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

GEMINUS 233
secondly, that it does not anywhere mention the name of
Posidonius (not, perhaps, an insuperable objection) ; and,
thirdly, that there are views expressed in it which are not
those held by Posidonius but contrary to them. Again, the
writer knows how to give a sound judgement as between
divergent views, writes in good style on the whole, and can
hardly have been the mere compiler of extracts from Posidonius
which the view in question assumes him to be. It
seems in any case safer to assume that the Isagoge and the
egrjyrjo-is were separate works. At the same time, the Isagoge,
as we have it, contains errors which we cannot attribute to
Geminus. The choice, therefore, seems to lie between two
alternatives : either the book is by Geminus in the main, but
has in the course of centuries suffered deterioration by interpolations,
mistakes of copyists, and so on, or it is a compilation
of extracts from an original Isagoge by Geminus with foreign
and inferior elements introduced either by the compiler himself
or by other prentice hands. The result is a tolerable elementary
treatise suitable for teaching purposes and containing
the most important doctrines of Greek astronomy represented
from the standpoint of Hipparchus. Chapter 1 treats of the
zodiac, the solar year, the irregularity of the sun's motion,
which is explained by the eccentric position of the sun's orbit
relatively to the zodiac, the order and the periods of revolution
of the planets and the moon. In § 23 we are told that all
the fixed stars do not lie on one spherical surface, but some
are farther away than others—a doctrine due to the Stoics.
Chapter 2, again, treats of the twelve signs of the zodiac,
chapter 3 of the constellations, chapter 4 of the axis of
the universe and the poles, chapter 5 of the circles on the
sphere (the equator and the parallel circles, arctic, summertropical,
winter- tropical, antarctic, the colure-circles, the zodiac
or ecliptic, the horizon, the meridian, and the Milky Way),
chapter 6 of Day and Night, their relative lengths in different
latitudes, their lengthening and shortening, chapter 7 of
the times which the twelve signs take to rise. Chapter 8
is
a clear, interesting and valuable chapter on the calendar,
the length of months and years and the various cycles, the
octaeteris, the 16-years and 160-years cycles, the 19-years
cycle of Euctemon (and Meton), and the cycle of Callippus
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.