Adage

google

ref

mid 16th century: from French, from Latin adagium ‘saying’, based on an early form of aio ‘I say’.

wiktionary

ref

Borrowed from Middle French adage, from Latin adā̆gium.

etymonline

ref

adage (n.)

"brief, familiar proverb," 1540s, French adage (16c.), from Latin adagium "adage, proverb," apparently a collateral form of adagio, from ad "to" (see ad-) + *agi-, root of aio "I say," which is perhaps cognate with Armenian ar-ac "proverb," asem "to say." But some find this unlikely and suggest the second element might be related to agein "set in motion, drive, urge" (from PIE root *ag- "to drive, draw out or forth, move"). Related: Adagial.