Veblen, Oswald, 1880-1960, Young, John Wesley, 1879-1932 · Boston, New York [etc.] Ginn and Company · leaf 313
chthe four planes of the pencil on l2 meet lr But £4 meets three of thepairs of homologous planes in points of their lines of intersection,since, by hypothesis, it meets three of the lines mv m2, ms, mt. Hencein the projectivity on li there are three invariant points, and hence(Assumption P) every… … §103] THE REGULUS 299 Definition. If lv l2, l3 are three lines no two of which are in thesame plane, the set of all lines which meet each of the three given linesis called a regulus. The lines lv Z2, l3 are called directrices of this regulus. It is clear that no two lines of a regulus can…
Geometry, Projective
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