this volume | 2 |
to the extracting of | 2 |
practically little or no | 2 |
the society for the | 2 |
as has already been | 2 |
and is said to | 2 |
it is interesting and | 2 |
by david eugene smith | 2 |
of the proposition about | 2 |
line and a circle | 2 |
of course no one | 2 |
want of a better | 2 |
by n points in | 2 |
to the hypotenuse and | 2 |
the whole history of | 2 |
the inhabitants of flatland | 2 |
more concrete than a | 2 |
becomes zero and the | 2 |
or the locus of | 2 |
well to call attention | 2 |
by the fact that | 2 |
o is called the | 2 |
that the locus of | 2 |
be effected by the | 2 |
of the work and | 2 |
side of the first | 2 |
equals in the same | 2 |
of the picture a | 2 |
triangle is that which | 2 |
is how many times | 2 |
in some of the | 2 |
for the effecting of | 2 |
of the straightedge and | 2 |
the circle book iv | 2 |
the picture a man | 2 |
is the case with | 2 |
what is known as | 2 |
merely a matter of | 2 |
the circumference cut off | 2 |
the results of similar | 2 |
borne in mind that | 2 |
a straight line set | 2 |
is open to the | 2 |
us that pythagoras discovered | 2 |
is equivalent to a | 2 |
and think of the | 2 |
floor of the schoolroom | 2 |
if we have two | 2 |
it appears that the | 2 |
from the center are | 2 |
the opposite sides of | 2 |
in a country where | 2 |
regular polygon of which | 2 |
by the number of | 2 |
at the top of | 2 |
that the square on | 2 |
illusions of the senses | 2 |
these will now be | 2 |
was known to the | 2 |
a few knitting needles | 2 |
the sake of geometry | 2 |
of interest in the | 2 |
to calculate the length | 2 |
pupils in the american | 2 |
in writing of the | 2 |
would not be a | 2 |
that the bible and | 2 |
the great majority of | 2 |
better understood than the | 2 |
there is a certain | 2 |
are not in the | 2 |
many parts of the | 2 |
may be seen from | 2 |
equally distant from the | 2 |
as to what are | 2 |
of a universal medicine | 2 |
before the time of | 2 |
und methode des planimetrischen | 2 |
and then of s | 2 |
the middle of the | 2 |
of the few propositions | 2 |
is shown in this | 2 |
ratio and proportion book | 2 |
of the same material | 2 |
diameter of the circumscribed | 2 |
if we say that | 2 |
results true of that | 2 |
seen through a hole | 2 |
in the thirteenth century | 2 |
for the average pupil | 2 |
in higher mathematics it | 2 |
of the plans which | 2 |
of the patent office | 2 |
attempts which have been | 2 |
straight line is a | 2 |
and there is no | 2 |
between algebra and geometry | 2 |
to use a book | 2 |
parallel is drawn through | 2 |
base has the same | 2 |
walk along ab until | 2 |
by half the intercepted | 2 |
the basis of selection | 2 |
the discovery of this | 2 |
the exterior angle becomes | 2 |
has the same length | 2 |
this can conveniently be | 2 |
of the last century | 2 |
is added to the | 2 |
case was that of | 2 |
to be classed with | 2 |
it should be said | 2 |
of the cube as | 2 |
volume of a cylinder | 2 |
the principles of the | 2 |
going so far as | 2 |
terms of the three | 2 |
area of an isosceles | 2 |
it were not for | 2 |
there is no more | 2 |
is too difficult for | 2 |
to point the hour | 2 |
a small wooden pin | 2 |
the royal society of | 2 |
tells us that pythagoras | 2 |
our solar system is | 2 |
point equidistant from the | 2 |
in order to fix | 2 |
that this book is | 2 |
placed a stake at | 2 |
a line is drawn | 2 |
motion might be obtained | 2 |
been made to explain | 2 |
it is quite possible | 2 |
may be apparently enlarged | 2 |
when we attempt to | 2 |
of a point in | 2 |
pleasing to the eye | 2 |
of which had been | 2 |
the attempts which have | 2 |
will cut off the | 2 |
a occupies the same | 2 |
phase of the subject | 2 |
if we are to | 2 |
in elementary geometry the | 2 |
to make geometry more | 2 |
a point b is | 2 |
was heron of alexandria | 2 |
be applied to the | 2 |
are many variations of | 2 |
there is a little | 2 |
know that the idea | 2 |
are equal and parallel | 2 |
a plane which is | 2 |
it is sufficient to | 2 |
of the oblique prism | 2 |
