Landmark writings in western mathematics 1640-1940

1042 Pages·2005·6.355 MB·English

by  Ivor Grattan-Guinness

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Landmark Writings
in Western Mathematics
1640–1940
This page intentionally left blank
Landmark Writings
in Western Mathematics
1640–1940
Editedby
I. Grattan-Guinness
EditorialBoard
Roger Cooke
Leo Corry
Pierre Crépel
Niccolo Guicciardini
2005
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TABLE OF CONTENTS
Inmanycasesashorttitleoradescriptionofthewritingisgiven.Thedateisthatoffirst
publication;thefirsteditionisinvolvedunlessotherwiseindicated.
0.Introduction(I.Grattan-Guinness)......................................... ix
1.1649RenéDescartes,Geometria(M.Serfati)............................... 1
2.1656JohnWallis,Arithmeticainfinitorum(JacquelineStedall)............... 23
3.1673ChristiaanHuygens,bookonthependulumclock(JoellaG.Yoder)...... 33
4. 1684–1693 Gottfried Wilhelm Leibniz, first three papers on the calculus
(C.S.Roero).................................................. 46
5.1687IsaacNewton,Philosophianaturalisprincipiamathematica(NiccolòGui-
cciardini)..................................................... 59
6.1713JakobBernoulli,Arsconjectandi(IvoSchneider)....................... 88
7.1718AbrahamDeMoivre,Thedoctrineofchances(IvoSchneider)........... 105
8.1734GeorgeBerkeley,Theanalyst(D.M.Jesseph).......................... 121
9.1738DanielBernoulli,Hydrodynamica(G.K.Mikhailov).................... 131
10.1742ColinMacLaurin,Atreatiseoffluxions(ErikSageng).................. 143
11.1743JeanleRondd’Alembert,Traitédedynamique(PierreCrépel).......... 159
12.1744LeonhardEuler,bookonthecalculusofvariations(CraigG.Fraser)..... 168
13.1748LeonhardEuler,‘Introduction’toanalysis(KarinReich)................ 181
14.1755LeonhardEuler,treatiseonthedifferentialcalculus(S.S.Demidov)...... 191
15. 1764 Thomas Bayes, An essay towards solving a problem in the doctrine of
chances(A.I.Dale)............................................ 199
16.1788JosephLouisLagrange,Méchaniqueanalitique(HelmutPulte).......... 208
17.1795GaspardMonge,Géométriedescriptive(JoëlSakarovitch).............. 225
18. 1796,1799–1827P.S. Laplace,Expositiondusystème du mondeand Traité du
mécaniquecéleste(I.Grattan-Guinness)......................... 242
19.1797JosephLouisLagrange,Théoriedesfonctionsanalytiques(CraigG.Fraser) 258
v
vi Tableofcontents
20.1797–1800S.F.Lacroix,Traitéducalculdifférentieletducalculintégral(João
CaramalhoDomingues)........................................ 277
21.1799–1802Jean-EtienneMontucla,Histoiredesmathématiques,secondedition
(PierreCrépelandAlainCoste)................................. 292
22.1801CarlFriedrichGauss,Disquisitionesarithmeticae(O.Neumann)........ 303
23.1809CarlFriedrichGauss,bookoncelestialmechanics(CurtisWilson)....... 316
24. 1812, 1814 P.S. Laplace, Théorie analytique des probabilités and Essai
philosophiquesurlesprobabilités(StephenM.Stigler)........... 329
25. 1821, 1823 A.-L. Cauchy, Cours d’analyse and Résumé of the calculus
(I.Grattan-Guinness).......................................... 341
26.1822JosephFourier,Théorieanalytiquedelachaleur(I.Grattan-Guinness)... 354
27.1822JeanVictorPoncelet,Traitédespropriétésprojectivesdesfigures(Jeremy
Gray)........................................................ 366
28.1825,1827A.-L.Cauchy,twomemoirsoncomplex-variablefunctiontheory(the
lateF.Smithies)............................................... 377
29. 1826 Niels Henrik Abel, paper on the irresolvability of the quintic equation
(RogerCooke)................................................ 391
30. 1828 George Green, An essay on the mathematical analysis of electricity and
magnetism(I.Grattan-Guinness)................................ 403
31.1829C.G.J.Jacobi,bookonellipticfunctions(RogerCooke)................ 412
32.1844HermannG.Grassmann,Ausdehnungslehre(AlbertC.Lewis)........... 431
33. 1847 Karl Georg Christian von Staudt, book on projective geometry (Karin
Reich)....................................................... 441
34.1851BernhardRiemann,thesisonthetheoryoffunctionsofacomplexvariable
(PeterUllrich)................................................ 448
35.1853WilliamRowanHamilton,Lecturesonquaternions(AlbertC.Lewis).... 460
36.1854GeorgeBoole,Aninvestigationofthelawsofthoughtonwhicharefounded
the mathematical theory of logic and probabilities (I. Grattan-
Guinness).................................................... 470
