早期數學字彙的歷史 (N)

Last revision: Aug. 3, 1999

NABLA (as a name for the "del" or Hamiltonian operator). The following is taken from A History of Vector Analysis by Michael J. Crowe:
Nabla was the name suggested to [Peter Guthrie] Tait by Robertson Smith because of the similarity of the symbol to an Assyrian harp. See [1; 143]. Maxwell used the word only once in his published writings, and that was in a poem, "To the Chief Musician upon Nabla, A Tyndallic Ode." The "Chief Musician upon Nabla" was Tait. The poem was published in Nature and is given in [1; 171--174].
This citation is from note 27 to chapter four of "A history of vector analysis" by Michael J. Crowe (originally published by University of Notre Dame Press in 1967, and republished by Dover in 1985). The note is on page 146 of the Dover edition. Reference [1] above is Cargil Gilston Knott, "Life and Scientific Work of Peter Guthrie Tait", Cambridge, England, 1911. (This information is from Michele Benzi.)

The term nabla was used by both Heaviside and Hamilton (Cajori vol. 2, page 135; Kline, page 780).

According to Schwartzman (p. 142) Hamilton introduced this term.

Webster's Third New International Dictionary defines nabla as "an ancient stringed instrument probably like a Hebrew harp of 10 or 12 strings -- called also nebel." The dictionary also says that the mathematical operator is "probably so called from the resemblance of its symbol, the inverted Greek delta, to a harp."

The term NAPIERIAN LOGARITHM presumably occurs in Trait de Calcul differ幯tiel et int嶲ral by Sylvestre Francois Lacroix, since the OED2 shows its use in English in 1816 in Peacock and Herschel's translation of of this work: "a system of logarithms, which we shall call Napierian."

Naper's Logarithms and Napier's logarithm appear in the 1771 edition of the Encyclopaedia Britannica [James A. Landau].

NAPIER'S CONSTANT has been suggested for the number 2.718..., according to e: The Story of a Number by Eli Maor (1994). Maor writes that Napier came close to discovering the constant. The term Napier's constant was used twice in an episode of The X-Files titled "Paper Clip" which originally aired on Sept. 29, 1995.

NATURAL LOGARITHM. According ot the DSB, Thomas Fantet de Lagny (1660-1734) "attempted to establish trigonometric tables through the use of transcription into binary arithmetic, which he termed 'natural logarithm' and the properties of which he discovered independently of Leibniz."

In the sense of a logarithm to be base e, Boyer (page 423) implies that Pietro Mengoli (1625-1686) coined the term.

Natural logarithm is found in the 1771 edition of the Encyclopaedia Britannica [James A. Landau].

NATURAL NUMBER. Chuquet (1484) used the term progression naturelle for the sequence 1, 2, 3, 4, etc.

Natural number appears in 1763 in The method of increments by William Emerson: "To find the product of all natural numbers from 1 to 100" (OED2).

Natural number, defined as the numbers 1, 2, 3, 4, 5, etc., appears in the 1771 Encyclopaedia Britannica in the Logarithm article.

Apparently, except for the various Random House dictionaries, all modern dictionaries define the term natural number to exclude 0. [The term whole number is defined to include 0.]

Bertrand Russell in his 1919 Introduction to Mathematical Philosophy writes:

To the average educated person of the present day, the obvious starting-point of mathematics would be the series of whole numbers,
1, 2, 3, 4, . . . etc.

Probably only a person with some mathematical knowledge would think of beginning with 0 instead of with 1, but we will presume this degree of knowledge; we will take as our starting-point the series:

0, 1, 2, 3, . . . n, n + 1, . . .

and it is this series that we shall mean when we speak of the "series of natural numbers."

John Conway writes:
The older nomenclature was that "natural number" meant "positive integer." This was unfortunate, because the set of non-negative integers is really much more "natural" in the sense that it has simpler properties. So starting in about the 1960s lots of people (including me) started to use "natural number" in the inclusive sense. After all, for the positive integers we have the much better term "positive integer."
Stephen Cole Kleene (1909-1994), in his Mathematical logic (John Wiley & Sons, 1967) wrote (p. 176):
Some authors use "natural numbers" as a synonym for "positive integers" 1, 2, 3, ..., obliging one to use the more cumbersome name "nonnegative integers" for 0, 1, 2, .... Besides, in this age, we should accept 0 on the same footing with 1, 2, 3, ... .
[Carlos C廥ar de Arajo, Sam Kutler]

NEGATIVE. According to Burton (page 245), Brahmagupta introduced negative numbers and a word equivalent to negative.

