Principles of pro greffrve and rotatory Motion. 5 77 
manner it might have been determined, had q_ moved 
in an oppofite direction. 
dor. 4. Hence alfo we may eafily determine the mo- 
tion of each body after the ftroke, fuppofing cphad not 
been moving in a diredtion parallel to the motion of p, 
by refolving qJs motion into two parts, one parallel to 
the motion of f, and the other perpendicular ; and 
finding by the preceding what would be the effedl of the 
parallel motions, and then compounding qJs motion, af- 
ter the ftroke from that confederation, with the motion 
it had in a diredtion perpendicular thereto before the 
ftroke. 
Cor. 5. The point a of the body p wilLdefcribe (when 
that body after the ftroke has any progreflive motion) 
the common cycloid. 
Cor. 6. Hence, therefore, the times of the revolutions 
of each body may be determined as in Prop. vi. 
Cor. 7. If the bodies had any rotatory motion before 
impadt, every thing relative to the motion of the bodies 
after the ftroke might have been determined from the 
fame principles. 
