VOL. XXrX.] PHILOSOPHICAL TRANSACTIONS. 141 



position of that book, but also the last proposition, on which that scholium was 

 written. If the word ut, which in that scholium may have been accidentally 

 omitted between the words erit and ejus, be restored, that scholium will agree 

 with the two propositions, and with the rest of his writings, and the objection 

 will vanish. 



Thus much concerning the nature and history of these methods, it will not 

 be amiss to make some observations on them. 



In the Commercium Epistolicum, mention is made of three tracts written by 

 Mr. Leibnitz, after a copy of Mr. Newton's Principia Philosophiae had been sent 

 to Hanover for him, and after he had seen an account of that book published 

 in the Acta Eruditorum for January and February 1689. And in those tracts 

 the principal propositions of that book are composed in a new manner, and 

 claimed by Mr. Leibnitz as if he had found them himself before the publishing 

 of the said book. But Mr. Leibnitz cannot be a witness in his own cause. It 

 lies upon him either to prove that he found them before Mr. Newton, or to 

 quit his claim. 



In the last of those three tracts, the 20th proposition (which is the chief of 

 Mr. Newton's propositions) is made a corollary of the IQth proposition^ and 

 the 19th has an erroneous demonstration adapted to it. It lies upon him either 

 to satisfy the world that the demonstration is not erroneous, or to acknowledge 

 that he did not find that and the 20th proposition thereby, but tried to adapt a 

 demonstration to Mr. Newton's proposition, to make it his own. For he repre- 

 sents in his 20th proposition^ that he knew not how Mr. Newton came by it, 

 and consequently that he found it himself, without the assistance of Mr* 

 Newton. 



By the errors in the 15th and IQth proposition of the third tracts Dr. Keill 

 has showed that when Mr. Leibnitz wrote these three tracts, he did not well 

 understand the ways of working in second differences. And this is further 

 manifest by the 1 0th, 1 ith, and 12th propositions of this third tract. For these 

 he lays down as the foundation of his infinitesimal analysis, in arguing about 

 centrifugal forces, and proposes the first of them with relation to the centre of 

 curvity of the orb, but uses this proposition in the two next, with relation to 

 the centre of circulation. And by confounding these two centres with one 

 another, in the fundamental propositions, on which he grounds this calculus, 

 he erred in the superstructure, and for want of skill in second and third differ- 

 ences, was not able to extricate himself from the errors. And this is further 

 confirmed by the 6th article of the second tract. For that article is erroneous, 

 and the error arises from his not knowing how to argue well about second and 



