Numbers are the highest degree of knowledge. It is knowledge itself.

Shall we not, then, lay down a law, in the first place, that boys shall abstain altogether from wine till their eighteenth year, thereby teaching that it is wrong to add fire to fire, as through a funnel, pouring it into their body and soul before they proceed to the labor of life, thus exercising a caution as to the maddening habits of youth.

Their military training will ensure success in war, but they must maintain unity by not allowing the state to grow to large, and by ensuring that the measures for promotion and demotion from one class to another are carried out. Above all they must maintain the educational system unchanged; for on education everything else depends, and it is an illusion to imagine that mere legislation without it can effect anything of consequence.

The true runner comes to the finish and receives the prize and is crowned.

No trace of slavery ought to mix with the studies of the freeborn man. No study, pursued under compulsion, remains rooted in the memory.

The science [geometry] is pursued for the sake of the knowledge of what eternally exists, and not of what comes for a moment into existence, and then perishes.

The object of knowledge is what exists and its function to know about reality.