176 



LIMITS AND FLUXIONS 



whereby they are continually increas'd, are call'd the 

 Fluxions of these Quantities " (p. 3). '*This is 

 the Notion of Fluxions as deliver'd by Leibnitz and 

 his Followers. But these Fluxions, we shall, in the 

 following Sheets, cali by the Names of Moments^ 

 Increments and Dccreinents ; that is, Moments or 

 Increments when the variable Quantities are increas- 

 ing, and Decrements when they are decreasi ng " (p. 4). 



"As the Point b is 

 continually nearer to a 

 Coincidence with the 

 Tangent TBG the 

 nearer it approaches the 

 Point of Contact B; so 

 if we conceive the Ordi- 

 nate cb to be moved on 

 till it concides with CB ; 

 the very first moment 

 before its Coincidence, the Curve B(^, and Right 

 line BG will be infinitely, or rather indefinitely 

 near a Coincidence with each other ; and conse- 

 quently, in that Case, the Increments B^, and eb 

 will come indefinitely near to measure the Ratio 

 of the Fluxions of the Absciss and Ordinate AC, 

 and CB, or the Velocities with which they flow at 

 the Point B . . . and therefore (because when any 

 Ouantity is increas'd or decreas'd, but by only 

 an infinitely or indefinitely small Particle, that 

 Ouantity may be consider'd as remaining the same 

 as it was before ;) these Increments may be taken 

 as Proportional to, or for the Fluxions in ali Opera- 



