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On the Two Systems of Generating Regions on a Quadric in Space of even Order


     

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A quadric in space of three dimensions contains infinitely many straight liner, which fall into two distinct systems such that two lines intersect only when they belong to different systems. That an analogous property holds for the generating planes of a quadric in space of five dimensions was proved from line-geometric considerations by Cayley in 1873, and also independently by the writer.
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  • On the Two Systems of Generating Regions on a Quadric in Space of even Order

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Abstract


A quadric in space of three dimensions contains infinitely many straight liner, which fall into two distinct systems such that two lines intersect only when they belong to different systems. That an analogous property holds for the generating planes of a quadric in space of five dimensions was proved from line-geometric considerations by Cayley in 1873, and also independently by the writer.