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resolution (n.)

late 14c., resolucioun, "a breaking or reducing into parts; process of breaking up, dissolution," from Old French resolution (14c.) and directly from Latin resolutionem (nominative resolutio) "process of reducing things into simpler forms," noun of action from past participle stem of resolvere "to loosen" (see resolve (v.)).

From the notion of "process of resolving or reducing a non-material thing into simpler forms" (late 14c.) as a method of problem-solving comes the sense of "a solving" (as of mathematical problems), recorded by 1540s, as is that of "power of holding firmly, character of acting with a fixed purpose" (compare resolute (adj.)). The meaning "steadfastness of purpose" is by 1580s. The meaning "effect of an optical instrument in rendering component parts of objects distinguishable" is by 1860. In Middle English it also could mean "a paraphrase" (as a breaking up and rearranging of a text or translation). 

In mid-15c. it also meant "frame of mind," often implying a pious or moral determination. By 1580s as "a statement upon some matter;" hence "formal decision or expression of a meeting or assembly," c. 1600. New Year's resolution in reference to a specific intention to better oneself is from at least the 1780s, and through 19c. they generally were of a pious nature.

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Definitions of resolution from WordNet

resolution (n.)
a formal expression by a meeting; agreed to by a vote;
Synonyms: declaration / resolve
resolution (n.)
the ability of a microscope or telescope to measure the angular separation of images that are close together;
Synonyms: resolving power
resolution (n.)
the trait of being resolute;
it was his unshakeable resolution to finish the work
Synonyms: resoluteness / firmness / firmness of purpose / resolve
resolution (n.)
finding a solution to a problem;
Synonyms: solving
resolution (n.)
something settled or resolved; the outcome of decision making;
they never did achieve a final resolution of their differences
Synonyms: settlement / closure
resolution (n.)
analysis into clear-cut components;
Synonyms: resolving
resolution (n.)
(computer science) the number of pixels per square inch on a computer-generated display; the greater the resolution, the better the picture;
resolution (n.)
the subsidence of swelling or other signs of inflammation (especially in a lung);
resolution (n.)
(music) a dissonant chord is followed by a consonant chord;
resolution (n.)
a statement that solves a problem or explains how to solve the problem;
Synonyms: solution / answer / result / solvent
resolution (n.)
a decision to do something or to behave in a certain manner;
he always wrote down his New Year's resolutions
From wordnet.princeton.edu