The Science of the Shulba: A Study in Early Hindu Geometry c17.2

c17.2

It has been observed before that in the sacrificial rituals of the early Hindus it is oftentimes necessary to construct an altar differing in area from another by a specified amount. For instance, the *Sautrāmaṇikī-vedi* is stated to be equal to one-third of the *Mahāvedi*¹ and the *vedi* of the *Aśvamedha* double the latter.² The *Lakṣa-homa-vedi* and *Koṭihoma-vedi* are respectively four and twenty-five times the *Pākayājñikī-vedi*.³ Again it is said that the primitive Fire-altar, *Caturasra-śyenacit*, should have an area of seven and a half square puruṣas at the time of the first construction. At the second construction its area shall have to be 8½ square puruṣas; at the third 9½ square puruṣas. In the same manner the area of the *Agni* should be increased by one square puruṣa at each successive construction up to 101½ square puruṣas. The earliest reference to this mode of increment of the *Agni*, as has been stated before, is found in the *Śatapatha Brāhmaṇa*.⁴ And the practice continued during the succeeding ages.⁵ Now it is the strict injunction of the *Śruti*, that the primitive shape of the Fire-altar must not be disturbed during the course of successive constructions.⁶