早期數學字彙的歷史 (D)

Last revision: July 29, 1999

DECAGON appears in English in 1571 in A geometrical practise named Pantometria by Thomas Digges (1546?-1595) (although the spelling decagonum is used).

DECIMAL is derived from the Latin decimus, meaning "tenth." According to Smith (vol. 2, page 14), in the early printed books numbers which are multiples of 10 were occasionally called decimal numbers, citing Pellos (1492, fol. 4), who speaks of "numbre simple," "nubre desenal," and "nubre plus que desenal" and Ortega (1512, 1515 ed., fols. 4, 5), who has "lo numero simplice," "lo numero decenale," and "lo numero composto."

Decimal occurs in English in 1608 in the title Disme: The Art of Tenths, or Decimall Arithmetike. This work is a translation by Robert Norman of La Thiende, by Simon Stevin (1548-1620), which was published in Flemish and in French in 1585.

The word DECIMAL POINT appears in the 1771 edition of the Encyclopaedia Britannica in the article "Arithmetick": "The point thus prefixed is called the decimal point" [James A. Landau].

The term DEFINITE INTEGRAL is defined by Sylvestre-Fran蔞is Lacroix (1765-1843) in Trait du calcul diff廨entiel et integral (Cajori 1919, page 272).

DEGREE (angle measure) is found in English in about 1386 in Chaucer's Canterbury Tales: "The yonge sonne That in the Ram is foure degrees vp ronne" (OED2). He again used the word in about 1391 in A Treatise on the Astrolabe: "9. Next this folewith the cercle of the daies, that ben figured in manere of degres, that contenen in nombre 365, dividid also with longe strikes fro 5 to 5, and the nombre in augrym writen under that cercle."

DEGREE (of a polynomial) is found in 1730-6, Bailey (folio): "Parodic Degree (in Algebra) is the index or exponent of any power; so in numbers, 1. is the parodick degree, or exponent of the root or side; 2. of the square, 3. of the cube, etc" (OED2).

DEGREE OF FREEDOM (in statistics) is found in R. A. Fisher, Jrnl. R. Statistical Soc. LXXXV 88 (OED2).

DEL (as a name for the symbol) is found in 1901 in Vector Analysis, A text-book for the use of students of mathematics and physics founded upon the lectures of J. Willard Gibbs by Edwin Bidwell Wilson (1879-1964):

There seems, however, to be no universally recognized name for it, although owing to the frequent occurrence of the symbol some name is a practical necessity. It has been found by experience that the monosyllable del is so short and easy to pronounce that even in complicated formulae in which (the symbol) occurs a number of times no inconvenience to the speaker or hearer arises from the repetition (OED2).
According to Stein and Barcellos (page 836), this is the first appearance in print of the word del.

The term DELTAHEDRON was coined by H. Martyn Cundy. The word may occur in Mathematical Models (1961), by him and A. P. Rollett.

DEMOIVRE'S THEOREM appears in the Century Dictionary (1889-1897).

DEPENDENT VARIABLE is found in 1852 in Differential Calculus by Isaac Todhunter (OED2).

DERIVATIVE. This term was not used by Isaac Newton, who instead used the term fluxion.

Julio Gonz嫮ez Cabill鏮 believes that this word was first used in the calculus sense (in Latin, derivata) by Gottfried Wilhelm Leibniz (1646-1716) around 1677:

Aequationem differentialem voco talem qua valor ipsius dx exprimitur, quaeque ex alia derivata est, qua valor ipsius x exprimebatur [cf. page 156 of Leibniz' "Mathematische Schriften," vol. I, edited by C. I. Gerhardt, Verlag von A. Asher & Comp., Berlin, 1849].
John Conway points out that, in the above, it could be argued that Leibniz is merely using the word "derived" in its ordinary sense.

Some writers attribute the word derivative to Joseph Louis Lagrange (1736-1813), who used deriv嶪 de la fonction and fonction deriv嶪 de la fonction as early as 1772 in "Sur une nouvelle espece de calcul relatif a la diff廨entiation et a l'integration des quantit廥 variables," Nouveaux Memoires de l'Academie royale des Sciences etBelles-Lettres de Berlin. Lagrange states, for instance (first pages):

...on designe de m瘱e par u'' une fonction deriv嶪 de u' de la m瘱e mani廨e que u' l'est de u, et par u''' une fonction deriv嶪 de m瘱e de u'' et ainsi, ...

... les fonctions u, u', u'', u''', uIV, ... derivent l'une de l'autre par une m瘱e loi de sorte qu'on pourra les trouver aisement par une meme operation r廧et嶪. [the functions u, u', u'', u''', uIV, ... are derived one another from the same law, such that ...]

The term DESCRIPTIVE GEOMETRY occurs in the title G廩m彋rie Descriptive (1795) by Gaspard Monge (1746-1818).

