5 ms·

Fancy Euclid's “Elements” in TeX

345 points by mci 7y ago

enriquto 7y ago
I am in awe at the beauty of this thing
- NotSammyHagar 7y ago
  Yes, I just want to yell "wow" out loud. My LaTex phd thesis was so ugly.
  - deleted 7y ago
    [deleted]
ZeroGravitas 7y ago
I have a reproduction copy of this book, and always intended to find some time to recreate a few pages of it in SVG as a way of expanding my knowledge of that technology. This is far beyond anything I even dreamt of doing. Really great stuff.
ddavis 7y ago
Maybe not as fancy, but here's a version with Greek and English side by side: http://farside.ph.utexas.edu/Books/Euclid/Elements.pdf http://farside.ph.utexas.edu/Books/Euclid/Elements.pdf
- no_identd 7y ago
  You might wanna try Heath's translation, here: https://archive.org/details/euclid_heath_2nd_ed https://archive.org/details/euclid_heath_2nd_ed It's the most detailed and complete translation, addressing numerous issues. Not all, thought, there's one grave translation error unaddressed in pretty much all translations, and more importantly, repeated in ALMOST all translations: http://cgm.cs.mcgill.ca/~godfried/teaching/dm-reading-assignments/Euclid-Second-Proposition-Math-Intell.pdf http://cgm.cs.mcgill.ca/~godfried/teaching/dm-reading-assign... Even today, most mathematicians aren't aware of the difference. (And this despite the fact that the Wikipedia article on the axiom DOES mention it.) I wish we'd have Byrne-style drawings of The Elements as implemented in this paper, albeit the authors of it & the various precursor papers to it seem unaware of the above, too—and hence (almost) reinvent the wheel: https://link.springer.com/article/10.1007/s10472-018-9603-0 https://link.springer.com/article/10.1007/s10472-018-9603-0 (Note: There exists a 'secret' sequel to that paper, which one can find here: http://t-news.cn/Floc2018/FLoC2018-pages/preprint_cX1w.pdf http://t-news.cn/Floc2018/FLoC2018-pages/preprint_cX1w.pdf — I say 'secret' as they only cite the above indirectly, by citing "Mark Bickford, Rich Eaton, and Ariel Kellison. Nuprl Theory: euclidean plane geometry, 2018.", which makes the connection between them undiscoverable via services like citationgecko.com & Google Scholar.)
nixpulvis 7y ago
Awesome LaTeX: https://github.com/egeerardyn/awesome-LaTeX https://github.com/egeerardyn/awesome-LaTeX
- Jaxan 7y ago
  This was actually done with ConTeXt, not LaTeX.
  - nixpulvis 7y ago
    Interesting, how do Tex Live, LaTeX and ConTeXt related to each other?
    - capnrefsmmat 7y ago
      LaTeX and ConTeXt are two packages that provide sets of macros for the base TeX typesetting system. LaTeX provides macros for things like sectioning, tables of contents, figures, and so on, and the configurable styling of everything separately from the content; ConTeXt's macros are more focused on precise page layout than semantic document structure. TeX Live is a TeX distribution, meaning it contains TeX, LaTeX, ConTeXt, and a variety of other macro packages (including packages building on top of LaTeX, for example), fonts, and so on.
    - Jaxan 7y ago
      TeX live is a distribution and it comes with many things (TeX, LaTeX, ConTeXt, fonts, ...). Both LaTeX and ConTeXt are built on top of bare TeX and add lots of features. I have used ConTeXt a quite a bit, and it seems to be more designed to typeset whole books, whereas LaTeX is very good at scientific papers.
pgtan 7y ago
MetaPost is so underrated. Glad, this project shows the strength of the language.
- yannis 7y ago
  It is gaining a bit of traction with LuaLaTeX and the luamplib library, but unfortunately PGF/tikZ seems to be the preferred library for many projects.
  - xvilka 7y ago
    I hope LaTeX 3 will be released soon, to address many problems of the 2nd version.
  - adiM 7y ago
    I often wonder how hard it will be to have a metapost backend for PGF.
svat 7y ago
