PROPERTIES of the CIRCLE. 47 
But fince 57 ( = fum of the perpendiculars drawn from P or 
AP +BP+CP-+DP +EP 
Q to the fides of the pentagon) = = 
ay =AQ+EQ+6Q+HQ+EQ, and fince the fum of the 
PGYI33 
{quares of perpendiculars drawn from P to the fides of the pen- 
tagon, has been demonttrated equal to the fum of the fquares of 
as SANE We ay eared 
perpendiculars from Q to the fame, eee 
~ ALT + Q'4 1 +EQ =<". And as the cir- 
cumference of the circle, which has PO for its ea is me 
vided 1 into five equal parts, in the points a, 4, ¢, d, k, Oc. +. Oa 
+08 +00 ‘x Od =r x aaeOD 3 ed x” , and Oc. +02 +08 
——d ee 
ars” + Od ak <= % x OP a a Wherefore, 
2 4 
es Shah tle FOF BBL Od 2 De 08 +08 
+05 + 0d = =a +e < = US xp = XS 
xr= hae the fum of the fourth powers of perpendiculars 
drawn from both P and Q to the fides of the pentagon. 
In the fame way is it demonftrated, that the fum of the fourth 
powers of perpendiculars drawn from P to the fides of any regu- 
Jar circumfcribing figure of an odd number, 2, of fides, is equal 
to the fum of the fourth powers of perpendiculars drawn from 
eee, 
