This collection of studies by Edward Kennedy looks first at questions of spherical astronomy, celestial mapping and planetary models, and then deals with astrological calculations. Throughout the author emphasises the importance of advances in mathematics for understanding the development of medieval Arabic sciences. This collection of studies based on previously unexploited manuscript sources in Arabic and Persian. They were written by authors from the 9th through the 15th centuries, whose locations reached from south China in the east through Central Asia, the Middle and Near East, and North Africa, to Spain in the west. The topics are predominately astronomical rather than astrological. The former include eclipse predictions, problems in spherical astronomy, non-ptolemaic planetary theory, and the achievements of Ulugh Beg and his observatory. Astrological subjects treated are the method of calculating the ascendant, and how to determine astrological houses and lots. An astrological history of the career of Genghis Khan is also described.