Principles of progrejfive and rotatory Motion . 567 
fame (for in this paper I mean to confine my enquiries 
to fuch cafes) imagine all the particles of the body to be 
referred to that plane orthographically, which fuppofi- 
fition not affedting the angular motion of the body, the 
centrifugal force of all the particles, to caul'e the body 
to revolve about an axis perpendicular to that plane, will 
remain unaltered. Let lmno (fig. 7.) be that plane, 
and fuppofe a force to act at a in the direction pa lying- 
in the fame plane, which produce until it meets i.n, 
palling through the center of gravity g, perpendicular- 
ly in d ; then by Cor. 2. Prop. vm. the center of gra- 
vity g will begin its motion in a line parallel to pa, or 
perpendicular to ln ; and confequently the center c, 
about which the body begins to revolve, muft lie fome- 
where in the line ln. Now the centrifugal force of any 
particle/) is pxpe ; let fall pa perpendicular to ln, then 
the effedt of that force at c, in a direction perpendicu- 
lar to ln, will bspxpa, and in the direction cl it will 
be pxca ; but as the fum of all the quantities pxpa~. o, 
and the fum of all the quanties p x ca = the body mul- 
tiplied into cg, it follows from the fame reafoningas in 
Prop. III. that the point g will continue to move in a 
direction perpendicular to ln ; and alfo, as the forces 
p x ca a£t in a direction perpendicular to that in which 
the center- of gravity moves, its motion muft be conti- 
... nued 
