Etymology
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clear (v.)

mid-14c., "make clear (an obscure subject) in the mind, explain, elucidate;" late 14c., "make clean, cleanse, purify; clarify (a liquid), remove what clouds or diminishes brightness or transparency;" also "prove innocent, vindicate;" of the weather, sea, sky, clouds, etc., "clear up, become fair or calm;" from clear (adj.).  Related: Cleared; clearing.

Intransitive sense of "become free from murkiness" is from 1580s. Meaning "to free from obstructions" is from 1520s; that of "to free from entanglement" is from 1590s; that of "pass (an obstacle) without entanglement or collision" is from 1630s. Sense of "to remove (something) out of the way" is from 1670s; that of "to clear land of trees and underbrush" is from 1690s. Meaning "to leap clear over" is first attested 1791. Meaning "to gain (a sum of money) in clear profit" is from 1719. Meaning "get approval for (a proposal, etc.) from authority" is from 1944; meaning "establish as suitable for national security work" is from 1948.

To clear (one's) throat is from 1881; earlier clear (one's) voice (1701). To clear out "depart, leave" (1825), perhaps is from the notion of ships satisfying customs, harbor regulations, etc., then setting sail. To get clear of is from 1590s. To clear up is from 1620s of weather, 1690s as "make clear to the mind." Clear the deck (1802) is from sailing ships. Clear the air in the figurative sense is from late 14c. To clear the coast (1520s) was to make it suitable for landing.

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clear (n.)

early 13c., in place names, "a clearing, a forest glade," from Old French noun use of the adjective (see clear (adj.)). In Middle English also "a beautiful person" (mid-14c.). From c. 1500 as "brightness." The notion in in the clear (1715) is "a clear space."

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clear (adj.)

c. 1300, "giving light, shining, luminous;" also "not turbid; transparent, allowing light to pass through; free from impurities; morally pure, guiltless, innocent;" of colors, "bright, pure;" of weather or the sky or sea, "not stormy; mild, fair, not overcast, fully light, free from darkness or clouds;" of the eyes or vision, "clear, keen;" of the voice or sound, "plainly audible, distinct, resonant;" of the mind, "keen-witted, perspicacious;" of words or speech, "readily understood, manifest to the mind, lucid" (an Old English word for this was sweotol "distinct, clear, evident"); of land, "cleared, leveled;" from Old French cler "clear" (of sight and hearing), "light, bright, shining; sparse" (12c., Modern French clair), from Latin clarus "clear, loud," of sounds; figuratively "manifest, plain, evident," in transferred use, of sights, "bright, distinct;" also "illustrious, famous, glorious" (source of Italian chiaro, Spanish claro), from PIE *kle-ro-, from root *kele- (2) "to shout."

The prehistoric sense evolution to light and color involves an identification of the spreading of sound and the spreading of light (compare English loud, used of colors; German hell "clear, bright, shining," of pitch, "distinct, ringing, high").

Also in Middle English "beautiful, magnificent, excellent" (c. 1300); of possession or title, "unrestricted, unconditional, absolute," early 15c. Of complexion, from c. 1300. Sense of "free from encumbrance," later largely nautical, developed c. 1500. Meaning "obvious to the senses" is from 1835. Clear-sighted is from 1580s (clear-eyed is from 1520s); clear-headed is from 1709. For coast is clear see clear (v.).

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clear (adv.)

c. 1300, "completely, quite, entirely, wholly," c. 1300, from clear (adj.) or adverbial use of the adjective in Old French. From early 14c. as "plainly, lucidly;" mid-14c. as "loudly, with distinctness of sound;" late 14c. as "brightly, brilliantly."

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air (n.3)
"melody, tune, connected rhythmic succession of distinct musical sounds," 1580s, nativized from Italian aria (see aria), perhaps via French.
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air (n.1)

c. 1300, "invisible gases that surround the earth," from Old French air "atmosphere, breeze, weather" (12c.), from Latin aer "air, lower atmosphere, sky," from Greek aēr (genitive aeros) "mist, haze, clouds," later "atmosphere" (perhaps related to aenai "to blow, breathe"), which is of unknown origin. It is possibly from a PIE *awer- and thus related to aeirein "to raise" and arteria "windpipe, artery" (see aorta) on notion of "lifting, suspended, that which rises," but this has phonetic difficulties.

In Homer mostly "thick air, mist;" later "air" as one of the four elements. Words for "air" in Indo-European languages tend to be associated with wind, brightness, sky. In English, air replaced native lyft, luft (see loft (n.)). In old chemistry, air (with a qualifying adjective) was used of any gas.

To be in the air "in general awareness" is from 1875; up in the air "uncertain, doubtful" is from 1752. To build castles in the air "entertain visionary schemes that have no practical foundation" is from 1590s (in 17c. English had airmonger "one preoccupied with visionary projects"). Broadcasting sense (as in on the air, airplay) first recorded 1927. To give (someone) the air "dismiss" is from 1900. Air pollution is attested by 1870. Air guitar is by 1983. Air traffic controller is from 1956.

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air (n.2)
1590s, "manner, appearance" (as in an air of mystery); 1650s, "assumed manner, affected appearance" (especially in phrase put on airs, 1781), from French air "look, appearance, mien, bearing, tone" (Old French aire "reality, essence, nature, descent, extraction" (12c.); compare debonair), which is perhaps from Latin ager "place, field, productive land" (from PIE root *agro- "field") on notion of "place of origin."

But some French sources connect this Old French word with the source of air (n.1), and it also is possible these senses in English developed from or were influenced by air (n.1); compare sense development of atmosphere and Latin spiritus "breath, breeze," also "high spirit, pride," and the extended senses of anima.
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air (v.)
1520s, "expose to open air," 1520s, from air (n.1). Figurative sense of "expose ostentatiously, make public" is from 1610s of objects, 1862 of opinions, grievances, etc. Meaning "to broadcast" (originally on radio) is from 1933. Related: Aired; airing.
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clear-cut (adj.)

"formed with distinct outlines" (as if by cutting as opposed to molding), 1855, from clear (adj.) + past participle adjective from cut (v.).

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clear-cutting (n.)

"felling and removal of all the trees in a place," 1874, from clear (adj.) + cutting (n.), verbal noun from cut (v.).

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