The Science of the Shulba: A Study in Early Hindu Geometry c14.81

c14.81

the four rectangles surrounding it, *viz.*, *AFBO*, *BGCP*, *CHDQ*, *DEAR*, each of which contains three elementary squares. These can again be divided into two groups: one group consisting of nine elementary squares forming the square on the line *OB* and another group of a single elementary square on the side *OA*. Thus it is proved that $AB² = OA² + OB²$ If the side of each elementary square be one pada, we find a proof of Kātyāyana's first proposition, and if it measures two padas, a proof of his second proposition.