Page:Algebra, with Arithmetic and mensuration, from the Sanscrit.djvu/17

 DISSERTATION. v where his commentators understand him to allude to Arya-bhat't'a, to Brahmegupta, to the latter's scholiast Chaturve'da Prit'hudaca Swa'miV and to the other writers above mentioned. Most, if not all, of the treatises, to which he thus alludes, must have been extant, and in the hands of his commentators, when they wrote; as appears from their quotations of them; more especially those of Brahmegupta and Arya-bhat't'a, who are cited, and particularly the first mentioned, in several instances." A long and diligent research in various parts of India, has, how- ever, failed of recovering any part of the Padmanabha v'lja, (or Algebra of Padmana'bha,) and of the Algebraic and other works of Arya-bh atta.' But the translator has been more fortunate in regard to the works of Suii)'HARA and Brahmegupta, having in his collection Srid'hara's compendium of arithmetic, and a copy, incomplete however, of the text and scholia of Brah- megupta's Brahma-sidd'hanta, comprising among other no less interesting matter, a chapter treating of arithmetic and mensuration ; and another, the subject of which is algebra : both of them fortunately complete.* The commentary is a perpetual one ; successively quoting at length each A'erse of the text ; proceeding to the interpretation of it, word by word ; and subjoining elucidations and remarks : and its colophon, at the close of each chapter, gives the title of the work and name of the author.' Now the name, which is there given, Chaturve'da Prit'hudaca Swa'mi, is that of a cele- brated scholiast of Brahmegupta, frequently cited as such by the commen- tators of Bha'scara and by other astronomical writers: and the title of the work, Brahma-siddhunta, or sometimes Brahma sphuta-sidd' hdnta, corre- sponds, in the shorter form, to the known title of Brahmegupta's treatise in the usual references to it by Bha'scara's commentators;* and answers, in the longer form, to the designation of it, as indicated in an introductory couplet which is quoted from Brahmegupta by Lacshmida'sa, a scholiast of Bha'scara.^ Remarking this coincidence, the translator proceeded to collate, with the ' ^V'-g"'*- Ch. 5. note of Su'rtada'sa. Also V'tj.'gaii. § 174 ; and Lil. § 246 ad finem. ' Vitand-bhdshya by Chatuuve'da Piut'uu'daca Swa'mi, son of Mad'uu'su'dana, on the Brahma-sidiThdnta ; (or sometimes Brahma-sphuta-sidd'/tunta.) -' NoteC.
 * For example, under Z,)/. Ch. 11. ' Note G. ♦ Note B.
 * They often quote from the Drahma-sidd'hunta after premising a reference to Brahmegupta.