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- 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.".
- Desargues'_theorem thumbnail Desargues_theorem_alt.svg?width=300.
- Desargues'_theorem wikiPageExternalLink JavaGSPLinks.htm.
- Desargues'_theorem wikiPageExternalLink desargues.html.
- Desargues'_theorem wikiPageExternalLink DesarguesTheorem.html.
- Desargues'_theorem wikiPageExternalLink ?op=getobj&from=objects&id=4514.
- Desargues'_theorem wikiPageExternalLink Desargues.shtml.
- Desargues'_theorem wikiPageExternalLink MongeTheorem.shtml.
- Desargues'_theorem wikiPageID "358488".
- Desargues'_theorem wikiPageRevisionID "592829589".
- Desargues'_theorem first "M.I.".
- Desargues'_theorem hasPhotoCollection Desargues'_theorem.
- Desargues'_theorem id "d/d031320".
- Desargues'_theorem last "Voitsekhovskii".
- Desargues'_theorem title "Desargues assumption".
- Desargues'_theorem subject Category:Proof_without_words.
- Desargues'_theorem subject Category:Theorems_in_projective_geometry.
- Desargues'_theorem type Abstraction100002137.
- Desargues'_theorem type Communication100033020.
- Desargues'_theorem type Message106598915.
- Desargues'_theorem type Proposition106750804.
- Desargues'_theorem type Statement106722453.
- Desargues'_theorem type Theorem106752293.
- Desargues'_theorem type TheoremsInProjectiveGeometry.
- 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 "Satz von Desargues".
- Desargues'_theorem label "Stelling van Desargues".
- Desargues'_theorem label "Teorema de Desargues".
- Desargues'_theorem label "Teorema de Desargues".
- Desargues'_theorem label "Teorema di Desargues".
- Desargues'_theorem label "Théorème de Desargues".
- Desargues'_theorem label "Twierdzenie Desarguesa".
- Desargues'_theorem label "Теорема Дезарга".
- Desargues'_theorem label "مبرهنة ديسارغو".
- Desargues'_theorem label "デザルグの定理".
- Desargues'_theorem label "笛沙格定理".
- Desargues'_theorem sameAs Satz_von_Desargues.
- Desargues'_theorem sameAs Teorema_de_Desargues.
- Desargues'_theorem sameAs Théorème_de_Desargues.
- Desargues'_theorem sameAs Teorema_di_Desargues.
- Desargues'_theorem sameAs デザルグの定理.
- Desargues'_theorem sameAs 데자르그의_정리.
- Desargues'_theorem sameAs Stelling_van_Desargues.
- Desargues'_theorem sameAs Twierdzenie_Desarguesa.
- Desargues'_theorem sameAs Teorema_de_Desargues.
- Desargues'_theorem sameAs m.01_4_6.
- Desargues'_theorem sameAs Q841893.
- Desargues'_theorem sameAs Q841893.
- Desargues'_theorem sameAs Desargues'_theorem.
- Desargues'_theorem wasDerivedFrom Desargues'_theorem?oldid=592829589.
- Desargues'_theorem depiction Desargues_theorem_alt.svg.
- Desargues'_theorem isPrimaryTopicOf Desargues'_theorem.