The mathematical sciences particularly exhibit order symmetry and limitations; and these are the greatest forms of the beautiful.

Character gives us qualities, but it is in our actions — what we do — that we are happy or the reverse.

When people are friends, they have no need of justice, but when they are just, they need friendship in addition.

Of ill-temper there are three kinds: irascibility, bitterness, sullenness. It belongs to the ill-tempered man to be unable to bear either small slights or defeats but to be given to retaliation and revenge, and easily moved to anger by any chance deed or word. Ill-temper is accompanied by excitability of character, instability, bitter speech, and liability to take offence at trifles and to feel these feelings quickly and on slight occasions.

For as the interposition of a rivulet, however small, will occasion the line of the phalanx to fluctuate, so any trifling disagreement will be the cause of seditions; but they will not so soon flow from anything else as from the disagreement between virtue and vice, and next to that between poverty and riches.

For well-being and health, again, the homestead should be airy in summer, and sunny in winter. A homestead possessing these qualities would be longer than it is deep; and its main front would face the south.

All teaching and all intellectual learning come about from already existing knowledge.