PRINTED BOOKS, ETC, BEFORE i734 47 



the fluxion, vvhich coincides with the modem mode 

 of finding a derivative. Ditton considers the in- 

 crements as finite (p. 53). " These Momenta are in 

 proportion to one another as the Fluxions of the 

 flowing Quantities respectively, for 02, oy, ox, are 

 as 2, j>, i' ; and Mr. Newton had before expresly 

 told US ; that the Increments generated in a very small 

 Farticle of time were very nearly, as the Fluxions." 

 Evidently Ditton does not here overlook that 

 02, oy, ox represent the increments only *'very 

 nearly." He observes (p. 98) that \ve may " go 

 on with ease to the second, third, and any other 

 Fluxions ; neither are there any new Difficulties to 

 be met with." 



A second edition of Ditton's book was brought 

 out in 1726 by John Clarke. 



65. Ditton's first edition appeared at a time when 

 the Newton-Leibniz controversy was under way. 

 Leibniz had appealed to the Royal Society for 

 justice. That Society appointed a committee which 

 published a report containing letters and other 

 material hearing on the case, in a book called the 

 Commercium Epistolicum,'^ which figures prominently 

 in the lamentable controversy. From this book the 

 early use of infinitely small quantities on the part 

 of Newton is conspicuously evident. The book 

 makes it clear also that some of Newton's warmest 

 supporters were guilty of gross inaccuracy in the 

 use of the word "fluxion." 



' Commercium Epistolicuìn D. /ohannis Collins, et aliortttn de analysi 

 promota : jussu societatis regia in lucevi editum. Lendini, MDCCXII. 



