VOL. XKIX.] PHILOSOPHICAL TRANSACTIONS. 1*4^ 



method, and illustrated it with an example, and said that this method of tan- 

 gents was but a branch or corollary of his general method, and that he took 

 the method of tangents of Slusius to be of the same kind : and thereupon Mr. 

 Leibnitz, in his return from Paris through England and Holland into Germany, 

 was considering how to improve the method of tangents of Slusius, and extend 

 it to all sorts of Problems, as we showed above out of his letters. And in his 

 third letter Mr. Newton illustrated his method with Theorems for quadratures, 

 and examples thereof. And when he had made so large an explanation of his 

 method, that Mr. Leibnitz had got light into it, and had in his letter of 

 June 21, l677> explained how the method, which he was fallen into, answered 

 to the description which Mr. Newton had given of his method, in drawing of 

 tangents, giving the method of Slusius, proceeding without taking away frac- 

 tions and surds, and facilitating quadratures; for him to tell the Germans that 

 in the year l684, when he first published his differential method, he knew 

 nothing more of Mr. Newton's invention, than that he had a certain method 

 of tangents, is very extraordinary, and wants an explanation. 



At that time he explained nothing more concerning his own method, than 

 how to draw tangents and determine maxima and minima, without taking away 

 fractions or surds. He certainly knew that Mr* Newton's method would do all 

 this, and therefore ought in candour to have acknowledged it. After he had 

 thus far explained his own method^ he added that what he had there laid down, 

 were the principles of a much sublimer geometry, reaching to the most difficult 

 and valuable problems, which were scarcely to be resolved without the differential, 

 calculus, aut simili, or another like it. What he meant by the words aut 

 simili, was impossible for the Germans to understand without an interpreter. 

 He ought to have done Mr. Newton justice in plain intelligible language, and 

 told the Germans whose was the methodus similis, and of what extent and an- 

 tiquity it was, according to the notices he had received from> England; and to 

 have acknowledged that his own method was not so ancient. This would have 

 prevented disputes, and nothing less than this could fully deserve the name of 

 candour and justice. But afterwards, in his answer to Mr. Fatio, to tell the 

 Germans that in the year l684, when he first published the elements of his 

 calculus, he knew nothing of a methodus similis, nothing of any other method 

 than for drawing tangents_, was very strange, and wants an explanation. 



It lies upon him also to satisfy the world why, in his answer to Dr. Wallis 

 and Mr. Fatio, who had published that Mr. Newton was the oldest inventor of 

 that method by many years, he did not put in his claim of being the oldest 

 inventor thereof, but staid till the old mathematicians were dead, and then com^ 

 plained of the new mathematicians as novices ; attacked Mr. Newton himself> 



