142 PHILOSOPHICAL TRANSACTIONS. [aNNO 1714. 



third differences. When therefore he wrote those tracts he was but a learner, 

 and this he ought in candour to acknowledge. 



It seems therefore that he learned the differential method by means of Mr. 

 Newton's aforesaid three letters, compared with Dr. Barrow's Method of Tan- 

 gents; for 10 years after, when Mr. Newton's Principia Philosophiae came 

 abroad, he improved his knowledge in these matters, by trying to extend this 

 method to the principal propositions in that book, and by this means composed 

 the said three tracts. For the propositions contained in them, errors and trifles 

 excepted, are Mr. Newton's, or easy corollaries from them, being published by 

 him in other forms of words before. And yet Mr. Leibnitz published them as 

 invented by himself long before they were published by Mr. Newton. For in 

 the end of the first tract, he represents that he invented them all before Mr. 

 Newton's Principia Philosophiae came abroad, and some of them before he left 

 Paris, that is before Oct. 1676. And the second tract he concludes with these 

 words: " From what has been advanced, a great many things might be deduced, 

 accommodated to practice, but it shall have now sufficed, that I have laid down 

 geometrical principles, in which consisted the chief difficulty; and perhaps I 

 may seem to an attentive considerer to have opened some new ways, that were 

 pretty intricate before; for every thing answers to my Analysis of infinites, that 

 is, to the calculus of sums and differences, some of whose elements I have 

 given in the Acta Erudit. which I have expressed in as clear a manner as the 

 thing would bear." He pretends here that the " geometrical foundations in 

 which the chief difficulty consisted," were first laid by himself in this ver}' 

 tract, and that he himself had in this very tract opened " some new ways that 

 were intricate before." And yet Mr. Newton's Principia Philosophiae came 

 abroad almost two years before, and gave occasion to the writing of this tract, 

 and was written " in as plain a manner as the thing would bear," and contains 

 all these principles and all these new ways. And Mr. Leibnitz, when he pub- 

 lished that tract, knew all this, and therefore ought then to have acknowledged 

 that Mr. Newton was the first who laid the " geometrical foundations in which 

 the chief difficulty consists," and opened the " new ways that were intricate 

 before." In his answer to Mr. Fatio, he acknowledged all this, saying, 

 ** which method, no geometrician that I know of, had before Mr. Newton and 

 me; as none, before this celebrated geometrician, gave a public specimen that 

 he had it." And what he then acknowledged he ought in candour and honour 

 to acknowledge still upon all occasions. 



Mr. Leibnitz, in his letter of May !28th, 1697, wrote thus to Dr. Wallis: 

 " that Mr. Newton's method of fluxions had an affinity with my differential 



