no-show (n.)

"not in any degree, not at all," Middle English, from Old English na, from ne "not, no" + a "ever." The first element is 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." Ultimately identical to nay, and the differences of use are accidental.

As an adjective, "not any, not one, none" (c. 1200) it is reduced from Old English nan (see none), the final -n omitted first before consonants and then altogether. As an interjection making a negative reply to a statement or question, "not so," early 13c., from the adverb. As a noun, 1580s as "a denial; a negative vote," 1650s as "person who casts a negative vote."

Construction no X, no Y is attested from 1530s (in no peny no pardon). No problem as an interjection of assurance is attested by 1963. No way as a colloquial expression meaning "it can't be done" is attested by 1968 (noway (adv.) "not at all, in no respect, by no means" is from c. 1300). No-knock (adj.) in reference to police raids without permission or warning is by 1970, American English. Phrase no can do "it is not possible" is attested from 1827, a locution of English-speaking Chinese noted 19c. in China, Australia, and the West Coast of the United States.  

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]

Middle English sheuen, from Old English sceawian "to look at, see, gaze, behold, observe; inspect, examine; look for, choose," from Proto-Germanic *skauwojanan (source also of Old Saxon skauwon "to look at," Old Frisian skawia, Dutch schouwen, Old High German scouwon "to look at"), from Proto-Germanic root *skau- "behold, look at," from PIE *skou-, variant of root *keu- "to see, observe, perceive."

The causal meaning "let be seen; put in sight, make known" evolved c. 1200 for unknown reasons, seems to be unique to English (German schauen still means "look at"), and in a century displaced the older meaning. The sense of "explain, make clear" is from c. 1300, as the intransitive sense of "be seen, appear."

The spelling shew, popular 18c. and surviving into early 19c., represents an obsolete pronunciation (rhymes with view). The horse-racing sense of "finish third or in the top three" is by 1903, perhaps from an earlier sense in card-playing.