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单词 Chasles's Theorem
释义

Chasles's Theorem

If two projective Pencils of curves of orders and have no common curve, the Locus of theintersections of corresponding curves of the two is a curve of order through all the centers of eitherPencil. Conversely, if a curve of order contains all centers of a Pencil of order to themultiplicity demanded by Noether's Fundamental Theorem, then it is the Locus of the intersections of correspondingcurves of this Pencil and one of order projective therewith.

See also Noether's Fundamental Theorem, Pencil


References

Coolidge, J. L. A Treatise on Algebraic Plane Curves. New York: Dover, p. 33, 1959.


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