408 Biographical Account of [D>:c. 



abludentem praeterquam in verborum et notarum formulis, et 

 idea generationis quantitatum utriusque fundamentum continetur 

 in hoc lemmate." * 



This passage appeared in the first edition of the Priucipia, 

 published in 1686; it was continued in the second edition, pub- 

 lished in 1/1^? while the quarrel between Keill and Leibnitz 

 was at the hottest, f but it is not to be found in the edition of 

 1722. From this passage, there is complete evidence that 

 Newton admitted Leibnitz to have discovered the differential 

 calculus; which he never would have done, if he had furnished 

 him with a sufficient explanation of his own method to enable 

 him to understand it. 



5. Newton, then, was the original inventor ; Leibnitz knew 

 that he was in possession of some unknown method ; this seems 

 to have stimulated his invention. His differential calculus seems 

 to be founded on the method of tangents of Barrow, from which 

 it differs only in the notation. But it was the generalization of 

 that method which constituted the chief merit of Leibnitz. Had 

 Newton published his Treatise on Fluctions when it was origi- 

 nally written, he would have had no competitor nor coadjutor, 

 and Leibnitz's mathematical reputation would probably never 

 have risen beyond mediocrity. All concealment in matters of 

 science we consider as improper, and Natuie usually punishes it 

 by putting the same invention into the hands of some other 

 person, who deprives the real discoverer of a part of the reputa- 

 tion which he would otherwise have acquired. Newton's hesita- 

 tion, indeed, proceeded from an amiable and praise-worthy 

 motive ; yet it was a weakness, and, as, such, was punished by 

 raising up a competitor, who deprived him of his just share of 

 reputation, and gave him more trouble and uneasiness than that 

 which he sought to avoid by withholding his publication. 



6. It has been attempted by, some to compare Leibnitz to 

 Newton, and to hold him up as scarcely inferior to tha,t illustri- 

 ous man : but the comparison is very unequal. Leibnitz cer- 

 tainly was a very extraordinary man, and one of the greatest 

 geniuses that ever appeared among mankind : the extent of his 



* Newton's Prinripia, lib. ii. Scholium, at the end of lemma ii. p. 226, 

 of tlie edition of 1714. 



t Montucla assigns, as a reason why it was continued in that edition, that 

 Cotes, the editor, published it without Newton's knowledge, and against his 

 will. But thrre must be a mistake in this ; for after the preface there is an 

 advertisement, by Newton himself, mentioning a great number of additions 

 and improvements, wnich ho had made in that edition. A proof, not only 

 that he knew of the edition, but that he had been at some pains in correcting 

 and improving it. The paragraph then was retained, because Newton did not 

 wish to erase it. It was doubtless scratched out of the third edition at the 

 suggestion of Keill, or of some other English mathematician engaged in the 

 dispute. Newton's opinion of the dispute is sufficiently evident from his ac- 

 count of the Commcrcium Epistolicum, in the Phil. Trans. 



