A democracy exists whenever those who are free and are not well-off, being in the majority, are in sovereign control of government, an oligarchy when control lies with the rich and better-born, these being few.
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.
For well-being and health, again, the homestead should be airy in summer, and sunny in winter. A homestead possessing these qualities would be longer than it is deep; and its main front would face the south.
Even if you must have regard to wealth, in order to secure leisure, yet it is surely a bad thing that the greatest offices, such as those of kings and generals, should be bought. The law which allows this abuse makes wealth of more account than virtue, and the whole state becomes avaricious.
The society that loses its grip on the past is in danger, for it produces men who know nothing but the present, and who are not aware that life had been, and could be, different from what it is.
The first essential responsibility of the state is control of the market-place: there must be some official charged with the duty of seeing that honest dealing and good order prevail. For one of the well-nigh essential activities of all states is the buying and selling of goods to meet their mutual basic needs; this is the quickest way to self-sufficiency, which seems to be what moves men to combine under a single constitution.
A state is an association of similar persons whose aim is the best life possible. What is best is happiness, and to be happy is an active exercise of virtue and a complete employment of it.