Etymology
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doge (n.)

"chief magistrate of the old republics of Venice and Genoa," 1540s, from Venetian dialect doge, from Latin ducem, accusative of dux "leader" (from PIE root *deuk- "to lead"). Related: Dogate; dogeship.

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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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