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Borussia is the Latin word for Prussia, a former European state that comprised much of what today is Germany, Poland, Lithuania and Russia.
Clubs that are named Borussia are either based in the territory of this old kingdom, or are named after another entity that was named for Prussia. Borussia Monchengladbach is named for the former state of Prussia, while Borussia Dortmund is named after a beer brewery that was itself named for the former state.