Talk:Euclid's Elements

message: 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)
thread_title:  Book XIII not authentic? 

message: 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 on the subject. See also my comment on Talk:Euclid. - dcljr 10:01, 14 Aug 2004 (UTC)
thread_title:  Why this page should not be redirected or merged 

message: 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
::Perhaps Wikibooks or Wikisource would be a better place to put this. - dcljr (talk) 23:10, 23 Jun 2005 (UTC)
replies: text: Late to the party -- but this has been done on ProofWiki. --Matt Westwood 21:21, 22 August 2020 (UTC)
thread_title:  Carriage of The Elements to Wikipedia? 

message: Do you think this sentence is right?
:That other geometries could be logically consistent was one of the most important discoveries in mathematics, with vast implications for science and philosophy.
:: Gauss knew it was so profound and important that curved geometry mathematics was consistent, that he kept it secret knowing what Archimedes' adversaries did to him during the Punic Wars. Yes, I'm conjecturing. Jakewayd (talk) 03:09, 12 October 2018 (UTC)
replies: text: I think it's fine as it is. The next sentence explains why: Einstein's space-time. I'm not sure about a direct link to philosophy, but certainly there is an indirect one through relativity. - dcljr (talk) 23:02, 24 August 2005 (UTC)
thread_title:  Overstating the case? 

message: Thee is an error in section "Parallel postulate".
At the end of the section it reads:
* ... the "real" space in which we live can be non-Euclidean (for example, around black holes and neutron stars).
While it should say: 
* ... the real space in which we live is non-Euclidean and that's why there is a gravitational field in it.
If no one objects for a week I'm going o fix it. Jim 07:36, 24 November 2006 (UTC)
replies: text: Done. Jim 16:19, 13 December 2006 (UTC)
thread_title:  Parallel postulate 

message: I have amended the fourth postulate to read this way, changing congruent to equal:
All right angles are equal.
In standard usage congruence never applies to angles or sides, only to figures. This is all very straightforward and clear, since the standard term equal works perfectly well for angles and sides that are simply measured numerically. See Congruence (geometry); see also major British and American dictionaries: SOED, and M-W Collegiate (Congruent "2: superposable so as to be coincident throughout"; there is no "throughout" for sides or angles, since they are not compound as geometrical figures are).
The original Greek uses the word ἴσος (or strictly, its feminine plural form ἴσας; see Elements, p. 6, where the Greek is given and the translation is with equal). This word plainly means "equal". It needs to mean that, since Euclid immediately goes on to say things like this: "11. An obtuse angle is greater than a right-angle." Relations like greater than make sense in the context of relations like equality, but not of compounded qualities like congruence.
– Noetica♬♩ Talk 21:51, 10 December 2007 (UTC)
thread_title:  Fourth postulate: equal, not congruent 

message: In what form was The Elements originally? Was it gouged on many stone plates? Or in some other way? As far as I know, printing was only invented in the 15th century in Europe, and papyrus, let alone paper, was unkown to ancient Greeks. RokasT (talk) 20:02, 5 January 2008 (UTC)
replies: text: Wrong. Printing existed many thousands of years ago. If you meant block printing or movable type printing or printing press printing, only you'd know that. From my scant understanding, that work would have been on scrolls. Your question seems to assume that it was all written and then distributed rather than a work done over years. Your question also suggests that you aren't aware that Euclid was living in Egypt at that time, papyrus dates as far back as 3000 B.C.E. (and likely farther).174.131.48.89 (talk) 23:28, 7 August 2022 (UTC)
thread_title: The very original of The Elements

message: In the section "contents of the books" it is claimed that book 6 contains Thales theorem. Ain't Thales theorem proposition 31 in book 3?
Dafer45 (talk) 17:59, 27 March 2008 (UTC)
thread_title:  Thales theorem 

