Principles of progreffive and rotatory Motion. 575 
loft by ? at the point f by Ample impadt being equal to 
VxPxDCxfO 
V A f A x g\J V X Q^>< GC X FO /ITT 
V ~ Qx GC xFO + Px^OxDC ~ Qx GC x f O + P x^O x DC’ We 
have be the velocity loft by the point f, on fuppofition 
that the bodies are perfectly elaftic (fuppofing q/'to re- 
prefent the value of v) equal to — ~ > i Q - , 
and therefore by fim. triang. fc (fo) : cb : : fe (og) : ed— 
— the velocity loft by the center of 
2 x V x CLx GC xgO 
2 x Vx Q_x GC xgO 
Qx GC x FO + Px-O x~DC 
gravity g, and hence v - ^ GCxFO+ px,OxDc - 
V x Qx GC xFO + V xPx gO x DC — 2 x V x Qjx GC x gO . 
QxGCxFo+Fx^oxb e — ~ = the velocity 
of p after the ftroke. Now, as it appears from Prop, 
ix. that the progreffive motion of a body, when left to 
move freely, continues uniform and in the fame direc- 
tion, it follows, that the expreffions for the velocities 
of each body in the firft inftant after the ftroke, both in 
this and the preceding Propofition, will reprefent the 
uniform progreffive velocities with which the bodies will 
continue to move, and confequently the place of each 
body, at the end of any given time after impadt, may 
eafily be determined. 
Cor. 1. If the direction fa paffes through g, then fo 
and becoming infinite, we fhall have gc+Fx dc 
for the velocity of o., and f° r the 
velocity 
