particulars would have been the same in both; but as not one third of the Roman letters are numerals, so neither is the numeral value of those that are so, more or less, according to their place in alphabetical order; because D and C, which stand among the first letters of the alphabet, and M and L, whose station is in the centre, are of much greater numerical value than X and V, which are near the end.

But it has been supposed 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, it being the first letter of Centum, the Latin term for 100. Some also suppose, 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 denominate 50. But upon what just principle can any person imagine, that 1000 and 100 were the numbers which letters were first used to express? And what cause can be assigned why D, the first letter in the Latin word Decem, 10, should not rather have been chosen for 500, because it had a rude resemblance to half an M? But if these questions could be satisfactorily answered, there are other numerical letters which have never yet been accounted for at all. We therefore think 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 appears 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 they doubled, trebled, and quadrupled, to express two, three, and four, thus II, III, IIII. So far they could easily number the minums or strokes with a glance of the

eye; but they found, that if more were added, it would be necessary to number the strokes one by one; for this reason, when they came to five, 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 five to five, that is, from the fingers of one hand to the fingers of the other. Ovid has touched upon the original of this in his Festorum, lib. iii. and Vitruv. lib. iii. c. 1, has made the same remark.

After they had made this acute angle V, for five, they then added single strokes to the number of four, thus VI, VII, VIII, VIIII, and then, as the minums 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 they had doubled, trebled, and quadrupled this double acute angle, thus XX, XXX, XXXX, they then, for the same reason which induced them to make a single angle first, 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 was doubled, they then doubled the right angle, thus L, to denote one hundred, and having numbered this double right angle four times, thus II, III, IIII, when they came to the fifth number, as before, they reverted it, and put a single stroke before it, thus II, to denote five hundred; and when this five hundred was doubled, then they also doubled their double right angle, setting two double right angles opposite to each other, with a single stroke between them, thus III. to denote one thousand: when this note for one thousand had been repeated four times, they then put down 11,for five thousand;

IIIII, for ten thousand; and IIII, for fifty thousand.

That the Romans did not originally write M for one thousand, and C for one hundred, but square characters, as before shewn, we are expressly informed by Paulus Manutius; but the corners of the angles being cut off by transcribers for dispatch, these figures were gradually brought into what are now called numerical letters. When the corners of III were made round, it stood thus, CIO, which is so near the Gothic, that it soon deviated into that character; so that I having the corners made round, stood thus I, and then easily deviated into D. I also became a plain C by the same means; the single rectangle which denoted fifty, was, without any 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.

As a further proof of this assertion, let it be considered, that CID is still used for one thousand, and I for five hundred, instead of M and D; and this mark,, is sometimes used to denote one thousand, which may easily be derived from this figure, III, but cannot be deviations from, or corruptions of, the Roman letter M.

The Romans also expressed any number of thousands by a line drawn over any numeral less than one thousand; thus, V denotes five thousand, LX sixty thousand: so likewise M is one million, MM two millions, &c.

Upon the discovery of printing, and before capitals were invented, small letters served for numerals, which they have done ever since; not only when the Gothic characters were in their perfection,

but even after they ceased, and Roman was become the prevailing letter. Thus, in the time of printing in Gothic characters, í b‡ Ic dm were, and are still, of the same signification with capitals, when used as numerals. But here it should be observed, that the capital J is no numeral letter, though the lower-case j is as often and as significantly used as the vowel i, especially where the former is used as a closing letter, in ij iij vj vij viij deij, &c. though it is as right not to use j's at all, unless it were out of respect to antiquity; for in Roman lower-case numerals, which are of more modern date, the j is not regarded, but the i stands for a figure of 1, whereever it is used numerically.

ARITHMETICAL FIGURES.

THE above figures are nine in number, besides the cypher, or nought, which, though of itself of no signification, makes a great increase in the figure to which it is joined, either singly or progressively.

Figures require a founder's particular care to cast them exactly an n-thick, and to a true parallel, as the least deviation, where a number of them come together in table-work, destroys their arrangement, and causes an inconvenience in the justification, which cannot be altered without considerable loss of time, and frequently baffles the skill of the most ingenious compositor.

The excellence of figures does not consist in their having soft and fine strokes, but rather in such circles and lines as bear a proportion with the strength of the face. The improvement which has recently taken place, and is now generally adopted, of casting them to a fuller face than formerly, must be allowed to add considerably to their appearance, and to the beauty of the work in which they may be used.

Printers, at one time, thought it a great impropriety to use erect figures in Italic matter, judging that the obliquity of that character would be intercepted by them, and therefore had figures cast of the same inclination; but this peculiarity is entirely laid aside in England, though it still prevails in some parts abroad.

SCRATCHED FIGURES.

THOUGH Scratched figures are at present not used with us, yet, as their existence is not entirely done away, it might be construed an omission were we not to notice them, and specify in what particular they were formerly thought of utility.

They were used in that species of arithmetic called division, and are still considered in Germany, and other foreign parts, as essentially necessary; the dividing and divided figures being scratched as soon as they have been adjusted by subtraction and multiplication.

Having made some observations upon the numeral letters of the Romans, and on modern arithmetical figures, we will shew the manner adopted by the Greeks and Hebrews, of numerating in their characters, as well for the satisfaction of the curious, as for the instruction of those who may have occasion to become acquainted with them.

GREEK NUMERALS.

INSTEAD of seven letters used by the Romans, the Greeks employed their whole alphabet, and more than the alphabet; for they contrived three symbols more, and made their numerals to consist of twentyseven sorts, which they divided into three classes; the first, to contain units; the second, tens; and the