*aug- 1

"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.

late 14c., "become more severe;" c. 1400, "to make larger; become larger," from Old French augmenter "increase, enhance" (14c.), from Late Latin augmentare "to increase," from Latin augmentum "an increase, growth," from augere "to increase, make big, enlarge, enrich" (from PIE root *aug- (1) "to increase"). Related: Augmented; augmenting. As a noun from early 15c.