Book:John Fauvel/The History of Mathematics: A Reader

Subject Matter
An anthology of extracts of mathematical writings from antiquity to recent times

Contents

 * Acknowledgements


 * Introduction


 * Chapter 1 Origins


 * 1.A On the Origins of Number and Counting
 * 1.A1 Aristotle
 * 1.A2 Sir John Leslie
 * 1.A3 K. Lovell
 * 1.A4 Karl Menninger
 * 1.A5 Abraham Seidenberg


 * 1.B Evidence of Bone Artefacts
 * 1.B1 Jean de Heinzelin on the Ishango bone as evidence of early interest in number
 * 1.B2 Alexander Marshack on the Ishango bone as early lunar phase count


 * 1.C Megalithic Evidence and Comment
 * 1.C1 Alexander Thorn on the megalithic unit of length
 * 1.C2 Stuart Piggott on seeing ourselves in the past
 * 1.C3 Euan MacKie on the social implications of the megalithic yard
 * 1.C4 B. L. van der Waerden on neolithic mathematical science
 * 1.C5 Wilbur Knorr's critique of the interpretation of neolithic evidence


 * 1.D Egyptian Mathematics
 * 1.D1 Two problems from the Rhind papyrus
 * 1.D2 More problems from the Rhind papyrus
 * 1.D3 A scribe's letter
 * 1.D4 Greek views on the Egyptian origin of mathematics
 * 1.D5 Sir Alan Gardiner on the Egyptian concept of part
 * 1.D6 Arnold Buffum Chace on Egyptian mathematics as pure science
 * 1.D7 G. J. Toomer on Egyptian mathematics as strictly practical


 * 1.E Babylonian Mathematics
 * 1.E1 Some Babylonian problem texts
 * 1.E2 Sherlock Holmes in Babylon: an investigation by R. Creighton Buck
 * 1.E3 Jöran Friberg on the purpose of
 * 1.E4 The scribal art
 * 1.E5 Marvin Powell on two Sumerian texts
 * 1.E6 Jens Høyrup on the Sumerian origin of mathematics


 * '''Chapter 2 Mathematics in Classical Greece


 * 2.A Historical Summary
 * 2.A1 Proclus's summary
 * 2.A2 W. Burkert on whether Eudemus mentioned Pythagoras


 * 2.B Hippocrates' Quadrature of Lunes


 * 2.C Two Fifth-century Writers
 * 2.C1 Parmenides' The Way of Truth
 * 2.C2 Aristophanes: Meton squares the circle
 * 2.C3 Aristophanes: Strepsiades encounters the New Learning


 * 2.D The Quadrivium
 * 2.D1 Archytas
 * 2.D2 Plato
 * 2.D3 Proclus
 * 2.D4 Nicomachus
 * 2.D5 Boethius
 * 2.D6 Hrosvitha
 * 2.D7 Roger Bacon
 * 2.D8 W. Burkert on the Pythagorean tradition in education


 * 2.E Plato
 * 2.E1 Socrates and the slave boy
 * 2.E2 Mathematical studies for the philosopher ruler
 * 2.E3 Theaetetus investigates incommensurability
 * 2.E4 Lower and higher mathematics
 * 2.E5 Plato's cosmology
 * 2.E6 Freeborn studies and Athenian ignorance
 * 2.E7 A letter from Plato to Dionysius
 * 2.E8 Aristoxenus on Plato's lecture on the Good


 * 2.F Doubling the Cube
 * 2.F1 Theon on how the problem (may have) originated
 * 2.F2 Proclus on its reduction by Hippocrates
 * 2.F3 Eutocius's account of its early history, and an instrumental solution
 * 2.F4 Eutocius on Menaechmus's use of conic sections


 * 2.G Squaring the Circle
 * 2.G1 Proclus on the origin of the problem
 * 2.G2 Antiphon's quadrature
 * 2.G3 Bryson's quadrature
 * 2.G4 Pappus on the quadratrix


 * 2.H Aristotle
 * 2.H1 Principles of demonstrative reasoning
 * 2.H2 Geometrical analysis
 * 2.H3 The distinction between mathematics and other sciences
 * 2.H4 The Pythagoreans
 * 2.H5 Potential and actual infinities
 * 2.H6 Incommensurability


