[1] If the orbit was not a circle, what,
then, was it? By a happy stroke of philosophical genius he lit on the
ellipse. On bringing his hypothesis to the test of observation, he
found it was indeed so; and rising from the case of Mars to universal
statement, he generalized the law, that the planetary orbits are
elliptical, having the sun for their common focus.
[Footnote 1: ROBERT SMALL: _Astronomical Discoveries of Kepler_.]
Kepler had now determined the course of each planet. But there was no
known relation between the distances and times; and the evolution of
some harmony between these factors was to him an object of the greatest
interest and the most restless curiosity. Long he dwelt in the dream of
the Pythagorean harmonies. Then he essayed to determine it from the
regular geometrical solids, and afterwards from the divisions of
musical chords. Over twenty years he spent in these baffled efforts. At
length, on the 8th of March, 1618, it occurred to him, that, instead of
comparing the simple times, he should compare the numbers expressing
the similar powers, as squares, cubes, etc.; and lastly, he made the
very comparison on which his discovery was founded, between the squares
of the times and the cubes of the distances.
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