message: Is there any reason to believe that Euclid was referring to the specific "Royal Road", to which this article links, rather than to a metaphorical "special path" to make the learning easier for Ptolemy?Czrisher (talk) 21:00, 8 July 2008 (UTC)
replies: text: As with many things, it's not an either/or proposition. It may have contained simultaneous literal and figurative meaning. Jakewayd (talk) 03:12, 12 October 2018 (UTC)
thread_title:  Royal Road 

message: There seems to be an inconsistency.  The introduction says that the book was first published in type in 1482.  The "Editions" section lists the Editio princeps as being published in 1533.  Can someone clarify? Rknasc (talk) 14:44, 29 September 2008 (UTC)
thread_title:  Editio Princeps 

message: I am a new user of Wikipedia. I am researching school textbooks based on Euclid's Elements. So not academic works on the text of The Elements but classroom textbooks of School Geometry based on The Elements. I am interested in books from 19th centuary onwards.
I have nothing so far and would appreciate some titles. This research idea came out of once reading Lewis Carrol 'Euclid and his modern rivals' and the often qouted fact that "Euclid's Elements were the Geometry textbook for 2000 years"
I want to find out who wrote the schoolroom versions of Euclid and, if any are still in print, to study from them.78.147.178.174 (talk) 14:46, 21 November 2008 (UTC)
thread_title:  Euclid's Elements 

message: Which variant of Greek was it written in?  —Preceding unsigned comment added by 92.112.44.252 (talk) 21:15, 22 November 2008 (UTC)
replies: text: We're assuming it was first rendered in Greek by Euclid. The true original may have been rendered in an Egyptian, or as I'm speculating, a Hebrew script given the classic art depicting Euclid constructing a Star of David at angle. Jakewayd (talk) 03:13, 12 October 2018 (UTC)
thread_title:  Language 

message: I changed the article on Euclid considerably as well.
As I said in the talk page on the Euclid article, These are very essential additions to article, and I hope that people will look at them objectively and use this as an opportunity to make good, unbiased articles. Wikipedia gives us the opportunity to question history and rewrite it. As Orwell put it, "Who controls the present controls the past, who controls the past controls the future." We should look more deeply into Euclid and Elements, as to how it was written and transcribed, and the philosophies it propounded, as well as the social and political reasons behind any transcription.
NittyG (talk) 12:27, 10 January 2009 (UTC)
replies: text: Wikipedia most certainly does not give us the opportunity to rewrite history. Doing so would be engaging in original research, which is prohibited. It does give us the opportunity to update articles in Wikipedia when reliable sources have rewritten history. Finell (Talk) 01:56, 13 January 2009 (UTC)

text: No. As a title to this article, "Elements" is an insufficient title. This and related articles make clear that the title of the book is Elements. Finell (Talk) 01:46, 13 January 2009 (UTC)
replies: text:  Yes change the name as Elements is not Euclids work. --Tales23 (talk) 20:15, 15 January 2009 (UTC)

text: Encyclopaedia Brittannica says "flourished, c300BC, Alexandria, Egypt"; the OED says "A mathematician of Alexandria who flourished about 300 B.C."; the Encylopedia Americana says, "EUCLID OF ALEXANDRIA, Greek mathematician : fl. about 300 BC, taught geometry at Alexandria in the reign of Ptolemy I (323-285 BC)"; a couple of history of maths books I have agree. Does anyone say that he didn't? Myrvin (talk) 13:51, 12 July 2009 (UTC)
thread_title: Transcription and Historicization

message: The book is called Elements, not Euclid's Elements. At most we should mention in the first sentence, "Also known as "Euclid's Elements". I would like to change the article title, but I should wait a while, and there should be a discussion ahead of time.
NittyG (talk) 12:38, 10 January 2009 (UTC)
replies: text: No. As a title to this article, "Elements" is an insufficient title. This and related articles make clear that the title of the book is Elements. Finell (Talk) 01:46, 13 January 2009 (UTC)
replies: text:  Yes change the name as Elements is not Euclids work. --Tales23 (talk) 20:15, 15 January 2009 (UTC)
thread_title: Change "Euclid's Elements" to "Elements"

