An introduction to mathematics, by A. N. Whitehead.

138 INTRODUCTION TO MATHEMATICS
had been studied from a remote antiquity
without a suspicion of any connection between the two. Kepler was an astronomer,
but he was also an able geometer, and on the
subject of conic sections had arrived at ideas
in advance of his time. He is only one of
many examples of the falsity of the idea that
success in scientific research demands an exclusive absorption in one narrow line of study.
Novel ideas are more apt to spring from
an unusual assortment of knowledge-not
necessarily from vast knowledge, but from a
thorough conception of the methods and ideas
of distinct lines of thought. It will be remembered that Charles Darwin was helped
to arrive at his conception of the law of
evolution by reading Malthus' famous Essay
on Population, a work dealing with a different subject-at least, as it was then
thought.
Kepler enunciated three laws of planetary
motion, the first two in 1609, and the third
ten years later. They are as follows:
(1) The orbits of the planets are ellipses,
the sun being in the focus.
(2) As a planet moves in its orbit, the
radius vector from the sun to the planet
sweeps out equal areas in equal times.
(3) The squares of the periodic times of the
several planets are proportional to the cubes
of their major axes.