Two invariants, two quartics and a sextic. They are connected by the relation 212 = 2 i f?0 - D3 -3 jf 3.
The system of the quadratic and cubic, consisting of 15 forms, and that of two cubics, consisting of 26 forms, were obtained by Salmon and Clebsch; that of the cubic and quartic we owe to Sigmund Gundelfinger (Programm Stuttgart, 186 9, 1 -43); that of the quadratic and quintic to Winter (Programm Darmstadt, 1880); that of the quadratic and sextic to von Gall (Programm Lemgo, 3873); that of two quartics to Gordan (Math.
The analogous question of the classification of quartics (in particular non-singular quartics and nodal quartics) is considered in Zeuthen's memoir " Sur les differentes formes des courbes planes du quatrieme ordre " (Math.
The forms of the non-singular quartics are very numerous, but it is not necessary to go further into the question.
He determines in every case the characteristics (µ, v) of the corresponding systems of cubics (4p), (3 p, il), &c. The same problems, or most of them, and also the elementary problems in regard to quartics are solved by Zeuthen, who in the elaborate memoir " Almindelige Egenskaber, &c.," Danish Academy, t.