Liddell-Scott-Jones

κατάρχω (katarchō) to rule ^G:V

κατάρχω-ω,

make beginning of a thing, c.genitive, τίνες κατῆρξαν.. μάχης; [κατάρχωειν">Refs 4th c.BC+] lead the way, [Refs 6th c.BC+]; τὸ κατάρχωον αἰσθήσεως, τῆς κινήσεως, the source of perception, of motion, [Refs 2nd c.AD+], begin a thing, [Refs 6th c.BC+]: with participle, begin doing, [Refs 5th c.BC+]

__2 θανόντα δεσπόταν γόοις κατάρξω I will lead the dirge over.., [Refs 5th c.BC+]
__II middle, begin, like active, with genitive, [κατάρχωεται [prev\. author] “Ph.” 540; τοῖς κατηργμένοις τῆς πορείας Plato Philosophus [{5-6th c.BC}] “Phaedrus” 256d; κ. τῆς προσβολῆς 2nd c.BC: Polybius Historicus 2.67.1; τοῦ λόγου Plutarchus Biographus et Philosophus [{1-2nd c.AD}] 2.151e ">Refs 6th c.BC+]: with accusative, κ. νόμον, στεναγμόν, [κατάρχωεται μέλος">Refs 5th c.BC+] is beginning, [Refs 2nd c.AD+].
__II.2 in religious sense, begin the sacrificial ceremonies, once in [Refs 8th c.BC+] began [the sacrifice] with the washing of hands and sprinkling the barley on the victim's head, [κατάρχωομαι μέν, σφάγια δ᾽ ἄλλοισιν μέλει">Refs 8th c.BC+] I begin the rite, but leave the slaughter of the victim to others, [κατάρχωεσθαι τοῦ τράγου">Refs 5th c.BC+] make a beginning of the victim, i. e. consecrate him for sacrifice by cutting off the hair of his forehead, [κατάρχωοντο 5th c.BC: Herodotus Historicus 2.45 ">Refs 5th c.BC+]; πῶς δ᾽ αὖ κατάρξῃ θυμάτω; [Refs 5th c.BC+]: metaphorically, [Refs 1st c.AD+] —so later in active, [Refs 3rd c.AD+]
__II.2.b sacrifice, slay, ξίφει, φασγάνῳ κ., [Refs 5th c.BC+] — passive, ᾗ (i.e. τῇ θεᾷ) σὸν κατῆρκται σῶμα hath been devoted, [Refs]
__III active, rule, govern, with genitive, [Refs 4th c.AD+]
__IV κατάρξω ὑμᾶς ἐν σκορπίοις will chastise you.., [LXX]

_{LSJ Scripture Refs: LXX.1Kgs.12.24}