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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.