TEXT-BOOKS, 1*736-1741 173 



West-End of St. Paul's, MDCCXLI. This anony- 

 mous publication of 16 pages was reprinted in 1809 

 in the fourth edition of John Rowe's Doctrine of 

 Fluxions ; it constitutes a real contribution to the 

 logie of fluxions. The pamphlet is offered " as an 

 Explanation of the Doctrine itself, and not of Sir 

 Isaac's Manner of delivering it." '*About that," 

 he says, " I don't mean, nor pretend to take a Part 

 in any Controversy. " He defines fluxions thus : 

 **The word Fluxion properly apply'd always sup- 

 poses the Generation of some Quantity (term'd 

 Fluent or Flowing Quantity) with an equable, 

 accelerated, or retarded Velocity, and is itself the 

 Quantity which might be uniformly generated, in a 

 Constant Portion of Time, with the Amount or 

 Remainder of that Velocity, at the Instant of find- 

 ing such Pluxion." " Hence, it will appear that 

 the first Fluxions of Quantities are as the Velocities 

 with which those Quantities are increas'd ; that 

 second Fluxions are as the Increase or Decrease of 

 such Velocities ; and that by second, third, fourth, 

 etc. , Fluxions are meant Fluxions, whose Fluents 

 are themselves Fluxions to other proposed Quan- 

 tities ; and the manner of considering and determin- 

 ing them is the very same as tho' they were first 

 Fluxions, they being actually so to the Quantities 

 from which they are immediately derived " (p. 7). 



Then follows the lemma : 



"The Fluxion of the Area ABC, whether tri- 

 .angular or curvilinear, is the Rectangle ij." 



Suppose B to move along hV while the ordinate 



