Via Richard Muller, Theodore Beza answers as follows:
Indeed the term mediator describes nothing other than the office and work of reconciliation, which would not have been possible unless this one was at once both God and man. For if he had been only man, human nature would have remained ever separate from divinity: and if, similarly, he was only God, God could not have been conjoined with man: and thus Christ would not have been mediator, that is, would not have reconciled God and man, which Augustine intended by his statement, “Divinity without humanity does not mediate, and humanity without divinity does not mediate…” that is, Christ is not mediator or reconciler, as God alone or as man alone, but as the man-God and God-man, in one and the same person.
Epistolarum theologicarum Theodori Bezae Vezelii, p160
More from Muller next week (assuming I have an internet connection) where Ursinus helps us on the Trinity (in particular the eternal generation of the Son).