Actually, as I understand it (and I admit this isn't very far), the Greek text at this point is not certain. It may read eudokia (nominative), which would agree with the Authorised (King James) Version: Glory to God in the highest, and on earth peace, good will toward men., or it may read eudokias (genitive) which would be closer to the Latin version Faldage quotes.

It is also possible that the Greek says something completely different, as the NRSV says:
... and on earth peace among those whom he favours, with peace, goodwill among people, relegated to a footnote.

Bingley

Bingley