The Euclidean ideal of proof in The Elements and philological uncertainties of Heiberg's edition of the text

Bernard Vitrac (1, 2)

1 CRCSA - Centre Louis Gernet de recherches comparées sur les sociétés anciennes
2 ANHIMA - Anthropologie et Histoire des Mondes Antiques

In this chapter, I study the history of the text of Euclid's Elements including the use of the indirect medieval tradition in arabic and latin. I discuss the positions of Heiberg and Knorr. I propose a typology of the volontary alterations of Euclid's text during its transmission. Some textual criterias can be used to choice between local variants but they do not converge at the global level of an Ancient or medieval Version. The choice depends on the type of change (addition/deletion; change the order of exposition or proofs' modifications) ; it depends too of the Book or the kind of textual units concerned (Definition;Proposition;Porism;Lemma).

Mots clés: Euclid; Elements; proof; indirect medieval tradition; edition; history of the text; Zamberti; Peyrard; Heiberg; Knorr

Domaines: Histoire, Philosophie et Sociologie des sciences

Bernard Vitrac. The Euclidean ideal of proof in The Elements and philological uncertainties of Heiberg's edition of the text. 2007. ⟨hal-00175654⟩