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.

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.

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.

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

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

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

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