ARITHMETIC, His-roar or. Of Arith matte as a Seillee, we know bee very- little as to its state and progress among the ancients It is evident from the tare consideration of on wants, and earliest irapreassixe, that some knowiedse of numbers, or some mode of cam potation, however iraperfect, was coeval with acciety and as thetramactions amen became more complicated, it is reasonable to in than they would hit on devices for fardeeinw and sinapfifying their calculations. as sets that Abraham, ha-6aq retired from Chid der into Effie, &rine the time of a &mine was the first who tartit the inhabitants of thm country- a tondo* both of arithmetic aid as truneeny, of -which they were bah before imo rant; a cinema:owe the more probable, as k is well known that the science of astrammy was first cultivated the Cluldeans, and ouch advances nude is shot science as could not have been effected without the aid of arith metical calculations.
The Greeks inmeioed that the science of arithmetic, as well as that of geometry, origi. noted with the Emeians ; bit this rams; as for as respects priority of &revery, was evi dently ernmems, and no doubt arose from the circumstance of their derived all their first ideas of the arts and smencce, as well as many of their faiths, from the Egyptians Time, as the Egyptians believed that they were taught numbers by their god Them or Thot, who prisidederer commerce, the Greeks animed a similar office to their god Mercury_ As de Plamicians were the first trading peo ple, they naturally addicted thenmelves to the science and practice of arithmetic, which led Strabo to observe that the invention of the at be ed to them ; but, as the Chakkans were a more ancient people, this supposition is no less erroneous than the former. What ad vances were made by these people in the sici ewe we have no means of racermining, for nothing remains of the early writings on this subject, except what may be gathered from the commentary of Prudes on the Furst Book of Euclid's Elements. It appears that ahnost all nations were led to fix upon the some nu meral wale, or the COMMIS! method of nota and tion, numbers into tens, hundreds, ; a practice doubdces derII14 from the custom, as universally adopted in childhood, of countiom by the fingers ; being first reckoned singly from one to ten,1 and time succestiyely over again, would nain.1 rally lead to the decimal scale or the dimple dirŪm of numbers. But they represented their numbers by means of the letters of the alphabet in the place of the modern nmnerals. Thum the Jeers tided their alphabet into one units, nine tan, and nine hemikerk, inctudeig the final letters, as tt Aleph, 1, = Beth, 2, &c.
I to. Yeti, 10; then Caph, Lamed, Me de.. to p Koph, 100, 1 Rceh, et.c. to r Tea& final, WO- Thousands were sometimes expressed by the units annexed to Inn/died, as -tiro; 1434 ;sometimes by the word10t10, r 2300, and with other numerals prefix ed, to signify the number of thousands. To araid ursine the divine name of rre, Jehovah, in notation, they mistimed ID fir fifteen. To the alphabet of the Greeks were asekowel two numerical namely, a power to each letter in adEr, as a, Alpha, 1, eto to es, 0me g.; 24, =d a power similar to that adopted by the Jews, as s, Alpha, t, te. to c, Kappa, 10, ; to es, Omega, KO ; then 9110 was es pressed by the character z, and the thousands were denoted by a point under the ktters after this manner, 1000A SMO, &C. j the nuns.
bur of 10,000 was sometimes expressed by a small dud over the iota, thus, L but mathema ticians employed the letter MI, which, by j placing andei the small letters, indicated the number of thousands, as a far 10,000, 13 for 20,000, As. Diophannas and Pappas made Ms to repr t 10,0100, and then by the bil 1 tion of the letters, as AM*, for *000, etc. Apollonins &rid' ed numbers into perieds of for characters, to which he gave a local value very similar to the modern mode of notation_ The Greeks, however, were enabled., by means of
; their letters, to perform the common rules of subtraction, multiplication, and efi i vision, from which, no doubt, the idea was taken of working with letters in sue Algebra ; for it is worthy of eiservation, that in their multiplication they proceeded from left to right, as I. the multiplication of alixetra at present. The Greeks had likewise anther kind of no. Mien by mŪs of capitals, more property initials of the names of numbers, and were sued in iosseriptions, as I for is or pza, 1, II for rim, 5, A for Urn. 10,&c. The Ronan no tation, which is still used in and numbering chapters, arc. re aists of fire of their capital letters, namely, I one, V fire, X ten, L fifty, C one hundred, which are in creased in tile manner: the repetition of the Ps increases numbers by units, as II for two, III fur threr, fcc..; that of Vs increases num bers by tens, ae XX for twenty, Via for thirty, &a.; and that of C's increases num bers by hundred, as CO for two hundred, CCC for three hundred, de.; also a low cha racter before a greater crunkishes the valeta of the number, as I tare V, tims, IV, makes it km, I before X, thus, IX, makes it nine: on the ether hand, a le s character after a granter incomes the value of the number, as I osier V, thee, V1, makes it six, and I after X, time, tanker it eleven_ In what manner the Romans performed their arithmetical operations is not known; but it is most probable that, as they were not a commercial nation, they followed the simplest forma of calculation: we must therefore look for further information on this subject to the period when the Arabs or Sara cens introduced into Europe their mode of no tation, which is not only distinguished from the others by the peculiarity of the characters, but also by their value and disposition. Al though this notation consists of only nine di gits, with the cipher 0, yet by giving a local power to these figures, namely, that of units, tens, hundreds, thousands, &c. they may be made to express numbers to an indefinite ex tent. Besides, this mode also presents many advantages by the additional facility with which all arithmetical operations are thus per formed. By what nation this improvement was first made is not known. The Greeks, as before observed, were making advances to wards it by giving a local value to certain pe riods of four numbers each, but it does not ap pear that they proceeded any further. The Arabs introduced it into Europe about eight hundred years back, whence it soon circulated among the different European nations ; but al though the first use of this scale is commonly ascribed to them, yet they acknowledge them selves indebted to the Indians for it; and as this latter people were in many respects very ingenious, it is not at all improbable that they were the authors of the invention. The cul tivators of arithmetic in Europe may be dated from the thirteenth century, when Jordanus of Namur, the first writer on the subject that we know of; flourished. His arithmetic was published, with illustrations, by Joannes Faber Stapulensis, in the fifteenth century, but was less perfect than the treatises of Lucas de Bur-, go and Nicholas de Tartaglia in that and the subsequent centuries. In France, the subject of arithmetic was handled about the same time by Clavius and Remus; in Germany, by Sturinius, Stifelius, and Henischius ; and in England by Recorde, Diggs, and Buckley. After that period the writers on arithmetic be came too numerous to be particularly specified, but the names of Briggs, Emerson, Napier, Maclaurin, Hutton, and Bonnycastle, are en titled to notice, for having systematized, en larged, and in many particulars simplified the science.
ARK. The floating vessel in which Noah and his family were saved from the flood. It was 500 feet long, 90 broad, and 50 high.