44 LI MIT S AND FLUXIONS 



of Newton's tract of 1704 was Humphry Ditton's 

 Instiiution of Fluxions, 1706.^ Ditton was pro- 

 minent as a divine as well as a mathematician. 

 Like so many other Eiiglish writers on fluxions 

 during the eighteenth century, he had not been at 

 either of the great universities. He states in his 

 preface that he has also consulted and drawn from 

 the writings of John Bernoulli and some other 

 Continental writers. 



64. The reader of Ditton's hook is impressed by 

 the fact that he labours strenuously to make every- 

 thing plain. He takes the reader fully into his 

 confìdence. This is evident in the extracts which 

 follow (pp. 12-21) : — 



"Suppose any flowing Quantities, . . . as also 

 their Increments . . . which Increment imagine to 

 be generated in equal very small Tarticles of Time. 

 I conceive we may say without Scruple, that the 

 Fluxions are ihe velocities of those Increments, con- 

 sideraci not as actually genei'ated, but quatenus 

 Nascentia, as arising and beginning to be genei^ated. 

 As there is a vast difference between the Increments 

 consider'd as Finite, or really and actually generated ; 

 and the same considered only as Nasce?ttia or in the 

 first Moment of their Generation : So there is as 

 great a difference also between the Velocities of the 

 Increments, consider'd in this two fold respect. . . . 



^ An Institution of Fluxions : Containmg the First Pnnciples, The 

 Operatiovs, with some of the Uses and Applications of that Admirable 

 Method ; According to the Schet/te prefixd to his Iract of Qiiadraturcs, 

 by {its First Inventor) the hicoviparable Sir Isaac Newton. By 

 Humphry Ditton, London, 1706. 



