PROPERTIES of the CIRCLE. 47 



But fince 5 r ( = fum of the perpendiculars drawn from P or 



Q^to the fides of the pentagon) = 



2 r 



= AQ^+BCL+CCL+DCL+EQ. . and fmce the fum of the 



2 r 



fquares of perpendiculars drawn from P to the fides of the pen- 

 tagon, has been demonftrated equal to the fum of the fquares of 



perpendiculars from Q^to the fame, — — — — 



4 



r 



= AQ. + B^+CQ^ + Dq+EQ, = vg And as the cir . 



4T 2 



cumference of the circle, which has PO for its diameter, is di- 

 vided into five equal parts, in the points a, b, c, d t k, Oc -\-Qa 



4- 0^4-o/ + 6d = r X^|5? ± S£' and0^ 4 -r*0^ 4 + 0^ 4 



2 2 



JX 



4- 0£ + Od zz 4 X - — X — X £= *q — Wherefore, 



424 o 



4- 0£ 4- Od = -g~ 4- — g h -^p = -^X^= jf" 



X ^* = half the fum of the fourth powers of perpendiculars- 

 drawn from both P and Qjro 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 regtt- 

 lar circumfcribing figure of an odd number, «, of fides, is equal 

 to the fum of the fourth powers of perpendiculars drawn from 



