?R?DHARA

(fl. India, ninth century)

mathematics.

?r?dhara of whose life nothing is known save that he was a devotee of ?iva, wrote two works on arithmetic, the P?t?ganita and the P?t?ganitas?ra or Tri?atik?. and one work, now lost, on algebra. Since he seems to refer to the views of Mah?v?ra (fl, ninth century), and was used by ?ryabhata II (fl between ca, 950 and 1100) and cited by Abhayadeva Süri (fl, 1050). it can be concluded that he flourished in the ninth century.

The P?t?ganita is divided into two sections. The first, after metrological definitions, covers the mathematical operations of addition, subtraction, multiplication, and division; finding squares and square roots; finding cubes and cube roots; fractions; and proportions; the second gives solutions for problems involving mixtures, series, plane figures, volumes, shadows, and zero. The text, preserved in a unique manuscript in Kashmir, breaks off in the middle of the rules for determining the areas of plane figures in the second section. The Tri?atik? summarizes much of the material in the P?t?ganita, including the parts no longer available to us. In the Kashmir manuscript there is an anonymous commentary on the P?t?ganita, and the Tri?atik?; was commented on by Srídhara, himself and in Kannada (Kanarese), Telugu (by Vallabha), and Gujar?t?; the commentaries on the Tri?atik? ascribed to ?ambh?n?tha or ?ambh?d?sa (fl. 1428: Ganitapancavim?atik? or Ganitas?ra and to Vrnd?vana ?ukla (P?t?s?rat?k?) are still uncertain, pending an investigation of the manuscripts.

BIBLIOGRAPHY

The best work on?r?dhara. Is the introduction to K. S. Shukla’s valuable ed, and trans., The Patiganita of Sridharacarya (Lucknow. 1959). There is also a Russian trans, and study of the P?t?ganita by A. I. Volodarsky and O. F. Volkovoy in Fiziko-matematicheskie nauki v stranakh vostoka (Moscow, 1966), 141-246, The Tri?atik? was edited by Sudh?kara Dvivedin (Benares, 1899) and was largely translated into English by N, Ramanujacharia and G. R. Kaye. “The Tri?atik? of ?r?dhar?caria in Bibliotheca mathematica. 3rd ser., 13 (1912–1913), 203–217.

David Pingree