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”a new departure in algebra”

Al-Karaji, Abu Bakr ibn Muhammad ibn al Husayn and Woepcke, Franz. Extrait du Fakhrî, traité d’algèbre.

Paris, Imprimerie Impériale, 1853.

Contemporary half morocco.

First edition of the first translation into French, rarely found on the market, of parts of Al-Fakhri fi’l-jabr wa’l-muqabala (“Glorious on algebra”), a 10-century treatise on algebra. Written by the Persian mathematician al-Karaji, this treatise “offers the most complete or rather the only theory of algebraic calculus among the Arabs known to us up to the present time” (p. 4). Basing himself on the algebra of al-Khwarizmi and his followers, and on a translation of the Arithmetica of Diophantus, al-Karaji “made possible a new departure in algebra” in “the first account of the algebra of polynomials” (DSB). Abu Bakr ibn Muhammad ibn al Husayn al-Karaji, also known as al-Karkhi, was a Persian mathematician and engineer who worked in Baghdad in the 10th century. An original scholar, he is regarded as one of the earliest mathematicians who worked to free algebra from geometry. The extract of Al-Fakhri, his most important work, was edited and translated by the German orientalist and mathematician Franz Woepcke (1826-64), who spent most of his career in Paris. His translation of the manuscript of Al-Fakhri, which he had found in Paris, was published to illustrate the progress of Arab mathematicians in the 10th and 11th centuries. With the binding very lightly worn at the extremities; foxed throughout; a good copy.

DSB VII, pp. 240–246.