Jan P.Hogendijk is a member of the Department of Mathematics in the University of Utrecht . His research interest is the history of the mathematical sciences in Greek antiquity and medieval Islamic civilization. He has recently published an edition of the manthematical works of al-Jurjani(10th c.) and an analysis of the works of Abu Nasr ibn Iraq(ca.1000) on sundial theory. He now works on an edition and English translation of a ninth – century manual of geometrical problems by Nuaim ibn Musa. Between A.D 800and 1450, the most important centers for the study of what we now call the exact sciences – including the mathematical sciences of arithmetic ; geometry, and trigonometry and their applications in such fields as astronomy , astrology , geography, cartography, and optics – were not in Europe but in the vast, multinational Islamic word . Research from the last few decades has profoundly changed our understanding of the Islamic scientific tradition . We now know that it was even richer and more profound and has more complex relations to other cultures than we had previously thought.