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Is there any evidence that Fermat wrote on the margin of a book "I have discovered a truly marvelous demonstration of this proposition that this margin is too narrow to contain." Everyone repeats this, but is there an image of the note? And did people write on margins of books in the 17th century when books must have been truly expensive? Has any author looked at these questions?

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    $\begingroup$ "did people write on margins of books in the 17th century..." — Absolutely. The product was (and is) called marginalia. — "...when books must have been truly expensive?" — Yes. If books are expensive, you absolutely want to use their margins. Otherwise what would you have them do, buy a second book full of blank pages to write in? That'd be even more expensive! $\endgroup$ – Quuxplusone Feb 26 at 18:27
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    $\begingroup$ I was taught to always keep a pencil handy when reading in order to underline, circle, and write in margins, and probably assumed this is common, current, practice. Now I wonder what percentage of people actually do this. $\endgroup$ – Don Branson Feb 26 at 19:52
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    $\begingroup$ @DonBranson American public school children generally had it drilled into us not to ever write anything inside our books, which (until college) were typically school property and — given the US commitment to school funding — would often be re-used for literal decades before finally being retired. I know that I personally never grew out of the idea that I shouldn't "deface" books by writing in them, even the ones I own. Wynne's question sounds to me like it carries undertones of that same internalized hangup. $\endgroup$ – FeRD Feb 27 at 10:45
  • $\begingroup$ @FeRD - good point! $\endgroup$ – Don Branson Feb 27 at 14:00
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Yes, it is true. Fermat's own copy was used in the publication of Diophantus by Fermat's son Samuel, and he included Fermat's notes. The original with Fermat's handwriting is lost. https://www.joh.cam.ac.uk/library/special_collections/early_books/fermat.htm#:~:text=When%20reviewing%20his%20copy%20of,to%20fit%20in%20the%20margin. (The page with his most famous marginal note is reproduced, "Observatio Domini Petri de Fermat").

Fermat made many remarks on the margin of Diophantus. These remarks inspired Euler and others, and eventually all his statements were proved, though the proof of the last one took a while.

For the general question: yes people wrote on margins. I guess this was the original purpose of margins. Many old books were even bound with several blank pages in the beginning or more frequently at the end, to give more space for people to write their notes. Yes, books were expensive. But a book, especially a scientific one, was considered not a decoration object but rather a tool for work. And once one had some substantial thoughts or remarks when reading the text, the most natural place to record them was the margins, or sheets attached to the book. Please notice that paper for writing was also expensive.

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    $\begingroup$ +1 for contextualising contemporaneous margin writing. $\endgroup$ – J.G. Feb 26 at 6:40
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    $\begingroup$ Old books also had much larger margins than modern books - probably to accommodate the less accurate binding and trimming process. $\endgroup$ – jpa Feb 26 at 16:27
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    $\begingroup$ Do we have a source for “less accurate binding and trimming process”? I don't se why professional binders would need any more than a couple millimetres tolerance, just like printers didn't print characters all over the page. $\endgroup$ – DaG Feb 27 at 13:23
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    $\begingroup$ @AlexandreEremenko "Many old books were even bound with several blank pages [...] to give more space for people to write their notes". My impression is that while blank pages do give such space, the main reason they were there was to do with how books were printed/bound, where several (8/16/32) pages are printed on one sheet which is then folded and trimmed. Unless the book used an exact multiple of 8/16/32 pages, there would be blank ones left over. See Intentionally blank page on Wikipedia. $\endgroup$ – TripeHound Feb 28 at 10:51
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    $\begingroup$ @AlexandreEremenko In some cultures (if I'm not mistaken Iranian culture is one) people do write in the margins of books borrowed from the library. It's kind of like the comment culture here - to give notes to future readers of the book. I've never been to a library in Iran but I've been told by Iranian friends on two separate occasions that they enjoy reading margin notes from library books $\endgroup$ – slebetman Feb 28 at 13:44

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