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Classics of mathematics

Author: Ronald Calinger
Publisher: Oak Park, Ill. : Moore Pub. Co., ©1982.
Series: Classics series.
Edition/Format:   Print book : English : 1st edView all editions and formats
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Classics of mathematics.
Oak Park, Ill. : Moore Pub. Co., ©1982
(OCoLC)624470384
Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Ronald Calinger
ISBN: 0935610138 9780935610130
OCLC Number: 6331082
Description: xxv, 742 pages : illustrations ; 23 cm
Contents: INTRODUCTION : From A Mathematician's Apology / G. H. Hardy ; From Mathematics as an Element in the History of Thought / Alfred North Whitehead] --
I. PROTOMATHEMATICS IN THE LATE AGE OF STONE AND IN ANCIENT MESOPOTAMIA EGYPT : Introduction --
1. From The Exact Sciences in Antiquity / O. Neugebauer --
2. From the A'h-mose or Rhind Papyrus / James R. Newman --
3. Problem no. 14 of the Moscow Papyrus / Battiscombe Gunn and T. Eric Peet --
4. From the Old Testament of the Bible --
II. THE RISE OF THEORETICAL MATHEMATICS IN ANCIENT GREECE : Introduction --
A. Proclus {Biography of Proclus --
5. From The Catalogue of Geometers / Proclus} --
B. Pythagoras and his followers {Biography of Pythagoras of Samos --
6. From On Marvels 6 / Apollonius Paradoxagraphus --
7. From Book VII of the Elements: Definitions / Euclid --
8. From Prior Analytics i.23 (Irrationality of the Square Root of 2) / Aristotle --
9. From On Nicomachus' Introduction to Arithmetic (Arithmetic, Geometric and Harmonic Means) / Iamblichus --
10. From Commentary on Ptolemy's Harmonics / Porphyry --
11. From Metaphysics A5 / Aristotle --
12. From Commentary on Euclid i (Sum of the Angles of a Triangle) / Proclus --
13. From Convival Questions viii.2. (Pythagoras' Theorem) --
14. From On Slips in Greetings 5 / Lucian --
15. From Elements X. Scholium (The Irrational or Incommensurable) / Euclid --
16. From Elements X. Definitions (Commensurable and Incommensurable) / Euclid} --
C. Hippocrates of Chios {Biography of Hippocrates of Chios --
17. From Commentary on Aristotle's Physics A 2 / Philoponus --
18. From Commentary on Aristotle's Physics A 2 (Quadrature of Lunules, the Crescent-Shaped Figures Between Two Intersecting Arcs of Circles) / Simplicius} --
D. Plato {Biography of Plato --
19. From the Republic VI.510 (Approach to Mathematics) / Plato --
20. From the Republic VII.522-528 (The Quadrivium) / Plato --
21. From the Timaeus 53-56 / Plato} --
E. Eudoxus {Biography of Eudoxus --
22. From Book V of the Elements: Definitions (Theory of Proportions) / Euclid --
23. From Book XII.2 of the Elements (Method of Approximation, the So-called Method of Exhaustion) / Euclid} --
F. Aristotle {Biography of Aristotle --
24. From Posterior Analytics i.10 (First Principles or Theory of Statements) / Aristotle --
25. From Metaphysics 1066-1067 (The Infinite, the Essence of the Archimedean Postulate) / Aristotle --
26. From the Metaphysics 1068-1069 and Physics 231-240 (On the Continuous and Zeno's Paradoxes) / Aristotle}] --
III. THE HELLENISTIC AND ROMAN PERIODS : Introduction --
A. Euclid {Biography of Euclid --
27. From Book I of the Elements: Definitions, Postulates, Axioms, and Propositions 1-13 / Euclid --
28. From Book I of the Elements: Propositions 27-32 (Theory of Parallels) / Euclid --
29. From Book I of the Elements: Proposition 47 (Pythagorean Theorem) / Euclid --
30. From Book VII of the Elements: Propositions 1 and 2 (Euclidean Algorithm) / Euclid --
31. From Book IX of the Elements: Proposition 14 (Fundamental Theorem in the Theory of Numbers) / Euclid --
32. From Book IX of the Elements: Proposition 20 (Infinitude of Primes) / Euclid} --
B. Archimedes {Biography of Archimedes --
33. From On the Sphere and Cylinder I: Assumptions / Archimedes --
34. From On the Spheres and Cylinder I: Propositions 33 and 34 (Surface and Volume of a Sphere) / Archimedes --
35. From Measurement of a Circle: Proposition 3 (Approximation of Using in Essence Upper and Lower Limits) / Archimedes --