DETERMINANT (discriminant of a quantic) was introduced in 1801 by Carl Friedrich Gauss in his Disquisitiones arithmeticae:

Numerum bb - ac, a cuius indole proprietates formae (a, b, c) imprimis pendere in sequentibus docebimus, determinantem huius formae uocabimus.
(Cajori vol. 2, page 88; Smith vol. 2, page 476).

DETERMINANT (modern sense). Augustin-Louis Cauchy (1789-1857) was apparently the first to use determinant in its modern sense (Schwartzman, page 70). He employed the word in "Memoire sur les foctions qui ne peuvent obtenir que deux valeurs egales et des signes contraires par suite des transpositions operees entre les variables qu'elles renferment", addressed on November 30, 1812, and first published in Journal de l'Ecole Poytechnique, XVIIe Cahier, Tome X, Paris, 1815:

M. Gauss s'en est servi avec avantage dans ses Recherches analytiques pour decouvrir les proprietes generales des formes du second degre, c'est a dire des polynomes du second degre a deux ou plusieurs variables, et il a designe ces memes fonctions sous le nom de determinants. Je conserverai cette denomination qui fournit un moyen facile d'enoncer les resultats; j'observerai seulement qu'on donne aussi quelquefois aux fonctions dont il s'agit le nom de resultantes a deux ou a plusieurs lettres. Ainsi le deux expressions suivantes, determinant et resultante, devront etre regardees comme synonymes.
(Smith vol. 2, page 477; Julio Gonz嫮ez Cabill鏮.)

According to Katz, Arthur Cayley (1821-1895) introduced the word determinant as a replacement for several older terms.

DIAGONAL. Julio Gonz嫮ez Cabill鏮 says, "Heron of Alexandria is probably the first geometer to define the term diagonal (as the straight line drawn from angle to angle)."

DIALYTIC was used by James Joseph Sylvester (1814-1897) to refer to a method of eliminating a variable from two algebraic equations (Schwartzman, page 71).

DIAMETER. According to Smith (vol. 2, page 278), "Euclid used the word 'diameter' in relation to the line bisecting a circle and also to mean the diagonal of a square, the latter term being also found in the works of Heron."

DIFFERENTIABLE. Leibniz used the term differentiabilis in 1692 in Acta Eruditorum 11 (Struik, page 272).

The noun DIFFERENTIAL was coined by Leibniz, according to an Internet website. The word appears in English as a noun in 1704 in Lexicon technicum, or an universal English dictionary of arts and sciences by John Harris (OED2).

DIFFERENTIAL CALCULUS. The term calculus differentialis was introduced by Leibniz in 1684 in Acta Eruditorum 3. Before introducing this term, he used the expression methodus tangentium directa (Struik, page 271).

Leibniz wrote [source uncertain]: "Knowing thus the Algorithm of this calculus, which I call Differential Calculus, all differential equations can be solved by a common method."

The term DIFFERENTIAL COEFFICIENT was first used by Sylvestre-Fran蔞is Lacroix (1765-1843) in Trait du calcul diff廨entiel et integral (Cajori 1919, page 272).

DIFFERENTIAL EQUATION. Gottfried Wilhelm Leibniz (1646-1716) used the Latin aequationes differentiales in Acta Eruditorum, October 1684. See the entry "algorithm" for the context.

The term DIFFERENTIAL GEOMETRY was first used by Luigi Bianchi (1856-1928) in 1894 (Kline, page 554).

DIFFERENTIATE appears in English in 1816 in LaCroix's Differential and Integral Calculus (OED2).

DIGIT. According to Smith (vol. 2, page 12), the late Roman writers seem to have divided the numbers below 100 into digiti (fingers), articuli (joints), and compositi (composites of fingers and joints).

In English, Robert Recorde in the 1558 edition of the Ground of Artes wrote, "A diget is any numbre vnder 10."

The term DIGITADDITION was coined by D. R. Kaprekar, according to an Internet web page.

DIGRAPH was used in 1955 by F. Harary in Transactions of the American Mathematical Society. The term directed graph also occurs there (OED2).

DIOPHANTINE ANALYSIS appears in 1811 in the title An Elementary Investigation of the Theory of Numbers, with its application to the indeterminate and diophantine analysis by Peter Barlow (OED2).

An early use of the term DIOPHANTINE EQUATION in English is by Eliakim Hastings Moore (1862-1932) in an essay entitled "A Doubly-Infinite System of Simple Groups," published in the Bulletin of the New York Mathematical Society, vol. III, pp. 73-78, October 13, 1893 [Julio Gonz嫮ez Cabill鏮].

DIOPHANTINE PROBLEM. The phrase "Diophantus Problemes" appears in 1670 [James A. Landau].

DIRECT VARIATION is found in 1881 in Elements of Algebra by G. A. Wentworth [James A. Landau].

