VOL. XXIX.] PHILOSOPHICAL TRANSACTIONS. 145 



therefore, by the given sine of 30 degrees, gave him a series for the whole 

 circumference. If he had also a series for the whole circumference deduced 

 from the tangeut of 45 degrees, he is desired to tell the world what method he 

 had in those days, which could give him both those series. For the method by 

 the transmutation of figures will not do it. He is desired also to tell us why in 

 his said letters he did not mention more quadratures of the circle than one. 



And if in the year l674 he had the demonstration of a series for finding any 

 arc whose sine is given, he is desired to tell the world what it was ; and why in 

 his letter of May 12, 1676, he desired Mr. Oldenburg to procure from Mr. 

 Collins the demonstration of Mr. Newton's series for doing the same thing ; 

 and wherein his own series differed from Mr. Newton's. For on all these con- 

 siderations there is a suspicion that Mr. Newton's series, for finding the arc 

 whose sine is given, was communicated to him in England ; and that in the 

 year 1673 he began to communicate it as his own to some of his friends at 

 Paris, and the next year wrote of it as his own in his letters to Mr. Oldenburg, 

 in order to get the demonstration or method of finding such series. But the 

 year following, when Mr. Oldenburg sent him this series, and the series of Mr. 

 Gregory, and six other series, he dropped his pretence to this series for want 

 of a demonstration, and took time to consider the series sent him, and to com- 

 pare them with his own, as if his series were others different from those sent 

 him. And when he had found a demonstration of Gregory's series by a trans- 

 mutation of figures, he began to communicate it as his own to his friends at 

 Paris, as he represents in the Acta Eruditorum for April 1691, p. 178, saying, 

 " Now in 1675 I had by me a small tract I had composed, on the arithmetical 

 quadrature, which from that time was perused by my friends, &c." But the 

 letter, by which he had received this series from Mr. Oldenburg, he concealed 

 from his friends, and pretended to Mr. Oldenburg that he had this series a year 

 or two before the receipt of that letter. And the next year, oil receiving two 

 of Mr. Newton's series again by one George Mohr, he wrote to Mr. Olden- 

 burg in such a manner as if he had never seen them before, and on pretence of 

 their novelty, desired Mr. Oldenburg to procure from Mr. Collins Mr. New- 

 ton's method of finding them. If Mr. Leibnitz thinks fit to obviate this suspi- 

 cion, he is in the first place to prove that he had Mr. Gregory's series before he 

 received it from Mr. Oldenburg. 



It lies upon him also to tell the world what was the method by which the 

 several series of regression for the circle and hyperbola, sent to him by Mr. 

 Newton, June 13, 1676, and claimed as his own by his letter of August 27 

 following, were found by him, before he received them from Mr. Newton. 



And whereas Mr. Newton sent him, at his own request, a method of regres- 



VOL. VI. U 