36. From Quadrature of the Parabola: Introduction, Propositions 20, 23, and 24 / Archimedes --
37. From On the Equilibrium of Planes I: Propositions 6 and 7 (Principle of the Lever) / Archimedes --
38. From the Sand-Reckoner: Introduction and Section on Large Numbers / Archimedes --
39. From The Cattle Problem (Indeterminate Analysis) / Archimedes} --
C. Eratosthenes {Biography of Eratosthenes --
40. From Introduction to Arithmetic I: Chapters XII-XIII (Sieve for Finding Primes) / Nicomachus of Gerasa --
41. From On the Circular Motion of the Heavenly Bodies i.10.52 / Cleomedes} --
D. Apollonius {Biography of Apollonius --
42. From Conics: Introduction to Book One / Apollonius --
43. From Conics: Propositions 7 and 11 (Construction of Sections and Fundamental Properties) / Apollonius} --
E. Ptolemy {Biography of Claudius Ptolemy --
44. From the Syntaxis or Almagest i (Trigonometry: Table of Sines) / Claudius Ptolemy} --
F. Diophantus {Biography of Diophantus --
45. From the Dedication to Arithmetica (Algebraic Notation) / Diophantus --
46. From the Arithmetica (Origins of the Theory of Numbers) / Diophantus}] --
IV. ARABIC PRIMACY WITH HINDU, CHINESE, AND MAYA CONTRIBUTIONS : Introduction --
A. al-Khwarizmi {Biography of al-Khwarizmi --
47. From The Book of Algebra and Almucabola (Quadratic Equations in Algebra: Verbal Form) / al-Khwarizmi} --
B. 'Umar al-Khayyami {Biography of 'Umar al-Khayyami --
48. From the Algebra / 'Umar al-Khayyami} --
C. Bhaskara II {Biography of Bhaskara II --
49. From Lilavati (Arithmetic and Geometry) / Bhaskara II --
50. From Bijagnita (Algebra) / Bhaskara II} --
D. Zhang Chang {Biography of Zhang Chang --
51. From The Development of Mathematics in China and Japan (Problems in the Nine Chapters) / Yoshio Mikami} --
E. The Civilization of the Maya {Commentary --
52. From The Ancient Maya / Sylvanus Griswold Morley}] --
V. THE MEDIEVAL-RENAISSANCE-REFORMATION PERIODS IN EUROPE : Introduction / Joseph E. Brown, Rensselaer Polytechnic Institute --
A. Leonardo of Pisa {Biography of Leonardo of Pisa --
53. From Liber abbaci (The Rabbit Problem) / Leonardo of Pisa} --
B. Nicole Oresme {Biography of Nicole Oresme --
54. From De configurationibus (The Latitude of Forms) / Nicole Oresme --
55. From Questiones super geometriam Euclidis (The Latitude of Forms) / Nicole Oresme} --
C. Girolamo Cardano {Biography of Girolamo Cardano --
56. From the Artis Magnae / Girolamo Cardano} --
D. Francois Viete {Biography of Francois Viete --
57. From In artem analyticem isagoge (The New Algebra) / Francois Viete} --
E. Simon Stevin {Biography of Simon Stevin --
58. From De Thiende (Decimal Fractions) / Simon Stevin} --
F. John Napier {Biography of John Napier --
59. From Mirifici logarithmorum canonis constructio (Logarithms) / John Napier}] --
VI. THE SCIENTIFIC REVOLUTION AT ITS ZENITH : Introduction --
A. Algebra, coordinate geometry, and arithmetic {Biography of Rene Descartes --
60. From the Regulae (Rule IV: "In search for the truth of things a method is indispensable") / Rene Descartes --
61. From Discourse de la Methode (Four Fundamental Rules of Logic) / Rene Descartes --
62. From Geometrie (Theory of Equations) / Rene Descartes --
63. From Geometrie (The Principle of Nonhomogeneity) / Rene Descartes --
64. From a Letter to Bernard Frenicle de Bessy (October 10, 1640) (Are numbers of the form 2^(n+1) prime when n=2t?) / Pierre de Fermat --
65. From Two Letters of February 1657 (Find an Infinity of Integer Solutions for the "Pell" Equation) / Pierre de Fermat --
66. From Traite du triangle arithmetique... (The Pascal Triangle) / Blaise Pascal} --
B. Origins of the infinitesimal calculus {Biography of Johann Kepler --
67. From Nova stereometria doliorum vinariorum (Integration Methods) / Johann Kepler --
68. From Two New Sciences (Paradoxes of Infinity, the Relationship Between Points and Lines, the Order of an Infinity, Infinitesimals, the Concept of a Continuum) / Galileo Galilei --