DIRECTRIX. According to the DSB, Jan de Witt (1625-1672) "is credited with introducing the term 'directrix' for the parabola, but it is clear from his derivation that he does not use the term for the fixed line of our focus-directrix definition."

DISCRETE appears in English in 1570 in Sir Henry Billingsley's translation of Euclid's Elements: "Two contrary kynds of quantity; quantity discrete or number, and quantity continual or magnitude" (OED2).

DISCRIMINANT was introduced by James Joseph Sylvester (1814-1897) in 1852 in the Cambridge and Dublin Mathematical Journal, vol. I, 52. He used the word "for determinant, which is still found occasionally," according to the OED2, which attributes this information to H. T. Gerrans.

In 1876 George Salmon used discriminant in its modern sense in Mod. Higher Algebra (ed. 3): "The discriminant is equal to the product of the squares of all the differences of the differences of any two roots of the equation" (OED2).

DISJOINT, referring to intervals, occurs in "Differentiation with Respect to a Function of Limited Variation," P. J. Daniell, Transactions of the American Mathematical Society, Vol. 19, No. 4. (Oct., 1918).

Disjoint, referring to sets, is found in the phrase "two disjoint closed sets" in 1937 in Transactions of the American Mathematical Society (OED2).

DISJUNCTION. According to the University of St. Andrews website, "the logical term 'disjunction' is certainly due to the Stoics and it is thought to have originated with" Chrysippus of Soli (280 BC - 206 BC).

DISME is an obsolete English word meaning "tenth." It occurs in 1608 in the title Disme: The Art of Tenths, or Decimall Arithmetike. This work is a translation by Robert Norman of La Thiende, by Simon Stevin (1548-1620), which was published in Flemish and in French in 1585.

Disme was used by Shakespeare in Troilus and Cressida (ii, 2, 15), which was first published in 1609. The use of this word is one of the pieces of evidence cited by defenders of the theory that Shakespeare's plays were actually written someone else, perhaps Francis Bacon.

DISTRIBUTIVE. See commutative.

The term DIVERGENCE (of a vector field) was introduced by William Kingdon Clifford (1845-1879). Maxwell had earlier used the term convergence with a related meaning (Kline, page 785).

The DSB says that Maxwell introduced the term divergence in 1870; this seems to be incorrect.

DIVERGENT. See convergent.

DIVIDEND. Joannes de Muris (c. 1350) used dividendus (Smith vol. 2, page 131).

In English, the word is found in The Grovnd of Artes, by Robert Recorde, which was printed between 1540 and 1542: "Then begynne I at the hyghest lyne of the diuident, and seke how often I may haue the diuisor therin" (OED2).

The term DIVINE PROPORTION appears in 1509 in the title De Divina Proportione by Luca Pacioli (1445-1517). According to an Internet website, Pacioli coined the term.

Ramus wrote, "Christianis quibusdam divina quaedam proportio hic animadversa est..." in Scholarvm Mathematicarvm, Libri vnvs et triginta, Basel, 1569; ibid., 1578; Frankfort, 1599) (Smith vol. 2, page 291).

Kepler wrote, "Inter continuas proportiones unum singulare genus est proportionis divinae" (Frisch ed. of his Opera, I (1858).

DIVISION is found in English in "The crafte of nombrynge" (ca. 1300). The word is spelled dyuision (OED2).

Baker (1568) speaks of "Deuision or partition" and Digges (1572) says "To deuide or parte" (Smith vol. 2, page 129).

DIVISOR is found in English in "The crafte of nombrynge" (ca. 1300). The word is spelled dyvyser (OED2).

DODECAGON is dated ca. 1658 in MWCD10.

DOMAIN (the values that an independent variable of a function can take) appears in the Encyclopaedia Britannica of 1902 (OED2).

DOPPELVERH鶉TNISS. M鐽ius introduced the term Doppelschnittverh鄟tniss, meaning "ratio bisectionalis" or "double cut ratio," in his "Der barycentrische Calcul" (1827): gesammelte Werke, I (1885).

Jakob Steiner shortened the term to Doppelverh鄟tniss (Smith vol. 2, page 334).

See also anharmonic ratio and cross-ratio.

DOT PRODUCT is found in 1901 in Vector Analysis by J. Willard Gibbs and Edwin Bidwell Wilson:

The direct product is denoted by writing the two vectors with a dot between them as

 This is read A dot B and therefore may often be called the dot product instead of the direct product.

[This citation was provided by Joanne M. Despres of Merriam-Webster Inc.]

DUALITY. The term "principle of duality" was introduced by Joseph Diaz Geronne (1771-1859) in "Consid廨ations philosophiques sur les 幨幦ens de la science de l'彋endue," Annales 16 (1825-1826) (DSB).

DUMMY VARIABLE is dated 1957 in MWCD10.

DYAD (a third vector product) was used in 1884 by Josiah Willard Gibbs (1839-1903) and is found in his Vector-Analysis of 1901 and his Collected Works of 1928 (OED2).

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