Book 13
8
Thus if we regard objects independently of their attributes and investigate any aspect of them as so regarded, we shall not be guilty of any error on this account, any more than when we draw a diagram on the ground and say that a line is a foot long when it is not; because the error is not in the premisses.Cf. Aristot. Met. 14.2.9, 10. The best way to conduct an investigation in every case is to take that which does not exist in separation and consider it separately; which is just what the arithmetician or the geometrician does.
9
For man, qua man, is one indivisible thing; and the arithmetician assumes man to be one indivisible thing, and then considers whether there is any attribute of man qua indivisible. And the geometrician considers man neither qua man nor qua indivisible, but qua something solid. For clearly the attributes which would have belonged to man even if man were somehow not indivisible can belong to man irrespectively of his humanity or indivisibility.
10
Hence for this reason the geometricians are right in what they maintain, and treat of what really exists; i.e., the objects of geometry really exist. For things can exist in two ways, either in complete reality or as matter.i.e., potentially.
10
And since goodness is distinct from beauty (for it is always in actions that goodness is present, whereas beauty is also in immovable things), theyCf. Aristot. Met. 3.2.4. are in error who assert that the mathematical sciences tell us nothing about beauty or goodness;
11
for they describe and manifest these qualities in the highest degree, since it does not follow, because they manifest the effects and principles of beauty and goodness without naming them, that they do not treat of these qualities. The main species of beauty are orderly arrangement, proportion, and definiteness; and these are especially manifested by the mathematical sciences.
