'hemisphere' originates from Greek, specifically the word 'hēmisphairia' (ἡμισφαίρια), where 'hemi-' meant 'half' and 'sphaira' meant 'sphere' or 'ball'.

'hemisphere' passed into Late Latin/Medieval Latin as 'hemisphaerium' and via Old French/Latin forms was adopted into Middle English and eventually became the modern English 'hemisphere'.

Initially, it meant 'half of a sphere' in Greek; over time the term kept that geometric sense and extended to refer to halves of the Earth and halves of the brain.