Desargues's theorem

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.

Word History and Origins

Origin of Desargues's theorem¹

Named after G. Desargues

Example Sentences

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.

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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.

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

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Also LL', MM', and NN' meet in a point, and therefore in the same point S. Thus KK', LL', and MM' meet in a point, and so, by Desargues's theorem itself, A, B, and D are on a straight line.

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

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