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resolve (v.)

late 14c., resolven, "melt, dissolve, reduce to liquid; separate into component parts; alter, alter in form or nature by application of physical process," " intransitive sense from c. 1400; from Old French resolver or directly from Latin resolvere "to loosen, loose, unyoke, undo; explain; relax; set free; make void, dispel."

This is from re-, here perhaps intensive or meaning "back" (see re-), + solvere "to loosen, untie, release, explain," from PIE *se-lu-, from reflexive pronoun *s(w)e- (see idiom) + root *leu- "to loosen, divide, cut apart."

From the notion of "separate into components" comes the sense in optics (1785; see resolution). From the notion of "reduce by mental analysis into its basic forms" (late 14c.) comes the meaning "determine, decide upon" after analysis (1520s), hence "pass a resolution" (1580s); "decide, settle" a dispute, etc. (1610s). For sense evolution, compare resolute (adj.).

In Middle English also "vaporize a solid, condense a vapor into a liquid, etc.;" a mid-15c. document has Sche was resoluyd in-to terys where a later writer might have she dissolved in tears. Related: Resolved; resolving.

resolve (n.)

"determination, firmness or fixedness of purpose; a determination," 1590s, from resolve (v.).  Meaning "a determination of a deliberative body" is from 1650s.

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Definitions of resolve from WordNet
1
resolve (v.)
bring to an end; settle conclusively;
Synonyms: decide / settle / adjudicate
resolve (v.)
reach a conclusion after a discussion or deliberation;
Synonyms: conclude
resolve (v.)
reach a decision;
he resolved never to drink again
Synonyms: purpose
resolve (v.)
understand the meaning of;
Synonyms: answer
resolve (v.)
make clearly visible;
can this image be resolved?
resolve (v.)
cause to go into a solution;
Synonyms: dissolve / break up
resolve (v.)
find the solution;
Synonyms: solve
2
resolve (n.)
the trait of being resolute;
Synonyms: resoluteness / firmness / firmness of purpose / resolution
resolve (n.)
a formal expression by a meeting; agreed to by a vote;
Synonyms: resolution / declaration
From wordnet.princeton.edu