Talk:Euclid's Elements/GA1

GA review

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Nominator: David Eppstein (talk · contribs) 01:52, 19 September 2025 (UTC)

Reviewer: DoctorWhoFan91 (talk · contribs) 18:59, 19 September 2025 (UTC)

Will add initial remarks soon- article looks really good though. HSLover/DWF (talk) 18:59, 19 September 2025 (UTC)

Offtopic article talk

Aside: I don't think this article comes close to meeting GA criteria as I would interpret them. I have extensive criticisms (about 2000 words so far, but still a WIP) which I will post in a separate section on the talk page. –jacobolus (t) 00:50, 20 September 2025 (UTC)

Jacobolus. You know, because you have made occasional small edits over this period, that I have put significant work into improving this article over the last two months. And yet you wait until now to express any dissatisfaction with the way it has been going, to make any substantive edits, or to bring any remaining issues to the talk page (as you did in July for a different resolved issue), nor even to provide me any friendly warning before taking your as-yet-unspecified concerns directly to this review page. It is almost as if you would prefer to sabotage a GA nomination than to make the article better. I am sure that is not actually the case, but perhaps you can see how it could come across that way, especially given our not-too-long-ago repeated prickly interactions.

Frankly, the way you have handled this comes across as disrespectful. If you truly think I have been wasting two entire months of editing effort you should have said so much earlier. It would be much easier on my side to treat your editing with collegiality and respect if you would do me the courtesy of doing the same.

That said, if you do indeed have substantive improvements to request (or better, to do yourself), then obviously this article does not meet the stability requirements of GA and I withdraw this nomination. —David Eppstein (talk) 01:01, 20 September 2025 (UTC)

I'm sorry, I didn't realize you were planning a GA nomination, am not trying to blindside you, don't mean any disrespect, and very much appreciate your recent efforts, which have made significant improvements, and were not by any means wasted. I don't know what kind of "friendly warning" would be helpful: this note was intended to be the "friendly warning". With that said though, I personally find GA criteria somewhat mystifying and their application extremely inconsistent, so I won't try to stand in the way of a green badge here if the reviewer(s) think it's a useful marker. I'm generally pretty indifferent to badges, and my goal is that we can eventually end up with an excellent article. I'll try to post my comments ASAP. –jacobolus (t) 02:22, 20 September 2025 (UTC)

Ok, thanks for the clarification. I still would like to withdraw the nomination for now so that whatever you have in mind for more improvement can be done. (I think the weakest current parts are the pre-modern sections of "reception", which is mostly names and dates but not much about how it was used and how our understanding of it evolved, but I didn't think that needed to stand in the way of a GA nom.) —David Eppstein (talk) 04:55, 20 September 2025 (UTC)

@David Eppstein I just want to say that I'm the nominator here, and I do believe it's very close to GA criteria, so do not withdraw the nom. @Jacobolus I just want to say this was disrespectful to DE, as he said, and to me- I'm the reviewer, you shouldn't be trying to take over. Especially bcs you said this With that said though, I personally find GA criteria somewhat mystifying and their application extremely inconsistent: If you do not understand GA criteria (you saying it's not close to GA criteria makes me think you are thinking of FA criteria), you shouldn't be trying to review them, let alone trying to take over someone else a few hours in. HSLover/DWF (talk) 06:45, 20 September 2025 (UTC)

s/nominator/reviewer, right? If you still wish to proceed, I guess it shouldn't be a problem. Third party comments are allowed in GA reviews, though, so if Jacobolus can get his list of deficiencies ready in time for you to consider it in your review, he should be allowed to do that. —David Eppstein (talk) 06:52, 20 September 2025 (UTC)

He is allowed to, yes, but this wasn't the way to do it- he does it correctly on the talk page- and should have had this conversation on the talk page, too, linking here if needed- I have collpased this part as a result. I have seen his remarks- a few point I agree with and will be in my review- most is FA criteria- and does not come into purview here. HSLover/DWF (talk) 07:08, 20 September 2025 (UTC)

Also if User:DoctorWhoFan91 has specific feedback/comments, I don't mean to prevent them from posting them, and would be glad to help try to address them. Edit: Sorry, I don't know what you mean by "trying to take over". I posted my comments at Talk:Euclid's Elements § Great recent work; article still seems substantially incomplete and unbalanced. –jacobolus (t) 06:57, 20 September 2025 (UTC)

I meant you should have started this on the talk page, and pinged DE, instead of having this discussion on the GANR page, as it makes the page harder to read- I have collapsed this section as a result.

Images

• Are great, and amazing- could you add an image about the 5th postulate though, if possible- I know that the non-Euclidean geometry has one, but I'm thinking one that illustrates the postulate (optional)
  • @David Eppstein:: good image- caption should not be in radians though (the pi), as most people are more familiar with degrees. HSLover/DWF (talk) 07:58, 20 September 2025 (UTC)
    •  Done —David Eppstein (talk) 18:37, 20 September 2025 (UTC)

Lead

• All good

Background

• Despite this, Sialaros furthers that "the remarkably tight structure of the Elements reveals authorial control beyond the limits of a mere editor".: I'm confused what this means?

  Some authors have suggested that Euclid (or the author of the Elements, whoever he was) was a mere compiler of past results. Sialaros thinks that the "tight" structural organization of the Elements implies something more like authorship than compilation. That is, the structural organization and way things hold together is evidence of significant creative effort (probably filling in missing details, supplying proofs, adding new propositions, etc.). –jacobolus (t) 07:17, 20 September 2025 (UTC)

  Then that should probably be made more clear in the article, through addinng to/slighly changing the prose

  •  Done —David Eppstein (talk) 18:37, 20 September 2025 (UTC)

• (c. 470–410 BC, not to be confused with the contemporaneous physician Hippocrates of Kos): I'm not sure this is needed- it's not 400 BC, who's gonna mix them up?

  Hippocrates of Kos, "Father of Medicine", of the famous Hippocratic oath, is a much better known (by orders of magnitude) ancient Greek person named Hippocrates, but most people don't know which city these two were from. If you just say "XYZ was done by Hippocrates c. 450 BC", it's not unreasonable for people to imagine that the physician might have also had mathematics as a hobby. –jacobolus (t) 07:17, 20 September 2025 (UTC)

  Then I think it should be "... of Kos, the Father of Medicine)" or something, because I did not think of the famous Hippocrates when I saw "physician Hippocrates". HSLover/DWF (talk) 07:24, 20 September 2025 (UTC)

   Done Added "father of medicine" and moved to an efn. —David Eppstein (talk) 18:37, 20 September 2025 (UTC)

Selected editions

• Good, fine

References

• All references seem to be high enough quality- change digi.vatlib.it to Digital Vatican Library though, in note e.
  •  Done and improved matching of formatting with the other dig.vat.lib efn. —David Eppstein (talk) 18:37, 20 September 2025 (UTC)

Will get to the rest of the article later. HSLover/DWF (talk) 07:08, 20 September 2025 (UTC)

Contents

• Where are the numbers in the table from?
  •  Done Added that they come from the Heath edition. —David Eppstein (talk) 18:37, 20 September 2025 (UTC)
• The postulates (that is, axioms): I don't think the part in parenthesis is needed- just makes it more confusing who is calling what thing what
  •  Done —David Eppstein (talk) 18:37, 20 September 2025 (UTC)
• but its method of presentation makes it a natural fit.: probably attribute it to people, instead of to wiki-voice- like I understand it was the textbook for most of the western world, but that's not enough for it to be in wiki-voice
  •  Done Checking reveals that this editorialization is not in the source given. I replaced it with a clause about "despite its wide subsequent use as [a textbook]" (with a different source for that clause). —David Eppstein (talk) 21:05, 20 September 2025 (UTC)
• Might be too technical- slight explanation should be added(I know most are wikilinked, but an explanation in-article would still be good)
  • Book I- "magnitudes"
    •  Done. This one was surprisingly subtle and required a long gloss, because for modern readers these are just numbers (lengths, angles, or areas) but for Euclid they were not numbers. —David Eppstein (talk) 21:50, 20 September 2025 (UTC)
  • Book IV- "constructible"
    •  Done —David Eppstein (talk) 21:50, 20 September 2025 (UTC)
  • Book VI="Triangles and parallelograms which are under the same height are to one another as their bases"
    •  Done, but more significantly explained why this is important and expanded this section with material on two more of its propositions. —David Eppstein (talk) 01:47, 21 September 2025 (UTC)
  • Book VII-X: "Parity"
    •  Done, but also clarified the definition of "number", because this is less obvious than you would think. —David Eppstein (talk) 02:04, 21 September 2025 (UTC)
  • Book IX-"perfect numbers"
    •  Done —David Eppstein (talk) 02:10, 21 September 2025 (UTC)
  • Book X-"incommensurable"
    •  Done —David Eppstein (talk) 02:04, 21 September 2025 (UTC)
  • Book XI-"parallelepipeds"
    •  Done The difficulty here was finding a gloss that avoided the almost-equally-technical word parallelogram. —David Eppstein (talk) 02:33, 21 September 2025 (UTC)
• the method of exhaustion,[37] a precursor to integration,- the method of exhaustion (a precursor to integration),[37]
  • You wanted the footnote moved?  Done —David Eppstein (talk) 02:35, 21 September 2025 (UTC)
• (without however finding Euler's formula)- is that needed- the beginner wouldn't understand, the expert would know

