A history of Greek mathematics - Wilbourhall.org

GEMINUS 231
and make equal angles with it, the straight lines are equal. 1
As Apollonius wrote on the cylindrical helix and proved the
fact of its uniformity, we may fairly assume that Geminus
was here drawing upon Apollonius.
Enough has been said to show how invaluable a source of
information Geminus's work furnished to Proclus and all
writers on the history of mathematics who had access to it.
In astronomy we know that Geminus wrote an egrjyrjo-is of
Posidonius's work, the Meteorologica or irepi /zerecooow. This
is the source of the famous extract made from Geminus by
Alexander Aphrodisiensis, and reproduced by Simplicius in
his commentary on the Physics of Aristotle, 2
on which Schiaparelli
relied in his attempt to show that it was Heraclides of
Pontus, not Aristarchus of Samos, who first put forward the
heliocentric hypothesis. The extract is on the distinction
between physical and astronomical inquiry as applied to the
heavens. It is the business of the physicist to consider the
substance of the heaven and stars, their force and quality,
their coming into being and decay, and he is in a position to
prove the facts about their size, shape, and arrangement;
astronomy, on the other hand, ignores the physical side,
proving the arrangement of the heavenly bodies by considerations
based on the view that the heaven is a real /coV/zoy, and,
when it tells us of the shapes, sizes and distances of the earth,
sun and moon, of eclipses and conjunctions, and of the quality
and extent of the movements of the heavenly bodies, it is
connected with the mathematical investigation of quantity,
size, form, or shape, and uses arithmetic and geometry to
prove its conclusions. Astronomy deals, not with causes, but
with facts ; hence it often proceeds by hypotheses, stating
certain expedients by which the phenomena may be saved.
For example, why do the sun, the moon and the planets
appear to move irregularly ?
To explain the observed facts
we may assume, for instance, that the orbits are eccentric
circles or that the stars describe epicycles on a carrying
circle ; and then we have to go farther and examine other
ways in which it is possible for the phenomena to be brought
about. ' Hence we actually find a certain person [Heraclides
1
Proclus on Eucl. I, pp. 112. 22-113. 3, p. 251. 3-11.
2
Simpl. in Phys., pp. 291-2, ed. Diels.