144 PHILOSOPHICAL TRANSACTIONS. [aNNO 1714. 



not yet rejected it with his usual impatience, for want of such an instance, we 

 have reason to expect that he will at length explain its usefulness to the world. 



Mr. Newton, in his letter of Oct. 24, 1676, wrote that he had two methods 

 of resolving the inverse problems of tangents, and such like difficult ones ; one 

 of which consisted " in assuming a series for any unknown quantity, from which 

 all the rest might conveniently be deduced, and in collating the homologous 

 terms of the resulting equation, for determining the terms of the assumed 

 series." Mr. Leibnitz many years after published this method as his own, 

 claiming to himself the first invention of it. It remains that he either renounce 

 his claim publicly, or prove that he invented it before Mr. Newton wrote his 

 said letter. 



It lies upon him also to make a public acknowledgment of his receipt of Mr. 

 Oldenburg's letter of April 15, l675, wherein several converging series for 

 squaring of curves, and particularly that of Mr. James Gregory for finding the 

 arc by the given tangent, and thereby squaring the circle, were communicated 

 to him. He acknowledged it privately in his letter to Mr. Oldenburg, dated 

 May 20, 1675, still extant in his own hand-writing, and by Mr. Oldenburg 

 left entered in the letter-book of the Royal Society. But he has not yet 

 acknowledged it publicly, as he ought to have done, when he published that 

 series as his own. 



It lies upon him also to make a public acknowledgment of his having re- 

 ceived the extracts of Mr. James Gregory's letters, which, at his own request, 

 were sent to him at Paris, in June 16763 by Mr. Oldenburg, to peruse : among 

 which was Mr. James Gregory's letter of Feb. 15, 1671, concerning that series, 

 and Mr. Newton's letter of December 10, 1672, concerning the method of 

 fluxions. 



And whereas in his letter of Dec. 28, 1675, he wrote to Mr. Oldenburg, 

 that he had communicated that series above two years before to his friends at 

 Paris, and had written to him sometimes about it; and in his letter of May 12, 

 1676, said to Mr. Oldenburg that he had written to him about that series some 

 years before; and in his letter to Mr. Oldenburg, dated Aug. 27, 1676, that 

 he had communicated that series to his friends above three years before ; that 

 is, on his first coming from London to Paris : he is desired to tell us how it 

 came to pass, that when he received Mr. Oldenburg's letter of April 15, 1675, 

 he did not know that series to be his own. 



In his letters of July 15 and October 26, 1674, he tells us of but one series 

 for the circumference of a circle, and says that the method which gave him this 

 series, gave him also a series for any arc whose sine was given, though the pro- 

 portion of the arc to the whole circumference be not known. This method 



