A history of Greek mathematics - Wilbourhall.org

234 SUCCESSORS OF THE GREAT GEOMETERS
(76 years). Chapter 9 deals with the moon's phases, chapters
10,11 with eclipses of the sun and moon, chapter 1 2 with the
problem of accounting for the motions of the sun, moon and
planets, chapter 13 with Risings and Settings and the various
technical terms connected therewith, chapter 14 with the
circles described by the fixed stars, chapters 15 and 16 with
mathematical and physical geography, the zones, &c. (Geminus
follows Eratosthenes's evaluation of the circumference of the
earth, not that of Posidonius).
Chapter 17, on weather indications,
denies the popular theory that changes of atmospheric
conditions depend on the rising and setting of certain stars,
and states that the predictions of weather (e7TLar)/j.a(riai.) in
calendars (irapaiTrjyfiara) are only derived from experience
and observation, and have no scientific value. Chapter 18 is
on the k^Xiyjios, the shortest period which contains an integral
number of synodic months, of days, and of anomalistic revolutions
of the moon ; this period is three times the Chaldaean
period of 223 lunations used for predicting eclipses. The end
of the chapter deals with the maximum, mean, and minimum
daily motion of the moon. The chapter as a whole does not
correspond to the rest of the book ; it deals with more difficult
matters, and is
thought by Manitius to be a fragment only of
a discussion to which the compiler did not feel himself equal.
At the end of the work is a calendar (Parapegma) giving the
number of days taken by the sun to traverse each sign of
the zodiac, the risings and settings of various stars and the
weather indications noted by various astronomers, Democritus,
Eudoxus, Dositheus, Euctemon, Meton, Callippus ; this calendar
is unconnected with the rest of the book and the contents
are in several respects inconsistent with it, especially the
division of the year into quarters which follows^ Callippus
rather than Hipparchus. Hence it has been, since Boeckh's
time, generally considered not to be the work of Geminus.
Tittel, however, suggests that it is not impossible that Geminus
may have reproduced an older Parapegma of Callippus.