 * Chapter 3 Euclid's Elements


 * 3.A Introductory Comments by Proclus


 * 3.B Book I
 * 3.B1 Axiomatic foundations
 * 3.B2 The base angles of an isosceles triangle are equal (Proposition 5)
 * 3.B3 Propositions 6, 9, 11 and 20
 * 3.B4 The angles of a triangle are two right angles (Proposition 32)
 * 3.B5 Propositions 44, 45, 46 and 47


 * 3.C Books II -- VI
 * 3.C1 Book II: Definitions and Propositions 1, 4, 11 and 14
 * 3.C2 Book III: Definitions and Proposition 16
 * 3.C3 Book V: Definitions
 * 3.C4 Book VI: Definitions and Propositions 13, 30 and 31


 * 3.D The Number Theory Books
 * 3.D1 Book VII: Definitions
 * 3.D2 Book IX: Propositions 20, 21 and 22
 * 3.D3 Book IX: Proposition 36


 * 3.E Books X -- XIII
 * 3.E1 Book X: Definitions, Propositions 1 and 9, and Lemma 1
 * 3.E2 Book XI: Definitions
 * 3.E3 Book XII: Proposition 2
 * 3.E4 Book XIII: Statements of Propositions 13--18 and a final result


 * 3.F Scholarly and Personal Discovery of Euclid's Text
 * 3.F1 A. Aaboe on the textual basis
 * 3.F2 Later personal impacts


 * 3.G Historians Debate Geometrical Algebra
 * 3.G1 B. L. van der Waerden
 * 3.G2 Sabetai Unguru
 * 3.G3 B. L. van der Waerden
 * 3.G4 Sabetai Unguru
 * 3.G5 Ian Mueller
 * 3.G6 John L. Berggren


 * Chapter 4 Archimedes and Apollonius


 * 4.A Archimedes
 * 4.A1 Measurement of a circle
 * 4.A2 The sand-reckoner
 * 4.A3 Quadrature of the parabola
 * 4.A4 On the equilibrium of planes: Book I
 * 4.A5 On the sphere and cylinder: Book I
 * 4.A6 On the sphere and cylinder: Book II
 * 4.A7 On spirals
 * 4.A8 On conoids and spheroids
 * 4.A9 The method treating of mechanical problems


 * 4.B Later Accounts of the Life and Works of Archimedes
 * 4.B1 Plutarch
 * 4.B2 Vitruvius
 * 4.B3 John Wallis (1685)
 * 4.B4 Sir Thomas Heath


 * 4.C Diocles
 * 4.C1 Introduction to On Burning Mirrors
 * 4.C2 Diocles proves the focal property of the parabola
 * 4.C3 Diocles introduces the cissoid


 * 4.D Apollonius
 * 4.D1 General preface to Conics: to Eudemus
 * 4.D2 Prefaces to Books II, IV and V
 * 4.D3 Book I: First definitions
 * 4.D4 Apollonius introduces the parabola, hyperbola and ellipse
 * 4.D5 Some results on tangents and diameters'
 * 4.D6 How to find diameters, centres and tangents
 * 4.D7 Focal properties of hyperbolas and ellipses


 * Chapter 5 Mathematical Traditions in the Hellenistic Age
 * '5.A The Mathematical Sciences''
 * 5.A1 Proclus on the divisions of mathematical science
 * 5.A2 Pappus on mechanics
 * 5.A3 Optics
 * 5.A4 Music
 * 5.A5 Heron on geometric mensuration
 * 5.A6 Geodesy: Vitruvius on two useful theorems of the ancients


 * 5.B The Commentating Tradition
 * 5.B1 Theon on the purpose of his treatise
 * 5.B2 Proclus on critics of geometry
 * 5.B3 Pappus on analysis and synthesis
 * 5.B4 Pappus on three types of geometrical problem
 * 5.B5 Pappus on the sagacity of bees
 * 5.B6 Proclus on other commentators


 * 5.C Problems Whose Answers Are Numbers
 * 5.C1 Proclus on Pythagorean triples
 * 5.C2 Problems in Hero's Geometrica
 * 5.C3 The cattle problem
 * 5.C4 Problems from The Greek Anthology
 * 5.C5 An earlier and a later problem


 * 5.D Diophantus
 * 5.D1 Book I.7
 * 5.D2 Book I.27
 * 5.D3 Book II.8
 * 5.D4 Book III.10
 * 5.D5 Book IV(A).3
 * 5.D6 Book IV(A).9
 * 5.D7 Book VI(A).11
 * 5.D8 Book V(G).9
 * 5.D9 Book VI(G).19
 * 5.D10 Book VI(G).21


