FORMVLARVM DIFFERENTIALIVM. 183 



tum vero pofito ^V d x dy — 7. 



d Zzz2d X -{-Tidp-^^ dp -\-0, dq 



-^^dy ^'f'dp'-]-OJdq' ^^^' 



-}- 0."d(i". 

 Nc autem nimui multitudine formulaium obruamur, 

 ponamns in valore diff.rentiulis dZ vltimos termi- 

 nos cfle '^dp et '^''dp' cx natura enim aequatio- 

 num vltimarum ad quas calculus perducet , facile 

 apparebit enodationcm fpecialis huius exempli , vim 

 demondracionis gcneralis habcrc. Rationibus autem 

 fubdudis vti §. -^S. Diflert. I. ftdlum e(t , inuenie- 

 mus critcria integrabilitatis formulae Vdxdy fe- 

 qiientibus (eptem contineri acquationibus : 

 Olzo; 0'-oi OJzoi mz:o^ Tr^'zo:^^l"=.Oi^J"zo. 

 Eadem crireria igitur feqaciUibus quo.]Ue aequatio- 

 iiibus expreffi efle , intelligi dcbct : 



o — ( AL^ ) — (AL^ ) _ (■-£lL5_ ■) -4- ( 'h\' ) 



o — (4L^> — • ( '^♦.ti ) _ l i!5 > 



(±±1.) 



^d~idy^ 



xd' fy'\ [ d* x" \ (_^'"' \ .4_ /■ d d V \ 



^ ^dx-dy*' — ^dxdy^' ^dxdy-'' ^^ ^dxdy' 



O — ^dl^^' — ^d'x>dy' - ^Jxyry' ^- ^al'd>J ^d x dy> 



^ — ydx^dy'^ — ^di^dyi' \^^fj-yl ^ U x' dy' ^dxdyl 



/ d* H" >, , f d^ ) 



" ^JTTy^' "+" ^dxdy^-' 



** -^ quaruin 



