146 PHILOSOPHICAL TRANSACTIONS. [aNNO 1714. 



sion, which on the first reading he did not know to be his own, nor understood 

 it; but as soon as he understood it, he claimed as his own, by pretending that 

 he had found it long before, and had forgot it, as he perceived by his old 

 papers: it lies upon him, in point of candour and justice, either to prove that 

 he was the first inventor of this method, or to renounce his claim to it, for 

 preventing future disputes. 



Mr. Leibnitz, in his letter to Mr. Oldenburg dated Feb. 3, 1 672-3, claimed 

 a right to a certain property of a Series of numbers natural, triangular, pyra- 

 midal, triangulo-triangular, &c, and to make it his own, represented that he 

 wondered that Monsieur Paschal, in his book entitled Triangulum Arithmeti- 

 cum, should omit it. That book was published in the year ] 665, and contains 

 this property of the Series; and Mr. Leibnitz has not yet done him the justice 

 to acknowledge that he did not omit it. It lies upon him therefore in candour 

 and justice, to renounce his claim to this property, and to acknowledge Mr. 

 Paschal the first inventor. 



He is also to renounce all right to the differential method of Mouton, as 

 second inventor : for second inventors have no right. The sole right is in the 

 first inventor, until another finds out the same thing apart. In which case, to 

 take away the right of the first inventor, and divide it between him and that 

 other, would be an act of injustice. 



In his letter to Dr. Sloane, dated Dec. 29, 1711> he has told us that his 

 friends know how he came by the differential method. It lies upon him, in 

 point of candour, openly and plainly, and without further hesitation, to satisfy 

 the world how he came by it. 



In the same letter he has told us that he had this method above g years be- 

 fore he published it, and it follows from thence that he had it in the year 1675, 

 or before. And yet it is certain that he had it not when he wrote his letter to 

 Mr. Oldenburg dated Aug. 27, 1676, wherein he affirmed that Problems of 

 the inverse method of tangents, and many others, could not be reduced to 

 infinite Series, nor to equations or quadratures. It lies upon him therefore, in 

 point of candour, to tell us what he means by pretending to have found the 

 method before he had found it. 



We have showed that Mr. Leibnitz, in the end of the year 1676, in return- 

 ing home from France through England and Holland, was meditating how to 

 improve the method of Slusius for tangents, and extend it to all sorts of Pro- 

 blems, and for this end proposed the making of a general table of tangents : 

 and therefore had not yet found out the true improvement. But about half a 

 year after, when he was newly fallen upon the true improvement, he wrote 

 back: " I agree with the celebrated Mr. Newton, the famous M. Slusius's 



