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Vol. XXIII, 2000
VEDIC SOURCES OF THE "VEDIC MATHEMATICS
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Yajurveda mentions the following fractions, viz., Tryavi, Tryavi, Dityavāt, Dityauhi, Pancāvi, Pancāvi, Trivatsa, Trivatsā, Turyavāt and Turyauhi (Y.V. 18.26). The Satapatha Brāhmaṇa mentions the following operations of fractions, viz.,
+++= 1 (1.2.4.1; 3.6.3.5); } + 3 = (4, 1, 3.13-14); and = + = = 1 (4.6.7.3).
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Dr. S. N. Sen observes46 that the method of obtaining higher and higher numbers in multiples of ten is clearly indicated. It appears that the thinking out and naming of such large numbers were a favourite pastime of the ancient Indian mathematicians. The Vedic Hindus showed the same proficiency in devloping a scientific vocabulary of number names, in which the principles of addition, subtraction and multiplication were conveniently used. The system required the naming of the first nine digits, multiplying each of them by ten. The additive and the multiplicative principles are simultaneous used when, in the number concerned, the members from one to nine participate with multiples of ten.
Acquaintnce with the fundamental arithmetical operations with elementary fractions, progressive series is clearly indicated in the Vedic texts and their appendages.47 The Vedic hymns make several references to arithmatical principles, like the consecutivity of numbers from 1 to 10 (AV. 13.4), additions of numbers with multiple of 10 (A.V. 5.15), additions of 2 (YV. 18.24), Additions of 4 (YV. 18.25), mention of the digit 99 (RV. 1.84.3), multiple by 11 (AV. 19.47), numeral system (YV. 17.2), and fractions. 48
The various Sulba-sūtras that have been noted above have come down to us as parts of the Srauta-sutras and constitute Brāhmaṇic geometrical manuals for the construction of sacrificial altars. In the various rules given, certain assumptions are taken for granted. Most of the postulates of the Sulba are concerning the division of figures, such as straight lines, rectangles, circles and triangles, and a few of them are about other matters of importance.49 Of greater importance are the rules given in the Sulbas for the combination and transformation of rectilinear figures, specially the squares and the rectangles. The so-called 'Pythogorean' theorem of the square of the diagonal is more explicitely given in more or less the same language in all the
