Etymology
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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 "strong; stable," figuratively "constant, trusty" (from suffixed form of PIE root *dher- "to hold firmly, support").

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 from at least 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. The simple term buy it as slang for "suffer a mishap," especially "to die" is attested by 1825, and seems to have been picked up in airmen's jargon. Meanwhile 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.

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fate (n.)

late 14c., "one's lot or destiny; predetermined course of life;" also "one's guiding spirit," from Old French fate and directly from Latin fata (source also of Spanish hado, Portuguese fado, Italian fato), neuter plural of fatum "prophetic declaration of what must be, oracle, prediction," thus the Latin word's usual sense, "that which is ordained, destiny, fate," literally "thing spoken (by the gods)," from neuter past participle of fari "to speak," from PIE root *bha- (2) "to speak, tell, say." Often in a bad sense in Latin: "bad luck, ill fortune; mishap, ruin; a pest or plague."

From early 15c. as "power that rules destinies, agency which predetermines events; supernatural predetermination;" also "destiny personified." Meaning "that which must be" is from 1660s; sense of "final event" is from 1768. The Latin sense evolution is from "sentence of the Gods" (Greek theosphaton) to "lot, portion" (Greek moira, personified as a goddess in Homer).

The sense of "one of the three goddesses (Clotho, Lachesis, and Atropos) who determined the course of a human life" (or, as Blount has it, "the three Ladies of destiny") is in English by 1580s. Their Greek name was Moirai (see above), from a verb meaning "to receive one's share." Latin Parca "one of the three Fates or goddesses of fate" (source of French parque "a Fate;" Spanish parca "Death personified; the Grim Reaper") might be from parcere "act sparingly, refrain from; have mercy upon, forbear to injure or punish" (if so, probably here a euphemism) or plectere "to weave, plait." The native word in English was wyrd (see weird).

J'y suivais un serpent qui venait de me mordre
Quel repli de désirs, sa traîne!...Quel désordre
De trésors s'arrachant à mon avidité,
Et quelle sombre soif de la limpidité!
[Paul Valéry, from La Jeune Parque]
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