2003Journal of Jilin Institute of Chemical TechnologyRequires access

On the converse proposition of Desargues with projective geometry

Song Zhan

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Abstract

At first,with the theory of projective geometry,by means of projecting straight line onto infinite distance and introducing the projection of two intersecting lines onto two parallel lines as well as arbitrary quadrangle onto parallelogram,the converse proposition of Desargues within the plane area is proved.Then an auxiliary threepoint shape is made up by using the method of projective geometry.Finally the result of testifying the converse proposition of Desargues within the space is obtained.

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At first,with the theory of projective geometry,by means of projecting straight line onto infinite distance and introducing the projection of two intersecting lines onto two parallel lines as well as arbitrary quadrangle onto parallelogram,the converse proposition of Desargues within the plane area is proved.Then an auxiliary threepoint shape is made up by using the method of projective geometry.Finally the result of testifying the converse proposition of Desargues within the space is obtained.

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Available abstract

At first,with the theory of projective geometry,by means of projecting straight line onto infinite distance and introducing the projection of two intersecting lines onto two parallel lines as well as arbitrary quadrangle onto parallelogram,the converse proposition of Desargues within the plane area is proved.Then an auxiliary threepoint shape is made up by using the method of projective geometry.Finally the result of testifying the converse proposition of Desargues within the space is obtained.

Key concepts: Projective geometry, Converse, Projective space, Mathematics, Projective plane, Duality (order theory), Geometry, Parallelogram

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