250 DEMONSTRATIO SINGVLARIS 



XVI. Si nequatio propofita diuidatur pcr bx, 

 tum ca ita habcbitur expreda : 



, _ a _ c x'' — _ d X* — e x"' — ete' 



A" — b " b X 



quac cuin hypothefi Thcorematis A" — ^-V^^.v com- 

 parata , piacbet t ^l et 



As ., — ; a -+- c X» -4- d x'- -i- e X' -h ef. ) 

 q; .V _ — , 



idcoque 



T b t 



hinc autem .v pcr fequentem feriem exprimetur 

 .vcz^ + Cp. + ^Jf -t-t-:^J|:H-;S^V^ -\- ctc. 

 \bi poft diffcrentiationem in locum ipfius t \bique 

 fubftitu:itur l- Simili rationc , fi aequatio fub hac 

 rcpraelciitetur fbrma : 



,. — h I X — (t — d X* — e x'' — elc 



crit f :r:^ ct 



d) V — X — a — d X* — e x ^ — elc. 



nec non 



/]n ♦ 1 — a — d t* — e If — efc . 



ex quo fit 



difTerentiationibusabfolutis, pro t fubftituto — . Hinc 

 fi aequatio fucrit gradus m atque omiics planc cius 

 adfint tcrmini , tum hoc modo , (crics nuincro m 

 inuenientur pro valoribus radicum aequationis propo- 

 litac , totidcm fcilicct quot rndicibus ipla acquatio 



prae» 