69. From On the Transformation and Simplification of the Equations of Loci (Integration) / Pierre de Fermat --
70. From On a Method for the Evaluation of Maxima and Minima / Pierre de Fermat --
71. From On the Sines of a Quadrant of a Circle / Blaise Pascal} --
C. The discovery of the differential and integral calculus {Biography of Gottfried Wilhelm Leibniz --
72. From A New Method for Maxima and Minima as Well as Tangents, Which is Impeded Neither by Fractional nor by Irrational Quantities, and a Remarkable Type of Calculus for This (Differential Calculus) / Gottfried Wilhelm Leibniz --
73. From Supplementum geometriae dimensoriae... in Acta Eruditorum (1693) (The Fundamental Theorem of the Calculus) / Gottfried Wilhelm Leibniz --
74. From Specimens of a Universal (System of) Mathematics / Isaac Newton --
75. From a Letter to Henry Oldenburg on the Binomial Series (June 13, 1676) / Isaac Newton --
76. From Letter to Henry Oldenburg on General Method for Finding Quadratures (October 24, 1676) / Isaac Newton --
77. From Principia Mathematics (Prime and Ultimate Ratios: The Theory of Limits) / Isaac Newton --
78. From the Introduction to the Tractatus de quadratura curvarum / Isaac Newton} --
D. The Bernoullis {Biography of Jakob Bernoulli --
79. From Ars Conjectandi (The Law of Large Numbers) / Jakob Bernoulli --
80. From The Curvature of a Ray in Nonuniform Media (The Brachistochrone) / Johann Bernoulli}] --
VII. The Enlightenment (1720-1800) : Introduction --
A. Elaboration and criticism of mathematical analysis {Biography of Brook Taylor --
81. From Methodus Incrementorum Directa et Inversa (The Taylor Series) / Brook Taylor --
82. From The Analyst (Criticism of the Foundations of the Calculus) / George Berkeley --
83. From Treatise of Fluxions (On Series and Extremes) / Colin Maclaurin --
84. From Differential, Encyclopedie, Vol. 4 (On Limits) / Jean d'Alembert --
85. From Introductio in analysin infinitorum (Trigonometry) / Leonhard Euler --
Biography of Joseph-Louis Lagrange --
86. From Attempt at a New Method for Determining the Maxima and Minima of Indefinite Integral Formulas (The Calculus of Variations) / Joseph-Louis Lagrange --
87. From Mathematical Thought from Ancient to Modern Times (1972) (Taylor Series with Remainder) / Morris Kline} --
B. Topology, number theory, and probability {88. From the Problem of the Seven Bridges of Konigsberg (The Origins of Topology) / Leonhard Euler --
89. From Theorems on Residues Obtained by the Division of Powers (Number Theory: Power Residues) / Leonhard Euler --
90. From Demonstrations of Certain Arithmetical Theorems / Leonhard Euler --
Biography of Pierre-Simon Laplace --
91. From Essais philosophique sur les probabilites (The Theory of Probability) / Pierre-Simon Laplace}] --
VIII. THE NINETEENTH CENTURY : Introduction / Helena M. Pycior --
A. Algebra {Biography of Carl Friedrich Gauss --
92. From New Proof of the Theorem that Every Integral Rational Algebraic Function of One Variable Can be Decomposed into Real Factors of the First or Second Degree / Carl Friedrich Gauss --
Biography of Niels Abel --
93. From A Memoir on Algebraic Equations, Proving the Impossibility of a Solution of the General Equation of the Fifth Degree / Niels Abel --
Biography of Evariste Galois --
94. From the Testamentary Letter Sent to Augusts Chevalier (May 29, 1832) (Group Theory and Albelian Integrals) / Evariste Galois --
Biography of William Rowan Hamilton --
95. From Elements of Quaternions / William Rowan Hamilton --
Biography of George Boole --
96. From An Investigation of the Laws of Thought (The Joining of Algebra and Logic) / George Boole} --
B. Non-Euclidean geometries {Biography of Nikolai Ivanovich Lobachevsky --
97. From The Theory of Parallels (Hyperbolic Geometry) / Nikolai Ivanovich Lobachevsky --
Biography of Bernhard Riemann --
98. From On the Hypotheses Which Lie at the Foundations of Geometry / Bernhard Riemann} --
C. The arithmetization of mathematical analysis {Biography of Joseph Fourier --
99. From Joseph Fourier 1768-1839 / I. Grattan-Guinness --
