rum aequationum prima quadruplici vice, reliquae autem 

 triplici vice, vnde fequentes prodibunt aequationes difFe- 

 rentiales : 



+ {^-{-s) d z-\-{y-\-^) dv:zz o ; 



y. X' d' z-hoL'xddy-\-{2.-]-{^')xddz-hy^xddv +(a'+5/}</ 



( ' -\-{^'-\-e')dz-\-{y'-\-^')dv~o; 



VI. x'd' V -+ ot,"xd dy-\- ^^'x ddz-^- {t"-\- y") xddv-\- («'/+ V^^dy 

 ^{^"■\-z^')dz-^{y"-^Z:')dv — o', 



' VII. x^d^y + (4+a) X d'y^ ^xd' z-\-y x d'v + (2+2 a + 5} ddy 



VIII. ^V* s + a' .V dy + (4+(3') xd^^z 4- y'x d^v-^-^z a.'-\- $') d dy 

 + (2 4-2(3' + e'j'^'^^ + (^'V' + 4'}'^'^'^=oj 



IX. A- V* V 4- «"jr^^jK^- 13" a: d'z + (4+y " ) :c^» -y + (2 a"+<r"} ddy 

 -{-{^^>'-\-i")ddz-\-{2-\-2.y'iJrK")ddv—o; 



X. .V* i' j + {6+ol) xd'y -\-^xd*z-\-yxd'v-\- ((J+3 a + 5} </^ j 



+ (3i3+e}^^2; + (3y + ^j^''y = o; 



XI. a:* </' s + a!x d*y + (6 + (3') a: d'z + y' .v ^* v-\- (3 a'+a'} d'^ 



+ (6+3^' + £'}'^'^ + (3y + '^V'^ = o; 



XII. X' d^v + a".v^> + g>"x d'z + (6+y '/} x d'v-\- {'>,a."-\^") d'y 

 -\- ,:^ g>i'-\-s")d' z-\-{6-\- :iy'> ■\-^") d' v — o; 



XIII. X' d'y-\-{S-\-oi) xd'y -\-^x d' z-\-y xd' V ^^{iz-^-^cL-^-^B^dy 

 + (4.p+e}^*2 + (4y + <}'^*^' — o. 



_j^, §. 10. Harum aequationum fi fequens inftituatur 



combiuatio : 



XIII. 



