The Science of the Shulba: A Study in Early Hindu Geometry c15.69

c15.69

Having detected that this interpretation is open to such a serious objection, Heath modifies it and says: “But the words (*etāvanti jñeyāni*, etc.) also imply that the theorem of the square of the diagonal is also true of other rectangles not of the “recognisable” kind, that is rectangles in which the sides and the diagonal are not in the ratio of integers; this is indeed implied by the constructions for √2, √3, etc., up to √6 (*cf.* ii. 2, viii. 5).”³ But he would still presume that the remark implies that Āpastamba knew of no other rational rectangles that could be employed.