[ i«5 ] 
XVIII. On the Refolution of attractive Powers. By Edward 
Waring, M. D. F. R. S. and Lucafi^n ProfeJJor of Mafhe~ 
matics at Cambridge. 
Read May 28, 1789, 
1 • Jk FORCE a&ing at a given point* may be refolved by an 
JTjL infinite number of ways into two, three, or more ( \n ) 
forces acting at the fame point, either in the fame or different 
planes with the given force and each other ; and, vice verfd 9 
any number of fuch forces ading in the fame or different 
planes may be reduced into one. 
Ex. Fig. 1. Tab. III. Let a body A be a&ed on by three forces 
AB, AC, and AD, not being in the fame planes reduce any two of 
them AB and AC to one AE, by compleating the parallelogram 
ABEC ; then reduce the two forces AE and AD to one AF by 
completing the parallelogram AEFD, and the three forces AB, 
AC, and AD, are reduced to the one AF. 
2. If n forces a£t on the body A at the fame time, and any 
(n - 1) of them be reduced to one, the force refulting will be 
fituated in the fame plane with the remaining, and force equiva- 
lent to the ( n ) forces. 
3. If one force a be refolved into feveral others x 9 y, v 9 
&c. fituated in different planes, and the fines of the angles, 
which the forces y, 2 , v 9 &c. contain with the plane made by 
the direction of the forces x and a be refpe&ively j, s ' 9 j /X , &c. 
then will sjr^ s / z3z,$ / 'vz£z&c,~o. 
P R 0- 
