What Is Euclid's Sixth Postulate and Why Is It Important in Geometry?

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Euclid's sixth postulate, which states that "two lines do not contain a space," is not widely recognized in traditional Euclidean geometry and appears to be a modern addition. This postulate is sometimes referred to in discussions about the rigidity of triangles, offering an alternative to superposition in geometric proofs. The conversation highlights confusion over its origins, with references to a specific French source and a Wikipedia entry discussing modern interpretations of Euclidean principles. Participants express a lack of familiarity with this postulate, indicating it may not be part of standard geometric education. Understanding its context and implications could enhance comprehension of Euclidean geometry's evolution.
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Hey,

Has anybody heard of Euclid's sixth postulate ? It says : Two lines do not contain a space.

I don't know why, but I'm only finding this postulate in my things, not anywhere else... Help ? Thanks
 
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I'm not an expert on Euclidean geometry, but I've never heard of it.

Where exactly did you encounter this?
 
It is purely a modern invention
http://en.wikipedia.org/wiki/Euclidean_geometry
'Some modern treatments add a sixth postulate, the rigidity of the triangle, which can be used as an alternative to superposition.'

p 5. Coxeter, H.S.M. (1961). Introduction to Geometry. New York: Wiley.
 
Can someone give me insight on it ? Thank you.
 

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