But if the given curve has a node, then not only the Hessian passes through the node, but it has there a node the two branches at which touch respectively the two branches of the curve; and the node thus counts as six intersections; so if the curve has a cusp, then the Hessian not only passes through the cusp, but it has there a cusp through which it again passes, that is, there is a cuspidal branch touching the cuspidal branch of the curve, and besides a simple branch passing through the cusp, and hence the cusp counts as eight intersections.
by the Prussian Rhine province and the Hessian province of Rhein-Hessen; on the E.
This can be verified by equating to zero the five coefficients of the Hessian (ab) 2 axb2.
The quartic will have two pairs of equal roots, that is, will be a perfect square, if it and its Hessian merely differ by a numerical factor.
In 1864 he went as Hessian envoy to Vienna, retiring in 1872 when the post was abolished.