The compound adjective 'three-inch' is a transparent combination of the cardinal number and the unit of length. 'Three' descends from the Proto-Indo-European root trei-, a fundamental numeral that gave rise to its equivalents across Indo-European languages, including Latin tres and Greek treis. 'Inch' has a more specific journey, originating from the Latin uncia, meaning 'a twelfth part', which entered Old English as ynce via early medieval measurement systems. The compound itself follows a straightforward English pattern of number-noun modification, where the literal, combined meaning of 'three units of one inch' directly describes a precise physical dimension.

Structure: three (number) + inch (unit of measurement) - three: From Old English þrīe, þrēo, of Proto-Germanic origin; related to Dutch drie and German drei, from an Indo-European root shared by Latin tres and Greek treis. Functions as the numerical quantifier. - inch: From Old English ynce, a borrowing from Latin uncia 'twelfth part (of a foot or pound)'. Functions as the unit of measurement.