Etymology
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egg (n.)

"the body formed in the females of all animals (with the exception of a few of the lowest type) in which by impregnation the development of the fetus takes place," mid-14c., egge, mostly in northern England dialect, from Old Norse egg, from Proto-Germanic *ajja(m) (source also of Old Saxon, Middle Dutch, Dutch, Old High German, German ei, Gothic ada), probably from PIE *owyo-/*oyyo- "egg" (source also of Old Church Slavonic aja, Russian jajco, Breton ui, Welsh wy, Greek ōon, Latin ovum); possibly derived from root *awi- "bird."

This Norse-derived northern word vied in Middle English with native cognates eye, eai, from Old English æg, until finally displacing the others after c. 1500. Caxton (15c.) writes of a merchant (probably a north-country man) in a public house on the Thames who asked for eggs:

And the goode wyf answerde, that she coude speke no frenshe. And the marchaunt was angry, for he also coude speke no frenshe, but wolde have hadde egges, and she understode hym not. 

She did, however, recognize another customer's request for "eyren." Used of persons from c. 1600. Bad egg in the figurative sense is from 1855; bad eggs aren't always obvious to outward view (there was an old proverb, "bad bird, bad egg"). To have egg on (one's) face "look foolish" is attested by 1948.

[Young & Rubincam] realize full well that a crew can sometimes make or break a show. It can do little things to ruin a program or else, by giving it its best, can really get that all-important rating. They are mindful of an emcee of a variety show who already has been tabbed "old egg in your face" because the crew has managed to get him in such awkward positions on the TV screen. [Billboard, March 5, 1949] 
We don't have egg on our face. We have omelet all over our suits. [NBC News anchor Tom Brokaw, some time past 3 a.m. ET on Nov. 8, 2000, after the U.S. television networks called a winner, then retracted the call, in the Bush-Gore presidential election]

 Eggs Benedict is attested by 1898; various Benedicts are cited as the eponym, and the dish itself is said to have originated in the Waldorf-Astoria or Delmonico's, both in New York. The figure of speech represented in to have (or put) all (one's) eggs in one basket "to venture all one has in one speculation or investment" is attested by 1660s. The conundrum of the chicken (or hen) and the egg is attested from 1875.

Bumble, bramble, which came first, sir,
Eggs or chickens? Who can tell?
I'll never believe that the first egg burst, sir,
Before its mother was out of her shell.
[Mary Mapes Dodge, "Rhymes and Jingles," N.Y., 1875]
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hard (adj.)

Old English heard "solid and firm, not soft," also, "difficult to endure, carried on with great exertion," also, of persons, "severe, rigorous, harsh, cruel," from Proto-Germanic *hardu- (source also of Old Saxon hard, Old Frisian herd, Dutch hard, Old Norse harðr "hard," Old High German harto "extremely, very," German hart, Gothic hardus "hard"), from PIE *kortu-, suffixed form of root *kar- "hard."

Meaning "difficult to do" is from c. 1200. Of water, in reference to the presence of mineral salts, 1650s; of consonants, 1775. Hard of hearing preserves obsolete Middle English sense of "having difficulty in doing something." In the sense "strong, spiritous, fermented" from 1789 (as in hard cider, etc.), and this use probably is the origin of that in hard drugs (1955). Hard facts is from 1853; hard news in journalism is from 1918. Hard copy (as opposed to computer record) is from 1964; hard disk is from 1978; the computer hard drive is from 1983. Hard times "period of poverty" is from 1705. Hard money (1706) is specie, silver or gold coin, as opposed to paper. Hence 19c. U.S. hard (n.) "one who advocates the use of metallic money as the national currency" (1844). To play hard to get is from 1945. Hard rock as a pop music style recorded from 1967. To do something the hard way is from 1907.

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hard (adv.)

Old English hearde "firmly, severely," from hard (adj.). Meaning "with effort or energy, with difficulty" is late 14c.

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egg (v.)

"to incite, urge, encourage, instigate," c. 1200, from Old Norse eggja "to goad on, incite," from egg "edge" (see edge (n.)). The unrelated verb from egg (n.) is by 1808 in cookery, "to cover or mix with eggs;" the meaning "to pelt with (rotten) eggs" is from 1857. Related: Egged; egging.

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hard-headed (adj.)

also hardheaded, 1580s, "stubborn," from hardhead "dull person" (1510s), from hard (adj.) + -headed. Meaning "practical, shrewd" is attested from 1779. Compare Dutch hardhoofdig "stupid."

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hard-wired (adj.)

also hardwired, 1969, in computing, "with permanently connected circuits performing unchangeable functions;" transferred to human brains from 1971; from hard (adv.) + wire (v.).

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hard-bitten (adj.)

"tough, tough in a fight," literally "given to hard biting," 1715, originally of hunting dogs, from hard (adv.) + bitten, with the past participle used actively (as in free-spoken).

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hard-working (adj.)

also hardworking, 1708, from hard (adv.) + working (adj.).

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hard-line (adj.)

"uncompromising," 1958, originally in reference to Soviet communist policies, from the noun phrase (see hard (adj.) + line (n.)) in the political sense. Related: Hard-liner (1963).

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hard-cover (adj.)

of books, 1949, from hard (adj.) + cover (n.).

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