In 1622, Pope Gregory XV established a committee of cardinals called the Sacra Congregatio de Propaganda Fide (Latin for "sacred congregation for the propagation of the faith") to help arrange missionary work and increase the breadth of the Catholic faith. Occasionally, this was abbreviated down to just Propaganda, a word which in the 1790s began being used in irreligious contexts. By the mid-nineteenth century, the word had taken on a negative connotation and essentially described propaganda as what we imagine today. That Latin word from earlier, propaganda, is a gerund of the verb propagare, which meant "to propagate" (and is the etymon of our word propagate as well, for the curious). Once we break off the prefix pro-, the root takes us to the Proto-Indo-European reconstruction pag, meaning "to fasten".
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