Catálogo de la biblioteca Antonio Monteiro - INMABB

Incluye referencias bibliográficas e índices.

Acknowledgements xix --
Introduction xxiii --
Chapter 1 Origins [1] --
l.A On the Origins of Number and Counting [1] --
1.A1 Aristotle [1] --
1.A2 Sir John Leslie [2] --
1.A3 K. Lovell [2] --
1.A4 Karl Menninger [3] --
1.A5 Abraham Seidenberg [4] --
1.B Evidence of Bone Artefacts [5] --
1.B1 Jean de Heinzelin on the Ishango bone as evidence of early interest in number [5] --
1.B2 Alexander Marshack on the Ishango bone as early lunar phase count [6] --
l.C Megalithic Evidence and Comment [8] --
1.C1 Alexander Thom on the megalithic unit of length [8] --
1.C2 Stuart Piggott on seeing ourselves in the past [9] --
1.C3 Euan MacKie on the social implications of the megalithic yard [10] --
1.C4 B. L. van der Waerden on neolithic mathematical science [11] --
1.C5 Wilbur Knorr’s critique of the interpretation of neolithic evidence [12] --
l.D Egyptian Mathematics [14] --
1.D1 Two problems from the Rhind papyrus [14] --
1.D2 More problems from the Rhind papyrus [16] --
1.D3 A scribe’s letter [20] --
1.1) 4 Greek views on the Egyptian origin of mathematics [21] --
1.1) 5 Sir Alan Gardiner on the Egyptian concept of part [22] --
1.D6 Arnold Buffum Chace on Egyptian mathematics as pure science [22] --
1.D7 G. J. Toomer on Egyptian mathematics as strictly practical [23] --
1.E Babylonian Mathematics [24] --
1.E1 Some Babylonian problem texts [25] --
1.E2 Sherlock Holmes in Babylon: an investigation by R. Creighton Buck [32] --
1.E3 Jöran Friberg on the purpose of Plimpton 322 [40] --
1.E4 The scribal art [40] --
LES Marvin Powell on two Sumerian texts [42] --
1.E6 Jens Hoyrup on the Sumerian origin of mathematics [43] --
Chapter 2 Mathematics in Classical Greece [46] --
2.A Historical Summary [46] --
2.Al Proclus’s summary [46] --
2.A2 W. Burkert on whether Eudemus mentioned Pythagoras [48] --
2.B Hippocrates’ Quadrature of Lunes [49] --
2.C Two Fifth-century Writers [51] --
2.C1 Parmenides’ The Way of Truth [52] --
2.C2 Aristophanes: Meton squares the circle [53] --
2.C3 Aristophanes: Strepsiades encounters the New Learning [53] --
2.D The Quadrivium [56] --
2.D1 Archytas [57] --
2.D2 Plato [57] --
2.D3 Proclus [52] --
2.D4 Nicomachus [58] --
2.D5 Boethius [59] --
2.D6 Hrosvitha [59] --
2.D7 Roger Bacon [60] --
2.D8 W. Burkert on the Pythagorean tradition in education [60] --
2.E Plato [61] --
2.E1 Socrates and the slave boy [61] --
2.E2 Mathematical studies for the philosopher ruler [67] --
2.E3 Theaetetus investigates incommensurability [73] --
2.E4 Lower and higher mathematics [74] --
2.ES Plato’s cosmology [76] --
2.E6 Freeborn studies and Athenian ignorance [80] --
2.E7 A letter from Plato to Dionysius [81] --
2.E8 Aristoxenus on Plato’s lecture on the Good [82] --
2.F Doubling the Cube [82] --
2JF1 Theon on how the problem (may have) originated [83] --
2.F2 Proclus on its reduction by Hippocrates [83] --
2.F3 Eutocius’s account of its early history, and an instrumental solution [83] --
2.F4 Eutocius on Menaechmus’s use of conic sections [85] --
2.G Squaring the Circle [87] --
2.G1 Proclus on the origin of the problem [87] --
2.G2 Antiphon’s quadrature [87] --
2.G3 Bryson’s quadrature [89] --
2.G4 Pappus on the quadratrix [89] --
