Sambodhi 2000 Vol 23

Author(s): Jitendra B Shah, N M Kansara
Publisher: L D Indology Ahmedabad

Page 34

Vol. XXIII, 2000
VEDIC SOURCES OF THE 'VEDIC MATHEMATICS 27 are : (1) Miśraka or mixture; (2) Sredhi or progression or series; (3) Kşetra or plane figures; (4) Khāta or excavation; (5) Citi or stock; (6) Krākacika or saw; (7) Rāśi or mound; and (8) Chāyā or shadow. That all mathematical operations are variations of two fundamental operations on addition and subtraction was recognised by the Hindu mathematicians, from early times.86 For addition there were two processes, viz., Direct and Inverse. For subtraction too there were both such processes. But BKTM has not touched these two operations, and he seems to have taken for granted the current prevalent methods in India, which includes mere mechanical application of a set of formulae committed to memory. BKTM has started with the multiplication for which he has utilized the 'Urdhva-tiryak' sūtra. Medieval mathematicians use five methods, viz., Gomutrikā, Khanda, Bheda and Ista, as also the Kapāta-sandhi. Datta and Singh have noticed seven distinct modes of multiplication employed by the Hindus, viz., Door-junction Method, Gelosia Method, Cross Multiplication Method, Multiplication by Separation of Places, Zigzag Method, Parts Multiplication Method and Algennair Method.87 Out of these the Cross Multiplication Method is algebraic and has been compared to Tiryak-gunana or Vajrābhyāsa (cross multiplication) used in algebra.88 This method was known to the Hindu scholars of the eight century, or earlier. BKTM's method is a simplied version of this method. Division was not considered to be difficult, as the most satisfactory method of performing it had been evolved at a very early period. In fact no Hindu mathematician seems to have attached any great importance to this operation, as it was considered to be too elementary.89 A method of division by removing common factors seem to have been employed in India as mentioned in early Jain works (c. 160). The modern method of division is the Method of Long Division, invented in India about the 4th Century A.D., if not earlier. 90 BKTM utilises the 'Nikhilam' sūtra, the ‘Paravartya' sūtra, and some others for division. There is no comparable method to this in the medieval writers.
As regards the problems of factorisation, equations, squaring or cubing, or square-roots or cube-roots, decimals and geometrical operations, I would leave the comparison to veteran mathematicians, rather than venture in the field not quite familiar to me as a Sanskritist.