COMMENTATIO ad QUAESTIOJNEM MATHEMATICAM. 5i 



CoROi,LARiUM 1. QE"' = i^^,RF"' = ^^,SD"'=£i£2^. 

 Nam ex proporiione : AQ : QE'" z:: b -{• c : a 

 sequhur : QE'" = -—-^ X AQ 



= M^£^ ^Theor. XLIV.) 



COKOLLAEIUM2. 



= r , /\f I • n// ' L ^ 1 <Theor. I. Cor. i. et III. Cor. 2.) 



^ ^3 ,j,i,i^m + n-r) ^ 



r* r ' 



r{l+7n + n — r) 



COROLLARIUMO. 



AQ X BR X CS : QE'" x RF'" x SD'" = ^~ : - — ^^ . (Theor. XLIV. Cor. i.) 



= l + m + n — r:r; 

 quicum conferantur Theor. XXXVII. et XLII. Goroll. i. 

 Corollarium4. 



QE"'xRF"'xSD"':AE"'xBF"'xCD"'=-77-^ ■, : ; — (Theor.XXXlX. Gor.) 



=zR:2r. 



THEOREMA XLVI. Fig. 1. 



Distantia AQ centri Q unius cujuslibet ex tribus circuUs exinscriptis ab an- 

 gulo remoliore A trianguü ABC liarmonice dividitur in centro P circuli inscripti 

 atque in puncto uhi pervaditur latere BG angido Uli A subjecto. [Id est : 

 AQ X PE"' = AP X QE'". 

 Demonstratio. Vidimus AP : PE'" = S + c : « (Theor. XLII. Cor. 2) 

 Est vero eiiam AQ : QE"'zr b + c : a (ex Theor. anteced.) 



adeoque AP: PE'"=AQ : QE"', et AQ X PE'"= AP x QE'". 



THEOREMA XLVII. Fig. 1. 



Summa radiorum unius cujuslibet ex tribus circulis exinscriptis [ac circuli in- 



G 2 



I 



