## A Relation Between First Polars and First Osculants of Rational Cubics |

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binary forms canonical form Cayleyan common rays conic osculant conio corresponding lines corresponding points covariant cubic x3 cubio cusp parameter cusp tangents Differentiating with respect eliminating envelope is shown expressed as rational forms of order given curve Hessian homogeneous form involutions joining the points joining two corresponding Journ line joining line of flexes line osculant Math nodal cubic node obtained by taking osculant cubics osculants of rational ourve pair of corresponding parametric equations parametric form Plane Cubic Curves point cubic point locus point of contact point of inflexion point of intersection point of tangency points of inter polar conic polars of f Polars of points poloconic Projective Geometry Quartic Curves r-th rational cubic rational curve rational line cubic rational point respective values stationary tangents straight lines intersecting Substituting systems of curves ternary co-ordinates thesis touch the stationary tricuspidal quartic University of Wisconsin Winger