Ptolemy on Sundials
work relevant to sundials
. The problem it addresses in general terms is that of finding, through geometrical constructions on a plane, those arcs and angles by which a specific point may be determined on the celestial sphere. This is useful in the design of sundials, in which the position of the sun in the sky (that is, on the celestial sphere) needs to be related to the line traced out by the shadow of the gnomon (the pointer of the sundial) on the plane of the sundial itself. More specifically, Ptolemy's Analemma
seeks to derive the position of the sun in spherical co-ordinates given certain data such as the hour of day and the geographical latitude.
Ptolemy's advance over previous methods was to employ a more elegant and convenient system of spherical co-ordinates with which to identify points on the celestial sphere, and to employ a graphical technique ('nomographic', in modern terminology), for generating the necessary plane geometrical constructions, that was far more convenient than working through the problem using trigonometry.