Rashed, Roshdi Between arithmetic and algebra. Research on the history of Arabic mathematics. (Entre arithmétique et algèbre. Recherches sur l’histoire des mathématiques arabes.) (French) Zbl 0944.01019 Collection Sciences et Philosophie Arabes. Paris: Société d’Édition ”Les Belles Lettres”. 323 p. FF 230.00 (1984). This book is a collection of reprints of eleven articles on the history of algebra and number theory in the Arabic tradition, with a short introduction and an index of authors’ names. Most of the articles have been reproduced photographically, but some printer’s errors have been corrected. The articles are as follows: (1) “L’idée de l’algèbre selon Al-Khwarizmi”, 13 pp., also published in Fundamenta Scientiae (more detailed references are unavailable to the reviewer); (2) “Al-Karaji” [in Dictionary of scientific biography 7, 240–246, New York (1972–1978); per revr.]; (3) “Recommencements de l’algèbre aux XIe et XIIe siècles” [in Cultural context of medieval learning, 33–60, by J. E. Murdoch and E. D. Sylla, Reidel, Dordrecht, 1975; per revr.]; (4) “L’induction mathématique: al-Karaji, as-Samawal” [Arch. Hist. Exact Sci. 9, 1–21 (1972; Zbl 0261.01007)]; (5) “L’extraction de la racine \(n\)-ième et l’invention des fractions décimales” [ibid. 18, 191–243 (1978; Zbl 0389.01003)]; (6) “Résolution des équations numériques et algèbre: Saraf-al-Din al-Tusi, Viete” [ibid. 12, 244–290 (1974; Zbl 0341.01003)]; (7) “L’analyse diophantienne au Xe siècle: l‘exemple d’al-Khazin” [Rev. Hist. Sci. 32, 193–222 (1979; Zbl 0422.01005)]; (8) “Ibn al-Haytham et le théorème de Wilson” [Arch. Hist. Exact Sci. 22, 305–321 (1980; Zbl 0446.01004)]; (9) “Algèbre et linguistique: l’analyse combinatoire dans la science arabe” [in Boston studies in the philosophy of science, 383–399, edited by R. S. Cohen, Reidel, Dordrecht, 1973; per revr.]; (10) “Nombres amiables, parties aliquotes et nombres figures aux XIIème et XIVème siècles” [Arch. Hist. Exact Sci. 28, 107–147 (1983; Zbl 0517.01007)]; (11) “La notion de science occidentale” [in Human implications of scientific advance, 45–54, edited by E. G. Forbes, Edinburgh, 1978; per revr.].The book may confuse the general reader by its abundance of modern terminology and concepts such as “géométrie algébrique”, “study of curves by means of equations”, “element of the algebra of polynomials”, “infinitesimalist”, “so-called formula of Cardan”, etc. For the reader who can see through the terminological and notational machinery many of the articles are useful because they contain valuable information on unpublished Arabic sources. Reviewer: Jan P. Hogendijk (MR 88f:01060) Cited in 2 ReviewsCited in 7 Documents MSC: 01A75 Collected or selected works; reprintings or translations of classics Keywords:Al-Khwarizmi; Ibn al-Haytham Citations:Zbl 0261.01007; Zbl 0389.01003; Zbl 0341.01003; Zbl 0422.01005; Zbl 0446.01004; Zbl 0517.01007 × Cite Format Result Cite Review PDF