SIR ISAAC NEWTON 71 



Moreover, since all the parts of any planet A gravitate towards any 

 other planet B ; and the gravity of every part is to the gravity of the 

 whole as the matter of the part to the matter of the whole; and (by 

 law 3) to every action corresponds an equal reaction; therefore the 

 planet B will, on the other hand, gravitate towards all the parts of 

 the planet A; and its gravity towards any one part will be to the 

 gravity towards the whole as the matter of the part to the matter 

 of the whole. Q. E. D. 



Cor. I. Therefore the force of gravity towards any whole planet 

 arises from, and is compounded of, the forces of gravity towards all 

 its parts. Magnetic and electric attractions afford us examples of 

 this ; for all attraction towards the whole arises from the attractions 

 towards the several parts. The thing may be easily understood in 

 gravity, if we consider a greater planet as formed of a number of 

 lesser planets meeting together in one globe, for hence it would 

 appear that the force of the whole must arise from the forces of the 

 component parts. If it is objected that, according to this law, 

 all bodies with us must mutually gravitate one towards another, 

 I answer, that since the gravitation towards these bodies is to the 

 gravitation towards the whole earth as these bodies are to the 

 whole earth, the gravitation towards them must be far less than to fall 

 under the observation of our senses. 



Cor. 2. The force of gravity towards the several particles of 

 any body is reciprocally as the square of the distance from the 

 particles ; as appears from cor. 3, prop. 74, book I. 



