early 15c. (implied in curved), from Latin curvus "crooked, curved, bent," and curvare "to bend," both from PIE root *(s)ker- (2) "to turn, bend" (see ring, n.).

1690s, "curved line," from curve, v.. With reference to the female figure (usually plural, curves), from 1862; as a type of baseball pitch, from 1879.