I found an article that gives some excellent examples of this usage as well as practical tips for how to recognize it: Thomas Nelson, "The Third Qui, and Six Ways to Recognize It, or 'Who Happens, Maecenas?'"
Nelson begins by noting that there are three kinds of qui. The first two are ubiquitous, and found in the L&S entry for the first meaning of qui:
- Relative pronoun, e.g. "Qui dixit hoc mortuus est" = "He who said this has died."
- Interrogative adjective, e.g. "Qui vir hoc dixit?" = "Which man said this?"
The third meaning--which you are asking about--is under the second entry for qui in L&S:
- Interrogative/relative adverb: "in what manner? how? whereby? by what means? why?" Though it is used adverbially, L&S notes that it is an old ablative construction formed from quis.
Let's look at this more closely:
How rare is this form? Caesar and Livy never use it. Cicero uses it very rarely. Among poets and playwrights, however, it is quite common. Nelson looked through several plays by Plautus and Terence, and found that anywhere from 14-21% of the qui's are adverbial "how?"
What are some examples of this usage? Here are a few:
(1) First, the very first lines of Horace's Satires!
Qui fit, Maecenas, ut nemo, quam sibi sortem
seu ratio dederit seu fors1 obiecerit, illa
contentus vivat, laudet diversa sequentis?
The beginning "qui fit" means "How comes it...?"
(2) Next, consider a rare example from Cicero's In Verrem 2.5.3:
Vetus est quod dicam, et propter severitatem exempli nemini fortasse vestrum inauditum, L. Domitium praetorem in Sicilia, cum aper ingens ad eum adlatus esset, admiratum requisisse quis eum percussisset; cum audisset pastorem cuiusdam fuisse, eum vocari ad se iussisse; illum cupide ad praetorem quasi ad laudem atque ad praemium accucurrisse; quaesisse Domitium qui tantam bestiam percussisset; illum respondisse, venabulo; statim deinde iussu praetoris in crucem esse sublatum.
In this example, the praetor is not asking who struck the great beast: he is asking "by what means?" The answer, using the ablative of means, makes this clear: "With a hunting spear."
(3) Finally, as a representative example from the many examples that can be found in Plautus and Terence, consider the following lines from the Mercator:
Char. Plurimum tu scis. sed qui scis esse amicam illam meam?
Evt. Tute heri ipsus mihi narrasti.
Char: You know a lot. But how do you know that she is my girlfriend?
Evt: You yourself told me yesterday.
- How do I recognize this usage?
Nelson offers the following six practical tips:
- The whereby/how qui is usually interrogative.
- It is often marked further by being paired with a following quia: qui? quia “How . . . ? Because . . .”
- The most frequent associated idea is of knowing, with a form
of scire or gnoscere: qui scis, qui noveris? “How do you know?”
- Qui followed immediately by an adverb or comparative is
whereby/how/the way: qui minus quam . . . “How less than . . .”
- The obvious noun antecedent is not a person, but a tool:
machinas qui, “tools to __ with” (“with which to__”).
- If the context is of giving or seeking, qui is instrumental,
“how,” “a way,” “the means, “ e.g. da mi qui comparem “Give
me the means to buy . . .” There is no antecedent.