No Tapes! (yes - I use the Edna Mode voice)
Advice for better living
So you have a broken book. And you love this book. Do not apply tape to this book.
If the broken book is a paperback with a flat spine that is held together by glue (or not held together), there are ways to rebind it but again do not use tape. Use youtube or your handy neighbourhood bookbinder, but never tape.
I don't care if it's called book tape or archival or repositional or low tack. Adhesive and paper often mate for life and coming between them usually harms them both!
If love drives your actions, then secure the book with cotton ties (new shoelaces could work), place in a box to protect it, or even a ziploc bag. Or as this person did, needle and thread. Don't laugh it worked!