Mathematics is the language with which God has written the universe.

In time you may discover everything that can be discovered, and still your progress will only be progress away from humanity. The distance between you and them can one day become so great that your joyous cry over some new gain could be answered by an universal shriek of horror.

God is known by nature in his works, and by doctrine in his revealed word.

In the long run my observations have convinced me that some men, reasoning preposterously, first establish some conclusion in their minds which, either because of its being their own or because of their having received it from some person who has their entire confidence, impresses them so deeply that one finds it impossible ever to get it out of their heads.

But what exceeds all wonders, I have discovered four new planets and observed their proper and particular motions, different among themselves and from the motions of all the other stars; and these new planets move about another very large star [Jupiter] like Venus and Mercury, and perchance the other known planets, move about the Sun. As soon as this tract, which I shall send to all the philosophers and mathematicians as an announcement, is finished, I shall send a copy to the Most Serene Grand Duke, together with an excellent spyglass, so that he can verify all these truths.

I therefore concluded, and decided unhesitatingly, that there are three stars in the heavens moving about Jupiter, as Venus and Mercury about the Sun; which at length was established as clear as daylight by numerous other observations.

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.