17 S DE CRITERIIS INTEGRABIL. 



liquet autem imprimis ex quantltatibus tertiae co- 

 lumnae , de correfpondentibus primae iudicium fe- 

 rciidum efle. Sic ex : caula , fi in diflferentiali d V 

 terminus R^^ d r^^ defuerit , id pro certo indicio 

 erit, in dZ terminum it^dp^ non adelfe , fcu eife 



3^. Si propofita nunc fuerit formula differen- 

 tialis duplicata V dxdy^ in qua fundio V praeter 

 quantitates x et j, quarum differentialia ponuntur 

 conftantia , duas alias variabiles z et v cum earum 

 diffcrentialibus quibuscunque inuoluat ; criteria inte- 

 grabilitatis iftiusmodi formulae ex principiis modo 

 jexpofitis facile aflignari poterunt. Pofito enim 



dz zzpdx-^-p^dy dv zz.Xi^ dx -i-p^djr 



ap :ziqdx-\-q^ dy d\) —^ydx -\-^ dy 



dp^ zzq^dx-^q'^ dy dp^ zzC^' dx -^<\'^ dy 



dq nzrdx ^r'dy dq zntdx -^x^ dy 



dq^ znr^ dx-^^r^^dy dq^ — x^ dx -^x^^ dy 



dq^^zz.r^^dx-\-/^^dy etc. dq^^—x^^dx-^x^^^^dy etc, 



atque 



dVz=L\.dX'\'^dz-\'V dp -^Q^dq 4- ctc. 

 -^-mdj^^dv-hP^dp^^i^dq' 

 4-^^p -\-(^'dq'' 

 '\-'^'dp''\-0.d<\ +etc 



4-a^Vq^^ 



