The Science of the Shulba: A Study in Early Hindu Geometry c11.10
The Science of the Śulba: A Study in Early Hindu Geometry c11.10
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c11.10
If n is not a square number, simplification can be made by expressing it, when possible, as the sum of two square numbers. Thus if $n=p²+q²$ where p, q are rational quantities, then if x denote a side of the required square and c a side of the given square, we shall have $x²=(pc)²+(qc)²=(p²+q²)c²=nc².$ So that with one construction only, we shall get a square n times the given square. Kātyāyana has given some instances of this kind. He says: