We must say that there are as many squares as there are numbers.

E pur si muove. "Albeit It does move". (That's what Galileo purportedly muttered after torturers forced him to recant his theory that the earth orbits the sun.)

When the moon is ninety degrees away from the sun it sees but half the earth illuminated (the western half). For the other (the eastern half) is enveloped in night. Hence the moon itself is illuminated less brightly from the earth, and as a result its secondary light appears fainter to us.

I am certainly interested in a tribunal in which, for having used my reason, I was deemed little less than a heretic. Who knows but men will reduce me from the profession of a philosopher to that of historian of the Inquisition!

That sculpture is more admirable than painting for the reason that it contains relief and painting does not is completely false. ... Rather, how much more admirable the painting must be considered, if having no relief at all, it appears to have as much as sculpture!

You cannot teach a person something he does not already know, you can only bring what he does know to his awareness.

Alas! Your dear friend and servant Galileo has been for the last month hopelessly blind; so that this heaven, this earth, this universe, which I by my marvelous discoveries and clear demonstrations had enlarged a hundred thousand times beyond the belief of the wise men of bygone ages, henceforward for me is shrunk into such a small space as is filled by my own bodily sensations.