QVADAIVl DIFFERENTIALI. 109 



Sumtis enim tribus fuadtipnibns ipffas w, quac fint 

 Pj) 0.1 R ftatuatur aequatio integralis : 



O -^ ^f {j H- Qf (J -H ^y = Conft. 



■vnde liaec nafeitur aec]-uario differentialis : 



qaae a fradionibus libsrata hanc induit formam : 

 (X + |X + >«.) jj^j.4-j;^j(X(Q+ft)+f;L(P+R)+v(P+Q_ )) 



+>1('MQ+ R) ^P + f^(P + RyQ+ >/ (P + Q)^ R) 

 + X QR^ P-f- jiL P RiQ+ v^ Wqd R =: o 



cx qua forma^^ propofita refultat ftatuendo : 



r". X -f- [A. -f- V<±I O: 



2". XQ^R + i^PR + j/PQzro 



3°. X^P+^JL^Qj-yiR^o feu XP+iJLQ+i^RriCGnll. 



Vin. Si Mc ponumus X F4- [Jt Q+ ^'R =: <^ 

 €t PH-Q-i-R = ►% \t' finguias litteras ?, Q, R 

 hinc definire valeamus, ratione habita primae eon- 

 ditionis, qua efle oportec X -+- [ji -}:- K z::: 0^ reperie- 

 mus hos valores :. 



p 3X|*vS-4-(XX-»>?|Av)'a-^.CM. — v)V<(X\— |Xv)q(r— iX|UL vcS) 



~^ 9 Xft V 



O — 3XnvS-t»(M,)x-f,2X v)a -(-.(v— y V((mx.- — X:v)aa— 'sXix vaS) 

 ■D 3X|yivS-t.(vv-H.»X)u.)a[-f;.{X'— jJL)V(vv — -Xju,) cra-^tXlxva S 



Xfi V 



jXn» 



Tbi ligna radicalia ob XX— [j(.yirj^jJL-KM— Xjjl iii~ 

 tec fe cojdueuiunt. 



<D 3 IX 



