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.
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.
It forms all or part of: absolute; absolution; absolve; analysis; analytic; catalysis; catalyst; catalytic; dialysis; dissolve; electrolysis; electrolyte; forlorn; Hippolytus; hydrolysis; -less; loess; loose; lorn; lose; loss; Lysander; lysergic; lysis; -lysis; lyso-; lysol; lytic; -lytic; palsy; paralysis; pyrolusite; resolute; resolution; resolve; soluble; solute; solution; solve; solvent.
It is the hypothetical source of/evidence for its existence is provided by: Sanskrit lunati "cuts, cuts off," lavitram "sickle;" Greek lyein "to loosen, untie, slacken," lysus "a loosening;" Latin luere "to loose, release, atone for, expiate;" Old Norse lauss "loose, free, unencumbered; vacant; dissolute;" Old English losian "be lost, perish."