Mathematics in Ancient and Medieval India c5.s13.8

c5.s13.8

Besides Rule I, Nārāyaṇa (1356 A. D.) gives a fuller treatment of the Rule II in his *Gaṇitakaumudī* rediscovered later by French mathematician Fermat² in 1643 A. D. Nārāyaṇa's rule runs as follows. “The nearest square root of the non-square number, is multiplied by 2, increased by 1, and diminished by the residue of the square root. If it is a perfect square, it is added to the dividend to make it a perfect square. If the above number is not a perfect square, it should be increased by the successive terms of the arithmetic series whose first term is twice the nearest square root (of the non-square number) increased by 3 and common difference 2, until it becomes a perfect square. The unequal (successive) divisors thus obtained are multiplied by the preceding ones and by the product of the preceding ones taking one, two, three……all at a time and are placed ahead of those divisors. In case of equal divisors, each is multiplied by the (product of the preceding ones. Each of these is to be multiplied by the others (to get the divisors of the given number".¹