A history of Greek mathematics - Wilbourhall.org

196 APOLLONIUS OF PERGA
another hypothesis, that of eccentrics, was invented to account
for the movements of the superior planets only. We are at this
stage when we come to Apollonius. His enunciations show
that he understood the theory of epicycles in all its generality,
but he states specifically that the theory of eccentrics can only
be applied to
the three planets which can be at any distance
from the sun. The reason why he says that the eccentric
hypothesis will not serve for the inferior planets is that, in
order to make it
serve, we should have to suppose the circle
described by the centre of the eccentric circle to be greater
than the eccentric circle itself. (Even this generalization was
made later, at or before the time of Hipparchus.) Apollonius
further says in his enunciation about the eccentric that ' the
centre of the eccentric circle moves about the centre of the
zodiac in the direct order of the signs and at a s r peed equal to
that of the sun, while the star moves on the eccentric about
its centre in the inverse order of the signs and at a speed
equal to the anomaly \ It is clear from this that the theory
of eccentrics was invented for the specific purpose of explaining
the movements of Mars, Jupiter, and Saturn about the
sun and for that purpose alone. This explanation, combined
with the use of epicycles about the sun as centre to account
for the motions of A r enus and Mercury, amounted to the
system of Tycho Brahe that system
;
was therefore anticipated
by some one intermediate in date between Heraclides and
Apollonius and probably nearer to the latter, or it may
have been Apollonius himself who took this important step.
If it was, then Apollonius, coming after Aristarchus of
Samos, would be exactly the Tycho Brahe of the Copernicus
of antiquity. The actual propositions quoted by Ptolemy as
proved by Apollonius among others show mathematically at
what points, under each of the two hypotheses, the apparent
forward motion changes into apparent retrogradation and
vice versa, or the planet appears to be stationary.