Why Rob Archimedes of his Lemma?

The method of exhaustion is one of the greatest achievements of Greek mathematics, but the history of its development is not clear. First and foremost Archimedes’ role has been keenly debated, by and large undermined, so that even his name seems condemned to disappear in the name of the Eudoxus-Archimedes Lemma. In this paper we try to revaluate his role by a new interpretation (or, more precisely, by the refinement of an old one) of the historical development of the theory, underlining the theoretical relevance of the problem of addition/subtraction and comparison between curves. Dedicated to the memory of Professor Aldo Cossu