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had an idea of the anti- ardhachheda and anti - vargasalākā can be easily drawn. [3.5] TRKACHHEDA AND CATURTHACHHEDA
The terms trkachheda and caturthachheda (abbreviated as TC and CC respectively) occur frequently in the Dhavala. (Cf. DVL-III, p.56 and Cf. also Singh, A.N., pp. 7-8) As trka means 'tri' and caturtha means 'quadri',
TC(R) = logz R
CC(R) = log, R. For instance,
TC(81) = 4 and
CC(256) = 4. Their ideas seem to have been certainly inspired by and advanced after the idea of the ardhachheda.
and
(3.6] Virasena has been found to have applied the following laws of logarithms
log, P Q = log2 P + log, Q log2 (P = Q) = log2 P - logz Q
log2 pa = log2 P
log2 2P = p
log2 (P1)2 = 2 Plog2 P
log log2 (1)2 = log2 P + 1 + logzlog2P etc. (Cf. DVL - III, pp.21-24, 55 and 60, vide also Singh, A.N., pp.31-32)
In addition to the first three laws just mentioned above, Nemicandra sets forth the law
log2 log2 p = log2 Q + log, log2P. The important thing is that he is the first mathematician to have set forth these four laws through general and formal statements. (Cf. TLS, W.105 - 108, pp. 101 - 102 and for their expositions, vide Jadhav(2002)).
(3.7] Whatever we have presented and discussed so far shows that the Jaina school of Indian mathematics conceived of logarithms to the base 2, 3 and 4 but not to the general base.
Arhat Vacana, 15(4), 2003
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