Suppose a wizard whose Arcane Bond is a bonded item. Suppose the wizard owns multiple spellbooks.
A bonded object can be used once per day to cast any one spell that the wizard has in his spellbook and is capable of casting, even if the spell is not prepared.
(Bolded for emphasis. Note the singular: compare "in one of his spellbooks".)
Can the wizard select any spell from any spellbook he owns? Or does each wizard have one "primary" spellbook, one that is the only usable option for the ability? If so, what determines what spellbook is the one?
What about proximity to said spellbook? Does the wizard need to carry a spellbook in order to use the 1/day bonded item ability?
Moreover, what does his spellbook actually mean? What determines whether the wizard owns the spellbook? For instance, if a wizard buys a half-filled spellbook from a second-hand wizardry store, and fills some pages of it, does that count as his spellbook even though he isn't the sole author? If that's not the case, how can a wizard make a used spellbook his own?
Best Answer
Short Answer
'his spellbook' should be changed to something more sensible, like "any of their spellbooks" or "any spellbook on their person". The rules expect, for absolutely no good reason, that each wizard has exactly one spellbook and they carry it on their person at all times except for rare occasions when they are securing it hidden away in some variety of magically protected vault. Magically protected vault think and on person think don't seem to be aware of each other and on person think definitely dominates.
It's an easy fix, though-- you can even fix it just by getting creative with your definition of 'his spellbook' and claim that the RAW kinda works1
RAW Silliness
'his spellbook' is used several other times in the text. Let's look at what it means:
(emphasis added)
(Wayfinders)
(Memorize Page)
So, whatever 'his spellbook' is, it's the same 'his spellbook' that the Wizard has to study to prepare spells and that spells are instantly poofed into when the wizard levels up.
The spellbook a wizard starts with may or may not be 'his spellbook'; the rules refer to it only as a spellbook, much like those that can be purchased from the equipment section of the rulebook. Nonetheless, an entity need not be physically present to be studied, and adding spells to 'his spellbook' is possible both through levelling up and through the spell Memorize Page.
Since a wizard's spell are all in 'his spellbook' and a wizard preps by studying 'his spellbook' and adds spells to 'his spellbook' all without ever needing to physically interact with 'his spellbook' all you're doing by exploring the RAW wonkiness here is buffing wizards by making 'his spellbook' harder to destroy/endager/take away. That's... not really helpful for anything ever. Unless you're a wizard trying to protect 'his spellbook', which is currently a bunch of flamable paper in a backpack, in which case convincing your DM that 'his spellbook' is actually merely the platonic idea of a spellbook with no special relation to that specific physical copy may in fact be useful.
In any case, the RAW never specify what 'his spellbook' means, specifically, nor do they specify what ownership, possession, or 'his' means. Spellbook is relatively clear. Since the rules do not define these terms they are free to be defined however the GM sees fit, provided those definitions are compatible with the RAW.
1 Specifically, define a spellbook broadly-- a wizard's spellbook is the thing they stores their spells in. If they store their spells in several books it is the collection rather than any individual book that is 'his spellbook'; the books merely serve as component parts. You can additionally specify that ownership is possession, and more specifically physical possession, so that books in the wizard's personal library back at their estate don't count as 'his'. While this works (the second order consequences for magic items that rely on ownership and such are very much in line with the theme imposed on the wizard by this limitation), it's definitely gymnastic and it's probably simpler just to replace the rule with an equivalent and more clear-on-its-face houserule.
Oh, and obviously the 'his' in his spellbook is gender neutral.