42 INVESTIGATION of the 



__ r + 2 Otf 



2 ' 



+ r + Om, and r = 2 O w — 2 O ». Therefore Offl: 



r — O m = = G «, and r + O m zz * = A m. 



2 2 



Confequently we have 2xr + Om ^ ^> . > 



and 2 x r— O » = 2 r 3 — 6r xO« + 6rxO« - 2 X O » , and 



m . . , . • 35 r 3 + 30 r* x O » + 60 r X 07/ 

 thefe added together give -^ * .. I n 



-fr—i r 3 — 6 r a xO« + i2rx 0«* — 8 xOV, 



like manner, 2 x r— O « = 



and 2XV+0» 3 = 2r 3 + 6r , xO» + 6rXO» + 2 X Ok 3 , and 



o f 3 + 18 r a x O » + 36 r x 0~» 

 thefe added together give * , to 



■which if GA 3 ss 8 r 3 , the cube of the perpendicular to the 

 fide touching the circle in the point A, be added, we get 



AI r 3 + T g r 2 X O n + 36 r X pt 

 J*" 

 But the fum of the cubes of perpendiculars, drawn from 

 A and G to the fides of the pentagon is 25 r\ as has been 

 demonftrated, when P Q_ coincides with AG* Wherefore 



n^_±*.2r*XO» + 96rxQ7i 2 Qr Igir 3 + l3r * x 0« + 2 4 r 



4 

 X On zz 25 r 3 and 4 r X O n -f- 2 r xOn zzrK Now, if for 



. ,. , „. , ,. 4i^ 3 +i8r 2 xO//-f-36/-xO« _ 

 this value of r 3 , there be fubftituted r 3 in ' 



we 



