Veblen, Oswald, 1880-1960, Young, John Wesley, 1879-1932 · Boston, New York [etc.] Ginn and Company · leaf 58
= 4of Ex. 5 (cf. fig. 15, regarded as a plane figure). §17] PERSPECTIVE TETRAHEDRA 17. Perspective tetrahedra. As an application of the corollary ofthe last theorem we may now derive a theorem in space analogous tothe theorem of Desargues in the plane. Theorem 2. If two tetrahedra are perspective… … Fig. 16 Proof. Let the two tetrahedra be PJ^P^ and PjP^P^P^, and letthe lines PJ^, P%P^, PSPZ, P±Pl meet in the center of perspectivity 0.Two homologous edges P-Pj and P^Pf then clearly intersect; call thepoint of intersection Piy The points P12, i^3, P2S lie on the same line,since the triangles…
Geometry, Projective
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