ABSTRACT
Learned people in the Middle Ages, if they had any interest in the natural clock that was the sky and its celestial bodies, might have had recourse to a widely known Latin text that taught them how to compute the motions of the heavens. The celestial sphere was the fundamental referent of mathematical astronomy, and the fictitious circles of the equator and the lines of latitude, as well as the north and south poles, like the ecliptic, were in origin lines inscribed in the sky, on the inner surface of the imaginary sphere surrounding the spherical, central earth. A sphere is a solid body contained within a single surface, in the middle of which there is a point from which all straight lines drawn to the circumference are equal, and that point is called the center of the sphere. The sphere is divided in two ways, by substance and by accident.
