deduce v.

active word-forming element in English and in many verbs inherited from French and Latin, from Latin de "down, down from, from, off; concerning" (see de), also used as a prefix in Latin, usually meaning "down, off, away, from among, down from," but also "down to the bottom, totally" hence "completely" (intensive or completive), which is its sense in many English words.

As a Latin prefix it also had the function of undoing or reversing a verb's action, and hence it came to be used as a pure privative — "not, do the opposite of, undo" — which is its primary function as a living prefix in English, as in defrost (1895), defuse (1943), de-escalate (1964), etc. In some cases, a reduced form of dis-.

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."

early 15c., "to take away, separate, or remove in estimating or counting," from Latin deductus, past participle of deducere "lead down, bring away;" see deduce, with which it formerly was interchangeable. Deduct refers to taking away portions or amounts; subtract to taking away numbers. Related: Deducted; deducting.

Deduct is to lead away, set aside, in a general or distributive sense; subtract, to draw off, remove, in a literal or collective sense. In settling a mercantile account, certain items, as charges, losses, etc. are deducted by being added together and their total subtracted from the grand total of the transaction. [Century Dictionary]