If then this be so, those also which are between the two terms will be always finite, but if this be the case, it is clear now that there must necessarily be principles of demonstrations, and that there is not demonstration of all things, as we observed in the beginning, certain persons assert. For if there be principles, neither are all things demonstrable, nor can we progress to infinity, since that either of these should be, is nothing else than that there is no proposition immediate and indivisible, but that all things are divisible, since what is demonstrated is demonstrated from the term being inwardly introduced, and not from its being (outwardly) assumed. Wherefore if this may possibly proceed to infinity, the media between two terms might also possibly be infinite, but this is impossible, if predications upwards and downwards stop, and that they do stop, has been logically shown before, and analytically now.
Chapter 23
From what has been shown it appears plain that if one and the same thing is inherent in two, for instance, A in C and in D, when one is not predicated of the other, either not at all or not universally, then it is not always inherent according to something common. Thus to the isosceles and to the scalene triangle, the possession of angles equal to two right, is inherent according to something common, for it is inherent so far as each is a certain figure, and not so far as it is something else. This however is not always the case, for let B be that according to which A is
