meral letters, and introduction of specific symbols, in the nine digits, 1, 2, 3, &c.; and the cypher, 0, raising their value in a decuple progression, 10, 100, 1000, &c.

For simplicity, variety, and compass, this surely may rank among the noblest discoveries of human sagacity; if we attribute it thereto, and not rather to THE FATHER OF LIGHTS, the original Author of language, oral and written; from whom ultimately proceed "every good gift, and every perfect grace." And most justly did Abulfaragi eulogize the Indian discoverers, as Fodina Sapientiæ, “a pit of wisdom!"-How it was possible indeed for the Ancients to carry on such long arithmetical computations, as we find in the Bible, Herodotus, Manetho, Josephus, &c., by the help of such awkward, complicated, and embarrassed a mode of Notation as by numeral letters, is not easy to be conceived at the present day by those who are accustomed to the facility and dispatch of the Indian symbols. Their arithmetic must necessarily have been a species of algebraic calculation, such as we find in the problems of Diophantus, about the commencement of the Christian Era; and such as must have been used before him, by Hipparchus and Archimedes.

The following Table, XXI, exhibits the various numeral characters, and modes of Notation, employed by different nations. It will be found fuller, and more correct, than that of Beverege, which he calls Aurea Tabella, from its great utility in ancient numeration, p. 279, &c.

I. VULGAR NOTATION.

Of the several columns composing this Table, the first on the left hand represents the usual mode of reckoning, as far as one hundred thousand; the succeeding columns represent the Indian, which was the parent of our Notation, the Hebrew, Samaritan, Syriac, Arabic, the Greek, both by small letters and uncials, and the Roman. Our digits are evidently derived from the Indian, though with considerable variation in some. The cypher O was an improvement upon the Indian point, as being more conspicuous or legible, which we owe to the Arabian Astronomers.

II. INDIAN.

The characters here exhibited are such as occur in the writing of the principal Geographers, Astronomers, and Chronologers of the East. Thus, Ulug Beg, that learned Persian

prince, who flourished about A. D. 1440, represents the Greek Epoch as longer than the Arabian, by . V.. or 340700 days. See Beverege Chron. p. 291.

III. HEBREW. IV. SAMARITAN.

The Hebrew column is expressed in the Chaldee alphabet, which was introduced after the return of the Jews from the Babylonish Captivity, and perhaps by Ezra the Scribe. The primitive Hebrew character, such as it appears on ancient shekels, differed considerably from the Chaldee; and was the prototype, evidently, of the rude Samaritan character, which it greatly surpassed in symmetry and elegance. See the collection of sacred shekels, in the Apparatus prefixed to the first volume of the London Polyglott Bible, that noblest specimen of the Typographic art, as well as the most useful; p. 38.

= = 15.

In the primitive Hebrew notation, Iod denoted 10; whence by composition, 10+1=11, ♫ 10 + 2 = 12, &c. Instead of T, 10 +5=15, the Jews, to avoid profaning the sacred name IAH, substituted 1, 9 + 6 Here was a remarkable deviation from the most ancient mode, corresponding to our's, of placing the number 10 before the digits; and the same prevails in the higher numbers, NP 100+1=101; 2p, 102, &c. &, 401, an, 402, &c. pn 400 + 100-500; лn 400 + 400 - 800; P 400 + 400 + 100 = 900.

The Jews afterwards expressed the five centenary numbers after 400 by the five final letters of the Chaldee alphabet, Caph, 500; Mem, 600, &c..

To express thousands, the letters begin again, either with marks over them, or their value determined by their place in the

,הדמב ; 1430 = 30 + 400 + 1000,אתל,decimal progression: as

The Syriac alphabet, agreeing with the Hebrew and Samaritan, in the number and order of its letters, the mode of notation is the same, with some slight variations. Thus, 1. The number 15, is expressed by the numerals 10 and 5; because the Hebrew name of God, IAH, was not used in Syriac. 2. The number 20, is expressed by a double Caph, the initial and final; yet so as that the final Caph is removed in the succeeding 21, 22, &c. and the proper literal digit is substituted. The same redu

plication prevails in the number 50 and 70, 500 and 700. The value of the digits is also raised, in the decimal scale, by a point over the letter, raising the tens to hundreds; and the hundreds to thousands, by a point under the letter. Myriads, by a horizontal stroke under the letter.

VI. ARABIC.

The Arabic alphabet at present in use, differs widely from the primitive Arabic, or Cufic alphabet, in the number and order of its letters. The change was made by Ibn Mocla, in the tenth century.

The Cufic corresponded with the Syriac, from which it was evidently derived. The present alphabet is miserably deranged, both in the number and order of the letters, several new ones being added thereto; while the old ones, notwithstanding their dislocation, retain their primitive values in the Syriac or Hebrew alphabet, thus incontestibly demonstrating their common descent from the primæval alphabet; as will appear more plainly from their names and

powers.

Arabic Numerals.

Za, 7; Sin, 60; Shin, Da, 900; Ain, 70; Gain, Lam, 30; Mim, 40; Nun,

Alif, 1; Be, 2; Ta, 400; Tha, 500; Gim, 3; Hha, 8; Cha, 600; Dal, 4; Dhsal, 700; Re, 200; 300; Sad, 90; Dad, 800; Ta, 9; 1000; Fe, 80; Kaf, 100; Kef, 20; 50; Wau, 6; He, 5; Ie, or Ya, 10.

Hence it appears, that of these twenty-eight letters, only the two first, corresponding to Aleph and Beth, retain their proper place and value. The third letter, Ta, corresponding to Thau, the last of the Hebrew alphabet, still retains its primitive value; while the tenth Hebrew letter, Iod, is here thrust down to the last place, in Ie, or Ya, still retaining its primitive value, 10; and so on of the rest of the primitive letters.

In the column of Arabic numerals, I have only set down the first of the three complicated forms of the Arabic letters, at the beginning, middle, and end of words; but the three forms are used indiscriminately, which tends to create great confusion and embarrassment in their notation; of which Beverege furnishes some curious and involved specimens, remarkably resembling the algebraic notation; in one of which, a large number is made up of the following parts: 400 +60 + 2 × 1000 × 1000 :