Translation of J. D. Gergonne's Varities, Essai de dialectique rationelle (Essay about rational dielectic)
Inspired by Aris Makrides on hsm.stackexchange.com, I've decided to translate an old French paper by Joseph Diaz Gergonne, relating to logic. The paper is significant for being one of the earliest uses of the symbols $\subset$ and $\supset$ (which were written as C and Ɔ). Below you'll find the draft translation, which I may or may not revisit. I was able to finish the translation in one month by translating about 1 hour per day (to a rough draft).
Thanks to Calvin Khor, the typesetting for this translation is now much improved. I'll still leave the original LaTeX file here for anyone to tinker with as they see fit.
Some notes on terminology.
The most significant choice I had to make was how to translate étendue, which is defined by Larousse as dimension de quelque chose considéré dans l'espace qu'il occupe (dimension of something considered in the space which it occupies). Direct translations might include extensiveness, or extent; I found these to not really match the desired meaning, so I translated étendue as scope; thus Gergonne compares the relative scope of ideas, whether they contain each other, or are mutually exclusive in scope, etc, instead of the relative extensiveness of the ideas. I find this much more in line with the concept involved. But if you feel otherwise, or if there is sufficient precedent for translating this word in another way, please let me know and I can change it without too much effort.
Great Job! Ι have only one thing to suggest: that you keep the symbols "C" and "Ɔ", for historical reasons. Most fonts have the inverted “Ɔ” in their “special characters” section.
ReplyDeleteAris Makrides.
I'm working on it, LaTex is just being difficult at the moment. I tried XeLaTex, but still couldn't get the Ɔ to appear. I'm sure it's just a matter of using the right font, but I haven't gotten it yet...
DeleteI got it to work by changing the font to Linux Libertine O, but it's quite ugly and gives the text a 'fuzzy' appearance, so it's a compromise. I'll work on improving the font as I go.
DeleteI switched to using the Libertine package, which helps with the fuzziness. It looks best when downloaded, which is a bit annoying, but overall it's alright.
DeleteHi Sam, I found this via the recently posted answer on the math.SE post (https://math.stackexchange.com/questions/4115262/is-there-any-english-translation-of-this-gergonne-paper from where it was crossposted to HSM.SE). Congrats on finishing! I have a suggestion for the rotated text. One can simply use the `graphicx` package to literally rotate any (I presume) text (in text mode or math mode), as in https://latexref.xyz/_005crotatebox.html . From some trial-and-error to match the vertical height (as in the original document), I found that with Computer Modern (default font), I can make the following happen:
ReplyDeletehttps://imgur.com/a/8jcNxLB
Here is a fully working Minimal Working Example .tex file that doesn't even need XeLaTeX :)
\documentclass{article}
\usepackage{graphicx}
\begin{document}
\newcommand{\invC}{\rotatebox[x=0em,y=0.22em ]{180}{$C$}}
\newcommand{\invA}{\rotatebox[x=0em,y=0.22em ]{180}{$A$}}
\newcommand{\invN}{\rotatebox[x=0em,y=0.22em ]{180}{$N$}}
\newcommand{\inva}{\rotatebox[origin=c]{180}{$a$}}
\newcommand{\invn}{\rotatebox[origin=c]{180}{$n$}}
$C$ versus $\invC$, $(A,N,a,n)$ and $(\invA,\invN,\inva,\invn)$
\end{document}
If you should decide to stick with a different font, you will no doubt have to change the parameter 0.22em into something more appropriate.
I have "myself" recently translated a paper (Sommes De Cesaro Et Multiplicateurs Des Developpements on Harmoniques Spheriques, Aline Bonami & Jean-Louis Clerc) from French into English, and aside from personal use (as a mathematician) I'm not sure what I should do with it. Don't think I will make a hobby out of it :) so I won't start my own blog. I literally know no french (other than what I picked up while translating!) so had to make lots of guesses with the help of DeepL and Google Translate.
If you end up fixing the rotated symbols using the above, I'd love to be pinged (somehow, I guess a comment on math.SE? My account there is also Calvin Khor) to see the result!
My apologies for the conflict with the MathJax plugin on your website :) RIght-clicking will allow you to view the source! In the event it does not, here is the important code with dollar signs removed
Delete\usepackage{graphicx}
\newcommand{\invC}{\rotatebox[x=0em,y=0.22em ]{180}{$C$}}
\newcommand{\invA}{\rotatebox[x=0em,y=0.22em ]{180}{$A$}}
\newcommand{\invN}{\rotatebox[x=0em,y=0.22em ]{180}{$N$}}
\newcommand{\inva}{\rotatebox[origin=c]{180}{$a$}}
\newcommand{\invn}{\rotatebox[origin=c]{180}{$n$}}
C versus \invC, (A,N,a,n) and (\invA,\invN,\inva,\invn)
Brilliant! This is 10x better than my current workaround, and no XeLaTex is a big plus. I'll make the replacements today.
DeleteAlso, congrats on your own translation, it's a labor of love for sure. I personally learned French from school and on my own afterwards, but if you ever need to translate French again and want a better grounding or a reference, look at Stack's *Reading French in the Arts and Sciences*, I recently found it in a bookstore and I'm using it as a reference for some phrasing and review, it seems like a great resource.
Congratulations on translating this important paper on logic. You have made a historically significant contribution to that history through this translation. I thank you and salute you, sir!
ReplyDelete