 * Chapter 6 Islamic Mathematics


 * 6.A Commentators and Translators
 * 6.A1 The Banu Musa
 * 6.A2 Al-Sijzi
 * 6.A3 Omar Khayyam


 * 6.B Algebra
 * 6.B1 Al-Khwarizmi on the algebraic method
 * 6.B2 Abu-Kamil on the algebraic method
 * 6.B3 Omar Khayyam on the solution of cubic equations


 * 6.C The Foundations of Geometry
 * 6.C1 Al-Haytham on the parallel postulate
 * 6.C2 Omar Khayyam's critique of al-Haytham
 * 6.C3 Youshkevitch on the history of the parallel postulate


 * Chapter 7 Mathematics in Mediaeval Europe


 * 7.A The Thirteenth and Fourteenth Centuries
 * 7.A1 Leonardo Fibonacci
 * 7.A2 Jordanus de Nemore on problems involving numbers
 * 7.A3 M. Biagio: A quadratic equation masquerading as a quartic


 * 7.B The Fifteenth Century
 * 7.B1 Johannes Regiomontanus on triangles
 * 7.B2 Nicolas Chuquet on exponents
 * 7.B3 Luca Pacioli


 * Chapter 8 Sixteenth-century European Mathematics


 * 8.A The Development of Algebra in Italy
 * 8.A1 Antonio Maria Fior's challenge to Niccolò Tartaglia (1535)
 * 8.A2 Tartaglia's account of his meeting with Gerolamo Cardano in 1539
 * 8.A3 Tartaglia versus Ludovico Ferrari (1547)
 * 8.A4 Gerolamo Cardano
 * 8.A5 Rafael Bombelli


 * 8.B Renaissance Editors
 * 8.B1 John Dee to Federigo Commandino
 * 8.B2 Bernardino Baldi on Commandino
 * 8.B3 Paul Rose on Francesco Maurolico


 * 8.C Algebra at the Turn of the Century
 * 8.C1 Simon Stevin
 * 8.C2 François Viète


 * Chapter 9 Mathematical Sciences in Tudor and Stuart England


 * 9.A Robert Record
 * 9.A1 The Ground of Artes
 * 9.A2 The Pathway to Knowledge
 * 9.A3 The Castle of Knowledge
 * 9.A4 The Whetstone of Witte


 * 9.B John Dee
 * 9.B1 Mathematicall Praeface to Henry Billingsley's Euclid
 * 9.B2 Bisecting an angle, from Henry Billingsley's Euclid
 * 9.B3 Views of John Dee


 * 9.C The Value of Mathematical Sciences
 * 9.C1 Roger Ascham (1570)
 * 9.C2 William Kempe (1592)
 * 9.C3 Gabriel Harvey (1593)
 * 9.C4 Thomas Hylles (1600)
 * 9.C5 Francis Bacon (1603)


 * 9.D Thomas Harriot
 * 9.D1 Dedicatory poem by George Chapman
 * 9.D2 A sonnet by Harriot
 * 9.D3 Examples of Harriot's algebra
 * 9.D4 Letter to Harriot from William Lower
 * 9.D5 John Aubrey's brief life of Harriot
 * 9.D6 John Wallis on Harriot and Descartes
 * 9.D7 Recent historical accounts


 * 9.E Logarithms
 * 9.E1 John Napier's Preface to A Description of the Admirable Table of Logarithms
 * 9.E2 Henry Briggs on the early development of logarithms
 * 9.E3 William Lilly on the meeting of Napier and Briggs
 * 9.E4 Charles Hutton on Johannes Kepler's construction of logarithms
 * 9.E5 John Keil on the use of logarithms
 * 9.E6 Edmund Stone on definitions of logarithms


 * 9.F William Oughtred
 * 9.F1 Oughtred's Clavis Mathematicae
 * 9.F2 John Wallis on Oughtred's Clavis
 * 9.F3 Letters on the value of Oughtred's Clavis
 * 9.F4 John Aubrey on Oughtred


 * 9.G Brief Lives
 * 9.G1 Thomas Allen (1542-1632)
 * 9.G2 Sir Henry Savile (1549-1622)
 * 9.G3 Walter Warner (1550-1640)
 * 9.G4 Edmund Gunter (1581-1626)
 * 9.G5 Thomas Hobbes (1588-1679)
 * 9.G6 Sir Charles Cavendish (1591-1654)
 * 9.G7 René Descartes (1596-1650)
 * 9.G8 Edward Davenant
 * 9.G9 Seth Ward (1617-1689)
 * 9.G10 Sir Jonas Moore (1617-1679)


