Where does “Băeș” come from?

Băeș (Romanian) comes from Romanian băieș, from Romanian baie, from Hungarian bánya, from Proto-Slavic baňa, from Latin bāneum, from Latin balneum, from Ancient Greek βαλανεῖον, from Ancient Greek βᾰλᾰνεύς — bath-man.

Ancestry of “Băeș”, step by step

Step	Language	Word	Meaning
1	Romanian	băieș	miner
2	Romanian	baie	bathroom; bath, bathtub
3	Hungarian	bánya	mine; healing spring or bath
4	Proto-Slavic	baňa	bath, bathing, bathing place; dome; bulging,...
5	Latin	bāneum	attested in Pompeii
6	Latin	balneum	bath, bathing place, bathroom
7	Ancient Greek	βαλανεῖον	bath, bathing room; bathhouse
8	Ancient Greek	βᾰλᾰνεύς	bath-man

Every word from Ancient Greek βᾰλᾰνεύς →Every word from Ancient Greek βαλανεῖον →Every word from Latin balneum →