Geometry and Astronomy:

The need to portray an ideal world  of  perfect forms and proportions led  to the development of geometry by Pythagoras (583-500 B.C.) and Hippocrates of Chios (about 450 B.C.) (Fig.). 'The latter occupied himself with the  solution of problems which were unanswered for a long time. such as squaring the circle and doubling the cube. He  failed in both. but opened  the w;ly to study the geometry ofcurves. Eudoxus (408-355 B.C.)  was probably  the greatest Greek matliematician  and he was able to explain the motion of sun, moon and plancts by means of sets of concentric spheres, each rotatingabout an axis  fixed in the one  outside  it (Fig. 3.12). The model wascrude, and too simple to explain observed facts, even as known at that time. But the sets of actual metal spheres based on  this mode provided the basis for most of the  astronomical instruments for a long time.