早期數學字彙的歷史 (L)

Last revision: July 31, 1999

LAGRANGE MULTIPLIER. The term "Lagrange's method of undetermined multipliers" appears in J. W. Mellor, Higher Mathematics for Students of Chemistry and Physics (1912) [James A. Landau].

The term "Lagrange multiplier rule" appears in "The Problem of Mayer with Variable End Points," Gilbert Ames Bliss, Transactions of the American Mathematical Society, Vol. 19, No. 3. (Jul., 1918).

Lagrange multiplier is found in "Necessary Conditions in the Problems of Mayer in the Calculus of Variations," Gillie A. Larew, Transactions of the American Mathematical Society, Vol. 20, No. 1. (Jan., 1919): "The [lambda]'s appearing in this sum are the functions of x sometimes called Lagrange multipliers."

LAGRANGIAN (as a noun) occurs in P. A. M. Dirac, "The Lagrangian in quantum mechanics," Phys. Z. Sowjetunion 3 (1933).

LAPLACE'S COEFFICIENTS. According to Todhunter (1873), "the name Laplace's coefficients appears to have been first used" by William Whewell (1794-1866) [Chris Linton].

The term appears in 1845 in the Encyclopedia Metropolitana.

LAPLACE'S EQUATION appears in 1845 in the Encyclopedia Metropolitana.

LAPLACE'S FUNCTIONS appears in 1860 in the title On attractions, Laplace's functions and the figure of the Earth by John Henry Pratt (1809-1871). Todhunter (1873) writes, "The distinction between the coefficients and the functions is given for the first time to my knowledge in Pratt's Figure of the Earth" [Chris Linton].

The term LAPLACE'S OPERATOR was used in 1873 by James Clerk Maxwell in a Treatise on Electricity and Magnetism: "...an operator occurring in all parts of Physics, which we may refer to as Laplace's Operator" (OED2).

The term LAPLACE TRANSFORM was used by Boole and Poincar. According to the website of the University of St. Andrews, Boole and Poincar might otherwise have used the term Petzval transform but they were influenced by a student of J霩eph Miksa Petzval (1807-1891) who, after a falling out with his instructor, claimed incorrectly that Petzval had plagiarised Laplace's work.

LAPLACIAN (as a noun, for the differential operator) was used in 1935 by Pauling and Wilson in Introd. Quantum Mech. (OED2).

LATENT ROOT. According to Kai Willner, latent root and latent vector were introduced by James Joseph Sylvester in 1883.

LATTICE is found in "A New Principle in the Geometry of Numbers, with Some Applications," H. F. Blichfeldt, Transactions of the American Mathematical Society, Vol. 15, No. 3. (Jul., 1914): "If we define lattice-points as those points in space of n dimensions whose (rectangular) co顤dinates are positive or negative integers or zero..."

The term LATUS RECTUM was used by Gilles Personne de Roberval (1602-1675) in his lectures on Conic Sections. The lectures were printed posthumously under the title Propositum locum geometricum ad aequationem analyticam revocare,... in 1693 [Barnabas Hughes].

The term LAW OF INTERTIA OF QUADRATIC FORMS is due to James Joseph Sylvester (DSB).

The term LAW OF LARGE NUMBERS was coined by Sim廩n-Denis Poisson (1781-1840) (Burton, page 446).

The term LEAST ACTION was used by Lagrange (DSB).

LEAST COMMON DENOMINATOR is dated 1875 in MWCD10. The terms lowest common denominator and lowest common multiple (abbreviated L. C. M.) appear in 1881 in Elements of Algebra by G. A. Wentworth [James A. Landau].

The term LEBESGUE INTEGRAL was coined by William Henry Young (1863-1942), according to Hardy in his obituary of Young, which is quoted in Kramer, p. 643.

Forms of this term appear in these titles:

Ch. J. de la Vall嶪 Poussin, "Int嶲rales de Lebesgue. Fonctions d'ensemble. Classes de Baire" (Paris, 1916).

Ch. J. de la Vall嶪 Poussin, "Sur l'int嶲rale de Lebesgue," Transactions Amer. Math. Soc. 16 (1916).

F. Riesz, "Sur l'int嶲rale de Lebesgue," Acta. Math. 42 (1919-1920).

A. Denjoy, "Une extension de l'int嶲rale de M. Lebesgue," Comptes Rendus Acad. Sci. Paris 154 (1912).

Burton H. Camp, "Lebesgue Integrals Containing a Parameter, with Applications," Transactions of the American Mathematical Society, 15 (Jan., 1914).

