440 APPENDIX. 



motions were explained by the propositions in the three 

 first sections of the First Book, and still more particularly 

 (p. 311.), that from the phenomena and the things contained 

 in that First Book, the demonstration was given of the 

 elliptical orbits, the principle of gravitation, and the law 

 of the inverse square of the distances, in the case of all 

 planets and their satellites. It is manifest, therefore, that, 

 without having seen the Principia, Leibnitz may have 

 been so far enlightened by the view given of Newton s 

 labours, as to be set upon applying the differential calcu 

 lus to dynamical investigations, and to the motions of the 

 heavenly bodies as the most important of all. He found, 

 from the account of Newton s work, that he had succeeded 

 in solving the great problem by mathematical investiga 

 tion. He never had made any such attempt before ; he 

 now made it when he found Newton had successfully 

 made it ; and to a certain extent he himself succeeded. 



A great difficulty arises in examining these propositions 

 of Leibnitz and comparing them with Newton s, from the 

 singular manner of using the letters in the diagrams and 

 referring to them, as well as from the inaccurate printing. 

 It however appears clearly enough that there are incon 

 sistencies between different parts of his investigations ; and 

 Newton, when he breaks off with the words &quot; Newtoniana 

 tantum descripsit suo more, ac describendo nonnumquam &quot; 

 after, in partly the same terms, having charged him with 

 imitating fluxions and then erring in his imitation from 

 not well understanding that method, appears to have in 

 tended making a similar remark upon his copying the 

 dynamical propositions. (Riga.ud } App. XIX. XX.) No 

 doubt, if taken literally, and using the words centrifugal 

 force in the sense in which Newton and indeed all others 

 use it, there seems the greatest inaccuracy in the position 

 that it varies inversely as the cube of the distance or of 

 the radius vector, this being only true if the curve is a 

 circle. But when we find that by conatus centrifuyus he 

 means what would be the centrifugal force in a circle 



