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

236 SOME HANDBOOKS
XVI
SOME HANDBOOKS
The description of the handbook on the elements of
astronomy entitled the Introduction to the Phaenomena and
attributed to Geminus might properly have been reserved
for this chapter. It was. however, convenient to deal with
Geminus in close connexion with Posidonius ; for Geminus
wrote an exposition of Posidonius's Meteorologica related to the
original work in such a way that Simplicius, in quoting a long
passage from an epitome of this work, could attribute the
passage to either Geminus or Posidonius in Geminus ' ; '
and it
is evident that, in other subjects too, Geminus drew from, and
was influenced by, Posidonius.
The small work De motu circulari corporum caelestium by
Cleomedes (KXeofirjSovs kvkXlktj Oecopfa) in two Books is the
production of a much less competent person, but is much more
largely based on Posidonius.
This is proved by several references
to Posidonius by name, but it is specially true of the
very long first chapter of Book II (nearly half of the Book)
which seems for the most part to be copied bodily from
Posidonius, in accordance with the author's remark at the
end of Book I that, in giving the refutation of the Epicurean
assertion that the sun is just as large as it looks, namely one
foot in diameter, he will give so much as suffices for such an
introduction of the particular arguments used by 'certain
authors who have written whole treatises on this one topic
(i. e. the size of the sun), among whom is Posidonius '. The
interest of the book then lies mainly in what is quoted from
Posidonius ; its mathematical interest is almost ail.
The date of Cleomedes is not certainly ascertained, but, as
he mentions no author later than Posidonius, it is permissible
to suppose, with Hultsch, that he wrote about the middle of
the first century B. 0. As he seems to know nothing of the
works of Ptolemy, he can hardly, in any case, have lived
later than the beginning of the second century A. D.
Book I begins with a chapter the object of which is to
prove that the universe, which has the shape of a sphere,
is limited and surrounded by void extending without limit in
all directions, and to refute objections to this view. Then
follow chapters on the five parallel circles in the heaven and
the zones, habitable and uninhabitable (chap. 2)
; on the
motion of the fixed stars and the independent (irpoaiptTLKai)
movements of the planets including the sun and moon
(chap. 3); on the zodiac and the effect of the sun's motion in
it (chap. 4)
; on the inclination of the axis of the universe and
its effects on the lengths of days and nights at different places
(chap. 5); on the inequality in the rate of increase in the
lengths of the days and nights according to the time of year,
the different lengths of the seasons due to the motion of the
sun in an eccentric circle, the difference between a day-andnight
and an exact revolution of the universe owing to the
separate motion of the sun (chap. 6)
; on the habitable regions
of the globe including Britain and the island of Thule ' ', said
to have been visited by Pytheas, where, when the sun is in
Cancer and visible, the day is a month long ; and so on (chap. 7).
Chap. 8 purports to prove that the universe is a sphere by
proving first that the earth is a sphere, and then that the air
about it, and the ether about that, must necessarily make up
larger spheres. The earth is proved to be a sphere by the
method of exclusion ; it is assumed that the only possibilities
are that it is (a) flat and plane, or (b) hollow and deep, or
(c) square, or (d) pyramidal, or (e) spherical, and, the first four
hypotheses being successively disposed of, only the fifth
remains.
Chap. 9 maintains that the earth is in the centre of
the universe ;
chap. 10, on the size of the earth, contains the
interesting reproduction of the details of the measurements of
the earth by Posidonius and Eratosthenes respectively which
have been given above in their proper places (p. 220, pp. 1 06-7)
chap. 1 1
argues that the earth is in the relation of a point to,
i. e. is negligible in size in comparison with, the universe or
even the sun's circle, but not the moon's circle (cf. p. 3 above).
Book II, chap. 1, is evidently the 'piece de resistance, con-