Page:The New International Encyclopædia 1st ed. v. 01.djvu/403

ALGABDI. Rome. An architect of note, he designed the Villa Pamfili and the façade of Sant' Igiazio in Rome.

AL'GARO'BA. See.

ALGAROTTI, al'p-rot'te, (1712-64). An Italian author. He was born in Venice, studied at Rome and Bologna, and when twenty-one years old published in Paris his Neutonianismo per le donne ("The Newtonian Philosophy for Ladies"), a work on optics, on which his reputation was founded. Until 1839, he lived in France, and for many years enjoyed the friendship of Voltaire. On his return from a journey to Russia he first met Frederick the Great, who bestowed upon him the title of count, and in 1747 made him court chamberlain. He also enjoyed the favor of Augustus III. of Poland, and lived alternately in Berlin and Dresden until his return to Italy in 1754. He died at Pisa, where Frederick the Great raised a monument to his memory in the Campo Santo. He was a versatile man and a voluminous writer. In his day he was considered a good judge of painting and architecture, and his reputation is confirmed by his Saggi sopra la belle arti ("Essays on the Fine Arts"), and by the paintings he selected for the Dresden Gallery. His chief defect of style was the strong Gallic flavoring, due to a too faithful study of French literature. English readers are most likely to think of him as Carlyle's "young Venetian gentleman of elegance in dusky skin and very white linen." Algarotti's collected works appeared, with biography by D. Michelessi, Venice, 1791-94.

ALGAROVILLA, al'ga-ro-vel'ya (Sp. algarroba, from Ar. al-kharrubah, the carob tree). An astringent product of the Juga marthæ, an acacia growing in Colombia, the pods of which are said to be four times as rich in tannin as the best oak bark. Black ink is made from it; also a yellow dye; and it is useful in medicine.

ALGARVE, al-giir'va. The smallest and most southerly of the provinces of Portugal, situated between Andalusia and the Atlantic Ocean (Map: Portugal, A 4). Its area is 1873 square miles. The northern part of the province is occupied by a range of mountains of an average height of 4000 feet, which form the continuation of the Sierra Morena of Spain, and terminate in Cape St. Vincent, the south-western extremity of Europe. The highest ridges are destitute of vegetation, and the mountainous regions are but little adapted for agricultural purposes. From the main ridge the country slopes southward in jagged terraces and low hills, leaving a level tract of a few miles along the coast. The African heat of the climate is mitigated by the cool sea breeze. The only river of importance is the Guadiana, on the frontiers of Spain. The soil of the plain is but indifferently suited for the production of grain, or even of pasturage; but it produces many kinds of southern fruit, including figs, almonds, olives, and grapes. The mineral wealth is considerable, but its exploitation is insignificant. The principal occupations of the inhabitants are agriculture, fishing, and the production of sea salt. Population, 1890, 228,635. The inhabitants have preserved many of the characteristics of the Moors. The chief town is Faro. In ancient times it was much more extensive. It received its name from the Arabs, in whose language Algarve signifies "a land lying to the west." It was a Moorish province till 1253, when Alfonso III. united it to the crown of Portugal as a separate kingdom.

AL-GAZALI, äl'gȧ-zä'lė, or AL-GAZEL, äl'gȧ-zĕl', (1058-1111). A celebrated Arabian theologian and philosopher, born at Tun, in the province of Khorassan, in eastern Persia. He became a leader of the school of the Aseharites, or Orthodox, and was for a time professor of theology in the university at Bagdad. Subsequently he assumed the rule of the Sufis (see ), or Mystics, and thus for the most part continued until his death. His eloquence as a lecturer won for him the title of Zeïn-ed-Dîn, or &ldquo;Ornament of Religion,&rdquo; and his Revivification of the Sciences of Religion was so highly esteemed by Mussulmans that the saying arose that if only this work wore preserved the loss of all the rest of Islam would be but slight. He wrote also The Destruction of the Philosophers, in refutation of the ancient philosophic doctrine. He was severely attacked by ../Averroës/ (q.v.).

AL'GAZEL (Al is the Ar. article the). A gazelle; ordinarily the dorcas. See.

AL'GEBRA. A branch of pure mathematics that materially simplifies the solution of arithmetical problems, especially through the use of equations. It also forms the introduction to all of the higher branches of mathematical science, except pure geometry.

The name is derived from the title of the Arabic work by AM-Khuwarizmi (q.v.), Ilm al-jabr wa'l muqubalah, meaning "the science of redintegration and equation;" that is, the science that relates to the reduction of equations to integral form and to the transposition of terms. The title appeared thereafter in various forms, as ludus algebræ almugrabalæque, and algiebar and almachabel, but the abbreviation algebra was finally adopted. The science also went under various other names in the fifteenth and sixteenth centuries, as the ars magna (Cardan, 1545), the arte maggiore, the regola de la cosa (because the unknown quantity was denominated cosa, the "thing"), and hence in early English the cossike art, and in German the Coss.

The exact limitations of algebra are not generally agreed upon by mathematicians, and hence various definitions have been proposed for the science. It has been proposed to limit it to the theory of equations, as the etymology of the word would suggest; but this has become a separate branch of mathematics. Perhaps the most satisfactory definition, especially as it brings out the distinction between algebra and arithmetic, is that of Comte: "Algebra is the calculus of functions, and arithmetic is the calculus of values." This distinction would include some arithmetic in ordinary school algebra (e. g., the study of surds), and some algebra in common arithmetic (e.g., the formula for square root).

The oldest known manuscript in which algebra is treated is that of Ahmes, the Egyptian scribe, who, about 1700 B.C., copied a treatise dating perhaps from 2500 B.C. In this appears the simple equation in the form, "Hau (literally heap), its seventh, its whole, it makes 19," which, put in modern symbols, means

-|-aj=19. In Euclid's Elements (about 300

B.C.) a knowledge of certain quadratic equations is shown. It was Diophantus of Alexandria (q.v.), however, who made the first attempt (fourth