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Mathematical Expositions of Virasena in Dhavală Commentary : (209)
generally, by Vīrasena. Most probably, we do not find these methods elsewhere in a coordinated way. A term 'Dhruva rāși' (eternal set or number with a symbolism of 256/13 - 19 = has also been coined
13
by him. All these methods have been used to calculate the number of wrong-faithed beings through different sequences (Vol. 3, p. 52, - 74).
Out of these methods, the processes of cutting, dividing, spreading and removal are easily defined. Besides, the abstraction or alternation (vikalpa) has been two-foldly classified: (1) lower abstraction and (2) upper abstraction. Both these classes use the various sequences or series of geometrical cube or cubed-cube series. The lower abstraction is exemplified by calculating number of wrongfaithed beings as below:
Suppose the total Jīvas = 16, eternal number is 256/13, no. of wrong faithed beings is 13, then multiplying the total Jivas and eternal number, we get
16x 256 - 4096
13 13 The cube of Jiva no. 163 = 4096. Dividing this number by earlier number, we get,
Total no. of wrong-faithed beings = 13. Calculation of this quantity has also been made through other series involving cubed-numbers.
The upper abstraction has been three-foldly classified: (1) adopted (2) adopted-adopted and (3) adopted-multiplied.
These processes can be expressed in the following examples in calculating the no. of wrong faithed ones: (1) Adopted: (square of the total no. of Jivas/eternal number)
= (16 x 16 /256/13) = 13 (2) Adopted-adopted: (upper square of total no. of Jivas/ no. of wrong
faithed beings). = 162 x 162/13; (65536 /65536/13) = 13 (3) Adopted multiplier: (upper square of total no. of Jivas/upper
square of total no. of Jivas/no. of wrong faithed ones) = 65536/ 65536 /13 = 13
Similarly, we get an equation for knowing the no. of infernal wrong-faithed beings as below:
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