The Science of the Shulba: A Study in Early Hindu Geometry c18.59

c18.59

Now as regards the size of the *Āśvamedhika Agni*, Kātyāyana states clearly : "(It) is twice or thrice (the area of) the primitive *Agni* or twenty-onefold (*ekaviṃśavidha*)."¹ Such is also the opinion of the other Śulbakāras as well as of the *Brāhmaṇa*.² *Śatapatha Brāhmaṇa* mentions also of a particular school, according to which the total area of the altar should be 12½ square puruṣas.³ As regards the method of enlargement of the primitive falcon-shaped altar of 7½ square puruṣas by which we are to arrive at the construction of the altar for the Horse Sacrifice having the specific area sanctioned for it by the scriptures, one school advocates the proportional enlargement of every part of the construction, while another school the similar enlargement of only those parts which comprise the complete puruṣas, excluding the two aratnis in the wings and the prādeśa in the tail. For an altar with an area of 15 or 22½ square puruṣas enlarged on the first plan we shall have, it will be easily found, to take the *dvikaraṇī* or *trikaraṇī* of a puruṣa and proceed in the same way as in the construction of the primitive *Agni*. For an altar with an area of 21½ square puruṣas enlarged, but according to the second plan, the algebraic equation will be $7x² + ½x = 21½.$ Therefore x = 1/28(√2409 - 1).