...times, and of course proportional to the times of describing them. He also discovered by trials, that the cubes of the mean distances of the planets from the sun, are in the same proportion as the squares of the periodical times in which they revolve about the sun....

...possess the measure of our whole planetary system, as, according to the second • law of Kepler (qv), the cubes of the mean distances of the planets from the sun are as the squares of the periods of their revolutions (which have long been known). Therefore the...

...before the earth's orbit became a circle. But in the midst of all these vicissitudes, the major axes and mean motions of the planets remain permanently independent...that one cannot vary without affecting the other. With the exception of these two elements, it appears, that all the bodies are in motion, and every...

...planet and comet this force is reciprocally as the square of the distance from the sun; and, lastly, the squares of the periodic times, being proportional to the cubes of the mean distances, proves that the areas described in equal times by the radius vector of each body in the different orbits,...

...possess the measure cf our whole planetary system, as, according to the second law of Kepler (qv), the cubes of the mean distances of the planets from the sun are as the squares of the periods of their revolutions (which have long been known). Therefore the...

...before the earth's orbit became a circle. But in the midst of all these vicissitudes, the major axes and mean motions of the planets remain permanently independent...that one cannot vary without affecting the other. With the exception of these two elements, it appears that all the bodies are in motion, and every orbit...

...which Kepler might have apprized you that, the squares of the times of the planetary revolutions are as the cubes of the mean distances of the planets from the sun. But this was not all. It was not the tone for any mere physical truth. The enunciation was that of...

...possess the measure of our whole planetary system, as, according to the second law of Kepler (qv), the cubes of the mean distances of the planets from the sun are as the squares of the periods of their revolutions (which have long been known). Therefore the...

...EXPOSITION, THE analogy discovered by Kepler in the beginning of the seventeenth century, viz., that the cubes of the mean distances of the planets from the Sun are as the squares of their periodic times, is found to be invariably consistent with observation,...

...was in the age of Ptolemy. But, in the midst of all these vicissitudes, the length of the major axis and the mean motions of the planets remain permanently...do take place are transient, and depend only on the relative positions of the bodies. It is true that, according to theory, the radial disturbing force...