 Greek mathematics generally avoids any recourse to the actual infinite, and scholars have spoken of a “horror of infinity” typical of Greek mathematics. This is in general correct with respect to the way mathematical results are presented in their final and public presentation. However, one should keep in mind that no such “horror of infinity” is to be found when one looks at the heuristic strategies pursued by Greek mathematicians. In the case of Archimedes, this was made evident by the fortunate rediscovery of his method (found in 1906; see Netz and Noel 2007) where we see him using infinitary and mechanical considerations as tools he exploited for the discovery of geometrical theorems (see Knorr 1982, 1986 and Jullien 2015). For instance, in his description of the method for finding the proportion between the area of a parabolic segment and that of a related triangle, Archimedes thinks of geometric figures (the parabolic segment and the related triangle, in this case) as composed of infinitely many one-dimensional segments and then exploits the law of the lever to gain the determination of the relation between the areas in question. In a portion of the text of the method that has only recently become available (a section of proposition XIV, see Netz and Noel 2007), Archimedes explicitly operates with infinite collections.