________________
for the fifth, seventh, eleventh and other odd powers in any canonical work of the ancient Jainas.
To represent very large numbers by the Jaina mode is very long, slow, tiresome and clumsy. For instance, a 128 will be expressed as the varga-varga-varga - varga-varga - varga - varga of a or notationally
({{{(a?))))) By putting ordinal number of squaring, this was made short thus : the seventh varga (square) of a or notationally a?' ; vide DVL-III, p. 254 where 22' is given.
In this connection, A.N. Singh (p.7) followed by L.C. Jain (1982, pp. 29 and 51) opines that [a] the consideration of the successive squaring was certainly inspired by duplation
and [b] duplation must have been current in India before the advent of the place
value numerals.
Here we should turn our mind to the fact that the operation of duplation was considered important when the place value numerals were unknown. We do not find any trace of the operation in India. But it was considered to be very important by the Egyptians and was recognized as such in their works on arithmatic.2
By the way, it is still to be investigated in what way the process of the inspiration might have been held.
In a similar manner, the Jaina school of Indian mathematics was also conversant with the fractional indices as it is quite clear from the Table-B wherein the division law,
(a")
= a(man)
can be sought. [2.1.2] Statements
In the AS, we meet statements such as [a] HURTO........, 316 qui Uçat qui datarugaquit, 31Equi esuurufasduumatski:A.....
(v.427, p.349) the total number of developable human souls is equal to a number obtained by multiplying the sixth square (of 2) by the fifth square (of 2) or to a number that can be divided (by 2) ninety six times ; expressly
Arhat Vacana, 15(4), 2003
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