 This suggests that Xenocrates might have thought he could do with the notion of a line what Aristotle was prepared to do with notions such as man. Aristotle is prepared to say that a man is indivisible, and so a suitable unit for the arithmetician’s contemplation, in the sense that if you divide a man into two parts what you get is not two men (see Metaphysics XIII 3. 1078a23–26). Xenocrates may have thought the notion of a line could be made to work in the same way: beyond a certain point, divisions will no longer yield lines. It is difficult to think how he could have made this plausible; once again, one can see why Aristotle might have regarded Xenocrates’ position as unmathematical.