Shatkhandagama Pustak 04

Author(s): Pushpadant, Bhutbali, Hiralal Jain, Fulchandra Jain Shastri, Devkinandan, A N Upadhye
Publisher: Jain Sahityoddharak Fund Karyalay Amravati

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Suryaprajnapti and (ii) an original work called the Bhadrabahavi Samhita. He is mentioned by Malayagiri (c. 1150) in his commentary on the Suryaprajnapti, and has been quoted by Bhattotpala ( 966 )! Another Jaina astronomer of the name of Siddhasena has been quoteri by Varähamihira (505) and Bhattotpala. Mathematical quotations in Ardha-magadhi and Prakrit are met with in several works. The Dhavala contains a large number of such quotations. These quotations will be considered at their proper places, but it must be noted here that they prove beyond doubt the existence of mathematical works written by Jaina scholars which are now lost. Works written by Jaina scholars under the litle of Ksetra-sa masa and Karana-bhavana dealt with mathematics, but no such works are available to us now. Our knowledge of Jaina mathematics which is of an extremely fragmentary character is gleaned from a few non-mathematical works such as Sthananga-sutra, Tattvarthadhigamasutra-bhasya of Umasvati, Suryaprajnapti, Anuyogadvara-sutra, Triloka Prajnapti, Trilokasara, etc. To these may now be added the Dhavala.
The importance of the Dhavala. The Dhavala was written by Virasena in the beginning of the ninthcentury. Virasena was a philosopher and religious divine. He certainly was not & mathematician. The mathematical material contained in the Dhavala may therefore be attributed to previous writers, especially to the previous commentators of whom five have been mentioned by ludranandi in the Srutavatara. These commentators were Kundakunda, Shamakunda, Tumbulura, Samantabhadra and Bappadeva, of whom the first flourished about 200 A. D. and the last about 600 A. D. Most of the mathematical material in the Dhavala may therefore be taken to belong to the period 200 to 600 A, D. Thus the Dhavala becomes a work of first rate importance to the historian of Indian mathematics, as it supplies information about the darkest period of the history of Indian Mathematics--the period preceding the fifth century A. D. The view that the mathematical material in the Dhavala belongs to the period before 500 A. D. is corroborated by detailed study. For instance, many of the processes described in the Dhavala are not be found in any known mathematical work. Furthermore, there is a certain imperfection which, one acquainted with the later Indian mathematical works, can easily discern. The mathematics in the Dhavala lacks the finish and the refinement of the Aryabhatiya and later works.
Mathematical Content of the Dhavala
Numbers and Notation-The author of the Dhavala is fully conversant with the place value system of notation. Evidence of this is to be found everywhere: We quote some methods of expressing numbers taken from quotations given in the Dhavala
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2.
Brhat Samhita, ed. by S. Dvivedi, Benares, 18.5, p. 226. Silanka in his commentary on the Sutrakrtanga Sutra, smnyadhyayana, Sanuyogndvara, verse 28, quotes three rules regarding permutations and combinations. These rules are apparently taken from some Jaina mathematical work.