Veblen, Oswald, 1880-1960, Young, John Wesley, 1879-1932 · Boston, New York [etc.] Ginn and Company · leaf 303
. The points of intersection of these lineswith (1) are common to all the conies (3). The lines (4) are distinct, unless a1 = a3 or a2 — ar But if a1 = as,any point (xl, 0, x3) on the line x2 = 0 has the polar x^x1 + x^x3 = 0both with regard to (1) and with regard to (2). The self-polar figureis… … Fig. 100 The actual construction of the points is now a problem of the seconddegree. We have thus established (fig. 100) Theorem 12. If two conies have a common self-polar triangle (andno other common self-polar pair of point and line), they intersect infour distinct points (proper or improper).…
Geometry, Projective
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