It is clear, then, that the earth must be at the centre and immovable, not only for the reasons already given, but also because heavy bodies forcibly thrown quite straight upward return to the point from which they started, even if they are thrown to an infinite distance. From these considerations then it is clear that the earth does not move and does not lie elsewhere than at the centre.
The form of government is a democracy when the free, who are also poor and the majority, govern, and an oligarchy when the rich and the noble govern, they being at the same time few in number.
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.
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.
Most men appear to think that the art of despotic government is statesmanship, and what men affirm to be unjust and inexpedient in their own case they are not ashamed of practicing towards others; they demand just rule for themselves, but where other men are concerned they care nothing about it. Such behavior is irrational; unless the one party is, and the other is not, born to serve, in which case men have a right to command, not indeed all their fellows, but only those who are intended to be subjects; just as we ought not to hunt mankind, whether for food or sacrifice . .
Why is it that all those who have become eminent in philosophy, politics, poetry, or the arts are clearly of an atrabilious temperament and some of them to such an extent as to be affected by diseases caused by black bile?
Happiness, then, is co-extensive with contemplation, and the more people contemplate, the happier they are; not incidentally, but in virtue of their contemplation, because it is in itself precious. Thus happiness is a form of contemplation.
In a race, the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead.
Some things the legislator must find ready to his hand in a state, others he must provide. And therefore we can only say: May our state be constituted in such a manner as to be blessed with the goods of which fortune disposes (for we acknowledge her power): whereas virtue and goodness in the state are not a matter of chance but the result of knowledge and purpose. A city can be virtuous only when the citizens who have a share in the government are virtuous, and in our state all the citizens share in the government.
Happiness does not consist in amusement. In fact, it would be strange if our end were amusement, and if we were to labor and suffer hardships all our life long merely to amuse ourselves.... The happy life is regarded as a life in conformity with virtue. It is a life which involves effort and is not spent in amusement.
Take the case of just actions; just punishments and chastisements do indeed spring from a good principle, but they are good only because we cannot do without them - it would be better that neither individuals nor states should need anything of the sort - but actions which aim at honor and advantage are absolutely the best. The conditional action is only the choice of a lesser evil; whereas these are the foundation and creation of good. A good man may make the best even of poverty and disease, and the other ills of life.
To leave the number of births unrestricted, as is done in most states, inevitably causes poverty among the citizens, and poverty produces crime and faction.