Old English bog "shoulder, arm," extended in Old English to "twig, branch" (compare limb, n.1), from Proto-Germanic *bogaz (cognates: Old Norse bogr "shoulder," Old High German buog, German Bug "shoulder, hock, joint"), from PIE *bhagus "elbow, forearm" (cognates: Sanskrit bahus "arm," Armenian bazuk, Greek pakhys "forearm"). The "limb of a tree" sense is peculiar to English.