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.

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

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

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

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

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.

For a traveler going from any place toward the north, that pole of the daily rotation gradually climbs higher, while the opposite pole drops down an equal amount.