 * 9.H Advancement of Mathematics
 * 9.H1 John Pell's Idea of Mathematics
 * 9.H2 Letters between Pell and Cavendish
 * 9.H3 Hobbes and Wallis
 * 9.H4 The mathematical education of John Wallis
 * 9.H5 Samuel Pepys learns arithmetic


 * Chapter 10 Mathematics and the Scientific Revolution


 * 10.A Johannes Kepler
 * 10.A1 Planetary motion
 * 10.A2 Celestial harmony
 * 10.A3 The regular solids
 * 10.A4 The importance of geometry


 * 10.B Galileo Galilei
 * 10.B1 On mathematics and the world
 * 10.B2 The regular motion of the pendulum
 * 10.B3 Naturally accelerated motion
 * 10.B4 The time and distance laws for a falling body
 * 10.B5 The parabolic path of a projectile


 * Chapter 11 Descartes, Fermat and their Contemporaries


 * 11.A René Descartes
 * 11.A1 Descartes's method
 * 11.A2 The elementary arithmetical operations
 * 11.A3 The general method for solving any problem
 * 11.A4 Pappus on the locus to three, four or several lines
 * 11.A5 Descartes to Marin Mersenne
 * 11.A6 Descartes's solution to the Pappus problem
 * 11.A7 'Geometric' curves
 * 11.A8 Permissible and impermissible methods in geometry
 * 11.A9 The method of normals
 * 11.A10 H. J. M. Bos on Descartes's Geometry


 * 11.B Responses to Descartes's Geometry
 * 11.B1 Florimond Debeaune's inverse tangent problem
 * 11.B2 Philippe de la Hire on conic sections
 * 11.B3 Philippe de la Hire on the algebraic approach
 * 11.B4 Hendrik van Heuraet on the rectification of curves
 * 11.B5 Jan Hudde's rules


 * 11.C Pierre de Fermat
 * 11.C1 On maxima and minima and on tangents
 * 11.C2 A second method for finding maxima and minima
 * 11.C3 Fermat to Bernard de Frenicle on 'Fermat primes'
 * 11.C4 Fermat to Marin Mersenne on his 'little theorem'
 * 11.C5 Fermat's evaluation of an 'infinite' area
 * 11.C6 Fermat's challenge concerning $x^2 = A y^2 + 1$
 * 11.C7 On problems in the theory of numbers: a letter to Christaan Huygens
 * 11.C8 Fermat's last theorem


 * 11.D Girard Desargues
 * 11.D1 Preface to Rough Draft on Conics
 * 11.D2 The invariance of six points in involution
 * 11.D3 Desargues's involution theorem
 * 11.D4 Descartes to Desargues
 * 11.D5 Pascal's hexagon
 * 11.D6 Desargues's theorem on triangles in perspective
 * 11.D7 Philippe de la Hire's Sectiones Conicae


 * 11.E Infinitesimals, Indivisibles, Areas and Tangents
 * 11.E1 Gilles Personne de Roberval on the cycloid
 * 11.E2 Blaise Pascal to Pierre de Carcavy
 * 11.E3 Isaac Barrow on areas and tangents


 * Chapter 12 Isaac Newton


 * 12.A Newton's Invention of the Calculus
 * 12.A1 Tangents by motion and by the $o$-method
 * 12.A2 Rules for finding areas
 * 12.A3 The sine series and the cycloid
 * 12.A4 Quadrature as the inverse of fluxions
 * 12.A5 Finding fluxions of fluent quantities
 * 12.A6 Finding fluents from a fluxional relationship


 * 12.B Newton's Principia
 * 12.B1 Prefaces
 * 12.B2 Axioms, or laws of motion
 * 12.B3 The method of first and last ratios
 * 12.B4 The nature of first and last ratios
 * 12.B5 The determination of centripetal forces
 * 12.B6 The law of force for an elliptical orbit
 * 12.B7 Gravity obeys an inverse square law
 * 12.B8 Motion of the apsides
 * 12.B9 Against vortices
 * 12.B10 Rules of reasoning in philosophy
 * 12.B11 The shape of the planets
 * 12.B12 General scholium
 * 12.B13 Gravity


