Looking for an English translation of Levi-Civita's 1926 paper "Sur l'écart géodésique" ("On the geodesic deviation")

[JimWhoKnew]

I don't know what is the right sub-form for this question, so I post it here.

I'm looking for an English translation of Levi-Civita's 1926 paper "Sur l'écart géodésique" ("On the geodesic deviation"). Surprisingly, I couldn't find any translation on the web, although it is cited by many texts dealing with Fermi's coordinates.
Here is a link from Wikipedia to the original text. The paper begins on page 433 (book's numbering). Free OCR scans of the individual paper can also be found, but I'm not certain whether they are legit.
I tried to obtain a translation by using chatgpt and claude. Claude provided a readable summary, but unsatisfactory. The display of equations and inline mathematical symbols is poor.

I believe that many have faced a similar problem before. Is there a good tool (AI or otherwise) that provides a fine sentence-by-sentence translation, with a nice (LaTeX-like) display of the math?

I'd expect that with today's capabilities, such a task should be trivial. Am I that wrong?

Help will be appreciated.

 

[yisyelkencisi]

maybe tools like Mathpix Snip could help, i read somewhere that they’re very helpful. it can turn those equations into clean LaTeX that you can input the data into Claude 3.5 Sonnet for a context-sensitive translation.

 

[robphy]

Try google gemini.... with "Translate to English, together with typeset equations, into a pdf."
but you'll probably have to break up the document into chunks....
e.g., i want a line by line translation of the introduction and section 1 , including typeset equations, maintaining the rough page layout (so I can compare with the original)... in pdf format.
... of course, you'll have to check for correctness and hopefully-no-hallucinations.

(A few weeks ago, I was impressed when I asked it to render my handwritten notes as typeset equations.)

 

[JimWhoKnew]

Thanks @yisyelkencisi and @robphy.

The title of the thread was changed by the admins so it suits this specific forum better, but actually I'm interested in the more general question of finding an easy-to-use "mature" translation tool (and the new title may chase readers who are familiar with solutions away). If it was only the Levi-Civita paper, by the time it will take me to satisfactorily tweak the "general" engines, I can pay a French-speaking student for a manual translation.

Some commercial tools are available online. I thought that PF members may know more about this subject.

 

[robphy]

Thanks @yisyelkencisi and @robphy.

The title of the thread was changed by the admins so it suits this specific forum better, but actually I'm interested in the more general question of finding an easy-to-use "mature" translation tool (and the new title may chase readers who are familiar with solutions away). If it was only the Levi-Civita paper, by the time it will take me to satisfactorily tweak the "general" engines, I can pay a French-speaking student for a manual translation.

Some commercial tools are available online. I thought that PF members may know more about this subject.

I subscribe to Gemini Pro.
What I had posted in my reply is what I had tried,

(I drag-dropped a pdf of the section from your pdf.)

i want a line by line translation of the introduction and section 1 , including typeset equations, maintaining the rough page layout (so I can compare with the original)... in pdf format.

Your line-by-line translation containing both the Introduction and Section 1 is ready!

I have combined the two sections into a single document, formatted line-by-line to match the page breaks and visual layout of the original text, including all typeset equations.

Here are low-resolution images of some of the output.