To add some context, this is a version, prepared in ConTeXt and MetaPost by Sergey Slyusarev (@jemmybutton), of Oliver Byrne's 1847 work “The first six books of the elements of Euclid, in which coloured diagrams and symbols are used instead of letters for the greater ease of learners”. This linked post on habr.com is definitely worth reading; also see the sources on GitHub page here: https://github.com/jemmybutton/byrne-euclid https://github.com/jemmybutton/byrne-euclid A scan of Byrne's 1847 original here: https://archive.org/details/firstsixbooksofe00byrn/page/n6 https://archive.org/details/firstsixbooksofe00byrn/page/n6 Another person's (Nicholas Rougeux's) reproduction here: https://www.c82.net/euclid/about/ https://www.c82.net/euclid/about/ A publisher's attempt to “extend” Byrne's work from 6 to all 13 books here (Kickstarter + preorder; I don't believe it's done yet): https://www.kroneckerwallis.com/product/euclids-elements-completing-oliver-byrnes-work/ https://www.kroneckerwallis.com/product/euclids-elements-com... There's also a facsimile reproduction of Byrne's original by the publisher Taschen, with a review here that goes into some detail on Euclid editions and on Byrne: https://www.maa.org/publications/maa-reviews/the-first-six-books-of-the-elements-of-euclid https://www.maa.org/publications/maa-reviews/the-first-six-b...
- jen729w 7y ago
  I backed the Kickstarter, it’s gone to print and is due mid-year if memory serves.
- sohkamyung 7y ago
  > To add some context, this is a version, prepared in ConTeXt ... Nice (un)intended pun. :-)
- adrianratnapala 7y ago
  While mentioning ConTeXt, can anyone give me a sell job on when and why it might be nicer than LaTeX? It's not that I'm super fond of LaTeX, it's just that I assumed its warts were more or less inevitable in a stringy macro framework, and ConTeXt can't avoid that either.
  - adiM 7y ago
    Feature wise, both LaTeX and ConTeXt are similar. Where ConTeXt really shines is the ease of use and consistency of the interface. 1. No need to run `pdflatex; bibtex; pdflatex; pdflatex` multiple times. The wrapper script `context` takes care of that. 2. Easy to add graphic elements to the page and layout in a consistent and _fast_ manner. 3. Export to XML/XHTML/ePub. 4. Can compile XML. 5. Programatically generate documents using a Lua interface (this is different from LuaTeX; ConTeXt has a nice Lua interface called ConTeXt Lua Documents, so it seems that you are writing Lua code rather than a wrapper script). 6 Consistent of interface. See https://tex.stackexchange.com/questions/4987/why-should-i-be-interested-in-context/5007#5007 https://tex.stackexchange.com/questions/4987/why-should-i-be...
gwern 7y ago
The randomized initials/dropcaps are fun. But it seems that this doesn't replicate the original Bryne use of the Rose Caps (https://wiki.obormot.net/Main/BonusFontsDemo?demo_font_one=Rose+Caps https://wiki.obormot.net/Main/BonusFontsDemo?demo_font_one=R...), and uses a random sans serif font? It'd be cooler if it was generating randomized versions of the original initials.
meuk 7y ago
This is a bit random, but there are some formal systems for Euclid's elements out there (see, for example https://arxiv.org/abs/0810.4315 https://arxiv.org/abs/0810.4315). I think it should be possible to implement this in a dependently typed language like Idris, but haven't really worked on this (yet). Any thoughts?
- ratmice 7y ago
  Also see this: http://www.michaelbeeson.com/research/CheckEuclid/index.php http://www.michaelbeeson.com/research/CheckEuclid/index.php It seems a dependently typed language might be overkill, "The proofs described in this paper only need a rather weak logic. There are no function symbols", "only existential quantifiers; universal quantification over the free variables is left implicit." They wrote a translator then to convert the proofs to HOL, and Coq, you could presumably do the same for e.g. idris
  - meuk 7y ago
    Awesome, this was exactly the type of comment I was hoping for!
Grustaf 7y ago
Simply gorgeous
- rolandog 7y ago
  Couldn't agree more. I'm in awe.
defanor 7y ago
I like this style for formulae, though it can be not straightforward to translate into regular text or speech. And in this case there's another issue caused by color-coding: it's tricky to read with altered colors and/or on monochrome displays. Maybe the latter can be solved by using different styles for lines and filling, in addition to colors.

