[ 2 9 6 ] 
v + I -f K x 4- L 4. M a; 3 4- N x 4 4- O * 5 4- P * 6 
r. — 3 _ n—\ - 
X v 4- &c. = o. & confequenter crit nyv +n — 1 
A 4- hx-\- Cx'yv + n~ 2 x Dx Ex 4- Ex 1 4- Gx J 4- Hx + 
B4-2CX v + E4-2 t x + 3 G x 1, -^Hx 3 
n — 3 
X y v + &c. 
X V + 6cc. 
Ex quibus aequationibus, 11 tnethodis notis extermi- 
netur (v), habebimus aequationem, quae exprimit re- 
lationem inter (x) Sc (jy). Hujus autem aequationis 
ccefficientes aequari debent coefficientibus datae aequa- 
tionisjy -\-a-\-b x y + c d x + e x z ~\-y -f See. 
— o j & fi quantitates A, B, C, & c. exinde determi- 
nari poftunt, curva quadratur, eft enim v -|- A -[-Bat 
n — 1 
-\-Cx z xv + D + Ex -f- + Gx 3 +H/ 
X v ” + See. = o j aliter autem quadrari non poteft. 
Ex. Sit data aequatio y 1 x* — 1 = o, Sc fuppona- 
mus aequationem ad aream v z D 4 " E x ~\~ F x 7 + 
G a ; 3 -\- H x*z= o ; Sc erit 2 vy -j- E -\- 2 F x 4 ■ 3 G 
x z -)- 4 H x s = o, ita reducantur hae duae aequationes 
in unam, ut exterminatur (y), Sc refultat aequatio y z - 
16 H 1 A 6 + 24 HG X s + 16 HF 4- q G~ .y 4 + b h H + 12 F G 
4 x H^ + -4Gx i +Jt , x 2 4-t^ + D 
^6 gTTTTfV + 4FEx ± e; = o . debet autem 
fradlio 
i6H^ 6 + 24HG^+i6HF + Q G^ 4 + 8EH-f 12FG 
4 x H* + + G* 3 + F x' + 
*M- 6 G E -f 4 F* x* + 4 F E * + E* 
E x 4- U 
fequenter 
5 
efte x * — 1 5 6c con- 
4 h 
