Abū Kāmil, Shujā˓ ibn Aslam (ca. 850–ca. 930), also known as “the Egyptian Reckoner” (al‐ḥāsib al‐miṣrī) was, according to the encyclopedist Ibn Khaldūn's report on algebra in his Muqaddima, chronologically the second greatest algebraist after al‐Khwārizmī. He was certainly one of the most influential. The peak of his activity seems to have been at the end of the ninth century.
Although at the beginning of his Kitāb f ī'l‐jabr wa'l‐muqābala (Algebra) he refers to al‐Khwārizmī's similar work, Abū Kāmil's purpose is radically different, for he is addressing an audience of mathematicians presumed to have a thorough knowledge of Euclid's Elements. His Algebra consists of four main parts.
- a.
Like his predecessor, Abū Kāmil begins by explaining how to solve the six standard equations and to deal with algebraic expressions involving an unknown and square roots. The next section (Book II) contains, as in his predecessor's work, six examples of problems and the resolutions of various...
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Abū Kāmil. The Book of Algebra (Reproduction of the Arabic manuscript). Frankfurt: Institut für Geschichte der arabischislamischen Wissenschaften, 1986.
Levey, Martin. The Algebra of Abū Kāmil Ed. of the Hebrew translation of part a. Madison: University of Wisconsin, 1966.
Lorch, Richard and Jacques Sesiano. Edition of the Latin translation. Vestigia mathematica: Studies in Medieval and Early Modern Mathematics in Honor of H. L. L. Busard. Ed. M. Folkerts, and J. Hogendijk. Amsterdam: Rodopi, 1993. 215–52. and 315–452.
Sesiano, Jacques. Les Méthodes d'analyse indéterminée chez Abū Kāmil (On part c of the Algebra). Centaurus 21 (1977): 89–105.
Sesiano, Jacques. Le Kitāb al‐Misāḥa d'Abū Kāmil. Centaurus 38 (1996): 1–21.
Suter, Heinrich. Die Abhandlung des Abū Kāmil über das Fünfeck und Zehneck (On part b of the Algebra). Bibliotheca Mathematica 10 (1909/10): 15–42.
Suter, Heinrich. Das Buch der Seltenheiten der Rechenkunst von Abū Kāmil el‐Miṣrī (On the Book of the Birds). Bibliotheca Mathematica 11 (1910/11): 100–20.
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Sesiano, J. (2008). Abū Kāmil. In: Selin, H. (eds) Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-4425-0_9198
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