126 NEWTON S PRINCIPIA. 



how he laid the deep and solid foundations of the fabric 

 which we have been surveying. 



After examining the motions of a system of two bodies 

 with respect to one another, and their common centre of 

 gravity, and in space, as those motions are affected by the 

 mutual attractions of the two bodies themselves (in the 

 manner which we have already described), Newton pro 

 ceeds to the great problem of the Three Bodies, as it has 

 been termed, because the solution is so difficult, that gene 

 rally the attempt has been confined to the case of three only, 

 this also being sufficient for determining the more impor 

 tant disturbances of the moon s motions. The inquiry, 

 however, is general in the Principia ; and its subject is, 

 the motion, produced by the mutual actions upon one ano 

 ther of the bodies in a system. Thus, for example, the 

 inquiry already analysed regards the effect produced upon 

 their motion in space, by the mutual attractions of the 

 earth and moon; that to which we now are proceeding 

 regards their motion, as also influenced by the disturbing 

 force of the sun, and indeed, even by the smaller but 

 not evanescent disturbing forces of the other planets. So 

 as the former inquiry may be extended on the same prin 

 ciples to the motions of Jupiter and Saturn, and their 

 satellites; this new inquiry applies also to the disturbances 

 of their systems by ours, and of our system by theirs. 



Newton begins by showing that if the attracting force 

 increases as the distance of the bodies from each other, 

 any two, M and E, will revolve round their common 

 centre of gravity, G, in an ellipse having Gr for its centre. 

 This is plain from what was formerly proved when treat 

 ing of the conic sections, and also more lately respecting 

 the centre of gravity. If, then, each of these is attracted, 

 in the same manner, by a third body S, this force, being 

 resolved into two, one parallel to the line joining M and 



