ALGIERS ALL 



109 



tiuguished algebraists about the same time ; but the 

 science was afterwards greatly enriched by Vieta, 

 master of requests of queen Margaret of France, 

 who died in 1603, and by the Englishman Harriot, 

 who died in 1621, to whose labours the Flemish 

 mathematician Albert Girard, who died about 1630, 

 added his own with splendid success. Next appeared, 

 Descartes (q. v.) and Fermat, counsellor of the par- 

 liament of Toulouse, who died in 1664 ; and the 

 great Newton (q. v.) published in 1707 his Arithme- 

 tica Universalis. At the same time with him, Leib- 

 nitz acquired credit by some algebraical propositions. 

 After him, Maclaurin and Euler distinguished thejn- 

 selves in the most eminent manner by their additions 

 to this part of mathematical knowledge. In later 

 times, there have been constant efforts to raise alge- 

 Jbra to a higher degree of perfection. We may name 

 Lambert, d'Alembert, Lagrange, Ozanam, Saunder- 

 son, Clairaut, Cousin, Tempelhof, Kaestner, Bezout. 

 Gauss, &c. Algebra enables us to survey remote 

 and highly complicated relations. It is distinguished 

 by this, that each of its expressions contains exactly 

 the idea intended to be conveyed, while all other 

 languages, as those of words, of the arts, of symbols, 

 only approximate more or less to the proposed idea. 

 On this account an exact lexicon of two languages 

 can never be made, because every word in one is 

 connected with. ideas and associations different from 

 those belonging to the corresponding word in the 

 other. An algebraical formula, on the contrary, can 

 be understood equally well by the Frenchman and 

 the Hindoo, if they are both acquainted with the 

 signs. In Rosenthal's Encyc. of Mathem. Sciences, 

 i. 44, there is a list of the principal works on algebra. 

 The most important are, Wiedeburg on the Study of 

 Algebra, Jena, 1775, Eider's Algebra, translated by 

 Bernouilli into French, with notes by Lagrange. A 

 new and good edition of this translation appeared at 

 Lyons in 1795, in two vols. Kaussler translated 

 Lagrange's additions separately (Frankfort on the 

 Maine, 1796). The profound Maclaurin's Treatise 

 n Algebra (2d ed. London, 1756) is distinguished 

 among the old elementary books for solidity and 

 clearness. VVe find examples and explanations in 

 Saunderson's Elements of Algebra, Cambridge, 

 1740, two vols., 4to, translated into French by Jan- 

 conrt, Amsterdam, 1756. Clairaut's Algebra, which 

 was first published in 1746, has been several times 

 reprinted, lately in two vols., by Lacroix, with notes 

 by Lagrange and Laplace. Bezout's Algebra, in 

 the second part of his excellent work, Cours des 

 Mathematiques a F Usage de la Marine et de CArtil- 

 lerie, second ed. by Peyard, Paris, 1800, is well 

 written. The French have the most excellent ele- 

 mentary works in this as in every other branch of 

 mathematics. The first vol. of Vega's Lectures on 

 Mathematics, 3d ed., Vienna, 1802, contains a tho- 

 rough introduction to common arithmetic and alge- 

 bra. An excellent collection of problems in algebra 

 and other branches of mathematics, is that of Meier 

 Hirsch, a German, 2d ed., Berlin, 1811, which well 

 ileserves to be translated into other languages, be- 

 cause it contains the greatest variety of interesting 

 examples arranged in the best order. 

 ALGIERS. See Barbary. 



ALGOA or ZWARTKOP'S BAY, on the S. coast of 

 Africa, where ships may lie in five fathoms water, 

 a mile from the general landing-place. The bay 

 abounds in black whales and a variety of other fish. 

 500 miles E. from the Cape. Lon. of the landing- 

 place, 26 35' E. ; lat. 33 56' S. A small river of 

 the same name flows into it. Mr Barrow describes 

 the adjacent country as very fertile, and alxnmding in 

 useful animals. Fort Frederic is a recent establish- 

 ment on the shore of the bay, but as yet very small. 



