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.
The most important relationship we can all have is the one you have with yourself, the most important journey you can take is one of self-discovery. To know yourself, you must spend time with yourself, you must not be afraid to be alone. Knowing yourself is the beginning of all wisdom.
[I]t is rather the case that we desire something because we believe it to be good than that we believe a thing to be good because we desire it. It is the thought that starts things off.
Happiness itself is sufficient excuse. Beautiful things are right and true; so beautiful actions are those pleasing to the gods. Wise men have an inward sense of what is beautiful, and the highest wisdom is to trust this intuition and be guided by it. The answer to the last appeal of what is right lies within a man's own breast. Trust thyself.
Moral virtue is ... a mean between two vices, that of excess and that of defect, and ... it is no small task to hit the mean in each case, as it is not, for example, any chance comer, but only the geometer, who can find the center of a given circle.
But the whole vital process of the earth takes place so gradually and in periods of time which are so immense compared with the length of our life, that these changes are not observed, and before their course can be recorded from beginning to end whole nations perish and are destroyed.
The structural unity of the parts is such that, if any one of them is displaced or removed, the whole will be disjointed and disturbed. For a thing whose presence or absence makes no visible difference is not an organic part of the whole.
It is the activity of the intellect that constitutes complete human happiness - provided it be granted a complete span of life, for nothing that belongs to happiness can be incomplete.
If the state cannot be entirely composed of good men, and yet each citizen is expected to do his own business well, and must therefore have virtue, still inasmuch as all the citizens cannot be alike, the virtue of the citizen and of the good man cannot coincide. All must have the virtue of the good citizen - thus, and thus only, can the state be perfect; but they will not have the virtue of a good man, unless we assume that in the good state all the citizens must be good.
We ought, so far as it lies within our power, to aspire to immortality, and do all that we can to live in conformity with the highest that is within us; for even if it is small in quantity, in power and preciousness, it far excels all the rest.