Euclid's Elements (Jihe Yuanben), Vol 6

Proposition 4

In any equiangular triangles, the sides around the equal angles are proportional, and the sides subtending the equal angles are the corresponding sides.

A geometric diagram shows two nested or overlapping triangles sharing a common vertex. The vertices are labeled with celestial stems: 甲 (Jia), 乙 (Yi), 丙 (Bing), 丁 (Ding), 戊 (Wu), and 己 (Ji). A line segment 丁丙 is parallel to 己乙.

Explanation: In equiangular triangles ABC original: 甲乙丙 and DPC original: 丁丙戊, the angles BAC original: 甲丙乙 and DPC original: 丁戊丙, as well as ABC original: 乙甲丙 and DPC original: 丁丙戊, are all corresponding equal angles. The proposition states that the ratio of AB to BC is the same as the ratio of DP to PC, the ratio of AB to AC is the same as the ratio of DP to DE, and the ratio of AC to BC is the same as the ratio of DE to PC.