The Science of the Shulba: A Study in Early Hindu Geometry c15.112
The Science of the Śulba: A Study in Early Hindu Geometry c15.112
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c15.112
The early Hindus recognised that fresh rational rectangles can be derived from a known one by multiplying or dividing its sides and diagonal by any rational quantity. In other words, they found that if (p, q, r) be a rectangle, so that $p² + q² = r²,$ then another will be (lp, lq, lr), where l is any rational number, integral or fractional. Āpastamba has, indeed, derived certain new rational rectangles in the same way. He has, however, put the result thus:¹