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American dream [American dream 词源字典]: coined 1931 by James Truslow Adams (1878-1949), U.S. writer and popular historian (unrelated to the Massachusetts Adamses), in "Epic of America."
[The American Dream is] that dream of a land in which life should be better and richer and fuller for everyone, with opportunity for each according to ability or achievement. It is a difficult dream for the European upper classes to interpret adequately, and too many of us ourselves have grown weary and mistrustful of it. It is not a dream of motor cars and high wages merely, but a dream of social order in which each man and each woman shall be able to attain to the fullest stature of which they are innately capable, and be recognized by others for what they are, regardless of the fortuitous circumstances of birth or position. [Adams]
Others have used the term as they will.[American dream etymology, American dream origin, 英语词源]
back (n.): Old English bæc "back," from Proto-Germanic *bakam (cognates: Old Saxon and Middle Dutch bak, Old Frisian bek), with no known connections outside Germanic. In other modern Germanic languages the cognates mostly have been ousted in this sense ib words akin to Modern English ridge (cognates: Danish ryg, German Rücken). Many Indo-European languages show signs of once having distinguished the horizontal back of an animal (or a mountain range) from the upright back of a human. In other cases, a modern word for "back" may come from a word related to "spine" (Italian schiena, Russian spina) or "shoulder, shoulder blade" (Spanish espalda, Polish plecy).

To turn (one's) back on (someone or something) "ignore" is from early 14c. Behind (someone's) back "clandestinely" is from late 14c. To know (something) like the back of one's hand, implying familiarity, is first attested 1893. The first attested use of the phrase is from a dismissive speech made to a character in Robert Louis Stevenson's "Catriona":
If I durst speak to herself, you may be certain I would never dream of trusting it to you; because I know you like the back of my hand, and all your blustering talk is that much wind to me.
The story, a sequel to "Kidnapped," has a Scottish setting and context, and the back of my hand to you was noted in the late 19th century as a Scottish expression meaning "I will have nothing to do with you" [see Longmuir's edition of Jamieson's Scottish dictionary]. In English generally, the back of (one's) hand has been used to imply contempt and rejection since at least 1300. Perhaps the connection of a menacing dismissal is what made Stevenson choose that particular anatomical reference.
farm (n.): c. 1300, "fixed payment (usually in exchange for taxes collected, etc.), fixed rent," from Old French ferme "a rent, lease" (13c.), from Medieval Latin firma "fixed payment," from Latin firmare "to fix, settle, confirm, strengthen," from firmus "firm" (see firm (adj.)).

Sense of "tract of leased land" is first recorded early 14c.; that of "cultivated land" (leased or not) is 1520s. A word of confused history, but there is agreement that "the purely agricultural sense is comparatively modern" [Century Dictionary]. There is a set of Old English words that appear to be related in sound and sense; if these, too, are from Latin it would be a very early borrowing. Some books strenuously defend a theory that the Anglo-Saxon words are original (perhaps related to feorh "life").

Phrase buy the farm "die in battle," is at least from World War II, perhaps a cynical reference to the draftee's dream of getting out of the war and going home, in many cases to a peaceful farmstead. But fetch the farm is prisoner slang from at least 1879 for "get sent to the infirmary," with reference to the better diet and lighter duties there.