A tragedy is the imitation of an action that is serious and also, as having magnitude, complete in itself . . . with incidents arousing pity and fear, wherewith to accomplish its catharsis of such emotions.
Those who assert that the mathematical sciences say nothing of the beautiful or the good are in error. For these sciences say and prove a great deal about them; if they do not expressly mention them, but prove attributes which are their results or definitions, it is not true that they tell us nothing about them. The chief forms of beauty are order and symmetry and definiteness, which the mathematical sciences demonstrate in a special degree.
In the many forms of government which have sprung up there has always been an acknowledgement of justice and proportionate equality, although mankind fail in attaining them, as indeed I have already explained. Democracy, for example, arises out of the notion that those who are equal in any respect are equal in all respects; because men are equally free, they claim to be absolutely equal.
There are three things that are the motives of choice and three that are the motives of avoidance; namely, the noble, the expedient, and the pleasant, and their opposites, the base, the harmful, and the painful. Now in respect of all these the good man is likely to go right and the bad to go wrong, but especially in respect of pleasure; for pleasure is common to man with the lower animals, and also it is a concomitant of all the objects of choice, since both the noble and the expedient appear to us pleasant.
It is clear that there is some difference between ends: some ends are energeia [energy], while others are products which are additional to the energeia.
In a race, the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead.