Partial knowledge is more triumphant than complete knowledge; it takes things to be simpler than they are, and so makes its theory more popular and convincing.
Of lower states, of acts of routine and sense, we can tell somewhat; but the masterpieces of God, the total growths and universalmovements of the soul, he hideth; they are incalculable. I can know that truth is divine and helpful; but how it shall help me I can have no guess, for so to be is the sole inlet of so to know.
The mind of the scholar, if you would have it large and liberal, should come in contact with other minds. It is better that his armor should be somewhat bruised by rude encounters even, than hang forever rusting on the wall.
Conversation with a friend will only bear good fruit of knowledge when both think only of the matter under consideration and forget that they are friends.
We have no organ at all for knowledge, for truth: we know (or believe or imagine) precisely as much as may be useful in the interest of the human herd, the species: and even what is here called usefulness is in the end only a belief, something imagined and perhaps precisely that most fatal piece of stupidity by which we shall one day perish.
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.