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Caption: Mathematical Models by Arnold Emch - Series 3 (1925)
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these double points, let 0 be the center of projection and Q\ and Q% the two quadrics. T h e polar planes of 0 with respect to Q\ and Q2 intersect in a line d whose projection d' contains the two double points of C'4, as is easily proved by projective methods. 26. Quartic in space with one effective double-point. A s the pencil of quadrics through a quartic, determined by two quadrics Q\ and Q% has, in general, four quadrics with double points, i.e., cones or cylinders, which m a y be real or imaginary, w e do not restrict the generality of the result projectively, by assuming Qx and <92 as cylinders. In this model the cylinders touch in a point so that the quartic Ca has an effective double point. A s there are moreover two apparent double points, the C4 is rational. T h e construction of the apparent double points is indicated by yellow silk strings, Fig. 1. Fig. 2 [6]
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