NEWTON 21 



similes, ut et in figuris quae prò infinite parvis 

 haberi solent, modo caute procedas." 



Translation by John Stewart : 



* ' Intì'oduction 



34. *'I consider mathematica! quantities in this 

 place not as consisting of very small parts ; but 

 as describ'd by a continued motion. Lines are 

 describ'd, and thereby generated not by the appo- 

 sition of parts, but by the continued motion of 

 points ; superficies's by the motion of lines ; soHds 

 by the motion of superficies's ; angles by the rota- 

 tion of the sides ; portions of time by a continuai 

 flux : and so in other quantities. 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 

 genesis of rectangles. 



35. ** Therefore considering that quantities, which 

 increase in equal times, and by increasing are 

 generated, become greater or less according to the 

 greater or less velocity with which they increase 

 and are generated ; I sought a method of determin- 

 ing quantities from the velocities of the motions 

 or increments, with which they are generated ; and 

 calling these velocities of the motions or increments 

 Fluxions, and the generated quantities Fluents^ I 

 fell by degrees upon the Method of Fluxions, which 

 I have made use of here in the Quadrature of 

 Curves, in the years 1665 and 1666. 



