Euclid, Elements of Geometry, Book I, Proposition 42
(Edited by Dionysius Lardner, 1855)

Proposition XLII. Problem.
[Euclid, ed. Lardner, 1855, on Google Books]

(194) To construct a parallelogram equal to a given triangle (B A C) and having an angle equal to a given one (D).


Through the point A draw the right line A F parallel to B C, bisect B C the base of the triangle in E, A B C D E F G and at the point E, and with the right line C E make the angle C E F equal to the given one D; through C draw C G parallel to E F until it meet the line A F in G. C F is the required parallelogram.


Because E C is parallel to A G (const.), and E F parallel to C G, E G is a parallelogram, and has the angle C E F equal to the given one D (const.); and it is equal to the triangle B A C, because it is between the same parallels and on half of the base of the triangle (192).

Book I: Euclid, Book I (ed. Dionysius Lardner, 11th Edition, 1855)

Next: Proposition 43

Previous: Proposition 41

This proposition in other editions: