341] 
ON THE SEXTACTIC POINTS OF A PLANE CURVE. 
245 
49. We thence have 
1 
Jac. (U, H, VE) = 
3m-7 
(2l,£,@$x, g, *),($, 8,8$x, 9, »),(©, 8, g, *) 
(21', @XA, 5,0), (£', 33', ST&l, 5, a), (©', g', 5, O 
or multiplying the two sides by 
H, = 
the right-hand side is 
3m — 7 
EX 
X 
a, h, g 
K b, f 
9f, g 
Eg , 
Y , 
Hv 
Z 
(:m—l)A, (m —1)5, (m — 1) G, 
which is 
= E 
m — 1 
3?/z — 7 
A. , /4 , v 
X y F, Z 
4, 5, 0, 
if for a moment 
X — (21', ..$4, 5, C$a, h, g), 
F= $4, 5, (7$/q b,f), 
Z %A t 5, C%,/, c). 
50. Hence observing that these equations may be written 
X = (2T,. .-&A, B, C$d x A, d x B, d x C), 
Y = (21', ..$-4, 5, O$0^, d y B, d y C), 
Z ={W,..\A, B, G\d z A, d z B, d z G), 
and that we have 
0 = 
g, v 
d x , dy, d z 
A, B, G, 
we obtain for H Jac. (U, H, V, H) the value 
= H 
m — 1 
3m — 7 
(21', ...£4, B, G\dA, 05, 0(7), 
or throwing out the factor E, we have the required result.