246 LIMITS AND FLUXTONS 



edition of Vince vvas printed in 1805. From thìs 

 second edition we quote : 



P. I : *'The velocities with which flowing quan- 

 tities increase or decrease at any point of time, are 

 called ih.e. Jluxìons of those quantities at that instant. 



" As the velocities are in proportion to the 

 increments or decrements uniformly generated in 

 a given time, such increments or decrements will 

 represent the fluxions. "^ 



Vince also quotes Newton on the generation of 

 quantities by motion : '*Sir I. Newton, in the 

 Introduction to his Quadrature of Curves^ observes 

 that ' these geneses really take place in the nature 

 of things, and are daily seen in the motion of bodies. 

 And after this manner, the ancients, by drawing 

 moveable right lines along immoveable right lines, 

 taught the geneses of rectangles.'" 



Vince gives no formai definition of a //;;/// ; but 

 his philosophy of this subject is disclosed by the 

 two following quotations (pp. 4 and 5): " By 

 keeping the ratio of the vanishing quantities thus 

 expressed by finite quantities, it removes the 

 obscurity which may arise when we consider the 

 quantities themselves ; this is agreeable to the 

 reasoning of Sir I. Newton in his Principia^ Lib. I, 

 Sect. I, Lem. 7, 8, 9." 



" It has been said, that when the increments are 



^ "This is agreeable to Sir I. Newton's ideas on the subject. He 

 says : ' I sought a method of determining quantities from the velocities 

 of the motions or increments with which they are generated ; and call- 

 ing these velocities of the motions or increments, fluxions^ and the 

 generated quantities fluents, I fell by degrees upon the method of 

 fluxions.'— Introd. to Quad. Curves" 



