Yours, Etc.: Origins and Uses of 8 Sign-Offs
1540s, Middle French adage, from Latin adagium "adage, proverb," apparently from adagio, from ad- "to" (see ad-) + *agi-, root of aio "I say," from PIE *ag- "to speak." But Tucker thinks the second element is rather ago "set in motion, drive, urge."
a saying, often in metaphoric form, that embodies a common observation, such as "If the shoe fits, wear it,'' "Out of the frying pan, into the fire,'' or "Early to bed, early to rise, makes a man healthy, wealthy, and wise.'' The scholar Erasmus published a well-known collection of adages as Adagia in 1508. The word is from the Latin adagium, "proverb."