Below follows the passage I cited previously from Heath's
'Aristarchus of Samos' (OUP) which appears in the 1966 edition on
p87.
"Plato's point of view... is remarkable, not to say startling. We
follow him easily in his account of arithmetic and geometry as
abstract sciences concerned, not with material things, but with
mathematical numbers, mathematical points, lines, triangles,
squares, etc, as objects of pure thought. If we use diagrams in
geometry, it is only as illustrations; the triangle which we draw
is an imperfect representation of the real triangle of which we
*think*...
"But, one would surely say, the case would be different with
astronomy, a science dealing with the movements of the heavenly
bodies which we see. Not at all, says Plato with a fine audacity,
we do not attain to the real science of astronomy until we have
'dispensed with the starry heavens'. i.e. eliminated the visible
appearances altogether...
"There is no doubt that Plato distinguishes two astronomies, the
apparent and the real, the apparent being related to the real in
exactly the same way as practical (apparent) geometry which works
with diagrams is related to the real geometry. On the one side
there are the visible broideries or spangles in the visible
heavens, their visible movements and speeds, the orbits which they
are seen to describe, and the number of hours, days, or months
which they take to describe them. But this are only illustrations
of real heavens, real spangles, rea or essential speed or
slowness, real or true orbits, and periods which are not days,
months or years, but absolute numbers...
Essential speed and essential slowness seem to be, as Adam says,
simply mathematical counterparts of visible stars, because they
are said to be *carried* in the true motions of real astronomy,
and therefore cannot be the speed and slowness of the mathematical
bodies of which the visible stars are illustrations, but must be
those mathematical bodies themselves. The true figures in which
they move are their mathematical orbits, which we might now say
are the perfect ellipses of which the orbits of the visible
material planets are imperfect copies...
"In short, Plato conceives the subject-matter of astronomy to be a
mathematical heaven of which the visible heaven is a blurred and
impoerfect expression in time and space; and the science is a kind
of ideal kinematics, a study in which the visible movements of the
heavenly bodies are only useful as illustrations"
Alan