quotation (n.)

mid-15c., "numbering," later (1530s) "marginal notation," noun of action from quote (v.) or else from Medieval Latin quotationem (nominative quotatio), noun of action from past-participle stem of quotare "to number."

Meaning "an act of quoting or citing" is from 1640s; that of "passage quoted, that which is repeated or cited as the utterance of another speaker or writer" is from 1680s. Meaning "the current price of commodities or stocks, as published," is by 1812. Quotation mark, one of the marks to denote the beginning and end of a quotation, is attested by 1777.

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calculus (n.)
mathematical method of treating problems by the use of a system of algebraic notation, 1660s, from Latin calculus "reckoning, account," originally "pebble used as a reckoning counter," diminutive of calx (genitive calcis) "limestone" (see chalk (n.)). Modern mathematical sense is a shortening of differential calculus.

In medicine, the word also has been used from 1732 to mean kidney stones, etc., then generally for "concretion occurring accidentally in the animal body," such as dental plaque.
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gamut (n.)

1520s, "low G, lowest note in the medieval musical scale" (the system of notation devised by Guido d'Arezzo), a contraction of Medieval Latin gamma ut, from gamma, the Greek letter, used in medieval music notation to indicate the note below the A which began the classical scale, + ut (now do), the low note on the six-note musical scale that took names from syllables sung to those notes in a Latin sapphic hymn for St. John the Baptist's Day:

Ut queant laxisresonare fibris
Mira gestorum famuli tuorum,
Solve pollutis labiis reatum,
Sancte Iohannes.

The ut being the conjunction "that." Gamut also was used for "range of notes of a voice or instrument" (1630s), also "the whole musical scale," hence the figurative sense of "entire scale or range" of anything, first recorded 1620s. When the modern octave scale was set early 16c., si was added, changed to ti in Britain and U.S. to keep the syllables as different from each other as possible. Ut later was replaced by more sonorous do (n.). See also solmization.

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decimal (adj.)

c. 1600, "pertaining to a tenth or ten," from Medieval Latin decimalis "of tithes or tenths," from Latin decimus "tenth," from decem "ten" (from PIE root *dekm- "ten"). Applied to Arabic notation before modern use in reference to decimal fractions (fraction whose denominator is a power of 10) emerged 1610s. As a noun from 1640s, "a decimal fraction." Decimal point is by 1711; the use of the point seems to be due to Scottish mathematician John Napier, "Marvellous Merchiston," c. 1619.

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designation (n.)

late 14c., designacioun, "notation, representation, action of pointing or marking out," from Old French designacion or directly from Latin designationem (nominative designatio) "a marking out, specification," noun of action from past participle stem of designare "mark out, devise, choose, designate, appoint," from de "out" (see de-) + signare "to mark," from signum "identifying mark, sign" (see sign (n.)).

Sense of "nomination, a selecting and appointing" is from c. 1600. Meaning "a descriptive name" which designates, originally especially an addition to a name of a title, profession, trade, or occupation, is from 1824.

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zero (n.)
"figure which stands for naught in the Arabic notation," also "the absence of all quantity considered as quantity," c. 1600, from French zéro or directly from Italian zero, from Medieval Latin zephirum, from Arabic sifr "cipher," translation of Sanskrit sunya-m "empty place, desert, naught" (see cipher (n.)).

A brief history of the invention of "zero" can be found here. Meaning "worthless person" is recorded from 1813. As an adjective from 1810. Zero tolerance first recorded 1972, originally U.S. political language. Zero-sum in game theory is from 1944 (von Neumann), indicating that if one player wins X amount the other or others must lose X amount.
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era (n.)
1716, earlier aera (1610s), from Late Latin aera, era "an era or epoch from which time is reckoned" (7c.), probably identical with Latin aera "counters used for calculation," plural of aes (genitive aeris) "brass, copper, money" (see ore, also compare copper). The Latin word's use in chronology said to have begun in 5c. Spain (where the local era, aera Hispanica, began 38 B.C.E.; some say because of a tax levied that year). Other ancient eras included the Chaldean (autumn of 311 B.C.E.), the Era of Actium (31 B.C.E.), of Antioch (49 B.C.E.), of Tyre (126 B.C.E.), the Olympiadic (July 1, 776 B.C.E.) and the Seleucidan (autumn 312 B.C.E.). In English it originally meant "the starting point of an age" (compare epoch); meaning "system of chronological notation" is from 1640s; that of "historical period" is from 1741, as in the U.S. Era of Good Feeling (1817) was anything but.
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punctuation (n.)

1530s, "pointing of the psalms" (for the purpose of singing them), from Medieval Latin punctuationem (nominative punctuatio) "a marking with points in writing," noun of action from past-participle stem of punctuare "to mark with points or dots," from Latin punctus, past participle of pungere "to prick, pierce" (from suffixed form of PIE root *peuk- "to prick"). Meaning "system of inserting pauses in written matter" is recorded from 1660s.

The modern system of punctuation was gradually developed after the introduction of printing, primarily through the efforts of Aldus Manutius and his family. ... Long after the use of the present points became established, they were so indiscriminately employed that, if closely followed, they are often a hindrance rather than an aid in reading and understanding the text. There is still much uncertainty and arbitrariness in punctuation, but its chief office is now generally understood to be that of facilitating a clear comprehension of the sense. [Century Dictionary, 1895]
[P]unctuation is cold notation; it is not frustrated speech; it is typographic code. [Robert Bringhurst, "The Elements of Typographic Style," 2004]
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scientific (adj.)

1580s, "concerned with the acquisition of accurate and systematic knowledge of principles by observation and deduction," from French scientifique, from Medieval Latin scientificus "pertaining to science," from Latin scientia "knowledge" (see science) + -ficus "making, doing," from combining form of facere "to make, to do" (from PIE root *dhe- "to set, put"). The Latin word was used originally to translate Greek epistēmonikos "making knowledge" in Aristotle's "Ethics."

By 1670s as "guided by the principles of science," hence "learned, skillful;" by 1722 as "of, pertaining to, or used in science." By 1794 as "according to the rules of science."

Sciential (mid-15c., sciencial, "based on knowledge," from Latin scientialis) is the classical purists' choice for an adjective based on science. Scientic (1540s) and scient ("learned" late 15c.) also have been used. Scientistic (1878), however, is depreciative, "making pretentions to scientific method but not right."

The phrase scientific revolution for "rapid and widespread development of science" is attested from 1803; scientific method is by 1835; scientific notation is from 1961. Related: Scientifical; scientifically.

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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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