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

६८ गणितसारसंग्रह
and comprehensive, and who on the occasion when he met me in
person at Madras showed great interest in the contemplated
publication of the Gaṇita-sāra-saṅgraha and thereafter read a paper
on that work at the Fourth International Congress of Mathe-
maticians held at Rome in April 1908. Accordingly I requested him
to write an introduction to this edition of the Gaṇita-sāra-saṅgraha,
given in brief outline what he considers to be its value in building
up the history of Hindu mathematics. My thanks as well as the
thanks of all those who may as scholars become interested in this
publication are therefore due to him for his kindness in having
readily complied with my request; and I feel no doubt that his
introduction will be read with great appreciation.
Since the origin of the decimal system of notation and of the
conception and symbolic representation of zero are considered to
be important questions connected with the history of
Hindu mathematics, it is well to point out here that in the
Gaṇita-sārasaṅgraha twenty four notational places are mentioned,
commencing with the units place and ending with the place called
mahākṣōbha, and that the value of each succeeding place is taken
to be ten times the value of the immediately preceding place.
Although certain words forming the names of certain things are
utilized in this work to represent various numerical figures, still in
the numeration of of numbers with the aid of such words
the decimal system of notation is almost invariably followed.
If we took the words moon, eye, fire and sky to represent respectively
1, 2, 3 and 0, as their Sanskrit equivalents are understood in this
work, then, for instance, fire-sky-moon-eye would denote the number
2103, and moon-eye-sky-fire would denote 3021, since these nominal
numerals denoting numbers are generally repeated in order from
the units place upwards. This combination of nominal numerals
and the decimal system of notation has been adopted obviously for
the sake of securing metrical convenience and avoiding at the same
time cumbrous ways of mentioning numerical expressions; and it
may well be taken for granted that for the use of such nominal
numerals as well as the decimal system of notation Mahāvīrācārya
was indebted to his predecessors. The decimal system of notation is