(54) == 



§. 10. Qiio formiiliis lus fatis complicatas excmplo 

 illuftrcmiis , ponamus A zz: o et B — i , ac perucniemus ad 

 Icqucntes formulas conciuniores: 



xz^li-V^-J -^ lU^ — '-)' (3 V -+- -) ct 



3 



Quodfi hic loco V -V et V.r fcribamus X ct Y, quandoquidcm 

 hoc modo n.itura curuac non mutatur, tum vero climiucmus 



tcrminum (i — c^)', pcrucnietui* ad hanc aequationcm : 



5 X -i- Y (3 r -f- i) = (^5 -h 61^ -h 9 '"''' v^v/v^ 

 quac acquatio dcnuo quadrari debcrct ad raiionalcm cfricicn- 

 dam , tum vcro littcra v afcenfura ciret ad poteftatcm rcpti- 

 mam , vndc ccrtc ncmo dctcrmiuationcm huius litterac lufci- 

 pict. 



Eiiolutlo cafiis. 



quo U = / V. 



§. 11. Hic igitur occurrcnt binac fequcntcs formulae 

 integrandac : 



/9 c; >/ (a -f- (3 / cO ct /c; 9 V ]/ (a H- (3 / v) , 



qtifls mox patebit itidcm effc intcgrabilcs. Si cnim ponatur 

 / (a ^ p / v) == /, crit / v = '-—-? , confcquentcr 



c - '---;y-- , ergo dv rr iiLi!^-L^ . 

 Prior forma abibit in hanc: t.1^1 (tt — a), cuius intcgralc cll 

 ^'' — tllL , qnamobrcm habcmus : 



s 



/3a;/(a-.pA)=:il^j!^(3f^/v---^«)- 



Pro 



