Aristotle (b. 384, Stagira—d. 322 bc, Chalcis) Greek philosopher and scientist whose thought determined the course of Western intellectual his¬ tory for two millenia. He was the son of the court physician to Amyntas III, grandfather of Alexander the Great. In 367 he became a student at the Academy of Plato in Athens; he remained there for 20 years. After Pla¬ to’s death in 348/347, he returned to Macedonia, where he became tutor to the young Alexander. In 335 he founded his own school in Athens, the Lyceum. His intellectual range was vast, covering most of the sciences and many of the arts. He worked in physics, chemistry, biology, zoology, and botany; in psychology, political theory, and ethics; in logic and meta¬ physics; and in history, literary theory, and rhetoric. He invented the study of formal logic, devising for it a finished system, known as syllogistic, that was considered the sum of the discipline until the 19th century; his work in zoology, both observational and theoretical, also was not surpassed until the 19th century. His ethical and political theory, especially his con¬ ception of the ethical virtues and of human flourishing (“happiness”), continue to exert great influence in philosophical debate. He wrote pro- lifically; his major surviving works include the Organon, De Anima (“On the Soul”), Physics, Metaphysics, Nicomachean Ethics, Eudemian Ethics, Magna Moralia, Politics, Rhetoric, and Poetics, as well as other works on natural history and science. See also teleology.
arithmetic Branch of mathematics that deals with the properties of numbers and ways of combining them through addition, subtraction, mul¬ tiplication, and division. Initially it dealt only with the counting numbers, but its definition has broadened to include all real numbers. The most important arithmetic properties (where a and b are real numbers) are the commutative laws of addition and multiplication, a + b = b + a and ab = ba; the associative laws of addition and multiplication, a + (b + c) = (a + b) + c and a{bc) = {ab)c\ and the distributive law, which connects addition and multiplication, a(b + c) = ab + ac. These properties include subtrac¬ tion (addition of a negative number) and division (multiplication by a FRACTION).
Arius \'ar-e-os\ (b. c. 250, Libya—d. 336, Constantinople, Byzantine Empire) Christian priest and heretic whose teachings gave rise to the doc¬ trine of Arianism. He was leader of a Christian community near Alexan¬ dria, Egypt, where he preached doctrines that combined Neoplatonism with a literal, rationalist interpretation of biblical texts. By asserting the abso¬ lute oneness and immutability of God, he called into question the divin¬ ity of Christ. His views were publicized through his major work, Thalia
Ariosto, woodcut after a drawing by Titian from the third edition of Orlando furioso , 1532.
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(c. 323). In 325 the Council of Nicaea declared him a heretic. He was striving to compromise his views and win readmission to the church when he died suddenly in Constantinople. The Arian heresy posed a threat to Christian orthodoxy for several centuries.
Arizona State (pop., 2000: 5,130,632), southwestern U.S. Bordered by Mexico and the U.S. states of Utah, New Mexico, California, and Nevada, it covers 113,999 sq mi (295,256 sq km). Its capital is Phoenix. Its high¬ est point is Humphreys Peak, at 12,633 ft (3,850 m). The site of Grand Canyon and Petrified Forest national parks, Arizona also contains much of America’s Indian tribal lands. Humans settled the area more than 25,000 years ago. Nomadic Apache and Navajo Indians arrived after the collapse of the Anasazi and Hohokam civilizations. They were followed in the 16th century by Spanish treasure seekers from Mexico, including Francisco Vazquez de Coronado, establishing Mexico’s claim to the area. In 1776 the Mexican army built a presidio at Tucson. After the Mexican War, Ari¬ zona was ceded to the U.S. as part of New Mexico in 1848; the Gadsden Purchase added to it in 1853. Organized as a territory in 1863, Arizona became the 48th state in 1912. Though still lightly populated, it has grown rapidly in population in recent decades, largely because of its climate. About one-fifth of the population is Spanish-speaking, while about 5% is American Indian, including Navajo, Hopi, Apache, Papago, and Pima. Its diverse economy includes agriculture, mining, aerospace, electronics, and tourism.
Arjan Vor-j9n\ (b. 1581—d. 1606) Fifth Guru of the Sikhs (1581-1606) and jts first martyr. He compiled the volume of Sikh scripture on which the Adi Granth is based, and he completed the Golden Temple at Amritsar, India. The first Guru to serve as both temporal and spiritual head of Sikhism, he built up Amritsar as a commercial centre and enlarged mis¬ sionary efforts. He was also a prolific poet and writer of hymns. He pros¬ pered under the tolerant Mughal emperor Akbar but was tortured to death by Akbar’s successor for not altering the Adi Granth to remove passages that gave offense to Hinduism or Islam.
Arjuna \'3r-ju-n9\ One of the five brothers who are the heroes of the Mahabharata. His reluctance to go into battle prompts Krishna, manifested as his friend and charioteer, to deliver the discourse on duty that consti¬ tutes the Bhagavadgita. An exemplar of skill, duty, and compassion as well as a seeker of true knowledge, Arjuna is a central figure in Hindu myth and theology.
Ark of the Covenant In Judaism and Christianity, the ornate, gold- plated wooden chest that in biblical times housed the two tablets of the Law given to Moses by God. The Levites carried the Ark during the Hebrews’ wandering in the wilderness. Following the conquest of Canaan, it was kept at Shiloh but was sometimes carried into battle by the Israelites. David took it to Jerusalem, and Solomon placed it in the Temple of Jerusalem, where it rested in the Holy of Holies and was seen only by the high priest on Yom Kippur. It is believed to have been captured when Jerusalem fell to the Babylonians in 586 bc, and its subsequent fate is unknown.
Arkansas State (pop., 2000: 2,673,400), south-central U.S. Bordered by Missouri, Tennessee, Mississippi, Louisiana, Texas, and Oklahoma, it covers 53,178 sq mi (137,730 sq km). Its capital is Little Rock, and its highest point is Mount Magazine, at 2,753 ft (839 m). The earliest inhab¬ itants were Indian bluff dwellers along the Mississippi River c. ad 500. Mound-building cultures later left burial mounds along the river. Spanish and French explorers traversed the region in the 16th- 17th centuries; the first permanent European settlement was founded at Arkansas Post in 1686. Acquired by the U.S. as part of the Louisiana Purchase, Arkansas Territory was established in 1819; the state’s current boundaries were fixed in 1828. Arkansas became the 25th state in 1836. It seceded in 1861 to join the Confederacy in the American Civil War; it was readmitted to the Union in 1868. Following Reconstruction, a rigid policy of segrega¬ tion lasted until 1957, when court-ordered desegregation of the schools was implemented. Once dominated by agriculture, the state’s economy now also includes mining and manufacturing. Tourism is promoted, espe¬ cially by the mineral springs at Hot Springs National Park and resorts in the Ozark Mountains.
Arkansas River River, rising in central Colorado, U.S. At 1,450 mi (2,333 km) long, it flows east through southern Kansas and southeast across northeastern Oklahoma and bisects Arkansas, where it empties into the Mississippi River. Navigable for 650 mi (1,046 km), its largest tributar¬ ies are the Canadian and Cimarron rivers. It is believed to have been