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Based on a wide variety of previously unstudied sources, these articles explain how science was applied to three aspects of Islamic ritual in the Middle Ages: the regulation of the lunar calendar; the organization of the times of the five daily prayers; and the determination of the sacred direction (qibla) towards the Kaaba in Mecca. Simple procedures of folk astronomy were used by the scholars of religious law who determined popular practice; more complicated mathematical methods law who were provided by the scientists - and this proved a powerful incentive for the development of scientific analysis and research. Some of these procedures were to have far-reaching consequences. For example, the astronomical alignment of the Kaaba - known to various medieval writers, but long forgotten - led to the adoption of similar alignments for the qibla, and the final article shows how these were calculated, whether from whether from astronomical observation or geographical computation, and their impact on the orientation of religious and secular architecture across the Islamic world.