Curve
late Middle English: from Latin curvare ‘to bend’, from curvus ‘bent’. The noun dates from the late 17th century.
wiktionary
From Latin curvus(“bent, curved”). Doublet of curb.
etymonline
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]