The life of theoretical philosophy is the best and happiest a man can lead. Few men are capable of it and then only intermittently. For the rest there is a second-best way of life, that of moral virtue and practical wisdom.
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.
The real difference between democracy and oligarchy is poverty and wealth. Wherever men rule by reason of their wealth, whether they be few or many, that is an oligarchy, and where the poor rule, that is a democracy.
Greatness of spirit is to bear finely both good fourtune and bad, honor and disgrace, and not to think highly of luxury or attention or power or victories in contests, and to possess a certain depth and magnitude of spirit.
Hence both women and children must be educated with an eye to the constitution, if indeed it makes any difference to the virtue of a city-state that its children be virtuous, and its women too. And it must make a difference, since half the free population are women, and from children come those who participate in the constitution.