ioS DE RADICIBVS 



Vtl quoniam inde habetur bb~ 3 ac~ l(aa-$b) 



(zaa—^b)-^ $ a V (^(a a - $ b)' -w) 



pro bb-^ac hi oriuntur limites 



bb-$ac^k(M~zb)(zaa-~$b)-\-\a(4ia-$b]^(aa--zb) 



bb-zac^\(aa-$b)(2aa-zb)-~\a{aa-zb)V ( aa~$b). 

 Vnde deducimus 



a -^TF < ' ; feu 



6_i— j_a_c - ^o — V [ aa — z &) \» 

 aa — jfttf^V 3 J ' 



Quoties ergo formulae vrElT valor intra hos li- 



,a-+-^(aa — z b) S2 _ ,a — V(«a — j 6)\, 



mites (-^ 1 — -3 y et ( _— - — J ) 2 continetur 



certi fumus omnes radices noftrae aequationis cubi- 

 cae efle reales. In quo adeo confiftit caracter com- 

 pletus quem quaerimus, 



Corollarium 



1. 



Quia limites inuenti locum habere nequeunt 

 nifi aa — $b fit quantitas pofitiua , hinc ftatim per- 

 fpicuum eft radices reales efle non pofle nifi iit 

 aa)>$b'. quod criterium iam in fupra allatis con- 

 tinetur. 



Corollarium 2. 



Deinde cum ambo limites fint quadrata ideo^ 



— 3 a ( 

 T^-zb 



debet 



que quantitates pofitiuae , valor formulae y^ix 



