Arnauld and Nicole, excerpt from The Port-Royal Logic

Some food for thought:

According to Arnauld and Nicole (A&N), when we use a name to refer to something at two different times, it can actually refer to two different things. The name “Rome” refers to a city made of brick and also to a different city made of marble. Under what conditions, according to A&N, are there different things referred to by the same name? In the case of Rome, the matter making up the city was almost entirely different on the two occasions. Would there be two different things if the matter making them up were only slightly different? ... if the matter making them up were identical, but the matter was arranged differently? if ... the matter and arrangement of matter is identical but the matter is hotter the second time? ... if the matter was identical and arranged identically, but time has simply passed?

If I lived in Rome for many centuries, would it be true for me to say that I have lived in multiple cities (according to A&N)? You, in contrast, lived in Rome, Italy for a few years and then moved to Rome, New York. Intuitively, I would contrast my case with yours by saying “I’ve lived in the same Rome for centuries” or “I’ve lived in the same city for centuries.” Are these claims actually true, according to A&N?