Basic Mathematics

Author(s): L C Jain
Publisher: Rajasthan Prakrit Bharti Sansthan Jaipur

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couplet. Virsena, interprets the above as
C = 3D +
3D +
355 D
16 D
113
=
-113
which gives a =
355 -
Singh75 remarks, “the term “Sahitam was used in the sense of addition as well as 'multiplication', i.e., repeated addition, a num in the Vedānga Jyotişa but has been used in that double sense by Aryabhata (c. +499) and succeeding mathematicians. This leads one to conclude that the above quotation is from some work written before the fifth century A. D., when “Sahitam" was being used in both the senses of multiplication as well as addition. It would appear, therefore, that the so called Chinese value of 7 = 355 was also known in India and was perhaps used in India earlier than in China. It might be that the Chinese got this value from India, through Buddhist missionaries or perhaps they found out the value independently." According to him, “Another noteworthy feature in the above quotation is the remark 'finer than the fine'; from this it follows that a 'fine' value of a was already known. This fine value of a may have been ✓ 10 or 22. In the latter, the connection with Aryabhata's value is obvious--the third convergent being a close approximation than the second."76 (g) An infinite process
For disproving a prevalent theory regarding the shape of the universe, Virsena found the volume of frustum of a cone by an infinite process of cutting it. Out of the frustum he first cut out a cylinder from it and stretched the remaining figure into a long prism which could again be cut into tetrahedrons of various volumes tending to zero area. From the point of view of history of mathematics, Singh77 could find out the following items of interest :
(i) It was assumed that a body with curved boundaries could be
deformed into another with plane boundaries in such a way that its volume remained unchanged. In particular, if the hollowed out cone of figure is deformed which has plane boundaries, then the volume remains unchanged.
75. History of Mathematics in India from Jaina Sources, The Jaina Anti
quary, Vol. xvii, no. ii, Dec. 1950, Arrah, pp. 54–69. 76. Cf. ibid. 77. Cf. ibid.
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