c. 1300, "harm, injury; hurt or loss to person, character, or estate," from Old French damage, domage "loss caused by injury" (12c., Modern French dommage), from dam "damage," from Latin damnum "loss, hurt, damage" (see damn). In law (as damages) "the value in money of what was lost or withheld, that which is given to repair a cost," from c. 1400. Colloquial sense of "cost, expense" is by 1755. Damage control "action taken to limit the effect of an accident or error" is attested by 1933 in U.S. Navy jargon.
"to save from loss at sea," as a ship or goods, 1706, a back-formation from salvage (n.) or salvable. Related: Salved; salving.
"one who scientifically treats or studies mental illness," 1864, from French aliéniste, from alienation in the sense of "insanity, loss of mental faculty," from Latin alienare "deprive of reason, drive mad," literally "to make another's, estrange" (see alienate). The mental sense of alienare has since mostly died out in English, but Middle English had aliened from mind "deranged, not rational" (late 14c.), and alienation was used from 15c. in a sense of "loss or derangement of mental faculties, insanity."
figurative sense is attested from 1832, from profit-and-loss accounting, where the final figure calculated is the bottom line on the page. Also (especially as an adjective) bottom-line, bottomline.