94 



PMf 



!df. 



Quo nunc ex hac aequatione tarn dz quam z exeant, ponendum est 

 i)U = pX+qY + r; 



d^(p% + qy — «j) d'(p%' + qy— t;') d'^Cppi'+qy" — ^') 



deinde esse debet 



p% + qy — »^ p%+qy'— " px' + qy"— »^ 



d'(p%"'+qy"'— O dMp;^" + qy-— v'O 



P/C"' + py" — f'" px^ + qy" — i-" 



Evolvere igitur oportet d' (p>j + qy,— t^y ha ut in differentiatiöne sola "z 

 ceu variabilis tractetur, a, b, c, e, f pro constantibus habitis. Est autem 

 d'^CpX + qy— ^) = pd''^+ qd^y— d'v+ Ji d'' p + y d'- q 

 Pars prior p d' x + q 'l'' y — <1^ " est 



= p d"X + qd» Y — d>ü = d» (pX + qY — U) — Xd'p — Vd^q 

 ^^,— Bl*v — Xd'p — Yd*q, vi aeguationis (i). At vefo _est 4*p 5= V, 

 ^.q^ <,, d»r = r'd»x + r'd'y + r'-d«u + r^d»p + r" d .q" 

 _.j.^_}.r'» + r"v + r"p + r"q; d'p = P, d^q=Q. Hinc fit 



d^px+qi-^) 



— r 



X— r' 



+ Q 



— X 



r'^.v + r'|% + r" 

 ^X±Vi-Zl _ — p| _Q 



Permutando ^^j, n, v, cum äS'»!' i*'» %". l". f"; %'", V", «^"'; %", »i", v", 

 reliqui quatuor quotientes prodeiint. Qui omnes erunt inter se et primo 

 aequales, quippe a v,x,ri indepeadentes , si ponatur 

 2)r^4.X=o 

 5)r"+Y=o 

 4) r' -P=--pr'^ 

 5),^'— Q=:~qr^ 

 Hinc prodit i) X = — r' j 

 2) Y=s — r" 



