# Symbols & Abbreviations

expreſſes the word therefore.
. . . . becauſe.
=
. . . . equal. This ſign of equality may be read equal to, or is equal to, or are equal to; but any diſcrepancy in regard to the introduction of the auxiliary verbs is, are, &c. cannot affect the geometrical rigour.
means the ſame as if the words ‘not equal’ were written.
>
ſignifies greater than.
<
. . . . leſs than.
. . . . not greater than.
. . . . not leſs than.
+
is read plus (more), the ſign of addition; when interpoſed between two or more magnitudes, ſignifies their ſum.
is read minus (leſs), ſignifies ſubtraction; and when placed between two quantities denotes that the latter is to be taken from the former.
×
this ſign expreſſes the product of two or more numbers when placed between them in arithmetic and algebra; but in geometry it is generally uſed to expreſs a rectangle, when placed between “two ſtraight lines which contain one of its right angles.” A rectangle may alſo be repreſented by placing a point betwen two of its counterminous ſides.
: :: :

expreſſes an analogy or proportion; thus, if A, B, C and D, repreſent four magnitudes, and A has to B the ſame ratio that C has to D, the propoſition is thus briefly written,

A : B :: C : D
A : B = C : D
or A / B = C / D .

This equality or ſameneſs of ratio is read,

as A is to B, ſo is C to D;
or A is to B, as C is to D.

ſignifies parallel to.
. . . . perpendicular to.
. . . . angle.
. . . . right angle.
. . . . two right angles.
or
briefly deſignates a point.
>, =, or <
ſignifies greater, equal, or leſs than.
2
The ſquare deſcribed on a line is conciſely written thus.
2 · 2
In the ſame manner twice the ſquare of, is expreſſed.
def.
ſignifies definition.
pos.
. . . . poſtulate.
ax.
. . . . axiom.
hyp.
. . . . hypotheſis. It may be neceſſary here to remark that the hypotheſis is the condition aſſumed or taken for granted. Thus, the hypotheſis of the propoſition given in the Introduction, is that the triangle is iſoſecles, or that its legs are equal.
conſt.
. . . . conſtruction. The conſtruction is the change made in the original figure, by drawing lines, making angles, deſcribing circles, &c. in order to adapt it to the argument of the demonſtration or the ſolution of the problem. The conditions under which theſe changes are made, are indisputable as thoſe contained in the hypotheſis. For inſtance, if we make an angle equal to a given angle, theſe two angles are equal by conſtruction.
Q. E. D.
. . . . Quod erat demonſtrandum.
. . . .Which was to be demonſtrated.