Note that Euclid's treatment in its statement or its "proof" never refers
the traditional equation, a^{2}+b^{2}=c^{2}.
In one alternative proof for this theorem illustrated in the java sketch
below, we consider 4 congruent right triangles and 2 squares and then the
same 4 triangles and the square on the side of the hypotenuse arranged
inside of a square with side "a+b" . Can you explain how this sketch
justifies the theorem?