Lagrange’s formula 120, 278,
300, 405
Lagrange’s theorem 299
Lagrangian (unit) 300
Lagrangian description 300
Lagrangian multipliers 300
Lambert, Johann Heinrich
283, 300–301, 392, 477
Landa, Diego de 332
Langlands, Robert 194
Laplace, Pierre-Simon,
marquis de 69, 245,
301–302, 356, 399, 414
Laplace operator 302
Laplace transform 302
latent vector. See eigenvector
lateral surface 115
Latin square 174, 302–303
latitude 105, 154, 337
lattice 366
lattice method 159
lattice point 164, 166
lattice polygon 164–165, 166
law of averages 303, 304
law of conservation of energy
309
law of continuity 309
law of cosines 5–6, 16, 78,
303, 303–304, 506
law of excluded middle 304
law of falling bodies 213
law of identity 304
law of large numbers 71–72,
303, 304, 399, 414–415, 436
law of noncontradiction 304
law of sines 1–2, 78, 303,
303–304, 463, 507
law of the lever 18, 69, 304
laws of gravity 353
laws of planetary motion
291–293
laws of thought 26, 304–305
lawyer paradox 374–375
leading coefficient 305
least common denominator
83
least common multiple 83,
305
least-integer function. See
ceiling function
least squares method 107,
218, 302, 305–307, 308, 445
Lebesgue, Henri-Léon 58, 307
LeBlanc, Louis 227
Leçons sur les séries
trigonométriques (Lebesgue)
307
Lectiones geometricae
(Barrow) 36
Lectures on Quaternions
(Hamilton) 520
left derivative 307–308
left-handed system 369, 448
left identity 257
left/right, limit from the 313
Legendre, Adrien-Marie 187,
308
Legendre polynomials 308
Legendre symbol 308
Lehmer, D. H. 436
Leibniz, Gottfried Wilhelm
122, 208, 308, 308–309,
523–525
and calculus notation 249,
488
and differential 132
and discovery of calculus
57–58, 211, 227, 240,
272, 352, 494
and double integrals 148
and formal logic 199, 228
Leibniz’s series. See Gregory
series
Leibniz’s theorem 418
lemma 498–499
length 309–310
lens 76
Leonardo of Pisa. See Fibonacci
Les méthodes nouvelles de la
méchanique céleste
(Poincaré) 399
Let’s Make a Deal! (game
show) 343
letterbox principle. See
pigeonhole principle
“A Letter on Asymptotic
Series” (Bayes) 39
Letters to a German Princess
(Euler) 174
levers and pulleys 19–20
L’Hôpital, Guillaume François,
marquis de 40, 58, 310
L’Hôpital’s rule 40, 310–311
Lho shu square 325, 326
Lhuilier, Simon 474
liar’s paradox 289, 311, 374,
458
Liber abaci (Fibonacci) 156,
191–192
Liber de ludo aleae (Cardano)
414
Liber quadratorum (Fibonacci)
192
life tables (mortality tables)
311–312, 415
ligancy 472
likelihood 197
Lilavati (Bha¯skara) 41–42
limit 312–313
d’Alembert and 8–9
and analytic number theory
13
Bolzano’s work on 47
and chain rule 70–71
ε- δdefinition of 529
and definition of tangent
492
derivative as 132
devised by Cauchy 66
in history of calculus 58
Lindemann, Carl Louis
Ferdinand von 11, 297,
313–314, 393, 477
line 314, 315
linear algebra 314, 491
linear-congruence method
436–437
linear equation 34, 156, 163,
314–315
linear interpolation 277–278
linearly dependent/
independent 315
Linear Perspective (Taylor)
494
linear programming 316
linear transformation 7,
316–317
line integral. See contour
integral
Liouville, Joseph 11, 59, 215,
317–318
Liouville’s constant (Liouville’s
number) 11, 317
Listing, Johann 295, 339, 340
Littlewood, John 246
Liu Hui 73
Li Ye (Li Chi, Li Zhi) 73, 318
Lobachevskian geometry. See
hyperbolic geometry
Lobachevsky, Nikolai
Ivanovich 46–47, 171, 219,
227, 255, 318, 355, 377,
455
local maximum/minimum
330–331, 331, 468
locus (loci) 319
logarithm 247, 252, 284,
319–320, 342, 411, 461, 466
history of 53–54, 55,
291–293, 345–346
of matrix 157
logarithmic differentiation
258–259
logarithmic function
152–153, 153, 320–321, 337
logarithmic graph 235
logarithmic scale 118, 321,
369, 466
logarithmic spiral 39, 474
Logarithmorum chilias prima
(Briggs) 54
logically equivalent 515
logic gates 88
Logic of Chance (Venn) 524
long division 37, 37–38, 38,
146, 349, 404, 433
longitude 105, 154–155, 337,
445
long radius 321
Loomis, Elisha Scott 425
loop (graph theory) 233
Lorentz, Hendrik 398
Lovelace, Augusta Ada 33,
321–322, 322
lowest terms. See reduced form
Loyd, Sam 465–466
lozenge 376, 474
Lucas, Edouard 502
lune 251–252, 322, 322–323
Lyapunov, Aleksandr
Mikhailovich 69, 356, 415
M
Maclaurin, Colin 107–108,
324, 496
Maclaurin series. See Taylor
series
Madhava of Sangamagramma
264, 324–325
magic constant 325
magic division square 327,
327
magic multiplication square
327, 327
magic rectangle 328, 328
magic square 149, 149–150,
325, 325–328, 326, 327
magnitude 328–329
al-Mahani 18
major arc 18
major premise 27
Malthus, Thomas 407
Mandelbrot, Benoit 204
Mandelbrot set 204
Manière universelle de Mr.
Desargues (Bosse) 124
mapping. See function
Markov, Andrei 415
Markov chains 296
The Mathematical Analysis of
Logic (Boole) 48
“Mathematical Contribution
to the Theory of Evolution”
(Pearson) 387
Mathematical Dissertations
(Simpson) 464
mathematical induction. See
induction
“The Mathematical Theory of
Communication” (Shannon
and Weaver) 461
A Mathematician’s Apology
(Hardy) 246
Mathematische Grundlagen
der Quantenmechanik (von
Neumann) 351
matrix (matrices) 109, 119,
126–128, 221–222, 314,
329
matrix addition 329–330
matrix algebra 68, 458
matrix inverse. See inverse
matrix
matrix multiplication 241,
330
matrix operations 329–330
Matyasevic, Yuri 137
maximin strategy 217
maximum/minimum 89, 133,
310, 330–332, 331
Mayan mathematics 332–333
McManus, Chris 118
mean (average) 44, 333–334,
480, 537
mean. See expected value
mean value 334
mean-value theorem 22,
94–95, 119, 184, 211, 262,
311, 334–335, 442, 450
Index 561