__BhaskaraÕs 1 ^{st}
Proof__

He used the following diagrams in proving the Pythagorean Theorem.

In the above diagrams, the blue triangles are all congruent and
the yellow squares are congruent.

First we need to find the area of the big square two different
ways.

First let's find the area using the area formula for a square.

Area=c^2.

Now, lets find the area by finding the area of each of the
components and then sum the areas.

Area of the blue
triangles = 4(1/2)ab

Area of the yellow
square = (b-a)^2

Therefore,

Area of the big square
= 4(1/2)ab + (b-a)^2

= 2ab + b^2 - 2ab + a^2

= b^2 + a^2

Since, the square has the same area no matter how you find it

Area = c^2 = a^2 + b^2