Ibn al-Shatir
Mathematical techniques developed in the 13th to 14th centuries by Mo'ayyeduddin al-Urdi, Nasir al-Din al-Tusi, and Ibn al-Shatir for geocentric models of planetary motions closely resemble some of those used later by Copernicus in his heliocentric models. Copernicus used what is now known as the Urdi lemma and the Tusi couple in the same planetary models as found in Arabic sources. Furthermore, the exact replacement of the equant by two epicycles used by Copernicus in the "Commentariolus" was found in an earlier work by Ibn al-Shatir (d. c. 1375) of Damascus. Ibn al-Shatir's lunar and Mercury models are also identical to those of Copernicus. This has led some scholars to argue that Copernicus must have had access to some yet to be identified work on the ideas of those earlier astronomers. However, no likely candidate for this conjectured work has yet come to light, and other scholars have argued that Copernicus could well have developed these ideas independently of the late Islamic tradition. Nevertheless, Copernicus cited some of the Islamic astronomers whose theories and observations he used in "De Revolutionibus", namely al-Battani, Thabit ibn Qurra, al-Zarqali, Averroes, and al-Bitruji.