V. On plane cubics

In this paper the first few sections are devoted to certain constructions for the cubic, its Hessian, and its Cayleyan. Assuming three collinear inflexions for the cubic, and the tangents at these points,i. e ., eight conditions, one more point determines the cubic, and, consequently, also the Hessian and Cayleyan. Taking this point on one of the known harmonic polars, the remaining two points in which the harmonic polar meets the cubic are found by a quadratic construction, and triangular symmetry completes the determination of the cubic; the inflexional tangents to the Hessian and the cusps on the Cayleyan are found by linear constructions; and the pairs of points in which these curves are met by the harmonic polar, by quadratic constructions.