The painting "The Oath of the Horatii"
http://rexcurry.net/pledgehoratii.html
might have inspired (or enlarged) the myth of the Roman salute. The
myth was also inspired by early movies that showed fictional Roman
scenes using a straight-arm salute. Those movies were inspired by the
original straight-arm salute of the pledge of allegiance to the U.S. flag
(from 1892). The "Roman salute" myth was reinforced when the salute
was adopted as the "Olympic salute" used at Olympic games on or before 1924.