-§*$ ) 65 ( £?f~ 



V. d i x-\-*d\v-\-$d z y-\-yddx-\-$ddyzzzo 

 VI. d*y+a.'d z x-\-p'd'y-\-y'ddx-\-$'ddyzzz o. 

 Iam vcro totium negotium eo redit, vt ex acquatione V, fub- 

 fidio aequationum praecedcntium I. II. III. IV. eliminari que- 

 ant, omnia differentialia ipfius y, fcilicet d 3 y, ddy, dy et y, 

 quod omnino fuccedcre dcbere ex rei natura intelligitur; hac 

 autem eliminatione facla, prodibit aequatio differcntialis quarti 

 gradus, quam fola differentialia ipfius x ingrediuntur. Ope- 

 rofum autem foret, fi hanc fubftitutionem re ipfa perficere vel- 

 lemus, quare rem ita tentabimus, vt fupponamus, aequatio- 

 nem noftram quaefitam prodire, per fequentem combinatio- 

 nem: V-t-MV. -f- [x III -+- yJL -+- glzzz o. Hinc autem 

 confequemur: 



d*x+xd'x +pd\y-\-y ddx -\-5ddy 



-\-\d z y-\\a'ddx-\--K^ddy -\-\y'dx-\-\$'dy 

 -\p.d'x -\-\y.addx\-\K^ddy-\-[Kydx-\-\K$dy 



-\-%ddx -\-yddy -\-v*'dx -\-vfi'dy-\-vy'x-\-v$'y 



-\-^ctdx -\-^dy-\-^yx-\-^$yzzO. 

 In qua aequatione quum per hypothefin fola differentialia 

 ipfius x reperiri debeant , coefficieutes ipforum tfy, ddy, dy 

 et y nihilo aequari debent , ex quo fequentes prodibunt ae- 

 quationes : 



p-+-X=o , £+ X(3M-jji£-f v— o ; *.$'+ \K$-\vp'-\-$zz:o ; v$'+z$zzO. 

 Hinc autem deducuntur fequentes valores : 

 X = -(3; ,a = (3'; vz=-$, <> = $>, 

 quare acquatio noftra erit : 



d t x-\-(a.+\K)d'x-\-(y-\-\ a'+ \Ka+ ?+)ddx-\(\y i+^y+vaJ+^a.) dx 



-\-(v'y-\-^y)xzzL o, fiue 



d i x+(x+^Y x M^'- a '^y+ s 'W x M aS '-- oL, ^^y-^y) dx 



-+-($'y-$y')xzz,o , 

 ficque iam adcpti fumus acquationem differentialem , quam 



fola 



