Veblen, Oswald, 1880-1960, Young, John Wesley, 1879-1932 · Boston, New York [etc.] Ginn and Company · leaf 76
ties. We proceed now to the proof of a chainof theorems, which lead to the fundamental result that any projectivetransformation between two distinct one-dimensional primitive formsof the same kind can be obtained as the resultant of two perspectivities. Theorem 3. If [P], [Pr], [P~\ are pencils of… … Proof Let 0 be the common point of the lines I, I, I. If Px, P2, Ps are three points of [P], and %%% and P^PjPj the corresponding points of [P], [P!] (fig. 24), it is clear that the triangles P^P^, .PjP/P/, PjPiPs are perspective from 0.* By Desargues theorem (Theorem 1, Chap. II) homologous sides…
Geometry, Projective
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