As Woepcke[143] pointed out, the reading of numbers of this kind shows that
the notation adopted by the Hindus tended to bring out the place idea. No
other language than the Sanskrit has made such consistent application, in
numeration, of the decimal system of numbers. The introduction of myriads
as in the Greek, and thousands as in Arabic and in modern numeration, is
really a step away from a decimal scheme. So in the numbers below one
hundred, in English, eleven and twelve are out of harmony with the rest of
the -teens, while the naming of all the numbers between ten and twenty is
not analogous to the naming of the numbers above twenty. To conform to our
written system we should have ten-one, ten-two, ten-three, and so on, as we
have twenty-one, twenty-two, and the like. The Sanskrit is consistent, the
units, however, preceding the tens and hundreds. Nor did any other ancient
people carry the numeration as far as did the Hindus.[144]
{43}
When the _a[.n]kapalli_,[145] the decimal-place system of writing numbers,
was perfected, the tenth symbol was called the _['s][=u]nyabindu_,
generally shortened to _['s][=u]nya_ (the void). Brockhaus[146] has well
said that if there was any invention for which the Hindus, by all their
philosophy and religion, were well fitted, it was the invention of a symbol
for zero. This making of nothingness the crux of a tremendous achievement
was a step in complete harmony with the genius of the Hindu.
It is generally thought that this _['s][=u]nya_ as a symbol was not used
before about 500 A.D., although some writers have placed it earlier.[147]
Since [=A]ryabha[t.]a gives our common method of extracting roots, it would
seem that he may have known a decimal notation,[148] although he did not
use the characters from which our numerals are derived.[149] Moreover, he
frequently speaks of the {44} void.[150] If he refers to a symbol this
would put the zero as far back as 500 A.D., but of course he may have
referred merely to the concept of nothingness.
A little later, but also in the sixth century, Var[=a]ha-Mihira[151] wrote
a work entitled _B[r.]hat Sa[m.]hit[=a]_[152] in which he frequently uses
_['s][=u]nya_ in speaking of numerals, so that it has been thought that he
was referring to a definite symbol. This, of course, would add to the
probability that [=A]ryabha[t.]a was doing the same.
It should also be mentioned as a matter of interest, and somewhat related
to the question at issue, that Var[=a]ha-Mihira used the word-system with
place value[153] as explained above.
The first kind of alphabetic numerals and also the word-system (in both of
which the place value is used) are plays upon, or variations of, position
arithmetic, which would be most likely to occur in the country of its
origin.[154]
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