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I am precisely referring to the following, first volume of the textbook/lecture notes/monograph written by Beniamino Segre in the fifties of the twentieth century (I own a copy of the second volume)

Beniamino Segre, Forme differenziali e loro integrali. Vol. I.: Calcolo algebrico esterno e proprietà differenziali locali, Docet, Edizioni Universitarie. Roma: Istituto Nazionale di Alta Matematica 520 pp. (1951), MR49646, Zbl 0045.19702.

The copy of the book belonging to the Library of the University of Michigan has been digitized by Google, but does not seem available on the internet. I've been searching the used book market for a long time, but without success, so I've decided to ask Math.Overflow for help: does someone know where a digitized or even a paper copy of this opus could be available?

Why am I interested in such an old relic? Because possibly it is the only opus on differential forms written in Italian by a leading mathematician (if we do not consider the unpublished "Higher analysis" lecture notes of Gaetano Fichera). Furthermore, there are results that aren't easily available from sources other than the original publications (see for example this Q&A).

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Why not just do what Google did, digitize it yourself?

According to WorldCat the book is present in many libraries. You could borrow it and scan it using a book scanner. This may require an investment in such a device, but it is such a time saver when scanning speed is more important than scan quality. (I mean, you wouldn't use a book scanner to scan a photograph, but for a printed page it is entirely adequate.) A book scanner will scan a 500 page book such as this in less than half an hour, with an OCR-ed pdf file as output.

My own experience is in scanning old Ph.D. theses from my Institute. Here are examples of the output quality you can expect from a low-end book scanner (mine is from CZUR). The quality is less with newer books that have glossy pages, because of reflections. Older books give better results.

Note that a book scanner does not in any way damage the book, so you can safely use it on a library copy. The opened book is photographed from the top, software corrects for the curved pages and splits the two pages into separate images. It is usually operated with a foot pedal, while you turn the pages one by one.


Our library has the book, I have borrowed it and scanned it. It is not typeset but handwritten, in a beautiful regular handwriting. I guess this has become a lost skill.

Because it is handwritten, OCR fails and the scan is very large (140 MB). Transfer via a web browser is not ideal, if you write me an email I will send you a Dropbox link. [[email protected]]

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  • $\begingroup$ Thanks Carlo. I'll try to see if some of the libraries listed by WorldCat lets me bring out of the building the volume: I have already an old scanner, but unfortunately this is not portable. Possibly I'll accept later your answer. $\endgroup$ Commented Oct 29 at 5:30
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    $\begingroup$ if it does not work out for you, and you would be happy with such a solution, I could scan it for you (our library has the book and would allow me to borrow it) $\endgroup$ Commented Oct 29 at 6:56
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    $\begingroup$ I had some time this afternoon, and scanned it. $\endgroup$ Commented Oct 29 at 15:50
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    $\begingroup$ Carlo, you are wonderful. My librarian has not yet answered and you have already scanned the document... you deserve me accepting your question. And I'll write you as soon as possible. 😊 $\endgroup$ Commented Oct 29 at 16:29
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    $\begingroup$ I second Daniele, Carlo - you are wonderful. I very much appreciate your contribution, especially towards reference/history type questions. $\endgroup$
    – pinaki
    Commented Oct 30 at 3:19

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