of Central Forces. 391 
from which the body is projected, 2 any other 
place in the circle; draw the tangents V P, up, 
and the perpendicular CP, Cp, and join V, 4, 
and », A. Then by fimilar triangles CP: CV 
::CV:CA, thatis,; P:r::7r:CA= _ and 
x2 
Cp: Cuz: Cn: CA; that is, p:y is y: Pp , there- 
fore, p= 6 
It will eafily appear, that upon this fuppe- 
fition, the periodic times in different circles 
would be as the cubes of their diameters diretly ; 
taking it for granted that a revolution were 
peffible. 
Cor. 5. If 2==1, or the force be diredtly 
, pn 
as the diftance, then, wm = 2 xs? = —s°; 
> 
/ = x Py 
yin 
OR «Brey 
therefore by fubftitution and reduction p = 
sPr 
Po SF y ae 
hence becaufe in general, p= 
and 20s 
s Pr 4 
J (mnie) fea rey? —— 5? P? x? 
above is an equation to .an ellipfe, the centre 
of 
