Principles of progrejjwe and rotatory Motion . 549 
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P R O P. I. 
Let a and b be two indefinitely frnall bodies conneBled by a 
lever void of gravity , and fuppofe a force to act at any 
point d perpendicularly to the lever , to find the point about 
which the bodies wilt begin to revolve. 
From the property of the lever, the effect of the 
force acting at d (fig. 1 .) on the body a to the effect 
on b as bd : ad ; hence the ratio of the fpaces Am, b n, 
defcribed by the bodies a and b in the firft inftant of 
their motion, will be as ^ ^ ; join mn , and if ne- 
ceffary produce that line and ab to meet in c, which 
will manifeftly be the point about which the bodies be- 
gin to revolve. Hence from fimilar figures bc : ac : : 
(a a m) : : axadibx bd, or dc -db : ad + 
, r AxAD’ + BxBD* 
dc : : a x ad : b x bd, and confequently dc= BxBD _ Ax ad 
and therefore d is the center of percuflion or ofcillatioo 
to the point of fufpenfion c. 
Cor. 1. Hence, whatever be the magnitude of the 
ftroke at d, the point c will remain the fame. 
Cor. 1. If the force ads at the center of gravity g, 
the bodies will have no circular motion, for in this cafe 
B x bd— a x AD— o, and therefore dc becomes infinite. 
4 G a Cor. 
