Experiences of infinity and of generality in Book I of Euclid's Elements

TL;DR

This paper offers a new interpretative reading of Euclid's Book I, emphasizing the experiences of infinity it provides, as a foundation for exploring embodied cognition of infinity and its physical bases.

Contribution

It introduces a novel perspective on Euclid's Book I, linking geometric experiences of infinity to embodied cognition and material anchoring.

Findings

Highlights the experiential aspect of infinity in Euclidean geometry

Connects geometric understanding to embodied cognition theories

Provides a foundation for further research on infinity's material aspects

Abstract

This article proposes a reading of Book I of Euclid's Elements with an emphasis of the experiences of infinity supplied by it, as a preparatory study for a research on the embodied cognition of infinity and its material anchors. -- Cet article propose une lecture du premier livre des \'El\'ements d'Euclide. Il soutient qu'une telle lecture procure des exp\'eriences de l'infini. Il s'agit selon son auteur d'une \'etude pr\'eliminaire \`a une recherche sur la cognition incarn\'ee de l'infini et de ses ancrages mat\'eriels.