57 ° 
Mr. vince’s Tnveftigathn of the 
P R O P. XI. 
Let a body p (fig. 8.) moving with the velocity v, jlrikt 
the body o^at reft in the point a, and in a direction ad 
pajftng through the center of gravity of the ftr iking 
body ; to determine the velocity of each body after -the 
ftroke , fuppoftng them to be elaftic. 
The folution of this Propofition depending on the 
fame principles as that of Prop. III. we fliall have, put- 
ting v equal the velocity of the center of gravity g af- 
ter the ftroke, on fuppofition that the bodies were non- 
elaftic (dgc being fuppofed perpendicular to ab, and c 
the point about which the body q_ begins to revolve) 
•a x turn of all the * x Cp z j r , . 
r — — , andconfequently 
vx? x CB 
Vx P X CB — ' — -xt; ~+ 
CG 
VxPxCBxCG , • . ii i 
v = 7 , „ ; ■ - ■ — : 01 , ■ nr .i ; but it is well known, 
lum ot all the p x p C + r x CD 7 7 
that the fum of all the px />c j =cgx CD x q_, and hence 
v = V * P r ( ,' r * ,tb» and therefore if the bodies be fup- 
pofed elaftic, we have. ~ cg\p FE>c ^ or t ^ e velocity of 
the center of gravity g after the ftroke. Now to de- 
termine the velocity of p, we have t ^ ' cg + FTdc e< l ua ^ 
its velocity after the ftroke. from Angle impadt, and con- 
P x V x CD Qx v x cg 
CG 
fequently v 
U.xCG+l>xDC _ CLx GC+PxDC * S ve l° a ty 
loft 
