NEWTON 13 



increments may be esteemed as added, or affirm- 

 ative moments ; and the decrements as subducted, 

 or negative ones. But take care not to look upon 

 finite particles as such. Finite particles are not 

 moments, but the very quantities generated by the 

 moments. We are to conceive them as the just 

 nascent principles of finite magnitudes. Nor do we 

 in this Lemma regard the magnityde of the moments, 

 but their first proportion as nascent. It will be the 

 same thing, if, instead of moments, we use either 

 the Velocities of the increments and decrements 

 (which may also be called the motions, mutations, 

 and fluxions of quantities) or any finite quantities 

 proportional to those velocities. The coefficient of 

 any generating side is the quanti ty which arises by 

 applying the Genitum to that side. Wherefore the 

 sense of the Lemma is, that if the moments of any 

 quantities A, B, C, etc, increasing or decreasing by 

 a perpetuai flux, or the velocities of the mutations 

 which are proportional to them, be called a, b, e, etc, 

 the moment or mutation of the generated rectangle 

 AB will be ^B + ^A ; the moment of the generated 

 content ABC will be ^BC + ^AC + ^AB : . . . 



19. '' Case I. Any rectangle as AB augmented by 

 a perpetuai flux, when, as yet, there wanted of the 

 sides A and B half their moments \a and \b, was 

 A - i « into Vi-\b, ox K^-\a^-\bh^-\ab\ but 

 as soon as the sides A and B are augmented by the 

 other half moments ; the rectangle becomes t\.-\-\a 

 into B + J ^, or AB + è ^B + i ^ A + 1 ab. From this 

 rectangle subduct the former rectangle, and there 



