The actual source is Gregory the Great's sermons on Christmas. Not sure where the above comes from.

I provided it, and then asked for more. It gave me the following:

æternitatis gaudia. Nemo ab hac exsultatione secernitur, quia unus est omnium communis gaudii causa. Dominus enim noster peccatum venit redimere, non habuit. Excusent se tristitiae locum, quia vita commutata mortalitas consumpta est.

The actual text that follows is aeternitate laetitiam, so it matched aeternitate with the preceeding correctly and guessed rightly at the case of the object.

I asked for what would follow and its response:

"To provide an exact continuation, I’d need the full source text or reference."