Let AB be the given finite straight line.

Thus it is required to bisect the finite straight line AB.

Let the equilateral triangle ABC be constructed on it, [[I. 1](elem.1.1)] and let the angle ACB be bisected by the straight line CD; [[I. 9](elem.1.9)]

I say that the straight line AB has been bisected at the point D.

For, since AC is equal to CB, and CD is common,