Etymology
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dog (n.)

"quadruped of the genus Canis," Old English docga, a late, rare word, used in at least one Middle English source in reference specifically to a powerful breed of canine; other early Middle English uses tend to be depreciatory or abusive. Its origin remains one of the great mysteries of English etymology.

The word forced out Old English hund (the general Germanic and Indo-European word, from root from PIE root *kwon-) by 16c. and subsequently was picked up in many continental languages (French dogue (16c.), Danish dogge, German Dogge (16c.). The common Spanish word for "dog," perro, also is a mystery word of unknown origin, perhaps from Iberian. A group of Slavic "dog" words (Old Church Slavonic pisu, Polish pies, Serbo-Croatian pas) likewise is of unknown origin. 

In reference to persons, by c. 1200 in abuse or contempt as "a mean, worthless fellow, currish, sneaking scoundrel." Playfully abusive sense of "rakish man," especially if young, "a sport, a gallant" is from 1610s. Slang meaning "ugly woman" is from 1930s; that of "sexually aggressive man" is from 1950s.  

Many expressions — a dog's life (c. 1600), go to the dogs (1610s), dog-cheap (1520s), etc. — reflect the earlier hard use of the animals as hunting accessories, not pets. In ancient times, "the dog" was the worst throw in dice (attested in Greek, Latin, and Sanskrit, where the word for "the lucky player" was literally "the dog-killer"), which plausibly explains the Greek word for "danger," kindynos, which appears to be "play the dog" (but Beekes is against this).

Notwithstanding, as a dog hath a day, so may I perchance have time to declare it in deeds. [Princess Elizabeth, 1550]

Meaning "something poor or mediocre, a failure" is by 1936 in U.S. slang. From late 14c. as the name for a heavy metal clamp of some kind. Dog's age "a long time" is by 1836. Adjectival phrase dog-eat-dog "ruthlessly competitive" is by 1850s. Phrase put on the dog "get dressed up" (1934) may be from comparison of dog collars to the stiff stand-up shirt collars that in the 1890s were the height of male fashion (and were known as dog-collars from at least 1883).

And Caesar's spirit, ranging for revenge,
With Ate by his side come hot from Hell,
Shall in these confines with a monarch's voice
Cry Havoc! and let slip the dogs of war;
[Shakespeare, "Julius Caesar"]
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cut (v.)

c. 1300, "to make, with an edged tool or instrument, an incision in; make incisions for the purpose of dividing into two or more parts; remove by means of a cutting instrument;" of an implement, "have a cutting edge," according to Middle English Compendium from a presumed Old English *cyttan, "since ME has the normal regional variants of the vowel." Others suggest a possible Scandinavian etymology from North Germanic *kut- (source also of Swedish dialectal kuta "to cut," kuta "knife," Old Norse kuti "knife"), or that it is from Old French couteau "knife."

It has largely displaced Old English ceorfan (see carve (v.)), snian, and scieran (see shear). The past participle is also cut, though cutted sometimes has been used since Middle English.

From early 14c. as "to make or fashion by cutting or carving." From c. 1400 as "to intersect or cross." From early 15c. as "abridge or shorten by omitting a part."

Meaning "to wound the sensibilities of" is from 1580s (to cut the heart in the same sense is attested from early 14c.). Sense of "sever connection or relations with" is from 1630s.

Meaning "to be absent without excuse" is British university slang from 1794. Colloquial or slang sense of "move off with directness and rapidity" is from 1580s. Meaning "divide (a deck of cards) at random into parts before the deal" to prevent cheating is from 1530s.

Meaning "to dilute, adulterate" (liquor, etc.) is by 1930. Colloquial sense of "to divide or share" is by 1928, perhaps an image from meat-carving at table. As a director's call to halt recording or performing, by 1931 (in an article about Pete, the bulldog with the black-ringed eye in the Hal Roach studios shorts, who was said to know the word). The sense of "perform, execute" (c. 1600) is in cut capers "frisk about;" cut a dash "make a display."

To cut down is from late 14c. as "to fell;" by 1821 as "to slay" (as with a sword); 1857 as "to curtail." To cut (someone or something) down to size is from 1821 as "reduce to suitable dimensions;" the figurative sense, "reduce to the proper level of importance," is by 1927.

To cut in "enter suddenly and unceremoniously" is from 1610s; sense of "suddenly join in conversation, interrupt" is by 1830. To cut up "cut in pieces" is from 1570s. To cut back is from 1871 as "prune by cutting off shoots," 1913 in cinematography, "return to a previous scene by repeating a part of it," 1943 as "reduce, decrease" (of expenditures, etc.). To cut (something) short "abridge, curtail, interrupt" is from 1540s.

In nautical use to cut a feather (1620s) is to move so fast as to make water foam under the bow. To cut and run (1704) also is originally nautical, "cut cable and set sail immediately," as in an emergency, hence, generally, "to make off suddenly."

To cut the teeth "have the teeth grow through the gums" as an infant is from 1670s. To cut both ways in the figurative sense of "have a good and bad effect" is from c. 1600. To cut loose "set (something) free" is by 1828; intransitive sense "begin to act freely" is by 1909.

Cut it out "remove (something) by or as if by cutting" yielded a figurative use in the command cut it out! "Stop! That's enough!" by 1933. The evolution seems to have begun earlier. A piece attributed to the Chicago Live Stock World that made the rounds in trade publications 1901-02 begins:

When you get 'hot' about something and vow you are going to rip something or somebody up the back—cut it out.
If you feel disposed to try the plan of building yourself up by tearing some one else down—cut it out.

Playing on both senses, it ends with "Should you, after reading this preachy stuff, fear you might forget some of the good advice—cut it out."

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