The compound adjective 'three-county' is a modern English formation, transparently combining the cardinal number 'three' with the noun 'county'. The number 'three' has a deep Indo-European heritage, traceable to the PIE root tréyes, which evolved through Proto-Germanic into the Old English forms. 'County' entered English via the Norman French counté, itself derived from the Late Latin comitātus, a term rooted in the administrative and military jurisdiction of a comes (a companion to the emperor, later a count). The compound logically denotes an entity—such as a region, initiative, or agreement—that encompasses or pertains to three such administrative divisions, illustrating a straightforward pattern of English compounding for precise geographical or administrative description.

Structure: three (number) + county (administrative division) - three: From Old English þrīe, þrēo, from Proto-Germanic þrīz, from Proto-Indo-European tréyes. Functions as a cardinal number. - county: From Anglo-Norman counté, from Old French conté, from Late Latin comitātus ("jurisdiction of a count"), from Latin comes ("companion, count"). Functions as a noun denoting a territorial division.