ŚRīDHARA

(fl. India, ninth century)

mathematics.

Śrīdhara of whose life nothing is known save that he was a devotee of śiva, wrote two works on arithmetic, the Pātīganita and the Pātīganitasāra or Triśatikā. and one work, now lost, on algebra. Since he seems to refer to the views of Mahāvīra (fl, ninth century), and was used by Āryabhata 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 Pātīganita 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 Triśatikā summarizes much of the material in the Pātīganita, including the parts no longer available to us. In the Kashmir manuscript there is an anonymous commentary on the Pātīganita, and the Triśatikā; was commented on by Srídhara, himself and in Kannada (Kanarese), Telugu (by Vallabha), and Gujarātī; the commentaries on the Triśatikā ascribed to śambhūnātha or śambhūdāsa (fl. 1428: Ganitapancavimśatikā or Ganitasāra and to Vrndāvana śukla (Pātīsāratīkā) are still uncertain, pending an investigation of the manuscripts.

BIBLIOGRAPHY

The best work onśrīdhara. 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 Pātīganita by A. I. Volodarsky and O. F. Volkovoy in Fiziko-matematicheskie nauki v stranakh vostoka (Moscow, 1966), 141-246, The Triśatikā was edited by Sudhākara Dvivedin (Benares, 1899) and was largely translated into English by N, Ramanujacharia and G. R. Kaye. “The Triśatikā of Śrīdharācaria in Bibliotheca mathematica. 3rd ser., 13 (1912–1913), 203–217.

David Pingree