## cubics

Noun

- plural form of
*cubic*

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- For the cubic (ab) 2 axbx is a covariant because each symbol a, b occurs three times; we can first of all find its real expression as a simultaneous covariant of two
**cubics**, and then, by supposing the two**cubics**to merge into identity, find the expression of the quadratic covariant, of the single cubic, commonly known as the Hessian. - 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. - This author questioned the possibility of solving
**cubics**by pure algebra, and biquadratics by geometry. - Similarly as regards
**cubics**, or curves of any other order: a cubic depends on 9 constants, and the elementary problems are to find the number of the**cubics**(9 p), (8p, 1l), &c., which pass through 9 points, pass through 8 points and touch 1 line, &c.; but it is in the investigation convenient to seek for the characteristics of the systems of**cubics**(8p), &c., which satisfy 8 instead of 9 conditions. - The elementary problems in regard to
**cubics**are solved very completely by S.

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