FORMVL. DIFFERENTIALIVM. 171 



vnde pro criteriis integrabilitatis obtinemus fequentes 



aeqiiationes : 



I. ffSdxdy—f^dxcz o ; 



II. ffS^dxdy—f^dy-^j^^dx—ffKdxdyno 

 IIL ffS^^dxdy-^fi^dy^f^^dx-ffY}dxdy-0', 



\S. ff^^^^dxdy-fi^^dy--ffdx-ffy}^dxdy'=z.o 



V. fS^^^^dxdy-ffdyz^.o j, vlterius 



VL ff^dxdy-fcrdxzzLO', 



VIL ffVdxdy-f(T'dy-f(T'dx-ff^dxdy:=ZQ ; 



VIIL ffV^dxdy-fd^dy-^f^T^^dx-ff^d^xdy^zo ; 



IX. ffV^dxdy-fd^^dy-fd^^^dx-ff^^dxdyzzio ; 



X. ffT^ dxdy-fcT'^^dy^f<j^^ dx-^fffdxdy—o ,• 



XI. JfV^dxdyfcT^^^dyzzo. 



29. Vt vcro melius pateat , qualis forma his 

 aequationibus rite euolutis inducatur , e re erit le- 

 quentes ob(eruafle aequalitates : 



^TT^' — ^ ' ^ctx^dy — Vd «' M* rfy — V<t»' 



( d^ ^ ) (dd Q\_ /d_P \ 1 Vr 



\dx'dy' — ^d x^ ^ ^u x^ ^^ 



Wdy»-' — ^dxdj' ^d x'~ 



^dy^ 



