François Viète and his analysis of the Copernican 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 them 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 Viète significantly simplifies the calculation methods, and the third one is inspired by Tycho’s lunar model. In a previous paper, I analyzed the first model. In this paper, I describe and analyze the second one, leaving for a future work the third one. Extending the ellipse models used by Viète for the outer planets, I also show that every model of epicycle and deferent can be replaced by a planet revolving on a rotating ellipse.