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In A&G on indefinite pronouns there are two sentences of a similar structure:

Bonus liber melior est quisque quō mâior. (The larger a good book is, the better.)

Quō quisque est sollertior, hōc docet īrācundius (The keener witted a man is, the more impatiently he teaches.)

This quisque quo formulation does seem strange to me. What it is the function of quo here? Couldn't we simply omit the quo in the second sentence for example? if that's not the adverbial quo why not use the nom. case?

Does "quo...hoc" the same as "ut...ita"?

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Lewis & Short have hidden this in their entry for qui/quae/quod (and not, as I would have thought, in the dedicated entry for quo) – II,E,2,b:

Quo, abl. neutr., with compp. (with or without hoc, eo, or tanto): quo … eo, by how much, by so much, the … the: “quo difficilius, hoc praeclarius,” Cic. Off. 1, 19, 64.

So the construction is quo + comparative. It does not have to be followed by hoc, eo, etc.; instead it can stand on its own and then may be translated as “all the more …” For example, Cicero in De Amicitia 86, after describing circumstances where careless friendships can lead to problems, summarises:

Nam implicati ultro et citro vel usu diuturno vel etiam officiis repente in medio cursu amicitias exorta aliqua offensione disrumpimus. Quo etiam magis vituperanda est rei maxime necessariae tanta incuria.
For after we have been entagled from their side and from ours, be it by long acquaintance or even by obligations, we suddenly break up in the middle of the friendship because some offence has come up. All the more must such great carelessness in a matter of such necessity be criticized.

Then of course you have the quo … eo/hoc/tanto variant, which is the equivalent of the English the … the (which is weird enough itself, by the way—the Latin makes more sense to me personally). The construction has no particular connection to the indefinite pronoun, as can be seen by the example quoted by L & S (quo difficulius, hoc praeclarius), which is just put out there by Cicero as a general rule. Other examples are the proverbs:

  • Quo plura habent, eo cupiunt ampliora. (The more people have, the more they want.)
  • Quo plures hostes, tanto maior honor. (The more the enemies, the greater the glory.)

Note that instead of pro, you will also find quanto as a precedent for tanto, like this: quanto diutius abest, magis cupio tanto et magis desidero (Terence, Heautontimorumenos 3,1,15).

But if you want to say: “The larger a book is,” then you say: Quo maior est quisque liber (and not aliqui liber), which is what A & G are describing here.

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