FORMVLARVM DIFFERENTIALIVM. 4T^ 



Ex qiiibus igitiir infcrri debet formulam noflram 

 bis efle integrabilcm , et ipfum integralc reperietur 

 efle xyz; omiflis conflantibus adiicieudis. Conftat 

 autem nunc non folum fbrmulas 

 /M^.v ; fNdx ; /T.dx ; f?dx-f^''^Kdx ; f^^dx-f^^dx 

 /(Idx-f^-^Pdx-^-f^^Ndx i f0.dx~-l^^)<^dx+/^^^^dx 

 fore inte-;rabiles fed etiam has fequentes : 



J^^^Mdx ; /^'-mdx ; f''^TKdx ', fPdx ; f^dx 

 f* Pdx- 2/q^.v et /"^^P dx- 2/^dX. 

 Erit cnim 



/M d X = zp-\-yp' ; /'' M dx — zy 

 /Ndx — z-\-xp' i /'^Ndx=:xz ; /Pdx=izzx 

 /Q,dx-f^-^Pdx+f'^Ndx-oi J^'^Pdx-zf(ldx-o 



/^dx=j-\- xp ; /'■9^^A- — AT ; f^dx — zxy 

 /C>dx-/'^^dx+f^'^^dxz:o i /^'■^dx-2jQ.dxz:o. 



28. Quum exempla modo allata quam maxime 

 fint obuia nonnulKi adiungere placet eiusmodi for- 

 mularum differcntialium , quae non quidem per fe 

 integrabiles (unt , ope multiplicatorum tamen ad in- 

 tegrabil tatem perduci poterunt. Ponamus itaque 

 propofitam cflTe iflam formulam diffcrentialem : 



d X (x z" -h X y' — x' zp' ~ x" y p) 



pro qua multiplicatorcm (J) inucfligari oportet , ita 

 comparatum , vt 



<^dx[xz" -^-xy* - X zp' - X y p) 



E e * inte- 



