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These perspectives relations, that will be used in determining projections representation systems, defined from two projective operators:. Project from a vertex V.. Sections a straight s a bundle of concurrent lines to, b, c … Vertex V.. If we take these four elements of geometric shapes series and make straight lines we can determine quadruples of elements that have a specific value of your property, as we have defined the study quadruples of items ordered.

This value, as discussed, is the same in the case of quaternions in dotted lines and if a projection or sectional are of the other. The cross ratio of four lines of a single beam, is the number of points obtained as a straight section that does not contain any vertex of the beam. The cross ratio of four points of the same series, It is obtained as the straight projection from any point that does not contain the base of the series.

We say that the line and the beam are perspectival section or if you are projecting another. We therefore first definition of perspectivity between forms of the same class, but of a different nature Vs straight points. Can we establish a concept perspective similar between two beams or two series? We can give different definitions of perspectivity between two coplanar beams straight. Two beams of different vertices straight, V..

As in every theorem we can establish in projective geometry, can get one dual changing the element that determines. So, in the case of a series of points spectivity find a definition similar to that given for the straight beams:. We see therefore that there is a duality between the properties and theorems that link the point and straight from the plane by, may be obtained from each other by changing the words point and plane statements, and projection operations by section.

In summary of the above, we can present a simple diagram that will simplify the above. We will see later the importance of relationships to understand perspectives projective. These perspectives relations, that will be used in determining projections representation systems, defined from two projective operators: Projection Section Project from a vertex V..

Similarly we have the dual theorem: The cross ratio of four points of the same series, It is obtained as the straight projection from any point that does not contain the base of the series. Beam straight perspectivity. Each beam line vertex V and its beam homologous vertex V ' cut on that axis.

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## Geometría proyectiva: Perspectivity

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