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Homeomeric Lines in Greek Mathematics

Published online by Cambridge University Press:  26 January 2010

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

This article presents ancient documents on the subject of homeomeric lines. On the basis of such documents, the article reconstructs a definition of the notion as well as a proof of the result, which is left unproved in extant sources, that there are only three homeomeric lines: the straight line, the circumference, and the cylindrical helix. A point of particular historiographic interest is that homeomeric lines were the only class of lines defined directly as the extension of a mathematical property, a move that is unparalleled in Greek mathematics. The far-reaching connections between mathematical homeomery and key issues in the ancient cosmological debate are extensively discussed here. An analysis of its relevance as a foundational theme will be presented in a companion paper in a future issue of Science in Context.

Type
Research Article
Information
Science in Context , Volume 23 , Issue 1 , March 2010 , pp. 1 - 37
Copyright
Copyright © Cambridge University Press 2010

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