Ganitsara Sangrah

Author(s): Mahaviracharya, A N Upadhye, Hiralal Jain, L C Jain
Publisher: Jain Sanskriti Samrakshak Sangh

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is one of the connecting and missing links in the history of Mathematics.
I have traced these developments in a systematic form in the Jiva Tatva Pradipikā commentary on Gommatasāra, It abounds in symbolism for place value, logarithms, transfinite and finite cardinals, sets and operators. One may be confused to see that a single symbol has been used in various texts to denote various measures or operations. For example, zero as a circle stands for a negative sign, for one-sensed soul, for the agrihíta stage of soul ( for a void ), for filling up gaps, and for a place value. Sets are of varying. oscillating and constant types. A kind of well ordering concept seems to have been used in formation of sequences from the greatest transfinite set. Comparability also plays an important role in the treatment
Thus Mahāvīrāchārya had before him, the works of his predecessors, both in logistics and in arithmetica. He made a clear remark in this congestion, is verse 70, Chapter 1, for a study of Agama for further details. His work contains other elementary descriptions on series etc., found in details in Prakrit texts, referred above. It seems that his acquaintance with proper infinities in which monads alone played the role of division etc., made him to think of division by zero as a distribution in a logical way. If a sum is to be distributed to none, the sum would remain unaffeced.
The first four appendices contain practically the same matter as appeared in Rangāchārya's translation. The fifth appendix contains new collation material compiled at the instance of Dr H, I, Jain from certain manuscripts from Karanja. In the sixth appendix it has been thought useful to reproduce the preface of Professor Rargāchārya and introduction of Professor David Eugene Smith.
Thanks are due to Professor B. D. Dube for his kindness to give valuable suggestions. Thanks are also due to the proprietor of the Press for his kind co-operation.
I am grateful to my Principal, Shri G. R. Inamdar, and to my senior colleague, Prof. K. S. Rathore, for their affectionate patronage. My gratitude is also due to Prof. S. B. Gour for his close assistance,
JABALPUR, NOVEMBER 1963
L. C. JAIN