Euclid's Elements (Jihe Yuanben), Vol 6

Two geometric diagrams are positioned at the top of the page. On the right is a triangle with vertices labeled Jia (top), Yi (bottom left), and Bing (bottom right). On the left is a quadrilateral with vertices labeled Ding (top), Wu (left), Ji (right), and Geng (bottom).

...the angles opposite the corresponding similar sides—namely, angle Jia and Ding, Yi and Wu, and Bing and Ji—are each equal.

Proof: Construct angle Ji-Wu-Geng equal to angle Yi, and construct angle Geng-Ji-Wu equal to angle Bing. Let the lines Wu-Geng and Ji-Geng meet at Geng. Then angle Geng is equal to angle Jia Book 1, Proposition 32. Thus, the figures Jia-Yi-Bing and Geng-Wu-Ji are equiangular. Therefore, the ratio of Jia-Yi to Yi-Bing is as Geng-Wu to Wu-Ji Book 6, Proposition 4. Since the ratio of Jia-Yi to Yi-Bing was originally as Ding-Wu to Wu-Ji, then Geng-Wu to Wu-Ji is also as Ding-Wu to Wu-Ji Book 5, Proposition 11, and the two lines Ding-Wu and Geng-Wu must be equal Book 5, Proposition 9. Furthermore, the ratio of Yi-Bing to Jia-Bing is as Wu-Ji to Geng-Ji Book 6, Proposition 4. And since the ratio of Yi-Bing to Jia-Bing was originally as Wu-Ji to Ding-Ji, then Wu-Ji to Geng-Ji is as Wu-Ji to Ding-Ji...