Ibn al-Shatir
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 or Aristotelian cosmology, but rather to produce a model that was more consistent with empirical observations. For example, it was Ibn al-Shatir's concern for observational accuracy which led him to eliminate the epicycle in the Ptolemaic solar model and all the eccentrics, epicycles and equant in the Ptolemaic lunar model. His model was thus in better agreement with empirical observations than any previous model, and was also the first that permitted empirical testing. His work thus marked a turning point in astronomy, which may be considered a "Scientific Revolution before the Renaissance". His rectified model was later adapted into a heliocentric model by Copernicus, which was mathematically achieved by reversing the direction of the last vector connecting the Earth to the Sun.