Aristotle
the most renowned of Greek philosophers, born at Stagira, Macedonia, 384 B. C.; was for 20 years a student of philosophy in the school of Plato at Athens, but at the same time a teacher. After Plato's death, he opened a school of philosophy at the court of Hermias, King of Atarneus, in Mysia, whose adopted daughter ghter he he after- afte ward married. At the invitation of Philip of Macedon, he undertook the education of his son, Alexander. When Alexander succeeded to the throne, the philosopher returned to Athens and opened a school in the Lyceum. From being held in the covered walk (peripatos) of the Lyceum, the school obtained the name of the Peripatetic. The number of his separate treatises is given by Diogenes Laertius as 146; only 46 separate works bearing the name of the philosopher have come down to our time. He died at Chalcis, Eubœa, in the year 322 b. c. ARISTOTLE
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Aristœus
A charlatan who lived in the time of Cresus. He said that his soul would leave his body whenever he wished, and then return to it. Some maintain that it escaped in the sight of his wife and children in the figure of a stag. Wierius said that it took the shape of a crow. However that may be, Herodotus relates in his fourth book that Aristaus entering one day into a fuller's shop, fell dead therein, that the fuller ran to break the news to his parents, who came to bury him. But no corpse was to be found. The whole town was astonished, when some men returning from a voyage assured them that they had met Aristæus on the way to Crotona. It appeared that he was a species of vampire. Herodotus adds that he reappeared at the end of seven years, composed a poem and died anew. Leloyer, who regarded Aristœus as a sorcerer or ecstatic, quoted a certain Apollonius, who said that at the same hour as the vampire disappeared for the second time, he was transported to Sicily, where he became a schoolmaster. He is again heard of three hundred and forty years afterwards in the town of Metapontus, where he caused to be raised certain monuments which were to be seen in the time of Herodotus. So many wonderful happenings inspired the Sicilians with awe, and they raised a temple to him and worshipped him as a demi-god.
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Arithmancy
(Sometimes called wrongly Arithmomancy). Divination by means of numbers. The Greeks examined the number and value of the letters in the names of two combatants, and predicted that he whose name contained most letters, or letters of the greatest value, would be the victor. It was by means of this science that some diviners foretold that Hector would be overcome by Achilles. The Chaldeans, who also practised it, divided their alphabet into three parts, each composed of seven letters, which they attributed to the seven planets, in order to make predictions from them. The Platonists and the Pythagoreans were also strongly addicted to this method of divination, which comprehends also a part of the Jewish Kabala.
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Arithmetical Complement
that which a number wants to make it reach the next highest decimal denomination. Thus the arithmetical complement of 4 is 6, for 4+6 are = 10, and that of 642 is 358, because 642 + 358 are = 1,000. The arithmetical complement of a logarithm is what it wants to make it reach 10. ARITHMETICAL MEAN. (1) The number, whether it be an integer or a fraction, which is exactly intermediate between two others. Thus, 5 is the arithmetical mean between 2 and 8; for 2+3 are = 5, and 5+3 are =8. To find such a mean add the numbers together and divide their sum by 2; thus, 2+8=10, and 10÷2=5. (2) Any one of several numbers in an arithmetical ratio interposed between two other numbers. Thus, if 6, 9 and 12 be interposed between 3 and 15, any one of then may be called an arithmetical mean between these two numbers.
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Arithmetical Progression
a series of numbers increasing or diminishing uniformly by the same number. If they increase, the arithmetical progression is said to be ascending, and if they decrease, descending. Thus the series 3, 6, 9, 12, 15 is an ascending arithmetical progression, mounting up by the continued addition of 3; and the series 8, 6, 4, 2 is a descending one, falling regularly by 2.
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Arithmetical Proportion
the relation existing between four numbers, of which the first is as much greater or less than the second as the third is of the fourth; the equality of two differences or arithmetical ratios. In such cases the sum of the extremes is that of the means. ARI THORGILSSON (ä-rë tōr'gilsson), the father of Icelandic literature medium in writing his "Islendingabók, دو a concise history of Iceland from its settlement (about 870) until 1120. This work was finished between 1134 and 1138.
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Arius
the founder of Arianism. See ARIAN.
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Arizona
UNIVERSITY OF, a coeducational institution in Tucson, organized in 1891, reported at the end of 1919: Professors and instructors, 90; students, 968; volumes in the library, 32,000; grounds and buildings valued at $85,000; productive funds, $10,500; income, $700,- 000; president, Rufus B. Von Kleinsmid, Ph. D.
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Arizona
UNIVERSITY OF 252 Arizona and New Mexico was partly explored in 1539 by Marco de Nizan, in quest of the precious metals, and on his report Vasquez de Coronado organized an expedition in the following year and visited the Moqui villages and the New Mexican pueblos. About 1596 the first colony was established; in 1680 the Spaniards were driven out of the country; by 1695 they had recovered nearly all of it, and by 1720 Jesuit missionaries had established a number of missions, ranches and mining stations. There were serious Indian outbreaks in 1802 and 1827, and what is now Arizona and New Mexico was acquired by the United States by treaties in 1848 and 1853.
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Arjish Dagh
the loftiest peak of the peninsula of Asia Minor, at the western extremity of the Anti-Taurus Range, 13,150 feet; an exhausted volcano; on the N. and N. E. slopes are extensive glaciers.
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