A history of Greek mathematics - Wilbourhall.org

OTHER LOST WORKS 195
Astronomy.
We are told by Ptolemaeus Chennus * that Apollonius was
famed for his astronomy, and was called e (Epsilon) because
the form of that letter is associated with that of the moon, to
which his accurate researches principally related. Hippolytus
says he made the distance of the moon's circle from the surface
of the earth to be 500 myriads of stades. 2 This figure
can hardly be right, for, the diameter of the earth being,
according to Eratosthenes's evaluation, about eight myriads of
stades, this would make the distance of the moon from the
earth about 125 times the earth's radius.
This is an unlikely
figure, seeing that Aristarchus had given limits for the ratios
between the distance of the moon and its diameter, and
between the diameters of the moon and the earth, which lead
to about 1 9 as the ratio of the moon's distance to the earth's
radius.
Tannery suggests that perhaps Hippolytus made a
mistake in copying from his source and took the figure of
5,000,000 stades to be the length of the radius instead of the
diameter of the moon's orbit.
But we have better evidence of the achievements of Apollonius
in astronomy. In Ptolemy's Syntaxis 3 he appears as
an authority upon the hypotheses of epicycles and eccentrics
designed to account for the apparent motions of the planets.
The propositions of Apollonius quoted by Ptolemy contain
exact statements of
the alternative hypotheses, and from this
fact it was at one time concluded that Apollonius invented
the two hypotheses. This, however, is not the case. The
hypothesis of epicycles was already involved, though with
restricted application, in the theory of Heraclides of Pontus
that the two inferior planets, Mercury and Venus, revolve in
circles like satellites round the sun, while the sun itself
revolves in a circle round the earth ; that is, the two planets
describe epicycles about the material sun as moving centre.
In order to explain the motions of the superior planets by
means of epicycles it was necessary to conceive of an epicycle
about a point as moving centre which is
not a material but
a mathematical point. It was some time before this extension
of the theory of epicycles took place, and in the meantime
1
apud Photium, Cod. cxc, p. 151 b 18, ed. Bekker.
2
Hippol. Refut. iv. 8, p. 66, ed. Duncker.
3
Ptolemy, Syntaxis, xii. 1.
o 2