# Translations of Darboux's "Leçons Sur La Théorie Générale Des Surfaces"

This might be slightly stretching the boundary of acceptable questions, but I think this is the best group to ask.

I'm interested in the classic 1887 texts "Leçons Sur La Théorie Générale Des Surfaces Et Les Applications Géométriques Du Calcul Infinitésimal" by French mathematician Jean Gaston Darboux (and which can be read online in very high quality scans thanks to the University of California here). They were very influential in their time in establishing the fledgling field of differential geometry, and introduced many of its fundamental tools (such as, not surprisingly, the Darboux frame).

My question is, has this work ever been translated into English? I can find many editions of the original French version, but I have been unsuccessful in finding any of the four volumes in English. I've checked the usual suspects (Dover, etc.) and my University's catalogue, but nothing comes up for the straightforward translation of the title (Lessons on the General Theory of Surfaces and the Geometric Applications of Infinitesmal Calculus) or the author's name. Was it retitled, perhaps, in translation?

Secondly, and on a very related note, does anybody know for certain the copyright status of the original work (not any particular subsequent editions)? If this was published in America, I would expect the copyright to expire 70 years after Darboux's death in 1917, but perhaps things work differently in France. The UC site I linked above lists "Possible copyright status: NOT_IN_COPYRIGHT" but that doesn't sound very reassuring to me. If somebody were to attempt a translation today, would they run into any legal restrictions, or is it essentially in the public domain by now?

• The book is so beautifully written... It'd be a real challenge to translate it and not break that! Mar 30 '11 at 20:39
• I remember a similar discussion about the EGAs by Grothendieck. I know that in the end people just started translating the work without worrying much about copyright and that for two good reasons. The first one is that pure mathematics cannot be patented, so copyright laws only apply if you tried to sell the translated work, if you make it available to the public for free, not much can be said. The second reason is that this kind of work should be public and free anyway. So my suggestion in the end would be: start a wiki to translate the document and let the community participate! Mar 30 '11 at 22:12
• @David Kohler: Thanks very much for your comment; beginning a (possibly crowdsourced) translation effort is exactly what I had in mind, as I hinted not-so-subtly. Unfortunately, I don't think the copyright situation is quite as simple as you suggest. "copyright laws only apply if you tried to sell the translated work" sounds very suspicious to me. If I "translated" Harry Potter into another language I'm fairly certain I wouldn't be allowed to post it online even for free. But thanks for the encouraging words :) (Plus, I don't see why someone like Dover shouldn't publish it if it was done) Mar 30 '11 at 22:21
• French copyright laws also have the 70 years clause but the matters are a bit more complicated than that (after all, we're speaking of the French bureaucracy here) because some years don't count (due to WW I/II). The original editor no longer exists and there are plenty of new editions of reprints from publishers I never heard of (see amazon, for example). This strongly suggests (to me) that the copyright no longer applies. I couldn't find any evidence that there already is an English translation.
– t.b.
Mar 30 '11 at 23:15
• I'm letting my romantic ideas of pure mathematics protected from copyright law dominate my answer there :) I can understand how work of fiction should be protected, mathematics on the other hand as being a collaborative effort to raise human collective knowledge should be free of copyright in my opinion. After some research I ended up at the same conclusion than @Theo and would start a collective effort protected by some Creative Commons license to avoid nasty people like Dover or Springer. By the way I speak French as well, so I'd be happy to help, keep in touch! Mar 31 '11 at 8:15

I don't claim to be an expert in french, but I would be happy to help with translations from french into english. Sometimes, putting words into software like google translate will not be enough. For example, look at this sentence:

Soit $E = (C[0, 1], \mathbf{\mathbb{R}})$ le $\mathbf{\mathbb{R}}$-espace vectoriel des applications continues de $[0, 1]$ vers $\mathbf{\mathbb{R}}$, muni de la norme $N_\infty$.

It is not hard to translate such as sentence. However, words like "soit" which is the verb "to be" in the third person singular of the subjunctive may mean something else for a translator, where as here it means "given" or "let".

I'd be happy to help you translate specific sentences, but not a whole text!

Ben

• Thanks David :) I appreciate the offer, and I'll keep in touch with you if I go ahead with this, although my French is pretty strong as well. However, at the moment I'm just trying to determine if a) this has already been done, and b) if there are legal barriers to me doing it. Mar 30 '11 at 22:47
• Not to be too picky... but (that's the standard introduction to gereat displays if pickiness!) soit is in the imperative :) Apr 30 '11 at 2:52
• Hey, it looks like I am getting this party started. I've set up a project over at github.com/apetresc/Lecons-Sur-La-Theorie-Generale-Des-Surfaces. Can you read through the README and let me know if you'd be interested in volunteering as a Language Reviewer? I'd much appreciate it :) Thanks! Jul 28 '11 at 9:28
• @Adrian Petrescu Yeah I'd be willing to help :D
– user38268
Jul 28 '11 at 11:37
• @D Lim: Great! Please e-mail me at apetresc@gmail.com so we can coordinate further :) Jul 28 '11 at 11:43