Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math

Topic: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
Replies: 62   Last Post: Feb 22, 2014 12:11 AM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
ken quirici

Posts: 332
Registered: 1/29/05
Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
Posted: Feb 17, 2014 4:09 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Monday, February 17, 2014 9:42:41 AM UTC-5, David Hartley wrote:
> In message <a5d96867-54e8-4d1b-b960-1ea47819d7c4@googlegroups.com>, Ken
>
> Quirici <kquirici@yahoo.com> writes
>

> >It would be an interesting exercise (at least it seems to me) to
>
> >imagine this Euclidean axiomatic system INDEPENDENT of ANY pictures.
>
> >How many 'realities' would this system model? I suspect there are many
>
> >that have absolutely nothing to do with geometry. That is, take the
>
> >axioms as simply words that relate to each other in logical ways and
>
> >see what they can represent.
>
>
>
> I was going to suggest this to you, but you've got there on your own.
>
> Imagine trying to explain Euclid's proofs to a blind man. If it can't be
>
> done solely from the axioms and postulates, with no diagrams, then it's
>
> not a valid proof.
>
>
>
> It is indeed true that the explicit axioms and postulates in the
>
> Elements are not sufficient for even the simplest of his proofs.
>
>
>
> Most trivially, there's nothing to ensure that there even exist any
>
> points or lines.
>
>
>
> More importantly, as was raised at the start of this thread, without an
>
> axiom that ensures that certain circles intersect, most of the
>
> constructions fail.
>
>
>
> Consider a system consisting of a single straight line and the points
>
> thereon. It satisfies all Euclid's explicit postulates (and Pasch's
>
> axiom) but circles have only two points in their circumferences and
>
> circles with a common radius do not intersect. There are no equilateral
>
> triangles.
>
>


there's problem in that his definitions include (at least in Heath's translation) surface - that which has length and breadth only.

Does this vitiate your statement?

>
> So even if you take Euclid's postulates and add the existence of point
>
> and line, Pasch's axiom and any necessary order axioms, you still don't
>
> have enough to prove Proposition 1.
>
>
>
> Add an axiom that ensures there is a point not on a given line and it
>
> may be possible, I don't know.
>
>
>
> --
>
> David Hartley


Thanks. I'm hoping Moise's book on Elementary Geometry from an Advanced Standpoint will provide a sufficiently rigorous approach. Have you read it? If so, is it sufficiently rigorous?

Regards,

Ken


Date Subject Author
2/14/14
Read Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
ken quirici
2/14/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
ross.finlayson@gmail.com
2/15/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
thenewcalculus@gmail.com
2/15/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
bert
2/15/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
thenewcalculus@gmail.com
2/16/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
ross.finlayson@gmail.com
2/16/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
thenewcalculus@gmail.com
2/15/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
thenewcalculus@gmail.com
2/15/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
Brian Q. Hutchings
2/15/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
ken quirici
2/15/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
FredJeffries@gmail.com
2/15/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
ken quirici
2/15/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
thenewcalculus@gmail.com
2/16/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
ken quirici
2/16/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
ken quirici
2/16/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
thenewcalculus@gmail.com
2/17/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
ken quirici
2/17/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
thenewcalculus@gmail.com
2/17/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
ken quirici
2/17/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
thenewcalculus@gmail.com
2/17/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
ken quirici
2/17/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
thenewcalculus@gmail.com
2/17/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
ken quirici
2/17/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
thenewcalculus@gmail.com
2/17/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
YBM
2/18/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
thenewcalculus@gmail.com
2/17/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
David Hartley
2/17/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
thenewcalculus@gmail.com
2/17/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
ken quirici
2/17/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
David Hartley
2/17/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
ken quirici
2/19/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
David Hartley
2/20/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
thenewcalculus@gmail.com
2/17/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
ross.finlayson@gmail.com
2/18/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
thenewcalculus@gmail.com
2/17/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
ken quirici
2/17/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
thenewcalculus@gmail.com
2/17/14
Read book fourteen is the best (Hypsicles, to start with [ph* the
encyclopedic "curriculum
Brian Q. Hutchings
2/17/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
thenewcalculus@gmail.com
2/17/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
Ken.Pledger@vuw.ac.nz
2/17/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
thenewcalculus@gmail.com
2/18/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
David Bernier
2/18/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
thenewcalculus@gmail.com
2/18/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
Ken.Pledger@vuw.ac.nz
2/18/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
thenewcalculus@gmail.com
2/18/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
thenewcalculus@gmail.com
2/18/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
ken quirici
2/18/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
thenewcalculus@gmail.com
2/18/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
Wizard-Of-Oz
2/18/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
thenewcalculus@gmail.com
2/18/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
Wizard-Of-Oz
2/19/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
thenewcalculus@gmail.com
2/19/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
Wizard-Of-Oz
2/19/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
Brian Q. Hutchings
2/18/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
thenewcalculus@gmail.com
2/18/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
thenewcalculus@gmail.com
2/18/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
ken quirici
2/18/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
thenewcalculus@gmail.com
2/18/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
Brian Q. Hutchings
2/18/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
thenewcalculus@gmail.com
2/18/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
Brian Q. Hutchings
2/20/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
Brian Q. Hutchings
2/22/14
Read A discussion about my discussion with Ken Quirici.
thenewcalculus@gmail.com

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.