Page:First six books of the elements of Euclid 1847 Byrne.djvu/32

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

∥ signifies parallel to. $$\perp$$. . . . . . perpendicular to. $$\angle$$. . . . . . angle. . . . . . right angle.

. . . two right angles. or briefly designates a point.

&gt;, =, or &lt; signifies greater, equal, or less than. The square described on a line is concisely written thus, 2.

In the same manner twice the square of, is expressed by 2. 2. 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, &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 as 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.