The history of the fountain begins in 19 BC with the completion of the Aqua Virgo aqueduct by Marcus Vipsanius Agrippa during the rule of Augustus.  The name of the fountain is derived from the "trivium" referring to the three roads that converged there.  A fountain was erected in the piazza in the time of Nicholas V, later to be demolished and replaced by another unfinished project for the new fountain by Bernini.  This unfinished project was again demolished to make way for the Salvi's fountain.