braggadocio

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Coined by Edmund Spenser as the personification of vainglory, empty boasting, and arrogant pretension in his epic poem The Faerie Queene published in 1590. The word derives from brag, with an ending added from Italian words that were in vogue in English at the time.

So a braggart and a braggadocio would be one and the same.

The word passed into general use by 1594, and over the next two hundred years came to mean the kind of talk in which such people engage.