"public sale in which each bidder offers more than the previous bid," 1590s, from Latin auctionem (nominative auctio) "a sale by increasing bids, public sale," noun of action from past-participle stem of augere "to increase," from PIE root *aug- (1) "to increase." In northern England and Scotland, called a roup. In the U.S., something is sold at auction; in England, by auction.
"sell by auction," by 1723 (implied in auctioned), from auction (n.). Since early 19c., commonly with off (adv.). Related: Auctioning.