In a manner that shows contempt or scorn; with an attitude of deep disrespect.
From contemning plus -ly (adverbial suffix). This double-stacked construction (verb + -ing + -ly) creates an adverb from the participle form.
Medieval scholars would use 'contemningly' to describe how tyrants or villains behaved toward common people—it captures not just the action but the attitude behind it, the sneering dismissal that accompanies the contempt.
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