The Ptolemaic Legacy

By far the most important astronomical defense of geocentrism from antiquity is Ptolemy’s. The Hel- lenistic astronomer, who was still regarded as the “prince of astronomy” during the Renaissance, refutes the eccentricity of the Earth in Almagest I 5 (standard modern numbering). He bases his objection on considerations of how a hypothetical displacement of the Earth in different directions would alter celestial phenomena. He considers in particular the cases of terrestrial eccentricity on the equatorial plane or along the rotational axis. A “third” case, that the Earth is neither on the axis of the daily rotation nor on the equatorial plane, cumulates the disadvantages of both dislocations.

Therefore Ptolemy only mentions it but does not treat it extensively.

Concerning the first case, Ptolemy argues,

If we imagined [the Earth] removed towards the zenith or the nadir of some observer then, if he were at sphaera recta [at the equator], he would never experience equinox, since the horizon would always divide the heavens into two unequal parts, one above and one below the Earth; if he were at sphaera obliqua [at an arbitrary latitude], either, again, equinox would never occur at all, or [if it did occur], it would not be at a position halfway between summer and winter solstices, since these intervals would necessarily be unequal, because the equator, which is the greatest of all parallel circles drawn about the poles of the [daily] motion, would no longer be bisected by the horizon; instead [the horizon would bisect] one of the circles parallel to the equator, either to the north or to the south of it.