The Science of the Shulba: A Study in Early Hindu Geometry c19.s2.1

c19.s2.1

The construction of the *vedi* gives rise to a type of problems of indeterminate character, though in a few cases the physical conditions are so prescribed as to make them determinate.¹ For instance, the breadth of the *Gārhapatya* *vedi* shall have to be, according to the tradition of the scriptures, one vyāyāma.¹ But its form should be square according to some and circular according to others.² It is to be constructed with five layers of bricks, each layer consisting of 21 bricks. Further the rifts of bricks in two consecutive layers must not coincide. The shape of the bricks employed may be square or rectangular. Now the most interesting case is that in which the *vedi* and also the bricks employed in constructing it, are square in shape. It is said that three kinds of square bricks should be made with the sixth, fourth and third part of a vyāyāma as a side. The first layer (l₁) should be constructed with 9 bricks of the first kind and 12 bricks of the second kind, and the second layer (l₂) with 5 bricks of the third kind and 16 bricks of the first kind.³ That is, if we denote the bricks of different kinds thus: b₁ = v²/36, b₂ = v²/16, b₃ = v²/9, where v denotes a vyāyāma, then $l₁ = 9b₁ + 12b₂, l₂ = 5b₃ + 16b₁.$