776] 
ON THE JACOBIAN SEXTIC EQUATION. 
401 
The conclusion is that, starting from the Jacobian sextic 
(a, b, 0, d, 0, f g\z, l) 6 = 0, 
where ag + 9bf— 20d 2 = 0, and effecting upon it the Tschirnhausen-transformation 
X = — az 3 — ftbz* — 10c?, 
so as to obtain from it a sextic equation in X, this sextic equation in X is the resolvent 
sextic of the quintic equation 
(1, 0, c, 0, e, f#;r, 1) 5 = 0, 
where 
c = 2c?, e = - 9bf+ 36d 2 , f = a/(21 6h), 
and, A being the discriminant of the Jacobian sextic, then 
h = grug V (— A), = a?f s + b 3 g 2 + 60b 2 df* — 240bd s f+ 256c? 5 . 
As to the subject of the present paper, see in particular Brioschi, “lieber die 
Auflösung der Gleichungen vom fünften Grade,” Math. Annalen, t. xm. (1878), pp. 109— 
160, and the third Appendix to his translation of my Elliptic Functions, Milan, 1880, 
each containing references to the earlier papers. 
C. XI. 
51