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engaged. Applied, attached, semi-engaged, inserted, or seemingly partly buried in a wall or pier, such as a column with half or more of its shaft visible, quite distinct from a pilaster. A fluted engaged column with more or less than half its shaft exposed creates difficulties at the junction with the wall because of the entasis unless the whole shaft is tilted back towards the wall, as Burnet did with the Ionic columns at the Edwardian extension to the British Museum, London (1904–14).