The Science of the Shulba: A Study in Early Hindu Geometry c13.s1.1

c13.s1.1

For the construction of an altar of proper size and shape, as prescribed by the Holy Scriptures, it is sometimes necessary to describe a rectilinear figure having a given area. For instance, it is prescribed that the *vedi* of the *Pitṛyajña* must be a square of an area equal to one-ninth of that of the *Mahāvedi*.¹ Now the area of the *Mahāvedi* is given to be 972 square padas. So the problem becomes to construct a square having an area of 108 square padas. Again it is said that the *Sautrāmaṇikī-vedi* is of the form of an isosceles trapezium having an area equal to the third part of the *Mahāvedi*, that is, to 324 square padas. According to Āpastamba and Kātyāyana, this isosceles trapezium must be similar to the shape of the *Mahāvedi*. This case will be treated separately under "Similar figures." But Baudhāyana seems to have left the shape of the trapezium unrestricted. Hence there arises the problem: to find an isosceles trapezium having an area of 324 square padas. According to the tradition of some schools, it is necessary to construct square-shaped altars of area varying from 1½ to 6½ square puruṣas.²