Thanks, Pro and Qroqqa, for the clarifications. Qroqqa, what did Perseus do (besides cut off Medusa's head, of course) to get himself filtered? Is it that potty mouth of his?
By the way, do you think English sayings, like "Good things come in threes" and "Third time lucky" could go back to this Latin expression? There is a comparable saying in Slovene: "V tretje gre rado", which means something like "third time lucky".
Trium (genitive as in trium virorum) does seem to be an error that has crept in. Older books pretty consistently favour trinum. (Tritium in Google Books is a scanning error for italic trinum.) One source gives ternarium, which would I suppose be synonymous, as in the adverbs trini/terni. Annoyingly, Perseus is now filtered at work so I can't do the proper checking.