- ->i^:€ ) 57 ( 



Tbi A — ^ -4- a + |3' ; 



Bm i8-h6(a4-(3')H- y-4-^' + a/3'-a'(3-, 



C n: 6 + 6 (a + (3') + 3 (V -f- 5') + £ 4- ^' 



H- 4 (a |3' - a' p) 4- a (J' - a' 5 + (3' y - (3 y ; 



D=z 2(ap'-a'(3)-h2((3'y-(3y')-f-2(a^'-a'(J) 

 ^a^'-a'.^-f-p'e-pe'H-y5'-y/5i 



E = y <^' - y' <^ + y <5' - y ' a + ^' e - 5 £' i 

 F-e4'-£'<. 



§. 4. Vlteriiis propofitae fint hac aequationes dif- 

 ferentiales: 



I. X' d* y ~\-a x' d^ y -\- y x' d dy -^- e x d y -\- y\y 



-{-(^x^d^z + Sx^ddz-h^xdz + ^z — Oj 



II. X' d' z + ^' X' d' z -\- S' X' d d z + ^' X d z + &' z 



+ a.' x^ d' y + y' x'ddj + e'xdy-\- y{ y — o ; 



qiias quadriiplici vice difFerentiari oportet, vnde fequentes 

 emergunt aequationes: 



IIL X' d' y ■\-[\-\' 0.) X- d' y + [^ OL + y) x^ d' y 



+ [1 y + z) X d d y + [e + y^) d y -\- i^ x^ d* z 

 + ( 3 P + <J ) ^' '^' ^ + ( 2 ^ + (^ j jf </ </ z 

 + [\-\-^)dz~Q\ 



IV. a:* ^^ 2 + (4 + P') ^' '5'* 2 + ( 3 |3' + 5') X' d'z 



•\-[^l'-+^')x ddz-\-[^'-\^')dz-^oLixWy 

 + (3 a'+y') X'- ddy-\[2.y' .\i')xddy 

 ■\[z' + y{)dy — o\ 



Y . X* d" y -\- [% ->r a.) x' d' y \- [j z -\ 6 cL + y) x^ d* y 



+ (6a + 4y + e)x d' y -f ( 2y+ t2.e-{-y\)ddy 



-\-^x' d' z-\-[6^-\-Z) x' d*z 



-f (6(3 + 4<^ + ^)-*"^'- + (a^+2^+^)^<^^ = o; 



i^<!?fl Acad. Imp. Sc. Tom, III. P. IL H VI. 



