which would only save the phenomena. The Maragha astronomers also realized that the Aristotelian view of motion in the universe being only circular or linear was not true, as the Tusi-couple showed that linear motion could also be produced by applying circular motions only. Unlike the ancient Greek and Hellenistic astronomers who were not concerned with the coherence between the mathematical and physical principles of a planetary theory, Islamic astronomers insisted on the need to match the mathematics with the real world surrounding them, which gradually evolved from a reality based on Aristotelian physics to one based on an empirical and mathematical physics after the work of Ibn al-Shatir. The Maragha Revolution was thus characterized by a shift away from the philosophical foundations of Aristotelian cosmology and Ptolemaic astronomy and towards a greater emphasis on the empirical observation and mathematization of astronomy and of nature in general, as exemplified in the works of Ibn al-Shatir, Qushji, al-Birjandi and al-Khafri. Other achievements of the Maragha school include the first empirical observational evidence for the Earth's rotation on its axis by al-Tusi and Qushji, the separation of natural philosophy from astronomy by Ibn al-Shatir and Qushji, the rejection of the Ptolemaic model on empirical rather than philosophical grounds by Ibn al-Shatir, and the development of a non-Ptolemaic model by Ibn al-Shatir that was mathematically identical to the heliocentric Copernical model. Mo'ayyeduddin Urdi (d. 1266) was the first of the Maragheh astronomers to develop a non-Ptolemaic model, and he proposed a new theorem, the "Urdi lemma". Nasīr al-Dīn al-Tūsī (1201–1274) resolved significant problems in the Ptolemaic system by developing the Tusi-couple as an alternative to the physically problematic equant introduced by Ptolemy. Tusi's student Qutb al-Din al-Shirazi (1236–1311), in his The Limit of Accomplishment concerning Knowledge of the Heavens, discussed the possibility of heliocentrism. Al-Qazwīnī al-Kātibī, who also worked at the Maragheh observatory, in his Hikmat al-'Ain, wrote an argument for a heliocentric model, though he later abandoned the idea. Ibn al-Shatir (1304–1375) of Damascus, in A Final Inquiry Concerning the Rectification of Planetary Theory, incorporated the Urdi lemma, and eliminated the need for an equant by introducing an extra epicycle (the Tusi-couple), departing from the Ptolemaic system in a way that was mathematically identical to what Nicolaus Copernicus did in the 16th century. Unlike previous astronomers before him, Ibn al-Shatir was not concerned with adhering to the theoretical principles of natural philosophy