s that
such a symbol exists. The importance of such a sign, the fact that it is a
prerequisite to a place-value system, and the further fact that without it
the Hindu-Arabic numerals would never have dominated the computation system
of the western world, make it proper to devote a chapter to its origin and
history.

It was some centuries after the primitive Br[=a]hm[=i] and
Kharo[s.][t.]h[=i] numerals had made their appearance in India that the
zero first appeared there, although such a character was used by the
Babylonians[185] in the centuries immediately preceding the Christian era.
The symbol is [Babylonian zero symbol] or [Babylonian zero symbol], and
apparently it was not used in calculation. Nor does it always occur when
units of any order are lacking; thus 180 is written [Babylonian numerals
180] with the meaning three sixties and no units, since 181 immediately
following is [Babylonian numerals 181], three sixties and one unit.[186]
The main {52} use of this Babylonian symbol seems to have been in the
fractions, 60ths, 3600ths, etc., and somewhat similar to the Greek use of
[Greek: o], for [Greek: ouden], with the meaning _vacant_.

"The earliest undoubted occurrence of a zero in India is an inscription at
Gwalior, dated Samvat 933 (876 A.D.). Where 50 garlands are mentioned (line
20), 50 is written [Gwalior numerals 50]. 270 (line 4) is written [Gwalior
numerals 270]."[187] The Bakh[s.][=a]l[=i] Manuscript[188] probably
antedates this, using the point or dot as a zero symbol. Bayley mentions a
grant of Jaika Rashtrakuta of Bharuj, found at Okamandel, of date 738 A.D.,
which contains a zero, and also a coin with indistinct Gupta date 707 (897
A.D.), but the reliability of Bayley's work is questioned. As has been
noted, the appearance of the numerals in inscriptions and on coins would be
of much later occurrence than the origin and written exposition of the
system. From the period mentioned the spread was rapid over all of India,
save the southern part, where the Tamil and Malayalam people retain the old
system even to the present day.[189]

Aside from its appearance in early inscriptions, there is still another
indication of the Hindu origin of the symbol in the special treatment of
the concept zero in the early works on arithmetic. Brahmagupta, who lived
in Ujjain, the center of Indian astronomy,[190] in the early part {53} of
the seventh century, gives in his arithmetic[191] a distinct treatment of
the prop