A Disection Proof

Loomis 42

Part II, Proof 42, page 125 from E.S.Loomis, The Pythagorean Proposition (1940)

This is another re-drawing of the Loomis figure above.
The four images below show the disection and translation
of eight parts (from the base and riser squares)
into the hypotenuse square to enact the proof.

The base and riser squares are disected into four parts each. These parts are ready to move into the hypotenuse square. The translation of these parts begins by moving three parts from the riser square and two from the base square into the green area. Then all eight parts are moved enblock into the hypotenuse square. Finally, to complete the translation into the hypotenuse square, the three parts remaining in the right triangle are moved into place.

DANZ ART HOUSE


The base and riser squares are disected into four parts each. These parts are ready to move into the hypotenuse square.	The translation of these parts begins by moving three parts from the riser square and two from the base square into the green area.	Then all eight parts are moved enblock into the hypotenuse square.	Finally, to complete the translation into the hypotenuse square, the three parts remaining in the right triangle are moved into place.