extremity n.

early 15c., "outermost, farthest;" also "utter, total, in greatest degree" (opposed to moderate), from Old French extreme (13c.), from Latin extremus "outermost, utmost, farthest, last; the last part; extremity, boundary; highest or greatest degree," superlative of exterus (see exterior). In English as in Latin, not always felt as a superlative, hence more extreme, most extreme (which were condemned by Johnson). Extreme unction preserves the otherwise extinct sense of "last, latest" (15c.).

early 15c., "hands and feet, uttermost parts of the body," plural of extremity. Meaning "a person's last moments" is from c. 1600.