## quartics

Noun

- plural form of
*quartic*

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- 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.

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