Book 5
4
The relation of that which exceeds to that which is exceeded is numerically quite indefinite, for number is commensurate, and is not predicated of the incommensurate; whereas that which exceeds, in relation to that which is exceeded, is so much plus something more; and this something more is indefinite, for it is indifferently equal or not equal to the so much.
5
Thus not only are all these things said to be relative in respect of number, but also the equal and like and same, though in another way: for all these terms are used in respect of one. Things are the same whose essence is one; like whose quality is one; equal whose quantity is one. Now one is the starting-point and standard of number; and so all these relations involve number, though not all in the same way.
6
(b) Active and passive things are called relative in virtue of an active or passive potentiality or actualization of the potentialities; e.g., that which can heat is called relative to that which can be heated, because it can heat; and again the thing heating is called relative to the thing heated, and the thing cutting to the thing cut, because their potentialities are actualized. Numerical relations, on the other hand, are not actualized (except as has been described elsewhere)The reference is quite uncertain, but cf. Aristot. Met. 9.9.4, 5. The point is that the actualization of a numerical (or geometrical) relation does not imply an active functioning, as in the case of the potentialities just described.; they have no actualizations in respect of motion.
