Veblen, Oswald, 1880-1960, Young, John Wesley, 1879-1932 · Boston, New York [etc.] Ginn and Company · leaf 148
§47] PENCILS AND KANGES 133 That there is only one conic B2 through P satisfying the con-ditions of the theorem is to be seen as follows: Let QP meet p0 in S,and QP meet p0 in S (fig. 66). The points S and S must have thesame polar with regard to A2 and any conic B2, since this polarmust be the… … Fig. 67 T and T have the same polar, namely P0P, with regard to A2 andany conic B2. By the conditions of the theorem the projectivity PoST-^P0ST must be parabolic. Hence, by Theorem 23, Cor., Chap. IV, Q(P0ST,P0TS). Hence p and p must meet on P0Q in a point i? so as to form the quad-rangle BQPP.…
Geometry, Projective
Internet Archive · Wellesley College Library · Public Domain Mark 1.0. Free to use for anything.