  A very old example of "counts their edges and vertices" is being noted. Euler's famous mid-18th century polyhedron formula – that "vertices + faces = edges + 2" holds for all shapes that are topologically equivalent to a sphere – arguably marks the beginning of the now important mathematical field of topology; while this formula is very simple and relatively easy for children to discover for themselves with some nudges in the right direction by a teacher, it apparently went unnoticed by mathematicians for millennia. –jacobolus (t) 07:59, 20 September 2025 (UTC)

  Again, that is "the name is too technical and kinda unncessary"- hence either explain it a bit or remove it. HSLover/DWF (talk) 12:01, 20 September 2025 (UTC)

   Done: glossed the formula. I had a long reply here which missed the point and I removed it. —David Eppstein (talk) 01:10, 21 September 2025 (UTC)

• Not needed for GA, might be good-Expand upon these sections if you ever try for FA

Rest would come later. HSLover/DWF (talk) 07:43, 20 September 2025 (UTC)

Euclid's method and style of presentation

• No indication is given of the method of reasoning that led to the result, although the Data does provide instruction about how to approach the types of problems encountered in the first four books of the Elements.: This is confusing
• Alexandrian system of numerals.: Needs a small explanation in-article

Will finish up in a few hours. HSLover/DWF (talk) 07:58, 20 September 2025 (UTC)

Added a gloss for the numerals and a statement that Data is another book by Euclid. —David Eppstein (talk) 07:49, 21 September 2025 (UTC)

Reception

• What is an "ostraca"?
  •  Done. It's the plural of ostracon, a pottery fragment on which someone scratched writing. Here, it seems to be notes for the construction of a building maybe?
• Johannes de Tinemue,[65] possibly also known as John of Tynemouth - what?
  •  Done I just wrote it as John of Tynemouth. I'm not sure we need to be so careful to clarify that we don't know whether it was really John of Tynemouth or someone else also called John of Tynemouth. I saw a joke like this once about those crank theories about Shakespeare: did you know that the plays of William Shakespeare were not actually written by William Shakespeare, but by someone else, also called William Shakespeare? —David Eppstein (talk) 02:48, 21 September 2025 (UTC)
• The Elements is still considered a masterpiece in the application of logic to mathematics.- Again, where are the citations?
  • "Again"? Anyway, I simply removed the entire paragraph containing this WP:PEACOCK and largely information-free claim. The rest of the paragraph was misplaced and redundant with later material in the criticisms section. —David Eppstein (talk) 08:03, 21 September 2025 (UTC)

  "Again"- because there are a bunch of places, most/all of which are mentioned in the review which mentions, with only one/none citations for this. HSLover/DWF (talk) 08:55, 21 September 2025 (UTC)

