Veblen, Oswald, 1880-1960, Young, John Wesley, 1879-1932 · Boston, New York [etc.] Ginn and Company · leaf 149
P0L and P0Lr Hence Q(MNL, M&LJ* Definition. The set of all coniesthrough a point Q and tangent toa line p0 at a point P0, and suchthat no point of p except P0 hasthe same polar with regard to twoconies of the set, is called a pencilof conies of Type III (fig. 68). Definition. The set of all… … Fig. 68 Fig.69 Two conies of such a pencil (range) are said to have contact of thesecond order, or to oscidate, at PQ. Corollary 2 of Theorem 25 now gives at once: Theorem 26. Any line in theplane of a pencil of conies ofType III, which is not on either ofthe common points of the pencil, ismet by…
Geometry, Projective
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