Where does “Bagno” come from?

Bagno (Portuguese) comes from Italian bagno, from Latin bāneum, from Latin balneum, from Ancient Greek βαλανεῖον, from Ancient Greek βᾰλᾰνεύς — bath-man.

Ancestry of “Bagno”, step by step

Step	Language	Word	Meaning
1	Italian	bagno	bath; swim, bathe; bathroom
2	Latin	bāneum	attested in Pompeii
3	Latin	balneum	bath, bathing place, bathroom
4	Ancient Greek	βαλανεῖον	bath, bathing room; bathhouse
5	Ancient Greek	βᾰλᾰνεύς	bath-man

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