The elements of Euclid, explained and demonstrated in a new and most easie method with the uses of each proposition in all the parts of the mathematicks / by Claude Francois Milliet D'Chales, a Jesuit ; done out of French, corrected and augmented, and illustrated with nine copper plates, and the effigies of Euclid, by Reeve Williams ...

PROPOSITION X. PROBLEM.

TO Divide a Line given into two equal parts.

Let the Line AB be proposed to be Divided into Two equal parts, erect an Equilateral Triangle ABC, (by the 1st.) Divide the Angle ACB into two equal parts, (by the 9^th.) I say the Line AB is Divided into two equal parts in the Point E: viz. That the Lines AE, EB, are equal.

Demonstration. The Triangles ACE, BCE, have the Side CE common, and the Si es CA, CB, equal, since the Triangle ACB is Equilateral: The Angles ACE, BCE, are equal, because the Angle ACB was Divided into two equal parts; therefore (by the 4^th.) the Bases AE, EB, are equal.

USE.

THis Proposition is often made use of, our ordinary Practice obligeth us thereto. Wherefore Geometricians would that a Line should be divided at once, and not by several Trials, and that by an infallible method, the Practice of this is most useful in Dividing of Mea∣sures into smaller parts.