Quintic in A Sentence

    1

    Certain convariants of the quintic involve the same determinant factors as appeared in the system of the quartic; these are f, H, i, T and j, and are of special importance.

    2

    Hermite expresses the quintic in a forme-type in which the constants are invariants and the variables linear covariants.

    3

    His first notable work was a proof of the impossibility of solving the quintic equation by radicals.

    4

    Sylvester showed that the quintic might, in general, be expressed as the sum of three fifth powers, viz.