345 points by mci 7y ago

enriquto 7y ago

I am in awe at the beauty of this thing

NotSammyHagar 7y ago
Yes, I just want to yell "wow" out loud. My LaTex phd thesis was so ugly.
- deleted 7y ago
  [deleted]

ZeroGravitas 7y ago

I have a reproduction copy of this book, and always intended to find some time to recreate a few pages of it in SVG as a way of expanding my knowledge of that technology. This is far beyond anything I even dreamt of doing. Really great stuff.

ddavis 7y ago

Maybe not as fancy, but here's a version with Greek and English side by side: http://farside.ph.utexas.edu/Books/Euclid/Elements.pdf http://farside.ph.utexas.edu/Books/Euclid/Elements.pdf

no_identd 7y ago
You might wanna try Heath's translation, here: https://archive.org/details/euclid_heath_2nd_ed https://archive.org/details/euclid_heath_2nd_ed It's the most detailed and complete translation, addressing numerous issues. Not all, thought, there's one grave translation error unaddressed in pretty much all translations, and more importantly, repeated in ALMOST all translations: http://cgm.cs.mcgill.ca/~godfried/teaching/dm-reading-assignments/Euclid-Second-Proposition-Math-Intell.pdf http://cgm.cs.mcgill.ca/~godfried/teaching/dm-reading-assign... Even today, most mathematicians aren't aware of the difference. (And this despite the fact that the Wikipedia article on the axiom DOES mention it.) I wish we'd have Byrne-style drawings of The Elements as implemented in this paper, albeit the authors of it & the various precursor papers to it seem unaware of the above, too—and hence (almost) reinvent the wheel: https://link.springer.com/article/10.1007/s10472-018-9603-0 https://link.springer.com/article/10.1007/s10472-018-9603-0 (Note: There exists a 'secret' sequel to that paper, which one can find here: http://t-news.cn/Floc2018/FLoC2018-pages/preprint_cX1w.pdf http://t-news.cn/Floc2018/FLoC2018-pages/preprint_cX1w.pdf — I say 'secret' as they only cite the above indirectly, by citing "Mark Bickford, Rich Eaton, and Ariel Kellison. Nuprl Theory: euclidean plane geometry, 2018.", which makes the connection between them undiscoverable via services like citationgecko.com & Google Scholar.)

nixpulvis 7y ago

Awesome LaTeX: https://github.com/egeerardyn/awesome-LaTeX https://github.com/egeerardyn/awesome-LaTeX

Jaxan 7y ago
This was actually done with ConTeXt, not LaTeX.
- nixpulvis 7y ago
  Interesting, how do Tex Live, LaTeX and ConTeXt related to each other?
  - capnrefsmmat 7y ago
    LaTeX and ConTeXt are two packages that provide sets of macros for the base TeX typesetting system. LaTeX provides macros for things like sectioning, tables of contents, figures, and so on, and the configurable styling of everything separately from the content; ConTeXt's macros are more focused on precise page layout than semantic document structure. TeX Live is a TeX distribution, meaning it contains TeX, LaTeX, ConTeXt, and a variety of other macro packages (including packages building on top of LaTeX, for example), fonts, and so on.
  - Jaxan 7y ago
    TeX live is a distribution and it comes with many things (TeX, LaTeX, ConTeXt, fonts, ...). Both LaTeX and ConTeXt are built on top of bare TeX and add lots of features. I have used ConTeXt a quite a bit, and it seems to be more designed to typeset whole books, whereas LaTeX is very good at scientific papers.

pgtan 7y ago

MetaPost is so underrated. Glad, this project shows the strength of the language.

yannis 7y ago
It is gaining a bit of traction with LuaLaTeX and the luamplib library, but unfortunately PGF/tikZ seems to be the preferred library for many projects.
- xvilka 7y ago
  I hope LaTeX 3 will be released soon, to address many problems of the 2nd version.
- adiM 7y ago
  I often wonder how hard it will be to have a metapost backend for PGF.

