Euclid Vyu-kl3d\ (fl. c. 300 bc, Alexandria, Egypt) Greek mathematician of antiquity, known primarily for his highly influential treatise on geom¬ etry, the Elements. He founded a school in Alexandria during the reign of Ptolemy I. Little is known of his life, but there are many anecdotes. In the most famous, asked by Ptolemy if there is a shorter way to geometry than through his Elements , Euclid replies, “There is no royal road to geometry.” The Elements, based on the works of earlier mathematicians, is a brilliant synthesis of old and new. It has been a major influence on rational thought and a model for many philosophical treatises, and it has set a standard for logical thinking and methods of proof in the sciences. The starting point not just of Euclidean geometry but of an approach to reasoning, it is sometimes said to be the most translated, published, and studied work after the Bible.
Euclidean geometry Study of points, lines, angles, surfaces, and sol¬ ids based on Euclid’s axioms. Its importance lies less in its results than in the systematic method Euclid used to develop and present them. This axi¬ omatic method has been the model for many systems of rational thought, even outside mathematics, for over 2,000 years. From 10 axioms and pos¬ tulates, Euclid deduced 465 theorems, or propositions, concerning aspects of plane and solid geometric figures. This work was long held to consti¬ tute an accurate description of the physical world and to provide a suf¬ ficient basis for understanding it. During the 19th century, rejection of some of Euclid’s postulates resulted in two non-Euclidean geometries that proved just as valid and consistent.
Euclidean space In geometry, a two- or three-dimensional space in which the axioms and postulates of Euclidean geometry apply; also, a space in any finite number of dimensions, in which points are designated by coordinates (one for each dimension) and the distance between two points is given by a distance formula. The only conception of physical space for over 2,000 years, it remains the most compelling and useful way of mod¬ eling the world as it is experienced. Though non-Euclidean spaces, such as those that emerge from elliptic geometry and hyperbolic geometry, have led scientists to a better understanding of the universe and of mathemat¬ ics itself. Euclidean space remains the point of departure for their study.
eudaemonism Xyu-'de-mo-.ni-zonA In ethics, the view that the ultimate justification of virtuous activity is happiness. Virtuous activity may be conceived as a means to happiness, or well-being, or as partly constitu¬ tive of it (see teleological ethics). Ethical eudaemonism should be distin¬ guished from psychological eudaemonism, which holds that happiness is the ultimate motive of virtuous activity.
Eudocia Macrembolitissa Vyu-'do-sho-.mak-rom-.ba-b-'ti-soV (b. 1021, Constantinople, Byzantine Empire—d. 1096, Constantinople) Byz¬ antine empress and regent, called the wisest woman of her time. As the wife of Constantine X Ducas, she became regent for her three sons after his death (1067). To fend off the Seljuq Turks, she married a Cappado¬ cian general, Romanus Diogenes (later Romanus IV Diogenes). After his capture at the Battle of Manzikert (1071), Eudocia and her son Michael ruled jointly and deposed Romanus. After Michael succeeded to the throne, Eudocia entered a convent.
Eugene City (pop., 2000: 137,893), western Oregon, U.S. Located on the Willamette River, it was settled by Eugene Skinner in 1846. Named Eugene City in 1853, it grew as an agricultural and lumber centre with the arrival of the railroad in 1870. It is the site of the University of Oregon (founded 1872) and Northwest Christian College (1895). It is a tourist centre for the MacKenzie River recreational area and Willamette National Forest.
Eugene of Savoy orig. Francois-Eugene, prince de Savoie- Carignan (b. Oct. 18, 1663, Paris, France—d. April 24, 1736, Vienna, Austria) French-Austrian general. Born in Paris, he was the son of the count de Soissons, of the house of Savoy-Carignan, and of Olympe Man- cini (see Mancini family), niece of Jules Mazarin. Louis XIV severely restrained Eugene’s ambitions, prompting him to leave France and enter the service of Emperor Leopold I. He later served Joseph I and Charles VI. He quickly distinguished himself in battle and advanced in rank to impe¬ rial field marshal at age 29. He fought notably against the Turks in cen¬ tral Europe and the Balkans and against France in the War of the Grand
Alliance and the War of the Spanish Succession. With his friend the duke of Marlborough, he won the important victory at the Battle of Blenheim (1704) and ousted the French from Italy. In 1718 he won a great triumph over the Turks, taking the city of Belgrade. He later served as governor in the Austrian Netherlands (1714-24). An outstanding strategist and an inspired leader, he was regarded as one of the greatest soldiers of his gen¬ eration.
eugenics \yu-'je-niks\ Study of human improvement by genetic means. The first thorough exposition of eugenics was made by Francis Galton, who in Hereditary Genius (1869) proposed that a system of arranged marriages between men of distinction and women of wealth would even¬ tually produce a gifted race. The American Eugenics Society, founded in 1926, supported Galton’s theories. U.S. eugenicists also supported restric¬ tion on immigration from nations with “inferior” stock, such as Italy, Greece, and countries of eastern Europe, and argued for the sterilization of insane, retarded, and epileptic citizens. Sterilization laws were passed in more than half the states, and isolated instances of involuntary steril¬ ization continued into the 1970s. The assumptions of eugenicists came under sharp criticism beginning in the 1930s and were discredited after the German Nazis used eugenics to support the extermination of Jews, blacks, and homosexuals. See also genetics, race, social Darwinism.
Eugenie \oe-zha-'ne\ orig. Eugenia Maria de Montijo de Guzman (b. May 5, 1826, Granada, Spain—d. July 11, 1920, Madrid) Wife of Napoleon III and empress of France (1853-70). Daughter of a Spanish noble, she married Napoleon III in 1853 and came to have an important influence on her husband’s foreign policy. As a devoted Roman Catholic, she favored a strong papacy and supported Ultramontane causes. She also encouraged French opposition to a Prussian candidate for the Spanish throne in the controversy that precipitated the Franco-Prussian War. After the French defeat at Sedan, she joined her family in exile in England.
Eugenius \yu-'je-ne-os\ III orig. Bernard of Pisa (b. near Pisa—d. July 8, 1153, Tivoli, near Rome; beatified 1872; feast day July 8) Pope (1145-53). A Cistercian abbot, he was elected pope when Rome was on the verge of anarchy, and in 1146 he was forced into exile. While in France he supported Louis VII’s intention to launch the Second Crusade to free Edessa, an effort that ended in failure. He returned to Italy (1148), but the hostility of the Senate often kept him away from Rome. In the Treaty of Constance (1153) Eugenius fixed conditions for the coronation of Fred¬ erick I Barbarossa but died before it could take place.
euhemerism Nyii-'he-mo-.ri-zomX Attempt to find a historical basis for mythical beings and events. It takes its name from Euhemerus (fl. 300 bc), a Greek scholar who examined popular mythology in his Sacred His¬ tory and asserted that the gods originated as heroes or conquerors who were admired and later deified. Though modem scholars do not accept euhemerism as the sole explanation for the origin of gods, it is thought to be valid in some cases.
eukaryote \yu-'kar-e-,ot\ Any organism composed of one or more cells, each of which contains a clearly defined nucleus enclosed by a membrane, along with organelles (small, self-contained, cellular parts that perform specific functions). The organelles include mitochondria, CHLO- roplasts, a Golgi apparatus, an endoplasmic reticulum, and lysosomes. All organisms except bacteria are eukaryotes; bacteria are prokaryotes.