Euclid's Elements (Jihe Yuanben), Vol 6

the ratio of Yi-Bing to Jia-Bing is as Bing-Wu is to Ding-Wu Book 5, Proposition 16. Since the ratio of Jia-Yi to Yi-Bing is as Ding-Bing to Bing-Wu, and the ratio of Yi-Bing to Jia-Bing is as Bing-Wu to Ding-Wu, it follows by equality that the ratio of Jia-Yi to Jia-Bing is as Ding-Bing to Ding-Wu Book 5, Proposition 22.

Corollary: Any straight line within a triangle drawn parallel to one side and cutting the triangle must create a smaller triangle similar to the whole. For example, in triangle Jia-Yi-Bing, draw the line Ding-Wu parallel to Yi-Bing. The resulting triangle Jia-Ding-Wu must be similar to the whole triangle Jia-Yi-Bing. This is because the exterior angle Jia-Ding-Wu is equal to the interior angle Jia-Yi-Bing, and the exterior angle Jia-Wu-Ding is also equal to the interior angle Jia-Bing-Yi Book 1, Proposition 29.

A geometric diagram shows a triangle with vertices labeled Jia (top), Yi (bottom left), and Bing (bottom right). A horizontal line segment intersects the two sides, with endpoints labeled Ding (left) and Wu (right), creating a smaller triangle Jia-Ding-Wu similar to the larger triangle Jia-Yi-Bing.