Page:Popular Science Monthly Volume 81.djvu/612

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Here the characters for 1, 4, 6, and 7 are easily recognizable, while the 2, 3, 5, and 9 can be developed without difficulty.

This system is neither different from that of the Greeks nor superior to it. Neither has a zero, and in neither have the characters a value of place. That is, all of the important numbers must be designated by signs of their own. In our system 2 moved one place to the left becomes 20, but in Greek β′ = 2 and κ′ = 20. So, in the Nasik inscription 2 and 20 are designated by characters separate and distinct.

In this far there is similarity; but while the Greeks used the letters of their alphabet, the Hindus did not. The meaning of some of these signs, such as the strokes for 1, 2, and 3, is apparent, but the origin and meaning of others are not known. They may have been made from alphabetic characters, but as yet no theory has been substantiated.

It may be seen that all of the different systems of numerical notation which had been developed, whether in China, in India, or in Greece, had the same general characteristics: there was no zero, and the symbols had no place value. Because of this it was necessary to employ a great many different symbols. Such a system might be used for mathematical calculation, but it was bound to be complicated and intricate. What was needed was a system with fewer signs; but when this was constructed, as it was among the Romans, and the Greeks of Solon's time, it was so rigid and inflexible as to admit of no progress in mathematics. Something altogether different was needed.

Gradually, by processes of which we know little, a revolution was wrought in all mathematical work and new numeral systems were developed. This revolution was effected by the use of the counting-board, or, as we now call it, the abacus, from a Greek word the meaning of which is in dispute. At first all calculation was probably mental or performed upon the fingers, but as time went by, a mechanical device was perfected wherever men strove to make readier and more elaborate computations. This device is said to have been invented by the Chinese, though of such tradition there is no certain proof At all events it was used by the Chinese, the Babylonians, and the Hindus in immemorial times. The Greeks and the Romans had it; and it continued to be used in Europe throughout the middle ages. According to the "Dialogus de Scaccario" of the twelfth century, the officials of the exchequer reckoned the king of England's revenue by means of it. To this day it is employed generally in Russia, and in schools wherever children are learning to count.

Fundamentally the abacus consists of a board or table marked off in parallel columns within which counters can be placed. The principle is the same if the counters are strung along parallel wires. The important thing is that on the abacus each column has a value of its own, a value of place. Thus, several numerals may be employed with