Etymology
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keep (v.)

Middle English kēpen, from late Old English cepan (past tense cepte) "to seize, hold; seek after, desire," also "to observe or carry out in practice; look out for, regard, pay attention to," from Proto-Germanic *kopjan, which is of uncertain origin. Old English cepan was used c. 1000 to render Latin observare, so perhaps it is related to Old English capian "to look" (from Proto-Germanic *kap-), which would make the basic sense "to keep an eye on, see to it."

The word prob. belonged primarily to the vulgar and non-literary stratum of the language; but it comes up suddenly into literary use c. 1000, and that in many senses, indicating considerable previous development. [OED]

The senses exploded in Middle English: "to guard, defend" (12c.); "restrain (someone) from doing something" (early 13c.); "take care of, look after; protect or preserve (someone or something) from harm, damage, etc." (mid-13c.); "preserve, maintain, carry on" a shop, store, etc. (mid-14c.); "prevent from entering or leaving, force to remain or stay" (late 14c.); "preserve (something) without loss or change," also "not divulge" a secret, private information, etc., also "to last without spoiling" (late 14c.); "continue on" (a course, road, etc.), "adhere to" a course of action (late 14c.); "stay or remain" (early 15c.); "to continue" (doing something) (mid-15c.). It is used to translate both Latin conservare "preserve, keep safe" and tenere "to keep, retain."

From 1540s as "maintain for ready use;" 1706 as "have habitually in stock for sale." Meaning "financially support and privately control" (usually in reference to mistresses) is from 1540s; meaning "maintain in proper order" (of books, accounts) is from 1550s.

To keep at "work persistently" is from 1825; to keep on "continue, persist" is from 1580s. To keep up is from 1630s as "continue alongside, proceed in pace with," 1660s as "maintain in good order or condition, retain, preserve," 1680s as "support, hold in an existing state." To keep it up "continue (something) vigorously" is from 1752. To keep to "restrict (oneself) to" is from 1711. To keep off (trans.) "hinder from approach or attack" is from 1540s; to keep out (trans.) "prevent from entering" is from early 15c.

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set (v.)

Middle English setten, from Old English settan (transitive) "cause to sit; make or cause to rest as on a seat; cause to be put, placed, or seated;" also "put in a definite place," also "arrange, fix adjust; fix or appoint (a time) for some affair or transaction," and "cause (thoughts, affections) to dwell on."

This is from Proto-Germanic *(bi)satejanan "to cause to sit, set" (source also of Old Norse setja, Swedish sätta, Old Saxon settian, Old Frisian setta, Dutch zetten, German setzen, Gothic satjan), causative form of PIE *sod-, a variant of the root *sed- (1) "to sit." Also see set (n.2). It has been confused with sit (v.) at least since early 14c. 

The intransitive sense of "be seated" is from c. 1200; that of "sink down, descend, decline toward and pass below the horizon" (of the sun, moon, or stars) is by mid-13c., perhaps from similar use of the cognates in Scandinavian languages; figurative use of this is from c. 1600.

Many uses are highly idiomatic, the verb, like put, its nearest equivalent, and do, make, get, etc., having become of almost universal application, and taking its distinctive color from the context. [Century Dictionary]

The sense of "make or cause to do, act, or be; start, bring (something) to a certain state" (on fire, in order, etc.) and that of "mount a gemstone" are attested by mid-13c. That of "determine upon, resolve" is from c. 1300; hence be set against "resisting" (mid-14c.).

The sense of "make a table ready for a meal" is from late 14c.; that of "regulate or adjust by a standard" (of a clock, etc.) is from late 14c. In printing, "to place (types) in the proper order for reading; put into type," 1520s. From c. 1500 as "put words to music." From 1570s as "put (a broken or dislocated bone) in position." In cookery, plastering, etc., "become firm or solid in consistency" by 1736.

To set (one's) heart on (something) is from c. 1300 as "love, be devoted to;" c. 1400 as "have a desire for." To set (one's) mind is from mid-15c.; transitive set (one's mind) to "determine to accomplish" is from late 15c.  To set (something) on "incite to attack" (c. 1300) originally was in reference to hounds and game. To set an example is mid-14c. (set (v.) in the sense of "present" is from late Old English). The notion of "fix the value of" is behind old phrases such as set at naught "regard as nothing."

To set out is from c. 1300 as "display (for sale);" to set up shop "commence doing business" is from c. 1400.

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