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Desargues's theorem states that the truth of the first condition is necessary and sufficient for the truth of the second. In projective geometry, Desargues's 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 ...
Perspective (geometry) Two perspective triangles, with their perspective axis and center. Two figures in a plane are perspective from a point O, called the center of perspectivity, if the lines joining corresponding points of the figures all meet at O. Dually, the figures are said to be perspective from a line if the points of intersection of ...
Two perspective triangles, and their center and axis of perspectivity. In geometry, the Desargues configuration is a configuration of ten points and ten lines, with three points per line and three lines per point. It is named after Girard Desargues. The Desargues configuration can be constructed in two dimensions from the points and lines ...
The triangle ABC and the cevian triangle A'B'C' are in perspective and let DEF be the axis of perspectivity of the two triangles. The line DEF is the trilinear polar of the point Y. The line DEF is the central line associated with the triangle center X.
A plane is said to have the "minor affine Desargues property" when two triangles in parallel perspective, having two parallel sides, must also have the third sides parallel. If this property holds in the affine plane defined by a ternary ring, then there is an equivalence relation between "vectors" defined by pairs of points from the plane. [ 14 ]
Perspective (graphical) Linear or point-projection perspective (from Latin perspicere 'to see through') is one of two types of graphical projection perspective in the graphic arts; the other is parallel projection. [citation needed][dubious – discuss] Linear perspective is an approximate representation, generally on a flat surface, of an ...
The Penrose triangle, also known as the Penrose tribar, the impossible tribar, [ 1 ] or the impossible triangle, [ 2 ] is a triangular impossible object, an optical illusion consisting of an object which can be depicted in a perspective drawing. It cannot exist as a solid object in ordinary three-dimensional Euclidean space, although its ...
The triangle A'B'C' is the cevian triangle of Y. The ABC and the cevian triangle A'B'C' are in perspective and let DEF be the axis of perspectivity of the two triangles. The line DEF is the trilinear polar of the point Y. DEF is the central line associated with the triangle center X.