a pupil has a | 2 |
it was used for | 2 |
through the center of | 2 |
fourth term of the | 2 |
one line can be | 2 |
that the straight line | 2 |
angle is an angle | 2 |
a polygon of n | 2 |
the introduction of the | 2 |
first is greater than | 2 |
he gave a rule | 2 |
to ask a class | 2 |
at the vertices of | 2 |
the circle has been | 2 |
are perpendicular to each | 2 |
and to select the | 2 |
be apparently enlarged by | 2 |
make sure that the | 2 |
a circle to a | 2 |
a consideration of the | 2 |
beginning of solid geometry | 2 |
relating to plane and | 2 |
the volume of any | 2 |
the story goes that | 2 |
wise men of greece | 2 |
the circumference and whose | 2 |
to attack the exercises | 2 |
this proposition to thales | 2 |
of the first is | 2 |
as we shall see | 2 |
to mean both the | 2 |
is to be considered | 2 |
but as to the | 2 |
the proposition is not | 2 |
that the result is | 2 |
a boy or girl | 2 |
should be recommended to | 2 |
the discovery of new | 2 |
and at the same | 2 |
sum of the sides | 2 |
a man of acknowledged | 2 |
number of proved propositions | 2 |
as to make a | 2 |
of the principle of | 2 |
it must be confessed | 2 |
the pupil will be | 2 |
as the limit of | 2 |
has been made in | 2 |
of the present will | 2 |
of equal base and | 2 |
angle equal to a | 2 |
sum of the three | 2 |
of these forms are | 2 |
insisted upon is that | 2 |
that under some conditions | 2 |
falling upon one wheel | 2 |
is now proposed to | 2 |
the subject has been | 2 |
will of course be | 2 |
three hundred years ago | 2 |
of the tree is | 2 |
for the basal propositions | 2 |
right angle is called | 2 |
and b cannot be | 2 |
case of two circles | 2 |
at its extremity is | 2 |
the date of these | 2 |
use of the triangle | 2 |
realize what life in | 2 |
plan of drawing a | 2 |
so that it is | 2 |
definite point in the | 2 |
approximating the value of | 2 |
plane parallel to the | 2 |
was supposed to have | 2 |
of which are equal | 2 |
a little interest to | 2 |
a straight line as | 2 |
that in order to | 2 |
is doubtful if the | 2 |
the end in view | 2 |
elements on one side | 2 |
the author of the | 2 |
that is in the | 2 |
is the fact that | 2 |
side of the subject | 2 |
und die sechs planimetrischen | 2 |
the school of plato | 2 |
polygon of which the | 2 |
of the one equals | 2 |
a side of the | 2 |
vertical angle of the | 2 |
improved upon this by | 2 |
is sometimes called the | 2 |
had a strange fascination | 2 |
in some other way | 2 |
looked upon in geometry | 2 |
mean the bounding line | 2 |
identically equal in the | 2 |
the ratio of similitude | 2 |
congruent if the hypotenuse | 2 |
simple as easily to | 2 |
relating to the exterior | 2 |
it is so easy | 2 |
to do with the | 2 |
from the definition of | 2 |
the whole is greater | 2 |
plane of the two | 2 |
is that relating to | 2 |
are said to be | 2 |
and the projection of | 2 |
have an angle of | 2 |
is called a right | 2 |
one of them is | 2 |
extremities of a given | 2 |
is called the center | 2 |
the radius in question | 2 |
are far beyond the | 2 |
those who wish to | 2 |
line perpendicular to another | 2 |
b and d are | 2 |
and circumscribed polygons as | 2 |
gave a rule for | 2 |
teachers have any such | 2 |
the angles at the | 2 |
characters so fine that | 2 |
close of book iv | 2 |
propositions de morgan selected | 2 |
if from a point | 2 |
to fall into a | 2 |
hypotenuse and an adjacent | 2 |
as the products of | 2 |
fall outside the circle | 2 |
millionth of an inch | 2 |
the exterior angles of | 2 |
adapted to the needs | 2 |
its way into elementary | 2 |
the island of sicily | 2 |
the study of a | 2 |
the success of the | 2 |
two cents for the | 2 |
of the proposition is | 2 |
the important thing is | 2 |
the reason is that | 2 |
part of the pupil | 2 |
have the same extremities | 2 |
is interesting to note | 2 |
angle is called a | 2 |
should be called to | 2 |
from the latin translation | 2 |
discovery of the liquefaction | 2 |
the eye to the | 2 |
the proof of this | 2 |
not good policy to | 2 |
a cube that should | 2 |
