tiS m CRITERIIS INTEGRABIL. 



«^^^.-^^.^-t-ZP dx-fdxfmx 

 = (jSjk) -^-/P' dx+f?dj-fdxfndy-fdxfndf 



~\-ff!<idxdy 



o = {i£~^)-+-fP"dx+f?dz-fdxfNdz-rdxft<idz 



-J-//N dxdz 

 P-^r^:>-^P'^y -fdyf^dy 



O-ii^^-^J^^dj+fVdz-fdyfKdz-fdyltidii 



-{-ffiidydx 

 o=z(';£;,)-{-f?"dz-fdzrNdz. 



Vnde fequentes confequimur valores : 



^ ziz-f-Kdx', ^'--fiidy-fTi^dx-ffvdxdy 

 4" zz -fn dz -fi:'^dx -fvdxdz ; ^''' = -/tiVj' 

 ^^—"fn^dx-fii^^dy-fvdydz ', ^^--fn^^dz 



cx quibus colligitur : 



K zzifffQ^dxdydz —fiidx ; 



k' -=::fff(^ dxdydz-fTidy-fndx-^ffvdxdy 



K^' =.fff^' dxdydz^fitdz^fTi^^dx-ffvdxdz 



k'" zzfffQ^^dxdydz-fn^dy 



yy^—fff(^^dxdydz-fii'dZ''f'K"dy---ffvdydz 



K^ —flf(^dxdydz-fii"dz. 



43. Inuentis hac ratione valoribus litterarum 

 h, X, fx, y, TT, tt' ctc, ii, qui pro formula different ali 

 triplicata Vdxdydz in nihilum abeunt , criteria 

 fuppeditabunt, ex quibus de integrabiLtaie huiu«^modi 



formulue 



