FORMVLARVM DIFFERENTIALIVM. 195 



aJ integnibilitatcm pcrJucatur. Sit igitur quantitiis 

 (J) talis multiplicator , quem nunc fupponamus effc 

 tantum funcftioncm ipfius .v, qno ruppofito , euidcns 

 fit formulam <P [dy ~\-y v d x) integrationcm admit- 

 ter« debere , fiquidem (^ z ef x iam per fe intelligi- 

 tur cde integrabilis. Habemus vero tunc pro formu- 

 la nollra 



V- (p (p+y v) ; dV- d(p [p+y v) + (^[dp+vdy-^rydv) 

 Tnde deducitur 



M = !?(/) 4-7 ^') + <^Jj-^ N-4).j et P=CI), 

 itaque qiium effe debeat N — j^=:o, fiet <^v-<^J>_-o^ 

 ideoque ^ — v d x , feu Cp — f^^'^*, Integrale au- 

 tem ipfum iam erit j ^-'^'"^'' , ideoque totius formu- 

 laa propofitae : 



Enimuero operae pretium iam quoque erit inuefti- 

 gare multiplicatorcm gcncraliorcm , qui fundio fit 

 \triusquc x et/, et de quo ex antea monitis qui- 

 dem conf^at , eum huiusmodi exprimi forma : 



gjvdxY -.(lyef^^^^-^fe^^^^^zdx). 

 Statuamus autem vt antea hunc multipiicatorem (J), 

 et quum nunc fit 



V — <$>^/'4-i''^" + -) > "^c non dV — d(^{p-\-yv-\-z) 

 ^(^(^dp~\-y dv -\- V dy -\- dz) 



erit 



M =: (i|) (p -I- >"i^ + ~) -H 4^ i^ -+- 'S ■-> 



N n: C^ip +/ i' -1- ^) -H Cp V 



' B b a V-<P, 



