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1580s, "a reduced image," from Italian miniatura "manuscript illumination or small picture," from past participle of miniare "to illuminate a manuscript," from Latin miniare "to paint red," from minium "red lead," used in ancient times to make red ink, a word said to be of Iberian origin. Sense development is because pictures in medieval manuscripts were small, but no doubt there was influence as well from the similar-sounding Latin words that express smallness: minor, minimus, minutus, etc.
"small," 1714, from minature (n.). Of dog breeds, from 1889. Of golf, from 1893.