Basic Mathematics

Author(s): L C Jain
Publisher: Rajasthan Prakrit Bharti Sansthan Jaipur

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(called ardha-cheda at that time) and its rules of operation were known in India much earlier even before Napier (1550 A. D. to 1617 A, D.) and Burges (1552 A. D. to 1632 A. D.) discovered the logarithms. The author further shows that the examples used by Virasènācārya in his Dhavala were based on his knowledge of fraction-nianipulation, finite aud transfinite sets, geometric representation of algebraic equations and some processes extending to infinity etc. Virasenācārya has further quoted a new value of 71, viz. 355 (apart from 3, 10, 22) froin some earlier work, showing that this value of a (called later on as Chinese value of 77) was also known in India perhaps earlier than in China.
In Chapter 5, the author gives a description of certain common topics of basic mathematics as contained in various ancient Jaina canonical works and discovered by himself and by Kāpadiyā, Datta, Singh Nemichandra, Saraswati, Gupta etc. Topics like Parikarma (fundamental operations), Vyavahāra (subjects of treatment), simple equations, quadratic equations, varga (square), ghana (cube), Varga-Varga, Vikalpa (abstraction or permutations and combinations), place value notation, numeral systems, sequences (specially of dyadic type) and progressions (arithmetical and geometrical), mensuration (dealing with circles, cylinders, cone, pyramids, prisms and their frustra, symbolism etc. have been dealt with.
In Chapter 6, the author compares in brief some ancient mathematical schools, the Egyptian, the Greek and the Chinese with the Jaina School and remarks that the Jaina School of Mathematics formed one of the important sources of transmission and influence.
In the end the author has given a comprehensive bibliography in three parts :
(a) Source material (b) References and Books (c) Research Articles, which can be useful to any research worker of ancient Jain School of Mathematics.
No doubt the value of the works like the present one is more historical than mathematical during these days of advanced mathematics but the contributions made by the Indian Scholars in general and the Jaina Scholars in particular, to the development of mathematics during the period from nearly 500 B. C. to 1200 A. D. or so is itself a great achievement, now acknowledged even by western scholars, and deserve labour and sincere efforts in bringing out the same to the notice of the modern world. The present work by Prof. L. C. Jain is a modest attempt in this direction. He has got a keen interest in exploring the secrets of ancient mathematics developed in India and has a vast experience of more than two decades in this field. He
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