Le Livre XIV des Éléments d'Euclide : versions grecques et arabes (première partie)

L'étude était trop longue pour être publiée en une seule fois. La seconde partie est éditée dans SCIAMVS, 13 (2012), 3-156.International audienceIn this paper we publish and translate three versions of the so-called Book XIV of Euclid's Elements : one in Greek, two in arabic. This book deals with the comparison of two of the regular polyhedra, dodecaedron and icosahedron. It derives from a monography by Hypsicles, a geometer who lived in the first half of the second century B.C. We examine the history of this text from Antiquity to Middle-Ages, arabic and latin, its relationships with Euclid, Apollonius, Aristaios and Pappus. We compare the different versions, Greek, Arabic and arabo-Latin and we try to understand the very complex processus of transmission. As a study case, it can help also for the history of the transmission of Euclid's Elements themselves. The first part contains the general history of Book XIV-XV and the Greek tradition of Book XIV and his scholia (Greek text, french translation)