Ibn al-Shatir
Ibn al-Shatir (1304–1375), in his "A Final Inquiry Concerning the Rectification of Planetary Theory", eliminated the need for an equant by introducing an extra epicycle, departing from the Ptolemaic system in a way very similar to what Copernicus later also did. Ibn al-Shatir proposed a system that was only approximately geocentric, rather than exactly so, having demonstrated trigonometrically that the Earth was not the exact center of the universe. His rectification is later used in the Copernican model.