reduction n.

late 14c., reducen, "bring back" (to a place or state, a sense now obsolete), also "to diminish" (something), from Old French reducer (14c.), from Latin reducere "lead back, bring back," figuratively "restore, replace," from re- "back" (see re-) + ducere "bring, lead" (from PIE root *deuk- "to lead").

In Middle English largely with positive senses, including "bring back to virtue, restore to God; bring back to health." The specific meaning "bring to an inferior condition" is by 1570s; that of "bring to a lower rank" is by 1640s (military reduce to ranks is from 1802); that of "subdue by force of arms" is from 1610s. The sense of "to lower, diminish, lessen" is from 1787. Related: Reduced; reducing.

Proto-Indo-European root meaning "to lead."

It forms all or part of: abduce; abducent; abduct; abduction; adduce; aqueduct; circumduction; conduce; conducive; conduct; conductor; conduit; deduce; deduction; dock (n.1) "ship's berth;" doge; douche; ducal; ducat; Duce; duchess; duchy; duct; ductile; duke (n.); educate; education; induce; induction; introduce; introduction; misconduct; produce; production; reduce; reduction; seduce; seduction; subduce; subduction; taut; team (n.); teem (v.1) "abound, swarm, be prolific;" tie (n.); tow (v.); traduce; transducer; tug; zugzwang.

It is the hypothetical source of/evidence for its existence is provided by: Latin dux (genitive ducis) "leader, commander," in Late Latin "governor of a province," ducere "to lead;" Old English togian "to pull, drag," teonteon "to pull, drag;" German Zaum "bridle," ziehen "to draw, pull, drag;" Middle Welsh dygaf "I draw."