VOL. XXIX.] PHILOSOPHICAL TRANSACTIONS. 147 



method of tangents is not perfect. And I have now long since treated the 

 subject of tangents in a more general manner, viz. by the differences of the 

 ordinates." Which is as much as to say, that he had this improvement long 

 before those days. It lies upon him, in point of candour, to make us under- 

 stand that he pretended to this antiquity of his invention with some other 

 design, than to rival and supplant Mr. Newton, and to make us believe that he 

 had the differential method before Mr. Newton explained it to him by his 

 letters of June 13 and Oct. 24, 1676, and before Mr. Oldenburg sent him a 

 copy of Mr. Newton's letter of Dec. 10, 1672, concerning it. 



The editors of the Acta Eruditorum in June 1696, in giving an account of 

 the first two volumes of the mathematical works of Dr. Wallis, wrote thus, in 

 the style of Mr. Leibnitz : " Besides, Mr. Newton himself, no less remarkable 

 for his candour, than great merits in mathematics, acknowledged both in public 

 and private, when (by means of Mr. Oldenburg, then secretary of the Royal 

 Society of London) there was an epistolary correspondence between them, that 

 is, upwards of 10 years before, that Mr. Leibnitz had his differential Calculus, 

 and infinite Series, and also general methods for them ; and this Dr. Wallis in 

 the preface to his works, making mention of this correspondence, omitted, be- 

 cause perhaps he was not thoroughly acquainted with the matter. Besides, 

 Mr. Leibnitz's method of differences, of which Dr. Wallis makes mention in 

 the following words, viz. that none might allege, he had said nothing of the 

 differential Calculus, disclosed speculations which did not equally arise from 

 other principles." By the words here cited out of the preface to the first two 

 volumes of Dr. Wallis's works, it appears that Mr. Leibnitz had seen that part 

 of the preface, where Mr. Newton is said to have explained to him (in the 

 year 1676) the method of fluxions found by him 10 years before, or above. 

 Mr. Newton never allowed that Mr. Leibnitz had the differential method before 

 the year 1677. And Mr. Leibnitz himself, in the Acta Eruditorum for April 

 1691, p. 178, acknowledged that he found it after he returned home from 

 Paris to enter upon business, that is, after the year 1676. And as for his pre- 

 tended general method of infinite Series, it is so far frorti being general, that 

 it is of little or no use. I do not know that any other use has been made of 

 it, than to colour over the pretence of Mr. Leibnitz to the Series of Mr. Gre- 

 gory for squaring the circle. 



Mr. Leibnitz, in his answer to Mr. Fatio, printed in the Acta Eruditorum 

 for the year 17 00, p. 203, wrote thus: " Mr. Newton himself alone best 

 knows, and suffi^ciently declared to the public, when his Principia came out in 

 1687, that some new geometrical discoveries, which were common to us both, 

 were not owing to any light we received from each other, but to the medita- 



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