252 LIMITS AND FLUXIONS 



fixed ratio is called the Limiting Ratio of the 

 variable quantities. " 



William Dealtry, 1810, 18 16 



217. In the preface of Dealtry's Principles of 

 Fluxions ^ ( 1 8 1 6) we read : 



"The method of Fluxions rests upon a principle 

 purely analytical ; namely, the theory of Hmiting 

 ratios ; and the subject may therefore be considered 

 as one of pure mathematics, without any regard to 

 ideas of time and velocity. But the usuai manner 

 of treating it is to employ eonsiderations resulting 

 from the theory of motion. This was the pian of 

 Sir Isaac Newton in first delivering the principles of 

 the method ; and it is adopted in the foUowing 

 Work, from the belief, that it is well adapted for 

 illustration." 



Dealtry defines a ''fluxion of a quantity at any 

 point of time" as **its increment or decrement, 

 taken proportional to the velocity with which the 

 quantity flows at that time." . . . 



" When a quantity increases with a velocity which 

 continually varies, the quantity, which measures 

 the fluxion, is a limit between the preceding and 

 succeeding increments, and is ultimately equal to 

 either of them. " He explains that *'the word 

 ultimately is intended to denote that particular 

 instant, when the time is diminished sine limite^''' 



^ The Principles of Fluxions : Designed for the Use of Students in the 

 Universities. By William Dealtry, B.D., F.R.S., late Fellow of 

 Trinity College, Cambridge. 2nd ed., Cambridge, 1816. 



