...а^но, in any two Primar)' PlaH h 4 nets 47 1 The ELEJVEEI? TS Book III. nets compared together, the Squares of the Periodic Times are as the Cubes of the greater Axes <jif the Orbits, wherein. they are carried. And generally the agreement of the Places...

...demonftrated : If feveral bodies revolve with an equable motion in concentric circles, snd the fquares of the periodic times are as the cubes of the diftances from the common cen1 tre ; the centripetal forces will be reciprocally as the fquares of the diftances. Or, if bodies...

...befides, thefe Things muft be alfo granted, as being Mathematically demonftrated : If feveral Bodies revolve with an equable Motion in concentric Circles,...the Cubes of the Diftances from the common Centre 5 the Centripetal Forces will be reciprocally as the Squares of the Diftances ; or, if Bodies revolve...

...the velocity in a circle, radiua^i, then ^''rrt^ M. LA PLAQE shews that the law of Kepler, viz. that the squares of the periodic times are as the cubes of the axes, U not rigorous, and only obtains in as much as the mutual action of the planets, and their action...

...centripetal forces are as the distances of the revolving bodies from the centres of the circles. When the squares of the periodic times are as the cubes of the rays of the circles, and, consequently, the velocities in the subduplicate ratio of these rays inversely,...

...demonftrated. IF feveraf bodies revolve with an equable motion in concentric circles, and the fquares of the periodic times are as the cubes of the diftances from the common centre, the centripetal forces will be reciprocally as the fquares of the diftances. Or, if bodies revolve in orbits...

...satellites move in circular orbits, we may take 44",23 for the true distance, without much error; hence, as the squares of the periodic times are as the cubes of the distances, the distance of the first satellite comes out 33",09. The synodic revolutions were here...

...general harmony and universal law, which all the other moving bodies in the system observe ; namely, that the squares of the periodic times are as the cubes of the distances; but if the sun moves round the earth, that law is destroyed, and the general order of symmetry...

...general harmony and universal law, which all the other moving bodies in the system observe ; namely, that the squares of the periodic times are as the cubes of the distances ; but if the sun move* round the earth, that law is destroyed, and the general order of symmetry...

...their motions always conforming to the law discovered by Kepler, but first demonstrated by Newton, that the squares of the periodic times are as the cubes of the respective mean distances from the sun, or focal body. 3. Th« time of performing' their revolutions...