i5o DE MAXIMIS 



x—^ — ae ^_ bc — \ quarum frachonum nu-meratores 



reciproce per denominatores diuidendo , prodit BO.AD* 

 =(ac -\-beJ , fiue BC.ADn^^ + ^, fcilicet recftan- 

 gulum Diagonalium aequale rectangulo laterum oppofito- 

 rum. Q. E. D. 



Vosterioris 

 Demonflratio. 



Pofterioris Theorematis Demonftratio fponte fe ex- 

 erit. Cum enim BO : A D* = (a% + "%£;* -*£*&: 

 w+*»;+* : w+° lL. feu BO:AD> = (ae + bcy(ac 

 -\-be):{ab-\-cey(ac-\-be)\ erit ^Q 2 : kT>=(ae 

 ~\-bc) 2 :(ab-\-cey, feu BC:AD=ae-\-bc:ab-\ce. 

 Q. E. D. 



Figura 8. lam vero fi circulum in quo delcribendum eft qua- 



drilaterum ABDC determinare lubeat, ducatur ad cen- 

 trum O , v. gr. BO et demifib perpendiculo BE m AD, 

 et FO in BD; lateribus vt fnpra nuncupatis, AB=a, 

 AC=b, DC = c, B D := £ , radioque pofito =r\ ob 

 triangula fimilia BOF et BEA, obtinebitur BEr=^f , 

 proindeque AE + DEfeu ADz: ^^^ "^^' 

 In priori autem theoremate valor ipfius AD in meris 



habetur datis, nempe AD erit = ^%Z^t'^ S ' C °- 

 gnita vero A D , euoluere iam licet r ex aequatione 



AD^i^Ir ^ eVl.r^)^ ^ ^ fublatis fignis ^ 



dicalibus , 



