Etymology
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dependent (adj.)

also dependant, late 14c., "relying for existence on;" early 15c. as "contingent, related to some condition;" from Old French dependant, present-participle adjective from dependre "to hang down," from Latin dependere "to hang from, hang down; be dependent on, be derived," from de "from, down" (see de-) + pendere "to hang, cause to hang; weigh" (from PIE root *(s)pen- "to draw, stretch, spin").

For spelling, see dependant (n.). In some cases the English word is directly from Latin dependentem (nominative dependens), present participle of dependere. From early 15c. in the literal sense of "hanging down, pendent." From 1640s as "subordinate, under the control of or needing aid from an extraneous source." Dependent variable in mathematics is recorded from 1852.

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negative (n.)

late 14c., "a prohibition" (a sense now obsolete), also "absence, nonexistence; opposite," from Old French negatif and directly from Latin negativus (see negative (adj.)).

Meaning "a negative statement" is from 1560s. Sense of "that side of a question which denies what the opposite side affirms" is from 1570s. Meaning "the right or power of refusing assent" is from 1610s. Meaning "a negative quality" is from 1640s. In mathematics, "a negative number," from 1706. Photographic sense of "image in which the lights and shades are the opposite of those in nature" is recorded by 1853. As a response, "I refuse, disagree, no," from 1945, originally in radio communication. 

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remain (v.)

early 15c., remainen, "be left after the removal or loss of a part, number, or quality; survive," from Anglo-French remayn-, Old French remain- (as in il remaint "it remains"), stressed stem of remanoir "to stay, dwell, remain; be left; hold out," from Latin remanere "to remain, to stay behind; be left behind; endure, abide, last" (source also of Old Spanish remaner, Italian rimanere), from re- "back" (see re-) + manere "to stay, remain" (from PIE root *men- (3) "to remain").

Also from early 15c. as "continue" in someone's charge or possession; continue in a certain place or condition." From early 15c. in mathematics. Related: Remained; remaining.

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permutation (n.)

late 14c., permutacioun, "interchange, concurrent change; exchange of one thing, position, condition, etc., for another," from Old French permutacion "change, shift" (14c.), from Latin permutationem (nominative permutatio) "a change, alteration, revolution," noun of action from past participle stem of permutare "change thoroughly, exchange," from per "thoroughly" (see per) + mutare "to change" (from PIE root *mei- (1) "to change, go, move"). The sense of "a linear arrangement of objects resulting from a change of their order" is by 1710, originally in mathematics.

Permutation differs from combination in this, that in the latter there is no reference to the order in which the quantities are combined, whereas in the former this order is considered, and consequently the number of permutations always exceeds the number of combinations. [Century Dictionary]
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remainder (n.)

late 14c., remaindre, in law, a right of ownership designed to devolve upon a second party, from Anglo-French remeinder, Old French remaindre, noun use of infinitive, a variant of Old French remanoir "to stay, dwell, remain; be left; hold out," from Latin remanere "to remain, to stay behind; be left behind; endure, abide, last" (source also of Old Spanish remaner, Italian rimanere).

This is from re- "back" (see re-) + manere "to stay, remain" (from PIE root *men- (3) "to remain"). For noun use of infinitives in Anglo-French legalese, see waiver (n.).

The general meaning "that which remains, anything left over after separation, removal, etc." is by 1550s. In mathematics from 1570s. Specifically in publication, "what remains of an edition the sale of which has practically ceased and is sold at a reduced price" (1757).

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term (n.)
c. 1200, terme "limit in time, set or appointed period," from Old French terme "limit of time or place, date, appointed time, duration" (11c.), from Latin terminus "end, boundary line," in Medieval Latin "expression, definition," related to termen "boundary, end" (see terminus). Old English had termen "term, end," from Latin. Sense of "period of time during which something happens" first recorded c. 1300, especially of a school or law court session (mid-15c.).