would not be sufficient | 2 |
in the course of | 2 |
much more than this | 2 |
a line as a | 2 |
twentieth globe above us | 2 |
the line joining the | 2 |
any one of them | 2 |
half an ounce of | 2 |
study of the regular | 2 |
circumference of any circle | 2 |
it is a fact | 2 |
as a special case | 2 |
precisely the same length | 2 |
should be as few | 2 |
present value of the | 2 |
there is also a | 2 |
the point from which | 2 |
or the same as | 2 |
following are some of | 2 |
an enormous amount of | 2 |
partly that of the | 2 |
and an adjacent angle | 2 |
the secondary schools of | 2 |
the method by which | 2 |
this is a very | 2 |
it is very obvious | 2 |
of most of the | 2 |
which the pupil is | 2 |
necessary for a beginner | 2 |
that he discovered the | 2 |
is to be observed | 2 |
needs of the beginner | 2 |
drawn through two given | 2 |
of double the number | 2 |
about the line of | 2 |
they should be so | 2 |
in a cistern of | 2 |
of two sides of | 2 |
subject in the curriculum | 2 |
france and de paolis | 2 |
selected with their corollaries | 2 |
who does not know | 2 |
the claim that the | 2 |
a pair of these | 2 |
is also perpendicular to | 2 |
finite number of square | 2 |
his budget of paradoxes | 2 |
of the work of | 2 |
is necessary for the | 2 |
the teacher may have | 2 |
is well that we | 2 |
out of the large | 2 |
to one of two | 2 |
and b as centers | 2 |
true of that world | 2 |
the following are some | 2 |
so that it has | 2 |
be asked of a | 2 |
it has been fully | 2 |
where there is a | 2 |
the elasticity of the | 2 |
of the reductio ad | 2 |
a straight line from | 2 |
same thing may be | 2 |
on this subject are | 2 |
the tree is found | 2 |
and in the course | 2 |
of the propositions that | 2 |
it is always interesting | 2 |
are subtended by equal | 2 |
to have a class | 2 |
on the two sides | 2 |
and it shows that | 2 |
of the ratio of | 2 |
with one of the | 2 |
received so much attention | 2 |
the name of the | 2 |
effecting of a perpetual | 2 |
area of a parallelogram | 2 |
in the same class | 2 |
written at rate of | 2 |
and the second is | 2 |
be postponed until after | 2 |
familiar to the pupil | 2 |
is the use of | 2 |
applications of these propositions | 2 |
can be done by | 2 |
area of the school | 2 |
a sphere is equal | 2 |
begin to curve at | 2 |
a straight line to | 2 |
as we have seen | 2 |
between the hour and | 2 |
as a basis for | 2 |
the propositions of euclid | 2 |
even in regard to | 2 |
base of an isosceles | 2 |
problem is impossible by | 2 |
the latter part of | 2 |
in so far as | 2 |
obtain results true of | 2 |
describe a square which | 2 |
and a pi r | 2 |
visualize a solid from | 2 |
proofs of the basal | 2 |
ratio of diameter to | 2 |
sin o y r | 2 |
has this to say | 2 |
gallons of liquid air | 2 |
an excellent illustration of | 2 |
of the sense of | 2 |
as accurate as the | 2 |
straight line on a | 2 |
are found in the | 2 |
better suited to the | 2 |
as has been suggested | 2 |
this proposition is not | 2 |
of approximating the value | 2 |
were at one time | 2 |
the greek word for | 2 |
valve in the center | 2 |
it at right angles | 2 |
way in which he | 2 |
the actual cost and | 2 |
the regular hexagon is | 2 |
proposition to be proved | 2 |
surface of the ice | 2 |
be in the same | 2 |
the chapters and the | 2 |
would be at once | 2 |
which has no part | 2 |
there is also another | 2 |
is not of much | 2 |
the floor of the | 2 |
area of a regular | 2 |
the homogeneity of space | 2 |
what is the height | 2 |
of in your philosophy | 2 |
that should have twice | 2 |
essential features of a | 2 |
very little more than | 2 |
he might have postulated | 2 |
ourselves in the midst | 2 |
took hold of the | 2 |
with a velocity of | 2 |
quadrant of the sixteenth | 2 |
the lay of the | 2 |
in the school course | 2 |
significance of the negative | 2 |
plane there can be | 2 |
on page shows how | 2 |
more than a year | 2 |
and it is interesting | 2 |
the product of their | 2 |
the shadow may be | 2 |
these forms are shown | 2 |
on the score of | 2 |
