A history of Greek mathematics - Wilbourhall.org

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 retrogradations, as they respectively
appear to us, of the five planets, and the saving of the phenomena
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 misapprehension
; for Apollonius already understood the theory of epicycles
in all its generality. According to Theon, the epicyclehypothesis
is more according to nature ' ' ; but it was presumably
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 hypothesis,
though known to Hipparchus, does not seem to have
occurred to Apollonius.
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