Hans Walser, [20161014]
Generalization of Pythagoras
1
Problem
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
2
Proof
without words
(using the principle of Cavalieri)
Fig. 1: First step
Fig. 2: Second step
Fig. 3: Third step
References