Two Approaches to Foundations in Greek Mathematics: Apollonius and Geminus.
Résumé
The article is the sequel of a previous one dealing with homeomeric lines and published in Science in Context 23 (2010), 1-37. It aims at discussing foundational issues in Greek mathematics. It does so by considering the two key characters in the study of mathematical homeomery, namely, Apollonius and Geminus, and by analysing 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 such a mathematical well-established field of discourse as “foundations of mathematics,” a fact that is by no means obvious, and that the authors involved in it set out a variety of philosophical, scholarly, and mathematical tools in developing their investigations.
L'article, qui se rattache à une étude précédente sur les lignes homéomères publiée dans Science in Context 23 (2010), 1-37, montre l'existence d'un domaine de recherche ancien sur les fondements des mathématiques en analysant les contributions d'Apollonius et de Géminus et les différents outils de recherche qu'ils mettent en œuvre.