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 make an Isosceles Triangle which hath each of the Angles on the Base double to the Third.

To make the Isosceles Triangle ABD, which may have each of its Angle ABD, ADB, double to the Angle A; divide the Line AB (by the 11th. of the 2d.) in such manner that the Square AC be equal to the Rectangle AB, BC. De∣scribe on the Center A, at the opening AB, a Circle BD; in which you shall inscribe BD equal to AC. Draw the Line DC, and describe a Circle about the Triangle ACD, (by the 5th.)

Demonstration. Seeing that the Square of CA, or BD, is equal to the Rectangle comprehended under AB, BC; the Line BD shall touch the Circle ACD, in the Point D, (by the 37th. of the 3d.) thence the Angle BDC shall be equal to the Angle A comprehended in the Alternate Segment CAD, (by the 32d. of the Third.) Now the Angle BCD exteriour in

respect of the Triangle ACD, is equal to the Angle A and CDB; therefore the Angle BCD is equal to the Angle BDA. Moreover the Angle ADB, is equal to the Angle ABD, (by the 5th. of the 1st.) thence the Angles BCD, DBC, are equal; and (by the 6th. of the 1st.) the Sides BD, DC, shall be equal. And seeing BD is equal to AC, the Sides AC, CD, shall be equal, and the Angles A and CDA shall be so also. Therefore the Angle ADB is double to the Angle A.