Etymology
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ducat (n.)

name of various silver or gold coins in use in several European countries, late 14c., from Old French ducat (late 14c.), Italian ducato (12c.), Medieval Latin ducatus "coin," originally "duchy," from dux (genitive ducis) "duke," from PIE root *deuk- "to lead."

Apparently so called for the name or effigy of Roger II of Sicily, Duke of Apulia, which first issued the coins (c. 1140). Byzantine emperor Constantine X had the Greek form doux struck on his coins during his reign (1059-1067). Over the years it was a unit of currency of varying value in Holland, Russia, Austria, Sweden, Venice, etc. It remained popular as English slang for "money" or "ticket" from its prominence in "The Merchant of Venice."

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*deuk- 
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."
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