10 DISSERTATION SECOND. (part ii. 



tangent. This series he communicated to Oldenburgh in 

 in 1674, and received from him in return an account of the 

 progress made by Newton and Gregory in the invention of 

 scries. In 1676, Newton described his method of quadra- 

 tures at the request of Oldenburgh, in order that it might be 

 transmitted to Leibnitz in the two letters already mentioned, 

 as of such value by recording the views which guided that 

 great geometer in his earliest, and some of his most impor- 

 tant discoveries. The method of fluxions is not communi- 

 cated in these letters ; nor are the principles of it in any 

 way suggested ; though there are, in the last letter, two sen- 

 tences in transposed characters, which ascertain that New- 

 ton was then in possession of that method, and employed in 

 speaking of it the same language in which it was afterwards 

 made known. In the following year, Leibnitz, in a letter to 

 Oldenburgh, introduces differentials, and the methods of his 

 calculus for the first time. This letter, 1 which is very im- 

 portant, clearly proves that the author was then in full pos- 

 session of the principles of his calculus ; and had even in- 

 vented the algorithm and notation. 



From these facts, and they are all that bear directly on 

 the question concerning the invention of the infinitesimal 

 analysis, if they be fairly and dispassionately examined, I 

 think that no doubt can remain, that Newton was the first 

 inventor of that analysis, which he called by the name of 

 Fluxions ; but that, in the communications made by him, or 

 his friends, to Leibnitz, there was nothing that could convey 

 any idea of the principle on which that analysis was founded, 

 or of the algorithm which it involved. Tire things stated 

 were merely results ; and though some of those relating to 

 the tangents of curves might shew the author to be in pos- 

 session of a method of investigation different from infinite 



1 Commercium Epistolicum, No. 66, 



