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mesh (n.)

late 14c., mesche, "open space in a net or netting," probably from late Old English max "net," earlier mæscre, from Proto-Germanic *mask- (source also of Old Norse möskvi, Danish maske, Swedish maska, Old Saxon masca, Middle Dutch maessce, Dutch maas "mesh," Old High German masca, German Masche "mesh"), from PIE *mezg- "to knit, plait, twist" (source also of Lithuanian mezgu, megzti "to knit," mazgas "knot"). In machinery, "the engagement of the teeth in gearing" (by 1875). Mesh-work in netting is attested by 1785.

mesh (v.)

1530s, originally in the figurative sense of "entangle, involve;" the literal transitive sense of "to catch in a net, entangle" is from 1540s; from mesh (n.). Literal sense "to become enmeshed" is from 1580s. Intransitive sense of "become engaged," as the teeth of one wheel with those of another, is by 1850. The figurative sense of "to fit in, combine" is by 1944. Related: Meshed; meshing.

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Definitions of mesh from WordNet
1
mesh (n.)
the number of openings per linear inch of a screen; measures size of particles;
a 100 mesh screen
100 mesh powdered cellulose
mesh (n.)
contact by fitting together;
the meshing of gears
Synonyms: engagement / meshing / interlocking
mesh (n.)
the topology of a network whose components are all connected directly to every other component;
Synonyms: mesh topology
mesh (n.)
an open fabric of string or rope or wire woven together at regular intervals;
Synonyms: net / network / meshing / meshwork
mesh (n.)
the act of interlocking or meshing;
Synonyms: meshing / interlock / interlocking
2
mesh (v.)
keep engaged;
Synonyms: engage / lock / operate
mesh (v.)
coordinate in such a way that all parts work together effectively;
Synonyms: interlock
mesh (v.)
work together in harmony;
mesh (v.)
entangle or catch in (or as if in) a mesh;
Synonyms: enmesh / ensnarl
From wordnet.princeton.edu