Etymology
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mile (n.)

unit of linear measure in Great Britain, the U.S., and a few other countries, formerly used in most European countries before the metric system; Old English mil, from West Germanic *milja (source also of Middle Dutch mile, Dutch mijl, Old High German mila, German Meile), from Latin milia "thousands," plural of mille "a thousand" (neuter plural was mistaken in Germanic as a fem. singular), which is of unknown origin.

The Latin word also is the source of French mille, Italian miglio, Spanish milla. The Scandinavian words (Old Norse mila, etc.) are from English. An ancient Roman mile was 1,000 double paces (one step with each foot), for about 4,860 feet, but many local variants developed, in part in an attempt to reconcile the mile with the agricultural system of measurements. Consequently, old European miles were of various lengths. The medieval English mile was 6,610 feet; the old London mile was 5,000 feet. In Germany, Holland, and Scandinavia in the Middle Ages, the Latin word was applied arbitrarily to the ancient Germanic rasta, a measure of from 3.25 to 6 English miles. In England the ordinary mile was set by legal act at 320 perches (5,280 feet) by statute in Elizabeth's reign.

In Middle English the word also was a unit of time, "about 20 minutes," roughly what was required to walk a mile. The word has been used generically since 1580s for "a great distance." Mile-a-minute (adj.) "very fast" is attested from 1957 in railroad publications (automobiles had attained 60 mph by 1903).

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last (adj.)

c. 1200, "latest, final, following all others," a contraction of Old English latost (adj.) "slowest, latest," superlative of læt (see late); in some uses from late (adv.). Cognate with Old Frisian lest, Dutch laatst, Old High German laggost, German letzt.

Meaning "last in space, furthest, most remote" is from late 14c.; meaning "most unlikely or unsuitable" is from mid-15c. Meaning "most recent, next before the present" (as in last night, last September) is from late 14c.; latest would be more correct, but idiom rules and the last time I saw her might mean the most recent time this hour or the final time forever.

The biblical last days ("belonging to the end") is attested from late 14c. Last hurrah is from the title of Edwin O'Connor's 1956 novel. Last word "final, definitive statement" is from 1650s. A dying person's last words so called by 1740. As an adjective, last-minute attested from 1913. Last-chance (adj.) is from 1962. Expression if it's the last thing I do, expressing strong determination, is attested by 1905.

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last (n.1)

"wooden model of a human foot used by shoemakers," from Old English læste "shoemaker's last," earlier last "track, footprint, footstep, trace," from Proto-Germanic *laisti- (source also of Old Norse leistr "the foot," Middle Dutch, Dutch leest "form, model, last," Old High German leist "track, footprint," German Leisten "last," Gothic laistjan "to follow"), related to Old English læran "to teach," from PIE root *lois- "furrow, track."

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last (n.2)
late Old English, "the last or final man, object, time, etc.," from last (adj.). From late 14c. as "most recent person, latest comer." Also in Middle English as a noun, "duration" (early 14c.), from the verb. Phrase at (the) last is from c. 1200; extended form long last is from 1520s. To the last is from c. 1400.
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last (adv.)
c. 1200, "most recently;" early 13c., "finally, after all others" (contrasted to first), contraction of Old English lætest (adv.), superlative of late (see late).
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last (v.)

"endure, go on existing," from Old English læstan "to continue, endure," earlier "follow (a leader), accomplish, carry out, perform," from Proto-Germanic *laistjan "to follow a track" (source also of Gothic laistjan "to follow after," Old Frisian lasta "to fulfill, to pay (duties)," German leisten "to perform, achieve, afford"), from PIE root *lois- "furrow, track." It is related to last (n.1), but not to last (adj.). Related: Lasted; lasting.

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last-ditch (adj.)

"on the last line of defense," 1909, from an image attested by 1715, from a quote attributed to William of Orange (1650-1702), who is said to have uttered it defiantly during the French invasion of 1672; if so, originally in a Netherlands context.

We have no space to enter into the detail of the heroic struggle maintained by the young stadtholder and his faithful Dutchmen; how they laid their country under water, and successfully kept the powerful invader at bay. Once the contest seemed utterly hopeless. William was advised to compromise the matter, and yield up Holland as the conquest of Louis XIV. "No," replied he; "I mean to die in the last ditch." A speech alone sufficient to render his memory immortal. [Agnes Strickland, "Lives of the Queens of England," London, 1847]
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milepost (n.)

also mile-post, "post set up to mark the distance by miles along a highway, etc.," 1768, from mile + post (n.1).

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milliary (adj.)

"pertaining to the ancient Roman mile," 1640s, from Latin milliarius, from mille (see mile (n.)). As a noun, "a milestone," c. 1600, from Latin milliarium.

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milestone (n.)

also mile-stone, "stone or pillar set up on a highway or other line of travel to mark the distance in miles," 1746, from mile + stone (n.).

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