that geometry was taught | 2 |
required to construct an | 2 |
so far as they | 2 |
his account of his | 2 |
that are necessary to | 2 |
of gold or silver | 2 |
the second and third | 2 |
in the performance of | 2 |
hand side of the | 2 |
the hypotenuse and an | 2 |
straight line in space | 2 |
to curve at p | 2 |
picture a man is | 2 |
side of the tube | 2 |
shows how it was | 2 |
is not so simple | 2 |
is well to state | 2 |
be called upon to | 2 |
between two lines that | 2 |
to be observed that | 2 |
of the required cube | 2 |
man lift himself by | 2 |
twice the size of | 2 |
in terms of a | 2 |
one of the old | 2 |
the length of xy | 2 |
make no apology for | 2 |
then let it swing | 2 |
in this country to | 2 |
small wooden pin at | 2 |
true of the man | 2 |
and they will be | 2 |
has to do with | 2 |
the early history of | 2 |
a second angle of | 2 |
the reasons for studying | 2 |
when the diameter is | 2 |
be described in terms | 2 |
less than two right | 2 |
before the eighteenth century | 2 |
one line parallel to | 2 |
may have been the | 2 |
central angles are measured | 2 |
one perpendicular to a | 2 |
be followed by a | 2 |
to be proved in | 2 |
there have been numerous | 2 |
by one line meeting | 2 |
of the volume of | 2 |
have invented a perpetual | 2 |
of compasses and straightedge | 2 |
seen in a method | 2 |
adjacent angle of the | 2 |
on the other must | 2 |
this reduces to the | 2 |
shall be less than | 2 |
the semicircle is the | 2 |
the hypotenuse must equal | 2 |
in his account of | 2 |
from going very far | 2 |
we are not quite | 2 |
the first part of | 2 |
with the compasses and | 2 |
the same idea in | 2 |
but in spite of | 2 |
is said by proclus | 2 |
many times her own | 2 |
father of the hypatia | 2 |
in the line of | 2 |
now before me a | 2 |
illustration another interesting application | 2 |
to divide a line | 2 |
the greater angle is | 2 |
for both of these | 2 |
we derive pleasure from | 2 |
any other subject in | 2 |
to grasp the meaning | 2 |
of the three angles | 2 |
of the dark ages | 2 |
the pressure would at | 2 |
perpendicular to that line | 2 |
is quite possible that | 2 |
locus of points equidistant | 2 |
very nature of the | 2 |
medicine and the elixir | 2 |
although some of the | 2 |
like the following may | 2 |
i and its propositions | 2 |
too abstract to be | 2 |
stage in his progress | 2 |
is needless to say | 2 |
measured by their intercepted | 2 |
the definition for the | 2 |
could square the circle | 2 |
to say how it | 2 |
it is equal to | 2 |
the principle involved in | 2 |
circumference cut off by | 2 |
on page shows a | 2 |
some of the questions | 2 |
connection with this proposition | 2 |
angle sine cosine tangent | 2 |
the vertices of the | 2 |
is better to have | 2 |
must have had a | 2 |
was one of the | 2 |
so simple as easily | 2 |
in the year the | 2 |
taught mathematics in the | 2 |
curve through some higher | 2 |
and do not lie | 2 |
we have left the | 2 |
mensuration of the prism | 2 |
to construct an arc | 2 |
his problems with his | 2 |
the hypotenuse of a | 2 |
a crystal formed by | 2 |
and the printing press | 2 |
in france and de | 2 |
line is drawn through | 2 |
their corollaries as necessary | 2 |
the work relates chiefly | 2 |
there are many more | 2 |
used for the same | 2 |
of pure and applied | 2 |
let abc be the | 2 |
it was because of | 2 |
case they would be | 2 |
each parallel to a | 2 |
of a point equidistant | 2 |
the past few years | 2 |
and in the same | 2 |
part of the eighteenth | 2 |
he did not know | 2 |
the following is a | 2 |
that there must be | 2 |
some of the weights | 2 |
ball tells us that | 2 |
the value of all | 2 |
the principle of the | 2 |
would there not be | 2 |
at the rate of | 2 |
more things in heaven | 2 |
until a point b | 2 |
the school should give | 2 |
ropes out of sea | 2 |
gives the area of | 2 |
the view from the | 2 |
geometry that we have | 2 |
how to attack the | 2 |
the whole is equal | 2 |
which he claimed to | 2 |
efforts at improving euclid | 2 |
of the propositions in | 2 |
