248 NOTES TO BOOK III. 



these Planets, according to his assumption, the Periodic 

 Time of the Planet in its Epicycle was to the Periodic 

 Time of the Epicyclical Center on the Deferent, as the 

 synodical Revolution of the Planet to the tropical Revo- 

 lution of the Earth above the Sun. For the three supe- 

 rior Planets, Mars, Jupiter, and Saturn, the Radius of 

 the Deferent was equal to the Radius of the Planet's 

 orbit, and the Radius of the Epicycle was equal to the 

 Radius of the Earth's orbit ; the Periodic Time of the 

 Planet in its Epicycle was to the Periodic Time of the 

 Epicyclical Center on the Deferent, as the synodical 

 Revolution of the Planet to the tropical Revolution of the 

 same Planet. 



Ptolemy might obviously have made the geometrical 

 motions of all the Planets correspond with the observa- 

 tions by one of these two modes of construction ; but he 

 appears to have adopted this double form of the theory, 

 in order that in the inferior, as well as in the superior 

 Planets, he might give the smaller of the two Radii to 

 the Epicycle : that is, in order that he might make the 

 smaller circle move round the larger, not vice versa. 

 Littrovfs Note. 



