Centripetal Forces . 
On moveable Centers , 
PROP. XI. 
i. Given the refpedlive places of {n) bodies S, S', S", S' 7 ', 
&c. in the curves A, A', A ", A'", &c. at the fame time, 
and in the fame plane, and the forces of all the bodies adin^ 
on S, except two, S' and S" ; to find the forces of the two 
bodies S' and S" on the body S. 
This propofition may be relolved by the method given in 
Prop. 4. for to produce the fame effect the fame finite forces 
will be requifite, whether the centers of forces reft or move in 
given curves. 
1.2. If the bodies S, S', S", See, move in different planes, 
then all the forces atting on the body, except three, may be 
given, which may be acquired from the method given in the 
fame propofition. 
Hence it appears, that 2 n forces may be requifite to be found 
from the conditions of the problem to determine all the bodies 
to move in their refpe&ive curves, when they are all fituated in 
the fame plane, and that 3 x n forces may be requifite in 
different planes, See, if the force of one body (S') on another 
(S") does not at all depend on the force of the fame body 
(S') on any other (S'") ; and if the fame can be predicated of 
the reft, then n . n — 3 forces of the above mentioned bodies in 
the fame, or n . » — 4 forces in different planes may be alfumed 
at will. 
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