PROPERTIES of the CIRCLE, . 
3 3 
we get are = “5. ~ ; and if r* be fubftituted for its equal in 
gs ritzoPxOn+ 6orxO7” ve ger 357 HIST? K boi 
: es 4 ; j AL's 2 
Wherefore the fum of the cubes of perpendiculars drawn from 
the point G to the fides of the pentagon, is equal to the fum of 
the cubes of perpendiculars drawn from the point A to the 
fame. 
SINCE 2x7pOm +2X7r—On =4r43 rx 20m—20n 
Pan2h 
+37X 2xOm +2X On +2x0m'—2xOn* = = , and 
axOm +On=*, we have 37 X 2X Om—2x On + 
2xOm _—Or = 47. But a0"—202n=r7 therefore 
2X Om —On =73, or Om —On’ = a® 
= a : 
Ir P, inftead of bifecting the arc BK, be any point between 
B and K. the fum of the cubes of perpendiculars drawn from it 
to the fides of the circum{fctribing pentagon, is equal to the fum 
of. the cubes of perpendiculars drawn from Q to the fame. For 
fince Oc + O2 +04 =04+ Od and Oc — O04, Od— Oa 
and O&, begin together, and become maxima together, Oc—O4 
has toOka given ratio. Let that be the ratio of m to 1. Then 
Oc—Ob= mxOk, and Od—Oa4 = Oc—O5 40/4 = 
m+1xOk Oc=Ob+mxOk,Oa=Od—m+tixOs 
—3 ——3. j 2 —_— ‘ i 2 
Oc = O06 +3"X0Ob XOk+3m'*xObxOk +m?x 
Of. Oa = Od = 3xme1 XO | 
. a= Od —3xm+1XO0d XOk+3xm+1xOdx 
F 2 a 
