In projective geometry, Desargues's theorem, named after Girard Desargues, states: Two triangles are in perspective axially if and only if they are in...

projective geometry. Desargues' theorem, the Desargues graph, and the crater Desargues on the Moon are named in his honour. Born in Lyon, Desargues came from a...

previous example, to obtain the projective Moulton plane. Desargues's theorem is not a valid theorem in either the Moulton plane or the projective Moulton...

Girard Desargues. The Desargues configuration can be constructed in two dimensions from the points and lines occurring in Desargues's theorem, in three...

mathematician Gerhard Hessenberg proved that Pappus's theorem implies Desargues's theorem. In general, Pappus's theorem holds for some projective plane if and only...

over a (commutative) field. Equivalently Pappus's hexagon theorem and Desargues's theorem are supposed to be true. A large part of the results remain...

Desarguesian planes (those that are isomorphic with a PG(2, q)) satisfy Desargues's theorem and are projective planes over finite fields, but there are many...

over a (commutative) field. Equivalently Pappus's hexagon theorem and Desargues's theorem are supposed to be true. A large part of the results remain...

three dimensions. Monge's theorem can also be proved by using Desargues' theorem. Another easy proof uses Menelaus' theorem, since the ratios can be calculated...

satisfy Desargues' theorem (named after Girard Desargues), or in other words a plane that is not a Desarguesian plane. The theorem of Desargues is true...

many interesting figures on parabolas and hyperbolas. Desargues's theorem Brianchon's theorem Unicursal hexagram Pascal 1640, translation Smith 1959...

De Bruijn–Erdős theorem (incidence geometry) De Gua's theorem (geometry) Desargues's theorem (projective geometry) Descartes's theorem (plane geometry)...

treatment of the geometries here possible seem to me desirable. Desargues's theorem: If two triangles lie on a plane such that the lines connecting corresponding...

like a "5"). Anamorphosis Curvilinear perspective Cutaway drawing Desargues's theorem Filmmaking Optical illusion Perspective control Perspective (graphical)...

section Crystal Cuisenaire rods Desargues' theorem Right circular cone Hyperboloid Napkin ring problem Pappus's centroid theorem Paraboloid Polyhedron Defect...

Brianchon's theorem Ceva's theorem Desargues's theorem Menelaus's theorem Pascal's theorem Poncelet's closure theorem Ptolemy's theorem Apollonian circles...

ABC\doublebarwedge abc} to indicate that triangles ABC and abc are perspective. Desargues' theorem states that a central couple of triangles is axial. The converse statement...

According to Kahn's Theorem, it is fulfilled by "ovoidal" Möbius planes only; thus, it is the analog for Möbius planes of Desargues' Theorem for projective...

theorem is not necessarily true in all projective geometries; it is a property that some geometries satisfy but others don't. For example, Desargues'...

geometric system. Desargues's study on conic sections drew the attention of 16-year-old Blaise Pascal and helped him formulate Pascal's theorem. The works of...

projective plane in which the little Desargues theorem holds. This theorem states that a restricted form of Desargues' theorem holds for every line in the plane...

The Desargues graph has one vertex for each point, one vertex for each line, and one edge for every incident point-line pair. Desargues' theorem, named...

have fixed points, so that the dual of A is A itself. For example, Desargues' theorem is self-dual in this sense under the standard duality in projective...

these are: Desargues' theorem ⇔ Converse of Desargues' theorem Pascal's theorem ⇔ Brianchon's theorem Menelaus' theorem ⇔ Ceva's theorem Not only statements...

spaces; such embeddability is a consequence of a property known as Desargues' theorem, not shared by all projective planes. In addition to its familiar...

triangulation de Longchamps point Desargues' theorem Droz-Farny line theorem Encyclopedia of Triangle Centers Equal incircles theorem Equal parallelians point...

significant for projective planes due to the universal validity of Desargues' theorem in higher dimensions. In contrast, the analytic approach is to define...

Hilbert, 1980 (1899). The Foundations of Geometry, 2nd edition, §22 Desargues Theorem, Chicago: Open Court Pambuccian, Victor; Schacht, Celia (2021), "The...

geometry, where he is known for proving that Desargues' theorem is a consequence of Pappus's hexagon theorem, and differential geometry where he is known...

skew field k. Axioms 4a and 4b are equivalent to Desargues' theorem. When Pappus's hexagon theorem holds in the affine geometry, k is commutative and...