In his Ars Magna (1545) Cardano referred to negative numbers as numeri ficti. In speaking of the roots of an equation, he wrote, "una semper est rei uera aestimatio, altera ei aequalis, ficta" (Smith vol. 2, page 260).

Stifel (1544) called negative numbers "absurd." He spoke of zero as "quod mediat inter numeros veros et numeros absurdos" (Smith vol. 2, page 260).

The word negative was used by Scheubel (1551) (Smith vol. 2, page 260).

Napier (c. 1600) used the adjective defectivi to designate negative numbers (Smith vol. 2, page 260).

NEIGHBORHOOD OF A POINT appears in 1891 in G. L. Cathcart's translation of Harnack's Introductory Study of Elementary Differential and Integral Calculus (OED2).

NEPHROID was used for the bicuspid epicycloid by Richard Anthony Proctor (1837-1888) in 1878 in A treatise on the cycloid and all forms of cycloidal curves:

The epicycloid with two cusps (the dotted curve of fig. 39, which, from its shape, we may call the nephroid) presents also many interesting relations.
This citation was provided by Julio Gonz嫮ez Cabill鏮. According to E. W. Lockwood, in 1879 Freeth used the same name for another curve, Freeth's Nephroid.

The term NET was coined by J. Kelley. He had considered using the term "way" so the analog of subsequence would be "subway." E. J. McShane also proposed the term "stream" since he thought it was intuitive to think of the relation of the directed set as "being downstream from" (McShane, Partial Orderings and Moore-Smith Limits, 1950, p. 282).

NEWTON-RAPHSON METHOD. Florian Cajori writes on page 203 of his History of Mathematics (1919):

Perhaps the name "Newton-Raphson method" would be a designation more nearly representing the facts of history.
Cajori subsequently uses the term throughout the book. He may have written the same thing in the 1893 edition, which I have not seen.

NEXT TO CONVEX. In a post to the geometry forum, Michael E. Gage wrote that he believed the term was coined by Gromov in "Hyberbolic manifolds, groups and actions," Annals of Mathematics Studies, v. 97, page 183.

NILPOTENT. See idempotent.

The term NINE-POINT CIRCLE first appears in 1820 in "Recherches sur la d彋ermination d'une hyperbola 廦uilat廨e, au moyen de quatres conditions donn嶪s" by Charles-Julien Brianchon (1783-1864) and Poncelet (DSB).

NODE. In 1753 Daniel Bernoulli used the Latin word noeud [James A. Landau].

NOETHERIAN RING occurs in "On integrally closed Noetherian rings" and "The intersection theorem on Noetherian rings," both of which are by Yoshida, Michio; Sakuma, Motoyoshi in J. Sci. Hiroshima Univ., Ser. A 17, 311-315 (1954).

The term NOETHER'S THEOREM is found in Sybil D. Jervis, "On professor Elliott's proof of Noether's theorem," Tohoku Math. J. 39 (1934).

The term NOMOGRAPHY is due to Philbert Maurice d'Ocagne (1862-1938). It occurs in his Trait de nomographie (1899) (DSB).

NONAGON is dated 1639 in MWCD10.

The term NON-EUCLIDEAN GEOMETRY was introduced by Carl Friedrich Gauss (1777-1855) (Sommerville). Gauss had earlier used the terms anti-Euclidean geometry and astral geometry (Kline, page 872).

NONPARAMETRIC (referring to a statistical inference) first appears in a 1942 paper by Jacob Wolfowitz (1910-1981), according to the University of St. Andrews website.

NORM in algebra was introduced in 1832 as the Latin norma by Carl Friedrich Gauss (1777-1855) in Commentationes Recentiones Soc. R. Scient. Gottingensis VII. Class. math. 98.

In 1856 Hamilton used norm to refer to a2 + b2 for the complex number a + ib.

In 1921 the term norm refers to sqrt (a2 + b2) for the complex number a + ib in Proceedings of the National Academy of Science VII. 84.

