Etymology
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e- 

the later Romans evidently found words beginning in sc-, sp-, st- difficult or unpleasant to pronounce; in Late Latin forms begin to emerge in i- (such as ispatium, ispiritu), and from 5c. this shifted to e-. The development was carried into the Romanic languages, especially Old French, and the French words were modified further after 15c. by natural loss of -s- (the suppression being marked by an acute accent on the e-), while in other cases the word was formally corrected back to the Latin spelling (for example spécial). Hence French état for Old French estat for Latin status, etc. It also affected Romanic borrowings from Germanic (such as espy, eschew).

A different e- is a reduced form of Latin ex- before consonants (see ex-), and the e- in enough is an unfelt survival of an Old English alternative form of ge-.

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waste (adj.)
c. 1300, of land, "desolate, uncultivated," from Anglo-French and Old North French waste (Old French gaste), from Latin vastus "empty, desolate," from PIE *wasto-, extended suffixed form of root *eue- "to leave, abandon, give out." From c. 1400 as "superfluous, excess;" 1670s as "unfit for use." Waste-paper attested from 1580s.
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waste (n.)
c. 1200, "desolate regions," from Anglo-French and Old North French wast "waste, damage, destruction; wasteland, moor" (Old French gast), from Latin vastum, neuter of vastus "empty, desolate," from PIE *wasto-, extended suffixed form of root *eue- "to leave, abandon, give out."

Replaced or merged with Old English westen, woesten "a desert, wilderness," from the Latin word. Meanings "consumption, depletion," also "useless expenditure" are from c. 1300; sense of "refuse matter" is attested from c. 1400. Waste basket first recorded 1850.
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waste (v.)
c. 1200, "devastate, ravage, ruin," from Anglo-French and Old North French waster "to waste, squander, spoil, ruin" (Old French gaster; Modern French gâter), altered (by influence of Frankish *wostjan) from Latin vastare "lay waste," from vastus "empty, desolate," from PIE *wasto-, extended suffixed form of root *eue- "to leave, abandon, give out." Related: wasted; wasting.

The Germanic word also existed in Old English as westan "to lay waste, ravage." Spanish gastar, Italian guastare also are from Germanic. Meaning "to lose strength or health; pine; weaken" is attested from c. 1300; the sense of "squander, spend or consume uselessly" is first recorded mid-14c.; meaning "to kill" is from 1964. Waste not, want not attested from 1778.
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e-mail 

1982, short for electronic mail (1977; see electronic + mail (n.1)); this led to the contemptuous application of snail mail (1983) to the old system.

Even aerial navigation in 1999 was found too slow to convey and deliver the mails. The pneumatic tube system was even swifter, and with such facilities at hand it is not surprising that people in San Francisco received four daily editions of the Manhattan journals, although the distance between Sandy Hook and the Golden Gate is a matter of 3,600 miles. ["Looking Forward," Arthur Bird, 1899]

Associated Press style guide collapsed it to email 2011.

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E. coli (n.)

bacteria inhabiting the gut of man and animals, by 1921, short for Escherichia coli (1911), named for German physician Theodor Escherich (1857-1911) with Latin genitive of colon "colon" (see colon (n.2)).

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E pluribus unum 

motto of the United States, being one nation formed by uniting several states, 1782, Latin, from e "out of" (see ex-); ablative plural of plus "more" (see plus (n.)); neuter of unus "one" (from PIE root *oi-no- "one, unique"). Not found in classical Latin, though a variant of the phrase appears in Virgil (color est e pluribus unum); the full phrase was the motto of the popular Gentleman's Magazine from 1731 into the 1750s.

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wastewater (n.)
also waste-water, mid-15c., from waste (adj.) + water (n.1).
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exhaust (n.)

"waste gas," 1848, originally from steam engines, from exhaust (v.). In reference to internal combustion engines by 1896. Exhaust pipe, which carries away waste gas or steam from an engine, is by 1849.

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