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- Monge's_theorem abstract "In geometry, Monge's theorem, named after Gaspard Monge, states that for any three circles in a plane, none of which is inside one of the others, the intersection points of each of the three pairs of external tangent lines are collinear.For any two circles in a plane, an external tangent is a line that is tangent to both circles but does not pass between them. There are two such external tangent lines for any two circles. Each such pair has a unique intersection point in the projective plane. Monge's theorem states that the three such points given by each circle always in a straight line. In the case of two of the circles being of equal size, the two external tangent lines are parallel. In this case Monge's theorem asserts that the other two intersection points must lie on a line parallel to those two external tangents. In other words if the two external tangents are considered to intersect at the point at infinity, then the other two intersection points must be on a line passing through the same point at infinity, so the line between them takes the same angle as the external tangent.".
- Monge's_theorem thumbnail Monge_theorem.svg?width=300.
- Monge's_theorem wikiPageExternalLink MongesCircleTheorem.html.
- Monge's_theorem wikiPageExternalLink 0486205452.html.
- Monge's_theorem wikiPageExternalLink MongeTheorem.shtml.
- Monge's_theorem wikiPageExternalLink threecircles.shtml.
- Monge's_theorem wikiPageID "14573037".
- Monge's_theorem wikiPageRevisionID "574304590".
- Monge's_theorem hasPhotoCollection Monge's_theorem.
- Monge's_theorem subject Category:Articles_containing_proofs.
- Monge's_theorem subject Category:Circles.
- Monge's_theorem subject Category:Euclidean_plane_geometry.
- Monge's_theorem subject Category:Theorems_in_geometry.
- Monge's_theorem type Abstraction100002137.
- Monge's_theorem type Attribute100024264.
- Monge's_theorem type Circle113873502.
- Monge's_theorem type Circles.
- Monge's_theorem type Communication100033020.
- Monge's_theorem type ConicSection113872975.
- Monge's_theorem type Ellipse113878306.
- Monge's_theorem type Figure113862780.
- Monge's_theorem type Message106598915.
- Monge's_theorem type PlaneFigure113863186.
- Monge's_theorem type Proposition106750804.
- Monge's_theorem type Shape100027807.
- Monge's_theorem type Statement106722453.
- Monge's_theorem type Theorem106752293.
- Monge's_theorem type TheoremsInGeometry.
- Monge's_theorem comment "In geometry, Monge's theorem, named after Gaspard Monge, states that for any three circles in a plane, none of which is inside one of the others, the intersection points of each of the three pairs of external tangent lines are collinear.For any two circles in a plane, an external tangent is a line that is tangent to both circles but does not pass between them. There are two such external tangent lines for any two circles. Each such pair has a unique intersection point in the projective plane.".
- Monge's_theorem label "Monge's theorem".
- Monge's_theorem label "Teorema de Monge".
- Monge's_theorem label "Twierdzenie Mongego".
- Monge's_theorem label "Теорема Монжа".
- Monge's_theorem sameAs Twierdzenie_Mongego.
- Monge's_theorem sameAs Teorema_de_Monge.
- Monge's_theorem sameAs m.03d89yl.
- Monge's_theorem sameAs Q2981012.
- Monge's_theorem sameAs Q2981012.
- Monge's_theorem sameAs Monge's_theorem.
- Monge's_theorem wasDerivedFrom Monge's_theorem?oldid=574304590.
- Monge's_theorem depiction Monge_theorem.svg.
- Monge's_theorem isPrimaryTopicOf Monge's_theorem.
