2. NUMERAL CHARACTERS, or marks used for nota tion of numbers.
Next in use and importance to alphabetic characters. is that class of characters known by the name of numerals. These are unquestionably one species of real character, and probably the only one that could with advantage be adopted into general use. For an account of the origin and progress of numeral notation, see ArtiTilmETic.
The idea of number suggests itself, by abstracting from objects every circumstance except their indivi• duality. It is probable, that, when men first began the practice of numeration, they would proceed by taking sonic of the objects immediately before their eyes, and intimating., that those of which they were speaking were equal to them in number. As the objects most univer sally present to all men are the fingers, these would of course be the earliest measure of numbers ; and numera tion would thus be formed into a scale either of Jives or tens. The former have sometimes been found, the latter, or the dccuple progression, is nearly universal. The process of numeration being commenced, it would be necessary, in order to carry it on, that some marks should be found to denote the numbers in their progress. It is probable that the earliest, as it was the simplest species of mark, would be a mere notch upon a board, the repetition of which would designate the number of objects to be counted. It is evident, that, in this mode of notation, the eye can easily and readily' recognise the different numbers only a very little way. One, two, three, and even four, can be easily distinguished, as we find in the dials of church clocks, but farther' than this the power of distinction becomes difficult, and is at Iwo entirely lost. After four strokes are put down, there fore, it is necessary to make some alteration in tire marl.. to slim where 'a new series is to commence. could most easily' be done, by making a diagonal stroke through the four preceding. A progression would then take place by a new series of strokes, and. at the end of the second five, a diagonal in the opposite direction would point out the second termination. Here we have the evident origin of the Roman mode of notation. The first diagonal produced the V, the Iglark of five, the second the X, the mark of ten. After ten the same notation would go on to a second ten, which would be denoted by a double X, a third by a triple, and a fourth by a quadruple X. The same difficulty of distinguish ing by the cyc beyond four similar figures, would make it necessary, at the fifth ten, to introduce another change. This was done by a horizontal line at the bottom, making a figure similar to L. At the tenth ten another addition became necessary, which produced the figure C, after wards modified into a C for one hundred. By a similar process, the fifth hundred was marked by a new line 0, which soon passed into a ll, the mark for 500. The tenth hundred became double co, easily changing into an 1\1 for 1000. This mode of notation of numbers, which is the rudest and most simple, was retained to the last among the Romans, improved in a small degree by certain abbreviations ; and it is radically the same as at this day is used by the Chinese ; only as the Chinese mode of writing is in perpendicular, not horizontal, lines, the position of their numeral marks corresponds to that peculiarity in their mode of writing.
The inconvenience of this mode of notation, where the objects of numeration were much extended, would soon be felt, and some more convenient way of reckoning would be sought. Among those people where the use of letters had been introduced, a ready substitute was found in the alphabetic characters ; and these we find actually so employed at a very early period among the Hebrews, and their immediate neighbours, from whom the invention passed to the Greeks. The Hebrew alpha bet had only 22 letters, but several of these having two forms, it became easy to construct three series of numeral marks, nine in each, and, by using these according to the decuple progression, to denote units, tens, and hundreds, numeral notation as far as a thousand was made easy. Thousands were expressed, by using the same marks with an accent annexed. This mode of numeral nota tion was exactly copied by the Greeks, who, to complete their three series of nines, inserted three additional marks, called the episemon, the koppa, and the sanpi. Thousands they expressed also by the same characters, with an accent below.* In this manner an extensive numeral notation was obtained ; but it had the great inconvenience, that the large numbers, being expressed by one entire mark, could not readily, in performing arithmetical operations, be broken into smaller constituent parts. These opera tions, therefore, became cumbersome and difficult in a high degree. The complete remedy for this incon venience was found, by that immense improvement in the mode of numeral notation, of confining the whole numeral characters to one series only, and giving this series successively the power of the second, the third, or any higher series, by means of position alone ; the same characters in the first row denoting units, in the second tens, in the third hundreds, and so forward as far as numeral expression is required.
This may justly be set down as the perfection of nu meral notation, and gives modern arithmetic the most decided superiority over the ancient. It is commonly supposed to have been derived to us from the Arabs, who are thought to have learned it from the Indians. Some doubts, however, have been lately started upon this point ; and Alice de Villoison, in the 2d volume of his ?necdota Greca, quotes an Italian author, who main tains, that our modern numeral characters were derived from the Greekslehaving been used by them in the times of the emperors for expressing weights and measures, and afterwards extended to express any kind of number. It is not perhaps easy to determine the point, nor is it of much importance ; but it is curious to observe, that something of this mode of notation appears in the He brew numerals ; for though with them three series of characters were used for units, tens and hundreds, and thousands were denoted by applying to these respective ly au accentual mark, yet frequently, too, when both thousands and hundreds were to be put down together, the thousands were signified, by merely placing the pro per numeral without an accent, before the mark for the hundreds,—an approach undoubtedly to the modern mode of notation, though it does not appear to have ever led to farther improvements.
As the best illustration of this subject, specimens of different kinds of numeral characters are given in Plate XL. See also NUMBER and NUMERAL NOTATION.