A Ptolemaic lunar model of the 17th century: François Viète and his first lunar model

In his unfinished Ad harmonicon coeleste, François Viète (1540–1603) approaches astronomical models in a purely mathematical way, analyzing the equations involved in the geometrical models and suggesting new geometrical approaches, usually equivalent but simpler. After dealing with the Copernican planetary models, he develops three different lunar models. The first one describes a model geometrically similar but not identical to the Ptolemaic lunar model. The second is identical to that of Copernicus, but offers simpler calculation methods, and the third one is inspired by Tycho’s lunar model in the Progymnasmata. In this paper, I describe and analyze the first (Ptolemaic) model, leaving the other two for future works.