The Science of the Shulba: A Study in Early Hindu Geometry c15.71

c15.71

Let us next turn to find how the passages in question have been explained by the orthodox commentators. Amongst them, the most elaborate explanation of the expression *tābhirjñeyābhir*, etc., is found to be that of Karavindasvāmī. According to him, the word *jñeya* implies that variety of quadrilaterals in which of the sides and the diagonal any two being given, the third “can be known” with the help of the theorem of the square of the diagonal; or it denotes the rectangles which "can be conceived in mind," the sides and the diagonal of them being expressible in terms of commensurable quantities.¹ The first explanation is given also by Sundararāja and the alternative one by Kapardisvāmī. Sundararāja is silent about the true import of the word *jñeyāni* in *etāvanti jñeyāni*, etc. In the opinion of Karavindasvāmī and Kapardisvāmī, it implies those rectangles in which the sides and the diagonal "can be known in terms of numbers which are rational (*śuddhamūla*, lit. 'which are perfect roots')."²