The term may occur in W. H. Young, "On a new method in the theory of integration," Proc. London Math. Soc. 9 (1910). [James A. Landau]

LEG (for a side of a triangle not the hypotenuse) was used in English in 1659 by Joseph Moxon in Globes (OED2).

LEMMA appears in English in the 1570 translation by Sir Henry Billingsley of Euclid's Elements (OED2). [The plural of lemma can be written lemmas or lemmata.]

LEMNISCATE. Jacob Bernoulli named this curve the lemniscus in Acta Eruditorum in 1694. He wrote, "...formam refert jacentis notae octonarii [infinity symbol], seu complicitae in nodum fasciae, sive lemnisci" (Smith vol. 2, page 329).

The term LEMOINE POINT was coined in 1884 by Joseph Jean Baptiste Neuberg (1840-1926) and named for Emile Michel Hyacinthe Lemoine (1840-1912).

Lemoine referred to the point as the center of antiparallel medians. The point had been earlier noted by LHuilier in 1809, Grebe in 1847, and others prior to Lemoine's extensive discussion in 1873 [Clark Kimberling].

See also symmedian point.

L'HOSPITAL'S RULE. James A. Landau has found in J. W. Mellor, Higher Mathematics for Students of Chemistry and Physics, 4th ed. (1912), the sentence, "This is the so-called rule of l'Hopital." Presumably earlier uses of the term exist.

The rule is named for Guillaume-Francois-Antoine de l'Hospital (1661-1704), although the rule was discovered by Johann Bernoulli. The rule and its proof appear in a 1694 letter from him to l'Hospital.

The family later changed the spelling of the name to l'H皫ital.

LIE GROUP. The term groupes de Lie began to be used by Elie Cartan (1869-1951) around 1930 to designate those (topological) groups that were first investigated by the Norwegian mathematician Sophus Lie (1842-1899) under the name "continuous groups" (of transformations) [Carlos C廥ar de Arajo].

An early use of the term is Hans Schwerdtfeger, "Sur une formule de H. Poincare relative a la theorie des groupes de S. Lie," Enseign. Math. 32 (1933).

The term LIMAシN was coined in 1650 by Gilles Persone de Roberval (1602-1675) (Encyclopaedia Britannica, article: "Geometry"). It is sometimes called Pascal's lima蔞n, for 尒ienne Pascal (1588?-1651), the first person to study it. Boyer (page 395) writes that "on the suggestion of Roberval" the curve is named for Pascal.

LIMIT was used by Isaac Newton: "Quibus Terminis, sive Limitibus respondent semicirculi Limites, sive Termini." This citation is from a. 1727, Opuscula I (OED2).

Gregory used terminatio for limit of a series (DSB).

LIMIT POINT is dated 1905 in MWCD10.

LINEAR ALGEBRA is dated ca. 1884 in English in MWCD10.

The DSB seems to imply that the term algebra linearia is used by Rafael Bombelli (1526-1572) in Book IV of his Algebra to refer to the application of geometrical methods to algebra.

LINEAR COMBINATION occurs in "On the Extension of Delaunay's Method in the Lunar Theory to the General Problem of Planetary Motion," G. W. Hill, Transactions of the American Mathematical Society, Vol. 1, No. 2. (Apr., 1900).

The phrases linear independence, linear dependence, linearly independent, and linearly dependent appear in the 1907 edition of Introduction to Higher Algebra by Maxime B瀿her [James A. Landau].

LINEAR DIFFERENTIAL EQUATION appears in the 1872 second edition of A Treatise on the Calculus of Finite Differences by George Boole [James A. Landau].

LINEAR EQUATION appears in English in 1816 in a translation of Lacroix's Differential and Integral Calculus (OED2).

LINEAR FUNCTION is dated 1855-60 in RHUD2.

LINEAR PRODUCT. This term was used by Hermann Grassman in his Ausdehnungslehre (1844).

The term LINEAR PROGRAMMING was used in 1949 by George B. Dantzig (1914- ) in Econometria XVII 203 (OED2).

LINEAR TRANSFORMATION appears in the Century Dictionary (1889-1897).

LINE FUNCTION was the term used for functional by Vito Volterra (1860-1940), according to the DSB.

The term LINE INTEGRAL was used in in 1873 by James Clerk Maxwell in a Treatise on Electricity and Magnetism in the phrase "Line-Integral of Electric Force, or Electromotive Force along an Art of a Curve" (OED2).

The term LITUUS (Latin for the curved wand used by the Roman pagan priests known as augurs) was chosen by Roger Cotes (1682-1716) for the locus of a point moving such that the area of a circular sector remains constant, and it appears in his Harmonia Mensurarum, published posthumously in Cambridge, 1722 (Julio Gonz嫮ez Cabill鏮).

