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A major branch of mathematics that, at an elementary level, involves applying the rules of arithmetic to numbers, and to letters that stand for unknown numbers, with the main aim of solving equations. Beyond the algebra learned in high school is the much vaster and more profound subject of abstract algebra.

The word itself comes from al-jebr, which is Arabic for "the reunion of broken parts;" it first appeared in the title of a book, Al-jebr w'al-mugabalah, by the 9th century Persian scholar, Abu Ja'far Ben Musa, also known as al-Khowarizmi – probably the greatest mathematician of his age, and as famous among Arabs as Euclid and Aristotle are to the Western World.

History of algebra

The oldest work in the West on algebra is that of Diophantus of Alexandria, in the 4th century AD. It consisted originally of 13 books, and contained arithmetical problems; only six books are now extant. The modern Europeans got their first acquaintance with algebra, not directly from the Greeks, but, like most other knowledge, from the Arabs, who derived it, in turn, from the Hindus. The chief European source was the work of Mohammed Ben Musa, who lived in the time of Calif Al Maman (812-833); it was translated into English by Rosen (1831). An Italian merchant Leonardo Boccio, of Pisa, traveling in the East about 1200, acquired a knowledge of the science, and introduced it among his countrymen upon his return; he left a manuscript work on algebra.

The first work on algebra after the revival of learning is that of the Minorite friar Paciolo or Luca Borgo (Venice, 1494). Scipio Ferreo in Bologna discovered, in 1505, the solution of one case of cubic equations. Tartaglia of Brescia carried cubic equations still further, and passed on his discoveries to Girolamo Cardano of Milan as a secret. Cardano extended the discovery himself and published, in 1545, the solution known as "Cardano's rule." Ludovico Ferrari and Bombelli (1572) gave the solution of biquadratic equations.

Algebra was first cultivated in Germany by Christain Rudolf, in a work printed in 1524; Stifel follwed with his Arithmetica Integra(1544). Robert Recorde in England, and Pelletier in France, wrote in about 1550. Vieta a Frenchman (d. 1603), first made the grand step of using letters to denote the known quantities as well as the unknown. Harriot, in England (1631), and Girard, in Holland (1629) still further improved on the advances made by Vieta.

The Géométrie of Descartes introduced a major new approach in algebra. It applied geometry to algebra, and was the first to represent the nature of curves by means of equations. Fermat also contributed to the science; and so did the Arithmetica Universalis of Newton.

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