To cause to shatter into fragments; to break into pieces or splinters.
From dis- + shiver (to break into fragments). 'Shiver' comes from Old English 'scifran' (to split or divide). The dis- prefix intensifies or emphasizes the sense of shattering.
Old English and Middle English speakers loved using 'dis-' as an intensifier, making words stronger—not just 'shiver' (break), but 'disshiver' (really shatter). Modern English mostly abandoned this intensifying 'dis-', preferring 'un-' for reversals.
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