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 XIII. PROBLEM.

TO find a mean Proportional between Two Lines.

If you would have a mean Proportional between the Lines LV, VR: having joyned them together on a strait Line, divide the Line LR into two equal parts in the point M; and having descri∣bed a Semi-circle LTR on the Center M; draw the perpendicular VT, it shall be a mean Proportional between LV, VR. Draw the Lines LT, TR.

Demonstration. The Angle LTR, described in a Semi-circle, is right (by the 31st. of the 3d.) and (by the 8th.) the Triangles LVT, TVR, are like; there

is thence the same Reason in the Tri∣angle LVT, of LV to VT, as of VT to VR in the Triangle TVR, (by the 4th.) So then VT is a mean Proportional between LV and VR.

USE.

WE Reduce to a Square any Rect∣angular Parallelogram whatever by this Proposition. For example, in the Rectangle comprehended under LV, VR, I will demonstrate hereafter, that the Square of VT is equal to a Rectangle comprehended under LV, and VR.