84 Pfciff 



evanescani ^). (^nod si auteni d'^ f — jponalur?='o, eritN(l''M-Md''N==o, 



sive = . IIiiic esse dehet 



M N '.■-11' r-'ai f 



Est aulem l'^(^ — p;:^) = '1'^^ — pd'^Äi — %d''p; porro ex tlieoreinate notissi- 

 mo de diiTerenlialibus functionum plurium variabilium,, cum sint- K, et t- 

 tuntiiones iv>v y, a, b, c, erit d''^=d''Z, d''% = d*X; liinc :'; It 



d^^— pd>';« = d»Z — pd»X = d»(Z — pX) +Xd'p 

 = d'q + Xd'p, ob Z — pX = q. 



Inde prodit d^ (^— p%) = d*q + Xd"p— xA^^. 



Jatn vero est d'q = q'd'x + q"d"y- + q'"d'z -|- q"''d"p, 



vel ob d"x = ;»j, d'y==o, d''z=^, d^p = w, eilt d*q= q'>j+^ $*+ 1"^'^' 



cum praeterea sit d^p =^, p^dJ^^g-^^^^ _^^^ ^^^^,, ^^,^„^^ 



• t, t «» Q 1 , I . • /Hl 1 



q 

 — p 





i—Y% 



,. .,.;,, • f^ H^—VlC i d^C^"'— p;k",> r -^ :,.:.. ,,' :,f 

 bimili modo piodeunt quotientes — j ; — , -j;^ j — , pennutando tan- 



,Xy^ -f a*'-^^P^ 5— P?<i -;, . ■, -..0 



tiim in expressione inventa ^, X-cam ^', 3i'r ^'> ^'« J'»"^ evidens .est, condi- 

 lionem praedictam adimpjleri, sive tres quotientes aequales fieri, &» ponatur 



2) q"" + X = o 



3) q— P = -pq''1 



inm enim tres isti quotientes abeiint in q '. 



Ilinc prodit X = — q' 



r = q ' + pq" 



ünde invenilnr ex aequatione ( i ) 



' - Z =*=pX +. q = q — pq • 



1} Si ijiianfitas u a pturiBus aTiU penJcn» , s<>cun(Iuin itnam «unm t, g, y <liffer«nl«liir, crterü coor 

 ^rantinm »Dstjr habilM, tum — - breviUtJ« caiissa, , designo perÄ?', «•;,<' 



