capiatur, vt euanefciu pofito x—f^ habebitur 



§. 7. Tum autem erit ex variabilitate ipfins j: 



fi^\ — — ct a {ij5 __yj. gf- 



^^ y^ ix + %y',^ (X-+-SB3')» i x -h d y ]^ 



vbi fi conftans D ita determinetur, vt integrale euanefcat po- 

 fito jf — /, erit 



Hinc fi Ilatuatur 



— ^— = ^' H- . P^ + ^' -h etc. 



Pjc4-(^^ j:-(-ai:> xH-55jy x-H(£:y 



erit fundio illa folius j', littera Y indicata 



Y — aUf-hiiy^ — ^^^Hif — x ) 1 PM/-^-^ :yi— 3?8f/ — X) _j_ gj.^^ 



(y-<-3l7-tx-r2l j) ' [f~h^yi{x + ^y) 



§. 8. Haec quidem exprefTio adhuc continet variabi- 

 iem jr, quae autem eliminabitur ftatuendo a^3i:a9(, |3^~|3^, 

 y''zz:'y€, et ita porro, quo fado Y ita exprimetur: 



Y = "^ -I- ^-^ - H- ^^ -f- etc. 



vnde porro deducitur 



/YBj/ = a/(/-4-3(O-+-(3^(/-+-58)0-+-v/(/+^J')-^ctc. 

 Cum igitur vi regulae §. 5. expofitae fit 



integrnle quaefitum erit 



a/(j:-F5i)')-f-(3/(;c-H5Bj')-+-y/(jf-^-<i:y) -+- etc. 

 quod cum fimul fit inteerale formulae /" ^^-*— , nulla conftan- 

 tis ratione habita, aTeuerare certo pofTumus, integrale comple- 

 tum aequationis homogeneae rationalii V d x-\- Q^dj ~ o elTe 



X 3 / 



