1520s, from French laxité, from Latin laxitatem (nominative laxitas) "width, spaciousness," from laxus "loose, lax" (see lax). An earlier noun was laxation (late 14c.). Laxness is from 1630s.
1540s, "state or quality of being ample," from French amplitude or directly from Latin amplitudinem (nominative amplitudo) "wide extent, width," from amplus "large, spacious" (see ample). Amplitude modulation in reference to radio wave broadcast (as opposed to frequency modulation) first attested 1921, usually abbreviated A.M. Related: Amplitudinous.
1630s, "a tangle;" 1832, "a broken thread, a loose end," from ravel (v.). As the name of a weaving instrument for guiding separate yarns, 1805, also raddle, but this is perhaps a separate word influenced by ravel.
RADDLE. In New England, an instrument consisting of a wooden bar, with a row of upright pegs set in it, which is employed by domestic weavers to keep the warp of a proper width, and prevent it from becoming entangled when it is wound upon the beam of a loom. [Bartlett, "Dictionary of Americanisms," 1848]