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of periods of time rises on to a Muhurta ( 48 Minutes), a day, a fortnight, a month, a year, a Yuga a Purvanga, a Purva, and so on to a Palyopama and a Sagaropama and ultimately to an Utsarpini and Avasarpini which constitute a Kalpa. The longest period of timo conceived and denominated is a Pudgala-parivartana (for which see p. 330 text and explanatory note).
In interpreting the mathematical part of these texts I again received very valuable assistance from my colleague Mr. K. D. Panday, professor of mathematics in King Edward College, Amraoti. Without his help here, as in the previous volume, it would have been almost an impossible task for me to explain adequately the mathematical portions. As I mentioned in the previous volume, Dr. Avadhesh Narain singh, professor of Mathematics in the Lucknow University and author of the History of Hindu Mathematics, has taken a keen interest in the mathematical contents of these texts. He has now studied the mathematical portions of the III volume and has obliged me by writing out a dissertation on the mathema. tical contents of that volume. The same is being published hore under the caption " Mathematics of Dhavala.” It is expected that he would continue his valuable study of these texts and the readers might look forward to a very interesting note on the geometrics of the present volume in the volume to be issued next.
Another topic dealt with in the Hindi Introduction of this volurne is an answer to the objection raised in a certain quarter that Jaina traditions prohibit the study of these Sacred Texts by layınen, and therefore these texts should neither be published in a printed form, nor should they be taught in Jaina Pathasalas, nor should they be allowed to be read anywhere by any body except by the Jaina ascetics. A critical examination of all the traditions bearing on this subject shows that an injunction against the study of Siddhanta by the laymer is found in a few books dealing with the duties of Jaina house-holders. But all these books are found to have been written by a few obscure and insignificant writers belonging to a period subsequent to the 12th century A. D. Again, they either do not make clear what is meant by Siddhanta, or explain it in a manner so as to make the present texts, as well as all other available books, fall outside the sphere of Siddhanta. The injunction is, moreover, in direct conflict with the statements of the most ancient and authoritative Jaina writers who have strongly recommended the study of the Jaina texts of the highest kind by all, laymen as well as ascetics. The author of the Dhavala himself lays down in clear and unmistakable terms at every step of his commentary that the Sutras as well as the commentary are so designed
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