proprius

Proprius, propria, proprium, first and second declension. The core sense is "belonging to this one and to no other", which is why it sits opposite communis, "shared", and alienus, "someone else's". What the thing belongs to goes in the genitive or the dative: proprium hominis est ridere, "laughing is peculiar to man".

The false friend is obvious once flagged. English "proper" now means correct or respectable, and Latin proprius never does; it means "own". The logicians made the second sense technical, a proprium being a property found in every member of a species and nowhere else, and that is the sense behind "proper noun". Spanish propio and French propre still lead with "own".