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Situating the Debate on “Geometrical Algebra” within the Framework of Premodern Algebra

Published online by Cambridge University Press:  12 May 2016

Michalis Sialaros  and
Jean Christianidis
Michalis Sialaros
Affiliation:
Humboldt-Universität zu Berlin, Berlin, Germany E-mail: msiala01@mail.bbk.ac.uk
Jean Christianidis
Affiliation:
National and Kapodistrian University of Athens and Centre Alexandre Koyré, Paris E-mail: ichrist@phs.uoa.gr
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Argument

The aim of this paper is to employ the newly contextualized historiographical category of “premodern algebra” in order to revisit the arguably most controversial topic of the last decades in the field of Greek mathematics, namely the debate on “geometrical algebra.” Within this framework, we shift focus from the discrepancy among the views expressed in the debate to some of the historiographical assumptions and methodological approaches that the opposing sides shared. Moreover, by using a series of propositions related to Elem. II.5 as a case study, we discuss Euclid's geometrical proofs, the so-called “semi-algebraic” alternative demonstrations attributed to Heron of Alexandria, as well as the solutions given by Diophantus, al-Sulamī, and al-Khwārizmī to the corresponding numerical problem. This comparative analysis offers a new reading of Heron's practice, highlights the significance of contextualizing “premodern algebra,” and indicates that the origins of algebraic reasoning should be sought in the problem-solving practice, rather than in the theorem-proving tradition.

Type
Research Article
Information
Science in Context , Volume 29 , Issue 2 , June 2016 , pp. 129 - 150
Copyright
Copyright © Cambridge University Press 2016 

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