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ALGAROVILLA ALGEBRA 301 and Bologna, he visited France and England, and in Paris wrote " Newtonianism for Ladies " (Neutonianismo per le dame, 1734). He then went to Russia with Lord Baltimore, and pub- lished an account of the country, and in Ger- many became acquainted with Frederick, then crown prince of Prussia, one of whose first acts on coming to the throne was to invite Algarotti to his court. Henceforth the Italian lived in close intercourse with the king. He was created a count, appointed chamberlain, employed occasionally in diplomatic affairs, and commissioned by the elector of Saxony to collect works of art for the Dresden gallery. ALGAROVILLA, an astringent substance, pro- duced by the tree juga Martha, an acacia, found at Santa Marta in New Granada. The portions taken to England, and examined by Dr. Ure, were pods bruised and agglutinated with the extractive exudation of the seeds and husks. It is replete with tannin, and for tan- ning leather possesses more than four times the strength of good oak bark. It is also well adapted for the manufacture of black ink, for a yellow dye, and for an astringent medicine. ALGARVE, the southernmost province of Por- tugal, bounded by Alemtejo, Spain, and the At- lantic ; area, 1,872 sq. m. ; pop. in 1868, 177,- 342. It is watered by several small rivers and by the Guadiana, which divides it from Spain. A considerable mountain range in the north forms a watershed between it and Alemtejo. The S. W. part of the province is mountainous and rocky, and of wild and dreary aspect. The plains and valleys produce fruits in abundance, among them dates, figs, almonds, and oranges, which, with wines and fish, form the chief ex- ports. The principal towns are Faro, the cap- ital, Tavira, and Lagos, all on the S. coast, which ends in Cape St. Vincent, the S. W. ex- tremity of Europe. Algarve originally ex- tended over much of S. Spain, and also in- cluded a portion of N. "W". Africa, where the name is still retained by a province of Morocco (El GharMe, the western land). It constituted a Moorish kingdom till the 13th century, when it was gradually conquered, and the part W. of the Guadiana finally annexed to Portugal as Algarve d'aquem Mar (this side the sea) in 1253. The African portion was conquered by Alfonso V. and formed into the province of A1-. garve d'alem Mar (beyond the sea) in 1471 ; and his successors are still called kings of Por- tugal and the Algarves. ALGAZZALI, Abu Hamed Mohammed, a Moslem philosopher, born at Tus, Persia, about 1058, died in 1111. His father was a dealer in cot- ton thread (gaszal, whence the name Algazzali), and on his death the son was intrusted to the care of a sufi, or mystical philosopher. He be- came a professor of theology at Bagdad, and attracted hundreds to his lectures. Anxious to attain to the purest state of which man is capable, he found that for this purpose the soul must be purified from all connection with earth. Accordingly he distributed his wealth, and sought in Syria, in solitary communion with himself, to attain that ecstatic state for which he longed. He spent some time in this manner, and in travelling, settling at last at Nishapoor, and there he passed the remainder of his days, some- times, as he says, experiencing the highest bliss of the ecstatic state, but only occasionally, and for a short time. He was a very prolific writer, but his works were not all considered entirely orthodox by the Mohammedans, and one of them was condemned to be burned on account of some strictures on the Mohamme- dan law. One of his works attained so high a reputation among the Moslems, that they sometimes said, if all Islam were destroyed, it would be but a slight loss provided Algazzali's work on the "Revivification of the Sciences of Religion" were preserved. (See Lewes's " Biographical History of Philosophy.") ALGEBRA (Arab, al-jaber, the science of so- lution), originally, a kind of higher arithmetic in which the numbers are replaced by symbols ; but by later applications the symbols are used as well for geometrical quantities in space, or in mechanics for velocities, distances, and times, so that at present algebra occupies itself with quantities in general, whatever be their nature. The oldest work on this science is that of Dio- phantus of Alexandria, a Greek writer, who possibly flourished as early as the 4th century, of which the six books that have come down to us do not contain the elements, but the theory of the evolution of powers, and the method of solving undetermined problems. Many prob- lems of this kind were by the ancients consid- ered determined, as they threw out all solu- tions in irrational quantities. The Brahmins of Hindostan also had a knowledge of algebra, as well as the Arabs ; but to whom belongs the priority of the invention it is at present impos- sible to determine. It is only known that this science was introduced into Christian Europe by the Moors of Spain, a little before the year 1100. For the first three centuries after its introduction it was chiefly studied in Italy, and Lucas Paciolus de Burgo (Luca di Borgo) was the first European writer on the subject. His principal work, Summa Arithmetica et Geo- metrica, was published in Venice in 1494, and republished in 1523. He mentions a Pisan merchant, Leonardo Bonaccio, who lived in the beginning of the 13th century, and learned algebra in travelling among the Arabs along the coast of Africa and in the Levant. Some historians give to him the honor of having in- troduced this science in Europe, while others, among them Montucla, the great historian of mathematics, mention Paolo de. 1'Abacco and Belmondo of Padua, who preceded Bonaccio. From the works of Luca di Borgo it appears that in 1500 the science did not go beyond equations of the second degree, the negative solutions were rejected, and the symbols con- sisted chiefly of abbreviations of words. Great advance was made by Jerome Cardan, who in 1545 published his Ars Magna, in which he