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 XXII. PROBLEM.

TO make a Triangle having its Sides equal to Three Right Lines given, provided that Two of them be greater than the Third.

Let it be proposed to make a Tri∣angle, having its Three Sides equal to the Three given Lines, AB, D, E, take with your Compasses the Line D, and putting one Foot thereof in the Point B, make an Arch: Then take in your Compasses the Line E, and put∣ting one Foot in the Point A, cross with the other Foot the former Arch in C; Draw the Lines AC, BC. I say that the Triangle ABC, is what you desire.

Demonstration. The Side AC is equal to the Line E, since it is the Ra∣dius of an Arch drawn on the Center A, equal in Length to the Line E, likewise the Side BC is equal to the Line D: Therefore the Three Sides AC, BC, AD, are equal to the Lines E, D, AB.

USE.

WE make use of this Proposition to make a Figure equal, or like unto another, for having Divided the Figure into Triangles; and making other Triangles, having their Sides equal to the sides of the Triangles in the proposed figure, we shall have a Figure like unto the same in all Respects. But if we desire it should be only like thereunto, but lesser, for Ex∣ample, if we would have the Form of any Plain or Piece of Ground on Paper; having Divided the same into Triangles, and measured all their Sides, we make Triangles like unto those of the Plain, by the help of a Scale of equal parts, from which we take the number of Parts, which their Sides contain, whether Feet, Rods, or any other measure, and applying them as is here Taught.