FORMVL. DIPFERENTIALIVM. 147 



patet forinulam 



dx{3f'^l<^cix- !ip'^?dx-^-f(ldx) 



integrabilem eflfe. In genere autem fi (latuatur 



WzzfMdx; N^zzfNdx; ?' z= fiV-n^ ) dx ;' 



Q[-f{(l-V')dxctc. 



tum vero quoquc 



m^'—fWdx; N^^zzfN^dx; VzrifCV-K'')^^; 



(^'zz:f{(l-?")dx etc. 



liquet , pro integrabilitate formulae dx/V dx re-^ 

 quiri , vt omnes hae quantitates M', N', P' etc; 

 M", N^^, P^' etc. vera fint integralia. 



13. Propofita nunc fif fbrmula dif!ercntialis, 

 d xfd xfV d X, pro qua inueftiganda fint criteria ,' 

 ex quibus de eius integrabiiitate indicare liceat , \'bi 

 quidem ftatim patet , hanc formulam integrationem 

 non admittere , nifi formulae \dx et d xfV d x 

 integrabiles fint. Pofito igitur vt antea : 



dW ^Md x-^-Ndj ^? dp + U ^« ^^ ^ 



bina critcria integrabilitatis huius formulae mox' i|i- 

 notefcunt , fequentibus aequationibus comprehenfa : 



- _ d~? ddO d^^U 



d X d X — d X 



2^ :iddK ^md^-'V _ 



d X d X dx^' ' 



Quomodo vero tertium inucftigari debeat , ex iis 

 quae antea docuimus liquet. Statuamus fcilicet 

 fdxfdxfWdxzzf\''dx et ponamus 



T 2 dV' 



