...radii, ie the distances (Principia, Book I, Prop. 4, Cor. 6). The squares of the periodic times of the planets are as the cubes of their mean distances from the sun1 (Ibid., Book III, Phen. 4 : Kepler's Third Law). Therefore, the centripetal forces of the planets...

...the radii, ie the distances (Princ., Lib. i, prop. 4, Cor. 6). The squares of the periodic times of the planets are as the cubes of their mean distances from the sun (Kepler's 3rd law). .•. The centripetal forces of the planets tending to the sun are inversely as...

...the discovery of his well-known " Harmonic " law (the squares of the periodic times of revolution of the planets are as the cubes of their mean distances from the Sun). The misery in which Kepler lived forms a painful contrast with the services which he performed for...

...planet, moves over equal spaces in equal times. 3. That the squares of the times of the revolutions of the planets are as the cubes of their mean distances from the sun. Galileo, who died in 1642, advanced the science by his observations and by the new revelations he made...

...would sweep over equal areas in equal times; and that the squares of the periods of orbit of any two planets are as the cubes of their mean distances from the sun. At the end of September 1619 Kepler was working as provincial mathematician in the Austrian city of...