100. From Theorie analytique de la chaleur / Joseph Fourier --
101. From "On the Continuity of Functions Defined by Power Series" / Niels Abel --
Biography of Augustin-Louis Cauchy --
102. From Cours d'analyse de l'Ecole Royale Polytechnique / Augustin-Louis Cauchy --
103. From Resume des lecons... sur le calcul infinitesimal (On the Derivative as a Limit) / Augustin-Louis Cauchy --
104. From Resume des lecons... sur le calcul infinitesimal (First Rigorous Proof About Derivatives) / Augustin-Louis Cauchy --
Biography of Karl Weierstrass --
105. From Lectures on the Differential Calculus / Karl Weierstrass --
106. From a Letter to Hermann Amandus Schwarz (May 5, 1875) / Karl Weierstrass --
107. From Encounters with Mathematics (Riemann on Physcis and Partial Differential Equations) / Lars Garding} --
D. Number theory, set theory, and symbolic logic {108. From Carl Friedrich Gauss: A Biography (A Discussion of the Disquisitiones arithmeticae, including Congruences and the Fundamental Theorem of Arithmetic) / Tord Hall --
Biography of Ernst Eduard Kummer --
109. From On the Theory of Complex Numbers (Theory of Ideal Prime Factors) / Ernst Eduard Kummer --
Biography of Richard Dedekind --
110. From Stetigkeit und irrationale Zahlen (Continuity, Irrational Numbers, and Dedekind Cuts) / Richard Dedekind --
111. From Was send und was sollen die Zahlen? (Simply Infinite Systems) / Richard Dedekind --
Biography of Georg Cantor --
112. From Grundlagen einer Allgemeinen Mannigfaltigkeitslehre (Fundamental Series) / Georg Cantor --
113. From a Letter to Richard Dedekind (Transfinite Cardinal Numbers and Set Theory) / Georg Cantor --
Biography of Gottlob Frege --
114. From Begriffsschrift (Symbolic Logic) / Gottlob Frege --
115. From Die Grundlagen der Arithmetik (Definition of Number in Logical Terms) / Gottlob Frege --
Biography of Giuseppe Peano --
116. From Arithmeticas principia (Set of Axioms for Integers) / Giuseppe Peano --
117. From Introduction to Mathematical Philosophy (The Definition of Number) / Bertrand Russell}] --
IX. THE EARLY TWENTIETH CENTURY TO 1932 : Introduction / Helena M. Pycior --
A. Creativity and the Paris problems {Biography of Henri Poincare --
118. From Science and Method / Henri Poincare --
119. From Mathematical Problems: Lecture Delivered Before the International Congress of Mathematicians at Paris in 1900 / David Hilbert --
Biography of Ernst Zermelo --
120. From a Letter to David Hilbert (September 24, 1904) / Ernst Zermelo} --
B. Foundational crisis and undecidability {121. From Correspondence Between Bertrand Russell and Gottlob Frege (June 16 and 22, 1902) (Russell Paradox and Logicist School) / Bertrand Russell and Gottlob Frege --
122. From a Letter to Jean van Heijenoort Concerning the Publication of the Russell-Frege Correspondence (November 23, 1962) --
123. From Principia Mathematica (Russell's Solution to the Burali-Forti Paradox and to His Own) / Alfred North Whitehead and Bertrand Russell --
Biography of L. E. J. Brouwer --
124. From Intuitionism and Formalism / L. E. J. Brouwer --
125. From Intuitionistic Reflections on Formalism / L. E. J. Brouwer --
126. From Some Metamathematical Results on Completeness and Consistency / Kurt Godel --
127. From Uber formal unentscheidbare Satze der Principia mathematica und verwandter Systeme I / Kurt Godel --
128. From On Completeness and Consistency / Kurt Godel} --
C. Selected topics: the development of general abstract theories {129. From the Preface to Analysis Situs (Algebraic Topology) / Henri Poincare --
130. From An Introduction to the Foundations and Fundamental Concepts of Mathematics / Howard Eves and Carroll V. Newsom --
Biography of Henri Lebesgue --
131. From The Development of the Integral Concept / Henri Lebesgue --
132. Proof of a Fundamental Theorem in the Theory of Algebras / R. Brauer, H. Hasse, E. Noether --
Biography of George David Birkhoff --
133. From Proof of the Ergodic Theorem / George David Birkhoff}.
Series Title: Classics series.
