Ptolemy's Theories of the Latitude of the Planets in the Almagest, Handy Tables, and Planetary Hypotheses

Abstract

The theory of planetary latitude in Book 13 of the Almagest is known, if at all, for its complexity. This has the pleasant result that there is only a small literature on it and that literature is on a high level of technical competence. The same, by the way, is true of latitude theory in general. There are recent expositions by Pedersen and Neugebauer, earlier ones by Delambre and Herz, and a few briefer treatments. Paradoxically, the complexity of Ptolemy's theory is both its strength and its weakness, its strength because he reached it by doing everything right, at least in principle, its weakness because it is ultimately wrong, as was later recognized by Ptolemy himself, who went on to remedy its deficiencies. It is, as we may say, wrong for the right reasons. And since being wrong for the right reasons is more or less the subject of this collection – for is not most interesting older science wrong for the right reasons? – Ptolemy's latitude theory seems quite appropriate. Our object here is to explain the latitude theory, first its original form in the Almagest, then its later modifications in the Handy Tables and Planetary Hypotheses, each of which shows improvements, and to investigate its observational foundation, for it is the observations that are the cause of both its strength and its weakness. It is unusual to find any revisions in the work of an ancient scientist, but in the case of Ptolemy's latitude theory three distinct stages are known, which may be unique, showing that he himself knew something was wrong and twice set out to correct it.

Additional details