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On Roman Republic and on imperial coins we see representations of statues, both equestrian and pedestrian, of Consuls adn Ediles, Emperors, Empresses, and Caesars.  Statues also appear in the interior and on the pediments, and on the steps of temples and triumphal arches, widh form the types of numerous Roman coins. 

Amongst other denarii of the Cornelia moneyers, relating to Sulla (the Dictator), is on, which, bearing for legend L. SVLLA IMP., and for type a military figure on horseback seems to derive illustration from a passage in Cicero, wherin he mentions a gilt statue of Sulla on horseback, erected to his honor in Rome. 

An equestrian statue was customarily erected in a city on the occasion of the reigning prince's arrival within its walls.  Vallant enumberates seven different equestrian statues of Augustus, as represented on rare coins, chiefly silver.  The statue of an Emperor or horseback (Imperator eques) is to be seen frequently on Imperial medals, sometimes in a military dress (paludatus), at other times in the garb of peace (habitu pacificatoris.)

See Cornelia.