[Denote by I the inflexions and by R the intersections of the 4-ic with
the nodal tangents. Then from the Hessian 1 + R = 0, and from the
nodal tangents R = 0, so that 1=0. See Ch. XVIII, S 1, Ex. 6;
§ 9, Ex. 6.j

§10.
In § 9 we made use of the theorem that, if the curve
/ (x, y) = passes through the intersections of <j> (x, y) =
and \jf(x,y) = 0, then we can put/ in the form Afy + B-f,
where A and B are polynomials in x and y.
We are here using Cartesian coordinates, and taking/, <$>, ty
as the -C X C K , G m , G n of § 9.
We shall suppose that the intersections of $ = 0, v/r =
are ordinary distinct points of /= 0, <p — 0, \jr = 0, and give
a proof of the result with this limitation. We may suppose
the axes of reference taken perfectly generally.
