Signior Bassanio, hear me: If I do not put on a sober habit, Talk with respect, and swear but now and then, Wear prayer-books in my pocket, look demurely, Nay more, while grace is saying, hood mine eyes Thus with my hat, and sigh, and say ’amen’; Use all the observance of civility, Like one well studied in a sad ostent To please his grandam, never trust me more.
There are no more uses of "demure" in the play.
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the shy, demure, innocent type
The fire in her eyes belied an otherwise demure countenance.