We must say that there are as many squares as there are numbers.
They who depend upon manifest observations will philosophize better than those who persist in opinions repugnant to the senses.
Who would dare assert that we know all there is to be known?
I do not know what to say in a case so surprising, so unlooked for and so novel.
It is necessary for the Bible, in order to be accommodated to the understanding of every man, to speak many things which appear to differ from the absolute truth so far as the bare meaning of the words is concerned.
To understand the Universe, you must understand the language in which it’s written, the language of Mathematics.
For my part I consider the earth very noble and admirable precisely because of the diverse alterations, changes, generations, etc. that occur in it incessantly.
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!
Nonetheless, it moves.
In the future, there will be opened a gateway and a road to a large and excellent science into which minds more piercing than mine shall penetrate to recesses still deeper.
To me, a great ineptitude exists on the part of those who would have it that God made the universe more in proportion to the small capacity of their reason than to His immense, His infinite, power.
The greatness and the glory of God shine forth marvelously in all His works, and is to be read above all in the open book of the heavens.
The fear of infinity is a form of myopia that destroys the possibility of seeing the actual infinite, even though it in its highest form has created and sustains us.
My dear Kepler, I wish that we might laugh at the stupidity of the human herd. What do you have to say about the principal philosophers of this academy who are filled with the stubbornness of an asp and do not want to look at either the planets, the moon or the telescope, even though I have freely and deliberately offered them the opportunity a thousand times? Truly, just as the asp stops its ears, so do these philosophers shut their eyes to the light of truth.
To apply oneself to great inventions, starting from the smallest beginnings, is no task for ordinary minds; to divine that wonderful arts lie hid behind trivial and childish things is a conception for superhuman talents.
There is not a single effect in Nature, not even the least that exists, such that the most ingenious theorists can ever arrive at a complete understanding of it. This vain presumption of understanding everything can have no other basis than never understanding anything. For anyone who had experienced just once the perfect understanding of one single thing, and had truly tasted how knowledge is attained, would recognise that of the infinity of other truths he understands nothing.
Philosophy is written in this all-encompassing book that is constantly open to our eyes, that is the universe; but it cannot be understood unless one first learns to understand the language and knows the characters in which it is written. It is written in mathematical language, and its characters are triangles, circles, and other geometrical figures; without these it is humanly impossible to understand a word of it, and one wanders in a dark labyrinth.
I do not feel obliged to believe that the same God who has endowed us with senses, reason, and intellect has intended us to forgo their use and by some other means to give us knowledge which we can attain by them.
I entertain no doubts as to the truth of the transfinites, which I have recognized with God’s help.
Who would set a limit to the mind? Who would dare assert that we know all there is to be known?
All inconveniences will be removed as you propound them. Up to this point, only the first and most general reasons have been mentioned which render it not entirely improbable that the daily rotation belongs to the earth rather than to the rest of the universe.