That the universe is spherical. FIRST WE must remark that the universe is spherical in form, partly because this form being a perfect whole requiring no joints, is the most complete of all, partly because it makes the most capacious form, which is best suited to contain and preserve everything; or again because all the constituent parts of the universe, that is the sun, moon, and the planets appear in this form; or because everything strives to attain this form, as appears in the case of drops of water and other fluid bodies if they attempt to define themselves. So no one will doubt that this form belongs to the heavenly bodies.

That the earth is also spherical. That the earth is also spherical is therefore beyond question, because it presses from all sides upon its center. Although by reason of the elevations of the mountains and the depressions of the valleys a perfect circle cannot be understood, yet this does not affect the general spherical nature of the earth. This appears in the following manner. To those who journey towards the North the North pole of the daily revolution of the heavenly sphere seems gradually to rise, while the opposite seems to sink. Most of the stars in the region of the Bear seem not to set, while some of the Southern stars seem not to rise at all. So Italy does not see Canopus which is visible to the Egyptians. And Italy sees the outermost star of the Stream, which our region of as colder zone does not know. On the other hand to those who go towards the South the others seem to rise and those to sink which are high in our region. Moreover, the inclination of the poles to the diameter of the earth bears always the same relation, which could happen only in the case of a sphere. So it is evident that the earth is included between the two poles, and is therefore spherical in form. Let us add that the inhabitants of the East do not observe the eclipse of the sun or of the moon which occurs in the evening, and the inhabitants of the West those which occur in the morning, while those who dwell between see those later and these earlier. That the water also has the same form can be observed from the ships, in that the land which cannot be seen from the deck, is visible from the mast-tree. And conversely if a light be placed at the masthead it seems to those who remain on the shores gradually to sink and at last still sinking to disappear. It is clear that the water also according to its nature continually presses like the earth downward, and does not rise above its banks higher than its convexity permits. So the land extends above the ocean as much as the land happens to be higher.

Whether the earth has a circular motion, and concerning the location of the earth. As it has been already shown that the earth has the form of a sphere, we must consider whether a movement also coincides with this form, and what place the earth holds in the universe. Without this there will be no secure results to be obtained in regard to the heavenly phenomena. The great majority of authors of course agree that the earth stands still in the center of the universe, and consider it inconceivable and ridiculous to suppose the opposite. But if the matter is carefully weighed it will be seen that the question is not yet settled and therefore by no means to be regarded lightly. Every change of place which is observed is due, namely, to a movement of the observed object or of the observer, or to movements of both, naturally in different directions, for if the observed object and the observer move in the same manner and in the same direction no movement will be seen. Now it is from the earth that the revolution of the heavens is observed and it is produced for our eyes. Therefore if the earth undergoes no movement this movement must take place in everything outside of the earth, but in the opposite direction than if everything on the earth moved, and of this kind is the daily revolution. So this appears to affect the whole universe, that is, everything outside the earth with the single exception of the earth itself. If, however, one should admit that this movement was not peculiar to the heavens, but that the earth revolved from west to east, and if this was carefully considered in regard to the apparent rising and setting of the sun, the moon and the stars, it would be discovered that this was the real situation. Since the sky, which contains and shelters all things, is the common seat of all things, it is not easy to understand why motion should not be ascribed rather to the thing contained than to the containing, to the located rather than to the location. From this supposition follows another question of no less importance, concerning the place of the earth, although it has been accepted and believed by almost all, that the earth occupies the center of the universe. But if one should suppose that the earth is not at the center of the universe, that, however, the distance between the two is not great enough to be measured on the orbits of the fixed stars, but would be noticeable and perceptible on the orbit of the sun or of the planets: and if one was further of the opinion that the movements of the planets appeared to be irregular as if they were governed by a center other than the earth, then such a one could perhaps have given the true reasons for the apparently irregular movement. For since the planets appear now nearer and now farther from the earth, this shows necessarily that the center of their revolutions is not the center of the earth: although it does not settle whether the earth increases and decreases the distance from them or they their distance from the earth.