--3=51 ) 74- C 



x^ddz-\-cL*xdy-\-^'xdz-Y- y* y -{-l* z — o\ 

 tumqne ftatuantur 



dy — pdx; dz — p*dx\ ddy — qdx^\ ddz — q'dx*\ 

 illis valonbus introdudis fiet : 



X' q -{- a. X p -\- ^ X p' -\- y y -^r'^ z ^ o ; 



x' q' 4- a' .V p -f- p' X p* -\- y'y -h^' z — O. 



Vlterius fit pro priori aequatione multiplicator Cj) et pro 

 pofteriori vl/, et concipiamus aequationem 



(P{x' q -\-oLXp -\-^xp' -\- yy -\-$ z) 

 -\- \|y {x^ q* -\- a) X /> -h (3' X p' -\- y' y -\-V z)~o\ 

 efle integrabilem, vnde, quum criteria integrabilitatis prae- 

 beant has aequationes: 



exiftentibus 



N=:v4)-FY'vjy; N' — 545-f-yv|y 



P :r a A' Cp -i- a' A- vp ; P' =: p x Cf) -f- p' A' v^ 



Q =: x" (p Q' — x^- 4» 



fuppofito nimirum quod Cj) et vj^ non nifi fundiones quan- 



titaiis X inuoluant, effe debebit : 



j;' </ </ (f) + ( 4 - a) .t ^ Cj) — a' .r ^ v[/ 



x" d d ^ -\- {^- ^^ ) X d ^ - i^ X d (^ 



^,. ( 2 _ p/ + y ) v{. 4- ( o^ _ p ) C}) = o ; 

 quae aequationes nunc iterum ipfius formae propofitae 

 funt, ideoque fufficiet, fi pro Cf) et vj^ valores particuiares, 



his 



