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Honestly, "a fourth" sounds in this example much more pleasant to my ears. I was just thinking _(about) how it could be possible. Again I say: my school textbooks suck greatly!

Thank you!!!

I think that using "a" makes it less definite, hence "a fourth Rome", ie it's not definite because it hasn't yet happened.

"There's always a first time" - In general.
"There's always the first...