Responsibility: edited by Ronald Calinger.

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    schema:description "VIII. THE NINETEENTH CENTURY : Introduction / Helena M. Pycior -- A. Algebra {Biography of Carl Friedrich Gauss -- 92. From New Proof of the Theorem that Every Integral Rational Algebraic Function of One Variable Can be Decomposed into Real Factors of the First or Second Degree / Carl Friedrich Gauss -- Biography of Niels Abel -- 93. From A Memoir on Algebraic Equations, Proving the Impossibility of a Solution of the General Equation of the Fifth Degree / Niels Abel -- Biography of Evariste Galois -- 94. From the Testamentary Letter Sent to Augusts Chevalier (May 29, 1832) (Group Theory and Albelian Integrals) / Evariste Galois -- Biography of William Rowan Hamilton -- 95. From Elements of Quaternions / William Rowan Hamilton -- Biography of George Boole -- 96. From An Investigation of the Laws of Thought (The Joining of Algebra and Logic) / George Boole} -- B. Non-Euclidean geometries {Biography of Nikolai Ivanovich Lobachevsky -- 97. From The Theory of Parallels (Hyperbolic Geometry) / Nikolai Ivanovich Lobachevsky -- Biography of Bernhard Riemann -- 98. From On the Hypotheses Which Lie at the Foundations of Geometry / Bernhard Riemann} -- C. The arithmetization of mathematical analysis {Biography of Joseph Fourier -- 99. From Joseph Fourier 1768-1839 / I. Grattan-Guinness -- 100. From Theorie analytique de la chaleur / Joseph Fourier -- 101. From "On the Continuity of Functions Defined by Power Series" / Niels Abel -- Biography of Augustin-Louis Cauchy -- 102. From Cours d'analyse de l'Ecole Royale Polytechnique / Augustin-Louis Cauchy -- 103. From Resume des lecons... sur le calcul infinitesimal (On the Derivative as a Limit) / Augustin-Louis Cauchy -- 104. From Resume des lecons... sur le calcul infinitesimal (First Rigorous Proof About Derivatives) / Augustin-Louis Cauchy -- Biography of Karl Weierstrass -- 105. From Lectures on the Differential Calculus / Karl Weierstrass -- 106. From a Letter to Hermann Amandus Schwarz (May 5, 1875) / Karl Weierstrass -- 107. From Encounters with Mathematics (Riemann on Physcis and Partial Differential Equations) / Lars Garding} -- D. Number theory, set theory, and symbolic logic {108. From Carl Friedrich Gauss: A Biography (A Discussion of the Disquisitiones arithmeticae, including Congruences and the Fundamental Theorem of Arithmetic) / Tord Hall -- Biography of Ernst Eduard Kummer -- 109. From On the Theory of Complex Numbers (Theory of Ideal Prime Factors) / Ernst Eduard Kummer -- Biography of Richard Dedekind -- 110. From Stetigkeit und irrationale Zahlen (Continuity, Irrational Numbers, and Dedekind Cuts) / Richard Dedekind -- 111. From Was send und was sollen die Zahlen? (Simply Infinite Systems) / Richard Dedekind -- Biography of Georg Cantor -- 112. From Grundlagen einer Allgemeinen Mannigfaltigkeitslehre (Fundamental Series) / Georg Cantor -- 113. From a Letter to Richard Dedekind (Transfinite Cardinal Numbers and Set Theory) / Georg Cantor -- Biography of Gottlob Frege -- 114. From Begriffsschrift (Symbolic Logic) / Gottlob Frege -- 115. From Die Grundlagen der Arithmetik (Definition of Number in Logical Terms) / Gottlob Frege -- Biography of Giuseppe Peano -- 116. From Arithmeticas principia (Set of Axioms for Integers) / Giuseppe Peano -- 117. From Introduction to Mathematical Philosophy (The Definition of Number) / Bertrand Russell}] -- IX. THE EARLY TWENTIETH CENTURY TO 1932 : Introduction / Helena M. Pycior -- A. Creativity and the Paris problems {Biography of Henri Poincare -- 118. From Science and Method / Henri Poincare -- 119. From Mathematical Problems: Lecture Delivered Before the International Congress of Mathematicians at Paris in 1900 / David Hilbert -- Biography of Ernst Zermelo -- 120. From a Letter to David Hilbert (September 24, 1904) / Ernst Zermelo} -- B. Foundational crisis and