Etymology
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lucid (adj.)
1590s, "bright, shining" (a sense now obsolete or restricted), from Latin lucidus "light, bright, clear," figuratively "perspicuous, lucid, clear," from lucere "to shine," from lux (genitive lucis) "light," from PIE root *leuk- "to shine, be bright."

Sense of "easy to understand, free from obscurity of meaning, marked by intellectual clarity" first recorded 1786. Lucid interval "period of calm or temporary sanity" (1580s) is from Medieval Latin lucida intervalla (plural), common in medieval legal documents (non est compos mentis, sed gaudet lucidis intervallis, etc.). The notion probably is of a period of calm and clear during a storm. Related: Lucidly; lucidness (1640s).
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lucida (n.)
in astronomy, "star easily seen by the naked eye," also "brightest star in a constellation or group," 1727, from Modern Latin lucida (stella) "bright star," from fem. of Latin lucidus "light, bright, clear" (see lucid). Plural lucidae. Astronomy has used lucid for "visible to the naked eye" since 1690s.
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*leuk- 

Proto-Indo-European root meaning "light, brightness."

It forms all or part of: allumette; elucidate; illumination; illustration; lea; leukemia; leuko-; light (n.) "brightness, radiant energy;" lightning; limn; link (n.2) "torch of pitch, tow, etc.;" lucent; lucid; Lucifer; luciferase; luciferous; lucifugous; lucubrate; lucubration; luculent; lumen; Luminal; luminary; luminate; luminescence; luminous; luna; lunacy; lunar; Lunarian; lunate; lunation; lunatic; lune; lunette; luni-; luster; lustrum; lux; pellucid; sublunary; translucent.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit rocate "shines;" Armenian lois "light," lusin "moon;" Greek leukos "bright, shining, white;" Latin lucere "to shine," lux "light," lucidus "clear;" Old Church Slavonic luci "light;" Lithuanian laukas "pale;" Welsh llug "gleam, glimmer;" Old Irish loche "lightning," luchair "brightness;" Hittite lukezi "is bright;" Old English leht, leoht "light, daylight; spiritual illumination," German Licht, Gothic liuhaþ "light."

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lunatic (n.)
"lunatic person," late 14c., from lunatic (adj.). Originally one with lucid intervals; later, in legal use, a general term for a person of unsound mind.
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luculent (adj.)

early 15c., "luminous, bright;" 1590s, "evident, lucid," from Latin luculentus "full of light, bright, splendid," from the stem of lux "light" (from PIE root *leuk- "light, brightness").

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elucidate (v.)

"make clear or manifest, throw light upon, explain, render intelligible," 1560s, perhaps via French élucider (15c.) or directly from Late Latin elucidatus, past participle of elucidare "make light or clear," from assimilated form of ex "out, away" (see ex-) + lucidus "light, bright, clear," figuratively "perspicuous, lucid, clear," from lucere "to shine" (from PIE root *leuk- "to shine, be bright"). Related: Elucidated; elucidates; elucidating.

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lucidity (n.)
1650s, "brightness," from French lucidité, from Late Latin luciditas, from Latin lucidus "light, bright, clear," from lucere "to shine," from PIE *louk-eyo-, suffixed (iterative) form of root *leuk- "light, brightness." Meaning "intellectual clarity, transparency of expression" is by 1851.
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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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