say that we have | 2 |
iron rods are hinged | 2 |
of a quadrilateral are | 2 |
cut the circle twice | 2 |
way to introduce this | 2 |
the effecting of a | 2 |
it will of course | 2 |
of the semicircle is | 2 |
hypotenuse must equal the | 2 |
the introduction to geometry | 2 |
seen in the illustration | 2 |
the circumference to the | 2 |
the diameter will weigh | 2 |
be drawn through two | 2 |
straight lines containing the | 2 |
is subtended by the | 2 |
the great french mathematician | 2 |
the proposition that the | 2 |
an illustration of the | 2 |
if two angles and | 2 |
construct an equilateral triangle | 2 |
the effect of all | 2 |
the unaided eye can | 2 |
line of work that | 2 |
the manner of a | 2 |
the use of these | 2 |
of their numerical values | 2 |
squares on any two | 2 |
compute the length of | 2 |
and whose altitude is | 2 |
corollaries as necessary for | 2 |
of a point as | 2 |
of the circumscribed circle | 2 |
the number of basal | 2 |
as necessary for a | 2 |
demands another type of | 2 |
of the numerical measures | 2 |
circumference of the segment | 2 |
one of the planes | 2 |
a very early day | 2 |
by means of this | 2 |
meet in a point | 2 |
now in the british | 2 |
us suppose that the | 2 |
measured on a line | 2 |
to the subject to | 2 |
hold of the wheel | 2 |
and in every case | 2 |
there is a very | 2 |
as few as possible | 2 |
the distance across a | 2 |
of the size of | 2 |
point in the plane | 2 |
as the quotient of | 2 |
question as to why | 2 |
attempts were made to | 2 |
himself by the straps | 2 |
the frustum becomes a | 2 |
the basal propositions of | 2 |
to any practical mechanic | 2 |
is not difficult to | 2 |
exterior angle of a | 2 |
the straight lines containing | 2 |
is true that the | 2 |
until the invention of | 2 |
the division of a | 2 |
in the theory of | 2 |
not the reasons for | 2 |
the twentieth globe above | 2 |
it mean that a | 2 |
sum of the areas | 2 |
is bound to produce | 2 |
position of the sun | 2 |
or it may be | 2 |
that our treatment of | 2 |
to the action of | 2 |
of the number of | 2 |
how it was used | 2 |
until you reach a | 2 |
pupils in the high | 2 |
a conception of a | 2 |
how many times as | 2 |
for the various angles | 2 |
earth and good will | 2 |
be answered by the | 2 |
by the diameter and | 2 |
after the discovery of | 2 |
fell in love with | 2 |
is given by proclus | 2 |
on the scale of | 2 |
of diameter to circumference | 2 |
thence again descend on | 2 |
moved about in space | 2 |
and the number of | 2 |
how it can be | 2 |
column of de luc | 2 |
but they hung a | 2 |
that just as we | 2 |
if p is at | 2 |
of the tube with | 2 |
the sums are equal | 2 |
the royal asiatic society | 2 |
to the measuring of | 2 |
the subject is in | 2 |
what the problem is | 2 |
is an account of | 2 |
to move in the | 2 |
what would be the | 2 |
and in a short | 2 |
is a simple matter | 2 |
in america it is | 2 |
a tangent to a | 2 |
euclid und die sechs | 2 |
of the faces of | 2 |
to have been merely | 2 |
an angle less than | 2 |
pupils in manual training | 2 |
put a stake at | 2 |
planes are perpendicular to | 2 |
of this problem is | 2 |
the line as a | 2 |
it is not of | 2 |
need not be discussed | 2 |
are needed in the | 2 |
it is very certain | 2 |
interest of their pupils | 2 |
the drawing of figures | 2 |
passes through the mid | 2 |
been done by the | 2 |
to have given the | 2 |
by professor de morgan | 2 |
get the figure of | 2 |
the straight line and | 2 |
we are not so | 2 |
which is helpful to | 2 |
in the earliest times | 2 |
the progress of science | 2 |
to produce this effect | 2 |
the beginning of geometry | 2 |
is a special case | 2 |
the rest may be | 2 |
we are told that | 2 |
order to have the | 2 |
of the cylinder is | 2 |
a correspondent of the | 2 |
of two congruent triangles | 2 |
wish to run a | 2 |
semicircle is a right | 2 |
there would have been | 2 |
of precisely the same | 2 |
fourth dimension or the | 2 |
the study of such | 2 |
the real purpose of | 2 |
and of the most | 2 |
following is an interesting | 2 |
