The Hindu-Arabic Numerals | Page 8

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.
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[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]
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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 B��hler, 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
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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 numerals, but a vertical arrangement for four.[101] Now where did China get these forms? Surely not from India, for she had them, as her monuments and literature[102] show, long before the Hindus knew them. The tradition is that China brought her civilization around the north of Tibet, from Mongolia, the primitive habitat being Mesopotamia, or possibly the oases of Turkestan. Now what numerals did Mesopotamia use? The Babylonian system, simple in its general principles but very complicated in many of its details, is now well known.[103] In particular, one, two, and three were represented by vertical arrow-heads. Why, then, did the Chinese write {29} theirs horizontally? The problem now takes a new interest when we find that these Babylonian forms were not the primitive