...in one of their foci. 3°. The squares of the times of the revolutions of the planets about the sun, are proportional to the cubes of their mean distances from the sun. 184. From these laws, derived from observation, Newton deduced the law of universal gravitation. We...

...science as containing the third of his celebrated laws, viz. : that the squares of the periodic times of the planets are proportional to the cubes of their mean distances from the sun. Such was the transport with which this discovery, which for 17 years had baffled all his skill and...

...are proportional to the times of describing them ; and that the squares of the periods of different planets are proportional to the cubes of their mean distances from the sun, — he may well be excused the exultation with which he announced the completion of his discoveries,...

...are proportional to the times of describing them ; and that the squares of the periods of different planets are proportional to the cubes of their mean distances from the sun, — he may well be excused the exultation with which he announced the completion of his discoveries,...

...center of the sun is one of the foci. 3°. The squares of the times of revolution of the different planets are proportional to the cubes of their mean distances from the sun, or the semi.major axes of their orbits. These laws relate only to the center of inertia of each planet,...

...their revolutions about the sun, since, by KEPLER'S third law, the squares of their periodic times are proportional to the cubes of their mean distances from the sun, that is, to the cubes of the serai-major axes of their orbits. The ratios of these distances are therefore...

...their revolutions about the sun, since, by KEPLER'S third law, the squares of their periodic times are proportional to the cubes of their mean distances from the sun, that is, to the cubes of the semi-major axes of their orbits. The ratios of these distances are therefore...

...reverse is the case. This may be deduced from Xeplcr's third law, that the squares of the periodic times of the planets are proportional to the cubes of their mean distances, — a law which is proved, from mechanical considerations, to bo true of all cases of planetary motion....

...approximation to a little science, when he announced the law that the squares of the periodic times of the planets are proportional to the cubes of their mean distances from the sun. It has been generally believed that these three great laws of planetary motion were not only discovered...

...planets is an ellipse, in which the Sun occupies one focus. (3.) The squares of the periodic times of the planets are proportional to the cubes of their mean distances from the Sun. Each of the smaller systems constituted by a planet and its satellites is subject to the same three...