First Reading Assignment From A Mathematician's Apology-G. H. Hardy, page 1 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-mose 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 Second Reading Assignment 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 Third Reading Assignment 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 Fourth Reading Assignment 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) Fifth Reading Assignment 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 (Definitions only) Biography of Dedekind, page 625 Reading 110: From Stetigkeit und irrationale Zahlen (Continuity, Irrational Numbers, and Dedekind Cuts)-Richard Dedekind Reading 23: From Book XII.2 of the Elements (Method of Approximation, the So-called Method of Exhaustion)-Euclid Sixth Reading Assignment Biography of Archimedes, page 131 Reading 33: From Sphere and Cylinder I: Greeting and Assumptions-Arcimedes 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 Seventh Reading Assignment 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 Eighth Reading Assignment Biography of Apollonius, page 159 Reading 42: From Conics: Introduction to Book One-Apollonius Reading 43: From Conics: Propositions 7 and 11-Apollonius Ninth Reading Assignment 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) Tenth Reading Assignment 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 Marquis Zhang Cang, page 212 Reading 49: From a Description of the Nine Chapters on the Mathematical Art (Jiuzhang suanshu)-Li Yan and Du Shiran Eleventh Reading Assignment 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 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 Twelfth Reading Assignment Biography of Cardano, page 261 Reading 56: From the Ars Magna-Girolamo Cardano Biography of Viete, page 267 outside reading Biography of Stevin, page 273 Reading 58: From De Thiende (Decimal Fractions)-Simon Stevin Biography of Napier, page 281 Thirteenth Reading Assignment 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)-Rene 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) Fourteenth Reading Assignment 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 Fifteenth Reading Assignment 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", Encyclopedie, 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