A very full account of Aristotle's writings and of his system (from the Hegelian point of view), by Prof. Stahr, is given in Smith, Diet, of Gr. and Roman Biog. etc., vol. i. For an excellent sketch of the Lift of Aristotle, by Prof. Park, see Bibliothcca Sacra, vol. i. The literature of the subject is copiously given in Stahr's article above referred to. See also Maurice, Moral and Metapli. Philosophy, ch. vi, div. iii ; Hau- reau, Philosophic Scliolastiqtie, vol. i; Gioberti, Tntrod. a l' etude de la Pkilnso/Jtie, i, 08 ; Litter, History ofPhi- losophy, vol. iii; North British Rev. Nov. 1858; Am. Bib. Repos. July, 1842; Meth. Quart. Rev. July, 1853, 342 sq. ; Biese, Plains. d.Arisfofe (Berlin, 1835, 2 vols. 8vo) ; St. Ililaire, Logique d'Aristote (Par. 1838, 2 vols. 8vo); Ravaisson, La Mitaphjshpie d'Aristote (Paris, 1840, 2 vols. 8vo) ; Vacherot, Theorie des prem.principes scion Aristote (Par. 1836, 8vo) ; Simon, du Dieu d'Aris- tote (Par. 1840, 8vo). ; Wetzor u. Welte, Kircken-Lexi- J;on, i, 412. For references as to the influence of Aris- totle on Christian theology, see Scholasticism.
Arithmetic, or the science of numbers, was un- questionably practised as an art in the dawn of civil- ization ; since to put things or their symbols together (addition), and to take one thing from another (sub- traction), must have been coeval with the earliest ef-
ARIUS
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forts of the human mind ; and what are termed multi- plication and division are only abbreviated forms of ad- dition and subtraction. The origin, however, of the earliest and most necessar)- of the arts and sciences is lost in the shades of antiquity, since it arose long be- fore the period when men began to take special notice and make some kind of record of their discoveries and pursuits. In the absence of positive information, we seem authorized in referring the lirst knowledge of arithmetic to the East (see Edinburgh Review, xviii, 185). From India, Chaldaja, Phoenicia, and Egypt the science passed to the Greeks, who extended its laws, improved its processes, and widened its sphere. To what extent the Orientals carried their acquaintance with arithmetic cannot be determined. The greatest discovery in this department of the mathematics, namely, the establishment of our system of ciphers, or of figures considered as distinct from the letters of the alphabet, belongs undoubtedly, not to Arabia, as is generally supposed, but to the remote East, probably India. It is to be regretted that the name of the dis- coverer is unknown, for the invention must be reckon- ed among the greatest of human achievements. Our numerals were made known to these AVestern parts by the Arabians, who, though they were nothing more than the mediums of transmission, have enjoyed the honor of giving them their name. These numerals were unknown to the Greeks, who made use of the let- ters of the alphabet for arithmetical purposes (see En- cyclopedia Metropolitana, s. v.). The Hebrews were not a scientific, but a religious and practical nation. What they borrowed from others of the arts of life they used without surrounding it with theory, or ex- panding and framing it into a system. So with arith- metic, designated by them by some form of the verb il3"0, manati , signifying to determine, limit, and thence to number. Of their knowledge of this science little is known more than may be fairly inferred from the pur- suits and trades which they carried on, for the suc- cessful prosecution of which some skill at least in its simpler processes must have been absolutely necessary; and the large amounts which appear here and there in the sacred books serve to show that their acquaintance with the art of reckoning was considerable. See Number. Even in fractions they were not inexperi- enced (Gesenius, Lehrgeb. p. 704). For figures, the Jews, after the Babylonish exile, made use of the let- ters of the alphabet, as appears from the inscriptions on the so-called Samaritan coins (Eckhel, Doctr. Num. i, iii, 468) ; and it is not unlikely that the ancient He- brews did the same, as well as the Greeks, who bor- rowed their alphabet from the Phoenicians, neighbors of the Israelites, and employed it instead of numerals (Schmidt, Biblischer Mathematicus, Tub. 1735, 1749). — Kitto, s. v. See Abbreviation.
Arius.born toward the close of the third century, in Libya, according to others, in Alexandria. He wrote a theological work, Timlin, extracts from which are given in the writings of Athanasius. He died in 336. For his doctrines and their history, see Arianism.
Ark is used in the Bible to designate three vessels of special importance.
1. Noah's Ark (fiat), tebah'; Sept. «/3wr<5c, a rh st : Josephus \dpvaZ, a coffer; Vulg. area, Gen. vi, 11), different from the term "pIX, arm', applied to the " ark'' of the covenant, and other receptacles which we know to have been chests or coffers, but the same that is applied to the " ark" in which Moses was hid (Exod. ii, 3), the only other part of Scripture in which it oc- curs. In the latter passage the Septuagint renders it Otjli], a ship; but the truth seems to be that aron de- notes any kind <>t' chest or coffer, while the exclusive application of tebah to the vessels of Noah and of Mo- ses would suggest the probability that it was restricted to such chests or arks as were intended to float upon