• "that two circles with centers at the distance of their radius will intersect in two points."- what does this mean?
  • It means that if you draw File:Byrne 35 diagram 1.png (two circles having the same line segment as their radius, the vesica piscis, the figure James Joyce was so worked up about) then the two circles will actually cross each other instead of somehow mysteriously not crossing. It's obvious but even obvious things require a proof or an assumption. Probably it would help to add an illustration here; I just have to find the right one. —David Eppstein (talk) 02:48, 21 September 2025 (UTC)
• "degenerate cases."- small inline explanation
  • Significantly reworded here, I hope more clearly. —David Eppstein (talk) 08:03, 21 September 2025 (UTC)
• "first-order theory"-same
  • Removed instead, to tighten this section and because it's more of an advanced topic than readers need to worry about here. First-order basically means that the variables are only the things themselves and not sets of things, which is subsumed in the point about this system only using points as variables. —David Eppstein (talk) 08:03, 21 September 2025 (UTC)
• " certain important concepts such as the cross ratio."-what is the cross ratio, why is it important?
  • Add a parenthesis for why it is important. —David Eppstein (talk) 08:03, 21 September 2025 (UTC)
• Mathematician and historian W. W. Rouse Ball put the criticisms in perspective, remarking that "the fact that for two thousand years [the Elements] was the usual text-book on the subject raises a strong presumption that it is not unsuitable for that purpose."[47]- Make that less wikivoice
  •  Done —David Eppstein (talk) 20:49, 21 September 2025 (UTC)

Additionally, wherever the article says the Elements is great, use multiple citations(would be easy, half these citations probably say the Elements is great), not one- yes, the Elements is great, but we need to cite it. Will do the source check later when the changes have been made, @David Eppstein:. HSLover/DWF (talk) 12:13, 20 September 2025 (UTC)

•  Done. At least, I don't think there are any vacuous "Elements is great" statements, but I double-cited the comparatives at the start of the methodology, reception, and non-Euclidean geometry sections. I am about to leave for some travels so I may not be very responsive for the next few days. —David Eppstein (talk) 20:49, 21 September 2025 (UTC)

  PS the article also has improved sourcing in Books X and XII, and new paragraphs in Book II, at the start of "medieval", at the end of "renaissance", and at the start of "axiomatics" (renamed and refocused from "criticism"). —David Eppstein (talk) 00:12, 22 September 2025 (UTC)

Checked the added text-fine too. Doing a spot check of 15 refs.

• [1]:checks out
• [11]:checks out, says it's mathematical in general, and not just geometrical
• [20]:checks out, mentions and names them
• [31]: checks out, describes book III
• [41]: checks out
• [53]:checks out
• [61]: checks out (almost to the point of being verbatim)
• [72]: checks out, describes the various manuscripts
• [82]: checks out
• [89]: checks out
• [100]: checks out
• [111]: checks out, the author also says this
• [121]: checks out, gives the example and a lot of other things too
• [129]: checks out, matches description
• [135]: checks out, description correct

Spot check shows everything good, passing article, great work, @David Eppstein:. HSLover/DWF (talk) 18:22, 22 September 2025 (UTC)

Thanks! The near-verbatim source is a little worrisome, though; I found and removed some other old close paraphrasing but maybe I missed some. Will check. —David Eppstein (talk) 13:26, 23 September 2025 (UTC)

Yeah, kinda an issue, but it's just a rather technical line, so there isn't much change one can do to it, so I just let it be. HSLover/DWF (talk) 17:42, 23 September 2025 (UTC)

The source is PD but we do still need to either mark things as quotes or use our own words. Anyway, reworded a little further away. —David Eppstein (talk) 18:49, 23 September 2025 (UTC)

GA review (see here for what the criteria are, and here for what they are not)
It is reasonably well written. a (prose, spelling, and grammar): b (MoS for lead, layout, word choice, fiction, and lists): It is factually accurate and verifiable, as shown by a source spot-check. a (references): {{GAList/check|}y} b (citations to reliable sources): c (OR): d (copyvio and plagiarism): It is broad in its coverage. a (major aspects): b (focused): It follows the neutral point of view policy. Fair representation without bias: It is stable. No edit wars, etc.: It is illustrated by images, where possible and appropriate. a (images are tagged and non-free images have fair use rationales): b (appropriate use with suitable captions):
Overall: Pass/Fail:
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