In a way that causes death or has deadly consequences; in a way that results in failure or disaster.
From 'fatal' (from Latin 'fatalis'—determined by fate) plus '-ly' (adverb ending). Describes something that has fatal results.
Interestingly, 'fatal' comes from the same root as 'fate'—the Romans believed that some things were determined by the Fates, goddesses who controlled destiny. So 'fatally' literally means something happened as if determined by fate.
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