IS 13.] Sir Isaac Neivton. 405 



short, this paper contains so many important facts, and such 

 accurate reasoning, that it ought to be perused by every person 

 who wishes to form an accurate opinion on the dispute. We 

 think tliat the following conclusions may be drawn with almost 

 perfect certainty. 



1. The method of Auctions, and the differential calculus, are 

 absolutely the same in principle, and differ only in the notation. 

 The reasoning of Newton is rigidly accurate ; but that of Leib- 

 nitz, loose and unsatisfactory. The Leibnitzian notation is con- 

 ceived to have an advantage over the Newtonian : this advan- 

 tage, as far as it is real, applies only to the mode of expressing 

 the higher orders of Auctions ; and this mode might be intro- 

 duced, with facility, into the Newtonian notation. But it must 

 be admitted, that the notation introduced by Leibnitz into the 

 integral calculus has advantages, and, accordingly, it has been 

 universally adopted by British writers, which is not the case with 

 his mode of expressing the higher orders of Auctions. 



2. Newton was in possession of his method of Auctions many 

 years before Leibnitz thought of his differential calculus, or 

 indeed before Leibnitz had made any great progress in mathe- 

 matics. This is so obvious from the Commercium Epistolicum, 

 that we believe no one will think of calling it in question. 



3. Newton more than once announced to Leibnitz that he was 

 in possession of the Auctionary calculus, and points out its 

 advantages with peculiar emphasis ; but in none of his letters 

 does he explain the nature of this calculus. There is an explana- 

 tion of it, however, in Newton's Analysis per Equationes 

 Numero Terminorum Infinitas ; which was sent up to London 

 by Dr. Barrow, in manuscript. There can be no doubt that 

 Leibnitz saw this paper long before he wrote any thing respecting 

 the differential calculus. The notice, we allow, is very brief; 

 but it is much more than the information given to James Gre- 

 gory, who, notwithstanding, succeeded in discovering Newton's 

 method. 



4. Newion himself admitted, in his Piincipia, that Leibnitz 

 had invented his differential calculus without receiving any infor- 

 mation. This passage, which is of great importance to the 

 subject in hand, is as follows : — 



" In literas quai niihi cum geometra peritissimo G. G. Lcll- 

 vitio, annis abhinc decern intercedebant, cum significarem me 

 pompotem esse methodi determinandi maximas et minimas, 

 ducendi tangentes, et similia peiagendi, qure in terminis surdis 

 ;eque ac in rationalibus procederent, et Uteris transposes banc 

 sententiam involvcntibus {tlutu tsqutUione (JUOtCunque fititnUs 

 tjUaniitales invo&uenie, Jluxiones invenire, ct vice versa) eandera 

 celarem : rescripsit vir clarissinius se quoque in ejusmodi nic- 

 thodum incidisse ; et methoduin sui:m communicavit a meo vix 



