Mathematics in Ancient and Medieval India c5.s8.4

c5.s8.4

The ancient Indian mathematical works have not devoted much space to the methods of addition and subtraction in view of simple and self evident character, though such methods were described in details in the *Līlāvatī* of Bhāskara II ( 1150 A. D. ) and in two commentaries of *Līlāvatī* namely *Gaṇitāmṛta* of Sūryadāsa (1538 A. D.) and *Manorañjanā* of Rāmakṛṣṇa. Several methods of multiplication namely *kapāṭasandhi*, *gomūtrikā*, *khaṇḍa*, *bheda* and *iṣṭa* etc. were known. Datta and Singh have described this method fully in their *History of Hindu Mathematics*¹ as it appeared in the works of Mahāvīra (c. 850 A.D.), Śrīdhara (900 A.D.) and Śrīpati (1039 A.D.). The main feature of the method of *kapāṭasandhi* was that it was carried out in two stages : (1) the relative positions of the multiplicand and the multiplier followed by, (2) the rubbing out of figures of the multiplicand and substitution of the figures of the product in their places. The *kapāṭa* and *sandhi* owe their origin from the first and second stages respectively. The terms *hanana*, *vadha* or *kṣaya* which mean killing' or ‘destroying’ have been used in the works of Brahmagupta² (628 A. D.) in describing his process of multiplication. It seems to suggest that this method of *kapāṭasandhi* was known to India in 7th century A.D. This method reappeared in works of the Arabian scholars³ Al-Nasabī (c. 1025 A. D.), Al-Ḥaṣṣār (c. 1175 A. D.), Al-Kalasādi (c. 1475 A. D.).