loo Tfaff 



Cimi aneem siogulas qqantitatcs a, bi'c,.^'f^er'^x,«y>-iB,^,'^ W"ii eipresia;- 



concipere Kceat, fiinctioneg litteris F, F, F, f liisi'gArtäe, 'nee nöi» ips4 qn.-m- 

 tiias f, lanquaiu functiones 4''>tae- %v)V x, y, z, p^ q, u considerari possunt. 

 Itaque integratio aeqiiatioais proposkae his tandem »bsolvitnr aequaliOnibus : 



• i) ti* (xj^ y, z, ]^, ^, iT) *= ■^ [f (x» y. z. P' q. ") > f (X' 7. z> p» a> ") J 



2) F (x, y.'trf . q, u) — ■^' [£(x-, y. z, p, q, ")] 

 5) F (is, y, z p, q, u) = -^ [ f (x, y, z, p, q, \\)\. 



Si in praecedenLe solutione niunerator et denonunator formulac pro 



Y evohiintivr, nHiltiplicatione actu insiitula, illius termini 72 ad 56, huj.us 



ternrini 108 ad 60 reducuntar, reliquis se mutuo destruentibiis, sicque di- 



, Tiso • numeratore et denoniinaCore per commünem factOrem P> et ponendu 



9K jn - 9)1' 



-— = 2n', — - = gfl', pi-odit Y = — 7, existente 



P (T"'S^' — T"S"'+R''S^ — R^S^'^ + T^Ti."' — T"R^') 

 1+ R (S'T'''^ — S"T' + P'S" — P^'S" H- T" P'' — T'^'F^O 

 1+ S (R^P"— R"P^ + rpv,p.-/__rj.-./pv. I j^v.T' — R T^') 



'^* — ^-^T(R'S"— R^'S' + S'"P"— rS"P'"-|rR"P"— R"'P^') 

 l+R^P'^ — R"P' -f RS'— R"'S' + T'^p"'— T"'P'^ 

 V-j- s'"P^— S'P'"+S'T"'— S"'T'+R'^T'— R'T'^; 



porra 



)/'SVQ'"^g"'Qv^S'"X"— S"r"'+ R"" Q»— R' Q'»+R' T'^— R'^t'A 

 ^V +R^S"— .IV."S'' + T'"Q'''— T"Q'" j 



/S'T'"— S^T'+S^P'— P"'3^+ R"T' — R'T" + R'P'^ — R'^'F'N 

 ■r <3 ^ -}- R- S' — R^ S 4- P'" T" — T'" P'v J 



— 4. /S'Q' — S'Q-f-T'S — &'T" + P'Q'^ — P"Q''4.p*»T" — P^T'^'-v 

 ^' — "V+K^ -l-Q-T"— T'Q'^-jrP'S^— P^S" ) 



I / Q' R^ — R' Q" + R T ' — R T + P" q^—F' Q"' -f P" T" — P'" TA 



f /S 'Q — S-Q '+S P'"— S'"P + R'Q"— R'^Q'-f-R^P — R' P"- \ 



■^ [ +R"s'— R'S'' + P"Q"'--P"'Q" J 



