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, etc. 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 between two of its conterminous 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.
Small pie slice
. . . . angle.
Quarter of circle
. . . . right angle.
Two right angles
. . . . two right angles.
Three lines joined at a point or Two lines joined at a point
briefly designates a point.
>, =, or <
signifies greater, equal, or less than.
Line 2
The square described on a line is concisely written thus.
2 · Line 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 isosceles, 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, etc. 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.