curb (n.)

late 15c., "strap passing under the jaw of a horse" (attached to the bit of the bridle and used to restrain the animal), from Old French courbe "curb on a horse" (12c.), from Latin curvus, from curvare "to bend," from PIE root *sker- (2) "to turn, bend." The same word was used late 14c. in the sense of "a hump," and in Anglo-Latin as "curved or arched piece of timber" (late 13c.).

Meaning "enclosed framework" is from 1510s, probably originally with a notion of "curved;" extended to margins of garden beds by 1731; to "margin of joined, upright stones between a sidewalk and road" by 1791 (sometimes in this sense spelled kerb). Figurative sense of "a check, a restraint, that which holds back" is from 1610s.

curb (v.)

1520s, of horses, "to lead to a curb," from curb (n.). Figurative sense of "bend to one's will, hold in check" is from 1580s. Related: Curbed; curbing.

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Definitions of curb from WordNet
curb (v.)
lessen the intensity of; temper; hold in restraint; hold or keep within limits;
Synonyms: control / hold in / hold / contain / check / moderate
curb (v.)
keep to the curb;
curb your dogs
curb (v.)
place restrictions on;
Synonyms: restrict / curtail / cut back
curb (n.)
an edge between a sidewalk and a roadway consisting of a line of curbstones (usually forming part of a gutter);
Synonyms: curbing / kerb
curb (n.)
a horse's bit with an attached chain or strap to check the horse;
Synonyms: curb bit
curb (n.)
the act of restraining power or action or limiting excess;
Synonyms: bridle / check
Curb (n.)
a stock exchange in New York;
Synonyms: American Stock Exchange / amex