In 1949 A. Albert defines the norm of a vector P as the inner product P.P in Solid Analytic Geometry (OED2).

NORMAL (perpendicular) appears as a geometry term in the phrase "Normal Line" about 1696 in The English Euclide by Edmund Scarburgh, although the OED2 shows a slightly earlier non-mathematical use of the term to mean "right" or "rectangular."

NORMAL CURVE. According to Walker (p. 185), Karl Pearson did not coin this term. She writes, "Galton used it, as did also Lexis, and the writer has not found any reference which seems to be its first use."

The DSB says, "...Pearson's consistent and exclusive use of this term in his epoch-making publications led to its adoption throughout the statistical community."

The OED2 shows a use of "normal probability curve" by Karl Pearson (1857-1936) in 1893 in Nature 26 Oct. 615/2: "As verification note that for the normal probability curve 322 = 4 and 3 = 0."

"Normal curve" was used by Pearson in 1894 in Phil. Trans. R. Soc. A. CLXXXV. 72: "A frequency-curve, which for practical purposes, can be represented by the error curve, will for the remainder of this paper be termed a normal curve."

The term NORMAL DISTRIBUTION was first used by Galton in 1889, according to an Internet web page.

NORMAL EQUATION occurs in "On the Reducibility of Linear Groups," Leonard Eugene Dickson, Transactions of the American Mathematical Society, Vol. 4, No. 4. (Oct., 1903).

NORMALIZER appears in German as Normalisator in Theorie der Gruppen von endlicher Ordnung, 2nd ed., by A. Speiser [Huw Davies].

NORMAL SUBGROUP is found in Reinhold Baer, Groups with descending chain condition for normal subgroups, Duke Math. J. 16, 1-22 (1949).

NTH is dated 1852 in MWCD10.

NULL CLASS is found in "Sets of Independent Postulates for the Algebra of Logic," Edward V. Huntington, Transactions of the American Mathematical Society, Vol. 5, No. 3. (Jul., 1904).

NULL HYPOTHESIS is used in 1935 by Ronald Aylmer Fisher in Design of Experiments. He writes, "We may speak of this hypothesis as the 'null hypothesis,' and it should be noted that the null hypothesis is never proved or established, but is possibly disproved, in the course of experimentation."

NULLITY. Sylvester defined the nullity of a square matrix in 1884.

NULL SET appears (as "null-set") in 1906 in Theory of Sets and Points by W. H. and G. C. Young (OED2).

NUMBER LINE is dated 1960 in MWCD10.

NUMBER THEORY. According to Diogenes Laertius, Xenocrates of Chalcedon (396 BC - 314 BC) wrote a book titled The theory of numbers.

A letter written by Blaise Pascal to Fermat dated July 29, 1654, includes the sentence, "The Chevalier de M鋨 said to me that he found a falsehood in the theory of numbers for the following reason."

The term appears in 1798 in the title Essai sur la th廩rie des nombres by Adrien-Marie Legendre (1752-1833).

In English, theory of numbers appears in 1811 in the title An elementary investigation of the theory of numbers by Peter Barlow.

Number theory appears in 1912 in the Bulletin of the American Mathematical Society (OED2).

The words NUMERATOR and DENOMINATOR are found in Algorismus proportionum by Nicole Oresme (ca. 1323-1382). The work is in Latin but the words are spelled as they are in English, and are defined as "the number above the line" and "the number below the line" (Cajori vol. 1, page 91).

NUMERICAL ANALYSIS occurs in Randolph Church, "Numerical analysis of certain free distributive structures," Duke Math. J. 6 (1940).

NUMERICAL DIFFERENTIATION is found in W. G. Bickley, "Formulae for Numerical Differentiation," Math. Gaz. 25 (1941) [James A. Landau].

NUMERICAL INTEGRATION occurs in D. Jackson, "The Method of Numerical Integration in Exterior Ballistics," War Dept. Document 984, U.S. Govt. Printing Office (1921) and in C. St顤mer, "M彋hode d'int嶲ration num廨ique des 廦uations diff廨entielles ordinaires," C. R. Congr. Intern. Math. Strasbourg 1920, Toulouse, Privat, (1921) [James A. Landau].

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