svat 7y ago

To add some context, this is a version, prepared in ConTeXt and MetaPost by Sergey Slyusarev (@jemmybutton), of Oliver Byrne's 1847 work “The first six books of the elements of Euclid, in which coloured diagrams and symbols are used instead of letters for the greater ease of learners”. This linked post on habr.com is definitely worth reading; also see the sources on GitHub page here: https://github.com/jemmybutton/byrne-euclid https://github.com/jemmybutton/byrne-euclid A scan of Byrne's 1847 original here: https://archive.org/details/firstsixbooksofe00byrn/page/n6 https://archive.org/details/firstsixbooksofe00byrn/page/n6 Another person's (Nicholas Rougeux's) reproduction here: https://www.c82.net/euclid/about/ https://www.c82.net/euclid/about/ A publisher's attempt to “extend” Byrne's work from 6 to all 13 books here (Kickstarter + preorder; I don't believe it's done yet): https://www.kroneckerwallis.com/product/euclids-elements-completing-oliver-byrnes-work/ https://www.kroneckerwallis.com/product/euclids-elements-com... There's also a facsimile reproduction of Byrne's original by the publisher Taschen, with a review here that goes into some detail on Euclid editions and on Byrne: https://www.maa.org/publications/maa-reviews/the-first-six-books-of-the-elements-of-euclid https://www.maa.org/publications/maa-reviews/the-first-six-b...

jen729w 7y ago
I backed the Kickstarter, it’s gone to print and is due mid-year if memory serves.
sohkamyung 7y ago
> To add some context, this is a version, prepared in ConTeXt ... Nice (un)intended pun. :-)
adrianratnapala 7y ago
While mentioning ConTeXt, can anyone give me a sell job on when and why it might be nicer than LaTeX? It's not that I'm super fond of LaTeX, it's just that I assumed its warts were more or less inevitable in a stringy macro framework, and ConTeXt can't avoid that either.
- adiM 7y ago
  Feature wise, both LaTeX and ConTeXt are similar. Where ConTeXt really shines is the ease of use and consistency of the interface. 1. No need to run `pdflatex; bibtex; pdflatex; pdflatex` multiple times. The wrapper script `context` takes care of that. 2. Easy to add graphic elements to the page and layout in a consistent and _fast_ manner. 3. Export to XML/XHTML/ePub. 4. Can compile XML. 5. Programatically generate documents using a Lua interface (this is different from LuaTeX; ConTeXt has a nice Lua interface called ConTeXt Lua Documents, so it seems that you are writing Lua code rather than a wrapper script). 6 Consistent of interface. See https://tex.stackexchange.com/questions/4987/why-should-i-be-interested-in-context/5007#5007 https://tex.stackexchange.com/questions/4987/why-should-i-be...

gwern 7y ago

The randomized initials/dropcaps are fun. But it seems that this doesn't replicate the original Bryne use of the Rose Caps (https://wiki.obormot.net/Main/BonusFontsDemo?demo_font_one=Rose+Caps https://wiki.obormot.net/Main/BonusFontsDemo?demo_font_one=R...), and uses a random sans serif font? It'd be cooler if it was generating randomized versions of the original initials.

meuk 7y ago

This is a bit random, but there are some formal systems for Euclid's elements out there (see, for example https://arxiv.org/abs/0810.4315 https://arxiv.org/abs/0810.4315). I think it should be possible to implement this in a dependently typed language like Idris, but haven't really worked on this (yet). Any thoughts?

ratmice 7y ago
Also see this: http://www.michaelbeeson.com/research/CheckEuclid/index.php http://www.michaelbeeson.com/research/CheckEuclid/index.php It seems a dependently typed language might be overkill, "The proofs described in this paper only need a rather weak logic. There are no function symbols", "only existential quantifiers; universal quantification over the free variables is left implicit." They wrote a translator then to convert the proofs to HOL, and Coq, you could presumably do the same for e.g. idris
- meuk 7y ago
  Awesome, this was exactly the type of comment I was hoping for!

Grustaf 7y ago

Simply gorgeous

rolandog 7y ago
Couldn't agree more. I'm in awe.

defanor 7y ago

I like this style for formulae, though it can be not straightforward to translate into regular text or speech. And in this case there's another issue caused by color-coding: it's tricky to read with altered colors and/or on monochrome displays. Maybe the latter can be solved by using different styles for lines and filling, in addition to colors.