Veblen, Oswald, 1880-1960, Young, John Wesley, 1879-1932 · Boston, New York [etc.] Ginn and Company · leaf 119
Ssuch that if av b1 and a2, b2 areany two pairs of homologous linesof the two pencils, the points axb2and a2b1 are collinear with S.(A, E, P) Definition. The point S iscalled the center of homology ofthe pencils of lines. Proof. The two theorems being plane duals of each other, we mayconfine… … Fig. 47 the two pencils are perspective. Hence pairs of corresponding linesmeet on a line I; e.g. the lines AXBS and BXA3 meet on / as well asA1B2 and BXA2. To prove our theorem it remains only to show thatB2A3 and A2B3 also meet on I. But the latter follows at once fromTheorem 21, since the figure…
Geometry, Projective
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