"having no rim or rims" (of spectacles, etc.), by 1802, from rim (n.) + -less.
Entries linking to rimless
rim n.
Old English rima "edge, border, verge, coast," as in særima "seashore," literally "rim of the sea," and dægrima "dawn," literally "rim of the day." Related to Old Norse rime, rimi "a raised strip of land, ridge," Old Frisian rim "edge." "There are app. no parallel forms in the other Teutonic languages" [OED]. but with no other known cognates.
As "the circular part farthest from the axis of a wheel," c. 1400. The general sense of "border or edge of anything," typically a circular border raised above the enclosed surface, is by c. 1600. The snare drummer's rim shot (striking the rim and the head at once) is recorded from 1934. In political geography, rimland for "peripheral region of political or strategic significance" is by 1944.
-less
word-forming element meaning "lacking, cannot be, does not," from Old English -leas, from leas "free (from), devoid (of), false, feigned," from Proto-Germanic *lausaz (cognates: Dutch -loos, German -los "-less," Old Norse lauss "loose, free, vacant, dissolute," Middle Dutch los, German los "loose, free," Gothic laus "empty, vain"), from PIE root *leu- "to loosen, divide, cut apart." Related to loose and lease.