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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 ...
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 ...
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 ...
Emile Lemoine (1840–1912) In mathematics, modern triangle geometry, or new triangle geometry, is the body of knowledge relating to the properties of a triangle discovered and developed roughly since the beginning of the last quarter of the nineteenth century. Triangles and their properties were the subject of investigation since at least the ...
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 ...
A vanishing point is a point on the image plane of a perspective rendering where the two-dimensional perspective projections of mutually parallel lines in three-dimensional space appear to converge. When the set of parallel lines is perpendicular to a picture plane, the construction is known as one-point perspective, and their vanishing point ...
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 ]
For broader coverage of this topic, see Duality (mathematics). In projective geometry, duality or plane duality is a formalization of the striking symmetry of the roles played by points and lines in the definitions and theorems of projective planes. There are two approaches to the subject of duality, one through language (§ Principle of ...
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