message: The intro tells me that euclid lived and worked in Alexandria, where is the reference to it? Is it the known that Theon and Hypatia of Alexandria wrote and edited Euclids work. But where does it states that euclid was there aswell? (Tales23 (talk) 04:30, 13 January 2009 (UTC)
replies: text: Encyclopaedia Brittannica says "flourished, c300BC, Alexandria, Egypt"; the OED says "A mathematician of Alexandria who flourished about 300 B.C."; the Encylopedia Americana says, "EUCLID OF ALEXANDRIA, Greek mathematician : fl. about 300 BC, taught geometry at Alexandria in the reign of Ptolemy I (323-285 BC)"; a couple of history of maths books I have agree. Does anyone say that he didn't? Myrvin (talk) 13:51, 12 July 2009 (UTC)
thread_title:  Euclid and Alexandira 

message: Here are 2 scans of elements and 1 of euclid optics 
http://www.ibiblio.org/expo/vatican.exhibit/exhibit/d-mathematics/Greek_math.html --Tales23 (talk) 00:26, 19 January 2009 (UTC)
thread_title:  Images of Euclid Elements

message: There are separate articles on Euclid's Elements and Euclidean geometry. I've been working on the latter. I've deleted a little material from Elements that was actually about later work in geometry, not the Elements, and that therefore IMO belonged in the geometry article (where it was already discussed more fully).--76.167.77.165 (talk) 23:22, 14 February 2009 (UTC)
thread_title: Euclidean geometry as opposed to the Elements

message: The influence of Euclid's Elements extended beyond western culture. C.V.Raman, the Indian Physicist, described it the most remarkable works of all time. He added, " ... The pages of Euclid are like the opening bars of the music of the grand opera of Nature's great drama. So to say, they lift the veil and show to our vision a glimpse of a vast world of natural knowledge awaiting study." 89.241.245.58 (talk) 20:16, 29 April 2010 (UTC)
thread_title:  Influence 

message: The below two sentences are opaque, argumentative and well below the overall high quality of this Wikipedia article.
However, Proclus' papyrus manuscript has been copied to a paper which became available in Europe after 800 years. Therefore, the originality of Proclus' work might have been altered since it was copied by hand.[citation needed]
First of all, a mere technical point... Unlike the displayed certainty of this above insert, we don't actually know on what kind of writing material Proclus wrote down his commentary. It's no doubt very likely that it was papyrus but it's at least conceivable that it could also have been parchment. The bottom line is that we don't know and even more importantly it doesn't matter one iota, so why mention it? Obviously, this was only a way to introduce the argumentative insert/edit quoted above.
So, to the second and main point... Yes indeed, we don't have Proclus' actual original handwritten manuscript. What a surprise - NOT! What's the point of mentioning this when we don't have the original hand writings of a single ancient author (except for maybe the carbonized hand writings of Philodemus in Herculaneum). Anyone with even the most rudimentary understanding of manuscripts and textual transmission throughout the ages would have taken this for granted instead of wasting digital ink on underscoring the obvious.
So, why does he mention this at all? Well, the editor in question makes his intent clear in the next sentence where he puts into question the veracity of Proclus' writings on Euclid. This is a very dubious style of editing, clearly not a neutral point of view by any standard and IMHO it borders on vandalism. The veracity of Proclus' writings cannot be put into question merely on the basis of it being copied throughout the Middle Ages in monastic scriptoria. That's how not only to Proclus' writings but all ancient literature has come down to us, including Euclid's Elements itself. Therefore, this insert should be erased. Currently, it has a "citation needed" tag, but had the editor based his intervention on something more substantial than merely discovering the fact that Proclus' writings like all manuscripts has a textual tradition, then he surely would have written something more serious to begin with. It should be up to him to put in the effort to convince the rest of us that he should be taken seriously, there's no need to leave this kindergarten-level edit/insert for months in the introductory section of the article.
Abvgd (talk) 09:53, 4 January 2014 (UTC)
thread_title:  An argumentative insert bordering on vandalism 

