Tycho Brahe’s Appendix ad Observationes anni 1593 and the date of Brahe’s theory of Mars, the prototype for Kepler’s vicarious hypothesis

The Alfonsine and Prutenic tables of planetary latitudes, with which Tycho Brahe began his work, had several deficiencies, ultimately inherited from Ptolemy’s simplifications when he constructed tables for his extremely complicated models. In this paper, we analyze a manuscript that shows Brahe’s attempts at removing these deficiencies by trying several different options, some of which were, to say the least, audacious. We also offer an analysis of the manuscript that helps to date the creation of the non-bisected divided eccentricity model that underlies some of these attempts, and which would prove to be influential in the general history of modern astronomy.