More stars in the north are seen not to set, while in the south certain stars are no longer seen to rise.

The earth also is spherical, since it presses upon its center from every direction.

Therefore, having obtained the opportunity from these sources, I too began to consider the mobility of the earth.

We regard it as a certainty that the earth, enclosed between poles, is bounded by a spherical surface.

Yet if anyone believes that the earth rotates, surely he will hold that its motion is natural, not violent.

Therefore I would not have it unknown to Your Holiness, the the only thing which induced me to look for another way of reckoning the movements of the heavenly bodies was that I knew that mathematicians by no means agree in their investigation thereof.

Those who know that the consensus of many centuries has sanctioned the conception that the earth remains at rest in the middle of the heavens as its center, would, I reflected, regard it as an insane pronouncement if I made the opposite assertion that the earth moves.

Therefore, in the course of the work I have followed this plan: I describe in the first book all the positions of the orbits together with the movements which I ascribe to the Earth, in order that this book might contain, as it were, the general scheme of the universe.

To know that we know what we know, and to know that we do not know what we do not know, that is true knowledge.

Mathematics is written for mathematicians.

Of all things visible, the highest is the heaven of the fixed stars.

I am aware that a philosopher's ideas are not subject to the judgment of ordinary persons, because it is his endeavour to seek the truth in all things, to the extent permitted to human reason by God.

For I am not so enamoured of my own opinions that I disregard what others may think of them.

Therefore, when I considered this carefully, the contempt which I had to fear because of the novelty and apparent absurdity of my view, nearly induced me to abandon utterly the work I had begun.

Finally we shall place the Sun himself at the center of the Universe.

The earth together with its surrounding waters must in fact have such a shape as its shadow reveals, for it eclipses the moon with the arc of a perfect circle.

At rest, however, in the middle of everything is the sun.

So far as hypotheses are concerned, let no one expect anything certain from astronomy, which cannot furnish it, lest he accept as the truth ideas conceived for another purpose, and depart from this study a greater fool than when he entered it.

Moreover, since the sun remains stationary, whatever appears as a motion of the sun is really due rather to the motion of the earth.

First of all, we must note that the universe is spherical.