III. The ratio of the squares of the revolutionary periods for two planets is equal to the ratio of the cubes of their semi-major axes.
"This force, as to its value and direction, being ascertained, it will be attempted to show that it, cooperative with the force given, will, among other effects, produce those on which the first and second laws of Kepler are founded will not only give to the times and spaces of "falling" bodies agreeably to the Newtonian law, but will exhibit a reason why bodies must be accelerated in their "fall" agreeably to that law, and finally will not conflict with the third law of Kepler.
"This statement includes the first and second law of Kepler. His third law is, that "the squares of the periodic times of any two planets are to each other in the same proportion as the cubes of their mean distances from the sun." or "The square of the time which any planet takes to complete its orbit is proportional to the cube of its mean distance from the sun."
"That the argument, as to the third law of Kepler, gives rise to the curious result of a permitted libration in the eccentricities of planets, which (the forces in question remaining unchanged in their nature) can only arise from the interference of an extraneous cause." An Essay Upon Force and its Effect Upon Matter
See Also
Gravity
Kepler
Kepler Music of the Spheres
Kepler Music Theory
Kepler Theory of Harmony
Kepler's First Law
Kepler's Second Law
Propositions of Astronomy