1550s, from Middle French spiral (16c.), from Medieval Latin spiralis "winding around a fixed center, coiling" (mid-13c.), from Latin spira "a coil, fold, twist, spiral," from Greek speira "a winding, a coil, twist, wreath, anything wound or coiled," from PIE *sper-ya-, from base *sper- (2) "to turn, twist." Related: Spirally. Spiral galaxy first attested 1913.
1726 (implied in spiraled), transitive, from spiral (n.). Intransitive use by 1834. Transferred and figurative sense by 1922. Related: Spiraling.
1650s, from spiral (adj.). U.S. football sense is from 1896. Figurative sense of "progressive movement in one direction" is by 1897. Of books, spiral-bound (adj.) is from 1937.