Etymology
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-archy 

word-forming element meaning "rule," from Latin -archia, from Greek -arkhia "rule," from arkhos "leader, chief, ruler," from arkhē "beginning, origin, first place," verbal noun of arkhein "to be the first," hence "to begin" and "to rule" (see archon).

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arch- 

also archi-, word-forming element meaning "chief, principal; extreme, ultra; early, primitive," from Latinized form of Greek arkh-, arkhi- "first, chief, primeval," combining form of arkhos "a chief, leader, commander," arkhein "be first, begin" (see archon).

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-arch 

word-forming element meaning "a ruler," from Greek arkhos "leader, chief, ruler," from arkhē "beginning, origin, first place," verbal noun of arkhein "to be the first," hence "to begin" and "to rule" (see archon).

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