A PROBLEM AND ITS CONDITIONS. 303 



necessity admit that the sun, instead of being situated in the 

 centre of the terrestrial orbit, occupies a point outside that 

 centre, in such a manner that the earth must sometimes be 

 nearer to, and sometimes farther from, the sun. The distance 

 by which it departs from the centre of its orbit, which Coper- 

 nicus, like the ancients, supposed to be circular, is called its 

 eccentricity. 



Astronomers were long preoccupied with the idea of seek- 

 ing in this eccentricity a point where the movements should 

 appear equal. This point was the centre of the equant, a 

 name given to the eccentric circle described from the point 

 of equality or from the centre of the mean movements. 



Now, let us recall the principal condition of the problem 

 which Kepler had undertaken to solve. This condition re- 

 quired that the straight line drawn from the centre of our 

 globe to the centre of the sun, in a word, that the vector 

 radius, as it is called, should describe around the sun certain 

 angles, whose variability should agree with the results of 

 observation. 



Starting from this point, Kepler found that, for certain 

 positions of Mars (in the aphelion and perihelion, corresponding 

 to the minimum and maximum of velocity), the centre of the 

 orbit, always supposing it to be circular, divided into two equal 

 parts (or bisected) the total eccentricity : in other words, that it 

 exactly occupied the middle between the centre of the eccen- 

 tric and the equant of Ptolemseus ; but it did not appear to 

 him necessary to bisect it in other positions, intermediate be- 

 tween those of the aphelion and the perihelion. He established 



