ed. Ronald Calinger

Prentice Hall, 1995

- From
*A Mathematician's Apology*- G. H. Hardy, page 1

**This reading sets the tone for the course.** - Chapter I (Protomathematics in the Late Age of Stone and in Ancient Mesopotamia and Egypt) Introduction, page 7
- Reading 1: From
*The Exact Sciences in Antiquity*- O. Neugebauer - Reading 2: From the A'h-mosè or Rhind Papyrus
- Reading 3: Problem No. 14 of the Moscow Papyrus
- Reading 4: The Ancient Hebrews and Protomathematics Based on the Old Testament of the Bible
- Homework Assignment 1

- Chapter II (The Rise of Theoretical Mathematics in Ancient Greece) Introduction, page 37
- Biography of Proclus, page 47
- Reading 5: From "The Catalog of Geometers"-Proclus
- Biography of Pythagoras of Samos, page 50
- Reading 7: From Book VII of the
*Elements*: Definitions-Euclid - Reading 8: From
*Prior Analytics*i.23 (Irrationality of the Square Root of 2)-Aristotle - Reading 10: From
*Commentary on Ptolemy's Harmonics*(Arithmetic, Geometric and Harmonic Means)-Porphyry - Reading 12: From
*Commentary on Euclid*i (Sum of the Angles of a Triangle)-Proclus - Reading 13: From
*Convivial Questions*viii. 2. (Pythagoras' Theorem)-Plutarch - Reading 14: From
*On Slips in Greetings*5-Lucian - Homework Assignment 2

- Chapter III (Mathematics in the West During Hellenistic and Roman Times) Introduction, page 91
- Biography of Euclid, page 109
- Reading 27: From Book I of the
*Elements*: Definitions, Postulates, Axioms, and Propositions 1-13 - Reading 28: From Book I of the
*Elements*: Propositions 27-32 (Theory of Parallels) - Reading 29: From Book I of the
*Elements*: Proposition 47 (Pythagorean Theorem)-Euclid - Reading 30: From Book VII of the
*Elements*: Propositions 1 and 2 (Euclidean Algorithm) - Reading 15: From
*Elements*X. Scholium (The Irrational or Incommensurable)-Euclid - Reading 16: From
*Elements*X. Definitions-Euclid - Reading 31: From Book IX of the
*Elements*: Propositions 14 (Fundamental Theorem in the Theory of Numbers), 20 (Infinitude of Primes), and 25-30 - Homework Assignment 3

- Biography of Hippocrates, page 58
- Reading 17: From
*Commentary on Aristotle's Physics*A 2-Philoponus - Reading 18: From
*Commentary on Aristotle's Physics*A 2 (Quadrature of Lunules)-Philoponus (To the end of the left hand side of page 60) - Homework Assignment 4

- Biography of Eudoxus, page 74
- Reading 22: From Book V of the
*Elements*: Definitions and Propositions 1, 7, 9, and 10 (Theory of Proportions)-Eudoxus/Euclid - Reading 23: From Book XII.2 of the
*Elements*(Method of Approximation, the So-called Method of Exhaustion)-Euclid - Homework Assignment 5

- Biography of Archimedes, page 131
- Reading 33: From
*Sphere and Cylinder*I: Greeting and Assumptions-Archimedes - Reading 34: From
*Sphere and Cylinder*I: Propositions 33 and 34 (Surface and Volume of a Sphere)-Archimedes - Reading 35:
*Measurement of a Circle*: Propositions 1-3 (Approximation of Pi Using in Essence Upper and Lower Sums)-Archimedes - Reading 36: From
*Quadrature of the Parabola*: Introduction and Propositions 17-24-Archimedes - Homework Assignment 6

- Biography of Eratosthenes, page 153
- Reading 40: From
*Introduction to Arithmetic*I: Chapters XII and XIII (Sieve for Finding Primes)- Nichomachus of Gerasa - Biography of Diophantus, page 171
- Reading 45: From the Dedication to
*Arithmetica*(Algebraic Notation)-Diophantus - Reading 46: From
*Arithmetica*(Origins of Number Theory)-Diophantus - Homework Assignment 7

- Biography of Apollonius, page 159
- Reading 42: From
*Conics*: Introduction to Book One-Apollonius - Reading 43: From
*Conics*: Propositions 7 and 11-Apollonius - Homework Assignment 8

- Biography of Ptolemy, page 166
- Reading 44: From the
*Syntaxis*or*Almagest*i (Trigonometry: Table of Sines)-Claudius Ptolemy - Reading 7.B1, page 245 of
*The History of Mathematics: A Reader*, ed. John Fauvel and Jeremy Gray, Regiomontanus on Triangles (book on reserve) - Homework Assignment 9

- Chapter IV (Arabic Primacy with Chinese, Indian, and Maya Contributions) Introduction, page 177
- Biography of al-Kwarizmi, page 199
- Reading 47: From
*The Book of Algebra and Almucabola*(Quadratic Equations in Algebra: Verbal Form)-al-Kwarizmi - Biography of Umar al-Khayyami, page 204
- Reading 48: From the
*Algebra*-Umar al-Khayyami (just up to end of page 208)

Look carefully at the end notes! - Biography of Marquis Zhang Cang, page 212
- Reading 49: From a Description of the
*Nine Chapters on the Mathematical Art*(Jîuzhang suànshù)-Li Yan and Dù Shírán - Homework Assignment 10

