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Two Approaches to Foundations in Greek Mathematics: Apollonius and Geminus

Published online by Cambridge University Press:  04 May 2010

Fabio Acerbi
Fabio Acerbi*
Affiliation:
Centre National de la Recherche Scientifique, Unité Mixte de Recherche 8163 “Savoirs, textes, langage”, B.P. 60149 – 59653 Villeneuve d'Ascq Cedex, France
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Argument

This article is the sequel to an article published in the previous issue of Science in Context that dealt with homeomeric lines (Acerbi 2010). The present article deals with foundational issues in Greek mathematics. It considers two key characters in the study of mathematical homeomery, namely, Apollonius and Geminus, and analyzes in detail their approaches to foundational themes as they are attested in ancient sources. The main historiographical result of this paper is to show that there was a well-established mathematical field of discourse in “foundations of mathematics,” a fact that is by no means obvious. The paper argues that the authors involved in this field of discourse set up a variety of philosophical, scholarly, and mathematical tools that they used in developing their investigations.

Type
Research Article
Information
Science in Context , Volume 23 , Issue 2 , June 2010 , pp. 151 - 186
Copyright
Copyright © Cambridge University Press 2010

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