Now as there are three states in each case, two faulty either in the way of excess or defect, and one right, which is the mean state, of course all are in a way opposed to one another; the extremes, for instance, not only to the mean but also to one another, and the mean to the extremes: for just as the half is greater if compared with the less portion, and less if compared with the greater, so the mean states, compared with the defects, exceed, whether in feelings or actions, and _vice versa_. The brave man, for instance, shows as rash when compared with the coward, and cowardly when compared with the rash; similarly too the man of perfected self-mastery, viewed in comparison with the man destitute of all perception, shows like a man of no self-control, but in comparison with the man who really has no self-control, he looks like one destitute of all perception: and the liberal man compared with the stingy seems prodigal, and by the side of the prodigal, stingy. And so the extreme characters push away, so to speak, towards each other the man in the mean state; the brave man is called a rash man by the coward, and a coward by the rash man, and in the other cases accordingly. And there being this mutual opposition, the contrariety between the extremes is greater than between either and the mean, because they are further from one another than from the mean, just as the greater or less portion differ more from each other than either from the exact half. Again, in some cases an extreme will bear a resemblance to the mean; rashness, for instance, to courage, and prodigality to liberality; but between the extremes there is the greatest dissimilarity. Now things which are furthest from one another[20] are defined to be contrary, and so the further off the more contrary will they be. Further: of the extremes in some cases the excess, and in others the defect, is most opposed to the mean: to courage, for instance, not rashness which is the excess, but cowardice which is the defect; whereas to perfected self-mastery not insensibility which is the defect but absence of all self-control which is the excess.