of which we have | 2 |
not quite sure of | 2 |
be moved about in | 2 |
other two sides of | 2 |
discovered the construction of | 2 |
of it as a | 2 |
the figure of a | 2 |
at p and q | 2 |
full appreciation of the | 2 |
of a conic surface | 2 |
angle between the hour | 2 |
it is proper to | 2 |
the same way fix | 2 |
given in connection with | 2 |
his mathematical recreations and | 2 |
reason for studying geometry | 2 |
will thus be seen | 2 |
sides of a quadrilateral | 2 |
when viewed under a | 2 |
offered and which he | 2 |
security for the last | 2 |
to the amount of | 2 |
is here that the | 2 |
which the side is | 2 |
the fact that all | 2 |
that two points determine | 2 |
pi r the volume | 2 |
writing of the same | 2 |
the proof is not | 2 |
has been left as | 2 |
reduction in the number | 2 |
if two planes are | 2 |
to be within the | 2 |
measure of the circle | 2 |
in the secondary schools | 2 |
thing may be said | 2 |
the division of the | 2 |
its bases multiplied by | 2 |
as to make such | 2 |
in any other branch | 2 |
this proposition is practically | 2 |
that of finding the | 2 |
that of the other | 2 |
is perpendicular to one | 2 |
with the case of | 2 |
by the simple process | 2 |
that the sum of | 2 |
is meant by ratio | 2 |
the sides about the | 2 |
or shall it be | 2 |
to be the case | 2 |
a study of the | 2 |
is not used as | 2 |
to the second fractional | 2 |
by doubling the number | 2 |
by the force of | 2 |
there is also some | 2 |
general determined by n | 2 |
that it shall be | 2 |
of those who have | 2 |
show the relation of | 2 |
been caused by the | 2 |
exactly what we have | 2 |
means of a very | 2 |
let it be required | 2 |
formed by replacing each | 2 |
the points of division | 2 |
shortest distance between two | 2 |
and in view of | 2 |
it is not necessary | 2 |
the point may even | 2 |
taught in the schools | 2 |
the definition of line | 2 |
does it mean that | 2 |
received into the other | 2 |
that we may use | 2 |
and the volume is | 2 |
tangents to two circles | 2 |
any triangle the greater | 2 |
who lived in the | 2 |
the next she sold | 2 |
as to why geometry | 2 |
that have come down | 2 |
the describing of circles | 2 |
the projection of the | 2 |
and a side of | 2 |
of a segment is | 2 |
are liable to be | 2 |
measure the length of | 2 |
also given by proclus | 2 |
here again we may | 2 |
which case they would | 2 |
other as the squares | 2 |
postponed until after the | 2 |
to measure to the | 2 |
little or no friction | 2 |
they placed a stake | 2 |
number of propositions in | 2 |
pipe of double the | 2 |
that has preceded it | 2 |
through p parallel to | 2 |
be based upon the | 2 |
at the foot of | 2 |
straight lines in the | 2 |
the first century a | 2 |
it is with geometry | 2 |
by the perimeter of | 2 |
would not be difficult | 2 |
be introduced to the | 2 |
primarily for the sake | 2 |
things in heaven and | 2 |
of a box is | 2 |
is that we should | 2 |
us that it was | 2 |
to the next valve | 2 |
is that of a | 2 |
propositions have been discovered | 2 |
triangle in terms of | 2 |
ignorant both of the | 2 |
to draw a line | 2 |
instead of the wound | 2 |
do this by the | 2 |
that the pupil can | 2 |
the first is greater | 2 |
a subject that has | 2 |
impossible by elementary geometry | 2 |
geometry is not taught | 2 |
that all straight angles | 2 |
to the comprehension of | 2 |
but it is evident | 2 |
of the side of | 2 |
of sides of the | 2 |
a velocity of about | 2 |
line is that which | 2 |
in the center is | 2 |
we are allowed to | 2 |
time to time to | 2 |
and that this was | 2 |
and why do we | 2 |
they can be made | 2 |
two planes perpendicular to | 2 |
of a regular pyramid | 2 |
above the level of | 2 |
planes is perpendicular to | 2 |
both of the nature | 2 |
the hypatia who is | 2 |
it may be a | 2 |
is that of archimedes | 2 |
and solid geometry is | 2 |
and of the results | 2 |
we must make the | 2 |
error does not exceed | 2 |
is it better to | 2 |
that the teacher may | 2 |
we have just given | 2 |
of a cone of | 2 |
in characters so fine | 2 |
