Another Way to Prove the Preceding Theorem.
In a square A B D C, trace four similar and equal triangles; cut them out and dispose them as shown in [Fig. 1]. You will have in the middle an empty space forming a great square, which just has one of the sides of the hypotenuse of the right-angled triangle A E B.
Trace the outlines of this square and remount the triangles one against the other, H C E, against A E B, and C D G, against B F G, you will get the Fig. below.
Fig. 1.
The successively covered and uncovered parts of the two squares have not changed in extent. But this time the uncovered part is formed of the two squares 2 and 3 which correspond to those constructed on the two other sides of the triangle, A E B.
This very simple demonstration has the advantage of being applicable to any rectangle.