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Three Collinear Points Forming Rectangles?

Proposition 1: If from A, the vertex of any triangle ABC, there be drawn AD to any point D in the base, and DE, DF be drawn parallel to AC, AB meeting AB, AC in E, F, the sum of the rectangles BAE, CAF will be equal to the square of AD together with the rectangle BDC.

Note: In this context, rectangle BAE means the area of the rectangle formed if its sides were of lengths BE and EA.


Source: Matthew Stewart's General Theorems, 1746