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Mathematical Expositions of Virasena in Dhavală Commentary :
(211).
Smith has pointed out that many algebraic processes were developed in India much earlier and they influenced even Europe. Concept of Relative Numeration (Alpa-bahutva)
The Jaina texts mention the relative numeration related with investigation doors and spiritual stages. We find the preliminary form of this process in Prajñāpanā etc. TP and Dhavalā have also described them in a little different way. Umāsvāti made this as one of the disquisition doors. In comparison to other texts, Vīrasena has given sixteen sets of relative numeration given below in Table 3. Their speciality is that they do not contain measurable or countable numbers in general. They have mostly innumerables. Their practical numeration is, thus, not possible. Even the term a little more or less' is also related with immeasurable numbers. It is clear from Table 3 that the past time is sufficiently larger that the present time (1 Samaya) and the future.is endless and even many times infinite with respect to the past. From the Table, it seems that the relative numeration forms a category of super worldly measure. Conclusion
The above brief description indicates that Vīrasena has not only utilized the contemporary mathematical processes, but he has also made
Table 3. Sixteen Classes of Relative Numeration (Vol. 3, p. 30) 1. Present time Least . 2. Non-liberatable Infinite times, 3. Liberation time Infinite times 4. Liberated Numerable times
beings Non-liberatable Innumerable 6. Past time a little more than beings
times Liberatable Infinite times 8. Liberatable a little more than wrong faithed
beings General wrong a little more 10. Worldly being a little more than faithed
than 8 Total living A little more
12. Mattergy
infinite times 11 being
than 10 13 Future time infinite times 14 Total time a little more than
13 15 Non-occupied Infinite times16 Total space a little more than universe 14
15 many new points and processes during his days. It could be evident that a substantial amount of studies on Jaina mathematics have led to
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