A history of Greek mathematics Vol.II from Aristarchus to Diophantus by Heath, Thomas Little, Sir, 1921

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.
232 SUCCESSORS OF THE GREAT GEOMETERS
of Pontus] coming forward and saying that, even on the
assumption that the earth moves in a certain ivay, while
the sun is in a certain way at rest, the apparent irregularity
with reference to the sun may be saved! Philological considerations
as well as the other notices which we possess
about Heraclides make it practically certain that ' Heraclides
of Pontus ' is an interpolation and that Geminus said tl?
simply, ' a certain person ', without any name, though he
doubtless meant Aristarchus of Samos. 1
Simplicius says that Alexander quoted this extract from
the epitome of the egijyrjo-is by Geminus. As the original
work was apparently made the subject of an abridgement, we
gather that it must have been of considerable scope. It is
'
a question whether egrjyrjcris means commentary ' or ex-
'
position ' ; I am inclined to think that the latter interpretation
is the correct one, and that Geminus reproduced Posidonius's
work in its entirety with elucidations and comments ; this
seems to me to be suggested by the words added by Simplicius
immediately after the extract this ' is the account given by
Geminus, or Posidonius in Geminus, of the difference between
physics and astronomy', which seems to imply that Geminus
in our passage reproduced Posidonius textually.
' '
Introduction to the Phaenomena attributed to Geminus.
There remains the treatise, purporting to be by Geminus,
which has come down to us under the title Teyiivov elaaycoyr)
els ra ouv6neva. 2 What, if any, is the relation of this work
to the exposition of Posidonius's Meteorologica or the epitome
of it just mentioned? One view is that the original Isagoge
of Geminus and the e^rjyrjo-Ls of Posidonius were one and the
same work, though the Isagoge as we have it is not by
Geminus, but„by an unknown compiler. The objections to
this are, first, that it does not contain the extract given by
Simplicius, which would have come in usefully at the beginning
of an Introduction to Astrononi}^ nor the other extract
given by Alexander from Geminus and relating to the rainbow
which seems likewise to have come from the egijyrjo-Ls 3 ;
1
Cf. Aristarchus of Samos, pp. 275-83.
2
Edited by Manitius (Teubner, 1898).
3
Alex. Aphr. on Aristotle's Meteorologica, iii. 4, 9 (Ideler. ii, p. 128;
p. 152. 10, Hayduck).