148 PHILOSOPHICAL TRANSACTIONS. [aNNO 1714. 



tions of each apart, and that they were explained by me JO years before, i. e. 

 in 1677." In the book of Principles here referred to, Mr. Newton did not 

 acknowledge that Mr. Leibnitz found this method without receiving light into 

 it from Mr. Newton's letters abovementioned ; and Dr. Wallis had lately told 

 him the contrary, without being then confuted or contradicted. And if 

 Mr. Leibnitz had found the method without the assistance of Mr. Newton, 

 yet second inventors have no right. 



Mr. Leibnitz in his aforesaid answer to Mr. Fatio, wrote further : " I can 

 affirm, when in l684, I published the elements of my Calculus, that I did 

 not know any thing more of Mr. Newton's inventions in this kind, than what 

 he formerly signified to me by his letters, viz. that he could find tangents with- 

 out taking away surds; which Huygens afterwards also signified to me he could 

 do, though I still know no more of that Calculus ; but at length, on seeing 

 Mr. Newton's book of Principia, I was fully satisfied that he had made much 

 greater discoveries." Here he again acknowledged that the book of Principles 

 gave him great light into Mr. Newton's method: and yet he now denies that 

 this book contains any thing of that method in it. Here he pretended that 

 before that book came abroad he knew nothing more of Mr. Newton's inven- 

 tions of this kind, than that he had a certain method of tangents, and that by 

 that book he received the first light into Mr. Newton's method of fluxions : 

 but in his letter of June 21, l677i he acknowledged that Mr. Newton's method 

 extended also to quadratures of curvilinear figures, and was like his own. His 

 words are to the following purpose : *' I suppose what Mr. Newton would con- 

 ceal, about the method of drawing tangents, differs not from this. And what 

 confirms me in this opinion is, that he adds, that upon the same foundation 

 quadratures may likewise be rendered more easy ; for such figures are always 

 quadrable, whose ordinate drawn into the difference of the absciss becomes the 

 difference of any quantity." 



Mr. Newton had in his three letters abovementioned (copies of which Mr, 

 Leibnitz had received from Mr. Oldenburg) represented his method so general, 

 as by the help of equations, finite and infinite, to determine maxima and mi- 

 nima, tangents, areas, solid contents, centres of gravity, lengths and curvities 

 of curve lines and curvilinear figures; and this without taking away radicals; 

 and to extend to the like Problems in curves usually called mechanical, and to 

 inverse Problems of tangents, and others more difficult, and to almost all 

 Problems, except perhaps some numeral ones like those of Diophantus. And 

 Mr. Leibnitz, in his letter of Aug. 27, 1676, represented that he could not 

 believe that Mr. Newton's method was so general. Mr. Newton in the first 

 of his three letters set down his method of tangents deduced from this general 



