The Science of the Shulba: A Study in Early Hindu Geometry c14.26

c14.26

From this one might surmise that the ancient Hindus were aware only of the arithmetical character of the theorem and then by an imperfect generalisation applied it to rational rectangles. But such a surmise will be too hasty. For there cannot be absolutely any doubt about the fact that the Hindus fully recognised the most general geometrical character of the theorem and employed its truth universally. Indeed, we find instances of its application to cases of rectangles whose sides cannot be represented by rational quantities. For instance, for the construction of the *Sautrāmaṇikī-vedi*, application is made of the right-angled triangle (15/√3, 36/√3, 39/√3) or (5√3, 12√3, 13√3) and for the *Aśvamedhikī-vedi* of the right-angled triangle (15√2, 36√2, 39√2).