Page:Euclid's Elements 1714 Barrow translation.djvu/26

14

To biect, or divide into two equal parts, a right-lined angle given BAC.

a Take AD = to AE, and draw the line DE; upon which b make an equilateral triangle DFE. draw the right line AF; it hall biect the angle.

For AD c = AE, and the ide AF is common, and the bae DF c = FE. d therefore the angle DAF = EAF. Which was to be done.

Hence it appears, how an angle may be cut into any equal parts, as 4, 8, 16, &c. to wit, by biecting each part again.

The method of cutting angles into any equal parts required, by a Rule and Compas, is as yet unknown to Geometricians.

To biect a right line given AB.

Upon the line given AB a erect an equilateral triangle ABC; and b biect the angle C with the right line CD. That line hall alo biect the line given AB.

For AC c = BC, and the ide CD is common, and the angle ACD c = BCD. therefore AD d = BD. Which was to be done.

The practice of this and the precedent Propoition is eaily hewn by the contruction of the 1. Prop. of this Book.