Book Title: Shatkhandagama Pustak 03
Author(s): Pushpadant, Bhutbali, Hiralal Jain, Fulchandra Jain Shastri, Devkinandan, A N Upadhye
Publisher: Jain Sahityoddharak Fund Karyalay Amravati

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Page 20
________________ iii the two and half Dvipas or mainlands over which the human population is spread. ( Page 38-43 ) 4. Scientific Importance of the Work. The distribution of souls in the various stages of spiritual advancement and the varieties of life and existence is tased upon certain Jaina dogmas which are in their nature inscrutable. An attempt has been made by the authors of the Sutras and the Commentary to put the distribution in a precise mathematical from. The authors have made full use of the mathematical knowledge of their times, which reveals a considerably high state of development during the earliest centuries of the Christian era when the Sutras were composed, as well as during the latter part of the 8th and the earlier part of the 9th century when the commentary was written. The author of the Sutras shows a clear conception of infinity and orders of infinity within infinity in their application to matter, time and space. Within the sphere of finite numbers he mentions figures from one to hundred, thousand, tens and hundreds of thousands, and crores, also their multiples, squares and square roots, as well as the fundamental operations of arithmetic, namely, addition, subtraction, multiplication and division. The commentator has amplified this knowledge considerably in the light of what was known at his time. Several practical methods of division have been explained. There is a free use of the place value notation. The use of fruction has been frequently made in order to arrive at quotients with particular divisors, or to determine divisors when a particular quotient is given. This indicates the kuowledge of fractions at that stage. The processes of evolution and involution are identical with those current in modern mathematics. Thus, we notice the use of powers ( Vargita-samvargita ) and roots ( Varga-mula ). This indicates that the author of Dhavala had a clear knowledge of the law of indices and possibly of the theory of logarithms, as may be inferred from the relations shown between the Varga-shalakas and Ardhacchedas I The role of three was an operation well known to the author for the purposes of showing variations. We also find the use of the summation of an arithmetic series. The author is also found to have employed the mensuration formula for a circle. The ratio of the circumference to the diameter is taken as & little less than 10, and it is just possible that approximations to this value in a fractional form to a fair degree of accuracy were known to the author. It may be hoped that the work will considerably widen our knowledge about the state of mathematics and its application to the problems of life in ancient India. As I have already acknowledged in my foreword, my colleague Professor K. D. Panday, M. A, bas interpreted for me many of the author's formulas and has also assisted in framing the illustrations, while Dr. Avadhesh Narain Singh, D. sc., Professor The number of times that a particular figure is multiplied by itself is its Vargashalākas, while the number of times that a particular figure is successively halved is its ardbacchedas. Jain Education International For Private & Personal Use Only www.jainelibrary.org

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