Etymology
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Logos (n.)

1580s, "the divine Word, second person of the Christian Trinity," from Greek logos "word, speech, statement, discourse," also "computation, account," also "reason," from PIE *log-o-, suffixed form of root *leg- (1) "to collect, gather," with derivatives meaning "to speak," on notion of "to pick out words." The Greek word was used by Neo-Platonists in metaphysical and theological senses involving notions of both "reason" and "word" and subsequently picked up by New Testament writers.

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Decalogue (n.)

"Ten Commandments," late 14c., from Latin decalogus, from Greek dekalogos, from the phrase hoi deka logoi used to translate "Ten Commandments" in Septuagint. See deca- + Logos.

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apologue (n.)
"moral fable, fictitious story intended to convey useful truths," 1550s, from French apologue, from Latin apologus, from Greek apologos "a story, tale, fable," from apo "off, away from" (see apo-) + logos "speech" (see Logos). Literally, "(that which comes) from a speech."
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trilogy (n.)
series of three related works, 1660s, from Greek trilogia "series of three related tragedies performed at Athens at the festival of Dionysus," from tri- "three" (see three) + logos "story" (see Logos).
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logogriph (n.)
type of word puzzle based on synonyms, etc., and often in the form of a verse, 1590s, from French logogriphe, from Greek logos "word" (see Logos) + gripos/griphos "riddle," a figurative use, literally "fishing basket, creel," probably from a pre-Greek word in a lost Mediterranean language. "The variation [p/ph] is typical for Pre-Greek words; such an origin for a fisherman's word is quite understandable" [Beekes].
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logistic (adj.)
"pertaining to logic," 1620s, from Medieval Latin logisticus, from Greek logistikos "skilled in calculating; endued with reason," from logistes "a calculator," from logos "calculation, proportion" (see Logos). Related: Logistical (1560s); logistically. Logistics, from this word, in the sense "art of arithmetical calculation" is from 1650s.
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neologism (n.)

1772 (in a translation from French), "practice of innovation in language, the use of new words or old words in new senses," from French néologisme (18c.), from neo- "new" (see neo-) + Greek logos "word" (see Logos) + -ism. Meaning "new word or expression" is from 1803. Neological "characterized by new words or phrases" is attested from 1754. Related: Neologically.

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analogous (adj.)

"corresponding (to some other) in particulars," 1640s, from Latin analogus, from Greek analogos "proportionate, according to due proportion," from ana "throughout; according to" (see ana-) + logos "ratio, proportion," a specialized use (see Logos). Used with to or with.

A term is analogous whose single signification applies with equal propriety to more than one object: as, the leg of the table, the leg of the animal. [William Flemming, "The Vocabulary of Philosophy," 1858]
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syllogism (n.)
late 14c., from Old French silogisme "a syllogism, scholastic argument based on a formula or proof" (13c., Modern French syllogisme), from Latin syllogismus, from Greek syllogismos "a syllogism," originally "inference, conclusion; computation, calculation," from syllogizesthai "bring together before the mind, compute, conclude," literally "think together," from assimilated form of syn- "together" (see syn-) + logizesthai "to reason, count," from logos "a reckoning, reason" (see Logos).
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logarithm (n.)

a mathematical function used to shorten calculation, 1610s, logarithmus, coined in Modern Latin by Scottish mathematician John Napier (1550-1617), literally "ratio-number," from Greek logos "proportion, ratio, word" (see Logos) + arithmos "number" (from PIE *erei-dhmo-, suffixed variant form of root *re- "to reason, count"). Napier invented them and published a table in 1614; the kind now chiefly in use were invented by his contemporary Henry Briggs (1561-1630), a professor of geometry at Gresham College, London.

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