The "seven mountains" referred to are actually the seven hills of Rome, and the "man of the seven mountains" was a term occasionally in use as a synonym for the Roman emperor – so Hamilton is drawing a parallel here between his plans for vesting power in a "unitary executive", or president – albeit one to be elected every four years – and the existence of an equivalent supreme power in a variety of other polities.

The earliest use of the term that I have found is in a letter written by Symmachus, the prefect of Rome in c.360 CE, where it is applied more generally to a Roman citizen.