In the manner or direction of a curtain; positioned or arranged like a curtain would be.
From curtain (from Old French cortine, from Latin cortina meaning 'hanging') combined with the directional suffix -wise (from Old English wīse meaning 'manner' or 'way'). The combination emerged in Middle English to describe spatial orientation.
The -wise suffix is incredibly productive in English—we use it for clockwise, likewise, and lengthwise—but curtainwise is a rarer gem that shows how medieval people thought spatially about draped fabric, which was precious and carefully positioned.
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