ALGONQUINS ; North American Indians on the As. 

 siniboin or Rainy Lake, and Prairie de Portage ; 

 formerly more numerous than at present ; their num- 

 ber amounts only to 600. This tribe was once 

 closely connected with the Iroquois Indians, and 

 considered as their protectors ; but their allies and 

 protegees soon began to rival their former masters in 

 the arts of hunting and of war, and quarrels arose, 

 which proved almost fatal to the existence of the A., 

 although they were assisted by the French. There 

 is a church devoted to the Romish religion in their 

 territory, but the exertions of the clergy nave hitherto 

 had little effect on their morals. They are in the 

 general practice of polygamy, and much given to the 

 use of intoxicating liquors. The country around 

 them is cultivated in miserable and detached patches, 

 and this .solely by their women, the men being en- 

 grossed with fishing and hunting. They are, like 

 most of the other Indians, declining, and in a miser- 

 able state. See Indians. 



ALGUAZIL ; in Spain, an officer whose business it 

 is to execute the decrees of a judge. 



ALHAMA ; the ancient Artigis Julia ; a town of 

 Spain, in Granada; Ion. 2 46' W. ; lat. 36 57' N. ; 

 on the Motril, twenty-five miles from Granada ; 

 population, 4,500. This place is celebrated for its 

 warm medicinal baths and drinking waters, its ro- 

 mantic situation between craggy mountains, and the 

 gallant defence of the Moors against the Spaniards, 

 1481, when the town was taken and sacked. The 

 kings of Spain have erected a grand building for the 

 use of invalids, with baths of free-stone, regulated to 

 different degrees of heat. On the surrounding 

 mountains the Rio Frio rises, and forms several cas- 

 cades. Washington Irving, in his Chronicle of 

 Granada, gives a spirited account of the taking of 

 A., " the key of Granada." Byron's translation of 

 the Romance Muy Doloroso, on the taking of A., is 

 familiar to every reader. 



ALHAMRA, MEDINAT ALHAMRA, or ALHAMBRA, i. e. 

 the Red City ; a splendid portion or suburb of 

 ancient Granada, when it was one of the principal 

 seats of the empire of the Moors in Spain. It was 

 the Alcazar, or royal palace of the kings of Grana- 

 da, but grew, by numerous additions, at last, into 

 another city, lb-nu-1 Khatib, or Alkatib, describes 

 it in his account of this kingdom and capital (which 

 is preserved in Casiri's Bibliotheca Arabico-Escuri- 

 alensis) as a most splendid place, where art and na- 

 ture rival each other hi magnificence. Seated on 

 the northern brow of a lofty eminence, which com- 

 mands a full view of the city of Granada on the one 

 side, and of a charming country on the other, A. 

 encloses in its ruined walls many monuments of an- 

 cient art, and traces of its former splendour. Our 

 limited room does not allow us to give a description 

 of the Arabian palace, commenced by Mohammed 

 Abu Abdillah Ben Nasr, the second of the Moorish 

 kings of Granada, and completed under Abu-1 Haj- 

 jaj, in the year of the Hegira 749, or A. D. 1348 ; 

 nor of the Spanish palace commenced by Charles V., 

 on a portion of the ruins of the Moorish edifices. It 

 is a place equally interesting for the artist, the anti- 

 quarian, and the historian. Mr Murphy's splendid 

 work on the Arabian Antiquities of Spain contains 

 many views of these ruins. See also History of the 

 Mahometan Empire in Spain, 4to, London, 1816, 

 with the supplement ; a Collection of Historical No- 

 tices and Poems on the Alhamra of Granada ; Swin- 

 burne's Travels through Spain ; and Washington 

 Irving's recent work, entitled, ' The Alhambra. 



ALI ; the son of Abu Taleb, who was uncle of 

 Mahomet. When the latter assembled his kinsmen, 

 and declared his prophetic mission, he asked wliicj; 

 among them would be his vizier, " I am the man,*' 