2.H Aristotle [92] --
2.H1 Principles of demonstrative reasoning [93] --
2.H2 Geometrical analysis [94] --
2.H3 The distinction between mathematics and other sciences [95] --
2.H4 The Pythagoreans [96] --
2.H5 Potential and actual infinities [96] --
2.H6 Incommensurability [98] --
Chapter 3 Euclid’s Elements [99] --
3.A Introductory Comments by Proclus [99] --
3.B Book I [100] --
3.B1 Axiomatic foundations [100] --
3.B2 The base angles of an isosceles triangle are equal (Proposition 5) [104] --
3.B3 Propositions 6, 9, 11 and 20 [107] --
3.B4 The angles of a triangle are two right angles (Proposition 32) [111] --
3.B5 Propositions 44, 45, 46 and 47 [112] --
3.C Books II-VI [117] --
3.C1 Book II: Definitions and Propositions 1,4, 11 and 14 [117] --
3.C2 Book III: Definitions and Proposition 16 [121] --
3.C3 Book V: Definitions [123] --
3.C4 Book VI: Definitions and Propositions 13, 30 and 31 [124] --
3.D The Number Theory Books [126] --
3.D1 Book VII: Definitions [126] --
3.D2 Book IX: Propositions 20, 21 and 22 [127] --
3.D3 Book IX: Proposition 36 [129] --
3.E Books X-XIII [132] --
3.E1 Book X: Definitions, Propositions 1 and 9, and Lemma 1 [132] --
3.E2 Book XI: Definitions [135] --
3.E3 Book XII: Proposition [2] --
3.E4 Book XIII: Statements of Propositions 13-18 and a final result [137] --
3.F Scholarly and Personal Discovery of Euclid's Text [138] --
3. Fl A. Aaboe on the textual basis [138] --
3.F2 Later personal impacts [140] --
Historians Debate Geometrical Algebra [140] --
3.G1 B. L. van der Waerden [140] --
3.G2 Sabetai Unguru [142] --
3.G3 B. L. van der Waerden [143] --
3.G4 Sabetai Unguru [143] --
3.G5 Ian Mueller [144] --
3.G6 John L. Berggren [146] --
Chapter 4 Archimedes and Apollonius [148] --
Archimedes [148] --
4.A1 Measurement of a circle [148] --
4.A2 The sand-reckoner [150] --
4.A3 Quadrature of the parabola [153] --
4.A4 On the equilibrium of planes: Book I [154] --
4.A5 On the sphere and cylinder: Book I [156] --
4.A6 On the sphere and cylinder: Book II [158] --
4.A7 On spirals [160] --
4.A8 On conoids and spheroids [165] --
4.A9 The method treating of mechanical problems [167] --
Later Accounts of the Life and Works of Archimedes [173] --
4.B1 Plutarch [173] --
4.B2 Vitruvius [176] --
4.B3 John Wallis (1685) [177] --
4.B4 Sir Thomas Heath [177] --
4.C Diocles [179] --
4.C1 Introduction to On Burning Mirrors [179] --
4.C2 Diocles proves the focal property of the parabola [180] --
4.C3 Diocles introduces the cissoid [181] --
4.D Apollonius [182] --
4.D1 General preface to Conics; to Eudemus [183] --
4.D2 Prefaces to Books II, IV and V [183] --
4.D3 Book I: First definitions [185] --
4.D4 Apollonius introduces the parabola, hyperbola and ellipse [186] --
4.D5 Some results on tangents and diameters [188] --
4.D6 How to find diameters, centres and tangents [191] --
4.D7 Focal properties of hyperbolas and ellipses [195] --

Chapter 5 Mathematical Traditions in the Hellenistic Age [197] --
5.A The Mathematical Sciences [191] --
5.A1 Proclus on the divisions of mathematical science [197] --
5.A2 Pappus on mechanics [199] --
5.A3 Optics [200] --
5.A4 Music [203] --
5.A5 Heron on geometric mensuration [205] --
5.A6 Geodesy: Vitruvius on two useful theorems of the ancients [206] --
