Archimedes’ quadratures

Abstract

In the paper we discuss the three methods that Archimedes employs to deal with the problem of the quadrature of a parabolic segment. We characterize the three approaches as heuristic, mechanical and geometric respectively. We investigate Archimedes’ own attitude towards the three methods, and we conclude with a critical presentation of the prevalent views concerning the matter, which have been expressed in the past by historians of mathematics.