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 VI: How to Determine the Mean and True Syzygies

Now that we’ve created our table of conjunctions and oppositions, how do we go about using it? As usual, Ptolemy walks through the process in a vacuum, so to help, I’ll follow along with the example Neugebauer does in History of Ancient Mathematical Astronomy on pages $123-124$, although somewhat slimmed down. In particular, I’ll walk through finding the true opposition from the year $718$ in the epoch for the first opposition in the year. Continue reading “Almagest Book VI: How to Determine the Mean and True Syzygies”

Almagest Book VI: Construction of the Table of Mean Syzygies

As promised in the last chapter, Ptolemy’s first task in eclipse prediction is going to be laying out a table of mean syzygies around which eclipses might be possible, so we can check those to see if an eclipse might occur instead of performing useless calculations where the sun and moon are nowhere near a syzygy. In this post, we’ll go over the construction of that table! Continue reading “Almagest Book VI: Construction of the Table of Mean Syzygies”