JEQVATIOmS DIFFERENTULTS: 49 

 :___£, cuius differentiale eft dx [x 3 -f- a x y y -+- b x) 



dx — a t ?jy 



xy — " x x -+- u y y-\-b 



Iam ex aequatione aflumta primo determinetur xy per x 



ficque fiet xy~ V c - z2 ~r — ; tum vero x x-\-ayy-\-b 

 per y, at ob (xx-\- ayy ~\-bf ___ c + (^/7 4- £) 2 , erit 



a* x -+- tf>7 -I- ^ — y ic -+- ( W -f- £) = ) 

 Qiiocirca habebitur aequatio differentialis ifta 



dxi/ ia a dy 



.y(c — 2 to:-;c + ) y(-'H- £ &+- 2a 'iX>+ ut i>*) 



,cuius propterea integralis eft afliimta fcu y _r- ^ fc ~^* ~ff 

 £. 24.. Etfi hoc integrale non eft completum, 

 tamen ,ex fuperioribus iacile completum reddetur. Po- 

 ^natur eninv: 



ady r etAz 



_V(c -+- b b -+- 2a6x}-+-aajy + ) — V^-+-<'M--atzzH-ual _ ~j 



ob f~c-\-bb\ g~ iab\ h~aa> erit 



z V( c-+-bb)(c-+-bb -i-2abee -4-aae+)z t: !*/{c-j-b b){c-+-bb-i- 2abzz ^.qaz*) 



y ■— " Cfi-Bbar-daeeZz 



hic ergo valor aequalis ftatuatur ipfi v ' " V^ x a ~~ — > et 

 aequatio hinc inter x et z refultans integralib erit com- 

 pleta huius aequationi difterentialis 



d xV2a a d z 



V(c - 2 b xx — x 4 ) — V(c_)-6"i-|- zabz^-i-aaz*) 



Qiiin etiam ex allatis patet , fi haec bina membra in- 

 fuper per numeros rationales quoscunque multiplicentur, 

 quemadmodum integrale completum inueniri oporteat. 



Tom.VI.Nou.Com. G §-25. 



