Quote
"True, the discovery is also claimed for India. The work relied on is the Apastamba-Sulba-Sutra, the date of which is put at least as early as the fifth or fourth century B.C., while it is remarked that the matter of it must have been much older than the book itself ... There is a proposition stating the theorem of Eucl. I. 47 as a fact in general terms, but without proof […] Certain considerations suggest doubts as to whether the proposition had been established by any proof applicable to all cases. Thus Apastamba mentions only seven rational right angle triangles; he had no general rule such as that attributed to Pythagoras for forming any number of rational right-angle triangles; [his words imply] that he knew no other such triangles. […] the theorem is enunciated and used as if it were of general application; there is, however, no sign of any general proof; there is nothing in fact to show that the assumption of its universal truth was founded on anything better than an imperfect induction from a certain number of cases, discovered empirically, of triangles with sides in the ratios of whole numbers in which the property (1) that the square on the longest side is equal to the sum of the squares on the other two was found to be always accompanied by the property (2) that the latter two sides include a right angle."
Thomas Heath (classicist)
