On the Revolutions of the Heavenly Spheres

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...this occurs in no other than a spherical figure. From which it is manifest that the earth is also enclosed between its poles, and because of this, it is a globe. Add also that the Eastern inhabitants do not perceive evening eclipses of the Sun and Moon, nor do those living in the West perceive morning ones; while they see those in the middle, the former later, but the latter sooner. Copernicus is explaining how time differences (longitude) prove the Earth's curvature. An eclipse happens at the same absolute time, but local time varies by location. Sailors also observe that water rests upon the same form, since land which is not visible from the ship is often seen from the top of the mast.

2 THE EARTH IS SPHERICAL.

Conversely, if something shining is placed at the top of the mast, as the ship moves away from the land, it seems to those remaining on the shore to gradually descend until at last it is hidden, as if setting.

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It is also certain that waters, flowing by their nature, always seek lower places—just as the earth does—and do not press further from the shore than its convexity allows. For this reason, the land is necessarily that much higher wherever it rises out of the Ocean.

How the earth with the water forms one globe. Chapter III.

A large decorative woodcut initial 'H' featuring a figure in profile within an ornate rectangular frame, beginning the word "Hic" (This).
This surrounding Ocean, therefore, pouring into seas in various places, fills its deeper descents. Thus there had to be less water than land, lest the water absorb the whole earth—as both strive toward the same center by their weight—but rather so that it might leave some parts of the land for the safety of living things, and all these islands open here and there. For is not the continent itself, the world of lands, anything other than an island larger than the others? Nor should certain of the Peripatetics Followers of Aristotle’s philosophy, who held traditional views on the "four elements." be heard, who declared all the water to be ten times larger than the whole earth. This was because in the transmutation of the elements, they take the conjecture that from one part of earth, ten parts of water are produced in the resolution. They say that the earth sticks out to some extent because, being cavernous, it is not balanced on all sides according to its gravity, and that the center of gravity is one thing, and the center of magnitude The geometric center. is another. But they are deceived by ignorance of the art of Geometry. They do not know that water cannot even be seven times greater without the whole center of gravity being emptied of earth, which would give place to the waters as being heavier than itself. Since spheres are to each other in the triple ratio original: "tripla ratione." In Euclidean geometry, this refers to the ratio of volumes being the cube of the ratio of the diameters ($r^3$). of their diameters.

Arithmetic ratio

If, therefore, the earth were surrounded by seven parts of water...