Sentence Examples

  • The Hessian in that case is a factor of f, and Q is the third power of u2,...
  • In Germany, Ips and Passau on the Danube, and Gross Almerode in Hesse, are the best known localities producing fireclay goods, the crucibles from the last-mentioned place, known as Hessian crucibles, going all over the world.
  • The church also contains the tombs of numerous Hessian landgraves and knights of the Teutonic Order.
  • Secondly, as to the inflections, the process is a similar one; it can be shown that the inflections are the intersections of the curve by a derivative curve called (after Ludwig Otto Hesse who first considered it) the Hessian, defined geometrically as the locus of a point such that its conic polar (§ 8 below) in regard to the curve breaks up into a pair of lines, and which has an equation H = o, where H is the determinant formed with the second differential coefficients of u in regard to the variables (x, y, z); H= o is thus a curve of the order 3 (m - 2), and the number of inflections is =3m(m-2).
  • 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.

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