Kitap 1
21
Further, why should a number 〈of units〉, taken together, be one thing? And further, in addition to the above objections, if the units are unlike, they should be treated as the thinkers who assume two or four elements treat those elements; for not one of them applies the term element to the common substrate, e.g. body, but to fire and earth—whether there is a common substrate (i.e. body) or not.In the Aristot. De Gen. et Corr. 320b 23Aristotle says that there is not.
22
As it is, the One is spoken of as though it were homogeneous, like fire or water. But if this is so, the numbers will not be substances. And if there is an absolute One which is a principle, clearly the term one is ambiguous; otherwise this is impossible.This last sentence shows that in what goes before A. has been regarding the Platonic One as a unit. If this is so, he says, substance cannot be composed of it. If on the other hand the One is something different from the unit, they ought to make this clear.
23
When we wish to refer substances to their principles we derive linesThe lines, planes, and solids here discussed are probably the Ideal lines, etc., which are immediately posterior to the Idea-Numbers. Cf. 30, Aristot. Met. 13.6.10, Aristot. Met. 13.9.2, and see Introduction. from Long and Short, a kind of Great and Small; and the plane from Wide and Narrow, and the solid body from Deep and Shallow. But in this case how can the plane contain a line,
