Etymology
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medium (n.)

1580s, "a middle ground, quality, or degree; that which holds a middle place or position," from Latin medium "the middle, midst, center; interval," noun use of neuter of adjective medius "in the middle, between; from the middle" (from PIE root *medhyo- "middle").

Many of the secondary senses are via the notion of "intervening substance through which a force or quality is conveyed" (1590s) and "intermediate agency, channel of communication" (c. 1600). From the former, via application to air, etc., comes the sense of "one's environment or conditions" (1865). From the latter comes the sense of "a print publication" (1795) which later grew into the meaning in media.

In spiritualism, "person who conveys spiritual messages," by 1853. In painting, in reference to oil, watercolor, etc., by 1854. The notion is "liquid with which pigments are ground or mixed to give them desired fluidity." Happy medium is the "golden mean," Horace's aurea mediocritas.

medium (adj.)

1660s, "average, middling," from medium (n.). The Latin adjective was medius. Meaning "intermediate" is from 1796. As a designation of size or weight, by 1711. As a designation of cooked meat between well-done and rare, it is attested from 1931; earlier was medium-rare (1881).

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Definitions of medium
1
medium (n.)
a means or instrumentality for storing or communicating information;
medium (n.)
the surrounding environment;
fish require an aqueous medium
medium (n.)
an intervening substance through which signals can travel as a means for communication;
medium (n.)
(bacteriology) a nutrient substance (solid or liquid) that is used to cultivate micro-organisms;
Synonyms: culture medium
medium (n.)
a liquid with which pigment is mixed by a painter;
medium (n.)
(biology) a substance in which specimens are preserved or displayed;
medium (n.)
an intervening substance through which something is achieved;
the dissolving medium is called a solvent
medium (n.)
a state that is intermediate between extremes; a middle position;
a happy medium
medium (n.)
someone who serves as an intermediary between the living and the dead;
he consulted several mediums
Synonyms: spiritualist / sensitive
medium (n.)
(usually plural) transmissions that are disseminated widely to the public;
Synonyms: mass medium
medium (n.)
an occupation for which you are especially well suited;
Synonyms: metier
2
medium (adj.)
around the middle of a scale of evaluation;
medium bombers
Synonyms: average / intermediate
medium (adj.)
(meat) cooked until there is just a little pink meat inside;
From wordnet.princeton.edu