1610s (implied in dissociated) "sever the association or connection of," especially "cut off from society," from Latin dissociatus, past participle of dissociare "to separate from companionship, disunite, set at variance," from dis- "apart" (see dis-) + sociare "to join," from socius "companion, ally," from PIE *sokw-yo-, suffixed form of root *sekw- (1) "to follow."
Attested from 1540s as a past-participle adjective meaning "separated." Dissociated in psychology (1890) was "characterized by mental disjunction," hence dissociated personality (1905) "pathological state in which two or more distinct personalities exist in the same person."
late 14c. dissolven, "to break up, disunite, separate into parts" (transitive, of material substances), also "to liquefy by the disintegrating action of a fluid," also intransitive, "become fluid, be converted from a solid to a liquid state," from Latin dissolvere "to loosen up, break apart," from dis- "apart" (see dis-) + solvere "to loosen, untie," from PIE *se-lu-, from reflexive pronoun *s(w)e- (see idiom) + root *leu- "to loosen, divide, cut apart."
General sense of "to melt, liquefy by means of heat or moisture" is from late 14c. Meaning "to disband" (a parliament or an assembly) is attested from early 15c. Related: Dissolved; dissolving.
early 14c., "separate into parts or pieces," from Latin dividere "to force apart, cleave, distribute," from assimilated form of dis- "apart" (see dis-) + -videre "to separate," which, according to de Vaan, is from PIE *(d)uid- "to separate, distinguish" (source also of Sanskrit avidhat "allotted," Old Avestan vida- "to devote oneself to"). He writes: "The original PIE verb ... (which became thematic in Latin) meant 'to divide in two, separate'. It lost initial *d- through dissimilation in front of the next dental stop, and was reinforced by dis- in Latin ...." Also compare devise.
It is attested from late 14c. as "sever the union or connection with," also "disunite, cause to disagree in opinion." Intransitive sense of "become separated into parts" is from 1520s. Mathematical sense "perform the operation of division" is from early 15c. Divide and rule (c. 1600) translates Latin divide et impera, a maxim of Machiavelli. Related: Divided; dividing.