Etymology
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metric (adj.)

"pertaining to the system of weights and measures based on the meter," 1855, from French métrique, from mèter (see meter (n.2)). In this sense, metrical is attested from 1797. Metric system is attested by 1855.

metric (n.)

"science of versification," 1760, from Latinized form of Greek he metrikē "prosody," plural of metron "meter, a verse; that by which anything is measured; measure, length, size, limit, proportion" (from PIE root *me- (2) "to measure"). Middle English had metrik "the branch of music which deals with measure or time" (late 15c.), from Medieval Latin metricus.

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Definitions of metric
1
metric (n.)
a function of a topological space that gives, for any two points in the space, a value equal to the distance between them;
Synonyms: metric function
metric (n.)
a decimal unit of measurement of the metric system (based on meters and kilograms and seconds);
convert all the measurements to metric units
it is easier to work in metric
Synonyms: metric unit
metric (n.)
a system of related measures that facilitates the quantification of some particular characteristic;
Synonyms: system of measurement
2
metric (adj.)
based on the meter as a standard of measurement;
the metric system
Synonyms: metrical
metric (adj.)
the rhythmic arrangement of syllables;
Synonyms: measured / metrical
From wordnet.princeton.edu