English 'hemisphere' from Greek 'hēmisphaírion' — literally 'half-sphere,' from 'hēmi-' (half) + 'sphaîra' (globe).
A half of the earth, usually divided by the equator (north/south) or a meridian (east/west); a half of the brain.
From Latin 'hēmisphaerium,' from Greek 'hēmisphaírion,' composed of 'hēmi-' (half) + 'sphaîra' (ball, globe, sphere). Greek 'hēmi-' comes from PIE *sēmi- (half), which also produced Latin 'sēmi-' (half, as in 'semicircle'), Sanskrit 'sāmi-' (half), and Old High German 'sāmi-' (half). The two prefixes 'hemi-' and 'semi-' are thus cognates — the same PIE word inherited through Greek and Latin respectively. Greek 'sphaîra' is of uncertain origin, possibly pre-Greek, referring originally to a ball used in games before being applied
Greek 'hēmi-' and Latin 'sēmi-' are the same PIE word *sēmi- (half) that evolved differently in each language. English uses both: 'hemisphere' (Greek half), 'semicircle' (Latin half). The term 'cerebral hemisphere' (for the two halves of the brain) was coined in the 17th century, and the popular idea that the left hemisphere is 'logical' while the right is 'creative' is a vast oversimplification of brain neuroscience.