 * 12.C Newton's Letters to Leibniz
 * 12.C1 From the Epistola Prior
 * 12.C2 From the Epistola Posterior


 * 12.D Newton on Geometry
 * 12.D1 On the locus to three or four lines
 * 12.D2 The enumeration of cubics
 * 12.D3 On geometry and algebra
 * 12.D4 Newton's projective transformation


 * 12.E Newton's Image in English Poetry
 * 12.E1 Alexander Pope, Epitaph
 * 12.E2 Alexander Pope, An Essay on Man, Epistle II
 * 12.E3 William Wordsworth, The Prelude, Book III
 * 12.E4 William Blake, Jerusalem, Chapter 1


 * 12.F Biographical and Historical Comments
 * 12.F1 Bernard de Fontenelle's Eulogy of Newton
 * 12.F2 Voltaire on Descartes and Newton
 * 12.F3 Voltaire on gravity as a physical truth
 * 12.F4 John Maynard Keynes on Newton the man
 * 12.F5 D. T. Whiteside on Newton, the mathematician


 * Chapter 13 Leibniz and his Followers


 * 13.A Leibniz's Invention of the Calculus
 * 13.A1 A notation for the calculus
 * 13.A2 Debeaune's inverse tangent problem
 * 13.A3 The first publication of the calculus


 * 13.B Johann Bernoulli and the Marquis de l'Hôpital
 * 13.B1 Bernoulli's lecture to l'Hôpital on the solution to Debeaune's problem
 * 13.B2 Bernoulli on the integration of rational functions
 * 13.B3 Bernoulli on the inverse problem of central forces
 * 13.B4 O. Spiess on Bernoulli's first meeting with l'Hôpital
 * 13.B5 Preface to l'Hôpital's Analyse des Infiniment Petits
 * 13.B6 L'Hôpital on the foundations of the calculus
 * 13.B7 Stone's preface to the English edition of l'Hôpital's Analyse des Infiniment Petits


 * Chapter 14 Euler and his Contemporaries


 * 14.A Euler on Analysis
 * 14.A1 A general method for solving linear ordinary differential equations
 * 14.A2 Euler's unification of the theory of elementary functions
 * 14.A3 Logarithms
 * 14.A4 The algebraic theory of conics
 * 14.A5 The theory of elimination


 * 14.B Euler and Others on the Motion of the Moon
 * 14.B1 Pierre de Maupertuis on the figure of the Earth
 * 14.B2 Correspondence between Euler and Alexis-Claude Clairaut
 * 14.B3 Clairaut on the system of the world according to the principles of universal gravitation
 * 14.B4 Euler to Clairaut, 2 June 1750


 * 14.C Euler's Later Work
 * 14.C1 A general principle of mechanics
 * 14.C2 Fermat's last theorem and the theory of numbers
 * 14.C3 The motion of a vibrating string''
 * 14.C4 Nicolas Condorcet's Elogium of Euler


 * 14.D Some of Euler's Contemporaries
 * 14.D1 Jean-Paul de Gua on the use of algebra in geometry
 * 14.D2 Gabriel Cramer on the theory of algebraic curves
 * 14.D3 Jean d'Alembert on algebra, geometry and mechanics
 * 14.D4 Joseph Louis Lagrange on solvability by radicals
 * 14.D5 Joseph Louis Lagrange's additions to Euler's Algebra
 * 14.D6 Johann Heinrich Lambert on the making of maps


 * Chapter 15 Gauss, and the Origins of Structural Algebra


 * 15.A Gauss's Mathematical Writings
 * 15.A1 Gauss's mathematical diary for 1796
 * 15.A2 Critiques of attempts on the fundamental theorem of algebra
 * 15.A3 The constructibility of the regular $17$-gon
 * 15.A4 The charms of number theory
 * 15.A5 Curvature and the differential geometry of surfaces


 * 15.B Gauss's Correspondence
 * 15.B1 Three letters between Gauss and Sophie Germain
 * 15.B2 Three letters between Gauss and Friedrich Wilhelm Bessel


 * 15.C Two Number Theorists
 * 15.C1 Adrien Marie Legendre on quadratic reciprocity
 * 15.C2 E. E. Kummer: Ideal numbers and Fermat's last theorem


