134 rHlLOSOPHICAL TBANSACTIONS. [aNNO 1714. 



chose rather to use the new symbols dx and dy^ though there is nothing which 

 can be done by these symbols, but may be done by single letters. 



The next year Mr. Newton's Principia Philosophiae came out, a book full of 

 such problems as Mr. Leibnitz had called the most curious and difficult, &c. 

 And the Marquis de L'Hospital thus speaks of it, presque tout de calcul ; com- 

 posed almost wholly of this calculus. And Mr. Leibnitz himself, in a letter to 

 Mr. Newton, dated from Hanover, March -r^, 1693, and stiil extant in his 

 own hand-writing, and communicated to the Royal Society, acknowledged the 

 same thing in these words : " You had surprisingly enlarged geometry by your 

 series, but by your Principia you have shown that you have penetrated into what 

 was beyond the reach of the common analysis. I also have endeavoured, by 

 using proper symbols for expressing the sums and differences, to reduce to a 

 kind of analysis, that geometry which I call transcendent, and not without suc- 

 cess." And again, in his answer to Mr. Fatio, printed in the Acta Eruditorum 

 of May 1700, p. 203, 1. 21, he acknowledged the same thing. In the second 

 lemma of the second book of these Principles, the elements of this calculus 

 are demonstrated synthetically, and at the end of the lemma there is a scholium 

 in these words : " When I signified, in the letters that passed 10 years since, 

 between me and M. Leibnitz, that I had a method of determining maxima and 

 minima, of drawing tangents, &c. which succeeded as well in surd as in rational 

 terms ; and concealed the same by transposing the letters including this pro- 

 position, having an equation given, that involves any number of fluents or 

 flowing quantities, to find the fluxions, and vice vers^ ; Mr. Leibnitz replied, 

 that he had likewise hit on such a method, and which he communicated to me, 

 scarcely differing from mine, except in the form of the words and symbols ; the 

 foundation of both is contained in this lemma." In those letters, and in an- 

 other dated Dec. 10, 1672, a copy of which, at that time, was sent to Mr. 

 Leibnitz by Mr. Oldenburg, as is mentioned above, Mr. Newton had so far 

 explained his method, that it was not difficult for Mr. Leibnitz, by the help of 

 Dr. Barrow's method of tangents, to collect it from those letters. And it is 

 certain, by the arguments above-mentioned, that he did not know it before the 

 writing of those letters. 



Dr. Wallis had received copies of Mr. Newton's two letters, of June 13 and 

 Oct. 24, 1676, from Mr. Oldenburg, and published several things out of them 

 in his Algebra, printed in English l683, and in Latin 1 6^3; and soon after 

 had intimation from Holland to print the letters entire, because Mr. Newton's 

 notions of fluxions passed there with applause by the name of the differential 

 method of Mr. Leibnitz. And thereupon he took notice of this matter in the 



