Eulenspiegel Vofiil-on-.shpe-gslA English Voil-on-.spe-golV Till Ger¬ man peasant trickster of folk and literary tales. The historical Till is said to have died in 1350; anecdotes associated with his name were printed c. 1500 in Low German and from 1515 in High German. In the tales the stupid yet cunning peasant demonstrates his superiority to the narrow, dishonest, condescending townsmen, as well as to the clergy and nobil¬ ity. The tales were translated into Dutch and English (c. 1520), French (1532), and Latin (1558).
Euler Voi-laA, Leonhard (b. April 15, 1707, Basel, Switz.—d. Sept. 18, 1783, St. Petersburg, Russia) Swiss mathematician. In 1733 he suc¬ ceeded Daniel Bernoulli (see Bernoulli family) at the St. Petersburg Acad¬ emy of Sciences. There he developed the theory of trigonometric and logarithmic functions and advanced mathematics generally. Under the patronage of Frederick the Great, he worked at the Berlin Academy for many years (1744-66), where he developed the concept of function in mathematical analysis and discovered the imaginary logarithms of nega¬ tive numbers. Throughout his life he was interested in number theory. In
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642 i Euler's formula > Europa
addition to inspiring the use of arithmetic terms in writing mathematics and physics, Euler introduced many symbols that became standard, including £ for summation; Jn for the sum of divisors of ir, e for the base of the natural logarithm; a, b, and c for the sides of a triangle with A, B, and C for the opposite angles; f[x) for a function; n for the ratio of the circumference to the diameter of a circle; and i for V-l. He is considered one of the greatest mathematicians of all time.
Euler's formula Either of two important mathematical theorems of Leonhard Euler. The first is a topological invariance (see topology) relat¬ ing the number of faces, vertices, and edges of any polyhedron. It is writ¬ ten F + V = E + 2, where F is the number of faces, V the number of vertices, and E the number of edges. A cube, for example, has 6 faces, 8 vertices, and 12 edges, and satisfies this formula. The second formula, used in trigonometry, says e “ = cos x + /sin x where e is the base of the natural logarithm and / is the square root of -1 (see irrational number). When x is equal to n or 2k, the formula yields two elegant expressions relating n, e, and /: = -1 and e 2lli = 1.
Eumenes Vyii-ma-.nezX II (d. 160/159 bc) King of Pergamum (197 bc-c. 160). He continued the policy of his father, Attalus I Soter, of coopera¬ tion with Rome. He helped defeat Antiochus III, thus enlarging his realm. He brought his kingdom to its height and made it a great centre of Greek culture; in particular, he is credited with constructing nearly all the pub¬ lic buildings and sculpture on the Pergamum acropolis. He was suspected of disloyalty in the Roman struggle against Perseus; Rome subsequently withdrew its support, and Eumenes’s power and the glory of Pergamum declined. His brother Attalus II became coruler c. 160 bc.
Eumolpus \yu-'mal-p3s\ Mythological ancestor of the priestly class, the Eumolpids, at Eleusis in ancient Greece. His name means “sweet singer.” Three divergent identities for him exist in legend: he is the father, son, or pupil of Musaeus, a mythical singer connected with Orpheus, in one; an originator of the Eleusinian Mysteries in another; and a king of Thrace and son of Poseidon in a third.
eunuch Vyii-nokV Castrated human male. From remote antiquity on, eunuchs were employed in the Middle East and China as guards and ser¬ vants in harems or other women’s quarters and as chamberlains to kings. The eunuchs’ confidential position frequently enabled them to exercise an important influence over their royal masters. Many of the patriarchs of Constantinople during Byzantine times were eunuchs. Eunuch advisers disappeared as a class only with the end of the Ottoman Empire. See also CASTRATO.
euonymus \yu-'a-n3-m9s\ Any of about 170 species of shrubs, woody climbers, and small trees that make up the genus Euonymus (family Celas- traceae), native to temperate Asia, North America, and Europe, including many popular landscape ornamental shrubs and ground covers. The winged spindle tree ( E. alata ), also called burning bush, is a handsome shrub with corky winged stems. Wood of the common spindle tree {E. europaea) is used for pegs and spindles; several varieties are grown as ornamentals.
euphonium \yu-'fo-ne-9m\ or tenor tuba Large valved brass instru¬ ment, the leading lower-pitched instrument in military bands. It developed from the valved bugle and cornet in Germany c. 1840. It has four valves and a wide conical bore resembling the tuba’s. Its range is an octave below the trumpet and comet. It is played either vertically or with the bell fac¬ ing forward. The very similar baritone has the same range and transpo¬ sition and is distinguished only by its narrower bore. Both are essential members of bands of all kinds and are often given significant solo roles.
euphorbia See spurge
Euphranor \yu-'fra-nor\ (b. c. 390 bc, Greece—d. c. 325, Athens?) Greek sculptor and painter active in Athens. The only surviving work identified as his is the fragments of a colossal marble statue of Apollo (c. 330 bc) found in the agora at Athens. Other recorded (but lost) works suggest that he was one of the foremost Athenian artists of the mid 4th century bc. He also wrote treatises on proportion and colour.
Euphrates \yu-'fra-tez\ River Turkish Firat Nehri \f3-'rat-ne-'re\ Arabic Nahr al Furat River, Middle East. The largest river in South¬ west Asia, it rises in Turkey and flows southeast across Syria and through Iraq. Formed by the confluence of the Karasu and the Murat rivers in the high Armenian plateau, the Euphrates descends between major ranges of the Taurus Mountains to the Syrian plateau. It then flows through western
and central Iraq to unite with the Tigris and continues, as Shatt al-Arab, to the Persian Gulf. In all, it is 1,740 mi (2,800 km) long. Its valley was heavily irrigated in ancient times, and many great cities, some of whose ruins remain, lined its banks. With the Tigris, it defines an area known historically as Mesopotamia.
Euphronius \yu-'fro-ne-9s\ or Euphronios (fl. c. 520^-70 bc, Ath¬ ens, Greece) Greek vase painter and potter. His signature has been iden¬ tified on 20 vessels, 8 that he signed as painter and 12 as potter. He was an outstanding early proponent of red-figure pottery. His best-known work as a painter is a krater in the Louvre depicting Herakles wrestling Antaeus. As a potter, he worked with the finest vase painters of his time. His great¬ est rival was Euthymides.
Eure River \'oer\ River, northern France. From its source in the Perche Hills it flows chiefly through agricultural and wooded regions on its 140-mi (225-km) course, passing through Chartres below the cathedral, which is located on high ground on its left bank. It joins the Seine above Rouen.
Euripides Vyu-'ri-po-.dezN (b. c. 484 bc, Athens—d. 406 bc, Macedonia) Greek playwright. With Aeschylus and Sophocles, he is recognized as one of Athens’s three great tragic dramatists. An associate of the philosopher Anaxagoras, he expressed his questions about Greek religion in his plays. Beginning in 455, he was repeatedly chosen to compete in the dramatic festival of Dionysus; he won his first victory in 441. He competed 22 times, writing four plays for each occasion. Of his 92 plays, about 19 survive, including Medea (431), Hippolytus (428), Electra (418), The Trojan Women (415), Ion (413), Iphigenia at Aulis (406), and The Bac- chae (406). Many of his plays include prologues and rely on a DEUS ex machina. Unlike Aeschylus and Sophocles, Euripides made his characters’ tragic fates stem almost entirely from their own flawed natures and uncon¬ trolled passions. In his plays chance, disorder, and human irrationality and immorality frequently result in apparently meaningless suffering that is looked on with indifference by the gods.
Euripus See Chalkis