________________
(TLS, v.76, the third quarter, p.69) Or the ardhachheda of the ardhachheda (of a number) is certainly (khalu) (the vargasalakā of the number). i.e.
AC(AC(R)) = r. On comparing these two definitions of vargasalakā, we have
VS(R) = AC(AC(R))
VS(R) = log2 log2 R. A.N. Singh (p.7) is the first mathematician who recognized that
VS(R) = log2 log2 R. The Jaina school of Indian mathematics created a new nomenclature viz. vargasalākā for log, log2. In addition to log, log2, the school has used log2log, log2 and logzloglog, log2 as operators in context of equations and inequations as well ; vide DVL-III, pp. 21-24 and for exposition, consult : A.N. Singh, p.8, L.C. Jain, 1976, pp. 88-92 and Navjyoti Singh, pp.31-32. But the school did not give any new nomenclature to them. The exact reason behind it is that the idea of varagašatākā in Jaina theory of logarithms is the counterpart of that of ordinal successive squaring in Jaina theory of indices. (3.4) Madhavacandra was an immediate pupil of Nemicandra as he himself claimed to be ; vide TLS, p.768. He has written, in Sanskrit, a commentary, on the TLS. He gives the following rule -
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(TLS, below v.75, p.68) The ardhachheda of a number (rāsi) is obtained by mutual multiplication of twos that are, in number, equal to the vargasalākā of the number. Similarly the number is obtained by mutual multiplication of twos that are, in number, equal to the ardhachheda of the number.
If VS(N) = 4 then N = ? According to the above definition,
AC(N) = 2.2.2.2
= 16
and
N = 2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2
= 65536. Here an important inference that the Jaina shool of Indian mathematics
Arhat Vacana, 15(4), 2003
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