The Science of the Shulba: A Study in Early Hindu Geometry c18.68

c18.68

It may be noted that the commentator Mahīdhara is of no help to us about this knotty point of the enlargement of the Fire-altar. According to his interpretation of Kātyāyana's rules, the area of the Fire-altar after an increment of m square puruṣas will be 7½×(1+m/7) square puruṣas. This interpretation evidently assumes a proportional enlargement of all the constituent parts of the primitive Fire-altar and hence should be discarded as being directly against the express intention of the *Sulba*. Another objection against it will be that the area of the Fire-altar at the final construction (the ninety-fifth construction) according to it will be 7½×(1+94/7) or 108 3/14 square puruṣas and hence much in excess of the maximum enlarged area, *viz.*, 101½ square puruṣas, permissible under the *Sulba*. Weber¹ informs us that such a method of enlargement of the Fire-altar is found in the *Paddhati* of Yājñikadeva. Its origin seems to be in the *Śatapatha Brāhmaṇa*.² But it was criticised and challenged even then.³ I cannot give the opinion of the commentator Rāma on this point as the relevant portion of his commentary is not available to me at present.