550 ' Mr. vince’s Invefligation of the 
Cor. 3. If the force adts at one of the bodies, the 
center of rotation c will coincide with the other body. 
Cor. 4. If the lever had been in motion before the 
ftroke, the point c, at the inftant of the flroke, would 
not have been difturbed. 
PROP. II. 
Let a given quantity of motion be communicated to the lever 
at 0, to determine the velocity of the center of gravity g. 
The fpace a m, defcribed by the body a in the firft 
inftant of motion, is as ^ : now cg = cd - pg = CD - 
A 
A x AD 2 + B x BD 4 BxBDxBG + AxADx AG . 
AG+ AD = — •: — AG+ AD = - — r > 
BxBD-AxAD 
alfo CA ~ CD + DA = 
A x AD 2 + B x BD 2 
BxBD-AxAD 
B x BD — A x AD 
B x BD x AB 
+ DA = 
B x BD — A x AD 
hence we have (ac) : («) : : 
BxBDx GB + AxADxAG / N _ BxBDxGB+AxADxAG 
BxBD-AxAD v CG V : AxBxAB ccG/Jtne 
velocity of the center of gravity : hence if the motion be 
communicated at g, the velocity becomes as B x ^ * >^ab AG ' ’ 
Let now the motion, which is fuppofed to be actually 
communicated to the rod at d, be equivalent to the mo- 
tion of a body whofe magnitude is g, and moving with a 
velocity v ; then if that motion be communicated at g, 
the velocity of the center of gravity is well known to be 
