Neither by nature, then, nor contrary to nature do the virtues arise in us; rather we are adapted by nature to receive them, and are made perfect by habit.
For nature by the same cause, provided it remain in the same condition, always produces the same effect, so that either coming-to-be or passing-away will always result.
But since there is but one aim for the entire state, it follows that education must be one and the same for all, and that the responsibility for it must be a public one, not the private affair which it now is, each man looking after his own children and teaching them privately whatever private curriculum he thinks they ought to study.
For as the interposition of a rivulet, however small, will occasion the line of the phalanx to fluctuate, so any trifling disagreement will be the cause of seditions; but they will not so soon flow from anything else as from the disagreement between virtue and vice, and next to that between poverty and riches.
[the virtues] cannot exist without Prudence. A proof of this is that everyone, even at the present day, in defining Virtue, after saying what disposition it is [i.e. moral virtue] and specifying the things with which it is concerned, adds that it is a disposition determined by the right principle; and the right principle is the principle determined by Prudence.
1 is not prime, by definition. 2 is an unnatural prime, 4 is an unnatural prime, and 6 is an unnatural prime. All other natural primes cannot be unnatural primes.
Two characteristic marks have above all others been recognized as distinguishing that which has soul in it from that which has not - movement and sensation.
The most perfect political community must be amongst those who are in the middle rank, and those states are best instituted wherein these are a larger and more respectable part, if possible, than both the other; or, if that cannot be, at least than either of them separate.
... the friendship of worthless people has a bad effect (because they take part, unstable as they are, in worthless pursuits, and actually become bad through each other's influence). But the friendship of the good is good, and increases in goodness because of their association. They seem even to become better men by exercising their friendship and improving each other; for the traits that they admire in each other get transferred to themselves.