134 DE CRITERIIS INTEGRABIL. 



dV^Mdx-^Ndj-^-V^p-^Qdq-^-Rdr-^-nc, Vdu, erit 



d? dcIQ d'R d^U 



^ d X d X d X — d x"^ 



Quuin iam dV aequetur formulae differentiali, quae 

 per hypothefin integrabilis eft , per omnem nutem 

 integrationem formulae diffcrentiales ad gradum pro- 

 xime inferiorem deprimantur ^ necefTum eft , Yt 

 formula diftcrentiahs V dx huiubmodi habeat for- 

 mam : 



VdxzziJ.dx-^vdj'{-i:dp-{'Kdq'{' , . . -^rdt^ 

 pofito nimirum dt:z:udxy hinc autem deducitur 



V :n [JL 4- vp^- TT ^-f- Kr . . . ^- rw atque 



dV^zr.d^K-^-pdv-^-qdix-^-rdK^. . udr-\-vdp-\-i:dq 



^Kdr.^.-^rdii. 



Qiuim vcro fuppofuerimus 



d\—.Mdx-\-]<^dy-^-Vdp-^Qdq^ 4-U^« 



fequentes hinc elicientur, ipfarum M, N, P, Q etc. 

 valores : 



M =:. (^-|) ^p (^p ^ ^ (^-) ^ r (|f) + etc. 



N = (^-f ) + p (^-^) ^- q (^-J ) -h r (f--) 4- etc. 



Q-- (lt> ^-^ ^ii) + ^ C-f) + ^ ^r^) -*- ^t^- + ^ 



etc. 



lam quum formula V dx fuppofita fit integrabilis , 

 neceffum ell, vt lequentts conditioneb locum habeam: 



