Principles of progrejjive and rotatory Motion. 561 
and parallel to nb , ab mull: be equal and parallel to tnn, 
therefore the angular velocity is juft the fame as if the 
force fh had not ailed. The center o of rotation at 
the beginning of the motion being thus determined, 
every thing relative to the motion of the bodies, after 
they are at. liberty to move freely, may be determined 
as in the preceding Propofitions. 
Cor. 1. Hence it appears, that whatever be the mag- 
nitude or direction of the force communicating the mo- 
tion, or the point at which it acts, the center of gravity 
will move in a line parallel to the direction of the force, 
for the triangles fhd, Gqzv being fimilar, gw muft be 
parallel tQ fd. 
Cor. 2. The fame is manifeftly true for any number 
of bodies ; for let (fig. 5.) e be a third body, and con- 
ceive it to be connected with the other two bodies A and 
b in their center of gravity g; then if fd reprefents the 
force ailing at the point d, it is evident from the laft 
Corol. and the fecond Prop, that the center of gravity 
moves with the fame velocity and in the fame direction, 
as if the fame motion had been communicated at g in a 
line rg parallel to fd, and that the center of gravity has 
the fame velocity communicated to it, as if the two bo- 
dies had been placed at g; conceive therefore the bodies 
’ 
A and b to be placed at g, and let the force ait at d, , and 
3 then 
