Book 13
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.
12
And inasmuch as it is evident that these (I mean, e.g., orderly arrangement and definiteness) are causes of many things, obviously they must also to some extent treat of the cause in this sense, i.e. the cause in the sense of the Beautiful. But we shall deal with this subject more explicitly elsewhere.There is no obvious fulfilment of this promise.
