"at the point of death," 16c., Latin, literally "in the farthest reaches," from ablative plural of extremus "extreme" (see extreme (adj.)).
Entries linking to in extremis
extreme adj.
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.).