Epitome of Ptolemy's Almagest

Book

...it has no resistance at all, due to the similarity of the parts of the spherical surface that bring this about. For each of its parts enters the place of its neighboring part, with no external body either yielding or resisting The author argues that because a sphere is perfectly uniform, it can rotate in place without pushing aside any surrounding "air" or "ether," unlike a jagged or square shape. Indeed, it is well established that this can happen to bodies of no other shape. We seem, therefore, to have shown sufficiently that the heavens are spherical and their motion is circular.

Second Conclusion.

Note

That the Earth is round.
What appears spherical to the senses, we are accustomed to calling "round." In every surface, one may consider a twofold division: namely, of longitude longitude: here referring to the East-West direction and of latitude latitude: here referring to the North-South direction. We understand longitude on the Earth's surface to be from West to East, and latitude to be across it [from North to South]. That the Earth is round according to its longitude is proven by this: that the stars do not rise or set, nor reach the meridian original: "meridianos"; the imaginary line running North-South through the zenith used to mark noon at the same time for those in the East and those in the West. Rather, they reach these points earlier for the former and later for the latter. This is detected by the evidence of an eclipsed moon. For by comparing the time of a single eclipse calculated by those in the East to the time of the same eclipse counted by those in the West, the time for the easterners is found to be greater than the time for the westerners in the calculation, but not in the event itself. For an eclipse occurs to the whole world at one and the same time. Hence, the sun must have receded further from the meridian of the easterners than from the meridian of the westerners due to the difference in time. A similar thing happens if the calculation of time is referred to the horizon; this would never occur unless the Earth were round. Furthermore, it may be added that in any number of observations noted for one and the same eclipse, the differences in the calculations are found to be proportional to the distances between the places where these eclipses were observed. It is necessary, therefore, for this dimension of the Earth to be convex original: "gibbosam"; literally "humped" or "bulging," used here to describe the outward curvature of the globe. For if it were hollow, the stars would be seen by those in the West before those in the East. If it were flat, they would appear to everyone at the same time. These possibilities do not agree with experience.

Moreover, it is more easily established that the transverse [North-South] dimension is convex. To someone proceeding from the South to the North, the height of the Pole Star original: "stelle polaris"; specifically Polaris, used for navigation and determining latitude is seen to increase. Other stars near it likewise have their midnight altitudes increased. Furthermore, some stars which previously rose and set now neither rise nor set [but remain always visible]. The opposite of these things happens if we travel from the North toward the South. And when we measure the distances of our stopping places, we find them proportional to the differences in the heights mentioned above. None of these things would be seen if this dimension were either flat or hollow. This phenomenon is universal, no matter where we begin a journey on Earth. This indeed serves as a sufficient proof of roundness, even if we were to ignore the observations of eclipses.

In the same way—or rather, even more easily—we shall declare that water is round, if we look up at the celestial bodies from the sea just as we do from the land. This is confirmed, moreover, by a manifest sign: to those staying out at sea, nothing is seen but sky and water. However, when we seek the shores, the mountains, rocks, citadels, and such things are seen to rise up little by little, as if they were emerging from the water. This would not happen if the water had a flat or hollow surface.

Third Conclusion.

That the Earth is situated in the middle of the world.
For unless it were established in the middle of the world original: "mundi"; in this period, the "world" refers to the entire created universe or cosmos, it would be necessary for the Earth to be either on the axis of the heaven’s motion but at an unequal distance from the two poles; or off the axis but equidistant from both poles; or likewise off the axis and unequally distant from the poles. But if the first of these positions were granted to the Earth, no horizon would divide the heavens into two equal parts, except for the "right" and "oblique" horizons—specifically, that one in whose surface is a straight line departing from the center of the world and connecting the Earth...