Proposition XXXVI. Theorem.
[Euclid, ed. Lardner, 1855, on Google Books]
| (166) | Parallelograms (B D and E G) on equal bases and between the same parallels are equal. |
Draw the right lines B F and C G.
Because the lines B C and F G are equal to the same E H (XXXIV), they are equal to one another; but they are also parallel, therefore B F and C G which join their extremities are parallel (XXXIII), and B G is a parallelogram; therefore equal to both B D and E G (XXXV), and therefore the parallelograms B D and E G are equal.
Book I: Euclid, Elements, Book I (ed. Dionysius Lardner, 11th Edition, 1855)
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This proposition in other editions:
It is here supposed that the equal bases are placed in the same right line.
(167) Cor.—If two opposite sides of a parallelogram be divided into the same number of equal parts, and the corresponding points of division be joined by right lines, these right lines will severally divide the parallelogram into as many equal parallelograms.