Reference: G. J. Toomer, Ptolemy's ALMAGEST
Springer-Verlag, New York, Heidelberg, Tokyo, 1984
In the preface of Book I Ptolemy divides theoretical
philosophy into three parts
The heavenly bodies are referred to as being eternal.
Mathematics spans the other two fields of theoretical philosophy.
theology, dealing with the "first cause" of motion which
is somewhere in the highest reaches of the universe and can only be imagined
physics, dealing with matter and motion. Such an order
of being is situated below the lunar sphere among corruptible bodies.
mathematics, dealing with form, motion, shape, number,
place, time, etc. Joins the first two areas because mathematics is an attribute
of all existing things, mortal and immortal( i.e. of an aethereal nature,
things beyond the lunar sphere)
"As for physics, mathematics can make a significant
contribution. For almost every peculiar attribute of material nature becomes
apparent from the peculiarities of its motion from place to place. Thus
one can distinguish the corruptible from the incorruptible by whether it
undergoes motion in a straight line or a circle, and heavy from light,
and passive from active, be whether it moves towards the centre or away
from the centre." ( p.36)
Ptolemy summarizes the ideas and reasons for the current
The rest of his book deals with mathematical techniques
for computing the positions of the stars and planets.
the heavens move like a sphere - "nature formed all earthly
and corruptible bodies out of shapes which are round but of unlike parts,
but all aethereal and divine bodies out of shapes which are of like parts
and spherical. ... it is plausible that the aether surrounding them, too,
being of the same nature, is spherical, and because of the likeness of
its parts moves in a circular and uniform fashion."
the earth is spherical
the earth is in the middle of the heavens
the earth is negligibly small compared to the heavens
the earth does not have any motion from place to place
(because of various physical arguments) nor does it rotate in a fixed place
( for example clouds and projectiles would never be seen moving towards
the east, the earth's rotation would always overtake them)