Spherical Astronomy in the Almagest
In Chapter 3 our exposition was unhistorical in so far as Ptolemy did not present his spherical trigonometry as an abstract mathematical theory. He developed it in close connection with spherical astronomy, and we dealt with the two subjects separately only in order to get a coherent survey of the complete mathematical apparatus implicit in the Almagest. Accordingly we must now consider the astronomical aspect of Ptolemy’s spherical trigonometry, examining a series of problems connected with the geometry of the celestial sphere and its diurnal revolution. Only the main problems are investigated while a number of minor corollaries, or theorems of secondary importance are left out.