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- Projective_harmonic_conjugate abstract "In projective geometry, the harmonic conjugate point of an ordered triple of points on the real projective line is defined by the following construction:Given three collinear points A, B, C, let L be a point not lying on their join and let any line through C meet LA, LB at M, N respectively. If AN and BM meet at K, and LK meets AB at D, then D is called the harmonic conjugate of C with respect to A, B.What is remarkable is that the point D does not depend on what point L is taken initially, nor upon what line through C is used to find M and N. This fact follows from Desargues theorem; it can also be defined in terms of the cross-ratio as (A, B; C, D) = −1.".
- Projective_harmonic_conjugate thumbnail Pappusharmonic.svg?width=300.
- Projective_harmonic_conjugate wikiPageExternalLink books?id=r3ILAAAAYAAJ.
- Projective_harmonic_conjugate wikiPageExternalLink text-idx?c=math;cc=math;view=toc;subview=short;idno=Lach015.
- Projective_harmonic_conjugate wikiPageExternalLink projective-geometry.
- Projective_harmonic_conjugate wikiPageID "16094600".
- Projective_harmonic_conjugate wikiPageLength "8412".
- Projective_harmonic_conjugate wikiPageOutDegree "24".
- Projective_harmonic_conjugate wikiPageRevisionID "639270256".
- Projective_harmonic_conjugate wikiPageWikiLink Additive_inverse.
- Projective_harmonic_conjugate wikiPageWikiLink Bertrand_Russell.
- Projective_harmonic_conjugate wikiPageWikiLink Category:Projective_geometry.
- Projective_harmonic_conjugate wikiPageWikiLink Complete_quadrangle.
- Projective_harmonic_conjugate wikiPageWikiLink Cornell_University.
- Projective_harmonic_conjugate wikiPageWikiLink Cross-ratio.
- Projective_harmonic_conjugate wikiPageWikiLink Cross_ratio.
- Projective_harmonic_conjugate wikiPageWikiLink Desargues_theorem.
- Projective_harmonic_conjugate wikiPageWikiLink H._S._M._Coxeter.
- Projective_harmonic_conjugate wikiPageWikiLink Harmonic_division.
- Projective_harmonic_conjugate wikiPageWikiLink Harold_Scott_MacDonald_Coxeter.
- Projective_harmonic_conjugate wikiPageWikiLink Inversive_geometry.
- Projective_harmonic_conjugate wikiPageWikiLink Karl_Georg_Christian_von_Staudt.
- Projective_harmonic_conjugate wikiPageWikiLink Karl_von_Staudt.
- Projective_harmonic_conjugate wikiPageWikiLink Midpoint.
- Projective_harmonic_conjugate wikiPageWikiLink Point_at_infinity.
- Projective_harmonic_conjugate wikiPageWikiLink Pole_and_polar.
- Projective_harmonic_conjugate wikiPageWikiLink Principles_of_Mathematics.
- Projective_harmonic_conjugate wikiPageWikiLink Projective_geometry.
- Projective_harmonic_conjugate wikiPageWikiLink Projective_range.
- Projective_harmonic_conjugate wikiPageWikiLink Real_number.
- Projective_harmonic_conjugate wikiPageWikiLink Real_numbers.
- Projective_harmonic_conjugate wikiPageWikiLink Real_projective_line.
- Projective_harmonic_conjugate wikiPageWikiLink The_Principles_of_Mathematics.
- Projective_harmonic_conjugate wikiPageWikiLink File:Fano_parallelogramm.svg.
- Projective_harmonic_conjugate wikiPageWikiLink File:Pappusharmonic.svg.
- Projective_harmonic_conjugate wikiPageWikiLink File:Real_projective_line.svg.
- Projective_harmonic_conjugate wikiPageWikiLinkText "Projective conics".
- Projective_harmonic_conjugate wikiPageWikiLinkText "Projective harmonic conjugate".
- Projective_harmonic_conjugate wikiPageWikiLinkText "fourth harmonic point".
- Projective_harmonic_conjugate wikiPageWikiLinkText "harmonic conjugates".
- Projective_harmonic_conjugate wikiPageWikiLinkText "harmonic ranges".
- Projective_harmonic_conjugate wikiPageWikiLinkText "projective harmonic conjugate".
- Projective_harmonic_conjugate hasPhotoCollection Projective_harmonic_conjugate.
- Projective_harmonic_conjugate wikiPageUsesTemplate Template:Cite_book.
- Projective_harmonic_conjugate wikiPageUsesTemplate Template:Main.
- Projective_harmonic_conjugate wikiPageUsesTemplate Template:Reflist.
- Projective_harmonic_conjugate subject Category:Projective_geometry.
- Projective_harmonic_conjugate comment "In projective geometry, the harmonic conjugate point of an ordered triple of points on the real projective line is defined by the following construction:Given three collinear points A, B, C, let L be a point not lying on their join and let any line through C meet LA, LB at M, N respectively.".
- Projective_harmonic_conjugate label "Projective harmonic conjugate".
- Projective_harmonic_conjugate sameAs Harmonische_Teilung.
- Projective_harmonic_conjugate sameAs Division_harmonique.
- Projective_harmonic_conjugate sameAs Harmonische_ligging.
- Projective_harmonic_conjugate sameAs Harmonisk_deling.
- Projective_harmonic_conjugate sameAs Conjugado_harmônico_projetivo.
- Projective_harmonic_conjugate sameAs m.03qp0nk.
- Projective_harmonic_conjugate sameAs Diviziune_armonică.
- Projective_harmonic_conjugate sameAs Гармоническая_четвёрка.
- Projective_harmonic_conjugate sameAs Q1101140.
- Projective_harmonic_conjugate sameAs Q1101140.
- Projective_harmonic_conjugate wasDerivedFrom Projective_harmonic_conjugate?oldid=639270256.
- Projective_harmonic_conjugate depiction Pappusharmonic.svg.
- Projective_harmonic_conjugate isPrimaryTopicOf Projective_harmonic_conjugate.