X70 DE CRITERIIS INTEGRABIL ' 



27. Deinde fi \lterius procedere yelimus, iu- 

 veniemus elfe : 



^ =r // Kdxdy "/k dx 



^' ^f/R' dx dy — /k dy —fK' dx —ffi: dx dy 



^"—ffR"dxdy-fK^dy-fK"dx-ffm'dxdy 



f-ffR"'dx dy -^fK" dx 



et 



cr zzffSdxdy — /^ dx 



c' zzffS'dx dy — /f dy — /^' dx —ffK dx dy 



cr"z=:ffS"dxdy-^f^'dy^f^"dx^ffK'dxdy 



<r'"—ffS'"dxdy--fl"dy^ffdx-ffK"dxdy 



(j^^^zzffS^^dxdy-ffdy. etc. 



a8. Hinc quidem nunc criteria integrabilitatis 

 qaaefita , faciliimo negotio erui potcrunt , ii enim 

 •valores ipfarum , K, tt, tt', k, k' k" etc. , qui nihilo ae- 

 quantur eadem fuppeditabunt. Si igitur fuerit 

 TLzzffV dxdy^t '' 



dZ—^hdx-^-ydz-i-mdp-^-K dq -4-^ dr 

 ^lkdy ^^rjii^pi^-xf dq' 4-g' dr' 



-\-K"dq"^fdr^' 

 ^fidr'" 

 tum euidens cft effe o-, o-' cr'' etc. z= o , fimiliterque 

 pofito tzz^y a coefficientes ipfarum dt per T, t' 

 etc. exprimantur, erunt quoque hae 7,^', T"etc. z:o, 



vude 



