brace: [14] English borrowed brace from Old French brace, which meant simply ‘(the length measured by) two arms’. It came from Latin bracchia, the plural of bracchium ‘arm’ (source of French bras ‘arm’, and also of various English technical terms, such as brachiopod [19], a type of shellfish, literally ‘arm-foot’). The word’s ultimate source was Greek brakhíōn ‘arm’, originally ‘upper arm’, which was formed from the comparative of brakhús ‘short’, a relative of English brief (the sense development is probably that the upper arm was named from being ‘shorter’ than the forearm).
Of the rather diverse range of meanings the word has in modern English, ‘pair’ derives from the original notion of ‘twoness’, while ‘strengthening or supporting structure’ owes much to the idea of ‘clasping’, mainly contained originally in the verb brace [14], from Old French bracier ‘put one’s arms around’ (a derivative of Old French brace). In English it now only means ‘support, strengthen’, the sense ‘clasp with the arms’ being reserved to embrace [14], from Old French embracer. => brief, embrace
brace (n.)
early 14c., "piece of armor for the arms," also "thong, strap for fastening," from Old French brace, braz "arms," also "length measured by two arms" (12c., Modern French bras "arm, power;" brasse "fathom, armful, breaststroke"), from Latin bracchia, plural of bracchium "an arm, a forearm," from Greek brakhion "an arm" (see brachio-). Applied to various devices for fastening and tightening on notion of clasping arms. Of dogs, "a couple, a pair" from c. 1400.
brace (v.)
mid-14c., "to seize, grasp," also "wrap, enshroud; tie up, fetter," from Old French bracier "to embrace," from brace "arms" (see brace (n.)). Meaning "to render firm or steady by tensing" is mid-15c., earlier in figurative sense "strengthen or comfort" (someone), early 15c., with later extension to tonics, etc. that "brace" the nerves (compare bracer "stiff drink"). Related: Braced; bracing.