The Science of the Shulba: A Study in Early Hindu Geometry c8.28

c8.28

Such is, in brief, a résumé of the more salient points in the elaborate and minute in details specifications of the shape and size of the principal sacrificial altars and of the geometrical knowledge presupposed in their construction, as we find them in the extant *Sulba*. What should be particularly emphasized now is the fact that those specifications are not due to the authors of the *Sulba* themselves. They do not even pretend to make any such claim. On the other hand, they have often and then expressly admitted to have taken them from earlier works. We, in fact, find that numerous passages of *Baudhāyana* and *Āpastamba Sulba* dealing with the spatial magnitudes of sacrificial altars as well as with the methods of their construction, end with the remark *iti vijñāyate* [or "it is known," "it is recognised or prescribed (by authorities)"].¹ Sometimes *iti abhyupadiśanti* ("thus they teach")² or *iti uktam* ("it has been said"),³ is used in the same sense. It has been rightly pointed out before by Garbe⁴ that all those passages of *Āpastamba* are literal quotations from the *Taittirīya Brāhmaṇa* or from the Brāhmaṇa-like portions of the *Taittirīya Saṃhitā* or *Āraṇyaka*. That is exactly true also of the similar passages of *Baudhāyana*.⁵ This writer is occasionally more explicit about his sources. In connexion with certain difference of opinions amongst the altar-builders about the proper size and shape of a particular altar,¹ Baudhāyana is found appealing to the authorities of the *Brāhmaṇa*, by name, for the purpose of arriving at a satisfactory settlement. “This is not right,” observes he, “as it will bring this opinion in contradiction with the ancient precepts. Regarding this point the *Brāhmaṇa* of some is as follows..., of others is...And the following is our *Brāhmaṇa*...”² By “our Brāhmaṇa” is meant the *Taittirīya Saṃhitā*, where indeed the quoted passage occurs.³ On a different occasion, in connexion with certain method of constructing a particular altar, Baudhāyana remarks: “There is also a *Brāhmaṇa* on this point.”⁴ Here again the reference is to the *Taittirīya Saṃhitā*.⁵ There are also other mentions of *Brāhmaṇa* in general by Baudhāyana.⁶ He has once quoted the *Maitrāyaṇīya Brāhmaṇa* by name.⁷ Kātyāyana is found to have appealed similarly to the authority of the “Śruti,” on two occasions.⁸ Āpastamba has sometimes observed that certain constructions are not sanctioned by the *Śruti*.⁹ Thereby he clearly implies that other matters about the spatial magnitudes of the sacrificial altars and the methods of constructing them, that have been recorded by him, are in full accordance with the teachings of the *Śruti* but are not his devices. This he has admitted also otherwise, as has been just pointed out. It will be further shown presently that we can, indeed, trace most of the matters contained in the *Śulba* to the earlier *Brāhmaṇa* and *Saṁhitā*.