Higher geometry; an introduction to advanced methods in analytic geometry (1922)
Woods, Frederick S. (Frederick Shenstone), 1864- · Boston, New York, Ginn and Company · leaf 236
I. If two conjugate polar lines in-tersect, each is tangent to the surfaceat their point of intersection. Let two conjugate polar lines, PQand LK, intersect at B. Since B lies in each of the lines PQ and LK its polar plane must containeach of these lines by the definition of conjugate polar lines.… … 224 THKEE-DIMENSIONAL GEOMETRY EXERCISES 1. Show that any chord drawn through a fixed point P, intersectingat infinity the polar plane of P with respect to a quadric, is bisected by P-Hence show that if a quadric is not tangent to the plane at infinity thereis a point such that all chords through…
Geometry, Analytic
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