Mathematics in Ancient and Medieval India c6.s8.8

c6.s8.8

treated the subject ( *vide Brāhmasphuṭasiddhānta*, ch. 12 ) in the section on : (i) *Kṣetra* ( plane figures ), (ii) *Khāta* ( cubic figures ), (iii) *Citi* ( piles of bricks–solid figures ), (iv) *Krakaca* ( saw-measurement of height of a solid like wood by cutting it into pieces with a saw ) and (v) *Chāyā* ( shadow–plane figures ). Brahmagupta's rules consist mainly of certain formulae and solution of certain plain rectilinear figures such as triangles and quadrilaterals. The classification and terminology of the Jaina author Mahāvīra ( c. 850 A. D. ) are more accurate and they clearly express the relation of those subjects to the main body of the *Gaṇita*. He calls first the *Kṣetragaṇita* and rest by the name *Khātagaṇita* or simply *Khāta*. Śrīdhara ( c. 900 A. D. ) and Bhāskara II ( c. 1150 A. D. ) included *rāśi* ( solid figures ) in addition to topics discussed by Brahmagupta. In addition to some formulae, Bhāskara II gave a new proof to theorem of square on the diagonal. But on the whole, geometrical knowledge of these authors is mostly based on the consideration of practical needs. There were no difinitions, no postulates, no axioms. Thereafter no original works on mathematics discussing geometry came out. But in the *Gaṇitakaumudī* of *Nārāyaṇa* ( c. 1356 A. D. ) and *Pātīsāra* of Muniśvara ( c. 1603 A. D. ), We fiind some independent solutions of geometrical problems previously worked out by Brahmagupta and Bhāskara II, though a quite a large number of commentaries¹ were written on the famous work *Līlāvatī* by Bhāskara II during this period. Euclid’s Elements came to be known to Indian scholars in the mid-fourteenth century though it was actually translated into Sanskrit first by Jagannātha (c. 1718 A. D.) (Vide p. 50–51).