Etymology
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ordinate (adj.)

late 14c., "regular, normal," of behavior, thoughts, etc., "properly directed, proper," from Latin ordinatus, past participle of ordinare "arrange, set in order," from ordo (genitive ordinis) "row, rank, series, arrangement" (see order (n.)). Related: Ordinately.

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ordinate (v.)

1560s, "ordain, appoint authoritatively" (a sense now obsolete); 1590s, "direct, dispose," from Latin ordinatus, past participle of ordinare "arrange, set in order," from ordo (genitive ordinis) "row, rank, series, arrangement" (see order (n.)). Related: Ordinated; ordinating.

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*ar- 
also arə-, Proto-Indo-European root meaning "to fit together."

It forms all or part of: adorn; alarm; aristarchy; aristo-; aristocracy; arm (n.1) "upper limb of the body;" arm (n.2) "weapon;" armada; armadillo; armament; armature; armilla; armistice; armoire; armor; armory; army; art (n.) "skill as a result of learning or practice;" arthralgia; arthritis; arthro-; arthropod; arthroscopy; article; articulate; artifact; artifice; artisan; artist; coordination; disarm; gendarme; harmony; inert; inertia; inordinate; ordain; order; ordinal; ordinance; ordinary; ordinate; ordnance; ornament; ornate; primordial; subordinate; suborn.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit irmah "arm," rtih "manner, mode;" Armenian arnam "make," armukn "elbow;" Greek arti "just," artios "complete, suitable," artizein "to prepare," arthron "a joint;" Latin ars (stem art-) "art, skill, craft," armus "shoulder," artus "joint," arma "weapons;" Old Prussian irmo "arm;" German art "manner, mode."
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coordinate (v.)

also co-ordinate, 1660s, "to place in the same rank," from Latin coordinare "to set in order, arrange," from co- "with, together" (see com-) + ordinatio "arrangement," from ordo "row, rank, series, arrangement" (see order (n.)).

Meaning "to arrange in proper position relative to each other" (transitive) is from 1847; that of "to work together in order" (intransitive) is from 1863. Related: Coordinated; coordinating.

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coordinate (n.)

also co-ordinate, 1823, in the mathematical sense ("each of two or more magnitudes used to define the position of a point, line, or plane"), especially with reference to the system invented by Descartes; from coordinate (adj.).

Hence, coordinates as a means of determining a location on the earth's surface (especially for aircraft), attested by 1960. The meaning "something of the same order, degree, or rank with another or others" is from 1850. In women's fashion, coordinates "set of matched clothing" is attested by 1959.

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