Euclid's Elements (Jihe Yuanben), Vol 6

Proposition 5

In equiangular triangles, the sides around the equal angles are proportional; those that are proportional are called corresponding sides.

Proof: Place the two triangles such that the bases Yi-Bing and Bing-Wu form a single straight line. Let Ding-Bing-Wu be the exterior angle to Jia-Yi-Bing. Since the angles Jia-Yi-Bing and Jia-Bing-Yi are together less than two right angles Book 1, Proposition 27, and the angles Ding-Wu-Bing and Jia-Bing-Yi are equal, the sum of angles Yi and Wu is also less than two right angles. Therefore, the lines Yi-Jia and Wu-Ding, when extended, must meet Book 1, Postulate 11. Let them meet at point Ji. Since the exterior angle Ding-Bing-Wu is equal to the interior angle Jia-Yi-Bing, the lines Ding-Bing and Ji-Yi must be parallel Book 1.

A geometric diagram shows two triangles sharing a common base line. The vertices are labeled with celestial stems: 甲 (Jia), 乙 (Yi), 丙 (Bing), 丁 (Ding), 戊 (Wu), and 己 (Ji). A line segment connects 丁 and 丙, and another line extends from 乙 through 甲 to meet a line from 戊 through 丁 at point 己.