Almagest Book XI: Verification of Jupiter Derivations

Now that we’ve gotten an understanding of the eccentricity and line of apsides for Jupiter, Ptolemy wants to demonstrate that they are correct. He plans to demonstrate this, as he did for Mars,

from the fact that the apparent intervals [in longitude] of the planet derived from the ratios we have thus found turn out to be the same as those observed.

Continue reading “Almagest Book XI: Verification of Jupiter Derivations”

Almagest Book XI: Jupiter’s Eccentricity

Now that we have established the periodic motion, anomalies, and epochs of the planet Mars, we shall next deal with those of Jupiter in the same way.

It certainly strikes me that splitting up the planets between books is an odd choice on Ptolemy’s part, but at least the methods will be familiar. As Ptolemy tells us:

Once again, we first take, to demonstrate [the position on] the apogee and [the ratio of] the eccentricity, three oppositions [in which Jupiter is] directly opposite the mean sun.

This will be directly paralleling the work we did in X.7-10 for Mars. So bring on the observations! Continue reading “Almagest Book XI: Jupiter’s Eccentricity”

Almagest Book X: Correction to the Periodic Motions

Back in IX.3, Ptolemy noted that the planetary periods

have been corrected by us, on the basis of the comparison of their positions which became possible after we had demonstrated their anomalies, as we shall explain at that point.

As a reminder, what he was telling us then, was that he had made corrections to the periods provided to him by Hipparchus. We’ll now go over those corrections for Mars. Continue reading “Almagest Book X: Correction to the Periodic Motions”