In a hasty, reckless, or forward-falling manner without thinking things through.
From 'headlong' (Middle English, from 'head' + 'long', meaning stretched out) plus the adverbial suffix '-ly'. The word originally meant literally falling head-first, but evolved to mean acting without caution.
This word is rarely used today, but it reveals how English speakers once loved adding '-ly' to almost any adjective—it's a relic of older, more verbose writing styles that preferred elaborate adverbs.
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