Middle English rop, from Old English rap "strong, heavy cord of considerable thickness," from Proto-Germanic *raipaz (source also of Old Norse reip, West Frisian reap, Middle Dutch, Dutch reep "rope," Old Frisian silrap "shoe-thong," Gothic skauda-raip "shoe-lace," Old High German, German reif "ring, hoop"). Technically, only cordage above one inch in circumference and below 10 (bigger-around than that is a cable). Nautical use varies. Finnish raippa "hoop, rope, twig" is a Germanic loan-word.
It is attested by early 14c. as "a noose, a snare." Rope of sand (1620s) was an old figure for anything lacking coherence or binding power.
To know the ropes "understand the way to do something" (1840, Dana) originally was a seaman's term. The phrase on the ropes "about to be defeated" is attested from 1924, a figurative extension from the fight ring, where being in or on the ropes was a figure by 1829.
To be at the end of (one's) rope "out of resources and options" is attested by 1680s. An earlier expression was have too long rope "have too much freedom" (late 15c.).
Rope formerly also figured in slang and extended-sense expressions related to punishment by hanging, such as John Roper's window "a noose," rope-ripe "deserving to be hanged," both 16c. The figurative phrase give someone (enough) rope (to hang himself) is by 1680s.
adjective suffix, "full of or characterized by," from Old English -ig, from Proto-Germanic *-iga- (source also of Dutch, Danish, German -ig, Gothic -egs), from PIE -(i)ko-, adjectival suffix, cognate with elements in Greek -ikos, Latin -icus (see -ic). Originally added to nouns in Old English; used from 13c. with verbs, and by 15c. even with other adjectives (for example crispy).
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Definitions of ropy from WordNet
of or resembling rope (or ropes) in being long and strong;