Opdscdla 253 



ergo 



alque 



Ergo 



THEOREMA XL 



28. Diictis c qiiovis puncto periplierlac circiill reclis lineis 

 perpcncliciilaribus ad lalera (|uaclrali circumscripli , erit aggre- 

 gatum cuboruin hanim perpcndiculariiiin aequale decern cubis 

 radii ipsius circiili. 



29. Ex aequationc x-\-j + z-{-u^^r cvecta ad lertiam 

 poiestatem habemus 



ix^-\-^-{-z'^-hu^ 



4 



u } 



^+ 3 x^j- + 3 x^c 4- 3 xhi + 3 j>-2x + 3 j's + 3 j'^u + 5 :;2^ 4- 3 = V 

 -^'5z^u-]rZu-x-\-Zu^jr->r'^u'^Z'^Sx^z-'t Gxju-\-&xzu-\-f)yz 

 = 64 r5 

 seu 

 x^+jl-Jrz^+u} . 



+ 3 jc J (j- +/) 4-3 u z (z-i- fO + 3 x\z 4- ?<) 4- ^J-{ z 4- «)V= 64 r* 

 4- 3 z2(j: + J- ) + 5 zf2(j: 4- j") 4 6jr_j-z+6a7r"-f Gxzu-\-Sjziq 

 sed x^ + j'^H- z^4- 1<' ^ I o 7-3 § 27, j:4-j-=:2r, ;34-zf=:Br, 

 j:2_^j-2_|_-2^_,^2^g^2 g ,g xj + uz^r^ § 26 



ergo 



1 o 7-^-\- 6 r^4- 36 7-34- 6 x^- z -i- 6 x^- m 4- 6 j: 3 r* 4- 6^ : m =: 64 »•' 

 et 



XJ Z + XJ U-\-X ZU +fZU =: 2 7'^ ; 



Ergo 



THEOREMA XII. 



3o. Ductis a qnovis puncto pcripheriae circuli reclis lineis 

 perpendicularibus ad lalera quadrati circumscripli, aggregatuni 

 omnium parallelepipedorum, quae fieri possuut perpendicularibus 

 hisce , irinis sumpiis, aequal dupluni cubi radii ipsius circuli. 



3i.A quocuDique punctoOperipheriae circuli ABCD(fig.7.) 

 ducantur rcclae lincae OA,OB, OC, ODad verlices an- 



