THEON OF SMYRNA 
243 
to the seven heavenly bodies and the sphere of the fixed stars. 
The whole of this passage (chaps. 15 to 16, pp. 138-47) is no 
doubt intended as the promised account of the ‘ harmony in 
the universe ’, although at the very end of the work Theon 
implies that this has still to be explained on the basis of 
Thrasyllus’s exposition combined with what he has already 
given himself. 
The next chapters deal with the forward movements, the 
stationary points, and the rétrogradations, as they respectively 
appear to us, of the five planets, and the ‘ saving of the pheno 
mena ’ by the alternative hypotheses of eccentric circles and 
epicycles (chaps. 17-30, pp. 147-78). These hypotheses are 
explained, and the identity of the motion produced by the 
two is shown by Adrastus in the case of the sun (chaps. 26,27, 
pp. 166-72). The proof is introduced with the interesting 
remark that ‘ Hipparchus says it is worthy of investigation 
by mathematicians why, on two hypotheses so different from 
one another, that of eccentric circles and that of concentric 
circles with epicycles, the same results appear to follow ’. It 
is not to be supposed that the proof of the identity could be 
other than easy to a mathematician like Hipparchus; the 
remark perhaps merely suggests that the two hypotheses were 
discovered quite independently, and it was not till later that 
the effect was discovered to be the same, when of course the 
fact would seem to be curious and a mathematical proof would 
immediately be sought. Another passage (p. 188) says that 
Hipparchus preferred the hypothesis of the epicycle, as being 
his own. If this means that Hipparchus claimed to have 
discovered the epicycle-hypothesis, it must be a misapprehen 
sion ; for Apollonius already understood the theory of epi 
cycles in all its generality. According to Theon, the epicycle- 
hypothesis is more ‘ according to nature ’ ; but it was presum 
ably preferred because it was applicable to all the planets, 
whereas the eccentric-hypothesis, when originally suggested, 
applied only to the three superior planets ; in order to make 
it apply to the inferior planets it is necessary to suppose the 
circle described by the centre of the eccentric to be greater 
than the eccentric circle itself, which extension of the hypo 
thesis, though known to Hipparchus, does not seem to have 
occurred to Apollonius. 
R 2