Can you mark which words you are intrested in? I don't see much more than several times the name "Anna Hendriksdotter" and in the center "Skol Bibel" (school bible).

Starting from the top, the first marking is the word år = year, so "year 1855".

The second and third marking seem to be gnaset och gnäsät. This seems not to be a standard Swedish word and I couldn't find a place with this name either.

The word at fourth marking (left-pointing arrow) I can't decipher.

The fifth marking looks like gnäsö, somewhat similar to two words above.

Finally, the last marking are actually two words: doter in continuation from the preceding line (Hindriksdoter) and something like gore, non sure what it means.

In summary I can't find any clue on the relationship  between An(n)a Hindriksdotter and Erik Andersson.

If we are in the area of Värnamo there is a locality northwest of there called Gnosjö, medieval Gnogse and dialectically were pronounced Gnoks.

Source: https://sv.wikipedia.org/wiki/Gnosj%C3%B6_socken

Your bible seems to have variants Gnaset, Gnåsåt, Gnäsö -> so it is the best guess I can come up with.

If it is originally a School Bible it could just be the different students writing their names in the book!

Since poor farm students couldn't afford it themselves they could likely loan one from the school up to their confirmation!

[We still do that in Danish schools when students borrow a book for the whole year, so an old trusty book can have a long lists of students]

After use, wear and tear it could have been sold off cheaply to a student or someone entirely else.