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 VIII. THEOREM.

A Perpendicular being drawn from the Right Angle of a Right Angled Tri∣angle to the opposite side, divideth the same into Two Triangles which are a like thereto.

If from the Right Angle ABC be drawn a perpendicular BD to the oppo∣site side AC, it will divide the Right Angled Triangle ABC into Two Trian∣gles ADB, BDC, which shall be like, or equiangular to the Triangle ABC.

Demonstration. The Triangles ABC, ADB, have the same Angle A; the Angle ADB, ABC, are right: they are thence equiangular (by the Cor. 2. of the 32d. of the 1st.) In like manner the Triangles BDC, ABC, have the Angle C common; and the Angles ABC, BDC, being right, they are also equal. Thence the Triangles ABC, DBC, are like.

USE.

WE measure inaccessable distances by a Square, according to this

Proposition. For example, if we would measure the distance DC, having drawn the perpendicular DB, and having put a Square at the Point B, in such manner, that by looking over one of its Sides BC, I see the Point C, and over its other Side I see the Point A; it is evident that there will be the same reason of AD to DB, as of DB to DC. So that multiplying DB by its self, and dividing that product by AD, the Quotient shall be DC.