Euclid's Elements (Jihe Yuanben), Vol 6

Corollaries

Proposition 2 Two parts

If a straight line is drawn parallel to one side of a triangle, it divides the other two sides into equal proportions. If a line divides two sides of a triangle into equal proportions, it is parallel to the remaining side.

A geometric diagram shows a triangle with vertices labeled A, B, and C original: 甲乙丙. A line segment DE original: 丁戊 is drawn across the triangle, parallel to the base BC original: 乙丙, effectively dividing sides AB and AC.

First explanation: Inside triangle ABC original: 甲乙丙, if a line DE original: 丁戊 is drawn parallel to BC original: 乙丙, the proposition states that DE original: 丁戊 divides AB original: 甲乙 and AC original: 甲丙 at points D original: 丁 and E original: 戊.

Elements of Geometry