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 XLVI. PROBLEM.

UPon a Right Line to describe a Square.

To describe a Square on the Right Line AB, erect two Perpendiculars AC, BD, equal to AB, and draw the Line BD.

Demonstration. The Angles at A and B being Right, the Lines AC, BD, are Parallel (by the 28^th.) they are also equal: Therefore the Lines AB, CD, are Parallel and equal (by the 33^d.) and the Angles at A and C, B and D, equal to Two Right (by the 29^th.) and seeing A and B are Right Angles, the Angles C and D shall be also Right. Thence the Figure AD hath all its Sides equal, and all its Angles Right, and consequently is a Square.