History of Hindu Mathematics: A Source Book v2.c17.s15.8

v2.c17.s15.8

"Considering the lesser root, greater root and interpolator (of a Square-nature) as the dividend, addend and divisor (respectively of a pulveriser), the (indeterminate) multiplier of it should be so taken as will make the residue of the *prakṛti* diminished by the square of that multiplier or the latter minus the *prakṛti* (as the case may be) the least. That residue divided by the (original) interpolator is the interpolator (of a new Square-nature); it should be reversed in sign in case of subtraction from the *prakṛti*. The quotient corresponding to that value of the multiplier is the (new) lesser root; thence the greater root. The same process should be followed repeatedly putting aside (each time) the previous roots and the interpolator. This process is called *Cakravâla* (or the 'Cyclic Method').¹ By this method, there will appear two integral roots corresponding to an equation with ± 1, ± 2 or ± 4 as interpolator. In order to derive integral roots corresponding to an equation with the additive unity from those of the equation with the interpolator ± 2 or ± 4 the Principle of Composition (should be applied)."²