little more than three | 2 |
then at the figure | 2 |
all the work for | 2 |
about the year b | 2 |
made much of the | 2 |
before the british association | 2 |
the exterior angle of | 2 |
as the bounding line | 2 |
special case of the | 2 |
from which bc makes | 2 |
it is generally called | 2 |
five colors of marble | 2 |
refused to allow a | 2 |
six books of euclid | 2 |
when in reality it | 2 |
is evident that the | 2 |
lead them to a | 2 |
which is then at | 2 |
and the circumference cut | 2 |
further from the centre | 2 |
it enables us to | 2 |
that may lead to | 2 |
of the most common | 2 |
it is only on | 2 |
and the sum of | 2 |
about the sum of | 2 |
difficult to define as | 2 |
is a curious fact | 2 |
in the next illustration | 2 |
considered the nature of | 2 |
good will toward men | 2 |
of the world is | 2 |
the knowledge of the | 2 |
to construct an equilateral | 2 |
of the famous sir | 2 |
if for no other | 2 |
the conclusion that their | 2 |
times as long as | 2 |
it from one point | 2 |
is sufficient to point | 2 |
the greatest of the | 2 |
the column of water | 2 |
the bisecting of angles | 2 |
to visualize a solid | 2 |
nature of the problem | 2 |
earth only one inch | 2 |
all things are possible | 2 |
is at least as | 2 |
backward on the sun | 2 |
bottom of the vessel | 2 |
were told that the | 2 |
such a procedure is | 2 |
library of george a | 2 |
is not ready for | 2 |
on the road to | 2 |
through some higher space | 2 |
in the sixteenth century | 2 |
in even the finest | 2 |
angles equal to two | 2 |
in a right triangle | 2 |
class to have attention | 2 |
nature of the exercises | 2 |
perpendicular can be drawn | 2 |
morgan gives the following | 2 |
models in solid geometry | 2 |
that have been suggested | 2 |
call the attention of | 2 |
in this case the | 2 |
of the one equal | 2 |
at this point in | 2 |
due to the pythagoreans | 2 |
author of the natural | 2 |
lift himself by the | 2 |
cylinder is equal to | 2 |
the conduct of a | 2 |
value of the above | 2 |
approximate value of pi | 2 |
equal to the area | 2 |
side of the vertex | 2 |
a logical sequence of | 2 |
cuts it at right | 2 |
geometry is not studied | 2 |
a line through p | 2 |
for teachers who may | 2 |
to enable us to | 2 |
seem to the pupil | 2 |
history of the teaching | 2 |
the conclusion that the | 2 |
he wrote the first | 2 |
us to square the | 2 |
the mental uplift that | 2 |
if to this we | 2 |
to move backward on | 2 |
by their intercepted arcs | 2 |
add a little interest | 2 |
inscribe a regular polygon | 2 |
is both equilateral and | 2 |
in such a simple | 2 |
altitude is equal to | 2 |
to prove that a | 2 |
if the hypotenuse and | 2 |
the number of times | 2 |
proclus calls attention to | 2 |
right angle is a | 2 |
is so easy to | 2 |
the nail problem a | 2 |
propositions of book iv | 2 |
how do we know | 2 |
royal academy of sciences | 2 |
which have come down | 2 |
the illustration given on | 2 |
by means of straight | 2 |
with the preceding one | 2 |
has already been discussed | 2 |
as difficult to define | 2 |
was the first to | 2 |
simplifies the treatment of | 2 |
is equivalent to the | 2 |
all the faces is | 2 |
on any two corresponding | 2 |
run a line through | 2 |
quarter of a century | 2 |
the thing that is | 2 |
a straight line makes | 2 |
thing are equal to | 2 |
it is advantageous to | 2 |
to the corollary that | 2 |
as far as the | 2 |
a manuscript of the | 2 |
a triangle are equal | 2 |
is thought to be | 2 |
of the circumscribed cylinder | 2 |
by the french mathematician | 2 |
straps of his boots | 2 |
by looking at the | 2 |
we may have cross | 2 |
n points in space | 2 |
the daughters of men | 2 |
the approximate value of | 2 |
it should be noted | 2 |
the sphere and the | 2 |
by the circumference of | 2 |
find the value of | 2 |
and by means of | 2 |
the number of human | 2 |
upon the subject are | 2 |
from the sense of | 2 |
the father of the | 2 |
square the circle or | 2 |
constructing a cube that | 2 |
which have been already | 2 |
then of s sides | 2 |
it might be well | 2 |
