A history of Greek mathematics - Wilbourhall.org

242 SOME HANDBOOKS
the earth, represented e.g. by mountains, are negligible in
comparison with the size of the whole, he quotes Eratosthenes
and Dicaearchus as claiming to have discovered that the
perpendicular height of the highest mountain above the normal
level of the land is no more than 1 stades ; and to obtain the
diameter of the earth he uses Eratosthenes's figure of approximately
252,000 stades for" the circumference of the earth,
which, with the Archimedean value of - 2 2
T
- for 7r, gives a
diameter of about 80,182 stades. The principal astronomical
circles in the heaven are next described (chaps. 5-12, pp.
129-35) ; then (chap. 12) the assumed maximum deviations in
latitude are given, that of the sun being put at 1°, that of the
moon and Venus at 12°, and those of the planets Mercury,
Mars, Jupiter and Saturn at 8°, 5°, 5° and 3° respectively; the
obliquity of the ecliptic is given as the side of a regular polygon
of 15 sides described in a circle, i.e. as 24° (chap. 23, p. 151).
Next the order of the orbits of the sun, moon and planets is explained
(the system is of course geocentric) ; we
are told (p. 138)
that ' some of the Pythagoreans ' made the order (reckoningoutwards
from the earth) to be moon, Mercury, Venus, sun,
Mars, Jupiter, Saturn, whereas (p. 142) Eratosthenes put the
sun next to the moon, and the mathematicians, agreeing with
Eratosthenes in this, differed only in the order in which they
placed Venus and Mercury after the sun, some putting Mercury
next and some Venus (p. 143). The order adopted by ' some
of the Pythagoreans ' is the Chaldaean order, which was not
followed by any Greek before Diogenes of Babylon (second
century B.C.);
'some of the Pythagoreans' are therefore the
later Pythagoreans (of whom Nicomachus was one) ; the other
order, moon, sun, Venus, Mercury, Mars, Jupiter, Saturn, was
that of Plato and the early Pythagoreans. In chap. 15
(p. 138 sq.) Theon quotes verses of Alexander 'the Aetolian'
(not really the ' Aetolian ', but Alexander of Ephesus, a contemporary
of Cicero, or possibly Alexander of Miletus, as
Chalcidius calls him) assigning to each of the planets (including
the earth, though stationary) with the sun and moon and
the sphere of" the fixed stars one note, the intervals between
the notes being so arranged as to bring the nine into an
octave, whereas with Eratosthenes and Plato the earth was
excluded, and the eight notes of the octachord were assigned