This is the paper:

“Variétés. Essai de dialectique rationnelle”. Annales de Mathématiques pures et appliquées, tome 7 (1816-1817), p. 189-228

(“Varieties. Essay about rational dialectic”, By J.D. Gergonne). Between else, in this paper we find the first use of the symbols “C” and “Ɔ”, which later evolved into the modern symbols “$\subset$” and “$\supset$”, used in set theory and, in older texts, for implication.

You can find it here, in French.

If there isn't any, I believe it deserves one. I would certainly do it, if I could.

Copied from Math StackExchange, after sugestion from the user Rob Arthan.

  • 1
    $\begingroup$ He was Joseph Diaz Gergonne: M.Gergonne stands for Monsieur (Mr) Gergonne. $\endgroup$ Commented Apr 28, 2021 at 11:49
  • 1
    $\begingroup$ Thanks, I should be more careful. $\endgroup$ Commented Apr 28, 2021 at 18:24
  • $\begingroup$ I'll look into translating this. I just finished Poisson's first memoir on electricity from french, from around the same time, and I rather like the process of translating anyway. $\endgroup$ Commented Apr 29, 2021 at 14:08
  • $\begingroup$ @SamGallagher Excellent! When you are done, please let us know how we can access your work. $\endgroup$ Commented Apr 29, 2021 at 18:35
  • 1
    $\begingroup$ @ArisMakrides I did a bit of the introduction and it's quite dense, being mostly about philosophy and whatnot, but it's not impossible. It will be slow going, and its dependent on my free time, so I wouldn't expect a copy in your hand tomorrow. Probably more like 2022... Either way, I'll post it on my history of math and science website: histomathsci.blogspot.com $\endgroup$ Commented Apr 29, 2021 at 18:55

2 Answers 2


Because I'm fond of translating old math and science papers, particularly from French and Latin, I decided to start a new translation project for this work into English. You can check the progress at my website here, where I post translations. This project could take some time, if only because the text requires careful reading to ensure the meaning is properly conveyed. I'm hoping to finish by this July.


Finished rough draft of the translation May 30, far ahead of schedule (hooray!). The translation is available here. Typesetting problems from a previous version are now fixed, but I also posted the original .tex for anyone to experiment with.

  • $\begingroup$ Have you tried machine translation of older texts? I am quite interested in exploring the utility of machine translation in symbolically heavy texts. $\endgroup$
    – ACR
    Commented May 31, 2021 at 18:36

I doubt that there is an English traslation, and old papers that quote it are in French (e.g. Peano, Origine du signe $\subset$ in L'Intermédiaire des Mathématiciens, 1903, or Giard, La « dialectique rationnelle » de Gergonne in Revue d'histoire des sciences, 1972, this paper in particular is very interesting, as it gives a detailed analysis of Gergonne's original paper that is not always so clear). Anyway, small parts are reported in the invaluable collection of Bocheński Formale Logik (1956), translated into English as A history of formal logic (1961). The translation is easy accessible (here a digitalized copy). You will find some excerps at page 277 ($\S$ 38.15 and 38.16), with this comment of Bocheński "This text is not altogeter clear; Gergonne seems to equate the (Aristotelian) use of variables with formalism. But we can see the idea of formalism becoming clearer", and at page 304 ($\S$ 40.12).

Maybe some other author translated wider excerpt of Gergonne's paper in English, but I haven't been able to find any of them.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.