The term LOCAL PROBABILITY is due to Morgan W. Crofton (1826-1915) (Cajori 1919, page 379).

LOCUS. According to Pappus, Apollonius mentions "the locus for three and four lines" in the third book of his Conics (about 220 B. C.) [James A. Landau].

Locus geometricus is an entry in the 1771 Encyclopaedia Britannica.

LOGARITHM was coined in Latin as logarithmus by John Napier (1550-1617) in 1614 in Mirifici Logarithmorum Canonis descriptio.

The word appears in English in a letter of March 10, 1615, from Henry Briggs to James Ussher: "Napier, Lord of Markinston, hath set my Head and Hands a Work with his new and admirable Logarithms. I hope to see him this summer, if it please God, for I never saw a book which pleased me better or made me more wonder."

In the Constructio, the phrase "artificial numbers" is used, rather than "logarithms."

Napier offered no explanation for the term logarithm, but in the Arithmetica logarithmica (1624), Briggs explains that the name came from their inventor because they exhibit numbers which preserve always the same ratio to one another.

[Older English-language dictionaries pronounce logarithm with an unvoiced th, as in thick and arithmetic.]

LOGARITHMIC CURVE. Johann Bernoulli used a phrase which is translated "logarithmic curve" in 1691/92 in Opera omnia (Struik, page 328). Logarithmic curve is an entry in the 1771 edition of the Encyclopaedia Britannica [James A. Landau].

LOGARITHMIC FUNCTION is found in the 1902 Encyclopaedia Britannica [James A. Landau].

The term LOGARITHMIC POTENTIAL was coined by Carl Gottfried Neumann (1832-1925) (DSB).

The term LOGARITHMIC SPIRAL was introduced by Pierre Varignon (1654-1722) in a paper he presented to the Paris Academy in 1704 and published in 1722.

Another term for this curve is equiangular spiral.

Jakob Bernoulli called the curve spira mirabilis (marvelous spiral).

LOGIC. According to the University of St. Andrews website, the term logic was introduced by Xenocrates of Chalcedon (396 BC - 314 BC). Aristotle's name for logic was analytics.

The term LOGISTIC CURVE is attributed to Edward Wright (ca. 1558-1615) (Thompson 1992, page 145). Wright was apparently referring to the logarithmic curve and was not using the term in the modern sense.

Pierre Francois Verhulst (1804-1849) introduced the term logistique as applied to the sigmoid curve [Julio Gonz嫮ez Cabill鏮]. Bonnie Shulman believes that "logistic," as coined by Verhulst, refers to the "log-like" qualities of the curve.

LONG DIVISION is found in 1827 in A Course of Mathematics by Charles Hutton: "Divide by the whole divisor at once, after the manner of Long division" (OED2).

The term LOWER SEMICONTINUITY was used by Ren-Louis Baire (1874-1932), according to Kramer (p. 575), who implies he coined the term.

The phrase LOWEST TERMS appears in the 1771 edition of the Encyclopaedia Britannica in the article "Algebra": "To reduce any fraction to its lowest terms" [James A. Landau].

The term LOXODROME is due to Willebrord Snell van Roijen (1581-1626) and was coined in 1624 (Smith and DSB, article: "Nunez Salaciense).

LUCAS-LEHMER TEST occurs in the title, "The Lucas-Lehmer test for Mersenne numbers," by S. Kravitz in the Fibonacci Quarterly 8, 1-3 (1970).

The term Lucas's test was used in 1932 by A. E. Western in "On Lucas's and Pepin's tests for the primeness of Mersenne's numbers," J. London Math. Soc. 7 (1932), and in 1935 by D. H. Lehmer in "On Lucas's test for the primality of Mersenne's numbers," J. London Math. Soc. 10 (1935).

The term LUCAS PSEUDOPRIME occurs in the title "Lucas Pseudoprimes" by Robert Baillie and Samuel S. Wagstaff Jr. in Math. Comput. 35, 1391-1417 (1980): "If n is composite, but (1) still holds, then we call n a Lucas pseudoprime with parameters P and Q ..." [Paul Pollack].

LUDOLPHIAN NUMBER. The number 3.14159... was often called the Ludolphische Zahl in Germany, for Ludolph van Ceulen (1540-1610).

In English, Ludolphian number is found in 1886 in G. S. Carr, Synopsis Pure & Applied Math (OED2).

In English, Ludolph's number is found in 1894 in History of Mathematics by Florian Cajori (OED2).

LUNE appears in English in 1704 in Lexicon technicum, or an universal English dictionary of arts and sciences by John Harris (OED2).

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