गणितसारसंग्रह (महावीराचार्य - प्रो. लक्ष्मीचन्द्र जैन सविस्तार हिन्दी अनुवाद सटीक)

xvi
is one of the connecting and missing links in the history of
Mathematics.
I have traced these developments in a systematic form in the
Jīva Tatva Pradīpikā commentary on Gommaṭasāra. 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 agrihīta 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 his connection, in verse 70, Chapter 1, for a study of Āgama
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 unaffected.
The first four appendices contain practically the same matter
as appeared in Raṅgāchārya's translation. The fifth appendix contains
new collation-material compiled at the instance of Dr H. L. Jain
from certain manuscripts from Karanja. In the sixth appendix it
has been thought useful to reproduce the preface of Professor
Raṅgāchārya 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