Although "Steagles" was never registered as an official NFL trademark (the offical name was simply the Eagles) this was the popular nickname regarding the team.
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Etymology: The word comes from the Steagles team in the National Football League, which played for one season during World War Two.
In 1943, the Philadelphia Eagles and the Pittsburgh Steelers combined teams due because of an NFL contraction to eight teams caused by a lack of quality players due to armed services obligations. The consolidated team was officially called the Philadelphia-Pittsburgh Eagles-Steelers, but fans and sportswriters eschewed the awkward, run-on official name and dubbed the new fused team "The Steagles".
The Steagles played four games at Philadelphia's Shibe Park and two games at Pittsburgh's Forbes Field, going 5-4-1, the first winning record in the history of pro football in Philadelphia. In 1944, the Eagles went back to being their own team, while the Steelers merged with the Chicago Cardinals (converting back to singular status in 1945).
Thus, a "Steagle" is a one-year phenomenon, a unique, exciting event. It also symolizes something less than ideal that seemingly has become better through its idealization over time.