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

[chemistry1]

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

 

[micromass]

I'm not an expert on Euclidean geometry, but I've never heard of it.

Where exactly did you encounter this?

 

[chemistry1]

Well, from this source :http://euclides.fr/bibliotheque/euclide/elements/livre_1.pdf

I suppose you speak French, if you're Belgian ? (I think..)

 

[jim mcnamara]

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.

 

[chemistry1]

Can someone give me insight on it ? Thank you.