message: Away back in 2008 [https://en.wikipedia.org/w/index.php?title=Euclid%27s_Elements&diff=229786827&oldid=227836296 this edit was made:
* from:  the ratio being  \sqrt{\tfrac{10}{3(5-\sqrt{5})}} 
* to: the ratio being  \sqrt{\tfrac{10}{3(5-\sqrt{5})}} = \sqrt{\tfrac{5+\sqrt{5}}{6}} 
This is not an equation (the two sides are not equal)... so I essentially reverted the 2008 edit.Jytdog (talk) 18:05, 11 June 2014 (UTC)
replies: text: Why do you believe that the two expressions are not equal? Their equivalence is an elementary exercise in rationalizing a denominator. Bill Cherowitzo  (talk) 00:05, 12 June 2014 (UTC)
replies: text: duh, sorry (facepalm)  Was going too fast earlier today.  thanks for correcting. Jytdog (talk) 00:29, 12 June 2014 (UTC)
replies: text: It took me a while to see how this worked, so for the benefit of anyone else whose algebra is also rusty, multiply both the numerator and denominator of the left hand fraction by (5 + sqrt^5), which of course leaves the fraction's value unchanged, and simplify the result to get the right hand side.  Works like magic!2A00:23C8:7907:4B01:A1AE:511E:9DBC:39ED (talk) 15:02, 31 October 2021 (UTC)
thread_title:  error since 2008 in apocrypha section? 

message: An IP has repeatedly tried to insert this –
None of the references for Euclid's work are prior to 15th century. The subject is yet to be proven.
into the criticism section. Leaving aside the fact that this is not a criticism of the work and the unintelligible second sentence, I would like to more directly address the intent of this inclusion. It appears that the IP's source is the religious conspiracy theory book Euclid and Jesus written by an Indian mathematician. The book claims that Euclid did not exist and this artificial persona was created as a foil by the Christian church. As one reviewer mentions, the book makes a compelling case by "connecting the dots". However, what this reviewer, and perhaps the IP, fails to realize is that the author of such a conspiracy theory is also selecting which dots to connect. This is a very standard technique for making a compelling case and one can find excellent examples of it in any Dan Brown novel, such as The Da Vinci Code. Since it is true that almost nothing is known about Euclid (what little there is coming mainly from Proclus), this seems to make him a target for such outlandish theories. (I have also seen, in print, the suggestion that Euclid was the alias of a Bourbaki-like group of Alexandrian mathematicians.) It is unlikely that anything concrete will ever be known about him –barring the discovery of a previously unknown interview with his wife published in the Alexandrian Monthly Papyri  – so we need to be vigilant about the overactive imaginations of some authors. --Bill Cherowitzo  (talk) 22:23, 16 May 2017 (UTC)
thread_title:  Fringe 

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thread_title:  External links modified 

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thread_title:  External links modified 

message: The vast body of literature developed by Euler throughout the 18th Century more than qualifies for the Enlightenment's full reincarnation of mathematical rigor. The statement at the beginning is demonstrably false. Jakewayd (talk) 02:49, 12 October 2018 (UTC)
replies: text: Yeah, the claim that its logical rigor wasn't surpassed is nonsense and factually not true. Many authors PRIOR to 1800 recognized flaws in the Elements' logic. Some of which were easily corrected (by adding axioms). But some of what we now recognized as "flaws" depend on our modern conceptions of geometry. For instance, in Euclid's time, I doubt anyone would argue that two intersecting line segments (i.e. X) required a postulate that lines were a continuous set of points in order to "prove" they intersected at a point - the drawing was sufficient proof (together with their priors).174.131.48.89 (talk) 00:34, 8 August 2022 (UTC)
thread_title:  Demonstrably False Statement on Mathematical Rigor Not Being Reached Until 19th Century 

