5$ 5, si] The Almagest 69 



the positions assigned to the stars in Ptolemy's catalogue 

 agrees better with their actual positions in the time of 

 Hipparchus, corrected for precession at the supposed rate of 

 36" annually, than with their actual positions in Ptolemy's 

 time. It is therefore probable that the catalogue as a 

 whole does not represent genuine observations made by 

 Ptolemy, but is substantially the catalogue of Hipparchus 

 corrected for precession and only occasionally modified by 

 new observations by Ptolemy or others. 



51. The last five books deal with the theory of the 

 planets, the most important of Ptolemy's original contribu- 

 tions to astronomy. The problem of giving a satisfactory 

 explanation of the motions of the planets was, on account 

 of their far greater irregularity, a much more difficult one 

 than the corresponding problem for the sun or moon. The 

 motions of the latter are so nearly uniform that their 

 irregularities may usually be regarded as of the nature of 

 small corrections, and for many purposes may be ignored. 

 The planets, however, as we have seen (chapter i., 14), do 

 not even always move from west to east, but stop at intervals, 

 move in the reverse direction for a time, stop again, and 

 then move again in the original direction. It was probably 

 recognised in early times, at latest by Eudoxus ( 26), that 

 in the case of three of the planets, Mars, Jupiter, and Saturn, 

 these motions could be represented roughly by supposing 

 each planet to oscillate to and fro on each side of a fictitious 

 planet, moving uniformly round the celestial sphere in or 

 near the ecliptic, and that Venus and Mercury could 

 similarly be regarded as oscillating to and fro on each side 

 of the sun. These rough motions could easily be inter- 

 preted by means of revolving spheres or of epicycles, as was 

 done by Eudoxus and probably again with more precision 

 by Apollonius. In the case of Jupiter, for example, we 

 may regard the planet as moving on an epicycle, the centre 

 of which, j\ describes uniformly a deferent, the centre of 

 which is the earth. The planet will then as seen from the 

 earth appear alternately to the east (as at j,) and to the 

 west (as at J 2 ) of the fictitious planet y; and the extent of 

 the oscillation on each side, and the interval between suc- 

 cessive appearances in the extreme positions (j b J 2 ) on either 

 side, can be made right by choosing appropriately the size 



