VOL. XXIX.] PHILOSOPHICAL TRANSACTIONS. 137 



Dr. Wallis had published g years before, without being then contradicted, 

 namely, that this method was invented by degrees in the years l665 and 1666. 

 Hereupon the editors of the Acta Lipsiensia in January 1705, in the style of 

 Mr. Leibnitz, or Mr. L. himself, in giving an account of this book, represented 

 that Mr. Leibnitz was the first inventor of the method, and that Mr. Newton 

 had substituted fluxions for differences. And this accusation gave a beginning 

 to this present controversy. 



For Mr. Keill, in an epistle published in the Philosophical Transactions for 

 September and October 17O8, retorted the accusation, asserting, " that Mr. 

 Newton was, beyond all dispute, the first inventor of the arithmetic of fluxions, 

 as would easily appear to any one who reads his letters, published by Dr. Wallis. 

 Though the same method, by only changing the name and manner of nota 

 tion, was afterwards published by Mr. Leibnitz in the Acta Eruditorum." 



Before Mr. Newton saw what had been published in the Acta Leipsica, he 

 expressed himself offended at the printing of this paragraph of Mr. Keill's let- 

 ter, lest it should create a controversy. And Mr. Leibnitz, understanding it 

 in a stronger sense than Mr. Keill intended it, complained of it as a calumny, 

 in a letter to Dr. Sloane, the secretary, dated March 4, 17 H, N. S. and moved 

 that the Royal Society would cause Mr. Keill to make a public recantation. 

 Mr. Keill chose rather to explain and defend what he had written ; and Mr. 

 Newton, on being showed the accusation in the Acta Lipsica, gave him leave 

 to do so. But Mr. Leibnitz, in a second letter to Dr. Sloane, dated Dec. 29, 

 1711, instead of making good his accusation, as he was bound to do, that it 

 might not be deemed a calumny, insisted only on his own candour, as if it 

 would be injustice to question it; and refused to tell how he came by the me- 

 thod ; and said that the Acta Lipsica had given every man his due, and that he 

 had concealed the invention above 9 years, (he should have said 7 years) that 

 nobody might pretend (he means that Mr. Newton might not pretend) to have 

 been before him in it; and called Mr. Keill a novice, unacquainted with things 

 past, and one that acted without authority from Mr. Newton, and a clamorous 

 man who deserved to be silenced, and desired that Mr. Newton himself would 

 give his opinion in the matter. He knew that Mr. Keill affirmed nothing more 

 than what Dr. Wallis had published 13 years before, without being then con- 

 tradicted. He knew that Mr. Newton had given his opinion on this matter, in 

 the introduction to his book of Quadratures, published before this controversy 

 began : but Dr. Wallis was dead ; the mathematicians which remained in Eng- 

 land were reckoned novices ; Mr. Leibnitz may question any man's candour 

 without injustice; and Mr. Newton must now retract what he had published, or 

 must be involved in wrangling disputes. 



VOL. VI. T 



