 If the urgency of problems related to the infinite reached Greek consciousness with Zeno’s paradoxes, the most influential discussion was due to Aristotle. In order to put Aristotle’s discussion in perspective, we need to list a number of ways in which mathematical infinity had emerged not only in philosophy, as we have described, but also in mathematics. We have already seen with Archytas the notion of spatial infinitude of the cosmos. But in number theory, the natural numbers were considered infinite, at least in the sense that given any natural number a greater one could be found. In geometry, we find both the infinite by addition (any segment can be extended) and by division (any segment can be halved). Thus, mathematics presented processes of iteration without limit. The most sophisticated technique for dealing with iterated processes in the measurements of plane and solid figures was developed by Eudoxus (4th century BCE), and we discuss it in  Section 2.1.