New Approaches and Parameters in the Parisian Alfonsine Tables

In this paper we examine several aspects of the Parisian Alfonsine Tables [henceforth PAT] that appeared in Latin around 1320, first in Paris and then diffused throughout Europe. Our focus is on the tables for precession/trepidation, the motion of the planetary apogees, the radices for mean motions, and the mean motions. The goal has been to identify sources for the parameters, and the result is that, for the most part, Andalusian zijes provided the required information, indicating continuity from the table-makers in al-Andalus to Latin Europe. We derive the parameter for the Alfonsine motion in precession from the length of the tropical year ascribed to Azarquiel by Abraham Ibn Ezra. Although the sources for some parameters in PAT have not been identified, there is no evidence that new observations played any role. Among the sources for PAT were the Toledan Tables and al-Battānī’s zij. In the case of the planetary apogees it is shown that the values in PAT were probably derived from those in al-Battānī’s zij, whereas those in the Toledan Tables were almost certainly derived from that zij, despite the fact that the Toledan Tables use sidereal coordinates and al-Battānī used tropical coordinates. In the case of the radices, again values in the Toledan Tables were derived from those in al- Battānī’s zij, but the values in PAT show no such affinity. The mean motions in PAT are closely related to those in several Maghribi zijes, which supports the suggestion that a lost work by Azarquiel may be the common source.