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

third, hundreds. Accordingly the first class consists of the nine following numerals, viz.

a B y δε 5 ૐ n

6

1 2 3 4 5 6 7 8 9

In this class, it may be observed, the Greek ft, or Stigma, is made an auxiliary numeral letter, to stand for 6, and is callod imionμov.

The second class includes the nine numerals which express tens, viz.

10 20 30 40 50 60 70 80 90 In this second class, a particular symbol, resembling much an inverted Hebrew lamed, serves to express 90, though others use an y in the room of it, to which, as well as the former, they give the name of koppa.

The third class contains the numerals which carry hundreds with them, and are

100 200 300 400 500 600 700 800 900

In this class the additional symbol which stands for 900, is a compound of a pi aud a sigma, for which reason it is called sanpi; though others represent it by a mark like this,.

To raise numbers to thousands, nothing else is required than to begin the alphabet again, and to mark each letter with a dot, or an acute under it, in the following manner:

Still higher numbers are noted with double acutes under them; thus,

The manner of joining these numerals may be learned from the following example:

Besides the above manner of counting by lowercase letters, the Greeks make choice of six capitals

Among the numeral letters, the pi is peculiar, for admitting the delta, eta, chi, and mu, into its centre, and for giving such an incorporated letter five times the value which it has of itself; as,

A5 times 10 are 50.

H5 times 100 are 500.

5 times 1000 are 5000.

M5 times 10,000 are 50,000.

To these inclosed numerals any part and quantity may be added, according to the value which is contained in each of the six numeral letters exhibited in the preceding page.

It should be observed, that when a numeral letter is marked at the top, it shews it to be a fraction; as, One-fourth. One-fifth. Five-eights.

HEBREW NUMERALS.

»

THE manner of counting by letters is derived from the Hebrews, who for that purpose made use of the letters of their alphabet, without the assistance of other symbols. Accordingly, the letters which express units, are,

ה

90 80 70 60 50 40 30 20 10
And these underneath, hundreds, viz.

ק

ף
ם ז
ד
ת
ש
י

१

900 800 700 600 500 400 300 200 100

In joining Hebrew letters for numbers, it is a rule to put the letter of a greater signification before a character of a less; as,

The numeral signification of the five final letters is sometimes expressed by compounds; as,

תתק by ץ תת byף תש byז תר by ם הק byך

500

600 700

800

900

with an acute over it, stands for 1000: but where the contents of a sum amount to above 1000, the letter to the right hand shews the order of thousands, and the & is doubly accented; thus

And if hundreds are added to them, the doubleaccented & is omitted, and only a common letter put at the beginning, to intimate the order of thousands;

In printed books and letters the Jews date their years (after the creation of the world) without putting an at the beginning, to imply 5000, and only set down the hundreds, and parts, of which their years consist above the thousands. But in this case

they seldom forget to put the letters p after the date, which is to inform the reader, that the date thus abridged, is according to the minor supputation.

In writing 15, the Jews choose to do it by 1, instead of Л, because these last letters are used in Jehovah; and therefore they think it a profanation of the Lord's name, if the said letters should be used for numerals. Neither do they express 16 by ", but make use of 1, because the two letters, jod and van, are likewise comprehended in the word Jehovah.

REFERENCES.

REFERENCES are all such marks and signs as are used in matter which has either side or bottom notes, and serve to direct the reader to the observations which are made upon such passages of the text as are distinguished by them, and demand a reference of the same likeness to be put to the notes, by which the matter is illustrated, or otherwise taken notice of.

References which are used in works with notes to them, are variously represented, though oftener by letters than other characters. Accordingly, some put common letters between parenthesis; thus (a), (b), (c), &c. Others, again, choose to see them betwixt crotchets, as [a], [b], [c], and so on to the end of the alphabet; instead of these, some begin the notes of every page with (a), in which they are as right as the former; and have this advantage besides, that the order of references is not so liable to be interrupted as by going through a whole alphabet. Were we authorised to vary from the customary mode of practise, we should recommend literal references to begin with every even page, if it has notes; and to carry them no further than to the