The Science of the Shulba: A Study in Early Hindu Geometry c17.70

c17.70

The geometrical operations intended to be performed in this case are similar to those indicated in the previous case. Here also are to be discerned two methods for the construction of the *Ekaśata-vidha Agni* or the Fire-altar of 101½ square puruṣas. According to the first method each unit of measure is √14 times the unit of measure employed in the construction of the primitive Fire-altar of 7½ square puruṣas, while according to the other, probably the more ancient one, it will be √(14 3/7) times. Though the principle of similarity of shapes is perfectly maintained in either methods, as regards the size, they of course yield only approximate results. For 7½ × 14 = 105 square puruṣas ; 7½ × 14 3/7 = 108 3/14 square puruṣas. The rationale of these results we shall indicate in the next chapter. We should but note here that as the second method ³ yields a result more deviating from the correct and desired one, *viz.*, 101½ square puruṣas, its correctness was challenged even before the time of the *Śatapatha Brāhmaṇa* (*c.* 2000 B.C.).