It is an infantile superstition of the human spirit that virginity would be thought a virtue and not the barrier that separates ignorance from knowledge.
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.
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.
The essential form of knowledge... is nothing but a representation of truth: for the truth of being and the truth of knowing are one, differing no more than the direct beam and the beam reflected.
When I behold a rich landscape, it is less to my purpose to recite correctly the order and superposition of the strata, than to know why all thought of multitude is lost in a tranquil sense of unity.
From whatever you wish to know and measure you must take your leave, at least for a time. Only when you have left the town can yousee how high its towers rise above the houses.
Too much openness and you accept every notion, idea, and hypothesis-which is tantamount to knowing nothing. Too much skepticism-especially rejection of new ideas before they are adequately tested-and you're not only unpleasantly grumpy, but also closed to the advance of science. A judicious mix is what we need.