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»oon surpassed all in Plato ’s school. He ate little, ami slept less :and that lie might not oversleep himself, Diogenes Laertius tells us,that he lay always with one hand out of the lied, having a ball ofbrass in it, which, by its falling into a bason of the same metal,awaked him. He had several conferences with a learned Jew atAthens, who instructed him in the sciences and religion of theEgyptians , and thereby saved him the trouble of travelling intoEgypt. 1 'pon the death of Plato he quilted Athens, and retiredto j^tarnya, where he married Pythias, the sister of Ilermias,.prince of Mysia. Philip king of Macedon having heard of hisgreat reputation, sent for him to be tutor to his son Alexander,then about 14 years of age: Aristotle accepted the offer ; and ineight years taught him rhetoric, natural philosophy, ethics, po-litics, and a certain sort of philosophy, which, says Plutarch , hetaught nobody else. Philip erected statues in honour of Aristotle ;and for his sake rebuilt Stagira , which had been almost ruined bythe wars. The last 14 years of his life he spent mostly at Athens,surrounded with every assistance which men and books could af-ford him, for prosecuting his philosophical inquries. Here hecomposed his principal works, particularly his Animal History ,which he undertook at the request of Alexander, who suppliedhiuu with subjects, and liberally rewarded him. Aristotle hadmany disciples, who, because he generally delivered his lectures
walking,' were denominated Peripatetics. Being accused of im-piety, lie wrote an apology for himself, addressed to the magi-strates ; lint he soon after quitted Athens, and spent the remain-der of his days at Chalcis, a city in Euboea. Some say that heput an end to himself by poison ; others that lie cast himself intothe strait of Euripus, because he could not comprehend the reasonof its ebbing and flowing; and some assert, that he died of thecolic, in the '<i3d year of his age, 15. C. 323. His body was car-ried away by his countrymen, who erected altars to his memory.11 is works may be classed under the heads ef rhetoric, poetry,politics, ethics, physics, mathematics, logic, and metaphysics;and, in the words of an elegant writer, “ whoever surveys thevariety and perfection of his productions, all delivered in thechastest style, in the clearest order, and the most pregnant bre-vity, is amazed at the immensity of his genius.” No philosopherlias had more commentators than Aristotle . His philosophy was,'almost universally received as a sacred system of truth. DesCartes was the first who had courage publicly to controvert hisdoctrines. The Editio Princeps of his works, Gr. 6 vol. fol.Venet. ap Aid. is very scarce and valuable. The Paris edition,1629, 2 vol. fol. is highly esteemed. As is Tyrrwhit’s edition ofthe Toetica, Oxon, 4to. 1794.
(1.) ARITHMETIC , [from number, and to
measure,] is a science which explains the properties of numbers,and shows the method or art of computing by them. The lateDr. Robertson justly stiles it, the most perfect of the sciences.
History of Arithmetic.
(2.) It is certain that something of Arithmetic was known fromthe first ages of the world. We cannot conceive how any mailendowed with reason can be without some knowledge of numbers.Some American nations, we are told, express their greatest num-ber three, by the term pattarrarorincouroac: hut that such nationsshould have'no idea of a greater number than this, is absolutelyincredible. Perhaps they may compute by threes, as we computebv tens; and this may "have occasioned the notion that they haveno greater number than three.
But though we cannot suppose any nation ever to have beenwithout some knowledge of numbers, yet mankind may havesubsisted for a considerable time, without bringing this science toany perfection, or computing by any regular scale, as 10, 60, Sec.Tins, however, was accomplished before the flood, as appears fromEnoch ’s prophecy, mentioned by the apostle Jude: Behold, theLord cometli with ten thousands of his saints.” This shows, thateven then they had ideas of numbers to any limits, and Com-puted them also by tens.
The directions given to Noah, concerning the dimensions ofthe ark, prove that he had a knowledge both of numbers andmeasures. When Rebekah was sent to Isaac, Abraham’s son, herrelations wished she might be the mother of thousands of millions;and if they were totally unacquainted with the nature of multi-plication, it is difficult to see how such a wisli could have beenformed.
Some nations, however, like the Europeans formerly, and theAfricans and Americans now, have doubtless been immersed inthe most abject and deplorable state of ignorance; and mighttherefore remain h r s. tnc time with very little knowledge ofnumbers. •
(3.) Dr. Chambers thinks it highly probable, that arithmetic,as a science, must have taken its rise from the introduction ofcommerce ; and consequently that it should he of Tyrian in-vention.
From Adi it p.t set into Egypt, says Josephus , by means ofAbraham. Here it was greatly cultivated and improved ; inso-much that a large part of the Egyptian philosophy and theologyseems to have turned altogether upon numbers. Ilence those
wonders related by them about unity, trinity, the numbers seven,ten, four, Sec. In fact, Kircher, (in his (Edip. -Egypt . tom. 2.p. 2.) shews, that the Egyptians explained every thing by num-bers. Pythagoras affirms, that the nature of numbers goes throughthe whole universe; and that the knowledge of numbers is theknowledge of the Deity .
From Egypt arithmetic was transmitted to the Greeks, whowere doubtless the first European nation among whom arithmeticarrived at any degree of perfection. M. Goguel is of opinion,they used pebbles in their calculations: a proof of which he ima-gines is, that the word which comes from 4’ipB', a lillle
stone, or Hint, among other things, signifies to calculate. Thesame, he thinks, is probable of the Romans; and derives theword calculation from the use of little stones (calculi) in their firstarithmetical operations.
This method, however, must have been but for a short time, sincewe find the Greeks very early made use of the letters of the al-phabet, taken according to llieir order, at first denoting the num-bers 1, 2, 3, 4, 5, 7, 8, <), 10, 20, 30, 40, 50, 60, 70, 80, 100,200, 300, 400, 500, 600, 700, and 800; to which they added thethree following, r, \ to represent 6, <J0, 900. The diffi-culty of performing arithmetical operations by such marks as thesemay easily be imagined, and is very conspicuous from Archi-medes ’s treatise concerning the dimensions of a circle.
(4.) A similar method was followed by the Romans ; and be-sides characters for each rank of classes, (hey introduced othersfor five, fifty, and five hundred. Their method is still used fordistinguishing tile chapters of hooks, and some other purposes.Their numeral letters and values are the following:
I V X L C
One, five, ten, fifty, one hundred,
1) M
Five hundred, one thousand.
Any number, however great, may be represented by repeatingand combining these according to the following rules :
1st, When the same letter is repeated twice, or oftener, its va-lue is represented as often. Thus 11, signifies two; XXX, thirty;CC, (wo hundred.
2d, When a numeral letter of less value is placed after oneof greater, their values are added: thus XI signifies eleven, LXVsixty-live, DCVIII signifies six hundred and eight, MDCXXYIIIone thousand six hundred and twenty-eight.
3d, When a numeral letter of less value is placed beforeone of greater, the value of the less is taken from that of the
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