In modern celestial mechanics, the goal is to construct a coordinate system in the heavens, and then to develop theories that will allow us to calculate the coordinates of the Sun, Moon and planets as functions of time. The goal of astronomy among ancient peoples was probably quite different; it was probably to develop methods of dealing with certain appearances in a coordinate system based upon the observer's horizon. These appearances include eclipses, the positions at which celestial objects rise and set, and methods of telling both the time of day and the time of the year by observations of risings and settings. This paper is concerned with discussions of these appearances. It deals with theories of motion only to the extent needed in discussing the appearances.