Euclid's Elements (Jihe Yuanben), Vol 6

A geometric diagram showing two parallel horizontal lines. Between these lines are several triangles and lines originating from points on the top line (labeled Geng, Jia, Ding, Xin) and extending to points on the bottom line (labeled Zi, Gui, Ren, Yi, Bing, Wu, Ji, Chou, Yin). The diagram illustrates the relationship between triangles and lines of equal height within parallel boundaries.

... [are] to the parallelogram Wu-Xin, in the same ratio as the base Yi-Bing is to Wu-Ji.

Proof: Place the four figures between the two parallel lines Geng-Xin and Zi-Yin. Every figure, when a perpendicular line is drawn from the vertex to the base, has a height equal to the figure itself. Therefore, figures of equal height must lie within parallel lines (see Definition 4, Volume 1). Within the line Zi-Yi, draw several base lines, each equal to Yi-Bing, such as Yi-Ren, Ren-Gui, and Gui-Zi. Within the line Ji-Yin, draw several base lines, each equal to Wu-Ji, such as Ji-Chou and Chou-Yin. Next, from point Jia and point Ding, draw lines such as Jia-Ren, Jia-Gui, Jia-Zi, Ding-Chou, and Ding-Yin. Since the triangles Jia-Yi-Bing, Jia-Yi-Ren, Jia-Ren-Gui, and Jia-Gui-Zi have equal bases and lie between parallel lines, they are equal.