resolution (n.)

early 15c., "dissolved, of loose structure," also "morally lax" (senses all obsolete), from Latin resolutus, past participle of resolvere "untie, unfasten, loose, loosen" (see resolve (v.)).

It emerged c. 1500 in the sense of "determined, decided, absolute, final," especially in the phrase resolute answer, which was "common in 16th c." [OED]. The notion is of "breaking (something) into parts" as the way to arrive at the truth of it and thus make the final determination (compare resolution).

The word has been used from 1530s of persons, "determined in mind, having a fixed resolve." Related: Resolutely; resoluteness. In Middle English a resolutif was a medicine to dissolve and disperse hardened matter (c. 1400).

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.