Where does “μαχαίριον” come from?

μαχαίριον (Koine Greek) comes from Ancient Greek μάχαιρα, from Ancient Greek μάχομαι, from Proto-Indo-European maHgʰ- — to fight.

Ancestry of “μαχαίριον”, step by step

Step	Language	Word	Meaning
1	Ancient Greek	μάχαιρα	large knife, short sword, dirk, dagger
2	Ancient Greek	μάχομαι	I make war, fight, battle; I quarrel, wrangle,...
3	Proto-Indo-European	maHgʰ-	to fight