The Science of the Shulba: A Study in Early Hindu Geometry c16.88

c16.88

It will be interesting to know the early history of the problem of the squaring of the circle and of its converse, the circling of the square, in India. Their origin dates, as has been noted before, earlier than the time of the *Ṛg-veda* (before 3000 B.C.). That was in connection with the construction of the three primarily essential sacrificial altars of the Vedic Hindus, namely the *Gārhapatya*, *Āhavanīya* and *Dakṣiṇāgni*. For these three altars had to be of the same area but of different shape, the first circular, the second square and the last semi-circular. Again, it has also been noted before, that *Gārhapatya* altar may have, according to certain authorities, an alternative shape of a square, besides its usual circular shape, but retaining the same area. The earliest express reference to this tradition is found in the *Śatapatha Brāhmaṇa* (c. 2000 B.C.).¹ It appears copiously in the Sūtra works.² From the latter we also learn of another ancient tradition that the *Dhiṣṇya*³ may be square or circular in shape but with the same area one square *piśila*. The form of an archaic variety of the *Śmaśāna-cit* ("Fire-altar of the shape of the cemetery ") is stated to be circular; according to some peoples and square according to others. As regards its size. the *Śatapatha Brāhmaṇa*, after referring to the earlier opinions, preferably approves of an area of one square puruṣa.⁴ Further instances of the early applications of the above problems are found in the *Taittirīya* and other *Saṃhitā* (c. 3000 B.C.)⁵ in connexion with the construction of *Ratha-cakra-cit*, *Samuhya-cit*, *Paricāyya-cit* and *Droṇa-cit* (alternative shape). In each of these cases, one has to draw at first a square equal in area to that of the primitive *Śyena-cit*, viz., 7½ square puruṣas and then that square has to be circled.⁶ This has been clearly described by Baudhāyana⁷ and Āpastamba⁸ and it was doubtless so before.¹ We occasionally meet with other instances of this kind in the earlier Hindu works.²