Veblen, Oswald, 1880-1960, Young, John Wesley, 1879-1932 · Boston, New York [etc.] Ginn and Company · leaf 129
Fig. 53 In like manner, if ij, P2, Pz, P±, and px are given, to construct thepoint P5 on any line I through P± of a point conic containing Pv P2, Ps, Piand of which p1 is the tangent at Pv we need only determine the pointsA = p^P^), B = I(i^), and C = (AB) (P2P3); then PXC meets I in P5(fig. 53). … Fig. 54 In case I is the tangent p± at PA, P5 coincides with Pi and the fol-lowing points are collinear (fig. 54): 4=MS®* B=Pi(Pxp2), c=(^)(^). § 42] TANGENTS 115 Hence we have the following theorem: Theorem 7. If the vertices Pv P2, P3, P4 of a simple quadrangle arepoints of a point conic, the…
Geometry, Projective
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