Caption: Mathematical Models by Arnold Emch - Series 4 (1928)
This is a reduced-resolution page image for fast online browsing.
EXTRACTED TEXT FROM PAGE:
IV Series 25 39. Relation Between Cubic and its Hessian and Cayleyan. Choosing the cubic in the normal form F = %is + x23 + Xss + 6m X X f z = 0, \tC the Hessian is H = Xi3 + x23 + x33 + 6 j X X X = 0, fLi2s in which 6 x = — (1 + 2w3)/m2. f From this is seen that for a given Hessian there are three cubics F for which the given H is the Hessian. As is well known the Hessian Fig. 16 is the locus of points P whose conical polars degenerate into pairs o lines. The locus of the vertices P' of these pairs coincides with H . The joins of P and P' envelope the Cayleyan, Fig. 16. C = m (uiz + u2s + Uzz) + (1 — 4m3) UiU2u3 = 0 of class 3. It bears the same relation to the sides of the coordinate triangle as H does with respect to the vertices. H touches the flextangents of F and the harmonic polars of the flexes of F are the cus-
| 
