The Science of the Shulba: A Study in Early Hindu Geometry c19.s2.14

c19.s2.14

A much more difficult problem of the same type arises in connexion with the construction of the falcon-shaped Fire-altar. Its total area is given to be 7½ a², where a = a puruṣa. It is laid down that the altar must be constructed in fire layers and the number of bricks employed in any layer must be 200. As before, the rifts of bricks in any two successive layers must not coincide. There is no injunction of the scriptures about the varieties of the bricks to be employed or about their relative size and shape. In one method of construction Baudhāyana employs four kinds of square bricks whose sides are respectively the fourth, fifth, sixth and tenth part of a. Let us take, in general, the areas of bricks to be a²/m, a²/n, a²/p, a²/q. If x, y, z, u be the number of bricks of each variety respectively that are employed in a layer, the problem amounts algebraically to the solution of the indeterminate equations $.x/m+y/n+z/p+u/q &= 7½, / x+y+z+u &= 200. (B)$ Baudhāyana gives two integral solutions of these equations :¹