Etymology
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curve (v.)

early 15c. (implied in curved), intransitive, "have or assume a curved form," from Latin curvus "crooked, curved, bent," and curvare "to bend," both from PIE root *sker- (2) "to turn, bend." Transitive sense of  "cause to take the shape of a curve, bend" is from 1660s.

curve (n.)

1690s, "curved line, a continuous bending without angles," from curve (v.). With reference to the female figure (usually plural, curves), from 1862; in reference to statistical graphs, by 1854; as a type of baseball pitch that does not move in a straight line, from 1879. An old name for it was slow. "Slows are balls simply tossed to the bat with a line of delivery so curved as to make them almost drop on the home base." [Chadwick's Base Ball Manual, 1874]

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Definitions of curve
1
curve (v.)
turn sharply; change direction abruptly;
Synonyms: swerve / sheer / trend / veer / slue / slew / cut
curve (v.)
extend in curves and turns;
Synonyms: wind / twist
curve (v.)
form an arch or curve;
her hips curve nicely
Synonyms: arch / arc
curve (v.)
bend or cause to bend;
the road curved sharply
Synonyms: crook
curve (v.)
form a curl, curve, or kink;
Synonyms: curl / kink
2
curve (n.)
the trace of a point whose direction of motion changes;
Synonyms: curved shape
curve (n.)
a line on a graph representing data;
curve (n.)
a pitch of a baseball that is thrown with spin so that its path curves as it approaches the batter;
Synonyms: curve ball / breaking ball / bender
curve (n.)
the property possessed by the curving of a line or surface;
Synonyms: curvature
curve (n.)
curved segment (of a road or river or railroad track etc.);
Synonyms: bend
From wordnet.princeton.edu