66 OUTLINES OF NATURAL PHILOSOPHY. 



a. Both this and the preceding proposition are conse- 

 quences of the equality that takes place between 

 the action and re-action of bodies. The quantity 

 of motion in any system is the same as if all the 

 parts of it were united in the centre of gravity of 

 the whole. 



b. Connected with this last, is a property of the 

 centre of gravity, which has been found of use in 

 the pure mathematics. If a plane figure be gene- 

 rated by the revolution of a given line, or a solid 

 by the revolution of a given plane figure ; the area 

 in the first case, or the solidity in the second, is 

 equal to the product of the generating quantity 

 into the length of the line, described by its centre 

 of gravity. 



The application of this theorem to the quadrature of 

 curves, or the cubature of solids, constitutes what 

 has been called the Centrobaric Method. The in- 

 vention of the method is ascribed to GULDINUS, but 

 the theorem above was known to PAPPUS, and no 

 doubt the application of it also. 



120. If there be a system of bodies acting any 

 how on one another, and if at any point of time we 

 compute the motions which these bodies would 

 have in the succeeding instant, were they all free 

 from their mutual action ; and if we also compute 

 the motions, which, in consequence of their mu- 

 tual action, they really have in that instant, the 

 motions which must be compounded with the first 



of 



