PROGRESS OF GEOMETRICAL ASTRONOMY. 173 



Eisted &quot; of circular rims, raoveablc one within the other, or 

 about poles, and contained circles which were to be brought 

 into the position of the ecliptic, and of a plane passing 

 through the sun and the poles of the ecliptic&quot; an instru 

 ment, therefore, which represented, as by a model, the rel 

 ative positions of certain imaginary lines and planes in tho 

 heavens ; which was adjusted by putting these representa 

 tive lines and planes into parallelism and coincidence M ith 

 the celestial ones ; and which depended for its use upon the 

 perception that the relations between these representative 

 lines and planes were equal to the relations between those 

 represented. 



Were there space, we might go on to point out how the 

 conception of the heavens as a revolving hollow sphere, 

 the discovery of the globular form of the earth, the expla 

 nation of the moon s phases, and indeed all the successive 

 steps taken, involved this same mental process. But we 

 must content ourselves with referring to the theory of ec 

 centrics and epicycles, as a further marked illustration of 

 it. As first suggested, and as proved by llipparchus to af 

 ford an explanation of the leading irregularities in the ce 

 lestial motions, this theory involved the perception that 

 the progressions, retrogressions, and variations of velocity 

 seen in the heavenly bodies, might be reconciled with their 

 assumed uniform movement in circles, by supposing that 

 the earth was not in the centre of their orbits ; or by sup 

 posing that they revolved in circles Avhose centres revolved 

 round the earth ; or by both. The discovery that this 

 would account for the appearances, was the discovery that 

 in certain geometrical diagrams the relations were such, 

 that the uniform motion of a point would, when looked at 

 from a particular position, present analogous irregularities ; 

 and the calculations of Hipparchus involved the belief that the 

 relations subsisting among these geometrical curves were 

 to the relations subsisting among the celestial orbits. 