5.B The Commentating Tradition [207] --
5.B1 Theon on the purpose of his treatise [207] --
5.B2 Proclus on critics of geometry [208] --
5.B3 Pappus on analysis and synthesis [208] --
5.B4 Pappus on three types of geometrical problem [209] --
5.B5 Pappus on the sagacity of bees [211] --
5.B6 Proclus on other commentators [212] --
5.C Problems Whose Answers Are Numbers [212] --
5.C1 Proclus on Pythagorean triples [212] --
5.C2 Problems in Hero’s Geometrica [213] --
5.C3 The cattle problem [214] --
5.C4 Problems from The Greek Anthology [214] --
5.C5 An earlier and a later problem [216] --
5. D Diophantus [217] --
5.D1 Book 1.7 [217] --
5.D2 Book 1.27 [218] --
5.D3 Book II.8 [218] --
5.D4 Book III. 10 [218] --
5.D5 Book IV(A).3 [219] --
5.D6 Book IV(A).9 [219] --
5.D7 Book VI(A).ll [220] --
5.D8 Book V(G).9 [220] --
5.D9 Book VI(G).19 [221] --
5. D10 Book VI(G).21 [221] --
Chapter 6 Islamic Mathematics [223] --
6. A Commentators and Translators [223] --
6. A1 The Banu Musa [223] --
6.A2 Al-Sijzi [224] --
6.A3 Omar Khayyam [225] --
6.B Algebra [228] --
6.B1 Al-Khwarizmi on the algebraic method [228] --
6.B2 Abu-Kamil on the algebraic method [232] --
6.B3 Omar Khayyam on the solution of cubic equations [233] --
6.C The Foundations of Geometry [235] --
6.C1 Al-Haytham on the parallel postulate [235] --
6.C2 Omar Khayyam’s critique of al-Haytham [236] --
6. C3 Youshkevitch on the history of the parallel postulate [237] --
Chapter 7 Mathematics in Mediaeval Europe [240] --
7.A The Thirteenth and Fourteenth Centuries [240] --
7. Al Leonardo Fibonacci [241] --
7.A2 Jordanus de Nemore on problems involving numbers [243] --
7.A3 M. Biagio: A quadratic equation masquerading as a quartic [244] --
7.B The Fifteenth Century [245] --
7.B1 Johannes Regiomontanus on triangles [245] --
7.B2 Nicolas Chuquet on exponents [247] --
7. B3 Luca Pacioli [249] --
Chapter 8 Sixteenth-century European Mathematics [253] --
8.A The Development of Algebra in Italy [253] --
8. Al Antonio Maria Fior’s challenge to Niccold Tartaglia (1535) [254] --
8.A2 Tartaglia’s account of his meeting with Gerolamo Cardano in 1539 [254] --
8.A3 Tartaglia versus Ludovico Ferrari (1547) [257] --
8.A4 Gerolamo Cardano [259] --
8.A5 Rafael Bombelli [263] --
8.B Renaissance Editors [265] --
8.B1 John Dee to Federigo Commandino [265] --
8.B2 Bernardino Baldi on Commandino [267] --
8.B3 Paul Rose on Francesco Maurolico [268] --
8. C Algebra at the Turn of the Century [270] --
8.C1 Simon Stevin [270] --
8. C2 Francois Viète [274] --
Chapter 9 Mathematical Sciences in Tudor and Stuart England [276] --
9. A Robert Record [276] --
9. A1 The Ground of Artes [216] --
9.A2 The Pathway to Knowledge [279] --
9.A3 The Castle of Knowledge [280] --
9.A4 The Whetstone of Witte [281] --
9.B John Dee [282] --
9.B1 Mathematical! Praeface to Henry Billingsley’s Euclid [283] --
9.B2 Bisecting an angle, from Henry Billingsley’s Euclid [286] --
9.B3 Views of John Dee [287] --
9.C The Value of Mathematical Sciences [289] --
9.C1 Roger Ascham (1570) [289] --
9.C2 William Kempe (1592) [289] --
9.C3 Gabriel Harvey (1593) [289] --
9.C4 Thomas Hylles (1600) [290] --
9.C5 Francis Bacon (1603) [290] --
9.D Thomas Harriot [291] --
9.D1 Dedicatory poem by George Chapman [291] --
