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ARISTOXENUS. were denned by simple ratios which were either
superpariicular (of the form ———j or multiple
(of the form _^ From this facts he or his followers
inferred, that no interval could be consonant which was denned by a ratio of a different kind; and hence they were obliged to maintain (contrary to the evidence of the senses), that such intervals as the octave and fourth (the eleventh], for example, were dissonant. Aristoxenus justly blamed them for their contempt of facts, but went into the opposite extreme of allowing too much authority to the decisions of the ear, though without denying the existence of a certain truth in the arithmetical theory (p. 33). He maintains, for instance, not only that every consonant interval added to the octave produces another consonance, which is true ; but also that t\\Q fourth is equal to two tones and a half (p. 56), the falsity of which proposition is not directly apparent to the ear, but indirectly would become evident by means of the very experiment which he suggests for the confirmation of it. (See Porphyr. Comm. in PtoL Harm, in Wallis, Op. vol. iii. p. 211, and Wallis's appendix, pp. 159,169 ; Burney, vol. i chap, v.; Theon Smyrn. p. 83, ed. Bulliald. and not. p. 202.) The titles of a good many other works of Aristoxenus have been collected from various sources by Meursius and others. (See Fabric. Bibl. Grace, vol. ii. p. 257 ; Clinton, F. H. vol. ii. appendix, c. 12.) Among them are lives of Pythagoras, Arcliytas, Socrates, Plato, and other
distinguished persons; and several treatises on subjects connected with music, including one Ilept TpayiK-fjs 'OjOXTjVecos, and one Tiepl AuAcoz' Tpri-trews. A fragment of cPv6/MKa <rT0i%€?a was edited by Morelli, Ven. 1785. A collection of fragments of the other works is given in the essay by Mahne referred to below.
The three books of 'Ap/JioviKa ffroixeTa were first edited in Latin, with the Harmonics of Ptolemy, by Ant. Gogavinus, Ven. 1562. The Greek text, with Alypius and Nicomachus, by Meursius (Lugd. Bat. 1616), who, like his predecessor, seems not to have had sufficient musical knowledge for the task. The last and best edition is at present that of Meibomius, printed (with a Latin version) in the Antiquae Musicae Auctores Septem, Amst. 1652.
(Mahne, Diatribe de Aristoxeno philosoplio Peri- patetico, Amst. 1793.) [W. F. I).]
ARISTOXENUS (*Apiffrfavos). 1. Of Se-linus in Sicily, a Greek poet, who is said to have been the first who wrote in anapaestic metres. Respecting the time at which he lived, it is expressly stated that he was older than Epicharmus, from about b. c. 540 to 445. (Schol. ad Aristoph. Plut. 487 ; Hephaestion, EncJdrid. p. 45, ed. Gaisf.) Eusebius (Chron. p. 333, ed. Mai) places him in 01. 29 (b. c. 664), but this statement requires some explanation. If he was born in that year, he cannot have been a Selinuntian, as Selinus was not founded till about b. c. 628. But Aristoxenus may perhaps have been among the first settlers at Selinus, and thus have come to be regarded as a Selinuntian.
2. A Cyrenaic philosopher, who appears not to have been distinguished for anything except his gluttony, whence he derived the surname of KcoAiif. (Athen. i. p. 7 ; Suid. s. v. 'Apio-To^evos.} [L. S.]
Moro. A cut. iii. 16, p. 233), who was a pupil of Alexander Philalethes (Galen. De Differ. Puls. iv. 10, vol. viii. p. 746), and must therefore have lived about the beginning of the Christian era. He was a follower of Herophilus (ibid.-C. 7. p. 734), and studied at the celebrated Herophilean school of medicine, established in Phrygia, at the village of Men-Carus, between Laodicea and Carura. He wrote a work ITepl ttjs 'Hpo<£iAou Azpecrews, De Herophili Secta9 of which the thirteenth book is quoted by Galen (ibid. c. 10. p. 746), and which is not now extant. (Mahne, " Diatribe de Aris toxeno," Amstel. 1793, 8vo.) [W. A. G.]
ARISTUS (''AporTos), of Salamis in Cyprus, a Greek historian, who wrote a history of Alexander the Great, in which he mentioned the embassy of the Romans to Alexander at Babylon. (Arrian, Anab. vii. 15 ; Athen. x. p. 436 ; Clemens Alex. Protrept. p. 16; Strab. xiv. p. 682.) That he lived a considerable time later than Alexander, may be inferred from Strabo (xv. p. 730), although it is impossible to determine the exact time at which he lived. Some writers are inclined to be lieve that Aristus, the historian, is the same per son as Aristus the academic philosopher, who was a contemporary and friend of Cicero, who taught philosophy at Athens, and by whom M. Brutus was instructed. This philosopher moreover was a brother of the celebrated Antiochus of Ascalon. But the opinion which identifies the historian and philopher, is a mere hypothesis, supported by nothing but the circumstance that both bore the same name. (Cic. Brut. 97, de Finib. v. 5, Academ. i. 3, ii. 4, Tuscul. Quaest. v. 8, ad AH. v. 10 ; Plut. Brut. 2.) [L. S.]
ARISTYLLUS ('ApiVruAAos), a Greek astro nomer, who appears to have lived about b. c. 233. (Plut. de PytJi. Orac. 18.) He wrote a work on the fixed stars (rfipriffis atrXavwv}, which was used by Hipparchus and Ptolemy (Mayn. Synt. vii. 2), and he is undoubtedly one of the two persons of this name who wrote commentaries on Aratus, which are now lost. [L. S.]
ARIUS or AREIUS fApem), the celebrated heretic, is said to have been a native of Libya, and must have been born shortly after the middle of the third century after Christ. His father's name appears to have been Ammonius. In the religious disputes which broke out at Alexandria in a. D. 306, Arius at first took the part of Mele-tius, but afterwards became reconciled to Peter, bishop of Alexandria, and the opponent of Mele-tius, who made Arius deacon. (Sozom. H. E. i. 15.) After this Arius again opposed Peter for his treatment of Meletius and his followers, and was in consequence excommunicated by Peter. After the death of the latter, Achillas, his successor in the see of Alexandria, not only forgave Arius his offence and admitted him deacon again, but ordained him presbyter, a. D. 313, and gave him the charge of the church called Baucalis at Alexandria. (Epiphan. Haeres. 68. 4.) The opinion that, after the death of Achillas, Arius himself wanted to become bishop of Alexandria, and that for this reason he was hostile to Alexander, who became the successor of Achillas, is a mere conjecture, based upon the fact, that Theodo-ret (H. E. i. 2) accuses Arius of envy against Alexander. The official position of Arius at Alexandria, by virtue of which he interpreted the Scriptures, had undoubtedly gained for him already