Rationalité et exprimabilité : une relecture médiévale du livre X des Éléments d'Euclide

Abstract : In this paper, we study the reception of Euclid's Elements by a 13th century mathematician : Campanus. We are interested in the nature og his work on Book X, and its theory of irrationality. In Robert of Chester's version, which Campanus used for his edition, two non euclidean notions appear, the notion of straight lines 'rationnal in length' and 'rational in power'. We ask the question if the introduction of these notions lead to a theory which is different from Euclid's. To answer that question, we examine the first definitions of Book X and some theorems of Book XIII, to which Campanus gives some additions called for by the introduction of the above notions.
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https://halshs.archives-ouvertes.fr/halshs-00070826
Contributor : Sabine Rommevaux <>
Submitted on : Sunday, May 21, 2006 - 9:32:21 AM
Last modification on : Tuesday, July 3, 2018 - 11:47:09 AM

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Sabine Rommevaux. Rationalité et exprimabilité : une relecture médiévale du livre X des Éléments d'Euclide. Revue d'Histoire des Mathématiques, Society Math De France, 2001, 7, pp.91-119. ⟨halshs-00070826⟩

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