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.
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.
"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]
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.