PREFACE. XV11 



been seen by Leibnitz. There can now be no doubt, however, 

 that Newton was right in thinking that Leibnitz had been 

 shown this MS., since a copy of part of it, in Leibnitz's hand, has 

 been found among the papers of Leibnitz preserved in the Royal 

 Library at Hanover 1 . It is, of course, possible that at the time 

 when this copy was taken Leibnitz was already acquainted in 

 some degree with the Differential Calculus, but it is difficult to 

 acquit him of a want of candour in never avowing in the course 

 of the long controversy respecting the discovery of Fluxions, 

 that he had not only seen this tract of Newton's, but had 

 actually taken a copy of part of it. He must have seen, also, 

 at the same time, that the MS. was an old one, and although 

 it does not contain the pointed letters which Newton sometimes 

 but by no means invariably employed to denote Fluxions, 

 Leibnitz could hardly fail to see, if he was acquainted with the 

 Differential Calculus, that the principle of Newton's method 

 was the same as that of his own. It is repeatedly stated by 

 Newton that what he claims is the first invention of the 

 method, and that he does not dispute about the particular 

 signs and symbols in which the method may be expressed. 

 Again, he often states that although, in the sense which he 

 employs, the method can have but one inventor, yet the method 

 may be improved, and the improvements belong to those who 

 make them. 



In some of these papers relating to the dispute with Leib- 

 nitz, Newton gives us some interesting information respecting 

 the times when several of his discoveries were made. Thus in 

 a passage, which has been quoted by Brewster 2 , he states that 

 he wrote the Principia in seventeen or eighteen months, begin- 

 ning in the end of December 1684, and sending it to the Royal 

 Society in May 1686, excepting that about ten or twelve of the 

 propositions were composed before, viz. the 1st and llth in 

 December 1679, the 6th, 7th, 8th, 9th, 10th, 12th, 13th and 17th, 

 Lib. i, and the 1st, 2nd, 3rd and 4th, Lib. II, in June and July 

 1684. The following extract will give an idea of Newton's pro- 

 digious mental activity at an earlier period of his life. 



1 See Gerhardt, Mathem. Schriften Leibnitzens, i. p. 7. 



2 Brewster's Life, Vol. i. p. 471. 



