Where does “arche-” come from?

arche- (Middle English) comes from Old English ærċe-, from Latin archi-, from Ancient Greek ἀρχι-, from Ancient Greek ἄρχω, from Proto-Indo-European h₂ergʰ- — to begin; to command, rule; to begin, rule,...

Ancestry of “arche-”, step by step

Step	Language	Word	Meaning
1	Old English	ærċe-	—
2	Latin	archi-	arch-, archi-
3	Ancient Greek	ἀρχι-	denotes primary importance or authority
4	Ancient Greek	ἄρχω	To begin; To lead, rule, govern, command; To be...
5	Proto-Indo-European	h₂ergʰ-	to begin; to command, rule; to begin, rule,...

Every word from Proto-Indo-European h₂ergʰ- →Every word from Ancient Greek ἄρχω →Every word from Ancient Greek ἀρχι- →