FOilMVL DIFFERENTIALIVM. iSi 



liderandam efle , vt fundionem triimi variabilium, 

 x% y^ z adeo vt ftatuere liceat : 



dv-pdx-{p^dy-\-fd.z dq zzr dx-\-r'dy ~\-r"d.z 

 tum vero d(^' -r' dxi-r'" dj + r^"^ dz 



dp -q dx-\-q' dy\q"dz dq"-r"dx-\-r^'^ dy +- r^ dz 

 dp' -q' dxi-q^^dyi-q^yz dq"'z: ^"'dx+r^^^dy 4-r^" dz 

 dp^-q^dx-^-q^^^dy \-q^dz df-r^^dx^-r^'' dj-^r^^^^^dz 



dq"" zir^ dx-H^^^^^dy^^r^^dz. 

 Hiiic autem liquet dV huiusmodi formam iiabere : 

 dV^iz-^-ldx-^r^^dv-^V dp -|-Q_ dq + ctc 

 -^-Ldy -\-?'dp^^(^ dq' 



-^-Mdz -^F^dp^-^-Q^^dq" 



^(^'dq'" 



Si vero fupponatur effe Zznff/Vdxdydz fitque 

 dZzn i dx-^-vdv^izdp -\-k dq + etc. 

 '^-'hdy ^'Ti^dp'-\-K' dq' 



-^lkdz -\-'ii"dp"-\'K^'dq" 



^K"'dq"' 

 ^K^-^dq'"' 

 K^ dq^' 



inuentio criteriorum integrabilitatis fbrmulac 

 \ d X dy d z eo reducitur , vt valores coeiHcientium 



23 ij Xj 



