346 RECHERCHES SUR i/ÉLIMINATION, ET SUR LA THÉORIE DES COURBES. [53 
f = - MNa + NLh + LMg - X 2 /, 
g = + MNh - NLb + LMf — M 2 g, 
h = 4- MNg + NLf — LMc — N 2 h. 
Nous écrirons de plus, pour abréger, 
bc — / 2 = , gh — af = Jp, V = abc — af 2 — bg 2 — ch 2 + Zfgh, 
ca— g 2 = 33, hf—bg= (S, 
ab — h 2 = (B, fg — ch = p|, 
bc — f 2 = (jH), &c. 
&c. 
et enfin 
ct> = ^X 2 + 33 M 2 + № + 2 Jpi¥iV 4- mNL + 2f§i¥iY 
On obtient identiquement 
Xa + M h + Ng = 0 , 
Xh +Jfb + M = 0, 
Xg + M f + Ne = 0 ; 
(gt) = X 2 <4> , (33) = M 2 $, (©) = N 2 ® , 
(JP) = №ï>, (®) = i™>, (|) = i№; 
/f-ilfXTJF=(^-X/)(X/ -%), 
<7g - YX© - (X/ - iX/) (Mg - Nh), 
Ah-Xil/^ = (ii i r-m) (Nh -X/); 
4X 2 i¥YJp + b (X 2 b + M 2 a) + c (N 2 a + X 2 c) — bc — 2X 2 aa = (X 2 & — M 2 u) (N 2 a + X 2 c), 
4i¥ 2 iVX€i + c (7¥ 2 c + N 2 b) + a (X 2 6 + i¥ 2 a) - ca - 2i¥ 2 6b = (M 2 c - N 2 6) (X 2 6 - M 2 a), 
4<N 2 LMffî + a (N 2 a + X 2 c) + b (i¥ 2 c 4- Y 2 6) - ab - 2i\^ 2 cc = (N 2 a - X 2 c) (M 2 c -N 2 b)-, 
4L 2 MN^i — a 2 4- 2a (i¥ 2 c + Y 2 6 ) = — (M 2 c — N 2 b) 2 , 
4i¥ 2 iVX33 — b 2 + 2b (Y 2 a 4- X 2 c) = — (N 2 a — X 2 c) 2 , 
4X r2 Xi¥GD - c 2 + 2c (X 2 5 + i¥ 2 a) = - ( X 2 6 - 4i 2 a) 2 ; 
X 2 Jiim 4- Ng (4- X/+ % - Nh) 4- i¥h (X/- % + Nh) - gh = - MN(Nh - Mg) 2 , 
M 2 Nm 4- Xh (- X/+ Mg + Nh) + Ni (X/+ Mg - iYA) - hf = - NL (Lf - Nh) 2 , 
N 2 LM(B + Mi (+ Lf- Mg + Nh) + Xg (X/+ Mg + Nh) - fg - - LM (Mg - Lf) 2 ; 
2VX 2 = — a 2 a 4- (ab — 2h 2 ) b 4- (ca — 2^ 2 ) c + 2 (af — 2gh) f — 2ag g — 2ah h , 
2 Vif 2 = + (a6 — 2A 2 ) a — 6 2 b 4- (6c — 2/ 2 ) c — 26/f + 2 (bg — 2 hf) g — 2bh h , 
2ViV 2 = + (ca — 2g 2 ) a + (6c — 2/ 2 ) b — c 2 c — 2c/f — 2c<7g 4- 2 (ch — 2fg) b ;