argument in favour of this notion, other than the merely imaginary
reflection that circular movement, and circular movement alone, was
"perfect," whatever "perfect" may have meant. It was further
believed to be impossible that the heavenly bodies could have any
other movements save those which were perfect. Assuming this, it
followed, in Ptolemy's opinion, and in that of those who came after
him for fourteen centuries, that all the tracks of the heavenly
bodies were in some way or other to be reduced to circles.

Ptolemy succeeded in devising a scheme by which the apparent changes
that take place in the heavens could, so far as he knew them, be
explained by certain combinations of circular movement. This seemed
to reconcile so completely the scheme of things celestial with the
geometrical instincts which pointed to the circle as the type of
perfect movement, that we can hardly wonder Ptolemy's theory met with
the astonishing success that attended it. We shall, therefore, set
forth with sufficient detail the various steps of this famous
doctrine.

Ptolemy commences with laying down the undoubted truth that the shape
of the earth is globular. The proofs which he gives of this
fundamental fact are quite satisfactory; they are indeed the same
proofs as we give today. There is, first of all, the well-known
circumstance of which our books on geography remind us, that when an
object is viewed at a distance across the sea, the lower part of the
object appears cut off by the interposing curved mass of water.

The sagacity of Ptolemy enabled him to adduce another argument,
which, though not quite so obvious as that just mentioned,
demonstrates the curvature of the earth in a very impressive manner