mediumyoudaoicibaDictYouDict[medium 词源字典]
medium: [16] Latin medius meant ‘middle’ (it came from an Indo-European source that also produced English mid and middle). Its neuter form, used as a noun, has given English medium, but it has made several other contributions to the language, including mean ‘average’, medial [16], median [16], mediate [16] (and its derivatives immediate [16] – etymologically ‘acting directly, without any mediation’ – and intermediate [17]), medieval [19] (literally ‘of the Middle Ages’), mediocre, meridian, mitten, and moiety.

Its Italian descendant is mezzo ‘half’, which has given English intermezzo [19], mezzanine [18], mezzosoprano [18], and mezzotint [18].
=> immediate, intermezzo, mean, median, mediate, middle, mitten[medium etymology, medium origin, 英语词源]
medium (n.)youdaoicibaDictYouDict
1580s, "a middle ground, quality, or degree," from Latin medium "the middle, midst, center; interval," noun use of neuter of adjective medius (see medial (adj.)). Meaning "intermediate agency, channel of communication" is from c. 1600. That of "person who conveys spiritual messages" first recorded 1853, from notion of "substance through which something is conveyed." Artistic sense (oil, watercolors, etc.) is from 1854. Happy medium is the "golden mean," Horace's aurea mediocritas.
medium (adj.)youdaoicibaDictYouDict
1660s, "average," from medium (n.). The Latin adjective was medius. Meaning "intermediate" is from 1796. As a size designation from 1711. as a designation of cooked meat, it is attested from 1931, short for medium-rare (1881).