On the equant point for the planets and the moon

Abstract

The introduction of the equant point signified a major improvement in the history of planetary models. Thanks to its incorporation in ancient planetary hypotheses, Greek astronomy reached a higher degree of accuracy in its predictive capabilities than any of its predecessors, an accuracy that would not be surpassed until as late as the seventieth century, when Kepler postulated his laws. In the Almagest, Ptolemy explains how he arrived at the necessity of the introduction of the equant point for Venus and Mercury. There is, however, some unsolved matter surrounding the argument Ptolemy gives and most scholars dispute that his observations of Venus were in fact the empirical basis from which Ptolemy built his model. These considerations led scholars to wonder about the real path Ptolemy took to discover the equant. In this paper, we present a simple argument through which Ptolemy might have arrived to the conclusion of the existence of an equant for the models of the planets, and to his conclusion of the bisection of the equant’s eccentricity by the centre of the deferent. Moreover, we show that this same argument could have been used to solve the problems posed by the second lunar anomaly.