those letters of the alphabet which are generally used for figures; as I, one; V, five; X, ten; L, fifty; C, a hundred; D, five hundred; M, a thousand, &c.

It is not agreed how the Roman numerals originally received their value. It has been supposed, as we have observed in the end of the article Number, that the Romans used M to denote 1000, because it is the first letter of mille, which is Latin for 1000; and C to denote 100, because it is the first letter of centum, which is Latin for 100. It has also been supposed, that D, being formed by dividing the old M in the middle, was therefore appointed to stand for 500, that is, half as much as the M stood for when it was whole; and that L being half a C, was, for the same reason, used to denote 50. But what reason is there to suppose, that 1000 and 100 were the numbers which letters were first used to express? And what reason can be assigned why D, the first letter in the Latin word decem, ten, should not rather have been chosen to stand for that number, than for 500, because it had a rude resemblance to half an M? But if these questions could be satisfactorily answered, there are other numeral letters which have never yet been accounted for at all. These considerations render it probable that the Romans did not, in their original intention, use letters to express numbers at all; the most natural account of the matter seems to be this:

The Romans probably put down a single stroke, I, for one, as is still the practice of those who score on a slate or with chalk: this stroke, I, they doubled, trebled, and quadrupled, to express 2, 3, and 4; thus, II, III, IV. So far they could easily number the strokes with a glance of the eye. But they presently found, that if more were added, it would soon be necessary to tell the strokes one by one: for this reason, when they came to 5, they expressed it by joining two strokes together in an acute angle thus, V; which will appear the more probable, if it be considered that the progression of the Roman numbers is from 5 to 5, i.e., from the fingers on one hand to the fingers on the other.—Ovid has touched upon the original of this in his Fastorum, lib. iii. and Vitruvius, lib. c. i. has made the same remark.

After they had made this acute angle V. for five, they added the single strokes to it to the number of 4, thus, VI, VII, VIII, IX, and then as the strokes could not be further multiplied without confusion, they doubled their acute angle, by prolonging the two lines beyond their intersection thus, X. to denote two fives, or ten. After this they doubled, trebled, and quadrupled, this double acute angle thus, XX, XXX, XXXX. they then, for the same reason which induced them first to make a single and then to double it, joined two single strokes in another form, and instead of an acute angle, made a right angle L, to denote fifty. When this 50 was doubled, they then doubled the right angle thus L, to denote 100, and having numbered this double right angle four times, thus LL, LLL, LLLL; when they came to the fifth number, as before, they reverted it, and put a single stroke before it thus, I, to denote 500; and when this 500 was doubled, they also doubled their double right angle, setting two double right angles opposite to each other, with a single stroke between them, thus DII to denote 1000: when this note for 1000 had been four times repeated, then they put down I for 1,000, II for 2,000, III for 3,000, IV for 4,000, V for 5,000, VI for 6,000, VII for 7,000, VIII for 8,000, IX for 9,000, X for 10,000, XI for 11,000, XII for 12,000, XIII for 13,000, XIV for 14,000, XV for 15,000, XVI for 16,000, XVII for 17,000, XVIII for 18,000, XIX for 19,000, XX for 20,000, XXX for 30,000, XXXX for 40,000, XXXX for 50,000, XXXX for 60,000, XXXX for 70,000, XXXX for 80,000, XXXX for 90,000, XXXX for 100,000, XXXX for 200,000, XXXX for 300,000, XXXX for 400,000, XXXX for 500,000, XXXX for 600,000, XXXX for 700,000, XXXX for 800,000, XXXX for 900,000, XXXX for 1,000,000.

That the Romans did not originally write M for 1000, and C for 100, but square characters, as they are written above, we are expressly informed by Paulus Manutius; but the corners of the angles being cut off by the transcribers for dispatch, these figures were gradually brought into what are now numeral letters. When the corners of M were made round, it stood thus CIO, which is so near the Gothic m, that it soon deviated into that letter; so I having the corner made round, it stood thus IO, and then easily deviated into D. E also became a plain C by the same means; the single rectangle which denoted 50, was, without alteration, a capital L; the double acute angle was an X; the single acute angle a V consonant; and a plain single stroke, the letter I.; and thus these seven letters, M, D, C, L, X, V, I, became numerals.

NUMERAL Characters of the Arabs, are those figures which are now used in all the operations or arithmetic in every nation of Europe. We have elsewhere shown that the Arabs derived the use of them most probably from India, (See Arithmetic, No. 5.) This opinion, however, though very generally received, has been controverted with some ingenuity. A writer in the Gentleman's Magazine, at a period when that miscellany was in its highest reputation, thus endeavours to prove that the Arabs derived their notations from the Greeks. "I maintain (says he) that the Indians received their numeral characters from the Arabians, and the Arabians from the Greeks, as from them they derived all their learning, which in some things they improved, but for the most part have altered. The numerical figures which they received from the Greeks are proofs of this alteration; which is so great, that without particular attention one can scarcely discover in them the vestiges of their origin. But when we compare them carefully, and without prejudice, we find in them manifest traces of the Greek figures. The Greek numerical figures were no other than the letters of their alphabet. A small stroke was the mark of unity. The B, being abridged of its two extremities, produced the 2. If you incline the x a little on its left side, and cut off its foot, and make the left horn round towards the left side, you will produce a 3; the A makes the 4, by..." Numerical raising the right leg perpendicularly, and lengthening it a little below the base, and lengthening the base on the left side. The forms the 5, by turning the lowest semicircle towards the right, which before was turned towards the left side. The number 5 forms the 6 by having its head taken off, and its body rounded. Z, by taking away the base, makes the 7. If we make the top and bottom of H round, we shall form an 8. The 8 is the 9 with very little alteration. The cypher o was only a point, to which one of the figures was added to make it stand for ten times as much. It was necessary to mark this point very strongly; and in order to form it better, a circle was made, which was filled up in the middle; but that circumstance was afterwards neglected. Theophanes, an historian of Constantinople, who lived in the ninth century, says expressly, that the Arabians retained the Greek figures, having no characters in their language to represent all the numbers. The Greeks observed in their numbers the decuple progression, which the Arabians have retained. Certain characters are found in the Greek alphabet, which are not used in reading, but only in calculation, and for this reason they are styled Episemata, that is to say, not, marks, in order to distinguish them from letters. The number 6 derives its form from one of these episemata, which was called επισημα. This episema forms the letter F among the Æolians and among the Latins. This was called the Digamma, so styled from its figure, which seems to have been one r placed upon another.

That this reasoning is plausible will hardly be questioned; but whether it be conclusive our readers must determine. It has not convinced ourselves; but through the whole of this work we wish to state candidly the different opinions held on every subject of curiosity and usefulness.