But of all other stupendous inventions, what sublimity of mind must have been his who conceived how to communicate his most secret thoughts to any other person, though very far distant either in time or place? And with no greater difficulty than the various arrangement of two dozen little signs upon paper? Let this be the seal of all the admirable inventions of man.

I would beg the wise and learned fathers [of the church] to consider with all diligence the difference which exists between matters of mere opinion and matters of demonstration.

But let us remember that we are dealing with infinities and indivisibles both of which transcend our finite understanding, the former on account of their magnitude, the latter because of their smallness.

One can understand nature only when one has learned the language and the signs in which it speaks to us; but this language is mathematics and these signs are methematical figures.

Facts which at first seem improbable will, even on scant explanation, drop the cloak which has hidden them and stand forth in naked and simple beauty.

Their vain presumption of knowing all can take beginning solely from their never having known anything; for if one has but once experienced the perfect knowledge of one thing, and truly tasted what it is to know, he shall perceive that of infinite other conclusions he understands not so much as one.

Take note, theologians, that in your desire to make matters of faith out of propositions relating to the fixity of sun and earth you run the risk of eventually having to condemn as heretics those who would declare the earth to stand still and the sun to change position-eventually, I say, at such a time as it might be physically or logically proved that the earth moves and the sun stands still.