This paper analyses a kinematic model for the solar motion by Quṭb al-Dīn al-Shīrāzī, a thirteenth-century Iranian astronomer at the Marāgha observatory in northwestern Iran. The purpose of this model is to account for the continuous decrease of the obliquity of the ecliptic and the solar eccentricity since the time of Ptolemy. Shīrāzī puts forward different versions of the model in his three major cosmographical works. In the final version, in his Tuḥfa, the mean ecliptic is defined by an eccentric (...) of fixed mean eccentricity and a mean obliquity fixed with respect to the celestial equator, and the center of the epicycle, which is inclined to the eccentric, moves on the eccentric with an annual period. By an additional slow motion of the sun on the epicycle, the true eccentricity of the solar deferent, defined by the annual motion of the sun, and the sun’s extreme declination from the equator change, accounting for the reduction of the eccentricity and the obliquity of the ecliptic since the time of Ptolemy. (shrink)