His first law states that the planets describe ellipses with the sun
at a focus of each ellipse.

His second law (a far more difficult one to prove) states that a line
drawn from a planet to the sun sweeps over equal areas in equal
times. These two laws were published in his great work, _Astronomia
Nova, sen. Physica Coelestis tradita commentariis de Motibus Stelloe;
Martis_, Prague, 1609.

It took him nine years more[3] to discover his third law, that the
squares of the periodic times are proportional to the cubes of the
mean distances from the sun.

These three laws contain implicitly the law of universal
gravitation. They are simply an alternative way of expressing that law
in dealing with planets, not particles. Only, the power of the
greatest human intellect is so utterly feeble that the meaning of the
words in Kepler's three laws could not be understood until expounded
by the logic of Newton's dynamics.

The joy with which Kepler contemplated the final demonstration of
these laws, the evolution of which had occupied twenty years, can
hardly be imagined by us. He has given some idea of it in a passage
in his work on _Harmonics_, which is not now quoted, only lest
someone might say it was egotistical--a term which is simply grotesque
when applied to such a man with such a life's work accomplished.

The whole book, _Astronomia Nova_, is a pleasure to read; the
mass of observations that are used, and the ingenuity of the