Etymology
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considerable (adj.)

mid-15c., "capable of being considered, conceivable," from Medieval Latin considerabilis "worthy to be considered," from Latin considerare "to look at closely, observe," probably literally "to observe the stars," from assimilated form of com "with, together" (see con-) + sidus (genitive sideris) "heavenly body, star, constellation" (see sidereal).

Meaning "pretty large" is from 1650s (implied in considerably), from now-archaic earlier sense of "Worthy of regard or attention" (1610s).

CONSIDERABLE. This word is still frequently used in the manner pointed out by Dr. Witherspoon in the following remark: "He is considerable of a surveyor; considerable of it may be found in the country. This manner of speaking prevails in the northern parts." [Pickering, "A Vocabulary, or Collection of Words and Phrases Which Have Been Supposed to be Peculiar to the United States of America," 1816]
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retrospection (n.)

1630s, "action of looking back," noun of action from past-participle stem of Latin retrospicere "look back," from retro "back" (see retro-) + specere "look at" (from PIE root *spek- "to observe"). Specifically "act of looking back on times past" (1729).

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considerate (adj.)

1570s, "marked by deliberation," from Latin consideratus, past participle of considerare "to look at closely, observe" (see consider). Of persons, "deliberate, prudent, given to consideration" 1580s; meaning "not unfeeling or rigorous, showing consideration for the circumstances or feelings of others" is from c. 1700. Related: Considerately; considerateness.

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annotation (n.)

mid-15c., "a written comment," from Latin annotationem (nominative annotatio), noun of action from past-participle stem of annotare "to observe, remark," from ad "to" (see ad-) + notare "to mark, note, make a note," from nota "mark, sign, means of recognition" (see note (n.)). Related: Annotations.

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circumspect (adj.)

"cautious, wary," literally "looking about on all sides," early 15c., from Latin circumspectus "deliberate, guarded, well-considered," past participle of circumspicere "look around, take heed," from circum "around, round about" (see circum-) + specere "to look" (from PIE root *spek- "to observe"). Related: Circumspectly; circumspectness.

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spy (v.)
mid-13c., "to watch stealthily," from Old French espiier "observe, watch closely, spy on, find out," probably from Frankish *spehon or some other Germanic source, from Proto-Germanic *spehon- (source also of Old High German *spehon "to look out for, scout, spy," German spähen "to spy," Middle Dutch spien), the Germanic survivals of the productive PIE root *spek- "to observe." Old English had spyrian "make a track, go, pursue; ask about, investigate," also a noun spyrigend "investigator, inquirer." Italian spiare, Spanish espiar also are Germanic loan-words. Meaning "to catch sight of" is from c. 1300. Children's game I spy so called by 1946.
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Anschauung (n.)

"sense-perception," 1833 as a German word in English, nativized from 1848, from German Anschauung "mode of view," literally "a looking at," from anschauen "to look at," from Middle High German aneschouwen, from an (see on) + Old High German scouwon "to look at" (from PIE root *keu- "to see, observe, perceive"). A term in Kantian philosophy.

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observatory (n.)

"building for observing astronomical phenomena," 1670s (in reference to Greenwich), from French observatoire, from observer (v.) "to observe, watch over, follow," from Latin observare "watch over," from ob "in front of, before" (see ob-) + servare "to watch, keep safe," from PIE root *ser- (1) "to protect."

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spectrum (n.)
1610s, "apparition, specter," from Latin spectrum (plural spectra) "an appearance, image, apparition, specter," from specere "to look at, view" (from PIE root *spek- "to observe"). Meaning "visible band showing the successive colors, formed from a beam of light passed through a prism" first recorded 1670s. Figurative sense of "entire range (of something)" is from 1936.
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specimen (n.)
1610s, "pattern, model," from Latin specimen "indication, mark, example, sign, evidence; that by which a thing is known, means of knowing," from specere "to look at" (from PIE root *spek- "to observe"). Meaning "single thing regarded as typical of its kind" first recorded 1650s. Compare species.
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