Show of force

In the morphology class the professor dropped the first two lines of the Aeneid on me to analyse for morphology. And I realized a few things in the process.

1. I don't use a consistent parsing order. Case, number and gender were never ordered the same way twice.
2. I'm not sure how transparent compounds were to native Latin speakers.
3. I have absolutely no idea how to analyse qui.

For #1, that's probably just me being put on the spot. I don't think I'd do that in writing. For #2 I suggested a morphological breakdown of profugus as follows.

pro-fug-us

But would a Latin speaker say that pro- had some specific meaning in the same way that re- or ad- had when prefixed to a verb? I know we're taught about Latin compounds as being this way, so I suspect so. I'll leave it at that. #3 was by far the most interesting. The professor was trying to get me to analyse qui (nom, s, masc). Now, if it had been qui (nom, pl, masc), I'd have had it. Obviously.

qu-i
who-nom.pl.masc

But how does the singular version break up? One possible solution.

qu-i
who-nom.s.masc

But it's not very satisfying. After all, how does -i signal nom.s.masc? I'm not thinking of anything off hand. So the solution I took in class was to not analyze it. Qui (nom, s, masc) is qui is qui. The professor pushed a bit, but I couldn't justify it so it stood as unanalyzable.