Page:Indian mathematics, Kaye (1915).djvu/34

 The only extant work by is like Mahāvīra's but shorter; but he is quoted as having dealt with quadratic equations, etc. Bhāskara's Līlāvatī is based on S'rīdhara's work and, besides the topics already mentioned, deals with combinations, while his Vīja-ganita, being a more systematic exposition of the algebraical topics dealt with by Brahmagupta, is the most complete of the Indian algebras. After the time of Bhāskara (born A.D. 1114) no Indian mathematical work of historical value or interest is known. Even before his time deterioration had set in and although a "college" was founded to perpetuate the teaching of Bhāskara it, apparently, took an astrological bias. 21. The Indian method of stating examples—particularly those involving algebraic equations—are of sufficient interest to be recorded here. The early works were rhetorical and not symbolical at all and even in modern times the nearest approach to a symbolic algebra consists of abbreviations of special terms. The only real symbol employed is the negative sign of operation, which is usually a dot placed above or at the side of the quantity affected. In the Bakhshāli Ms., a cross is used in place of the dot as the latter in the Sārada script is employed to indicate cipher or nought. The first mention of special terms to represent unknown quantities occurs in Bhāskara's Vīja-ganita which was written in the twelfth century of our era. Bhāskara says: "As many as (yāvat tāvat) and the colours 'black (kālaka), blue (nīlaka), yellow (pītaka) and red (lohitaka)' and others besides these have been selected by ancient teachers for names of values of unknown quantities." The term yāvat tāvat is understandable and so is the use of colours but the conjunction is not easy to understand. The use of two such diverse types as yāvat tāvat and kālaka