The compound adjective 'three-layer' is a transparent modern English formation. Its first element, 'three', descends from the Proto-Indo-European numeral treies-, a root foundational to counting systems across Indo-European languages, evident in Latin tres and Greek treis. The second element, 'layer', originates from the action of laying something down, derived from the Old English verb lecgan. The conceptual logic is straightforward: it literally describes an object composed of three distinct strata that have been placed or formed one upon another, moving from the ancient act of placing to the modern technical description of a composite structure.

Structure: three (number) + layer (stratum) - three: From Old English þrīe, þrēo, of Germanic origin; related to Dutch drie and German drei, from an Indo-European root shared by Latin tres and Greek treis. Functions as a numerical quantifier. - layer: From Middle English leyer, legger, an agent noun from leyen (to lay). The base verb lay (to place) is from Old English lecgan, of Germanic origin. Functions as a noun indicating a single thickness or stratum of material.