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As in the other sciences, astronomers in the Muslim lands built upon and greatly expanded earlier traditions. At the House of Knowledge founded in Baghdad by the Abbasid caliph Mamun, scientists translated many texts from Sanskrit, Pahlavi or Old Persian, Greek and Syriac into Arabic, notably the great Sanskrit astronomical tables and Ptolemy's astronomical treatise, the Almagest. Muslim astronomers accepted the geometrical structure of the universe expounded by Ptolemy, in which the earth rests motionless near the center of a series of eight spheres, which encompass it, but then faced the problem of reconciling the theoretical model with Aristotelian physics and physical realities derived from observation.

Some of the most impressive efforts to modify Ptolemaic theory were made at the observatory founded by Nasir al-Din Tusi in 1257 at Maragha in northwestern Iran and continued by his successors at Tabriz and Damascus. With the assistance of Chinese colleagues, Muslim astronomers worked out planetary models that depended solely on combinations of uniform circular motions. The astronomical tables compiled at Maragha served as a model for later Muslim astronomical efforts. The most famous imitator was the observatory founded in 1420 by the Timurid prince Ulughbeg at Samarkand in Central Asia, where the astronomer Ghiyath al-Din Jamshid al-Kashi worked out his own set of astronomical tables, with sections on diverse computations and eras, the knowledge of time, the course of the stars, and the position of the fixed stars. Essentially Ptolemaic, these tables have improved parameters and structure as well as additional material on the Chinese Uighur-calendar. They were widely admired and translated even as far away as England, where John Greaves, professor at Oxford, called attention to them in 1665.