divide (v.)
early 14c., from Latin dividere "to force apart, cleave, distribute," from dis- "apart" (see dis-) + -videre "to separate," from PIE root *weidh- "to separate" (see widow; also see with).

Mathematical sense is from early 15c. Divide and rule (c.1600) translates Latin divide et impera, a maxim of Machiavelli. Related: Divided; dividing.
divide (n.)
1640s, "act of dividing," from divide (v.). Meaning "watershed, separation between river valleys" is first recorded 1807, American English.