( 5^ ) 



mns. Cum etiTm inde fit x^ —fx'^ '^Is ^ ^ ii loco x* 



eius valor fcribicur, prodic 



x^ =: Cf * -4- g) X + / g 



x^ = (p + 2fg) X + Cr ^ + .^*) 



x' - rf- ^ 3 r g + g^) X ^- (/3 g + fg-:^ 



Eodem inodo, quousque iibuerii:, progredi iicec, ica uc 



omnes ahiores poccscaccs ip(jus x^ per calem formxv.fx+g 



cxhibeancur. 



LXII, 



Quodfi ergo hos valores tam in numeratore iV, quam 

 in denominatore M, fablliciiii-nus, manifesto ad calem 



formam pervemmus ^^ -- i -«^ _^--— ^ ubi facile m- 



telligicnr, numeratorem en denominatorem per eiusmodi 

 factorem communem m'iltipiicari posfe, uc, pofito 

 X^ zz. f ^ •¥ g '^ ^^ denominatore quantitas x peniciis ex- 

 llirpecur, quo flicco dehicus valor ipfius T obtinebitur. 

 Etenim 11 pro illo mulciplicacore fumimus p 4. q x^ 

 denominator fit a p -^ ( a q -^r h p) x -Ar h q x^ qui , 

 pofico x^ "^ f X -4- g^ indiiic formam (^aq-^bp-^fb q)x 

 4- (^/>4-^^^), ubi canciim oporcec /> en q ita deflnire , 



ut fiat ^ ^ 4- ^ /> "+- / i' fZ — o, five - =:---—. 



Sumto igitur p ^^^ - f b - a qi q ":=: b , denominator eric 

 a p "^ gb q'^^ q b^ -— a f b — ci^ ^ ideoque conlhns. 

 Numerator vero rum erit (^4-/3 x^ Qp -f q x^ qui ob 

 x^ zz f X 4- g^ reducirur ad formam • . . . 



