ARISTOTLE ARITHMETIC 707 regarded by Aristotle not as a product of the body, but as bestowed on it from outside, and as perfect only after its separation from the body by death. Proceeding from the principle that whatever is to be the goal and highest good of humanity must not depend on casual- ties and ever-changing minor circumstances, but must be certain in itself, and impart to every other good its value, he maintains that the eudaimonia, or highest possible pleasure which is conceivable for man, is derived only from the perfect satisfaction of those faculties which distinguish him from the beasts, that is, of the reasoning powers. Of his earliest pupils and followers, none but Theophrastus, and he not strictly a philosopher, is worth mentioning. The age after Aristotle's death was not favor- able to purely speculative philosophy. For three centuries Stoicism and Epicureanism took the place of his philosophy in the fa- vor of the educated world ; and these were succeeded by Neo-Platonism. Later the phi- losophy of Aristotle was rendered obnoxious to the fathers of the church by the pagan tendencies of its expounders at Alexandria, but a few, like Boethius, ventured to defend his views. Up to the llth century Aristotle was almost unknown to the Christian world, but he was a favorite with the Arabians of the 8th, 9th, 10th, and llth centuries. Through the Arabians, the scholastic writers of the llth century made acquaintance with his " Physics " and "Metaphysics," though by means of very imperfect translations; his "Logic" they had, though not extensively, known before. From that time Aristotle, though sometimes dispar- aged as a heretic, -remained for four centuries the authority of the Christian world in all mat- ters not strictly pertaining to dogmas. In the llth century the dispute between the nominal- ists and realists began to divide theologians; the realists asserting with Plato that our gen- eral notions, called universalia, are the sub- stance of things, that our ideas answer not only to the reality of objects, but contain their soul and life ; the nominalists, in the name of Aristotle, maintaining that these general no- tions are mere abstractions, inventions of the brain, not expressing the real substance of things. From the exposition that we have given, it appears that this pretended Aristote- lianism was a misunderstanding of Aristotle's philosophy, which, though it admits on the one hand that our general notions cannot be demonstrated to express the full substance of things, yet at the same time asserts that they are indispensable for every purpose of think- ing. -After the restoration of classical litera- ture in the 15th century, his writings were ex- tensively published, and his philosophy began to be better understood ; and it has been fur- ther developed by Bacon, Descartes, Spinoza, and Kant. Fichte, Schelling, and Hegel opposed it, though the latter adopted many of its ideas. It is, however, not so much by his philosophi- r 1 system that Aristotle has wielded his enor- mous influence, especially as this is only now beginning to be fully understood and justly ap- preciated, as by his logical inventions, and his method of philosophy in general. The best works on the contents, spirit, and bearings of the writings of Aristotle are Stahr's Aristote- lia (2 vols., Halle, 1830) ; Franz Biese's Phi- losophic des Aristoteles (2 vols., Berlin, 1835- '42); and "Aristotle," a posthumous work, by George Grote (London, 1872). The best com- plete edition of Aristotle is that of the academy of sciences at Berlin, by Immanuel Bekker (4 vols., Berlin, 1831-'6), with Latin transla- tions and extracts from the old commentaries. ARISTOXEMIS, a Greek writer on philosophy and music, a pupil of Aristotle, born at Taren- tum, Italy, flourished about 320 B. C. Ac- cording to Suidas, he published 450 works on all imaginable subjects. All these are lost ex- cepting his 'ApfioviKa Zro^em ("Principles of Harmony "), published in Latin at Leyden in 1562 by Gogarinus, and in 1616 in Greek by Meursius, and subsequently inserted by Meibom in the Antiques Musicm Auctores (2 vols. 4to, Amsterdam, 1652). Aristoxenus's theories of music were opposed to those of Pythagoras, who made music dependent upon mathematics, while the former admitted only the test of the ear. ARITHMETIC (Gr. apiQ^-riK.^ from api6[iEiv, to count), the science of the properties and rela- tions of numbers when expressed with figures or relations of figures. The accepted opinion is that we have derived this science from the Greeks, who obtained it from the Phoenicians ; but if we consider that the Chaldeans, one of the oldest nations, have given us the knowledge of certain astronomical cycles or periods, of which the determination required an advanced knowl- edge of arithmetic, it is evident that its origin is of much earlier date. The Hebrews and Greeks used the first nine letters of their alphabet for the numbers 1 to 9 ; the next nine letters for 10, 20, &c., to 90 ; and the others for hundreds ; while for thousands they recommenced the alphabet and added to each letter a mark or iota. The Romans followed a similar system, of which our Roman numerals are a specimen. But arithmetic did not reach its more modern state of progress until the introduction of the Arabic figures now used by all civilized nations. The Arabs admit that they obtained these fig- ures from Hindostan in the 10th century. They call them Indian figures, and arithmetic the In- dian science. Boethius, in his work De Oeome- tria, informs us that the disciples of Pythagoras used in their calculations nine peculiar figures, while others used the letters of the alphabet ; and it is probable that this philosopher, who had travelled considerably, had obtained this knowledge in Hindostan, and communicating it as a secret to his disciples, caused it to remain sterile in their hands. The Greeks in the ordi- nary way of writing expressed the fractions thus : while /?, y, <J, &c., stood for 2, 3, 4, &c., /?', y', d', represented , , ^, &c. The oldest text boqk
