Etymology
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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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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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wasted (adj.)
late 14c., "enfeebled," past-participle adjective from waste (v.). Slang meaning "intoxicated" is from 1950s.
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wastewater (n.)
also waste-water, mid-15c., from waste (adj.) + water (n.1).
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wastrel (n.)
"spendthrift, idler," 1847, from waste (v.) + pejorative suffix -rel. Earlier "something useless or imperfect" (1790).
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wasteful (adj.)
early 14c., "destructive," from waste (n.) + -ful. Meaning "lavish" is from mid-15c. Related: Wastefully; wastefulness.
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candle-waster (n.)

"one who wastes candles," specifically a contemptuous word for one who follows occupations considered unprofitable or harmful, 1590s, from candle + agent noun from waste (v.).

A whoreson book-worm, a candle-waster. [Ben Jonson, "Cynthia's Revels"]
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wasteland (n.)

1825 as one word, from waste (adj.) + land (n.). Figurative sense is attested from 1868. Eliot's poem is from 1922.

April is the cruellest month, breeding
Lilacs out of the dead land, mixing
Memory and desire, stirring
Dull roots with spring rain.
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