Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Desargues_theorem> ?p ?o }
- Desargues_theorem abstract "In projective geometry, Desargues' theorem, named after Girard Desargues, states:Two triangles are in perspective axially if and only if they are in perspective centrally.Denote the three vertices of one triangle by a, b and c, and those of the other by A, B and C. Axial perspectivity means that lines ab and AB meet in a point, lines ac and AC meet in a second point, and lines bc and BC meet in a third point, and that these three points all lie on a common line called the axis of perspectivity. Central perspectivity means that the three lines Aa, Bb and Cc are concurrent, at a point called the center of perspectivity.This intersection theorem is true in the usual Euclidean plane but special care needs to be taken in exceptional cases, as when a pair of sides are parallel, so that their "point of intersection" recedes to infinity. Mathematically the most satisfying way of resolving the issue of exceptional cases is to "complete" the Euclidean plane to a projective plane by "adding" points at infinity following Poncelet.Desargues's theorem is true for the real projective plane, for any projective space defined arithmetically from a field or division ring, for any projective space of dimension unequal to two, and for any projective space in which Pappus's theorem holds. However, there are some non-Desarguesian planes in which Desargues' theorem is false.".
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- Desargues_theorem wikiPageWikiLink Collinear.
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- Desargues_theorem wikiPageWikiLink Commutative.
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- Desargues_theorem wikiPageWikiLink Duality_(projective_geometry).
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- Desargues_theorem wikiPageWikiLink Field_(mathematics).
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- Desargues_theorem wikiPageWikiLink If_and_only_if.
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- Desargues_theorem wikiPageWikiLink Jean-Victor_Poncelet.
- Desargues_theorem wikiPageWikiLink John_Wiley_&_Sons.
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- Desargues_theorem wikiPageWikiLink Monges_theorem.
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- Desargues_theorem wikiPageWikiLink Pappuss_hexagon_theorem.
- Desargues_theorem wikiPageWikiLink Pascals_theorem.
- Desargues_theorem wikiPageWikiLink Perspective_(geometry).
- Desargues_theorem wikiPageWikiLink Perspectivity.
- Desargues_theorem wikiPageWikiLink PlanetMath.
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- Desargues_theorem wikiPageWikiLink Symmetry.
- Desargues_theorem wikiPageWikiLink Theorem.
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- Desargues_theorem wikiPageWikiLink Two-dimensional_space.
- Desargues_theorem wikiPageWikiLink Wedderburns_little_theorem.
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- Desargues_theorem wikiPageWikiLinkText "Converse of Desargues' theorem".
- Desargues_theorem wikiPageWikiLinkText "Desargues theorem".
- Desargues_theorem wikiPageWikiLinkText "Desargues".
- Desargues_theorem wikiPageWikiLinkText "Desargues' theorem".
- Desargues_theorem wikiPageWikiLinkText "corresponding axis of perspective".
- Desargues_theorem wikiPageWikiLinkText "desarguesian".
- Desargues_theorem wikiPageWikiLinkText "theorem of Desargues".
- Desargues_theorem wikiPageWikiLinkText "theorem".
- Desargues_theorem first "M.I.".
- Desargues_theorem hasPhotoCollection Desargues_theorem.
- Desargues_theorem id "d/d031320".
- Desargues_theorem last "Voitsekhovskii".
- Desargues_theorem title "Desargues assumption".
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- Desargues_theorem subject Category:Euclidean_plane_geometry.
- Desargues_theorem subject Category:Proof_without_words.
- Desargues_theorem subject Category:Theorems_in_geometry.
- Desargues_theorem subject Category:Theorems_in_plane_geometry.
- Desargues_theorem subject Category:Theorems_in_projective_geometry.
- Desargues_theorem type Redirect.
- Desargues_theorem comment "In projective geometry, Desargues' theorem, named after Girard Desargues, states:Two triangles are in perspective axially if and only if they are in perspective centrally.Denote the three vertices of one triangle by a, b and c, and those of the other by A, B and C.".
- Desargues_theorem label "Desargues theorem".
- Desargues_theorem label "Desargues' theorem".
- Desargues_theorem sameAs مبرهنة_ديسارغو.
- Desargues_theorem sameAs Satz_von_Desargues.
- Desargues_theorem sameAs Teorema_de_Desargues.
- Desargues_theorem sameAs Desarguesin_lause.