A vector treatment of the projective properties of plane curves
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1. Notations. Suppose that we have given a plan curve C, and a point O, not lying in the plane of the curve. If we draw vectors from point O, one to every point of the given curve, we produce a conical surface, the elements of which are vectors. If we then cut this surface by any plan, net passing thru the point O, the intersection will be a new plane curve bearing certain fixed relations to the original cuve C. In other words the two plane cuvers are projectively related. In this discussion we will denote arc length of the curve C by [omega], the curvature by 1/p([omega]), and a vector from point O to curve C by [lambda](omega] abreviated to [lambda].
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