sentences:  He declared the Ptolemaic system as an imaginary model, successful at predicting planetary positions, but not real or physical.Al-Btiruji's alternative system spread through most of Europe during the 13th century.Mathematical techniques developed in the 13th to 14th centuries by the Arab and Persian astronomers Mo'ayyeduddin al-Urdi, Nasir al-Din al-Tusi, and Ibn al-Shatir (died circa 1375) for geocentric models of planetary motions closely resemble some of the techniques used later by Copernicus in his heliocentric models.