c. 1600, "having a quality of dividing," from divis-, past-participle stem of Latin dividere "to divide" (see divide (v.)) + -ive. Meaning "creating division, producing discord" is from 1640s. Related: Divisively; divisiveness.
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.
word-forming element making adjectives from verbs, meaning "pertaining to, tending to; doing, serving to do," in some cases from Old French -if, but usually directly from Latin adjectival suffix -ivus (source also of Italian and Spanish -ivo). In some words borrowed from French at an early date it has been reduced to -y (as in hasty, tardy).
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Harper, D. (n.d.). Etymology of divisive. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/divisive