 * 15.D Galois Theory
 * 15.D1 Evariste Galois's letter to Auguste Chevalier
 * 15.D2 An unpublished preface by Galois
 * 15.D3 Augustin Louis Cauchy on the theory of permutations
 * 15.D4 Camille Jordan on the background to his work on the theory of groups


 * Chapter 16 Non-Euclidean Geometry


 * 16.A Seventeenth- and Eighteenth-century Developments
 * 16.A1 John Wallis's lecture on the parallel postulate
 * 16.A2 From Gerolamo Saccheri's Euclides Vindicatus
 * 16.A3 Johann Heinrich Lambert to Immanuel Kant
 * 16.A4 Kant on our intuition of space
 * 16.A5 Lambert on the consequences of a non-Euclidean postulate
 * 16.A6 Two attempts by Legendre on the parallel postulate


 * 16.B Early Nineteenth-century Developments
 * 16.B1 Ferdinand Karl Schweikart's memorandum to Gauss
 * 16.B2 Gauss on Janos Bolyai's Appendix
 * 16.B3 Nicolai Lobachevskii's theory of parallels
 * 16.B4 Correspondence between Wolfgang and Janos Bolyai
 * 16.B5 Janos Bolyai's The Science Absolute of Space


 * 16.C Later Nineteenth-century Developments
 * 16.C1 Roberto Bonola on the spread of non-Euclidean geometry
 * 16.C2 Bernhardt Riemann on the hypotheses which lie at the basis of geometry
 * 16.C3 Eugenio Beltrami on the interpretation of non-Euclidean geometry
 * 16.C4 Felix Klein on non-Euclidean and projective geometry
 * 16.C5 J. J. Gray on four questions about the history of non-Euclidean geometry


 * 16.D Influences on Literature
 * 16.D1 Fyodor Dostoevsky, from The Brothers Karamazov
 * 16.D2 Gabriel Garcia Marquez, from One Hundred Years of Solitude


 * Chapter 17 Projective Geometry in the Nineteenth Century


 * 17.A Developments in France
 * 17.A1 Jean Victor Poncelet on a general synthetic method in geometry
 * 17.A2 Michel Chasles
 * 17.A3 Joseph Diaz Gergonne on the principle of duality
 * 17.A4 M. Paul on students' studies at the Ecole Polytechnique


 * 17.B Developments in Germany
 * 17.B1 August Ferdinand Mobius
 * 17.B2 Julius Plücker on twenty-eight bitangents
 * 17.B3 From Alfred Clebsch's obituary of Julius Plücker
 * 17.B4 Christian Wiener's stereoscopic pictures of the twenty-seven lines on a cubic surface


 * Chapter 18 The Rigorization of the Calculus


 * 18.A Eighteenth-century Developments
 * 18.A1 George Berkeley's criticisms of the calculus
 * 18.A2 Colin MacLaurin on rigorizing the fluxional calculus
 * 18.A3 D'Alembert on differentials
 * 18.A4 Lagrange on derived functions
 * 18.A5 Lagrange on algebra and the theory of functions


 * 18.B Augustin Louis Cauchy and Bernard Bolzano
 * 18.B1 Bolzano on the intermediate value theorem
 * 18.B2 Cauchy's definitions
 * 18.B3 Cauchy on two important theorems of the calculus
 * 18.B4 J. V. Grabiner on the significance of Cauchy


 * 18.C Richard Dedekind and Georg Cantor
 * 18.C1 Dedekind on irrational numbers and the theorems of the calculus
 * 18.C2 Cantor's definition of the real numbers
 * 18.C3 The correspondence between Cantor and Dedekind
 * 18.C4 Cantor on the uncountability of the real numbers
 * 18.C5 Cantor's statement of the continuum hypothesis


 * Chapter 19 The Mechanization of Calculation


 * 19.A Leibniz on Calculating Machines in the Seventeenth Century


 * 19.B Charles Babbage
 * 19.B1 Babbage on Gaspard de Prony
 * 19.B2 Dionysius Lardner on the need for tables
 * 19.B3 Anthony Hyman's commentary on the analytical engine
 * 19.B4 Ada Lovelace on the analytical engine


 * 19.C Samuel Lilley on Machinery in Mathematics


 * 19.D Computer Proofs
 * 19.D1 Letter from Augustus De Morgan to William Rowan Hamilton
 * 19.D2 Donald J. Albers
 * 19.D3 F. F. Bonsall
 * 19.D4 Thomas Tymoczo


 * Sources


 * Name Index


 * Subject Index