Epitome of Ptolemy's Almagest

First [Book]

...touching. For no one having another horizon That is, if the Earth were not at the center, different observers would have horizons that do not bisect the heavens. would six signs Referring to the twelve signs of the Zodiac; seeing exactly six at any time proves the observer is at the center of the sphere. always appear above the horizon: the opposite of which is clearly experienced. Furthermore, another horizon would not divide the equinoctial equinoctial: the celestial equator into equal parts. Thus, there would be no equinox original: "equinoctium" when the sun is positioned in the middle of the two tropics; indeed, there would simply be no equinox on an oblique horizon, or it would occur when the sun is at unequal distances from the two tropics. For a horizon of this kind would not cut any of the circles—which they say the sun describes in its daily motion—into equal parts; or if by chance it did bisect any, it would not be the one in the middle of the two tropics. From this it would eventually follow that the increases and decreases of the days, just as they do not occur in equal times, so they would not be found to be reciprocal. I mean to say: if we mark two points equally distant from the point of the equinox, the increase of the day here would not be as much as the decrease of the day there. However, we find none of these accidents happen to the Earth; therefore, no one but a madman would assign it the position we just introduced. ¶ Likewise, the edges of shadows, which we mark on surfaces parallel to the horizon, are seen to describe straight lines when the sun is equally distant from the two tropics. This would hardly happen unless the Earth lay beneath the equinoctial circle. ¶ If, next, you were to place the Earth in a second position, it would result in no horizon dividing the heaven into equal parts, except for that one which the axis of the world falls upon perpendicularly, or in whose surface the center of the world is located. Therefore, the aforementioned inconveniences would accompany this position as well, with this additional point: that the magnitudes of the stars would necessarily appear to vary to our senses. For a different position of the stars above the horizon would bring about a multifaceted distance from the eye. ¶ But if you believe the Earth is located in a third position, all the aforementioned problems would happen indiscriminately. But also, lunar eclipses would not always occur at the opposition of the luminaries The "opposition of the luminaries" refers to the Full Moon, when the Sun and Moon are 180 degrees apart.; nor would lunar eclipses necessarily happen with the sun and moon being opposite along the diameter of the world. Since none of these things are observed, none of the three proposed positions can contain the Earth. It remains, therefore, that it resides in the middle of the world. ¶ We can, furthermore, confirm the same by direct argumentation. For we see heavy things descending freely along the semi-diameter of the world, falling upon the surface of the Earth at equal angles wherever we may be. Now, a line meeting a spherical surface at equal angles will, if continued, pass through its center. It is clear, therefore, that all the diameters which the world has intersect each other within the Earth. The point of such a section of diameters is necessarily held to be the center of the world. Therefore, it will be clear that the center of the world is found within the Earth, and thus the Earth is situated in the middle of the world.

Fourth Conclusion.

Me

Decorative drop cap initial 'T' featuring intertwining foliate patterns within a square border.
That the Earth, in respect to the firmament, has the nature of a point.

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¶ For wherever we are on the surface of the Earth, when considering the stars in various places, neither their magnitudes nor the distances between them are seen to vary. From this it is proven that they are held to be equally distant from the Earth, as the senses estimate it. The Earth, therefore, is the center of the sphere, and for that reason it attains the function of a point. ¶ The same applies to the Earth when compared to the sphere of the sun, which is found by other signs. For bodies placed at the centers of circular instruments Such as sundials or astrolabes. cast shadows that are moved far away, which the radiating sun itself carries around by its primary motion. From the regularity of the motion of the shadow, which we perceive by our senses, it is elicited that the sun moves regularly around the center of the instruments; and therefore, the centers of such instruments take the place of the center of the world, around which the primary motion is regulated. Since the thickness of the Earth introduces no variation in these things, we seem to have proposed the truth. ¶ Furthermore, the horizon hides half of the heaven from an eye existing upon it, and allows half to be seen. This is truly a property of no flat surface except one passing through the center of the sphere. It would happen otherwise if the Earth had a significant size in respect to the firmament.