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centre G of gravity, of A, C, and B, the attraction of 

 the three being (A + B + C) x G P. Therefore the 

 whole body, whatever be its form, attracts P in the line 

 P S, S being the body s centre of gravity, and with a 

 force proportional to the whole mass of the body multi 

 plied by the distance P S. But as the mutual attractions 

 of spherical bodies, the attraction of whose particles is 

 as their distance from one another, are as the distances 

 between the centres of those bodies, the attraction of the 

 whole body A B C is the same with that of a sphere of 

 equal mass whose centre is in S, the body s centre of 

 gravity. In like manner it may be demonstrated that the 

 attraction of several bodies A, B, C, towards any particle 

 P, is directed to their common centre of gravity S, and is 

 equal to that of a sphere placed there, and of a mass equal 

 to the sum of the whole bodies A, B, C ; and the at 

 tracted body will revolve in an ellipse with a force 

 directed towards its centre as if all the attracting bodies 

 were formed into one globe and placed in that centre. 



But if we would find the attraction of bodies whose 

 particles act according to any power n of the distance, we 

 must, to simplify the question, suppose these to be sym 

 metrical, that is, formed by the revolution of some plane 

 upon its axis. Let A M C H G be the solid, M G the 

 diameter of its extreme circle of revolution next to the 

 particle P ; draw P M and p m to any part of the circle, 

 and infinitely near each other, and take P D = P M, and 

 P o = P m ; D d will be equal to o M (d n being infi 

 nitely near D N), and the ring formed by the revolution 

 of M m round A B will be as the rectangle A M x M m, 

 or (because of the triangles A P M, m o M, being similar, 

 and D d = o M) P M x D d, or P D x D d. Let D N 

 be taken = i/ = force with which any particle attracts 

 at the distance P D = P M = x y that is as x n ; and if 



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