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 Poincaré. According
to the website of the University of St. Andrews, Boole and Poincaré might
otherwise have used the term Petzval transform but they were influenced
by a student of Józeph 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) coördinates
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 Siméon-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 Vallée Poussin, "Intégrales de Lebesgue. Fonctions d'ensemble. Classes de Baire" (Paris, 1916).

Ch. J. de la Vallée Poussin, "Sur l'intégrale de Lebesgue," *Transactions
Amer. Math. Soc.* 16 (1916).

F. Riesz, "Sur l'intégrale de Lebesgue," *Acta. Math.* 42 (1919-1920).

A. Denjoy, "Une extension de l'intégrale 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'Hôpital.

**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
César de Araújo].

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 **LIMAÇON** was coined in 1650 by Gilles Persone de Roberval
(1602-1675) (*Encyclopaedia Britannica,* article: "Geometry"). It
is sometimes called *Pascal's limaçon,* for Étienne 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 Bôcher [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 González Cabillón).

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 González Cabillón]. 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 René-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).