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As a leading scientist of the 13th century C. E. Qu?b al-D?n Sh?r?z? wrote three substantial works on hay’a (or the configuration of the celestial orbs):* * Nih?yat al-idr?k f? dir?yat al-afl?k (“The Limits of Attainment in the Understanding of the Heavens”), al-Tu?fa al-sh?h?ya f? ‘ilm al-hay’a (“The Royal Offering Regarding the Knowledge of the Configuration of the Heavens”), and Ikht?y?r?t-i Mu?affar? (“The Mu?affar? Elections”). Completed in less than four years and written in two of the classical languages of the Islamic world, Arabic and Persian, these works provide a fascinating window to the astronomical research carried out in Ilkhanid Persia. Sh?r?z? and his colleagues were driven by their desire to rid Ptolemaic astronomy from its perceived shortcomings. An intriguing trail of revisions and emendations in Sh?r?z?’s hay’a texts serves to highlight both those features of Sh?r?z?'s astronomy that were inherited from his predecessors, as well as his original contributions to this branch of astronomical research. As a renowned savant, Sh?r?z? spent a large portion of his career near centers of political power in Persia and Anatolia. A study of his scientific output and career as a scholar is an opportunity, therefore, for an examination of the patronage of science and of scientific works within the Ilkhanid realms. Not only was this patronage important to the work of scholars such as Sh?r?z? but it was critical to the founding and operation of one of the foremost scientific institutions of the medieval Islamic world, the Mar?gha observatory. The astronomical tradition in which Sh?r?z? carried out his research has many links, as well, to the astronomy of Early Modern Europe, as can be seen in the astronomical models of Copernicus.