Imagine a person used to decimal counting by means of the fingers having recourse to simple counting by making a mark for each suc cessive unit, as in a, 6, c, &c. At ten he might be expected to make some symbol that his handful was completed, and the a mark through the whole ten unit symbols, as at e, would do very well. This he might abbreviate, as at f, retaining only the symbol of a unit and that of the line drawn across. The handful of tens, or one hun dred. might be represented by retaining only the unit symbol and two ligatures, namely, that of the tens and that whioh made all the ten tens into one symbol, as at g. The ton hundreds would require a unit with three ligatures, or fens strokes altogether, which, if they were written without taken the pen off, might bo made as at /t, which might degenerate into A-, and finally into 1. Again, by cutting i into two halves, we have is or 91, which might suggest themselves as proper representatives of half a thousand, or five hundred. Similarly, bisection of f and g, or of o and q, would suggest p and r as proper symbols for the halves of ten and one hundred. The symbol a has resemblance to 1, f to X, p to C, h to M. in to D, p to V, and r to L.
We cannot find any precise information upon the time of the coin , mencement of the principle of local value which prevails to a certain extent throughout the Roman system,—namely, that a smaller symbol before a Larger one, in numbers less than one hundred, denotes a sub traction, after it an addition. This principle does not appear in the Pluenician or Palmyrene notations, which otherwise much resemble the Roman in their principle of notation, though they approximate to pure vicenary scales, both adopting distinct symbols for twenty.
The Chinese use three systems : the first, not very simple, and ancient ; the second, intentionally complicated, and employing symbols of words to denote numbers, is introduced in deeds and other instru ments, to render alteration difficult ; the third, a simplification of the first, supposed to have been made by the Jesuit missionaries.
For further information on the subject of this article, with abundant references, see the article ' Arithmetic' in the ` Enclopmdia Metropoli tans,' by Dr. Peacock.