Veblen, Oswald, 1880-1960, Young, John Wesley, 1879-1932 · Boston, New York [etc.] Ginn and Company · leaf 150
en conic of the pencil (range)is of Type III. Theorem 27. If a line p0 is tangent to a conic A2 at a point P0,there is one and only one conic tangent to p0 at P0 and passingthrough any other point P of the plane of A2 not on p0 or A2which determines for every point of p0 the same polar line as does… … P, and is such that if a is any tangent to A2 at a point Q, then q istransformed to a tangent q of B2 passing through qp0, and Q is trans-formed into the point of contact Q of q, collinear with Q and P0.Hence there is one conic of the required type through P. That there is only one is evident,…
Geometry, Projective
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