Etymology
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three (adj., n.)

"1 more than two; the number which is one more than two; a symbol representing this number;" Old English þreo, fem. and neuter (masc. þri, þrie), from Proto-Germanic *thrijiz (source also of Old Saxon thria, Old Frisian thre, Middle Dutch and Dutch drie, Old High German dri, German drei, Old Norse þrir, Danish tre), from nominative plural of PIE root *trei- "three" (source also of Sanskrit trayas, Avestan thri, Greek treis, Latin tres, Lithuanian trys, Old Church Slavonic trye, Irish and Welsh tri "three").

3-D first attested 1952, abbreviation of three-dimensional (1878). Three-piece suit is recorded from 1909. Three cheers for ______ is recorded from 1751. Three-martini lunch is attested from 1972. Three-ring circus is recorded by 1898. Three-sixty "complete turnaround" is from 1927, originally among aviators, in reference to the number of degrees in a full circle. Three musketeers translates French les trois mousquetaires, title of the 1844 novel by Alexandre Dumas père.

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way (n.)

Old English weg "road, path; course of travel; room, space, freedom of movement;" also, figuratively, "course of life" especially, in plural, "habits of life" as regards moral, ethical, or spiritual choices, from Proto-Germanic *wega- "course of travel, way" (source also of Old Saxon, Dutch weg, Old Norse vegr, Old Frisian wei, Old High German weg, German Weg, Gothic wigs "way"), from PIE root *wegh- "to go, move, transport in a vehicle."

From c. 1300 as "manner in which something occurs." Adverbial constructions attested since Middle English include this way "in this direction," that way "in that direction," both from late 15c.; out of the way "remote" (c. 1300). In the way "so placed as to impede" is from 1560s.

From the "course of life" sense comes way of life (c. 1600), get (or have) one's way (1590s), have it (one's) way (1709). From the "course of travel" sense comes the figurative go separate ways (1837); one way or (the) other (1550s); have it both ways (1847); and the figurative sense of come a long way (1922).

Adverbial phrase all the way "completely, to conclusion" is by 1915; sexual sense implied by 1924. Make way is from c. 1200. Ways and means "resources at a person's disposal" is attested from early 15c. (with mean (n.)). Way out "means of exit" is from 1926. Encouragement phrase way to go is short for that's the way to go.

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way (adv.)
c. 1200, short for away (adv.). Many expressions involving this are modern and American English colloquial, such as way-out "far off;" way back "a long time ago" (1887); way off "quite wrong" (1892). Any or all of these might have led to the slang adverbial meaning "very, extremely," attested by 1984 (as in way cool).
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Three Rs (n.)

1824; said to have been given as a toast by Sir William Curtis (1752-1829), a beloved lord mayor of London in the 1820s, who seems to have been a figure of fun to whom many mangled phrases were attributed. Among the toasts he is alleged to have given at public dinners were "The Female Ladies of London;" "The three C's—Cox, King, and Curtis;" and "The three R's—Reading, Writing, and Rithmetic."

It has been very much the fashion amongst a class of persons to attribute to Sir W. C. ... a vulgarity and ignorance of speech which are by no means consistent with his character and conduct. The worthy and hospitable baronet has a rapid mode of speech, but it is always correct ; and although some eccentricities are mixed up in his composition, he is highly honourable, and has been a very useful member of society, particularly to his London constituents. [The Mirror, Jan. 29, 1825]

After listing some examples, the article continues:

It is, however, very certain, that at a city festival some years ago, having indulged very freely, he fell asleep, when some wag, choosing to consider him dead, wrote his epitaph, which was found next morning pinned to the baronet's dress coat:—
"Here lies the great Curtis,
Of London, Lord May'r:
He's left this here world,
And gone to that there."
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cart-way (n.)
also cartway, "road on which carts may travel," mid-14c., from cart (n.) + way (n.).
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one-way (adj.)

1824, "leading in one direction only;" by 1887 in reference to travel tickets or fares; 1914 in reference to streets; 1940 in reference to windows, mirrors, etc.; from one + way (n.).

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Icknield Way 
prehistoric trackway from Norfolk to Dorset, Old English Iccenhilde, Icenhylte (903), which is of unknown meaning and origin. There was a Romano-British Iceni tribe in modern Norfolk. The name was transferred 12c. to the ancient Roman road from Burton on the Water to Templeborough.
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right of way (n.)

1767, "legal right, established by usage, to pass across grounds or property belonging to another." Of the path itself from 1805. By 1913 as "legal right of a pedestrian or vehicle to have precedence at a crossing or convergence." 

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side-way (n.)
also sideway, 1550s, lateral space for passage or movement," from side (n.) + way (n.).
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