Medieval astronomers and philosophers developed diverse theories about the causes of the celestial spheres' motions. They attempted to explain the spheres' motions in terms of the materials of which they were thought to be made, external movers such as celestial intelligences, and internal movers such as motive souls or impressed forces. Most of these models were qualitative, although a few incorporated quantitative analyses that related speed, motive force and resistance. By the end of the Middle Ages, the common opinion in Europe was that celestial bodies were moved by external intelligences, identified with the angels of revelation. The outermost moving sphere, which moved with the daily motion affecting all subordinate spheres, was moved by an unmoved mover, the Prime Mover, who was identified with God. Each of the lower spheres was moved by a subordinate spiritual mover (a replacement for Aristotle's multiple divine movers), called an intelligence.