Do the English have an ancient (obsolete) verb for the action of the book opening?
For example, in Russian we say otkrit' (open the book), but in the Old slavonic the verb razognuti (to unbend the book) was used.
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This is a very interesting question. There may not be an old word in English that does what you describe, but it is important to note that the English word "open" relative to a book meant something different in earlier times.
To open a book now usually means to part or spread the cover and the pages into a position so you can read the pages contained in the book.
However, books used to be made by folding sheets of paper larger than the page size and they would be sold without trimming the edges, so when you got your new book, it would be "unopened" meaning that you couldn't turn the pages. You had to "open" the book with a dull knife (like a letter opener) by ripping along the folds. (This is why some books have ragged edges of the text block, to evoke the memory of those ripped page edges.)
The OED has
e. transitive. To cut open the leaves of (a book) when they have been left joined along an edge during the making; to cut open (the leaves) of such a book.
You will find old books described (by knowledgable book dealers) as "unopened". This correctly means that the folded sheets are un-ripped; it doesn't mean that no-one has ever spread the covers and looked inside.
Until 1960, possibly later, Gallimard sold books unbound and uncut. 'Uncut' meant that the pages were still in their signatures with the outer edge of most pages presenting a folded edge. Before you read the book you had to 'cut the pages.' This was also the case in England 1820: even bound volumes had to have their pages cut.
There's an obscure joke, possibly Samuel Johnson, where a nouveau riche says "These books, they are my friends." To which the other replies, "I see you don't cut your friends." (Cutting your friend is to ignore them deliberately) Sorry, that's absurdly complicated. But 'Cut the pages,' or simply 'to cut,' is certainly an outdated word for opening a book.
The Shorter Oxford under 'paper' has -knife
[paper]-knife, a knife of ivory, wood, etc., used esp. to cut open the leaves of an uncut book.
The Middle English verb undon was often applied to opening a book (and many other objects).
c1300 SLeg.Fran.(1) (LdMisc 108)159 : He on-dude þe bok and þe furste þat he cam to Þat was a godspel. (He undid the book and the first that he came to - that was a gospel.)
a1325 SLeg.(Corp-C 145)354/166 : He…wende him sulf forþ is wei & þe oþer vndude þe bok. (He walked himself forth his way and the other undid the book.)
c1475 Mankind (Folg V.a.354)797 : All þe bokys in þe worlde, yf þei hade be wndon, Kowde not a cownselde ws bett. (All the books in the world, if they had been undone, could not have counseled us better.)
This meaning has since disappeared along with the book clasps that would have once been common on books. (To see a few examples of bindings, see "Medieval bindings" on the British Library site.)
One obsolete Middle English word for “open” is unschette (the opposite of modern shut), and a word that’s changed meaning and once meant opened is unlokynne (modern unlocked).
An old-fashioned word for reading a book that modern readers would still understand might be leaf through it.