37. 1863 Johann Peter Gustav Lejeune-Dirichlet, Vorlesungen über Zahlentheorie
(CatherineGoldstein).......................................... 480
38. 1867BernhardRiemann,posthumousthesis onthe representationof functions
bytrigonometricseries(DavidMascré).......................... 491
39.1867BernhardRiemann,posthumousthesis‘Onthehypotheseswhichlieatthe
foundationofgeometry’(JeremyGray)......................... 506
40. 1867William Thomsonand Peter GuthrieTait, Treatise on naturalphilosophy
(M.NortonWise)............................................. 521
Tableofcontents vii
41.1871StanleyJevons,Thetheoryofpoliticaleconomy(Jean-PierrePotierandJan
vanDaal)..................................................... 534
42. 1872 Felix Klein’s Erlangen Program, ‘Comparative considerations of recent
geometricalresearches’(JeremyGray).......................... 544
43.1872RichardDedekind,StetigkeitundirrationaleZahlen(RogerCooke)...... 553
44.1873JamesClerkMaxwell,Atreatiseonelectricityandmagnetism(F.Achard) 564
45.1877–1878J.W.Strutt,ThirdBaronRayleigh,Thetheoryofsound(JaHyonKu) 588
46. 1883GeorgCantor,paperonthe‘Foundationsofa generalsettheory’(Joseph
W.Dauben)................................................... 600
47.1888,1889RichardDedekindandGiuseppePeano,bookletsonthefoundations
ofarithmetic(J.Ferreirós)..................................... 613
48.1890HenriPoincaré,memoironthethree-bodyproblem(JuneBarrow-Green). 627
49.1892OliverHeaviside,Electricalpapers(IdoYavetz)....................... 639
50.1892WalterWilliamRouseBall,Mathematicalrecreationsandproblemsofpast
andpresenttimes(DavidSingmaster)........................... 653
51. 1892 Alexandr Mikhailovich Lyapunov, thesis on the stability of motion
(J.Mawhin).................................................. 664
52.1894HeinrichHertz,posthumousbookonmechanics(JesperLützen)......... 677
53.1895–1896HeinrichWeber,LehrbuchderAlgebra(LeoCorry).............. 690
54. 1897David Hilbert, reporton algebraicnumberfields (‘Zahlbericht’)(Norbert
Schappacher)................................................. 700
55.1899DavidHilbert,GrundlagenderGeometrie(MichaelToepell)............ 710
56.1900KarlPearson,paperonthechisquaregoodnessoffittest(M.E.Magnello) 724
57.1901DavidHilbert,paperon‘Mathematicalproblems’(MichielHazewinkel). 732
58.1904LordKelvin,Baltimorelecturesonmathematicalphysics(OleKnudsen). 748
59.1904–1906HenriLebesgueandRenéBaire,threebooksonmathematicalanaly-
sis(RogerCooke)............................................. 757
60.1909H.A.Lorentz,Lecturesonelectrontheory(A.J.Kox)................... 778
61. 1910–1913 A.N. Whitehead and Bertrand Russell, Principia mathematica
(I.Grattan-Guinness).......................................... 784
62. 1915–1934FederigoEnriquesandOscar Chisini, Lectureson‘thegeometrical
theoryofequationsandalgebraicfunctions’(A.Conte)........... 795
63.1916AlbertEinstein,reviewpaperongeneralrelativitytheory(T.Sauer)...... 802
64.1917D’ArcyWentworthThompson,Ongrowthandform(T.J.Horder)....... 823
65.1919–1923LeonardDickson,Historyofthetheoryofnumbers(DellaD.Fenster) 833
viii Tableofcontents
66.1923–1926PaulUrysohnandKarlMenger,papersondimensiontheory(Tony
Crilly)....................................................... 844
67.1925R.A.Fisher,Statisticalmethodsforresearchworkers(A.W.F.Edwards).. 856
68.1927GeorgeDavidBirkhoff,Dynamicalsystems(DavidAubin).............. 871
69. 1930, 1932 P.A.M. Dirac and J. von Neumann, books on quantum mechanics
(LaurieM.BrownandHelmutRechenberg)...................... 882
70.1930–1931B.L.vanderWaerden,ModerneAlgebra(K.-H.Schlote).......... 901
71.1931KurtGödel,paperontheincompletenesstheorems(RichardZach)....... 917
72.1931WalterAndrewShewhart,Economiccontrolofqualityofmanufactured
product(DenisBayart)........................................ 926
73.1931VitoVolterra,bookonmathematicalbiology(G.Israel)................. 936
74.1932S.Bochner,lecturesonFourierintegrals(RogerCooke)................ 945
75. 1933 A.N. Kolmogorov, Grundbegriffe der Wahrscheinlichkeitsrechnung (Jan
vonPlato).................................................... 960
76.1934,1935H.SeifertandW.Threlfall,andP.S.AlexandroffandH.Hopf,books
ontopology(AlainHerreman).................................. 970
77.1934–1939DavidHilbertandPaulBernays,GrundlagenderMathematik(Wil-
friedSiegandMarkRavaglia).................................. 981
Listofauthors...................................................... 1000
Index(I.Grattan-Guinness).......................................... 1004