Algar′di, Alessandro, one of the chief Italian sculptors of the seventeenth century; born 1602, died 1654. He lived and worked chiefly at Rome; executed the tomb of Leo XI in St. Peter's, a bronze statue of Innocent X, and a marble relief with life-size figures over the altar of St. Leo there.
Algaro′ba-bean. See Carob Tree.
Al′garot, a violently purgative and emetic white powder, precipitated from chloride of antimony in water; it was used in medicine by the physician Victor Algarotus in the sixteenth century.
Algarot′ti, Francesco, Count, born in 1712, died in 1764, an Italian writer on science, the fine arts, &c. He lived for some years in France and for a long time in Germany, Frederick the Great of Prussia having made him chamberlain and count. He wrote Neutonianismo per le donne; Saggi sopra le belle arti, his principal work on art; poems, letters, &c. Algarotti's works published at Venice in 17 vols. (1791-4) and illustrated by Tesi and Novelli are a chef-d'œuvre of typography. Frederick the Great erected at Pisa a monument to his memory.
Algarve (al-ga˙r′vā, meaning the land situated in the west), a maritime province of Portugal occupying the southern portion of the country, mountainous but with some fertile tracts. The title King of Algarve was held by the Kings of Portugal. Area, 1937 sq. miles; pop. 274,122.
Algau (a˙l′gou), a name for the south-western portion of Bavaria and the adjacent parts of Würtemberg and Tyrol, intersected by the Algau Alps. The Algau breed of cattle is one of the best in Germany.
Algazzali (a˙l-ga˙z-ä′lē), Abu Hamed Mohammed, an Arabian philosopher, Persian by birth; born 1058, died 1111. He was a most prolific author; an opponent of the prevailing Aristotelian philosophy of the day, and wrote against it the Destruction of the Philosophers, answered by Averroes in his Destruction of the Destruction.
Al′gebra (from the Arabic al, definite article, and jabbara, to make equal), a kind of generalized arithmetic, in which numbers or quantities and operations, often also the results of operations, are represented by symbols. Thus the expression xy + cz + dy2 denotes that a number represented by x is to be multiplied by a number represented by y, a number c multiplied by a number z, a number d by a number y multiplied by itself (or squared), and the sum taken of these three products. So the equation (as it is called) x2 - 7x + 12 = 0 expresses the fact that if a certain number x is multiplied by itself, and this result made less by seven times the number and greater by twelve, the result is 0. In this case x must either be 3 or 4 to produce the given result; but such an equation (or formula) as (a + b)(a - b) = a2 - b2 is always true whatever values may be assigned to a and b. Algebra is an invaluable instrument in intricate calculations of all kinds, and enables operations to be performed and results obtained that by arithmetic would be impossible, and its scope is still being extended.
The beginnings of algebraic method are to be found in Diophantus, a Greek of the fourth century of our era, but it was the Arabians that introduced algebra to Europe, and from them it received its name. The first Arabian treatise on algebra was published in the reign of the great Caliph Al Mamun (813-33) by Mohammed Ben Musa. Italian merchants were the first algebraists in Europe, and in 1202 Leonardo Fibonacci of Pisa, who had travelled and studied in the East, published a work treating of algebra as then understood in the Arabian school. From this time to the discovery of printing considerable attention was given to algebra, and the work of Ben Musa and another Arabian treatise, called the Rule of Algebra, were translated into Italian. The first printed work treating on algebra (also on arithmetic, &c.) appeared at Venice in 1494, the author being a monk called Luca Pacioli da Bergo, a Minorite friar. Rapid progress now began to be made, and among the names of those to whom advances are to be attributed are Tartaglia and Geronimo Cardano. About the middle of the sixteenth century the German Stifel introduced the signs +, -, √, and Robert Recorde the sign =. The last-named wrote the first English work on algebra in 1557. François
Vieta, a French mathematician (1540-1603), first adopted the method which has led to so great an extension of modern algebra, by being the first who used general symbols for known quantities as well as for unknown. It was he also who first made the application of algebra to geometry. Albert Girard, a Flemish mathematician in the seventeenth century, extended the theory of equations by the introduction of imaginary quantities. The Englishman Harriot, early in the seventeenth century, discovered negative roots, and established the equality between the number of roots and the units in the degree of the equation. He also invented the signs < >, and Oughtred that of ×. Descartes, though not the first to apply algebra to geometry, has, by the extent and importance of his applications, commonly acquired the credit of being so. The same discoveries have also been attributed to him as to Harriot, and their respective claims have caused much controversy. He obtained by means of algebra the definition and description of curves. Since his time algebra has been applied so widely in geometry and higher mathematics that we need only mention the names of Fermat, Wallis, Newton, Leibnitz, De Moivre, MacLaurin, Taylor, Euler, D'Alembert, Lagrange, Laplace, Fourier, Poisson, Gauss, Horner, De Morgan, Sylvester, Cayley. Boole, Jevons, and others have applied the algebraic method not only to formal logic but to political economy.—Bibliography: Chrystal, Algebra (2 vols.); Hobson, Trigonometry; Hardy, Pure Mathematics; Whittaker and Watson, Modern Analysis.