...extended the third of * Hist, de I'Astron. Mod. Tom. 11. these laws to the satellites of Jupiter, showing that the squares of their periodic times were as the cubes of their distances from the centre of the body round which they revolved. The imaginary apparatus of cycles and epicycles,—the...

...Cassini's observations had also extended the third of these^laws to the satellites of Jupiter, showing that the squares of their periodic times were as the cubes of their distances from the centre of the body round which they revolved. The imaginary apparatus of cycles and epicycles,—the...

...Cassini's observations had also extended the third of these laws to the satellites of Jupiter, showing that the squares of their periodic times were as the cubes of their distances from the centre of the body round which they revolved. The imaginary apparatus of cycles and epicycles, —...

...recognised, that the secondary planets obeyed the laws discovered by Kepler; and it was now first observed that the squares of their periodic times were as the cubes of the mean distances of the satellites from the primary planets. It was this which led Kepler, in the...

...attraction, it was equally probable, he thought, that the planets were kept in their orbits by gravitating towards the sun. \ Kepler had discovered the great...as the cubes of their distances from the sun, and hence\Wewton drew the important conclusion that the force of gravity or attraction, by which the planets...

...were kept in their orbits by gravitating towards the sun. Kepler had discovered the great law of tho planetary motions, that the squares of their periodic...their distances from the sun, and hence Newton drew tho important conclusion that the force of gravity or attraction, by whicli the planets were retained...

...— it was eijiidlly probunle, he thought, that the planets were kept in their orhits iiy gravitatlug towards the sun. Kepler had discovered the great law...attraction, by which the planets were retained in their orhits, varied as the square of their distances from the sun."* The words we have printed in italics...

...— it was equally jrrobable, he thought, that the planets were kept in their orbits by gravitating towards the sun. Kepler had discovered the great law...as the cubes of their distances from the sun; and hcntc Newton drew the important conclusion that the force of gravity, or attraction, by which the planets...

...and that of the Moon round the earth ; that each of them described equal areas in equal times, and that the squares of their periodic times were as the cubes of their distances. When these two last abstruse analogies, which, when Kepler at first observed them, were but little...

...times about the sun ; 2nd, that it moved in an ellipse of which the sun occupied the focus ; and, 3rd, that the squares of their periodic times were as the cubes of the greater axes of their orbits. Newton demonstrates by geometry that when the first takes place the...