Il quinto postulato di Euclide nel Commento di Proclo al primo libro degli Elementi

This article analyses the role of Euclid’s fifth postulate (also known as the “Parallel Postulate”) in Proclus’ Commentary on the first book of the Elements. Since Euclid included it among the postulates, he considered it indemonstrable; other ancient geometricians, though, disagreed with him and tried to find a proof of this fundamental principle. Proclus also thought so: in his Commentary, he reports various opinions on the postulate, together with Ptolemy’s attempt at proof, which he refutes, a paradoxical opinion of anonymous authors who even deny the fifth postulate, and his own attempt at proof. The analysis of these attempts at proof was made by Heath; the aim of this paper is to extend the study to all the parts of Proclus’ Commentary relating to the fifth postulate. A textual note on the term λημμάτιον used in reference to the fifth postulate closes the article. The distinction between axioms and postulates and the “squares of propositions” are dealt with in two final appendices.