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"hands and feet," uttermost parts of the body, early 15c., plural of extremity. Meaning "a person's last moments" is from c.1600.
late 14c., from Old French estremite (13c.), from Latin extremitatem (nominative extremitas) "the end of a thing," from extremus; see extreme, the etymological sense of which is better preserved in this word.
extremity ex·trem·i·ty (ĭk-strěm'ĭ-tē)
An end of an elongated or pointed structure.
A bodily limb or appendage.