The meaning "word or phrase used in a limited or precise sense" is first recorded late 14c., from Medieval Latin use of terminus to render Greek horos "boundary," employed in mathematics and logic. Hence in terms of "in the language or phraseology peculiar to." Meaning "completion of the period of pregnancy" is from 1844. Term-paper in U.S. educational sense is recorded from 1931.
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nous (n.)

college slang for "intelligence, wit, cleverness, common sense," 1706, from Greek nous, Attic form of noos "mind, intelligence, perception, intellect," which was taken in English in philosophy 1670s as "the perceptive and intelligent faculty." The Greek word is of uncertain origin. Beekes writes, "No doubt an old inherited verbal noun ..., though there is no certain etymology."

It is always difficult to find an English word to represent nous. The standard dictionary translation is "mind," but this does not have the correct connotations, particularly when the word is used in a religious philosophy. ... Mathematics, the world of ideas, and all thought about what is not sensible, have, for Pythagoras, Plato, and Plotinus, something divine; they constitute the activity of nous, or at least the nearest approach to its activity that we can conceive. [Bertrand Russell, "A History of Western Philosophy"]
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evolution (n.)
1620s, "an opening of what was rolled up," from Latin evolutionem (nominative evolutio) "unrolling (of a book)," noun of action from past participle stem of evolvere "to unroll" (see evolve).

Used in medicine, mathematics, and general writing in various senses including "growth to maturity and development of an individual living thing" (1660s). Modern use in biology, of species, first attested 1832 in works of Scottish geologist Charles Lyell. Charles Darwin used the word in print once only, in the closing paragraph of "The Origin of Species" (1859), and preferred descent with modification, in part because evolution already had been used in the discarded 18c. homunculus theory of embryological development (first proposed under this name by Bonnet, 1762) and in part because it carried a sense of "progress" not present in Darwin's idea. But Victorian belief in progress prevailed (and the advantages of brevity), and Herbert Spencer and other biologists after Darwin popularized evolution.
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entropy (n.)

1868, from German Entropie "measure of the disorder of a system," coined 1865 (on analogy of Energie) by German physicist Rudolph Clausius (1822-1888), in his work on the laws of thermodynamics, from Greek entropia "a turning toward," from en "in" (see en- (2)) + trope "a turning, a transformation" (from PIE root *trep- "to turn"). The notion is supposed to be "transformation contents." Related: Entropic.

It was not until 1865 that Clausius invented the word entropy as a suitable name for what he had been calling "the transformational content of the body." The new word made it possible to state the second law in the brief but portentous form: "The entropy of the universe tends toward a maximum," but Clausius did not view entropy as the basic concept for understanding that law. He preferred to express the physical meaning of the second law in terms of the concept of disgregation, another word that he coined, a concept that never became part of the accepted structure of thermodynamics. [Martin J. Klein, "The Scientific Style of Josiah Willard Gibbs," in "A Century of Mathematics in America," 1989]
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algebra (n.)

"formal mathematics; the analysis of equations; the art of reasoning about quantitative relations by the aid of a compact and highly systematized notation," 1550s, from Medieval Latin algebra, from Arabic "al-mukhtasar fi hisab al-jabr wa al-muqabala" ("the compendium on calculation by restoring and balancing"), the title of the famous 9c. treatise on equations by Baghdad mathematician Abu Ja'far Muhammad ibn Musa al-Khwarizmi. Arabic al jabr ("in vulgar pronunciation, al-jebr" [Klein]) "reunion of broken parts" (reducing fractions to integers in computation) was one of the two preparatory steps to solving algebraic equations; it is from Arabic jabara "reintegrate, reunite, consolidate." Al-Khwarizmi's book (translated into Latin in 12c.) also introduced Arabic numerals to the West. John Dee (16c.) calls it algiebar and almachabel. The accent shifted 17c. from second syllable to first.

The same word was used in English 15c.-16c. to mean "bone-setting," as was Medieval Latin algebra, a usage picked up probably from Arab medical men in Spain.

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