154. DE CRITERIIS INTEGRABIL. 



Tidz-^-^dp^-^-Qidq^ + Zdt'r 



tum vero ftatuatur 



V dx:iilx,dx-^ydj/-^'7:dp-\-yidq , . . . ^rdt 



-^v^dz-^nx^dp^-^-K^dq' ^a'ds^ 



ct ex iis qune § 2 monuimus, patet fi formula Vdx 

 fit integrabilis , fequentibus conditionibus fatisfieri 

 debere 



(If )=(ii)' m=i^h iif)=i'^y, (i^.]=(f|) "c, 



( ai'=(^')i (fT^=(d-f)' (a7>)=(fj) «c. 



( '4^^i'u^^i (If'=''^) '"=■ (^f)=(^-?'^ ^"=- ^"^- 



Ex § autem 3 viciflim concluditur, fi his conditionir 

 bus fuerit fatisfiidlum, formulam Vdx cfle integrabi- 

 lem NeccfTum igitur eft , vt valores litterarunt 

 f^ , V , v^ TT , Tt^ etc. per iitteras M , N ^)?, P , 9> etc, 

 detcrminentur , qnem in finem notetur efie r 

 V r::: [^. -f- y /) -4- TT ^ + H r . . , < 4- r « 



-^y^p^-h^^i^q^-^-yJr' -^a-U' 



deinde vero 



dV-dlk-^-pdy-^-vdp -\-qdi: -{- Tdq-^- rdM-Vkdr. .». 



-{-udr-^-t du 



-^-p^dy^-^-v^dp^-^-q^dn^-i^ii^dq^-i-r^dK^+yJdr'.... 



-{-t^dG-^-^-a-^di'. 



Hinc vero eliciiintur fequcntes valores litterarum 

 M,N,5^ etc. 



M:= 



