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

७० गणितसारसंग्रह
carried on–not to say cannot be even thought of easily–without a
symbol of some sort to represent it. Mahāvīrācārya gives, in the
very first chapter of his Gaṇita-sāra-saṅgraha, the results of the
operations of addition, subtraction, multiplication and division
carried on in relation to the zero quantity; and although he is wrong
in saying that a quantity, when divided by zero, remains unaltered,
and should have said, like Bhāskarācārya, that the quotient in such
a case is infinity, still the very mention of operations in relation to
zero is enough to show that Mahāvīrācārya must have been aware
of some symbolic representation of the zero quantity. Since
Brahmagupta, who must have lived at least 150 years before
Mahāvīrācārya, mentions in his work the results of operations in
relation to the zero quantity, it is not unreasonable to suppose that
before his time the zero must have had a symbol to represent it in
written calculations. That even Āryabhaṭa knew such a symbol is
not at all improbable. It is worthy of note in this connection that in
enumerating the nominal numerals in the first chapter of his work,
Mahāvīrācārya mentions the names denoting the nine figures from 1 to
9, and then gives in the end the names denoting zero, calling all the
ten by the name of saṅkhyā : and from this fact also, the inference
may well be drawn that the zero had a symbol, and that it was well
known that with the aid of the ten digits and the decimal system of
notation numerical quantites of all values may be definitely and
accurately expressed. What this known zero-symbol was, is, however,
a different question.
The labour and attention bestowed upon the study and trans-
lation and annotation of the Gaṇita-sāra-saṅgraha have made it
clear to me that I was justified in thinking that its publication might
prove useful in elucidating the condition of mathematical studies as
they flourished in South India among the Jainas in the ninth century
of the Christian era; and it has been to me a source of no small
satisfaction to feel that in bringing out this work in this form,
I have not wasted my time and thought on an, unprofitable
undertaking. The value of the work is undoubtedly more historical
than mathematical. But it cannot be denied that the step by step
construction of the history of Hindu culture is a worthy endeavour,