- Chapter V (The Medieval-Renaissance-Reformation Periods in Europe) Introduction, page 243
- Biography of Leonardo of Pisa, page 250
- Reading 53: From
*Liber abbaci*(The Rabbit Problem)-Leonardo of Pisa - Reading 7.A1, Leonardo Fibonacci, pages 241-243 of
*The History of Mathematics: A Reader*, ed. John Fauvel and Jeremy Gray (book on reserve) - Biography of Oresme, page 253
- Reading 54: From
*De configurationibus*(The Latitude of Forms)-Nicole Orseme - Reading 55: From
*Questiones super geometriam Euclidis*(The Latitude of Forms)-Nicole Oresme - Homework Assignment 11

- Biography of Cardano, page 261
- Reading 56: From the
*Ars Magna*-Girolamo Cardano - Biography of Viète, page 267
- Reading 57: From
*In artem analyticen isagoge*(The New Algebra)-François Viète - From
*The Analytic Art*-François Viète, translated by T. Richard Witmer (on reserve), Chapter V, On the Rules of ZeteticsThe following five readings are from

*The Analytic Art*-François Viète, translated by T. Richard Witmer (on reserve) - From
*Ad Logisticem Speciosam Notae Priores*(Preliminary Notes on Symbolic Logistic)-François Viète, Proposition I to Proposition XVI • - From
*Ad Logisticem Speciosam Notae Priores*(Preliminary Notes on Symbolic Logistic)-François Viète, Propositions XLVI, XLVIII, XLIX, L • - From
*Zeteticorum Libri Quinque*(Five Books of Zetetica), First Book, Zetetic I and Zetetic II, Fourth Book, Zetetic I • - From
*De Aequationum Recognitione et Emendatione Tractatus Duo*(Two Treatises on the Understanding and Amendment of Equations),*De Emendatione Aequationum Tractatus Secundus*(First Treatise: On Understanding Equations), Chapter VI, alternate Theorem III • - From
*De Aequationum Recognitione et Emendatione Tractatus Duo*(Two Treatises on the Understanding and Amendment of Equations),*De Emendatione Aequationum Tractatus Secundus*(Second Treatise:On the Amendment of Equations), Chapter I - Biography of Stevin, page 273
- Reading 58: From
*De Thiende*(Decimal Fractions)-Simon Stevin - Biography of Napier, page 281
- Homework Assignment 12

- Chapter VI (The Scientific Revolution at Its Zenith 1620-1720) Introduction, page 291
- Biography of Descartes, page 326
- Reading 62: From
*La Geometrie*(Theory of Equations)-René Descartes - Reading 63: From
*La Geometrie*(The Principle of Nonhomogeneity)-René Descartes - Pages 204-207 of
*The Geometry of Rene Descartes*, translated by Smith and Latham (Beginning with "Let us apply it...." and ending with "...are the required mean proportionals.") (book on reserve) - Biography of Fermat, page 341
- "On Analytic Geometry" (extract from
*Introduction aux Lieux Plans et Solides*)-Pierre de Fermat, pages 389-396 in*A Source Book in Mathematics*, by David Eugene Smith (book on reserve) - Homework Assignment 13

- Reading 69: From "On the Transformation and Simplification of the Equations of Loci" (Integration)-Pierre de Fermat
- Reading 70: From "On a Method for the Evaluation of Maxima and Minima"-Pierre de Fermat
- Biography of Leibniz, page 383
- Reading 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"-Gottfried Wilhelm Leibniz
- Reading 73: From "Supplementum geometriae dimensoriae. . . " in
*Acta Eruditorum*(The Fundamental Theorem of Calculus)-Gottfried Wilhelm Leibniz - Biography of Newton, page 395
- Reading 74: From
*Specimens of a Universal [System of] Mathematics*-Isaac Newton - Reading 75: From a Letter to Henry Oldenburg on the Binomial Series (June 13, 1676)-Isaac Newton
- Reading 76: From a Letter to Henry Oldenburg on a General Method for Finding Quadratures (October 24, 1676)-Isaac Newton
- Reading 77: From
*Principia Mathematica*(Prime and Ultimate Ratios: The Theory of Limits)-Isaac Newton (stop after Corollary of Lemma IV and begin again on page 410 after it reads "[Text is omitted here.]". Then read to the end.) - Reading 78: From the Introduction to the
*Tractatus de quadratura curvarum*-Isaac Newton - Homework Assignment 14

- Chapter VII (The Age of Enlightenment and the French Revolution 1720-1800) Introduction, page 429
- Biography of Taylor, page 465
- From
*Methodus Incrementorum Directa et Inversa*(The Taylor Series)-Brook Taylor - Biography of Berkeley, page 469
- Reading 82: From
*The Analyst*(Criticism of the Foundations of Calculus)-George Berkeley - Biography of Maclaurin, page 475
- Reading 83: From
*Treatise of Fluxions*(On Series and Extremes)-Colin Maclaurin - Biography of d'Alembert, page 479
- Reading 84: From "Differentiel",
*Encyclopédie*, Vol. 4 (On Limits)-Jean Le-Rond d'Alembert - Biography of Euler, page 486
- Reading 85: From
*Introductio in analysin infinitorum*I (Functions, Logarithms, and Trigonometry)- Leonhard Euler - Homework Assignment 15

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