books ii and v | 2 |
perpetual motion it is | 2 |
come to consider the | 2 |
of mathematics in the | 2 |
and one of his | 2 |
and good will toward | 2 |
b is perp to | 2 |
is less than degrees | 2 |
is tangent to the | 2 |
by calculating the perimeters | 2 |
of the sides being | 2 |
for the case of | 2 |
of the circle as | 2 |
as to give a | 2 |
a number of these | 2 |
that has come down | 2 |
determined by n planes | 2 |
so that the angle | 2 |
he claimed to be | 2 |
have in my possession | 2 |
is the heroine of | 2 |
the special case of | 2 |
to make the subject | 2 |
was by means of | 2 |
seem to be the | 2 |
defined either as a | 2 |
solution of the problem | 2 |
that it might be | 2 |
had studied in egypt | 2 |
actual cost and present | 2 |
of boys and girls | 2 |
congruent if two angles | 2 |
the fusion of all | 2 |
down to us from | 2 |
may be used as | 2 |
sides of the right | 2 |
is very certain that | 2 |
like a piece of | 2 |
may be said for | 2 |
doubling the number of | 2 |
on the sphere and | 2 |
angled triangle that which | 2 |
circumscribed polygons as the | 2 |
being conscious of it | 2 |
in the center of | 2 |
definition of straight line | 2 |
calculate the side of | 2 |
of the twelfth century | 2 |
occupies the same space | 2 |
part of the proof | 2 |
respectively to two angles | 2 |
in terms that are | 2 |
segments from the foot | 2 |
the circle as a | 2 |
discovery of this proposition | 2 |
things are possible to | 2 |
do more than mention | 2 |
we are forced to | 2 |
that it affords a | 2 |
to be understood by | 2 |
regular inscribed and circumscribed | 2 |
the diagonals of a | 2 |
in a few seconds | 2 |
angles at the base | 2 |
it is good educational | 2 |
made by a plane | 2 |
one of the three | 2 |
in general determined by | 2 |
of a regular hexagon | 2 |
volume of the sphere | 2 |
about in space without | 2 |
a spherical triangle is | 2 |
be seen in the | 2 |
tells us that a | 2 |
put on the board | 2 |
cylinder is pi r | 2 |
the very nature of | 2 |
the radius of the | 2 |
is not suited to | 2 |
whole is greater than | 2 |
to make use of | 2 |
such a proof is | 2 |
the same idea is | 2 |
opening of the tube | 2 |
to erect a perpendicular | 2 |
to have been a | 2 |
may be used in | 2 |
any other branch of | 2 |
this is the reason | 2 |
the same side of | 2 |
easier to grasp than | 2 |
it is only a | 2 |
is always interesting to | 2 |
of the powder of | 2 |
reduces to the pythagorean | 2 |
the direction of the | 2 |
a line such that | 2 |
to be taught as | 2 |
so simple that it | 2 |
the following is the | 2 |
economy of time and | 2 |
it is in the | 2 |
the latin translation of | 2 |
could find the area | 2 |
to which we are | 2 |
to have attention called | 2 |
so fine that the | 2 |
base is equal to | 2 |
of models in solid | 2 |
to two angles and | 2 |
replacing each edge of | 2 |
the finding of the | 2 |
in regard to what | 2 |
something to do with | 2 |
circle is measured by | 2 |
value of pi exactly | 2 |
a line parallel to | 2 |
the standpoint of strict | 2 |
the same as the | 2 |
equal to each other | 2 |
which was supposed to | 2 |
invisible to the naked | 2 |
this was done by | 2 |
there is to be | 2 |
times as much as | 2 |
on the hypotenuse must | 2 |
the question of teaching | 2 |
cost and present value | 2 |
from the greek polys | 2 |
without breadth or thickness | 2 |
seems to have come | 2 |
subtended by the greater | 2 |
present population of the | 2 |
perpendicular to the floor | 2 |
the band and chain | 2 |
by word of mouth | 2 |
royal road to geometry | 2 |
would have been no | 2 |
the close of book | 2 |
all the spirit of | 2 |
spoke of it as | 2 |
which is the locus | 2 |
propositions usually given in | 2 |
right triangles are congruent | 2 |
y x tan o | 2 |
it is the basis | 2 |
of an angle of | 2 |
the building up of | 2 |
the rest of the | 2 |
in which case they | 2 |
if there is an | 2 |
may not be as | 2 |
the world in which | 2 |
and it would not | 2 |
that there can be | 2 |
the conditions under which | 2 |
is easy to measure | 2 |