"negative reply," early 13c., from Old English na (adv.) "no, never, not at all," from ne "not, no" + a "ever." First element from Proto-Germanic *ne (source also of Old Norse, Old Frisian, Old High German ne, Gothic ni "not"), from PIE root *ne- "not." Second element is from Proto-Germanic *aiwi-, extended form of PIE root *aiw- "vital force, life, long life, eternity."
As an adjective meaning "not any" (c. 1200) it is reduced from Old English nan (see none), the final -n omitted first before consonants and then altogether. As a noun from c. 1300. Phrase no can do "it is not possible" is attested from 1827, a locution of English-speaking Chinese noted 19c. in China, Australia and West Coast of U.S. Construction no X, no Y attested from 1530s (in no peny no pardon). No problem as an interjection of assurance first attested 1963. No way as an expression meaning "it can't be done" is attested by 1968 (no way "by no means" is from c. 1400).
We repeated our advice again and again, but got no answer but a loud horse-laugh, and their national maxim of No can do: Europe fashion no do in China. ["Reminiscences of a Voyage to and from China," in "Paxton's Horticultural Register," London, 1836]
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