152 DE CRITERIIS INTEGR ABIL. 



His autem valoribus pro V5 ^'j^^^^* iiitrodudis, 

 obtinebimus fequentem aequationem : 



(N-g^-f^-etc.)/VV;.-V'(P-iA3-+i||R_etc.) 



+pl(Q-iil-^^^-eK.)-ili^{R-4-P-hcK.) 



^dx^^dx^ax^ i d x^ ^ d x * / 



+ V(;;//NV;i^-(w-i)F + (^-2)^'-(?«~3)j^'etc.) 



^ dx V ,. 2 y I. 2 •/ ^ I. 2 ^ I. 2 djc"*' 



^ d X 



h:=0 



R' 

 etc. 



10 



d d 1' 

 d X* 



etc 



:) 



vnde rubliitis terminis , qui propter primam con- 

 ditionem niliilo aequautur , habebimus : 



(N-^-^-f-f^etc.)/VVA'-V'(P-^4-3^-etc.) 



^ d x d X- ' ^ ^ d X ^ ^ d x^ ' 



+dli^^ ^'^-d^e^c. }--^(R-^+JO.-^etc.} 



etc. 



+ V(P'-.i^>3i§:etc.)-f:(Q!-3|£:+<S.ffetc.) 



+^I(R'-4l4'+^°-a"'"^-)etc. 



Ceterum fi ab hac poftrema aequatione fubtrahatur 

 (N/-.^' + ^/a'_jLR:e^c.)/V^A~ o 

 - abibit ea in fequentem, quae commodioris eft formae 



_>Ty ry^y. d.p/Vdx _ d.d. g^/v djc , d-^ R^ f Vdx , ^ ( -O 



qua aequatione iam alterum integrabilitatis criterium 

 quaefitum continebitur. Heic vero obferuari mere- 

 tur, pofito V =: V fmgula aequationis huius membra 



dertrui, 



b< 

 I 



