On Ptolemy’s improvement of the parameters of the latitude models for the superior planets

Abstract

In Almagest XIII, Ptolemy explains his latitude theories for the superior and inferior planets. There he provides, among other things, the values for the inclinationsof the planets eccentres and epicycles. The methods and observations Ptolemy usesto calculate the values of these inclinations are highly problematic and are one ofthe main reasons for the predictive difficulties of the models. This is because theyyield a final value for the inclinations of the eccentre and epicycle which are, in manycases, grossly incorrect. The latitude models for the superior planets in the PlanetaryHypotheses signify a definitive improvement in the sense that they provide very accurate inclinations for both the eccentre and the epicycle. The main purpose of the paperis to present a simple and plausible explanation of how Ptolemy could have arrivedat the accurate values he provides in the Planetary Hypotheses. As we will show, themethod we propose is consistent with Ptolemy’s general methodology when facingsimilar problems. Also, and crucially, we will show that they relate to the work hehad done in the Almagest on the latitude tables. Finally, we will show that in the yearshe was probably starting to work in his post-Almagest modifications, he had at hisdisposal potential observations which were very well suited to our method.