The Hindu-Arabic Numerals | Page 8

the wall opposite the entrance are representations of the
members of his family, much defaced, but with the names still legible.
It would seem that the excavation was made by order of a king named
Vedisiri, and "the inscription contains a list of gifts made on the
occasion of the performance of several yagnas or religious sacrifices,"
and numerals are to be seen in no less than thirty places.[76]
There is considerable dispute as to what numerals are really found in

these inscriptions, owing to the difficulty of deciphering them; but the
following, which have been copied from a rubbing, are probably
number forms:[77]
[Illustration]
The inscription itself, so important as containing the earliest
considerable Hindu numeral system connected with our own, is of
sufficient interest to warrant reproducing part of it in facsimile, as is
done on page 24.
{24}
[Illustration]
The next very noteworthy evidence of the numerals, and this quite
complete as will be seen, is found in certain other cave inscriptions
dating back to the first or second century A.D. In these, the Nasik[78]
cave inscriptions, the forms are as follows:
[Illustration]
From this time on, until the decimal system finally adopted the first
nine characters and replaced the rest of the Br[=a]hm[=i] notation by
adding the zero, the progress of these forms is well marked. It is
therefore well to present synoptically the best-known specimens that
have come down to us, and this is done in the table on page 25.[79]
{25}
TABLE SHOWING THE PROGRESS OF NUMBER FORMS IN
INDIA
NUMERALS 1 2 3 4 5 6 7 8 9 10 20 30 40 50 60 70 80 90 100 200
1000 A['s]oka[80] [Illustration] ['S]aka[81] [Illustration] A['s]oka[82]
[Illustration] N[=a]gar[=i][83] [Illustration] Nasik[84] [Illustration]
K[s.]atrapa[85] [Illustration] Ku[s.]ana [86] [Illustration] Gupta[87]
[Illustration] Valhab[=i][88] [Illustration] Nepal [89] [Illustration]

Kali[.n]ga[90] [Illustration] V[=a]k[=a][t.]aka[91] [Illustration]
[Most of these numerals are given by Bühler, loc. cit., Tafel IX.]
{26} With respect to these numerals it should first be noted that no zero
appears in the table, and as a matter of fact none existed in any of the
cases cited. It was therefore impossible to have any place value, and the
numbers like twenty, thirty, and other multiples of ten, one hundred,
and so on, required separate symbols except where they were written
out in words. The ancient Hindus had no less than twenty of these
symbols,[92] a number that was afterward greatly increased. The
following are examples of their method of indicating certain numbers
between one hundred and one thousand:
[93] [Numerals] for 174 [94] [Numerals] for 191 [95] [Numerals] for
269 [96] [Numerals] for 252 [97] [Numerals] for 400 [98] [Numerals]
for 356
{27}
To these may be added the following numerals below one hundred,
similar to those in the table:
[Numerals][99] for 90 [Numerals][100] for 70
We have thus far spoken of the Kharo[s.][t.]h[=i] and Br[=a]hm[=i]
numerals, and it remains to mention the third type, the word and letter
forms. These are, however, so closely connected with the perfecting of
the system by the invention of the zero that they are more appropriately
considered in the next chapter, particularly as they have little relation to
the problem of the origin of the forms known as the Arabic.
Having now examined types of the early forms it is appropriate to turn
our attention to the question of their origin. As to the first three there is
no question. The [1 vertical stroke] or [1 horizontal stroke] is simply
one stroke, or one stick laid down by the computer. The [2 vertical
strokes] or [2 horizontal strokes] represents two strokes or two sticks,
and so for the [3 vertical strokes] and [3 horizontal strokes]. From some

primitive [2 vertical strokes] came the two of Egypt, of Rome, of early
Greece, and of various other civilizations. It appears in the three
Egyptian numeral systems in the following forms:
Hieroglyphic [2 vertical strokes] Hieratic [Hieratic 2] Demotic
[Demotic 2]
The last of these is merely a cursive form as in the Arabic [Arabic 2],
which becomes our 2 if tipped through a right angle. From some
primitive [2 horizontal strokes] came the Chinese {28} symbol, which
is practically identical with the symbols found commonly in India from
150 B.C. to 700 A.D. In the cursive form it becomes [2 horizontal
strokes joined], and this was frequently used for two in Germany until
the 18th century. It finally went into the modern form 2, and the [3
horizontal strokes] in the same way became our 3.
There is, however, considerable ground for interesting speculation with
respect to these first three numerals. The earliest Hindu forms were
perpendicular. In the N[=a]n[=a] Gh[=a]t inscriptions they are vertical.
But long before either the A['s]oka or the N[=a]n[=a] Gh[=a]t
inscriptions the Chinese were using the horizontal forms for the first
three