And believe me, if I were again beginning my studies, I should follow the advice of Plato and start with the mathematical sciences, which proceed very cautiously and admit nothing as established until it has been rigorously demonstrated.

I do not feel obliged to believe that the same God who has endowed us with senses, reason, and intellect has intended us to forego their use.

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, Galileo, son of the late Vicenzo Galilei, swear that I never said that the prime numbers are useless. What I said was that you cannot count lunar craters by counting 2, 3, 5, 7.

In regard to the philosophers, if they be true philosophers, i.e., lovers of truth, they should not be irritated that the earth moves. Rather, if they realize that they have held a false belief, they should thank those have shown them the truth; and if their opinion stands firm that the earth doesn't move, they will have reason to boast than be angered.

The Universe is a grand book which cannot be read until one first learns to comprehend the language and become familiar with the characters in which it is composed. It is written in the language of mathematics.

Being infinitely amazed, so do I give thanks to God, Who has been pleased to make me the first observer of marvelous things, unrevealed to bygone ages.