nly partially solved the difficult question. He
unfortunately still clung to an ancient belief, which as yet remained
unquestioned; _i.e._ the great virtue, one might almost say, the
_divineness_, of circular motion. The ancients had been hag-ridden, so
to speak, by the circle; and it appeared to them that such a perfectly
formed curve was alone fitted for the celestial motions. Ptolemy
employed it throughout his system. According to him the "planets" (which
included, under the ancient view, both the sun and the moon), moved
around the earth in circles; but, as their changing positions in the sky
could not be altogether accounted for in this way, it was further
supposed that they performed additional circular movements, around
peculiarly placed centres, during the course of their orbital
revolutions. Thus the Ptolemaic system grew to be extremely
complicated; for astronomers did not hesitate to add new circular
movements whenever the celestial positions calculated for the planets
were found not to tally with the positions observed. In this manner,
indeed, they succeeded in doctoring the theory, so that it fairly
satisfied the observations made with the rough instruments of
pre-telescopic times.

Although Copernicus performed the immense service to astronomy of boldly
directing general attention to the central position of the sun, he
unfortunately took over for the new scheme the circular machinery of the
Ptolemaic system. It therefore remained for the famous Kepler, who lived
about a century after him, to find the complete solution. Just as
Copernicus, for instance, had broken free from tradition with regard to
the place of the sun; so did Kepler, in turn, break free from the spell
of circular motion, and thus set the coping-stone to the new
astronomical edifice. This astronomer showed, in fact, that if the paths
of the planets around the sun, and of the moon around the earth, were
not circles, but _ellipses_, the movements of these bodies about the sky
could be correctly accounted for. The extreme simplicity of such an
arrangement was far more acceptable than the bewildering intricacy of
movement required by the Ptolemaic theory. The Copernican system, as
amended by Kepler, therefore carried the day; and was further
strengthened, as we have already seen, by the telescopic observations of
Galileo and the researches of Newton into the effects of gravitation.

And here a word on the circle, now fallen from its high estat