Principles of progreffive and rotatory Motion . 551 
center of gravity, when the fame motion is actually com- 
municated to any point d. Now bd = bg + gd, and 
ad = ag-gd ; hence b x bgx bd + axadxag=bx bg 1 + 
A x AG 2 + GD x B x BG— A x AG = (becaufe B X BG — A x AG — o) 
B x bg 2 + a x ag 2 ; confequently the velocity becomes 
; and hence the center of gravity moves with the 
fame velocity, wherever the motion is communicated. 
Let a given elaflic body p, moving with a given velocity , 
be fuppofed to Jlrike the lever at the point D in a direc- 
tion perpendicular to it ; to determine the velocity of the 
center of gravity g after the Jlroke. 
Suppofe firft the body to be non-elaflic, and let v be 
the velocity of the center of gravity after the ftroke upon 
that fuppofition, and v the velocity of the ftriking 
body : then cg : cd : : v : = the velocity of the 
V vJ 
point d after the ftroke, or of the body p ; for the 
fame reafon - and ~g~j~ equal the velocities of a 
and B refpectively. Now, becaufe in revolving bodies, 
A + j3 ' A X tfX ACS 
Gxv Gxv BxBGxBD+AxADxAG 
• v — — — • 
B x BD x BG + A x AD x AG 
A x 13 x AB 
A + B * A -fr- -h B x BG + A x AG 
= the velocity of the 
PROP. Ill 
the 
