NUMERAL CHARACTERS. There are three simple and ob vious modes of constructing symbols of number. 1. By arbitrary invention. 2. By the choice of letters of the alphabet. 3. By a sys tem of repetitions of a single unit, as I, I I, III, 1III, &c., with marks of abbreviation. Some may doubt whether the first and third were ever really employed ; but it is not known that we can assign to the Indian numerals any other origin than the first, and the third explains the Roman system with a degree of consistency which is most extra ordinary, if it be only accidental coincidence.
Distinct numeral characters are found to have existed or to exist among the Chinese, Indians, and Arabs, &c., Phmniciaus, Palmyrenes; Hebrews, Egyptians, Greeks, and Romans; and others are given as in ancient use among the Mexicans. We shall here confine ourselves to the simplest explanation of those systems which will be wanted by the student of ancient literature. Of these, as it should seem, the Indian system may belong (though it may be doubted) to the first class ; the Hebrew and the common Greek system to the second ; the Roman, Plicenician, Pahnyrene, ancient Greek, Egyptian, and Chinese, to the third class.
The system received from the Hindus through the Arabs, and now adopted throughout Europe, has been gradually much altered in the forms of the symbols. The symbols we now use, especially in their old manuscript forms, 1, 2, 3,.4, 8, may be explained with reasonable probability upon the third system ; but not 5, 6, 7, 9. [ARITHMETIC.] The Hebrews used of their own alphabet, giving the finals a separate and particular value, as follows : The use of the final letters as signifying numbers is of newer date than the rest ; the old system required the junction of subordinate numbers to express 500, 600, &c. Numbers not expressed above were made by juxtaposition of letters denoting other numbers, according to a decimal subdivision, as among the Greeks ; the only exception being 15, which, as 10+5 or MI made a word signifying the Creator, they wrote as 9+ 6, or '1=. In a language like the Hebrew it would be impossible to prevent every combination of numbers from also stand ing for a word or words ; and the Oriental nations accordingly have frequently expressed dates by sentences. Thus " Hooshnng Shah is no more," rendered into Persian, expresses, in the numeral force of the letters, the year 837 of the Hegira, the date of the death of that prince.
The Greeks, in some enumerations, have three distinct methods of expressing numbers; but the first of them, which consists in the use of the letters of the alphabet to denote the successive books of a work, as in the Iliad,' is as much a method of naming as of counting. Some thing more to the point is the old system which occurs on inscriptions, in which the unit is represented by a single mark;five by II (the initial of 11ENTE), ten by A (that of AEKA), and 100 by H (that of HEKATON).
And in all cases five of any symbol are written by inclosing the symbol tints fal is five tens, and IHI is five hundreds. Thus 879 is 1111 HHH AAnnit, This ancient Greek method, as found on inscriptions (which, according to liellbronner, is alluded to in a written work by lierodian only), is supposed to be as old as the time of Solon. The Egyptian hieroglyphic system its on the same principle, but without abbreviations; the symbol of ten resembling that just given for five.
In describing the later Greek notation, we leave out of view the extensions made by the mathematicians, the principle of which is described in Atirrnatenc. It appears most distinctly that the system was made either at a time when the Greek alphabet was in possession of more letters than it permanently retained, or that it was introduced into Greece by communication with some nation (the Phrenioian, per haps) which had some additional letters. The l'ait of the Hebrew and Phoenician, which stands for six, and is wanting in the Greek alphabet, appears in the Greek numeral system under the name of irterwor and is expressed by a symbol resembling r, not very unlike the Vau turned the other way. The Koph and Ttsaddi appear wider the names of /slaws scary& and iriovior esters, with symbols expressed in our types by 5 and but the former is one behind its place in numerpl signification, being 90 among the Greeks and 100 in the East : the latter takes the same numeral place as the final Tsaddi in the Hebrew system. The word air will be a useful guide to the letters beginning the several males, as follows :— The grammarian Priscian would have it that I denoted unity, because the Greek word via, with a cut off, has t for its first letter ; that V is five, as being the fifth vowel, and X ten, as being the tenth consonant, of the Greek alphabet. Any explanation of this system which endeavours at an alphabetical deduction must, as far as has yet been seen, fail entirely in giving a probable origin. The following scheme, however, contains suggestions of some antiquity, and certainly, u before remarked, is either a true explanation or a most extraordinary coincidence. The account of it was revived in our day by Leslie, in an article In the 'Edinburgh Review; and afterwards in his 'Philosophy of Arithmetic.' But it may be found almost entire in the Curaus Mathematicus ' (1690, vol. i., p. 28) of Dechales, who gives it as the opinion of several of his time. And the earliest hints (by no means complete, and mixed with some absurdities) which we have found are in the ' De Numeris Libri Duo' of John Neviemagus, Paris, 1539, 8vo.