The line has magnitude in one way, the plane in two ways, and the solid in three ways, and beyond these there is no other magnitude because the three are all.
For any two portions of fire, small or great, will exhibit the same ratio of solid to void; but the upward movement of the greater is quicker than that of the less, just as the downward movement of a mass of gold or lead, or of any other body endowed with weight, is quicker in proportion to its size.
There is an ideal of excellence for any particular craft or occupation; similarly there must be an excellent that we can achieve as human beings. That is, we can live our lives as a whole in such a way that they can be judged not just as excellent in this respect or in that occupation, but as excellent, period. Only when we develop our truly human capacities sufficiently to achieve this human excellent will we have lives blessed with happiness.
Since we think we understand when we know the explanation, and there are four types of explanation (one, what it is to be a thing; one, that if certain things hold it is necessary that this does; another, what initiated the change; and fourth, the aim), all these are proved through the middle term.
Democracy 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.
The good man is he for whom, because he is virtuous, the things that are absolutely good are good; it is also plain that his use of these goods must be virtuous and in the absolute sense good.
Moral virtue is a mean . . . between two vices, one of excess and the other of defect; . . . it is such a mean because it aims at hitting the middle point in feelings and in actions. This is why it is a hard task to be good, for it is hard to find the middle point in anything.
Different men seek after happiness in different ways and by different means, and so make for themselves different modes of life and forms of government.
The soul has two parts, one rational and the other irrational. Let us now similarly divide the rational part, and let it be assumed that there are two rational faculties, one whereby we contemplate those things whose first principles are invariable, and one whereby we contemplate those things which admit of variation.