9.D2 A sonnet by Harriot [292] --
9.D3 Examples of Harriot’s algebra [292] --
9.D4 Letter to Harriot from William Lower [293] --
9.D5 John Aubrey’s brief life of Harriot [293] --
9.D6 John Wallis on Harriot and Descartes [294] --
9.D7 Recent historical accounts [295] --
9.E Logarithms [296] --
9.E1 John Napier’s Preface to A Description of the Admirable Table of Logarithms [296] --
9.E2 Henry Briggs on the early development of logarithms [297] --
9.E3 William Lilly on the meeting of Napier and Briggs [297] --
9.E4 Charles Hutton on Johannes Kepler’s construction of logarithms [298] --
9.E5 John Keil on the use of logarithms [300] --
9.E6 Edmund Stone on definitions of logarithms [300] --
9.F William Oughtred [301] --
9.F1 Oughtred’s Clavis Mathematicae [301] --
9.F2 John Wallis on Oughtred’s Clavis [302] --
9.F3 Letters on the value of Oughtred’s Clavis [303] --
9.F4 John Aubrey on Oughtred [304] --
9.G Brief Lives [305] --
9.G1 Thomas Allen (1542-1632) [305] --
9.G2 Sir Henry Savile (1549-1622) [306] --
9.G3 Walter Warner (1550-1640) [306] --
9.G4 Edmund Gunter (1581-1626) [307] --
9.G5 Thomas Hobbes (1588-1679) [307] --
9.G6 Sir Charles Cavendish (1591-1654) [308] --
9.G7 Rene Descartes (1596-1650) [308] --
9.G8 Edward Davenant [308] --
9.G9 Seth Ward (1617-1689) [309] --
9.G10 Sir Jonas Moore (1617-1679) [310] --
9.H Advancement of Mathematics [310] --
9. HI John Pell’s Idea of Mathematics [310] --
9.H2 Letters between Pell and Cavendish [314] --
9.H3 Hobbes and Wallis [316] --
9.H4 The mathematical education of John Wallis [316] --
9. H5 Samuel Pepys learns arithmetic [317] --
Chapter 10 Mathematics and the Scientific Revolution [319] --
10.A Johannes Kepler [320] --
10.Al Planetary motion [320] --
10.A2 Celestial harmony [324] --
10.A3 The regular solids [324] --
10.A4 The importance of geometry [327] --
10. B Galileo Galilei [328] --
10.B1 On mathematics and the world [328] --
10.B2 The regular motion of the pendulum [329] --
10.B3 Naturally accelerated motion [330] --
10.B4 The time and distance laws for a falling body [331] --
10.B5 The parabolic path of a projectile [334] --
Chapter 11 Descartes, Fermat and their Contemporaries [336] --
11. A Rene Descartes [336] --
11. Al Descartes’s method [337] --
11.A2 The elementary arithmetical operations [338] --
11.A3 The general method for solving any problem [339] --
11.A4 Pappus on the locus to three, four or several lines [340] --
11.A5 Descartes to Marin Mersenne [342] --
11.A6 Descartes’s solution to the Pappus problem [342] --
11.A7 ‘Geometric* curves [344] --
11.A8 Permissible and impermissible methods in geometry [346] --
11.A9 The method of normals [346] --
11.A10 H. J. M. Bos on Descartes’s Geometry [349] --
ll.B Responses to Descartes's Geometry [350] --
11.B1 Florimond Debeaune’s inverse tangent problem [351] --
11.B2 Philippe de la Hire on conic sections [352] --
11.B3 Philippe de la Hire on the algebraic approach [353] --
11.B4 Hendrik van Heuraet on the rectification of curves [354] --
11.B5 Jan Hudde’s rules [356] --
ll.C Pierre de Fermat [356] --
11.C1 On maxima and minima and on tangents [358] --
11.C2 A second method for finding maxima and minima [359] --
11.C3 Fermat to Bernard de Frenicle on ‘Fermat primes’ [361] --
11.C4 Fermat to Marin Mersenne on his ‘little theorem’ [361] --
11.C5 Fermat’s evaluation of an ‘infinite’ area [362] --
11.C6 Fermat’s challenge concerning x2 = Ay2 + 1 [364] --
11.C7 On problems in the theory of numbers: a letter to Christaan Huygens [364] --
11.C8 Fermat’s last theorem [365] --
1 l.D Girard Desargues [366] --
11.D1 Preface to Rough Draft on Conics [367] --
11.D2 The invariance of six points in involution [368] --
11.D3 Desargues’s involution theorem [368] --
11.D4 Descartes to Desargues [371] --
11.D5 Pascal’s hexagon [372] --
11.D6 Desargues’s theorem on triangles in perspective [373] --
11.D7 Philippe de la Hire’s Sectiones Conicae [373] --
11. E Infinitesimals., Indivisibles, Areas and Tangents [375] --
11.E1 Gilles Personne de Roberval on the cycloid [376] --
11.E2 Blaise Pascal to Pierre de Carcavy [378] --
11. E3 Isaac Barrow on areas and tangents [378] --

Chapter 12 Isaac Newton [380] --
12. A Newton’s Invention of the Calculus [381] --
12. A1 Tangents by motion and by the o-method [381] --
12.A2 Rules for finding areas [382] --
12.A3 The sine series and the cycloid [383] --
12.A4 Quadrature as the inverse of fluxions [384] --
12.A5 Finding fluxions of fluent quantities [385] --
12.A6 Finding fluents from a fluxional relationship [385] --
12.B Newton’s Principia [387] --
12.B1 Prefaces [388] --
12.B2 Axioms, or laws of motion [389] --
12.B3 The method of first and last ratios [391] --
12.B4 The nature of first and last ratios [393] --
12.B5 The determination of centripetal forces [394] --
12.B6 The law of force for an elliptical orbit [396] --
12.B7 Gravity obeys an inverse square law [397] --
12.B8 Motion of the apsides [398] --
12.B9 Against vortices [399] --
12.B10 Rules of reasoning in philosophy [400] --
12.B11 The shape of the planets [401] --
12.B12 General scholium [401] --
12.B13 Gravity [402] --
12.C Newton’s Letters to Leibniz [402] --
12.C1 From the Epistola Prior [402] --
12.C2 From the Epistola Posterior [404] --
12.1) Newton on Geometry [408] --
12.1) 1 On the locus to three or four lines [408] --
12.1) 2 The enumeration of cubics [410] --
12.D3 On geometry and algebra [410] --
12.1) 4 Newton’s projective transformation [414] --
12.E Newton's Image in English Poetry [415] --
12.El Alexander Pope, Epitaph [415] --
12.E2 Alexander Pope, An Essay on Man, Epistle II [415] --
12.E3 William Wordsworth, The Prelude, Book III [416] --
12.E4 William Blake, Jerusalem, Chapter 1 [417] --
12. F Biographical and Historical Comments [417] --
12.F1 Bernard de Fontenelle’s Eulogy of Newton [418] --
12.F2 Voltaire on Descartes and Newton [419] --
12.F3 Voltaire on gravity as a physical truth [420] --
12.F4 John Maynard Keynes on Newton the man [421] --
12. F5 D. T. Whiteside on Newton, the mathematician [422] --
Chapter 13 Leibniz and his Followers [424] --
13. A Leibniz’s Invention of the Calculus [424] --
13. A1 A notation for the calculus [425] --
13.A2 Debeaune’s inverse tangent problem [426] --
13.A3 The first publication of the calculus [428] --
13.B Johann Bernoulli and the Marquis de I’Hopital [435] --
13.B1 Bernoulli’s lecture to I’Hopital on the solution to Debeaune’s problem [436] --
13.B2 Bernoulli on the integration of rational functions [436] --
13.B3 Bernoulli on the inverse problem of central forces [439] --
13.B4 O. Spiess on Bernoulli’s first meeting with I’Hopital [441] --
13.B5 Preface to l’Hopital’s Analyse des Infiniment Petits [442] --
13.B6 L’Hopital on the foundations of the calculus [442] --
13. B7 Stone’s preface to the English edition of l’Hopital’s Analyse des Infiniment Petits [445] --
Chapter 14 Euler and his Contemporaries [446] --
14.A Euler on Analysis [446] --
14. A1 A general method for solving linear ordinary differential equations [447] --
14.A2 Euler’s unification of the theory of elementary functions [449] --
14.A3 Logarithms [451] --
14.A4 The algebraic theory of conics [452] --
14.A5 The theory of elimination [453] --
14.B Euler and Others on the Motion of the Moon [454] --
14.B1 Pierre de Maupertuis on the figure of the Earth [455] --
14.B2 Correspondence between Euler and Alexis-Claude Clairaut [456] --
14.B3 Clairaut on the system of the world according to the principles of universal gravitation [458] --
14.B4 Euler to Clairaut, 2 June 1750 [459] --
14.C Euler’s Later Work [460] --
14.C1 A general principle of mechanics [460] --
14.C2 Fermat’s last theorem and the theory of numbers [462] --
14.C3 The motion of a vibrating string [464] --
14.C4 Nicolas Condorcet’s Elogium of Euler [468] --
14.D Some of Euler’s Contemporaries [471] --
14.D1 Jean-Paul de Gua on the use of algebra in geometry [473] --
14.D2 Gabriel Cramer on the theory of algebraic curves [475] --
14.D3 Jean d’Alembert on algebra, geometry and mechanics [477] --
14.D4 Joseph Louis Lagrange on solvability by radicals [479] --
14.D5 Joseph Louis Lagrange’s additions to Euler’s Algebra [480] --
14.D6 Johann Heinrich Lambert on the making of maps [482] --
Chapter 15 Gauss, and the Origins of Structural Algebra [485] --
15.A Gauss’s Mathematical Writings [487] --
15.A1 Gauss’s mathematical diary for 1796 [487] --
15.A2 Critiques of attempts on the fundamental theorem of algebra [490] --
15.A3 The constructibility of the regular 17-gon [492] --
15.A4 The charms of number theory [493] --
15.A5 Curvature and the differential geometry of surfaces [494] --
15.B Gauss’s Correspondence [496] --
15.B1 Three letters between Gauss and Sophie Germain [496] --
15.B2 Three letters between Gauss and Friedrich Wilhelm Bessel [498] --
15.C 7W Number Theorists [499] --
15.C1 Adrien Marie Legendre on quadratic reciprocity [499] --
15.C2 E. E. Kummer: Ideal numbers and Fermat’s last theorem [500] --
15.D Galois Theory [502] --
15.D1 Evariste Galois’s letter to Auguste Chevalier [502] --
15.D2 An unpublished preface by Galois [504] --
15.D3 Augustin Louis Cauchy on the theory of permutations [505] --
15.D4 Camille Jordan on the background to his work on the theory of groups [507] --
Chapter 16 Non-Euclidean Geometry --
16. A Seventeenth- and Eighteenth-century Developments [508] --
16.Al John Wallis’s lecture on the parallel postulate [510] --
16.A2 From Gerolamo Saccheri’s Euclides Vindicatus [512] --
16.A3 Johann Heinrich Lambert to Immanuel Kant [514] --
16.A4 Kant on our intuition of space [515] --
16.A5 Lambert on the consequences of a non-Euclidean postulate [517] --
16.A6 Two attempts by Legendre on the parallel postulate [520] --
16.B Early Nineteenth-century Developments [522] --
16.B1 Ferdinand Karl Schweikart’s memorandum to Gauss [522] --
16.B2 Gauss on Janos Bolyai’s Appendix [523] --
16.B3 Nicolai Lobachevskii’s theory of parallels [524] --
16.B4 Correspondence between Wolfgang and Janos Bolyai [527] --
16.B5 Janos Bolyai’s The Science Absolute of Space [528] --
16.C Later Nineteenth-century Developments [529] --
16.C1 Roberto Bonola on the spread of non-Euclidean geometry [530] --
16.C2 Bernhardt Riemann on the hypotheses which lie at the basis of geometry [532] --
16.C3 Eugenio Beltrami on the interpretation of non-Euclidean geometry [533] --
16.C4 Felix Klein on non-Euclidean and projective geometry [534] --
16.C5 J. J. Gray on four questions about the history of nonEuclidean geometry [536] --
16.D Influences on Literature [537] --
16.D1 Fyodor Dostoevsky, from The Brothers Karamazov [538] --
16.D2 Gabriel Garcia Marquez, from One Hundred Years of Solitude [539] --
Chapter 17 Projective Geometry in the Nineteenth Century [541] --
17.A Developments in France [542] --
17.A1 Jean Victor Poncelet on a general synthetic method in geometry [542] --
17.A2 Michel Chasles [544] --
17.A3 Joseph Diaz Gergonne on the principle of duality [.546] --
17.A4 M. Paul on students’ studies at the Ecole Poly technique [548] --
17.B Developments in Germany [549] --
17.B1 August Ferdinand Mobius [549] --
17.B2 Julius Pliicker on twenty-eight bitangents [550] --
17.B3 From Alfred Clebsch’s obituary of Julius Plücker [552] --
17.B4 Christian Wiener’s stereoscopic pictures of the twenty-seven lines on a cubic surface [554] --
Chapter 18 The Rigorization of the Calculus [555] --
18. A Eighteenth-century Developments [556] --
18.A1 George Berkeley’s criticisms of the calculus [556] --
18.A2 Colin MacLaurin on rigorizing the fluxional calculus [558] --
18.A3 D’Alembert on differentials [558] --
18.A4 Lagrange on derived functions [561] --
18.A5 Lagrange on algebra and the theory of functions [562] --
18.B Augustin Louis Cauchy and Bernard Bolzano [563] --
18.B1 Bolzano on the intermediate value theorem [564] --
18.B2 Cauchy’s definitions [566] --
18.B3 Cauchy on two important theorems of the calculus [570] --
18.B4 J. V. Grabiner on the significance of Cauchy [571] --
18. C Richard Dedekind and Georg Cantor [572] --
18.C1 Dedekind on irrational numbers and the theorems of the calculus [573] --
18.C2 Cantor’s definition of the real numbers [577] --
18.C3 The correspondence between Cantor and Dedekind [578] --
18.C4 Cantor on the uncountability of the real numbers [579] --
18. C5 Cantor’s statement of the continuum hypothesis [580] --
Chapter 19 The Mechanization of Calculation [582] --
19. A Leibniz on Calculating Machines in the Seventeenth Century [582] --
19.B Charles Babbage [584] --
19. B1 Babbage on Gaspard de Prony [584] --
19.B2 Dionysius Lardner on the need for tables [586] --
19.B3 Anthony Hyman’s commentary on the analytical engine [587] --
19.B4 Ada Lovelace on the analytical engine [590] --
19.C Samuel Lilley on Machinery in Mathematics [594] --
19.D Computer Proofs [597] --
19.D1 Letter from Augustus De Morgan to William Rowan Hamilton [597] --
19.D2 Donald J. Albers [598] --
19.D3 F. F. Bonsall [599] --
19.D4 Thomas Tymoczo [599] --
Sources [601] --
Name Index [619] --
Subject Index [624] --

MR, 89m:01006