Talk:Euclid's Elements
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Okay, so who thinks this should redirect to Euclid? Can we have a show of hands, please? Actually, I think it might be nice to concentrate on Euclid's life in his article, even though we don't know much about it. I think this story (http://www.dsdk12.net/project/euclid/euclid.html) may be a lie ;) but this page (http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Euclid.html) manages to talk about it for a few paragraphs before getting to the mathematical details, so it could work. Then we could put the actual maths in this article. What do you think? -- Oliver P. 00:21 15 Jun 2003 (UTC)
I've expanded the material on this page quite a bit. Looking at the material in the entry on "Euclid," most of it seems to be duplicated here. Unless we can find some more significant biographical information (are other sources than MacTutor (http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Euclid.html) available?), I agree that the articles should be merged. JPB 06:16 6 Jul 2003 (UTC)
Well, this article could go through the books one by one, and summarise what is proven in each one. That would quite nice for this article, but would be a bit overwhelming if put into in the article on Euclid himself, which concentrates more on the overall significance of his work. -- Oliver P. 06:22 6 Jul 2003 (UTC)
- The usual practice in classics is to not to separate the author from work, unless there are lots of works, or we have an actual author bio, Cicero for instance. My OCD gives his life two lines, but has a bunch of content for his many lost works. Elements gets most of a paragraph, though this being the OCD, is mostly a discussion of the different manuscripts. I think in this case the Elements are worth a separate article, at least if somebody (me, I suppose :-) ) gets to work and adds the non-Elements info about Euclid. Separate articles for each book of Elements seems a little overboard though. Stan 13:09 6 Jul 2003 (UTC)
Euclid and Greek philosophers made a distinct between axiom and postulate. In fact, the Elements includes 5 of each. Should the five axioms be included here? An axiom is an assumption about everything. A postulate is an assumption about a particular science/area of study or an assumption that is not 'obvious'. gbeehler 11:28 6 Nov 03 (UTC)
- ??? They are included here at the top of the article, aren't they? MrJones 11:43, 6 Nov 2003 (UTC)
- No. The 5 postulates are stated and then called postulates and axioms??? For the record, the axioms given are: (A1) Things which are equal to the same thing are equal to each other. (A2) If equals be added to equals, the wholes are equal. (A3) If equals be subtracted from equals, the remainders are equal. (A4) Things which coincide with one another are equal to one another. (A5) The whole is greater than the part. I think it is important to state these because (1) the complete set was used as a foundation to the argument that the 5th postulate MUST be derivable from the other 9 (2) Saccheri tried to do just that and instead discovered non-Euclidian geometries -- which are logically consistent (3) this lead to the development of axiomatics. gbeehler 17:08, 6 Nov 2003 (UTC)
I removed this sentence because it's false:
- As Gödel proved, all axiomatic systems -- excepting the very simplest -- are either incomplete or contradict themselves, and this is no exception.
In fact, Hilbert's axioms for Euclidean geometry are complete. This was proven by Tarski. I'll add info about this to the page when I get a chance. -- Walt Pohl 14:39, 20 Mar 2004 (UTC)
I think the correct statement is something like, "As Godel proved, all axiomatic systems, sufficiently strong enough to express the arithmetic (addition, multiplication) of the natural numbers are either incomplete or contradict themselves." Certainly, it's very easy to come up with trivial axiomatic systems with only a couple axioms that are easy to verify as complete and consistent.
- Godel's is more subtle than that: It is possible in Any consistent, axiomatic system to formulate questions that cannot be answered.
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gobbledygook
This is gobbledygook: That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.
- That depends on what you mean by "gobbledygook". It's not nonsense, but it could be made clearer. —Rory ☺ 13:08, Sep 5, 2004 (UTC)
- Could we make it clearer? I've puzzled over it several times, and never quite figured it out. Brutannica 02:10, 8 Sep 2004 (UTC)
- It says that if you take two line segments (A, B) and draw another line segment (C) so that it crosses A nd B, and if that makes two acute angles (θ, φ) on the same side of C, then A and B, extended further, will meet on that side of C.
___ |C
A ___ |
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|θ /__
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|/ ...
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|φ \__
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B ___ |
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- Oh. Thanks! Could I modify the postulate then? At least let me change "less than two right angles" with "acute angles." Brutannica 03:03, 9 Sep 2004 (UTC)
- Hang on a sec. Are those postulates the original, translated ones? If so, then it wouldn't be right to alter them... instead, I should put the explanation after it in parentheses. Brutannica 00:08, 10 Sep 2004 (UTC)
- If they are translations they should say who translated them and they should be quoted. As long as we're just stating the postulates, rather than quoting, I think it's fair to put them in as plain language as we can. —Rory ☺ 12:18, Sep 10, 2004 (UTC)
- O.K.... Brutannica 04:15, 11 Sep 2004 (UTC)
Book XIII not authentic?
I don't think the following sentence is correct, although I have left it in the article:
- It is strongly suspected that book XIII was added to the others at a later date.
Was the author of that statement perhaps thinking of the so-called "Book XIV"? - dcljr 09:37, 14 Aug 2004 (UTC)
The information in Book XIII was certainly known to Euclid -- it had been demonstrated decades earlier by Theaetetus of Athens (http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Theaetetus.html). (The current Wiki page on Theaetetus is just a stubbish entry on Plato's dialogue with him.) --Crunchy Frog 18:15, 18 Aug 2004 (UTC)
Why this page should not be redirected or merged
There is more to Euclid than just the Elements. He wrote 4 other works we still have today and is credited with 4 more works which have been lost. All of this can be discussed in the Euclid article. The Elements, OTOH, is an almost neverending source of topics for dicsussion. For possible ideas, see this paper I wrote in college (http://www.obkb.com/dcljr/euclid.html) on the subject. See also my comment on Talk:Euclid. - dcljr 10:01, 14 Aug 2004 (UTC)
Carriage of The Elements to Wikipedia?
Although there are many other online sources for the Elements, do people feel that there would be anything to gain from a setup of the propositions on Wikipedia? I intend to work through the Elements someday, using Heath's Dover edition. I would scan the diagrams and present the narrative of the propositions in a contemporary vernacular; this all presupposes that we've internalized the two-millenium debate over The Elements and can link to appropriate articles. Refitting the narratives of Euclid's results in modern prose is also extremely presumptious, and likely unnecessary, but that's why I ask you people first. -Cory