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

गणितसारसंग्रह ६९
distinctly described by Āryabhaṭa, and there is evidence in his
writings to show that he was familiar with nominal numerals. Even
in his brief mnemonic method of representing numbers by certain
combinations of the consonants and vowels found in the Sanskrit
language, the decimal system of notation is taken for granted; and
ordinarily 19 notational places are provided for therein. Similarly
in Brahmagupta's writings also there is evidence to show that he
was acquainted with the use of nominal numerals and the decimal
system of notation. Both Āryabhaṭa and Brahmagupta claim that
their astronomical works are related to the Brahma-siddhānta; and
in a work of this name, which is said to form a part of what is
called Śākalya-saṁhitā and of which a manuscript copy is to be
found in the Government Oriental Manuscripts Library here,
numbers are expressed mainly by nominal numerals used in accordance
with the decimal system of notation. It is not of course meant to
convey that this work is necessarily the same as what was known
to Ārayabhaṭa and Brahmagupta; and the fact of its using nominal
numerals and the decimal system of notation is mentioned here for
nothing more than what it may be worth.
It is generally recognized that the origin of the conception of
zero is primarily due to the invention and practical utilization of a
system of notation wherein the several numerical figures used have
place-values apart from what is called their intrinsic value. In
writing out a number according to such a sytem of notation, any
notational place may be left empty when no figure with an intrinsic
value is wanted there. It is probable that owing to this very reason
the Sanskrit word śūnya, meaning 'empty', came to denote the zero;
and when it is borne in mind that the English word 'cipher' is derived
from an Arabic word having the same meaning as the Sanskrit śūnya,
we may safely arrive at the conclusion that in this country the
conception of the zero came naturally in the wake of the decimal
system of notation : and so early as in the fifth century of the
Christian era, Āryabhaṭa is known to have been fully aware of this
valuable mathematical conception. And in regard to the question
of a symbol to represent this conception, it is well worth
bearing in mind that operations with the zero cannot be