manus manum lavat.
hand washes hand.
This quote is also recorded by a contemporary of Petronius, Seneca the Younger, tutor to Emperor Nero, who employed Petronius as his "Style Consultant" (Arbiter Elegentiae). Seneca includes that identical quote in his satire the Apocolocyntosis, 9.9.
The most likely explanation is that it was a well-known adage current in that day that both men quoted for their needs.
Still, it is certainly Latin well worth knowing.
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