Middle English taken, from late Old English tacan "to grip, seize by force, lay hold of," from a Scandinavian source (such as Old Norse taka "take, grasp, lay hold," past tense tok, past participle tekinn; also compare Swedish ta, past participle tagit).

This is reconstructed to be from Proto-Germanic *takan- (source also of Middle Low German tacken, Middle Dutch taken, Gothic tekan "to touch"), from Germanic root *tak- "to take," which is of uncertain origin, perhaps originally meaning "to touch" [OED, 1989].

The weakened sense of "get to oneself, get in hand, obtain, receive, acquire" is by late 12c. As the principal verb for "to take," it gradually replaced Middle English nimen, from Old English niman, from the usual West Germanic verb, *nemanan (source of German nehmen, Dutch nemen; see nimble and compare nim).

OED calls take "one of the elemental words of the language;" take up alone has 55 varieties of meaning in that dictionary's 1989 edition. Already in Middle English one could take pity, charge, a nap, hostages, heed, the veil, fire, an answer, a concubine, a bath, pains, prisoners, place, possession, part, leave, advice, a breath, a spouse, a chance, comfort, flight, courage. Compare the range of senses in Latin capere "to take."

In the sense of "take effect, work," earliest in reference to transplants or grafts (mid-15c.). As "obtain (one's image) by drawing or painting" from c. 1600, hence the later use for photographic images. To take after "resemble" is from 1550s. Take that! accompanying a blow, etc., is by early 15c.

You can't take it with you (i.e. riches, to the grave) is the title of a popular Kaufman and Hart play from 1936; the idea in the quip is at least a century older. To take apart "dismantle" is by 1936.

To take five "go on a five-minute break" is by 1929, from the approximate time it takes to smoke a cigarette. Take it easy is recorded by 1880; the phrase take it or leave it is recorded from 1897. Colloquial figurative phrase what it takes "the right qualities" (for success) is by 1929. 

To take it "absorb punishment" is by 1862; take the rap "accept (undeserved) punishment" is from 1930 (compare rap (n.)); take the fall in a similar sense is by 1942 (compare fall guy, by 1906).

"that which is taken," in any sense, 1650s, from take (v.). The movie-making sense of "continuous section of film recorded at one time" is by 1916.

The specific sense of "money taken in" is by 1850 in reference to church collections (by 1931 in reference to money taken in from a single performance). The criminal sense of "money acquired by theft" is from 1888. The verb take in the sense of "cheat, defraud" is attested from 1920. On the take "amenable to bribery" is by 1930.

late 15c., "receiving," present-participle adjective from take (v.). By c. 1600 in the figurative sense of "captivating, attractive, pleasing." Related: Takingly. Colloquial taky "captivating, charming" is by 1854.

1769, originally in horse-racing, referring to races in which bigger horses were given more weight to carry, lighter ones less; see give (v.) + take (v.). The general sense is attested by 1778. Give and take had been paired in expressions involving mutual exchange from c. 1500.

Give or take as an indication of approximation is from 1958.

"exaggerated reaction to surprise," 1922, from double (adj.) + take (n.). Originally in stage comedy acting.

intransitive, "be agitated, display great excitement," early 15c., on the notion of "put on" a form, display, etc.; see take (v.) + on (prep.). To take (something) on "begin to do" is from late 12c.

also outtake, "rejected part of a film," 1960, from out- + take (n.) in the movie sense. Related: Out-takes.

also take-away, 1964 in reference to food-shops, from the verbal phrase; see take (v.) + away (adv.).

The verbal phrase is attested by early 12c. as "seize, take by force, arrest," by c. 1300 as "remove, withdraw." Take-away (n.) is by 1970 as "shop which sells prepared food to go."

also take-over, 1917, "an act of taking over," from verbal phrase take over "assume ownership, control, or management of" (1884), from take (v.) + over (adv.). By 1957 as "coup." Attested from 1958 in the corporate sense "assumption of control or ownership of a business by another." Also compare overtake.

"to take, take up in the hands in order to move, carry, or use; take unlawfully, steal" (archaic), Old English niman "to take, accept, receive, grasp, catch," from Proto-Germanic *nemanan (source also of Old Saxon niman, Old Frisian nima, Middle Dutch nemen, German nehmen, Gothic niman), perhaps from PIE root *nem- "assign, allot; take." The native word, replaced by Scandinavian-derived take (v.) and out of use from c. 1500 except in slang sense of "to steal," which endured into 19c. The derivatives numb and nimble remain in use.