message: The parallel postulate may be responsible for holding back mathematics of curved geometries. Imagine centuries of students being brow beaten into only accepting that flat space is the only cosmological possibility. Axiom as properly described by intellectually honest mathematicians and philosophers as opposed to postulates sets forth the possibility of there existing worlds where the standard assumptions of flatness do not come close to being true in those worlds. A postulate, as I suspect, appears to be an attempt to make mathematics dogmatic rather than inquisitive by Euclid's hand. Axioms are open admissions of assumptions of truth and permit other hypothetical axiomatic systems to be examined. Jakewayd (talk) 03:19, 12 October 2018 (UTC)
thread_title:  Embarrassing Absence of Discussion on the Parallel Postulate 

message: I would like to bring attention to the issue of having Stoicheia redirect to Euclid's Elements, it's own page having been deleted due to inadequate research on the multiple meanings of the word: in math, philosophy, Bible, language (Ancient Greek), history, science, publications, electronics, art, etc. I wrote about the subject on the talk page for the deleted/redirected word. I provided initial sources for citation in which to build a wiki on the word (and related words like stoicheion). 
The word was deleted in 2014 and a page does not appear to have been developed much. I am new as a contributor to Wikipedia. Seeking to add the contribution after discovering a problem when trying to learn more about the term following a lecture. Can someone [review] and see if this word can exist independently. Thank you. Roxanne-snowden (talk) 10:09, 7 July 2020 (UTC)
thread_title:  Remove the Redirect for "Stoicheia", Reinstate and Develop Independent Wiki 

message: According to MacTutor: the Andrea Tacquet page documents a $1654$ edition which also included some Archimedes.
This was the basis of the translation by William Whiston which is cited in this section.
Any reason to omit the Taquet? --Matt Westwood 21:26, 22 August 2020 (UTC)
thread_title:  Translations and editions -- reason to omit Andrea Tacquet? 

message: The Contents section states: "Book 2 ... concludes with a construction of the golden ratio and ..." I did not find the construction there. What is the number of the proposition? There is a construction of the golden ratio in Book 6, Proposition 30. (Euclid calls the major \varphi and minor \Phi the  and , usually translated as "extreme ratio" and "mean ratio".)  --Lambiam 06:32, 6 May 2021 (UTC)
thread_title:  Euclid's construction of the golden ratio 

message: I think it is a significant flaw that the lead does NOT explain WHAT it is that Elements does.
Consider this:
"Euclid (fl. 300 BCE) placed at the head of his Elements a series of ‘definitions’ (e.g., “A point is that which has no part”) and ‘common notions’ (e.g., “If equals be added to equals, the sums are equal”), and five ‘requests’.  Supposedly these items conveyed all of the information needed for inferring the theorems and solving the problems of geometry, but as a matter of fact they do not.  However, the requests (aitemata)—usually called ‘postulates’ in English—must at any rate be granted or Euclid's proofs will not go through."*
That quote seems to me to enormously improve understanding of what the Elements are so well-known for, and yet you'd be hard-pressed to show that there's any indication of the importance of the definitions, common notions, and requests in the lead as a basis for a rigorous system of mathematical or logical deduction which influenced so many. I also note that there's a subtle implication of "request" not present with the words 'postulate' and 'axiom'. (that is, the possibility of denying the request; which, it could be argued ,foreshadows non-Euclidean maths.) So I wonder if the more unusual, yet more faithful, translation is worthy of note?
*excerpted from (Torretti, Roberto, "Nineteenth Century Geometry", The Stanford Encyclopedia of Philosophy (Fall 2021 Edition), Edward N. Zalta (ed.), URL = <https://plato.stanford.edu/archives/fall2021/entries/geometry-19th/>. ) 174.131.48.89 (talk) 00:55, 8 August 2022 (UTC)
thread_title:  Flaw