Euclid, Book I, Proposition 37 (Lardner, 1855)

Proposition XXXVII. Theorem.
[Euclid, ed. Lardner, 1855, on Google Books]

(168)

Triangles (B A C and B F C) on the same base and between the same parallels are equal.

Through the point B draw B E parallel to C A, and draw B D parallel to C F, and produce A F to meet these lines at E and D. The figures B E A C and B D F C are parallelograms on the same base B C and between the same parallels, and therefore, (XXXV) equal; and the triangles B A C and B F C are their halves (XXXIV), and therefore also equal.

Euclid, Elements of Geometry, Book I, Proposition 37 (Edited by Dionysius Lardner, 1855)

Euclid, Elements of Geometry, Book I, Proposition 37
(Edited by Dionysius Lardner, 1855)