great Greek astronomer Ptolemy (died 168 )
published his standard treatise on the subject in the University of Alexandria, explaining the apparent motions among the fixed stars of the sun and planets by the conception of the earth at rest and the sun and the planets circling round it. During the next thirteen hundred years the number and the accuracy of the astronomical observations increased, with the result that the description of the motions of the planets on Ptolemy's hypothesis had to be made more and more complicated. Copernicus (born
1473 and died 1543 ) pointed out that the motions of these heavenly bodies could be explained in a simpler manner if the sun were supposed to rest, and the earth and planets were conceived as moving round it. However, he still thought of these motions as essentially circular, though modified by a set of small corrections arbitrarily superimposed on the primary circular motions. So the matter stood when Kepler was born at Stuttgart
in Germany in 1571 . There were two sciences, that of the geometry of conic sections and that of astronomy, both of which
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.
These laws proved to be only a stage towards a more fundamental development of ideas. Newton (born 1642 and died
1727 ) conceived the idea of universal gravitation, namely, that any two pieces of
matter attract each other with a force proportional to the product of their masses and inversely proportional to the square of their distance from each other. This sweeping general law, coupled with the three laws of