FORMVL. DIFFERENTIALIVM. 141 



Hiie aeqiiatlones intcr fe comparatae manifefto 

 odendLUit , requirita integrabilitatis fupra memorata 

 formulae notlrae Wdx competere, adeo vt iam qui- 

 dem abbquc \lia haentatione , lianc formulam iii- 

 te^rabiiem cfTc , pronunciare Iiceat. 



9. Ex hifce Theorematibus varia nunc deduci 

 poflunt Corollaria quam maxime notatu digna, quo- 

 rum potiora lieic recenfuiife haud pigebit : 

 1°) Cum ex aequatione propofita 



tum ex valore ipfius 



Vdxzzdxf mx-Vdy, f Ndx-\-dp{ fTdx-p^^Ndx)^ etc 



patet , ad integrabilitatem formulae Vdx neceflario 

 requiri, non folum vt formulae Mdx et ISidx fint in- 

 tegrabiles; fed etiamvtomnes quoque fequentesformuke: 



dx{?-f^dx); dxiQ:-f?dx^f^'-y\S^dx) ; 



dxiK-jQdx-^-f^^^Fdx-^f^^^Ndx^ctc, 

 integrationem admittant. 



11°) ViciiTim autem euidens eft, fi formula principah's 

 Vdx fuerlt integrabilis, omnes quoque has f ^rmulas : 



M^.v,- Ndx; dx{?-fNdx); dx[Q^f?dx^f'^Ndx) etc. 

 ita comparatas efle , vt integralia ipfis competant 

 llPj Ex valoribus ipfarum M,N,P § 8 allatis 

 liquet eflfe 



S 3 quae 



