To let them share in the highest offices is to take a risk; inevitably, their unjust standards will cause them to commit injustice, and their lack of judgement will lead them into error. On the other hand there is a risk in not giving them a share, and in their non participation, for when there are many who have no property and no honours they inevitably constitute a huge hostile element in the state. But it can still remain open to them to participate in deliberating and judging.
There is an error common to both oligarchies and to democracies: in the latter the demagogues, when the multitude are above the law, are always cutting the city in two by quarrels with the rich, whereas they should always profess to be maintaining their cause; just as in oligarchies the oligarchs should profess to maintain the cause of the people, . .
He who gives himself to a lover because he is a good man, and in the hope that he will be improved by his company, shows himself to be virtuous, even though the object of his affection turn out to be a villain, and to have no virtue; and if he is deceived he has committed a noble error. For he has proved that for his part he will do anything for anybody with a view to virtue and improvement, than which there can be nothing nobler.
Every limited mind demands a certain freedom of expression, and the man who cannot express himself satisfactorily without the stimulation derived from the spirited mode of two centuries ago should certainly be permitted to follow without undue restraint a practice so harmless, so free from essential error, and so sanctioned by precedent, as that of employing in his poetical compositions the smooth and inoffensive allowable rhyme.
The error of Socrates must be attributed to the false notion of unity from which he starts. Unity there should be, both of the family and of the state, but in some respects only. For there is a point at which a state may attain such a degree of unity as to be no longer a state, or at which, without actually ceasing to exist, it will become an inferior state, like harmony passing into unison, or rhythm which has been reduced to a single foot. The state, as I was saying, is a plurality which should be united and made into a community by education
Eratosthenes's only tools were sticks, eyes, feet, and brains; plus a zest for experiment. With those tools he correctly deduced the circumference of the Earth, to high precision, with an error of only a few percent. That's pretty good figuring for 2200 years ago.