undecidability {121. From Correspondence Between Bertrand Russell and Gottlob Frege (June 16 and 22, 1902) (Russell Paradox and Logicist School) / Bertrand Russell and Gottlob Frege -- 122. From a Letter to Jean van Heijenoort Concerning the Publication of the Russell-Frege Correspondence (November 23, 1962) -- 123. From Principia Mathematica (Russell's Solution to the Burali-Forti Paradox and to His Own) / Alfred North Whitehead and Bertrand Russell -- Biography of L. E. J. Brouwer -- 124. From Intuitionism and Formalism / L. E. J. Brouwer -- 125. From Intuitionistic Reflections on Formalism / L. E. J. Brouwer -- 126. From Some Metamathematical Results on Completeness and Consistency / Kurt Godel -- 127. From Uber formal unentscheidbare Satze der Principia mathematica und verwandter Systeme I / Kurt Godel -- 128. From On Completeness and Consistency / Kurt Godel} -- C. Selected topics: the development of general abstract theories {129. From the Preface to Analysis Situs (Algebraic Topology) / Henri Poincare -- 130. From An Introduction to the Foundations and Fundamental Concepts of Mathematics / Howard Eves and Carroll V. Newsom -- Biography of Henri Lebesgue -- 131. From The Development of the Integral Concept / Henri Lebesgue -- 132. Proof of a Fundamental Theorem in the Theory of Algebras / R. Brauer, H. Hasse, E. Noether -- Biography of George David Birkhoff -- 133. From Proof of the Ergodic Theorem / George David Birkhoff}."@en ;
    schema:description "IV. ARABIC PRIMACY WITH HINDU, CHINESE, AND MAYA CONTRIBUTIONS : Introduction -- A. al-Khwarizmi {Biography of al-Khwarizmi -- 47. From The Book of Algebra and Almucabola (Quadratic Equations in Algebra: Verbal Form) / al-Khwarizmi} -- B. 'Umar al-Khayyami {Biography of 'Umar al-Khayyami -- 48. From the Algebra / 'Umar al-Khayyami} -- C. Bhaskara II {Biography of Bhaskara II -- 49. From Lilavati (Arithmetic and Geometry) / Bhaskara II -- 50. From Bijagnita (Algebra) / Bhaskara II} -- D. Zhang Chang {Biography of Zhang Chang -- 51. From The Development of Mathematics in China and Japan (Problems in the Nine Chapters) / Yoshio Mikami} -- E. The Civilization of the Maya {Commentary -- 52. From The Ancient Maya / Sylvanus Griswold Morley}] -- V. THE MEDIEVAL-RENAISSANCE-REFORMATION PERIODS IN EUROPE : Introduction / Joseph E. Brown, Rensselaer Polytechnic Institute -- A. Leonardo of Pisa {Biography of Leonardo of Pisa -- 53. From Liber abbaci (The Rabbit Problem) / Leonardo of Pisa} -- B. Nicole Oresme {Biography of Nicole Oresme -- 54. From De configurationibus (The Latitude of Forms) / Nicole Oresme -- 55. From Questiones super geometriam Euclidis (The Latitude of Forms) / Nicole Oresme} -- C. Girolamo Cardano {Biography of Girolamo Cardano -- 56. From the Artis Magnae / Girolamo Cardano} -- D. Francois Viete {Biography of Francois Viete -- 57. From In artem analyticem isagoge (The New Algebra) / Francois Viete} -- E. Simon Stevin {Biography of Simon Stevin -- 58. From De Thiende (Decimal Fractions) / Simon Stevin} -- F. John Napier {Biography of John Napier -- 59. From Mirifici logarithmorum canonis constructio (Logarithms) / John Napier}] -- VI. THE SCIENTIFIC REVOLUTION AT ITS ZENITH : Introduction -- A. Algebra, coordinate geometry, and arithmetic {Biography of Rene Descartes -- 60. From the Regulae (Rule IV: "In search for the truth of things a method is indispensable") / Rene Descartes -- 61. From Discourse de la Methode (Four Fundamental Rules of Logic) / Rene Descartes -- 62. From Geometrie (Theory of Equations) / Rene Descartes -- 63. From Geometrie (The Principle of Nonhomogeneity) / Rene Descartes -- 64. From a Letter to Bernard Frenicle de Bessy (October 10, 1640) (Are numbers of the form 2^(n+1) prime when n=2t?) / Pierre de Fermat -- 65. From Two Letters of February 1657 (Find an Infinity of Integer Solutions for the "Pell" Equation) / Pierre de Fermat -- 66. From Traite du triangle arithmetique... (The