CIRCA RADICES AEQyATIONVM. 71 



tionem differentialem tertii gradus, quac f^6to A-^u 

 et B:z:l vt aequatio propofita fit y^^^^j—^u ita 

 fe habebit 



32( I -u^^d^y-i^^uududdy — ^^ududy-^-^yduzio 



furato fcilicct clemento ^^ conftante. Qucmadmo- 

 dum autem illa aequatio in hac contincatur , non 

 fcrfpicitur. 



XXI. 



Obferuo autem hanc aequationcm integrabilem 

 reddi fi multiplicetur per y , finguli enim termini 

 quatcnus fieri potefl integrati praebent \t fequitur : 



fyd'yz=zyddy-~'^dy^[ipQT 32] 



fuyd^yzzuyddy-ludy^-:^ uuy dudy^yiy^ du-\-lfuududy'' 



— 3/)7//«' [per- 32] 



fuuyduddy-uuydudy—uyydu—fuududy^-^-fyydu [per- 144] 



fuduydyz:ziuy^du—hfyydit[ per - 8^J 



fyyduznfyydu' [ per 5] 



irnde nafcitur haec forma intcgrata 



1(5 (i -«'j ( Q.yddy-dy^)-^^uuyjdudy -\- $ uy^ du zzQdi? 



quac ponendo y zz. z z , ob j j =1 5;*, y dy zz t^ z d z 

 et yddy-^-dy^zzyddy^^zzdz^ziLHLZ^ddz-^-Czzdz 

 ideoque 



^yddy:^j^z'ddz^4,zzdz feu ^yddy—dy^zn^z ddz 



induit hanc formam : 



^^{'i^—u)z ddz-^6uuz dudzAr^Su^di^zz.Qdu 

 vel ^4( i-u)ddz-^6uududz-\-su^du—^ 



^uac 



