Hans Walser, [20161014]

**Generalization of Pythagoras**

ŇIn the triangle *ABC* let any parallelograms *ABED*,
*BCFG* be drawn on *AB*, *AC* and let *DE*, *FG*
meet in *H*. Join *HB* and produce it to meet *AC *in
*K*. The sum of the parallelograms *ABED*, *BCFG* can then be shown to the equal to the parallelogram contained
by *AC*, *HB* in an angle equal to the sum of the angles *BAC,* *DHB*.Ó [1, Book IV]

Fig. 0: Red = Green + Blue

(using the principle of Cavalieri)

Fig. 1: First step

Fig. 2: Second step

Fig. 3: Third step

References