Thanks to the (re)discovery of Archimedes’Palimpsest, many aspects of Archimedes’mathematical practice have been subject to fresh analysis by historians of mathematics. One of these aspects, which is particularly important in the context of the treatise Method Concerning Mechanical Theorems, concerns the use made by Archimedes of mechanical considerations in mathematics. In this talk I shall focus on this aspect of Archimedes’ work. Drawing on an examination of Proposition 1 of the Method, which states that any segment of a parabola is four-thirds of the triangle which has the same base and equal height, I shall address the following questions: Does Archimedes really use mechanics in his mathematical practice? Should we identify in Archimedes’ Method the foundations of a way of practicing mathematics by using non-mathematical considerations?