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.independent

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 ]
David Bernier

Posts: 3,288
Registered: 12/13/04
Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
Posted: Feb 18, 2014 12:10 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On 02/17/2014 03:23 PM, Ken Pledger wrote:
> It's hard to know what to quote from this discussion, so I shall
> chicken out of doing so.
>
> Historically, there was a profound change in understanding of the
> foundations of mathematics around 1900, especially with Hilbert and the
> rise of modern logic. We now set up theories which are purely sets of
> formulae and rules for manipulating them. Then we relate those to
> models, and consider various metalogical matters (consistency,
> completeness, etc.). But we can't understand how earlier
> mathematicians thought if we try to force their work into this modern
> framework.
>
> The Greeks regarded geometrical objects as idealized physical
> objects. A line drawn with a pencil can be imagined getting thinner
> and thinner until it is an ideal line of zero thickness (Euclid I Def.
> 2). Geometrical objects can even be imagined as moved around and
> fitted on top of one another (Euclid I.4 proof), in which case they are
> equal (Euclid I Common Notion 4). It's easy to see why Plato liked
> geometry, because it gave such good examples of his theory of ideals.
>
> But thinking that way carries the danger of relying too much on
> physical intuition when looking at actual diagrams. That seems to have
> been the trap which Euclid fell into in I.1, when he assumed that the
> two circles would intersect. A clear view of such things was achieved
> by Pasch in the 19th century. I think Euclid I.16 is an even more
> significant example. Near the end of the proof he claims that one
> angle is greater than another (Common Notion 5: "The whole is greater
> than the part"). This is just an intuition based on the diagram, and
> in elliptic geometry it is actually false.
>
> However, remember that logically structured mathematics began in the
> 5th century B.C. (probably with Hippocrates), and was pursued by quite a
> small number of people in each generation. Just over a century later,
> those few dozen people had reached the level of Euclid's "Elements".
> Then in the 3rd century B.C. came the formidable achievements of
> Archimedes, not to mention Apollonius. Rather than emphasize the
> faults which we can see by modern hindsight, I prefer to admire the
> enormous achievement of the Greeks who reached such a high level in such
> a short time.
>
> Ken Pledger.
>


It's a blessing to have contributors such as you in sci.math .

With respect to Archimedes of Syracuse,
since he discovered the law of floating, partially submerged
and completely submerged uniform-density "bodies" that
goes by the name of Archimedes's Principle,
I've been wondering why he doesn't seem to be called
mathematical physicist or just plain theoretical physicist.

Or I guess I'm intrigued by why they say Galileo started physics, (the
science);
and Archimedes, well , I'm not exactly sure but obviously he's
famous with mathematicians (if he was a scientist, doesn't
that make him a physicist?).


David Bernier

--
http://www.bibliotecapleyades.net/sociopolitica/last_circle/1.htm


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.