138 PHILOSOPHICAL TRANSACTIONS. [aNNO 1/14. 



The Royal Society therefore, having as much authority over Mr. Leibnitz, 

 as over Mr. Keill, and being now twice pressed by Mr. Leibnitz to interpose, 

 and seeing no reason to condemn or censure Mr. Keill, without inquiring into 

 the matter; and that neither Mr. Newton nor Mr. Leibnitz (the only per- 

 sons alive who knew and remembered any thing of what had passed in these 

 matters 40 years before) could be witnesses for or against Mr. Keill; appointed a 

 numerous committee, to search old letters and papers, and report their opinion 

 on what they might find; and ordered the letters and papers, with the report of 

 their committee, to be published. And by these letters and papers it appeared 

 to them, that Mr. Newton had the method in or before the year 1 66q ; and it 

 did not appear to them, that Mr. Leibnitz had it before the year 1677. 



Mr. Leibnitz, to make himself the first inventor of the differential method, 

 has represented that Mr. Newton at first used the letter in the vulgar manner, 

 for the given increment of x, which destroys the advantages of the differential 

 method ; but after the writing of his Principia, changed into .r, substituting 

 x for dec. It lies upon him to prove that Mr. Newton ever changed into i*, 

 or used .r for ctcj or left off the use of the letter 0. Mr. Newton used the 

 letter in his Analysis written in or before the years 1669, and in his book of 

 Quadratures, and in his Principia Philosophiae, and still uses it in the very same 

 sense as at first. In his book of Quadratures he used it in conjunction with the 

 symbol i, and therefore did not use that symbol in its stead. These symbols 

 and .r are put for things of a different kind. The one is a moment, the other a 

 fluxion or velocity, as has been explained above. When the letter x is put for a 

 quantity which flows uniformly, the symbol i is an unit, and the letter a mo- 

 ment, and io and djc signify the same moment. Printed letters never signify 

 moments, unless when they are multiplied by the moment 0, either expressed 

 or understood, to make them infinitely little, and then the rectangles are put 

 for moments. 



Mr. Newton does not place his method in forms of symbols, nor confine 

 himself to any particular sort of symbols for fluents and fluxions. Where he 

 puts the areas of curves for fluents, he frequently puts the ©rdinates for fluxions 

 and denotes the fluxions by the symbols of the ordinates, as in his Analysis. 

 Where he puts lines for fluents, he puts any symbols for the velocities of the 

 points which describe the lines, that is, for the first fluxions; and any other 

 symbols for the increase of those velocities, that is, for the second fluxions, as 

 is frequently done in his Principia Philosophiae. And where he put the letters 

 X, yy z for fluents, he denotes their fluxions, either by other letters as />, 9, r, 

 or by the same letters in other forms as x, y, z, or i-, y, i, or by any lines, as 

 DE, FG, HI, considered as their exponents. And this is evident by his book of 



