Here Fig. 1 is evidently h2 + 4 ⧌.
Fig. 2 is evidently a2 + b2 + 4 ⧌.
∴ h2 + 4 ⧌ = a2 + b2 + 4 ⧌, the ⧌ all being congruent.
∴ h2 = a2 + b2.
The great Hindu mathematician, Bhaskara (born 1114 A.D.), proceeds in a somewhat similar manner. He draws this figure, but gives no proof. It is evident that he had in mind this relation:
h2 = 4 · ab/2 + (b - a)2 = a2 + b2.
A somewhat similar proof can be based upon the following figure: