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."
LAGRANGE'S THEOREM. Formule de Lagrange appears in Traité élémentaire de calcul différentiel et de calcul intégral (1797-1800) by Lacroix.
Lagrange's theorem appears in An Elementary Treatise on Curves, Functions and Forms (1846) by Benjamin Peirce: "The theorem (650) under this form of application, has been often called Laplace's Theorem; but, regarding this change as obvious and insignificant, we do not hesitate to discard the latter name, and give the whole honor of the theorem to its true author, Lagrange."
Lagrange's formula for interpolation appears in 1849 in An Introduction to the Differential and Integral Calculus, 2nd ed., by James Thomson.
Lagrange's method of approximation occurs in the third edition of An Elementary Treatise on the Theory of Equations (1875) by Isaac Todhunter.
LAGRANGIAN (as a noun) occurs in Th. Muir, "Note on the Lagrangian of a special unit determinant," Transactions Royal Soc. South Africa (1929).
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].
Laplace's coefficients appears in the title Mathematical tracts Part I: On Laplace's coefficients, the figure of the earth, the motion of a rigid body about its center of gravity, and precession and nutation (1840) by Matthew O'Brien.
LAPLACE'S EQUATION appears in 1845 in the Encyclopedia Metropolitana.
LAPLACE'S FUNCTIONS appears in 1855 in the title "On the solution of the equation of Laplace's functions" by Charles Graves (Bishop of Limerick). The paper was published in Proc. Dublin [James A. Landau].
Laplace's functions also 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 VALUE and VECTOR. See Eigenvalue.
The term LATIN SQUARE was named by Euler (as quarré latin) in 1782 in Verh. uitgegeven door het Zeeuwsch Genootschap d. Wetensch. te Vlissingen.
Latin square appears in English in 1890 in the title of a paper by Arthur Cayley, "On Latin Squares" in Messenger of Mathematics.
The term was introduced into statistics by R. A. Fisher, according to Tankard (p. 112). Fisher used the term in 1925 in Statistical Methods Res. Workers (OED2).
Graeco-Latin square appears in 1934 in R. A. Fisher and F. Yates, "The 6 x 6 Latin Squares," Proceedings of the Cambridge Philosophical Society 30, 492-507.
LATITUDE and LONGITUDE. Henry of Ghent used the word latitudo in connection with the concept of latitude of forms.
Nicole Oresme (1320-1382) used the terms latitude and longitude approximately in the sense of abscissa and ordinate.
LATTICE POINT is found in 1857 in Cayley, Coll. Math. Papers (1890) III. 40: "Imagine now in a plane, a rectangular system of coordinates (x, y) and the whole plane divided by lines parallel to the axes at distances = 1 from each other into squares of the dimension = 1. And let the angles which do not lie on the axes of coordinates be called lattice points (OED2).
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].
LAW OF COSINES is found in 1895 in Plane and spherical trigonometry, surveying and tables by George Albert Wentworth: "Law of Cosines. ... The square of any side of a triangle is equal to the sum of the squares of the other two sides, diminished by twice their product into the cosine of the included angle" [University of Michigan Digital Library].
The term LAW OF INTERTIA OF QUADRATIC FORMS is due to James Joseph Sylvester (DSB).
LAW OF LARGE NUMBERS. La loi de grands nombres appears in 1835 in Siméon-Denis Poisson (1781-1840), "Recherches sur la Probabilité des Jugements, Principalement en Matiére Criminelle," Comptes Rendus Hebdomadaires des Séances de l'Académie des Sciences, 1, 473-494 (James, 1998).
According to Porter (p. 12), Poisson coined the term in 1835.
LAW OF SINES (Snell's law). The law of sines is found in 1851-54 in Hand-books of natural philosophy and astronomy by Dionysius Lardner [University of Michigan Digital Library].
LAW OF SINES (trigonometry) is found in 1895 in Plane and spherical trigonometry, surveying and tables by George Albert Wentworth: "...the Law of Sines, which may be thus stated: The sides of a triangle are proportional to the sines of the opposite angles [University of Michigan Digital Library].
LAW OF TANGENTS is found in 1895 in Plane and spherical trigonometry, surveying and tables by George Albert Wentworth: "Hence the Law of Tangents: The difference of two sides of a triangle is to their sum as the tangent of half the difference of the opposite angles is to the tangent of half their sum" [University of Michigan Digital Library].
LAW OF THE ITERATED LOGARITHM is found in Philip Hartman and Aurel Wintner, "On the law of the iterated logarithm," Am. J. Math. 63, 169-176 (1941).
The term LEAST ACTION was used by Lagrange (DSB).
LEAST COMMON MULTIPLE. Common denominator appears in English in 1594 in Exercises by Blundevil: "Multiply the Denominators the one into the other, and the Product thereof shall bee a common Denominator to both fractions" (OED2).
Common divisor was used in 1674 by Samuel Jeake in Arithmetick, published in 1696: "Commensurable, called also Symmetral, is when the given Numbers have a Common Divisor" (OED2).
Least common multiple is found in 1823 in J. Mitchell, Dict. Math. & Phys. Sci.: "To find the least common Multiple of several Numbers" (OED2).
Least common denominator is found in 1844 in Introduction to The national arithmetic, on the inductive system by Benjamin Greenleaf: "RULE. - Reduce the fractions, if necessary, to the least common denominator. Then find the greatest common divisor of the numerators, which, written over the least common denominator, will give the greatest common divisor required" [University of Michigan Digital Library].
Lowest common denominator appears in 1854 in Arithmetic, oral and written, practically applied by means of suggestive questions by Thomas H. Palmer: "Suggestive Questions. - Are all the underlined factors to be found in the denominators of the fractions marked a and b? Should they be omitted, then, in finding the lowest common denominator? What is the product of the factors that are not underlined? (80·3·5.) Has this product every factor contained in all the given denominators? Will it form their common denominator, then? Does it contain no more factors than they do? Will it form, then, their lowest common denominator?" [University of Michigan Digital Library].
Least common dividend appears in 1857 in Mathematical Dictionary and Cyclopedia of Mathematical Science.
Lowest common multiple appears in 1873 in Test examples in algebra, especially adapted for use in connection with Olney's School, or University algebra by Edward Olney [University of Michigan Digital Library].
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.
In 1912, James Pierpont writes in Lectures on the Theory of Functions of Real Variables, volume II:
The author has chosen a definition which occurred to him many years ago, and which to him seems far more natural. In volume I it is shown that if the metric field be divided into a finite number of metric sets delta[1] ...What then is more natural than to ask what will happen if the cells delta[1], delta [2],... are infinite instead of finite in number? Form this apparently trivial question results a theory of L-integrals which contains the Lebesgue integrals as a special case, and which, furthermore, has the great advantage that not only is the relation of the new integrals to the ordinary or Riemannian integrals perfectly obvious, but also the form of reasoning employed in Riemann's theory may be taken over to develop the properties of the new integrals.The citation above, which was provided by James A. Landau, is from the preface, page iv.
Lebesgue integral appears in the title of N. J. Lennes, "Note on Lebesgue and Pierpont integral," Amer. Math. Soc. Bull. (1913). Landau believes it is likely that what Pierpont calls a Lebesgue integral is what Lennes calls a Pierpont integral.
Other 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 right triangle other than the hypotenuse is found in English in 1659 in Joseph Moxon, Globes (OED2).
Leg is used in the sense of one of the congruent sides of an isosceles triangle in 1702 Ralphson's Math. Dict.: "Isosceles Triangle is a Triangle that has two equal Legs" (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).
LEMOINE POINT. See symmedian point.
LEPTOKURTIC (and platykurtic and mesokurtic) were introduced by Karl Pearson, who wrote in Biometrika (1905) IV. 173: "Given two frequency distributions which have the same variability as measured by the standard deviation, they may be relatively more or less flat-topped than the normal curve. If more flat-topped I term them platykurtic, if less flat-topped leptokurtic, and if equally flat-topped mesokurtic" (OED2).
L'HOSPITAL'S RULE. In Differential and Integral Calculus (1902) by Virgil Snyder and John Irwin Hutchinson, the procedure is termed "evaluation by differentiation." The same term is used in Elementary Textbook of the Calculus (1912) by the same authors.
de l'Hosptial's theorem on indeterminate forms is found in approximately 1904 in the E. R. Hedrick translation of volume I of A Course in Mathematical Analysis by Edouard Goursat. The translation carries the date 1904, although a footnote references a work dated 1905 [James A. Landau].
In Differential and Integral Calculus (1908) by Daniel A. Murray, the procedure is shown but is not named.
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."
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 appears in L. Autonne, "Sur une application des groupes de M. Lie.," C. R. CXII. 570-573 (1891).
Lie group appears in English in H. B. Newson, "A new theory of collineations und their Lie groups," American J. 24, 109-172.
Lie group also appears in English in S. D. Zeldin, "On the quadratic ternary partial differential equation admitting Lie-groups of orders four and five.," American M. S. Bull. (1923).
LIKELIHOOD. The term was first used in its modern sense in R. A. Fisher's "On the 'Probable Error' of a Coefficient of Correlation Deduced from a Small Sample," Metron, 1, (1921), 3-32.
Formerly, likelihood was a synonym for probability, as it still is in everyday English. (See the entry on maximum likelihood and the passage quoted there for Fisher's attempt to distinguish the two. In 1921 Fisher referred to the value that maximizes the likelihood as "the optimum.")
Likelihood first appeared in a Bayesian context in H. Jeffreys's Theory of Probability (1939) [John Aldrich, based on David (2001)].
LIKELIHOOD PRINCIPLE. This expression burst into print in 1962, appearing in "Likelihood Inference and Time Series" by G. A. Barnard, G. M. Jenkins, C. B. Winsten (Journal of the Royal Statistical Society A, 125, 321-372), "On the Foundations of Statistical Inference" by A. Birnbaum (Journal of the American Statistical Association, 57, 269-306), and L. J. Savage et al, (1962) The Foundations of Statistical Inference. It must have been current for some time because the Savage volume records a conference in 1959; the term appears in Savage's contribution so the expression may have been his coining.
The principle (without a name) can be traced back to R. A. Fisher's writings of the 1920s though its clearest earlier manifestation is in Barnard's 1949 "Statistical Inference" (Journal of the Royal Statistical Society. Series B, 11, 115-149). On these earlier outings the principle attracted little attention.
The LIKELIHOOD RATIO figured in the test theory of J. Neyman and E. S. Pearson from the beginning, "On the Use of Certain Test Criteria for Purposes of Statistical Inference, Part I" Biometrika, (1928), 20A, 175-240. They usually referred to it as the likelihood although the phrase "likelihood ratio" appears incidentally in their "Problem of k Samples," Bulletin Académie Polonaise des Sciences et Lettres, A, (1931) 460-481. This phrase was more often used by others writing about Neyman and Pearson's work, e.g. Brandner "A Test of the Significance of the Difference of the Correlation Coefficients in Normal Bivariate Samples," Biometrika, 25, (1933), 102-109.
The standing of "likelihood ratio" was confirmed by S. S. Wilks's "The Large-Sample Distribution of the Likelihood Ratio for Testing Composite Hypotheses," Annals of Mathematical Statistics, 9, (1938), 60-620 [John Aldrich, based on David (2001)].
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. Gregory of St. Vincent (1584-1667) used terminus to mean the limit of a progression, according to Carl B. Boyer in The History of the Calculus and its Conceptual Development.
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).
In 1922 in Introduction to the Calculus, William F. Osgood writes: "Some writers find it convenient to use the expression 'a variable approaches a limit' to include the case that the variable becomes infinite. We shall not adopt this mode of expression, but shall understand the words 'approaches a limit' in their strict sense."
LIMIT POINT. Cantor used Häufungspunkt (accumulation point) in an 1872 paper "Über die Ausdehnung eines Satzes der Theorie der trigonometrischen Reihen," which appeared in Mathematische Annalen, Band 5, pp. 122-132 [Roger Cooke].
Limit point is found in English in "A Simple Proof of the Fundamental Cauchy-Goursat Theorem," Transactions of the American Mathematical Society, Vol. 1, No. 4. (Oct., 1900), pp. 499-506.
Point of accumulation appears in English in in E. W. Chittenden, "On the classification of points of accumulation in the theory of abstract sets," Bulletin A. M. S. 32 (1926).
LINE FUNCTION was the term used for functional by Vito Volterra (1860-1940), according to the DSB.
LINE GRAPH is dated ca. 1924 in MWCD10.
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 LINE OF EQUAL POWER was coined by Steiner.
LINEAR ALGEBRA. 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 associative algebra appears in 1870 as the title of a paper, "Linear Associative Algebra" by Benjamin Peirce. The paper was read before the National Academy of Sciences in Washington [James A. Landau].
Linear algebra occurs in 1875 in the title, "On the uses and transformations of linear algebra" by Benjamin Peirce, published in American Acad. Proc. 2 [James A. Landau].
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).
LINEAR DEPENDENCE appears in the 1907 edition of Introduction to Higher Algebra by Maxime Bôcher [James A. Landau].
LINEAR DIFFERENTIAL EQUATION appears in J. L. Lagrange, "Recherches sur les suites récurrentes don't les termed varient de plusieurs manières différentes, ou sur l'intégration des équations linéaires aux différences finies et partielles; et sur l'usage de ces équations dans la théorie des hasards," Nouv. Mém. Acad. R. Sci. Berlin 6 (1777) [James A. Landau].
LINEAR EQUATION appears in English the 1816 translation of Lacroix's Differential and Integral Calculus (OED2).
LINEAR FUNCTION. An 1857 English language translation of Gauss's Theoria motus has "...it is possible to assign a linear function alpha P + beta Q + gamma R + delta S + etc" and "And when it can be assumed that these are so small that their squares and products may be neglected, the corresponding changes, produced in the computed geocentric places of a heavenly body, can be obtained by means of the differential formulas given in the Second Section of the First Book. The computed places, therefore, which we obtain from the corrected elements, will be expressed by linear functions of the corrections of the elements, and their comparison with the observed places according to the principles before explained, will lead to the determination of the most probable values."
Linear function is found in English in volume I of An Elementary Treatise on Curves, Functions and Forces by Benjamin Peirce. The title page of this work has 1852; the copyright date on the reverse of the title page is 1841 [James A. Landau].
Linear function is also found in 1850 in The elements of analytical geometry by John Radford Young [University of Michigan Digital Library].
LINEAR INDEPENDENCE is found in 1901 in Linear Groups, with an exposition of the Galois field theory by Leonard Eugene Dickson [James A. Landau].
LINEAR OPERATOR. Linear operation appears in 1837 in Robert Murphy, "First Memoir on the Theory of Analytic Operations," Philosophical Transactions of the Royal Society of London, 127, 179-210. Murphy used "linear operation" in the sense of the modern term "linear operator" [Robert Emmett Bradley].
LINEAR PRODUCT. This term was used by Hermann Grassman in his Ausdehnungslehre (1844).
LINEAR PROGRAMMING. See programming.
LINEAR TRANSFORMATION appears in 1845 in Arthur Cayley, "On the Theory of Linear Transformations," Cambridge Math. J. 4, 193-209 [Romulo Lins].
LINEARLY DEPENDENT was used in 1893 in "A Doubly Infinite System of Simple Groups" by Eliakim Hastings Moore. The paper was read in 1893 and published in 1896 [James A. Landau].
LINEARLY INDEPENDENT is found in 1847 in "On the Theory of Involution in Geometry" by Arthur Cayley in the Cambridge and Dublin Mathematical Journal [University of Michigan Historical Math Collection].
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).
The term appears in the title of his 1868 paper, "On the Theory of Local Probability, applied to Straight Lines drawn at random in a plane; the methods used being also extended to the proof of certain new Theorems in the Integral Calculus," Trans. of London.
LOCUS is a Latin translation of the Greek word topos. Both words mean "place."
According to Pappus, Aristaeus (c. 370 to c. 300 BC) wrote a work called On Solid Loci (Topwn sterewn).
Pappus also mentions Euclid in connection with locus problems.
Apollonius mentioned the "locus for three and four lines" ("...ton epi treis kai tessaras grammas topon...") in the extant letter opening Book I of the Conica. Apollonius said in the first book that the third book contains propositions (III.54-56) relevant to the 3 and 4 line locus problem (and, since these propositions are new, Apollonius claimed Euclid could not have solved the problem completely--a claim that caused Pappus to call Apollonius a braggard (alazonikos). In Book III itself there is no mention of the locus problem [Michael N. Fried].
Locus appears in the title of a 1636 paper by Fermat, "Ad Locos Planos et Solidos Isagoge" ("Introduction to Plane and Solid Loci").
In English, locus is found in 1727-41 in Chambers Cyclopedia: "A locus is a line, any point of which may equally solve an indeterminate problem. ... All loci of the second degree are conic sections" (OED2).
Locus geometricus is an entry in the 1771 Encyclopaedia Britannica.
LOGARITHM. Before he coined the term logarithmus Napier called these numbers numeri artificiales, and the arguments of his logarithmic function were numeri naturales [Heinz Lueneburg].
Logarithmus was coined (in Latin) by John Napier (1550-1617) and appears in 1614 in his Mirifici Logarithmorum Canonis descriptio.
According to the OED2, "Napier does not explain his view of the literal meaning of logarithmus. It is commonly taken to mean 'ratio-number', and as thus interpreted it is not inappropriate, though its fitness is not obvious without explanation. Perhaps, however, Napier may have used logos merely in the sense of 'reckoning', 'calculation.'"
According to Briggs in Arithmetica logarithmica (1624), Napier used the term because logarithms exhibit numbers which preserve always the same ratio to one another.
According to Hacker (1970):
It undoubtedly was Napier's observation that logarithms of proportionals are "equidifferent" that led him to coin the name "logarithm," which occurs throughout the Descriptio but only in the title of the Constructio, which clearly was drafted first although published later. The many-meaning Greek word logos is therefore used in the sense of ratio. But there is an amusing play on words to which we might call attention since it does not seem to have been noticed. It is interesting that the Greeks also employed logos to distinguish reckoning, or that is to say mere calculation, from arithmos, which was generally reserved by them to indicate the use of number in the higher context of what today we call the theory of numbers. Napier's "logarithms" have indeed served both purposes.Logarithm appears in English in a letter of March 10, 1615, from Henry Briggs to James Ussher: "Napper, 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."
Logarithm appears in English in 1616 in E. Wright's English translation of the Descriptio: "This new course of Logarithmes doth cleane take away all the difficultye that heretofore hath beene in mathematicall calculations. [...] The Logarithmes of proportionall numbers are equally differing."
In the Constructio, which was drafted before the Descriptio, the term "artificial number" is used, rather than "logarithm." Napier adopted the term logarithmus before his discovery was announced.
Jobst Bürgi called the logarithm Die Rothe Zahl since the logarithms were printed in red and the antilogarithms in black in his Progress Tabulen, published in 1620 but conceived some years earlier (Smith vol. 2, page 523).
[Older English-language dictionaries pronounce logarithm with an unvoiced th, as in thick and arithmetic.]
LOGARITHMIC CURVE. Huygens proposed the terms hemihyperbola and linea logarithmica sive Neperiana.
Christiaan Huygens used logarithmica when he wrote in Latin and logarithmique when he wrote in French.
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. Lacroix used fonctions logarithmiques in Traité élémentaire de calcul différentiel et de calcul intégral (1797-1800).
Logarithmic function appears in 1831 in the second edition of Elements of the Differential Calculus (1836) by John Radford Young: "Thus, ax, a log x, sin x, &c., are transcendental functions: the first is an exponential function, the second a logarithmic function, and the third a circular function" [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 (Cajori 1919, page 156).
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.
LOGNORMAL. Logarithmic-normal was used in 1919 by S. Nydell in "The Mean Errors of the Characteristics in Logarithmic-Normal Distributions," Skandinavisk Aktuarietidskrift, 2, 134-144 (David, 1995).
Lognormal was used by J. H. Gaddun in Nature on Oct. 20, 1945: "It is proposed to call the distribution of x 'lognormal' when the distribution of log x is normal" (OED2).
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).
LOSS and LOSS FUNCTION in statistical decision theory. In the paper establishing the subject ("Contributions to the Theory of Statistical Estimation and Testing Hypotheses," Annals of Mathematical Statistics, 10, 299-326) Wald referred to "loss" but used "weight function" for the (modern) loss function. He continued to use weight function, for instance in his book Statistical Decision Functions (1950), while others adopted loss function. Arrow, Blackwell & Girshick’s "Bayes and Minimax Solutions of Sequential Decision Problems" (Econometrica, 17, (1949) 213-244) wrote L rather than W for the function and called it the loss function. A paper by Hodges & Lehmann ("Some Problems in Minimax Point Estimation," Annals of Mathematical Statistics, 21, (1950), 182-197) used loss function more freely but retained Wald’s W. [John Aldrich, based on David (2001) and JSTOR]
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 about 1675 in Cocker's Arithmetic, written by Edward Cocker (1631-1676): "Reduce a fraction to its lowest terms at the first Work" (OED2). (There is some dispute about whether Cocker in fact was the author of the work.)
LOXODROME. Pedro Nunez (Pedro Nonius) (1492-1577) announced his discovery and analysis of the curve in De arte navigandi. He called the curve the rumbus (Catholic Encyclopedia).
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. Lunula appears in A Geometricall Practise named Pantometria by Thomas Digges (1571): "Ye last figure called a Lunula" (OED2).
Lune appears in English in 1704 in Lexicon technicum, or an universal English dictionary of arts and sciences by John Harris (OED2).