'anhydrously' originates from English, formed from the adjective 'anhydrous' (from Greek 'anhydros'), plus the adverbial suffix '-ly'; in Greek, the prefix 'a-' meant 'without' and 'hydor' meant 'water'.

'anhydros' (Ancient Greek ἀν- ‘without’ + ὕδωρ ‘water’) passed into Late Latin as 'anhydrus', which yielded English 'anhydrous'; adding the English suffix '-ly' formed the modern adverb 'anhydrously'.

Initially, it meant ‘without water’ (as an adjective: anhydrous); the adverb preserved this sense as ‘in a water-free state.’