Equality is of two kinds, numerical and proportional; by the first I mean sameness of equality in number or size; by the second, equality of ratios.
AristotleAnd so long as they were at war, their power was preserved, but when they had attained empire they fell, for of the arts of peace they knew nothing, and had never engaged in any employment higher than war.
Aristotle1 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.
AristotleThe investigation of the truth is in one way hard, in another easy. An indication of this is found in the fact that no one is able to attain the truth adequately, while, on the other hand, no one fails entirely, but everyone says something true about the nature of all things, and while individually they contribute little or nothing to the truth, by the union of all a considerable amount is amassed.
AristotleIt is true, indeed, that the account Plato gives in 'Timaeus' is different from what he says in his so-called 'unwritten teachings.'
AristotleThe 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
Aristotle