Etymology
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mystagogue (n.)

"person who initiates into mysteries," 1550s, from Latin mystagogus "a guide to the mysteries," from Greek mystagōgos, from mystēs "one initiated into the mysteries" (see mystery (n.1)) + agōgos "leading, a leader," from agein "to lead" (from PIE root *ag- "to drive, draw out or forth, move"). Related: Mystagogic; mystagogical.

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mystagogy 

"interpretation of mysteries; the practice of a mystagogue," 1570s, from French mystagogie, from Latin mystagogia, from Greek mystagōgia "initiation into the mysteries," from mystagōgos "one who initiates into the mysteries" (see mystagogue). Related: Mystagoguery (1927).

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*ag- 

Proto-Indo-European root meaning "to drive, draw out or forth, move."

It forms all or part of: act; action; active; actor; actual; actuary; actuate; agency; agenda; agent; agile; agitation; agony; ambagious; ambassador; ambiguous; anagogical; antagonize; apagoge; assay; Auriga; auto-da-fe; axiom; cache; castigate; coagulate; cogent; cogitation; counteract; demagogue; embassy; epact; essay; exact; exacta; examine; exigency; exiguous; fumigation; glucagon; hypnagogic; interact; intransigent; isagoge; litigate; litigation; mitigate; mystagogue; navigate; objurgate; pedagogue; plutogogue; prodigal; protagonist; purge; react; redact; retroactive; squat; strategy; synagogue; transact; transaction; variegate.

It is the hypothetical source of/evidence for its existence is provided by: Greek agein "to lead, guide, drive, carry off," agon "assembly, contest in the games," agōgos "leader," axios "worth, worthy, weighing as much;" Sanskrit ajati "drives," ajirah "moving, active;" Latin actus "a doing; a driving, impulse, a setting in motion; a part in a play;" agere "to set in motion, drive, drive forward," hence "to do, perform," agilis "nimble, quick;" Old Norse aka "to drive;" Middle Irish ag "battle."

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