N?R?YAN?A

(fl. India, 1356)

mathematics.

Narayana, the son of Nrsimha (or Narasimha), was one of the most renowned Indian mathematicians of the medieval period. His Ganitakaumudi, on arithmetic and geometry, was composed in 1356; in it he refers to his Bijaganitavatamsa, on algebra (see Supplement). The Karmapradipik?, a commentary on the L?lav?ti of Bh?skara II (b. 1115), is found in several south Indian libraries attributed to Narayana; but the author, a follower of ?ryabha?a I (b. 476), may be the Kerala astronomer and mathematician M?dhava of Sa?gamagr?ma (ca. 1340–1425).

The Ganitakaumud? consists of rules (s?tras) and examples (ud?haranas), which in the only edition, the two-volume one of P. Dvivedi (Benares, 1936–1942), are given separate numberings that do not coincide with the division of the work into chapters

(vyavah?ras). In fact, the edition is based on a single manuscript which was evidently corrupt and perhaps incomplete. We do not really know in detail the contents of the Ga?itakaumud?. The B?jaga?it?vatamsa is preserved in a unique and incomplete manuscript at Benares; only the first part has been edited, by K. S. Shukla as a supplement to ?tam (1 , pt. 2 [1969- 1970]).

BIBLIOGRAPHY

Various rules from the Ganitakaumudi are discussed by B. Datta and A. N. Singh, History of Hindu Mathematics, 2 vols. (Lahore, 1935–1938), passim; and the section of that work devoted to magic squares is analyzed by S. Cammann, “Islamic and Indian Magic Squares,”in History of Religions, 8 (1968–1969), 181–209, 271–299, esp. 274 ff. The algebra of the Bijaganitavatamsa has been commented on by B. Datta, “Narayana’s Method for Finding Approximate Value of a Surd,”in Bulletin of the Calcutta Mathematical Society, 23 (1931), 187–194. See also R. Garver, “Concerning Two Square-Root Methods,”ibid., 23 (1932), 99–102; and “The Algebra of Narayana,"’ in Isis, 19 (1933), 472–485.

David Pingree

Nārāyana. The personification, in Hinduism, of the creative energy of Viṣṇu, associated, therefore, with the sun. It is Nārāyana, as the solar energy, moving on the face of the waters, which produces creation. He is also closely associated with Nara, so that nara-nārāyana constitute the union man—god, i.e. ātman is brahman.