The Science of the Shulba: A Study in Early Hindu Geometry c18.54

c18.54

*Thirdly*, the practice of the mention of an altar by reference to the area of a part of it, as has been supposed for the above interpretation, is unknown in the *Sulba* and earlier literatures of the Hindus. Thibaut once thought that such a thing had been implied in a certain rule of Baudhāyana. He says, " But according to the above sūtra² and its commentary the *Aśvamedhika Agni* was of a different nature. It had to comprise twenty-one puruṣas not including the lengthening of the two wings by one aratni each and of the tail by one prādeśa, so that its ātman consisted of twelve square puruṣas, its wings and tail of three puruṣas each. A proportional increase of the two aratnis and the prādeśa would amount to 1½ square puruṣas and then the agni would no longer be 'ekaviṁśa' as the śruti demands. Therefore the wings were lengthened only by the regular aratni (of 24 aṅgulis) and the tail by the regular prādeśa (12 aṅgulis). so that the increase of the agni caused thereby remained less than one square puruṣa and the agni preserved its character of ekaviṁśa.'' ³ Thibaut has been followed in this matter by Bürk.⁴ They are clearly in error.⁵ For the sūtra they had in view says absolutely nothing about the actual size of the *Aśvamedhika Agni*. The commentator Dvārakanātha Yajvā truly took the area of the Fire-altar to be 21½ square puruṣas. His use of the *trikaraṇī* of a puruṣa in the construction can be more easily and satisfactorily explained in a way different from that supposed by Thibaut and Bürk.