448 HISTORY OF FORMAL ASTRONOMY. 



much more marked, additional difficulties came in 

 his way ; and here again the true supposition, that 

 the oval is of that special kind called ellipse, was 

 adopted at first only in order to simplify calcu- 

 lation 8 , and the deviation from exactness in the 

 result was attributed to the inaccuracy of those 

 approximate processes. The supposition of the 

 oval had already been forced upon Purbach in the 

 case of Mercury, and upon Reinhold in the case of 

 the Moon. The center of the epicycle was made 

 to describe an egg-shaped figure in the former case, 

 and a lenticular figure in the latter 9 . 



It may serve to show the kind of labour by 

 which Kepler was led to his result, if we here enu- 

 merate, as he does in his forty-seventh chapter 10 , 

 six hypotheses, on which he calculated the longi- 

 tudes of Mars, in order to see which best agreed 

 with observation. 



1. The simple eccentricity. 



2. The bisection of the eccentricity, and the 

 duplication of the superior "part of the equation. 



3. The bisection of the eccentricity and a sta- 

 tionary point of equations, after the manner of 

 Ptolemy. 



4. The vicarious hypothesis by a free section 

 of the eccentricity made to agree as nearly as pos- 

 sible with the truth. 



8 De Stella Mortis, iv. c. 47- 9 L. U. K. Kepler, p. 30. 

 10 De Stella Martis, p. 228. 



