Jain Journal 1984 01

Author(s): Jain Bhawan Publication
Publisher: Jain Bhawan Publication

Page 23

96
JAIN JOURNAL
N
=
V(a2 + x) = a +
...................(15)
Where a and x are positive integers and the remainder x is less than the divisior' 2a ; otherwise or alternatively, we may use
N
= V(62__y) = b
................(16)
The approximation (15) was known to the Greek Heron of Alexandria (between c.50-C.200 A.D.),15 and even to the ancient Babylonians. 16 The Chinese Sun Tau (between 280 and 473 A.D)17 while extracting the square root of 234567 by a elaborate method, finally said : 18
"Thus we get 484 for the square root in the above and 968 for the hsia-fa, the remsiner being 311.”
311 Thus we have the answer : 484+050- which is equivalent to what we get by using the Eq. No. (15).
The Jaina Gem Dictionary19 gives the same rule as represented by Eq. No. (15). The TP 1.117 (Vol. 1)20 implies that the circumference of a circle of diameter one yojana was found out to be yojanas, which is in agreement with the use of the eq. No. (15) as we have
19
V10
= V(32+1)=3+4)
Likewise, using Eq. No. (15) or alternatively Eq. No. (16), the given circumferences of the solar mandalas can easily be generated. Exempli gratia, we may see that
CM,
= V10 D’m. = V10 (99640) 2
= V(315090)2 — 412100
(using eq. No. 16)
18 Cf. Smith, D.E., op. cit., p. 254. 16 Cf. Boyer, C. B. (1968), A History of Mathematics, p. 31. 17 See ISIS, Vol. 61, Part I (1970), p. 92. 18 Cf. Mikami, Y. (1961), The Development of Mathematics in China and Japan,
(Chalsea reprint, New York). 18 The Jaina "Gem Dictionary, pp. 154-155. Quoted by Gupta, R.C., Op, Cit. 20 Cf. TP 1.117 (Vol. I), edited by Upadhye, A. N. and Jain H. L. (1936), p, 14.