Pascal Triangle) / Blaise Pascal} -- B. Origins of the infinitesimal calculus {Biography of Johann Kepler -- 67. From Nova stereometria doliorum vinariorum (Integration Methods) / Johann Kepler -- 68. From Two New Sciences (Paradoxes of Infinity, the Relationship Between Points and Lines, the Order of an Infinity, Infinitesimals, the Concept of a Continuum) / Galileo Galilei -- 69. From On the Transformation and Simplification of the Equations of Loci (Integration) / Pierre de Fermat -- 70. From On a Method for the Evaluation of Maxima and Minima / Pierre de Fermat -- 71. From On the Sines of a Quadrant of a Circle / Blaise Pascal} -- C. The discovery of the differential and integral calculus {Biography of Gottfried Wilhelm Leibniz -- 72. From A New Method for Maxima and Minima as Well as Tangents, Which is Impeded Neither by Fractional nor by Irrational Quantities, and a Remarkable Type of Calculus for This (Differential Calculus) / Gottfried Wilhelm Leibniz -- 73. From Supplementum geometriae dimensoriae... in Acta Eruditorum (1693) (The Fundamental Theorem of the Calculus) / Gottfried Wilhelm Leibniz -- 74. From Specimens of a Universal (System of) Mathematics / Isaac Newton -- 75. From a Letter to Henry Oldenburg on the Binomial Series (June 13, 1676) / Isaac Newton -- 76. From Letter to Henry Oldenburg on General Method for Finding Quadratures (October 24, 1676) / Isaac Newton -- 77. From Principia Mathematics (Prime and Ultimate Ratios: The Theory of Limits) / Isaac Newton -- 78. From the Introduction to the Tractatus de quadratura curvarum / Isaac Newton} -- D. The Bernoullis {Biography of Jakob Bernoulli -- 79. From Ars Conjectandi (The Law of Large Numbers) / Jakob Bernoulli -- 80. From The Curvature of a Ray in Nonuniform Media (The Brachistochrone) / Johann Bernoulli}] -- VII. The Enlightenment (1720-1800) : Introduction -- A. Elaboration and criticism of mathematical analysis {Biography of Brook Taylor -- 81. From Methodus Incrementorum Directa et Inversa (The Taylor Series) / Brook Taylor -- 82. From The Analyst (Criticism of the Foundations of the Calculus) / George Berkeley -- 83. From Treatise of Fluxions (On Series and Extremes) / Colin Maclaurin -- 84. From Differential, Encyclopedie, Vol. 4 (On Limits) / Jean d'Alembert -- 85. From Introductio in analysin infinitorum (Trigonometry) / Leonhard Euler -- Biography of Joseph-Louis Lagrange -- 86. From Attempt at a New Method for Determining the Maxima and Minima of Indefinite Integral Formulas (The Calculus of Variations) / Joseph-Louis Lagrange -- 87. From Mathematical Thought from Ancient to Modern Times (1972) (Taylor Series with Remainder) / Morris Kline} -- B. Topology, number theory, and probability {88. From the Problem of the Seven Bridges of Konigsberg (The Origins of Topology) / Leonhard Euler -- 89. From Theorems on Residues Obtained by the Division of Powers (Number Theory: Power Residues) / Leonhard Euler -- 90. From Demonstrations of Certain Arithmetical Theorems / Leonhard Euler -- Biography of Pierre-Simon Laplace -- 91. From Essais philosophique sur les probabilites (The Theory of Probability) / Pierre-Simon Laplace}] --"@en ;
    schema:description "INTRODUCTION : From A Mathematician's Apology / G. H. Hardy ; From Mathematics as an Element in the History of Thought / Alfred North Whitehead] -- I. PROTOMATHEMATICS IN THE LATE AGE OF STONE AND IN ANCIENT MESOPOTAMIA EGYPT : Introduction -- 1. From The Exact Sciences in Antiquity / O. Neugebauer -- 2. From the A'h-mose or Rhind Papyrus / James R. Newman -- 3. Problem no. 14 of the Moscow Papyrus / Battiscombe Gunn and T. Eric Peet -- 4. From the Old Testament of the Bible -- II. THE RISE OF THEORETICAL MATHEMATICS IN ANCIENT GREECE : Introduction -- A. Proclus {Biography of Proclus -- 5. From The Catalogue of Geometers / Proclus} -- B. Pythagoras and his followers {Biography of Pythagoras of Samos -- 6. From On Marvels 6 / Apollonius