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(210) Nandanavana
[T2/n] = log. (T2/g) = g
where n = innumerable number, T = Total no. of Jīvas, g = no. of wrong faithed beings
Many other formulae have been given under the category of abstraction. Three types of series [square, cubic, cubed-cubic] have been mentioned along with the method of duplication.
Description of Series (Sequences)
The term 'sequence or series' means application of fundamental operations to an ordered set of many numbers. There are fourteen kinds of series-some arithmetical and some geometrical. They are described fully in a later text of Trilokasära Dhavală does not describe them, but has utilized many of them in its calculation. (Especially while illustrating the calculations related with abstractions, Vol. 3, page 52, 55, 61, 63). Their use indicates that Vīrasena was familiar with the arithmetical and geometrical progressions. Some of them are given below:
(1) Dyadic square sequence: 22,222,223...
(2) Dyadic cubic series: 2320,23.21 23.23... The general formula for summation of AP is: Sum = S = (n/2) (2a + n-1) c
where n = total no. terms; a= is first term; c= common difference The general formula for summation of G.P.;
S=((c" -1) a/c-1] where c is common ratio
33
When the series is complex, the equation for sum also becomes complex. Vīrasena has used geometric regression and progression processes in many places.
Permutation and Combination
Vīrasena does not have much material on this process. But he knew this process when he cited a verse regarding the total number of syllables, contained in vocable scriptures as 264 -1 equal to 1, 84, 46, 74, 40, 73, 70, 95, 51, 615. This is based on the fact that there are 34 vowels and 30 constants from which total number of syllables could be computed33. Śilanka has given a formula for number of permutations of n thing taken all at a time :
\n/n=n-1
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