In a manner relating to or characteristic of the Celts, their languages, cultures, or traditions.
From Celtic (the adjective) plus the adverbial suffix -ly, which converts adjectives into adverbs. This straightforward formation has been used in English academic writing since the 19th century.
Adding -ly to adjectives to make adverbs is so automatic in English that we barely notice it, but some words just sound silly when you do it—'Celtically' actually works pretty well compared to something like 'Latinically,' which everyone just says 'in Latin' instead.
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