236 - Of the SOLIDS 



Let the body B be cut by two planes, at right angles to AC, 

 and indefinitely near to one another, fo as to contain between 

 them a flice or thin fection of the body, to which A and A' 

 may be considered as gravitating, nearly in the direction of the 

 line AG perpendicular to that fection. 



The gravitation of A, therefore, to the aforefaid fection, will 

 be to that of A' to the fame, as the angular fpace fubtended by 

 that fection at A, to the angular fpace fubtended by it at A'. 

 But thefe angular fpaces, when the diftances are great, are in- 

 verfely as the fquares of thofe diftances, and therefore, alfo, the 

 gravitation of A toward the fection, will be to that of A', in- 

 verfely as the fquares of the diftances of A and A' from the 

 fection. Now thefe diftances may be accounted equal to CA 

 and CA', from which they can differ very little, wherever the 

 fection is made. 



The gravitations of A and A' toward the faid fection, are, 



therefore, as -^-^ to -r-^* And the fame may be proved of 

 AC AC 



the gravitation to all the other fections, or laminae, into which 

 the body can be divided by planes perpendicular to AC ; there- 

 fore the fums of all thefe gravitations, that is, the whole gravi- 

 tations of A to B, and of A' to B, will be in that fame ratio, 



that is, as -^-^ to -T-77^, or inverfely as the fquares of the di- 



AL A d 



ftances from C. Q. E. D. 



It is evident, that the greater the diftances AC, A'C are, the 

 nearer is this propofition to the truth, as the quantities rejected 

 in the demonftration, become lefs in refpect of the reft, in the 

 fame proportion that AC and A'C increafe. 



It is here aflumed, that the angular fpace fubtended by the 

 fame plane figure, is inverfely as the fquare of the diftance. 



This 



