Much Better Than My First Thought

navybrat: ..."book binder's tape" or "book repair tape".
This is black fabric tape, about the same size as duct tape, but the difference is fabric and the type of adhesive used is less destructive to old paper....

Tim in GA: This is also called "gaff" tape, and can probably be found more inexpensively if searched for by this name....

Thanks. This is much better than my first (quickly dismissed) thought of trying some plain ol' masking tape.

If I can't get this book fixed with all these fine recommendations, it'll be because... I'm so lazy.