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 XLII. PROBLEM.

TO make a Parallelogram equal to a Triangle given, in an Angle equal to a Right Lined Angle given.

It is required to make a Parallelo∣gram equal to the Triangle ABC, having an Angle equal to the Angle E. Divide the Base BC into two equal parts in D. Draw AG Parallel to BC, (by the 31^st.) make also the Angle CDF equal to the Angle E, (by the 23^d.) Then draw the Parallel CG; the figure FDCG is a Parallelogram, seeing the Lines FG, DC; DF, CG, are Paral∣lel. The Angle CDF is equal to the Angle E. I say that the Parallelogram is equal to the Triangle ABC.

Demonstration. The Triangle ADC is half of the Parallelogram FDCG, (by the 41^st.) it is also half the Tri∣angle ABC, because the Triangles ADC, ADB, are equal (by the 37^th.) Therefore the Triangle ABC is equal to the Parallelogram FDCG.