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.
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]