'eosin-rich' originates from the word 'eosin' (from Greek 'Ēōs' meaning 'dawn', named for its rosy color) combined with the English adjective 'rich' (from Old English 'rice' meaning 'powerful/abundant').

'eosin' entered scientific English in the 19th century from New Latin/Modern Greek (via the dye name 'eosinum' derived from Greek 'Ēōs'), while 'rich' descended from Old English 'rice'; the compound form 'eosin-rich' arose in modern English usage in medical and histological descriptions.

Initially, 'eosin' referred specifically to the dye; over time it also came to describe tissues that take up that dye ('staining with eosin'), while 'rich' shifted from a sense of power/wealth to the common modern sense 'abundant in', yielding the current sense 'abundant in eosin'.