Euclid's Elements (Jihe Yuanben), Vol 6

28 It is evident that since the exterior angle Jia-Bing-Yi is equal to the interior angle Ding-Wu-Bing, the line Jia-Bing is also parallel to Ji-Wu Book 1, Proposition 28. Because Jia-Ji-Ding-Bing is a parallelogram, the lines Jia-Ji and Ding-Bing are equal Book 1, Proposition 34.

In the triangle Yi-Wu-Ji, since the line Jia-Bing is parallel to the side Ji-Wu, the ratio of Jia-Yi to Ding-Bing (which is equal to Jia-Ji) is the same as the ratio of Yi-Bing to Bing-Wu Book 6, Proposition 2.

By alternation, the ratio of Jia-Yi to Yi-Bing is as Ding-Bing is to Bing-Wu Book 5, Proposition 16. Furthermore, since the line Ding-Bing in triangle Yi-Wu-Ji is parallel to side Ji-Yi, the ratio of Yi-Bing to Bing-Wu is as the ratio of Jia-Bing (which is equal to Ji-Ding) to Ding-Wu Book 6, Proposition 2. By alternation,