________________
(pp. 82-84), B.S. Jain (pp. 46-47), Anupam Jain (pp. 218 and 278-279) and so forth are noteworthy.
For modern theories of indices and logarithms, vide Bose, Smith (pp. 513-523), Cajori (pp. 140 and 149 - 152), Hooper (pp. 169 -193) and so forth. 2. ON THEORY OF INDICES
For any real number 'a' and a positive integer 'n', we define the nth power of 'a', notationally a", as
a = a.a.a............a (n times) Then 'a' is called the base and n is called the index of the nth power of 'a'. The word 'index' was used, in 1586 A.D., by Schoner while Michael Stifel (1486 ? - 1567) had used the word 'exponent' for the same purpose. (2.1) In the first section, we shall show that the principal laws of indices were known to the Jaina school of Indian mathematics. If m and n are integral or fractional and m > n, then for a, a = 0
a".a" = am+n ama" -am-n
(a")" = amn
(a) = aman). About these principal laws of indices, the Jaina school of Indian mathematics does speak but not formally. However, they can be corroborated by means of technical terms, statements and instances that occur in the above mentioned sources. [2.1.1] Technical Terms
The Jaina school of Indian mathematics began with the two terms: varga and ghana and went far with them as it is quite clear from the Table - A.
The school expressed powers greater than 3 again in terms of varga and ghana by employing the multiplication law of indices
(a")" = an vide Table - A.
Actually, this law is the Jaina mode of indicating power of a number. The mode is capable to indicate all possible even powers but can not indicate all possible odd powers except such as the ninth (ghana-ghana), twenty seventh (ghana-ghana-ghana) and so on. This is why we do not find such names
and
54
Arhat Vacana, 15(4), 2003
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