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* EUCLID. 265 EUDES. etry who flourished at Alexandria. Nothing is known of his life except that 1'roelua tells us that he lived in the time of Ptolemy I. (who reigned B.C. 300-283). it is probable that the period of his greatest activity was in the neighborhood of B.C. 300. His fame was so great among the Greeks that he was called <5 CTTO^eiuriJ?, 'the author of the Elements,' and even to-day 1 the name Euclid is synonymous with elementary geometry. His S-o(,f(io, or 'Elements,' were well known to the Arabs, a portion having been translated in the time of llarun -al-Rashid, a second (complete) translation being made under Al-Mamun and oth- ers appearing later. It was translated from Arabic into Latin by Adelardof Bath(c.ll20), from a copy obtained in Spain ; and this translation, under the name of Giovanni Campano (12G0), was printed in 1482 at Venice. Billingsley's translation from the Latin into English appeared in 1570. The extant works unquestionably ascribed to Euclid are the Elements (Stoi ftio); the Data {liAofxtm) ; the Phenomena (Qawdpcva); theOptics ('Otttiko) ; the Reflections (KuToirTpiKdj; the Division of the Scale {KuTuToni) k&vovoc), and a work, De Did- sionibus, known only through the Arabic. The best editions of Euclid's works are: Peyrard, Les (rums d' Euclid in i/rec, en latin et en francais (Paris, 3 vols., 1814-18); Heiberg and Menge, Opera Omnia (Leipzig, 7 vols.. 1883-90 ). One of the best biographies of Euclid is that by De Mor- gan, in Smith's Dictionary of Greek and Roman Biography (under Eucleides). Consult, also: Gow, History of Greek Mathematics (Cambridge, 1884). and the authorities referred to under Mathematics. EUCLID. A native of Megara (fifth or fourth century B.C.). founder of the Megarian School of Philosophy. He was early influenced by the works of Parmenides apparently, from whom he learned not only philosophy, but the art of disputation. The fame of Socrates at- tracted him to Athens, where he became a de- voted follower of the great teacher. He estab- lished a school of his own at Megara. the teach- ing of which was distinguished by its combina- tion of Socratic and Eleatie principles. Euclid held to the unity of Being, as taught by Par- menides (q.v.), with the reality of the intellect (vove, ) and the moral ideas as set forth by Socrates. This self -identical Being, he taught, is the only reality and constitutes the good; it is not sensuous but intellectual being, i.e. reason, truth, which is for man the siimmum bonuin. Alter Socrates's death (B.C. 399) Plato and other disciples attached themselves for a time to the Me- garian School. From Euclid Plato probably got the germs of his doctrine of ideas ( etSrj ), a technical term, which Euclid first introduced into philosophy. In antiquity six dialogues were current under Euclid's name, but their authentic- ity was doubted. Nothing has survived. The date of his death is unknown. Consult: Deychs, De Uegaricorum Doctrina, etc. (Bonn, 1827 1 : Mallet. Histoire de I'ceole de Migare (Paris. 184",) ; Hartenstein, "Ueber die Bedeutung der Megarisehen Schule," in his His- torisch-Philosophische .1 bhandlungen ( Leipzig, 1870) ; Bitter and Preller, Historia Philosophies Orascm (Gotha, 1SSS) : Zeller, Philosophic der Oriechen, ii. (Leipzig, 1889) ; Ueberweg, History of Philosophy, trans, ed.. vol. i. (New York, 1872 1. EUD-ffi'MONISM (Gk. eMai/xono>u5s, evdai monismoB, thinking one happy, ii 5, i <•■. well + Salnwv, daimOn, genius, spirit). The Aristo- telian view i hat I he chief end "t human In happiness, and thai happiness is not pleasure, but an activity desirable not as a means t" some further end, Out lor its own sake. What this activity is, is discoverable, according to Aristotle, by ascertaining what the distinctive function of man is. The distinctive function of man is an activity of the soul in accordance with reason. Hence human happiness is the activity of soul in accordance with virtue, virtue being ill" mean between excess and defect as determined by reason. Pleasure is an essential element in such a life, for "pleasure and life are yoked together and do not admit of separation, as pleasure is impossible without activity and activity is per- fected by pleasure." See Enebgism. EUDE'MUS (Lat., from Gk. EMtj/uos) OP Rhodes. A Greek philosopher. He was a disciple and friend of Aristotle. He composed a number of works defending the doctrine of his master, and is probably the author of the Eudemian Ethics, pub- lished with Aristotle's writings, and in large part a reproduction of Aristotle's own work, t la- so-called .Y ieoinaehean Ethics. Eudemus also wrote, among other books, a history of mathe- matics and astronomy, which, however, is not ex- tant. A summary of it appears, however, in a commentary on Euclid written by Proclus (e. 410- 85), and numerous extracts are found in the work of later writers. Spengel collected the fragments of these works that still exist (18G0, 2d ed. 1870). Mullach also published them in his Fragmenta Philosophorum Grwcorum (vol. iii., 1881). Consult also Gow, History of Greek Mathematics (Cambridge, 1884 i. EUDES, ed ( also called Etjdon, Eudo, andODo) . Duke of Aquitainc, belonging to the close of the seventh century and the beginning of the eighth. He was independent ruler of southern France from the river Loire to the Pyrenees. In 721 he signally defeated the Arabs, who, under the lead- ership of Es-Samah, had invaded his dominions and besieged his capital of Toulouse. A treaty with Austrasia was broken in 731, and forthwith Charles Martel, the famous Austrasian maire du palais, began to harass the northern portion of Aquitaine. At this juncture the Arabs, com- manded by Abd-er-Rahman, reinvaded France. Elides was obliged to request the help of Charles, and a joint army, directed by the latter, won the decisive victory of Tours (732, known in French history as the battle of Poitiers). Consult Vic and Vaissete, Histoire ginirale de Languedoc, vol. i. (5 vols., 1730-45). EUDES, ed, Jean (1601-80). The founder of the Roman Catholic congregation of the EuDISTS. He was born at Mezeray. Normandy, France. No- vember 14, 1601 ; educated at the Jesuit College at Caen; entered the Congregation of the Oratory in Paris. 1023; wis ordained priest 1020, ids,, to be the superior of the Oratory at Caen, L639, and then founded in 1043 the Congregation of the Mission Priests of Jesus and Mary for the purpose of giving instruction to priests in practical and missionary wink. The members are called, commonly, Eudists. I hey resemble the Oratorians in that they are all priests, take no vows, and are at liberty to leave the Congregation when they please. They arc under episcopal