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Topic: A flaw in modern axiomatic geometry?
Replies: 4   Last Post: May 1, 2013 4:23 PM

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LudovicoVan

Posts: 3,201
From: London
Registered: 2/8/08
Re: A flaw in modern axiomatic geometry?
Posted: May 1, 2013 4:23 PM
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"Butch Malahide" <fred.galvin@gmail.com> wrote in message
news:cea27a9c-4ebb-43ac-99a0-003daee679e4@r3g2000yqe.googlegroups.com...
> On Apr 30, 7:14 pm, "Julio Di Egidio" <ju...@diegidio.name> wrote:
>>
>> As I gather it, what he says is that from Playfair's axiom and his
>> lite-triangle axiom one can prove Pasch's axiom. But the two former
>> axioms
>> are common to Euclidean and non-Euclidean geometry, while Pasch's axiom
>> is
>> Euclidean only: hence the contradiction.

>
> Playfair's axiom? Isn't that the one that says that only one parallel
> to a given line can be drawn through a given point not on the line?
> That axiom is common to Euclidean and non-Euclidean geometry?


I had misread. Thank you and David Hartley for the feedback, after more
reading I see he had nailed it since the beginning.

Julio





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