Etymology
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Words related to Logos

*leg- (1)

Proto-Indo-European root meaning "to collect, gather," with derivatives meaning "to speak" on the notion of "to gather words, to pick out words."

It forms all or part of: alexia; analects; analogous; analogue; analogy; anthology; apologetic; apologue; apology; catalogue; coil; colleague; collect; college; collegial; Decalogue; delegate; dialect; dialogue; diligence; doxology; dyslexia; eclectic; eclogue; elect; election; epilogue; hapax legomenon; homologous; horology; ideologue; idiolect; intelligence; lectern; lectio difficilior; lection; lector; lecture; leech (n.2) "physician;" legacy; legal; legate; legend; legible; legion; legislator; legitimate; lesson; lexicon; ligneous; ligni-; logarithm; logic; logistic; logo-; logogriph; logopoeia; Logos; -logue; -logy; loyal; monologue; neglect; neologism; philology; privilege; prolegomenon; prologue; relegate; sacrilege; select; syllogism; tautology; trilogy.

It is the hypothetical source of/evidence for its existence is provided by: Greek legein "to say, tell, speak, declare; to count," originally, in Homer, "to pick out, select, collect, enumerate;" lexis "speech, diction;" logos "word, speech, thought, account;" Latin legere "to gather, choose, pluck; read," lignum "wood, firewood," literally "that which is gathered," legare "to depute, commission, charge," lex "law" (perhaps "collection of rules"); Albanian mb-ledh "to collect, harvest;" Gothic lisan "to collect, harvest," Lithuanian lesti "to pick, eat picking;" Hittite less-zi "to pick, gather."

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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]
analogue (n.)
1826, "an analogous thing," from French analogue (adj. and n.), from Latin analogus (adj.), from Greek analogos "proportionate, according to due proportion," from ana "throughout; according to" (see ana-) + logos "ratio, proportion," a specialized use (see Logos).

The word was used in English in Greek form (analogon) in 1810. Meaning "word corresponding with another" is from 1837. Computing sense, in reference to operating with numbers represented by some measurable quantity (as a slide-rule does; opposed to digital) is recorded from 1946.
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."
apology (n.)
Origin and meaning of apology
early 15c., "defense, justification," from Late Latin apologia, from Greek apologia "a speech in defense," from apologeisthai "to speak in one's defense," from apologos "an account, story," from apo "away from, off" (see apo-) + logos "speech" (see Logos).

In classical Greek, "a well-reasoned reply; a 'thought-out response' to the accusations made," as that of Socrates. The original English sense of "self-justification" yielded a meaning "frank expression of regret for wrong done," first recorded 1590s, but this was not the main sense until 18c. Johnson's dictionary defines it as "Defence; excuse," and adds, "Apology generally signifies rather excuse than vindication, and tends rather to extenuate the fault, than prove innocence," which might indicate the path of the sense shift. The old sense has tended to shift to the Latin form apologia (1784), known from early Christian writings in defense of the faith.
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.

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.

logic (n.)

mid-14c., logike, "branch of philosophy that treats of forms of thinking; the science of distinction of true from false reasoning," from Old French logique (13c.), from Latin (ars) logica "logic," from Greek (he) logike (techne) "(the) reasoning (art)," from fem. of logikos "pertaining to speaking or reasoning" (also "of or pertaining to speech"), from logos "reason, idea, word" (see Logos). Formerly also logick. Sometimes formerly plural, as in ethics, but this is not usual. Meaning "logical argumentation" is from c. 1600. Contemptuous logic-chopper "sophist, person who uses subtle distinctions in argument" is from 1846.

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.
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].