PEOGEESS OF GEOMETRICAL ASTKONOISIY. 1T3 



(sisted " of circular rims, moveable one within the other, or 

 about poles, and contained circles which were to be brought 

 into the position of the eclii:>tic, and of a plane passing 

 through the sun and the poles of the ecliptic " — an instru- 

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

 ative positions of certain imaginary lines and planes in th<^ 

 heavens ; which was adjusted by j^utting these representa- 

 tive lines and planes into parallelism and coincidence with 

 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 Hipparchus 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 whose 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 

 tqucJ, to the relations subsisting among the celestial orbits. 



