[ 3*9 3 
Book II. In the former, Magnitudes are conceived 
to be generated by Motion, and the Velocity of the 
generating Motion is the Fluxion of the Magnitude. 
Lines are fuppofed to be generated by the Motion of 
Points. The Velocity of the Point that defcribes the 
Line is its Fluxion, and meafures the Rate of its 
Increafe or Decreafe. Other Magnitudes may be 
reprefented by Lines that increafe or decreafe in the 
fame Proportion with them ; and their Fluxions will 
be in the fame Proportion as the Fluxions of thofe 
Lines, or the Velocities of the Points that defcribe 
them. When the Motion of a Point is uniform, its 
Velocity is conftant, and is meafured by the Space 
which is defcribed by it in a given Time. When 
the Motion varies, the Velocity at any Term of the 
Time is meafured by the Space which would be 
defcribed in a given Time, if the Motion was to be 
continued uniformly from that Term without any 
Variation. In order to determine that Space, and 
confequently the Velocity which is meafured' by ir. 
Four Axioms are propofed concerning variable Mo- 
tions, Two concerning Motions that are accelerated; 
and Two concerning fuclv as are retarded. The 
Firft is, That the Space defcribed by an accelerated' 
Motion is greater than the Space which would haVe 
been defcribed in the fame Time, if it had not been 
accelerated, but had continued uniform- from the 
Beginning of the Time. The Second is, That the 
Space which is defcribed by an accelerated Motion, is- 
lefs than the Space which is defcribed in an equal 
Time by the Motion which is acquired by that Ac- 
celeration continued afterwards uniformly.- By thefe^ 
and Two fimilar Axioms concerning retarded Mo- 
tions^, 
