136 PHILOSOPHICAL TRANSACTIONS. [aNNO 1714. 



of Mr. Oldenburg. And in several letters which followed hereupon, between 

 Mr. Leibnitz and Dr. Wallis, concerning this matter, Mr. Leibnitz denied not 

 that Mr. Newton had the method 10 years before the writing of those letters, 

 as Dr. Wallis had affirmed, and pretended not that he himself had the method 

 so early; brought no proof that he had it before the year l677i no proof even 

 for that, besides the concession of Mr. Newton that he had it so early ; affirmed 

 not that he had it earlier; commended Mr. Newton for his candour in this 

 matter; allowed that the methods agreed in the main, and said that he there- 

 fore used to call them by the common name of his Infinitesimal Analysis; repre- 

 sented, that as the methods of Vieta and Cartes were called by the common 

 name of Analysis Speciosa, and yet differed in some things; so perhaps the 

 methods of Mr. Newton and himself might differ in some things, and chal- 

 lenged to himself only those things wherein, as he conceived, they might differ, 

 naming the notation, the differential equations, and the exponential equations. 

 But in his letter of June 21, 1677, he reckoned differential equations common 

 to Mr. Newton and himself. 



This was the state of the dispute between Dr. Wallis and Mr. Leibnitz at 

 that time. And 4 years after, when Mr. Fatio suggested that Mr. Leibnitz, 

 the second inventor of this calculus, might borrow something from Mr. Newton, 

 the oldest inventor by many years; Mr. Leibnitz in his answer, published in the 

 Acta Eruditorum of May 1 700, allowed that Mr. Newton had found the method 

 apart, and did not deny that Mr. Newton was the oldest inventor by many 

 years, nor asserted any thing more to himself than that he also had found the 

 method apart, or without the assistance of Mr. Newton, and pretended that 

 when he first published it, he knew not that Mr. Newton had found any thing 

 more of it than the method of tangents. And in making this defence he 

 added : " Which method, no geometrician that I know of had, before Mr. 

 Newton and me, as none before him gave a public specimen of it, and none 

 before both the Bernoullis and me communicated it." Hitherto therefore Mr. 

 Leibnitz did not pretend to be the first inventor. He did not begin to put in 

 such a claim till after the death of Dr. Wallis, the last of the old men who 

 were acquainted with what had passed between the English and Mr. Leibnitz 

 40 years since. I'he Doctor died in October 1703, and Mr. Leibnitz began 

 not to put in this new claim before January 1705. 



Mr. Newton published his Treatise of Quadratures in the year 1704. This 

 treatise was written long before, many things being cited out of it in his letters 

 of October 24 and November 8, 1676. It relates to the method of fluxions; 

 and that it might not be taken for a new piece, Mr. Newton repeated what 



