190 NEWTON S PRINCIPIA. 



77? 



in c 2 is equal to , then the number of units of area in 



K 



P N B A will equal the number of units of time elapsed. 

 Thirdly. We may now proceed to consider the more 

 general case. We have 



dv K 



rt^f-a,&quot; 



Hence by division we have, 



fm m 



J v 



K 



Integrating throughout the motion 3 

 fm 



Hence, if from the velocities there be subtracted the 

 constant quantity ^, then these differences are in 



geometrical progression, when the times are in arithme 

 tical progression. 



s7 fvt 



Again, since v =- tnis equation gives 



dt X 



integrating throughout the motion, 



which ^ives x in terms of t. This equation is the same 

 as the more simple one, 



already established. 



