Only recently have the abundant sources relating to the application of astronomy to the needs of religious ritual in medieval Islam been studied, and it is now possible to write a new chapter in the history of Islamic astronomy. Simple techniques were advocated by the scholars of the religious law, highly sophisticated and complicated solutions were proposed by the Muslim scientists. It is not without interest to compare and contrast this activity, which lasted over a millennium, with that of the (...) monks of the Christian Middle Ages. The history of the latter has not yet been written, and cannot be written from textual sources alone, as is clearly shown by some of the astronomical instruments presented here. The present essay, in which both the Islamic and Christian traditions are discussed side by side for the first time, is very much a preliminary venture, primarily intended to point to the inherent interest of the available materials for the history of science as well as for several other disciplines. (shrink)