INDUCTIVE EPOCH OF HIPPARCHUS. 183 



and positions of the circles or spheres in which the 

 heavenly bodies were moved, in such a manner as to 

 account for their apparently irregular motions. We 

 may best understand what was the problem to be 

 solved, by calling to mind what we now know to be 

 the real motions of the heavens. The true motion 

 of the earth round the sun, and therefore the appa- 

 rent annual motion of the sun, is performed, not in 

 a circle of which the earth is the center, but in an 

 ellipse or oval, the earth being nearer to one end 

 than to the other; and the motion is most rapid 

 when the sun is at the nearer end of this oval. But 

 instead of an oval, we may suppose the sun to move 

 uniformly in a circle, the earth being now, not in 

 the center, but nearer to one side ; for on this sup- 

 position, the sun will appear to move most quickly 

 when he is nearest to the earth, or in his Perigee, 

 as that point is called. Such an orbit is called an 

 Eccentric, and the distance of the earth from the 

 center of the circle is called the Eccentricity. It 

 may easily be shown by geometrical reasoning, that 

 the inequality of apparent motion so produced, is 

 exactly the same in detail, as the inequality which 

 follows from the hypothesis of a small Epicycle, 

 turning uniformly on its axis, and carrying the sun 

 in its circumference, while the center of this epicycle 

 moves uniformly in a circle of which the earth is 

 the center. This identity of the results of the hypo- 

 thesis of the Eccentric and the Epicyle is proved by 

 Ptolemy in the third book of the "Almagest." 



