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A Conceptual Analysis of Early Arabic Algebra

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The Unity of Science in the Arabic Tradition

Part of the book series: Logic, Epistemology, and The Unity of Science ((LEUS,volume 11))

Abstract

Arabic algebra derives its epistemic value not from proofs but from correctly performing calculations using coequal polynomials. This idea of ‘mathematics as calculation’ had an important influence on the epistemological status of European mathematics until the seventeenth century. We analyze the basic concepts of early Arabic algebra such as the unknown and the equation and their subsequent changes within the Italian abacus tradition. We demonstrate that the use of these concepts has been problematic in several aspects. Early Arabic algebra reveals anomalies which can be attributed to the diversity of influences in which the al-jabr practice flourished. We argue that the concept of a symbolic equation as it emerges in algebra textbooks around 1550 is fundamentally different from the ‘equation’ as known in Arabic algebra.

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Authors and Affiliations

  1. Post-doctoral research fellow of the Research Foundation-Flandes (FWO-vlaanderen) Center for Logic and Philosophy of Science, Ghent University, Belgium

    Albrecht Heeffer

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  1. Albrecht Heeffer
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Editors and Affiliations

  1. Université Lille III U.F.R. de Philosophie Domaine Universitaire, Pont de Bois, 59653 Villeneuve d’Ascq, France

    Shahid Rahman  & Hassan Tahiri  & 

  2. Faculty of Divinity, University of Cambridge, West Road, Cambridge, United Kingdom CB3 9BS

    Tony Street

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Heeffer, A. (2008). A Conceptual Analysis of Early Arabic Algebra. In: Rahman, S., Street, T., Tahiri, H. (eds) The Unity of Science in the Arabic Tradition. Logic, Epistemology, and The Unity of Science, vol 11. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-8405-8_4

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