Desargues's theorem

American  

noun

Geometry.

1. the theorem that if two triangles are so related that the lines joining corresponding vertices meet in a point, then the extended corresponding lines of the two triangles meet in three points, all on the same line.

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Etymology

Origin of Desargues's theorem

Named after G. Desargues

Example Sentences

All the proofs proceed by the method of producing a specification of “points” and “straight lines” which satisfies axioms 1-5, and such that Desargues’s theorem does not hold.

From Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" by Various

But it requires Desargues’s theorem, and hence axiom 6, to prove that Harm.

From Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" by Various

Desargues's theorem and the theory of harmonic elements which depends on it have nothing to do with magnitudes at all.

From An Elementary Course in Synthetic Projective Geometry by Lehmer, Derrick Norman

It has been proved28 that Desargues’s theorem cannot be deduced from axioms 1-5, that is, if the geometry be confined to two dimensions.

From Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" by Various