Mathematics in Ancient and Medieval India c7.s5.164

c7.s5.164

“Take the lesser root, greater root and interpolator of a square nature ) as divident, interpolator and divisor. Select an arbitrary number so that its square diminished by *prakṛti* or the *prakṛti* diminished by square of the chosen number, ( as the case may be ) is the least. This ( difference ) divided by the original interpolator is the ( new ) interpolator; it should be reversed in sign in case of the subtraction from *prakṛti*. The quotient corresponding to that value of the multiplier is the ( new ) lesser root; likewise is obtained the greater root. The same process should be followed repeatedly putting aside ( each time ) the previous roots and the interpolator. This process is called *cakravāla* ( or the cyclic method ). 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 ).”