Tnde (cquitiir 



e-zz— !iz(ib-{-cx), fiue b -\- c x zz ~~^ ; 



hincqiie colligitiir 



x — '.:^^-t, fcu ^ — > - ' fc ' - » « . 



Aequatio autcm /> -|- ^ Jf ~ ^~tt^ difFcrcntiata pracbet 



'^"•^^ — ~»ri > — ~ ra~T » 



vnde dcdncitur 



^ .V — - "iJi-ll^i--*-^, at ob 

 b-i-cx — '-=^= flCt J = '-^13. 



1 i 1 z 



His ergo valnribus fubflitutis formula uoflra X ^.r rcddc- 

 tur rationalis. roflquam igitur cius intcgralc fuerit in- 

 ventum loco s valor antc iuucntus / (f +(^ + f jr)') — ^ — r x 

 crit (i)bflitucndus. 



II. Sin autcm y fucrit quantifas ncgatiua , ponatur 

 yrz — c c ct (3 — — a/^f, vt habcatur 



s — V(oi-^bcx-ccxx) — V{a + bl;- (b-i-cxy)> 

 \bi euidcns ef^ , quantitaicm a-\^ b b ncccffario cffc dcbcre 

 pofitiuam, quia aiioquin s cuadcrct imaginarium. Quani- 

 obrcm ponamus brcuitatis gratia 0L-\-bb—aa^ vt fiat 

 jrirt. "V [a a — {b + c x)') , ad quam formam rationalcm cfS- 

 cicndam flatuamus 



V [aa- {b-\-c .v)') — a - {b -\- c x) Zy 

 Vndc fumtis quadratis crit 



a a — {b -^- c xY — a a— 2 a z{b -{- c x) ~\- {b -\- c x)* z x 

 quac acquatio rcducitur ad hanc: 



~(b -\- c x) — — 2 a z -\-{b -\- c x)z Zf 

 vndc rcpcritur 



b 



