Alex-
"Solfeggio: They're not arbitrary; they're the first syllables of some latin or old french song, aren't they?"
Heck. Prob'ly. It's been so long since I studied it in college that the memories are a bit musty. It's taught using many different methods. The important part of the solfege/solfeggio method of sight-singing tho' is the concept of integrating sight reading with music theory.
Encyclopedia.com says solfege vocal exercises were invented by the Benedictine monk Guido d'Arezzo (c.990-1080).