yet 
‘ Hog. O- ‘W4pale m+y 
 * 
PROPERTIES of the CIRCLE. 45; 
drawn from Q to the fame, both when O é is = 0, and when it 
is a maximum, this equality muft exift whatever be the magni- 
tude of O& between thefe limits. 
AND in a fimilar manner is it demonftrated, that the fum of 
the cubes of perpendiculars drawn from P to the fides of any 
other regular figure of an odd number of fides circumfcribing 
the circle, is equal to the fum of the cubes of perpendiculars 
drawn from Q to the fame. For if Om, &c. or fuch parts of. 
perpendiculars drawn from A to the fides of any regular cir- 
cumfcribing figure of an odd number, 2; of fides as lie between 
O and G, be denoted by A, B, C, &c.; and Ou, &c. or fuch 
parts. of perpendiculars drawn from G to the fame as lie between 
Ovand A, be denoted by 2,4, ¢, &c. A+ B+C+ &e, to” 
n—tI aie ats, 
terms, —4 — b — &c. to terms, = 5, if ~—1 be a multiple. 
of 2 by aneven number. Alfo.A+B-+C+ &c. to ~— terms, 
ta+h2+c:+ &e.'to aa terms, = FB, and‘ A*-B3? 
gk CT: 30> z == 
+ C3 ig &c. to eae terms, —a3—b3—c3}— &c. to x 
7 
ier y ! 
{ 
w 
a 
at, But if n—T be a. multiple of 2. by an odd number; A + 
B+C+ &c. to- tt “A CATS Deits &c. to 7 Seis, 
4 
. 
“3 ny: “y Bt +C 3 Hcl) 96 “Mt terms, Ms “a +e + &e.to 
== ee Wade A+B + + ea. to 
terms 
