Mathematics in Ancient and Medieval India c6.s3.20

c6.s3.20

There cannot be any doubt that a little thought about the construction of the altars in class I will presuppose the knowledge from (i) to (iv) and class II a knowledge from (v) to (vii) and class III from that of (viii) to (ix) and knowledge of these three classes together leads to the formulation of rules from (x) to (xiii) besides many others which are not discussed by the *Śulbakāras*. Though these geometrical results mainly occur in the *Śulbasūtras* of Baudhāyana, Āpastamba, Kātyāyana and others, the authors never claimed that they were the first to discover the principles of geometry or apply them to the problems of the construction of altars. Whenever they described a proposition, they referred to their previous workers as quoted here : (i) it is so recognised or prescribed by the authorities, (ii) thus they teach, (iii) it has been so said (*iti abhyupadiśanti iti vijñāyate, iti uktam* etc.). It might be pointed out here that some of the lines occurring in the *Śulbasūtras* are found to be literal quotations from the *Taittirīya Saṃhitā* or *Taittirīya Brāhmaṇa* or the corresponding *Āraṇyaka*. *Baudhāyana* is occasionally more explicit about his sources. In connection with certain differences of opinions amongst the altar builders about the proper size and shape of a particular altar, *Baudhāyana* is found appealing to the authorities of the *Brahmaṇa*, by name for the purpose of arriving at a satisfactory settlement.¹