Paradoxagraphus -- 7. From Book VII of the Elements: Definitions / Euclid -- 8. From Prior Analytics i.23 (Irrationality of the Square Root of 2) / Aristotle -- 9. From On Nicomachus' Introduction to Arithmetic (Arithmetic, Geometric and Harmonic Means) / Iamblichus -- 10. From Commentary on Ptolemy's Harmonics / Porphyry -- 11. From Metaphysics A5 / Aristotle -- 12. From Commentary on Euclid i (Sum of the Angles of a Triangle) / Proclus -- 13. From Convival Questions viii.2. (Pythagoras' Theorem) -- 14. From On Slips in Greetings 5 / Lucian -- 15. From Elements X. Scholium (The Irrational or Incommensurable) / Euclid -- 16. From Elements X. Definitions (Commensurable and Incommensurable) / Euclid} -- C. Hippocrates of Chios {Biography of Hippocrates of Chios -- 17. From Commentary on Aristotle's Physics A 2 / Philoponus -- 18. From Commentary on Aristotle's Physics A 2 (Quadrature of Lunules, the Crescent-Shaped Figures Between Two Intersecting Arcs of Circles) / Simplicius} -- D. Plato {Biography of Plato -- 19. From the Republic VI.510 (Approach to Mathematics) / Plato -- 20. From the Republic VII.522-528 (The Quadrivium) / Plato -- 21. From the Timaeus 53-56 / Plato} -- E. Eudoxus {Biography of Eudoxus -- 22. From Book V of the Elements: Definitions (Theory of Proportions) / Euclid -- 23. From Book XII.2 of the Elements (Method of Approximation, the So-called Method of Exhaustion) / Euclid} -- F. Aristotle {Biography of Aristotle -- 24. From Posterior Analytics i.10 (First Principles or Theory of Statements) / Aristotle -- 25. From Metaphysics 1066-1067 (The Infinite, the Essence of the Archimedean Postulate) / Aristotle -- 26. From the Metaphysics 1068-1069 and Physics 231-240 (On the Continuous and Zeno's Paradoxes) / Aristotle}] -- III. THE HELLENISTIC AND ROMAN PERIODS : Introduction -- A. Euclid {Biography of Euclid -- 27. From Book I of the Elements: Definitions, Postulates, Axioms, and Propositions 1-13 / Euclid -- 28. From Book I of the Elements: Propositions 27-32 (Theory of Parallels) / Euclid -- 29. From Book I of the Elements: Proposition 47 (Pythagorean Theorem) / Euclid -- 30. From Book VII of the Elements: Propositions 1 and 2 (Euclidean Algorithm) / Euclid -- 31. From Book IX of the Elements: Proposition 14 (Fundamental Theorem in the Theory of Numbers) / Euclid -- 32. From Book IX of the Elements: Proposition 20 (Infinitude of Primes) / Euclid} -- B. Archimedes {Biography of Archimedes -- 33. From On the Sphere and Cylinder I: Assumptions / Archimedes -- 34. From On the Spheres and Cylinder I: Propositions 33 and 34 (Surface and Volume of a Sphere) / Archimedes -- 35. From Measurement of a Circle: Proposition 3 (Approximation of Using in Essence Upper and Lower Limits) / Archimedes -- 36. From Quadrature of the Parabola: Introduction, Propositions 20, 23, and 24 / Archimedes -- 37. From On the Equilibrium of Planes I: Propositions 6 and 7 (Principle of the Lever) / Archimedes -- 38. From the Sand-Reckoner: Introduction and Section on Large Numbers / Archimedes -- 39. From The Cattle Problem (Indeterminate Analysis) / Archimedes} -- C. Eratosthenes {Biography of Eratosthenes -- 40. From Introduction to Arithmetic I: Chapters XII-XIII (Sieve for Finding Primes) / Nicomachus of Gerasa -- 41. From On the Circular Motion of the Heavenly Bodies i.10.52 / Cleomedes} -- D. Apollonius {Biography of Apollonius -- 42. From Conics: Introduction to Book One / Apollonius -- 43. From Conics: Propositions 7 and 11 (Construction of Sections and Fundamental Properties) / Apollonius} -- E. Ptolemy {Biography of Claudius Ptolemy -- 44. From the Syntaxis or Almagest i (Trigonometry: Table of Sines) / Claudius Ptolemy} -- F. Diophantus {Biography of Diophantus -- 45. From the Dedication to Arithmetica (Algebraic Notation) / Diophantus -- 46. From the Arithmetica (Origins of the Theory of Numbers) / Diophantus}] --"@en ;
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