Table of Contents

PART I: EARLY MIDDLE AGES The Latin Encyclopedists 1. On the Quadrivium, or Four Mathematical Sciences Isidore of Seville 2. On Arithmetic Boethius 3. On the Universe and Its Parts Isidore of Seville 4. On the Order of the Planets Macrobius 5. On the Motion of Mercury and Venus Around the Sun a. Chalcidius b. Martianus Capella 6. On Ocean and Tides Macrobius PART II: LATER MIDDLE AGES The Translation of Greek and Arabic Science into Latin 7. A List of Translations Made from Arabic into Latin in the Twelfth Century Gerard of Cremona 8. A List of Translations Made from Greek into Latin in the Thirteenth Century William of Moerbeke The Reaction of the Universities and Theological Authorities to Aristotelian Science and Natural Philosophy 9. The Condemnation of Aristotle's Books on Natural Philosophy in 1210 at Paris 10. The Command to Expurgate Aristotle's Books on Natural Philosophy (1231) 11. The Natural Books of Aristotle in the Arts Curriculum at the University of Paris in 1255 12. Statute of the Faculty of Arts Drastically Curtailing the Discussion of Theological Questions (1272) 13. The Condemnation of 1277: A Selection of Articles Relevant to the History of Medieval Science 14. An Objection to Theological Restrictions in the Discussion of a Scientific Question John Buridan 15. An Assessment of Buridan's Objections Ludovicus (Luis) Coronel Classification of the Sciences Introduction Edward Grant 16. Classification of the Sciences Hugh of St. Victor 17. Classification of the Sciences Domingo Gundisalvo Logic Introduction John E. Murdoch 18. On Terms, "Suppositio," and Consequences William of Ockham Mathematics 19. On the Importance of Studying Mathematics Roger Bacon A. ARITHMETIC 20. Arabic Numerals and Arithmetic Operations in the Most Popular Algorism of the Middle Ages John of Sacrobosco 21. Propositions from a Theoretical Arithmetic Jordanus of Nemore B. ALGEBRA 22. Six Types of Rhetorical Algebraic Equations Al-Khwarizmi 23. Algebraic Propositions from the Treatise On Given Numbers Jordanus of Nemore C. NUMBER THEORY, PROBABILITY, AND INFINITE SERIES 24. Number Theory and Indeterminate Analysis Leonardo of Pisa (Fibonacci) 25. A Proposition on Mathematical Probability Nicole Oresme 26. Infinite Series Nicole Oresme D. PROPORTIONS 27. The Definitions of Book V of Euclid's Elements in a Thirteenth-Century Version, and Commentary Campanus of Novara 28. An Algorism of Ratios: Manipulation of Rational Exponents Nicole Oresme 29. Rational and Irrational Exponents Distinguished Nicole Oresme E. GEOMETRY 30. On the Division of Figures Leonardo of Pisa (Fibonacci) 3l. Two Medieval Versions of Archimedes' Quadrature of the Circle a. The Abbreviated Version of Pseudo-Bradwardine b. The Question of Albert of Saxony on the Quadrature of the Circle 32. The Trisection of an Angle a. Banu Musa b. Jordanus of Nemore 33. Constructions from an Applied Geometry Dominicus de Clavasio F. TRIGONOMETRY 34. Trigonometry of the Sine Richard of Wallingford Typical Scientific Questions Based on Aristotle's Major Physical Treatises Introduction Edward Grant 35. Questions on the Eight Books of Aristotle's Physics Albert of Saxony 36. Questions on the Four Books of Aristotle's On the Heavens (De caelo) John Buridan 37. Questions on the Two Books of Aristotle's On Generation and Corruption Albert of Saxony 38. Questions on The Four Books of Aristotle's Meteorologica Themon, Son of the Jew Physics A. STATICS, OR "THE SCIENCE OF WEIGHTS" Introduction Edward Grant 39. On the Theory of Weight Jordanus of Nemore B. MOTION 40. What is Motion? William of Ockham C. KINEMATICS 41. The Reduction of Curvilinear Velocities to Uniform Rectilinear Velocities Gerard of Brussels 42. Uniform and Nonuniform Motion and the Merton College Mean Speed Theorem William of Heytesbury 43. The Configuration of Qualities and Motions, Including a Geometric Proof of the Mean Speed Theorem Nicole Oresme D. DYNAMICS 44. Does Finite and Temporal Motion Require a Resistant Medium? The Responses of Averroes and Avempace in Comment 71 a. The Text of Aristotle b. Averroes' Expositio on the Text 45. The Mover or Cause in Natural Motion Averroes 46. The Medieval Aristotelian Principle of Motion: "Whatever Is Moved Is Moved by Another" St. Thomas Aquinas 47. External and Internal Resistances to Motion Albert of Saxony 48. The Impetus Theory of Projectile Motion John Buridan 49. On the Cause of Acceleration of Free-falling Bodies John Buridan 50. In Opposition to Aristotle: Contrary Motions Can Be Continuous without an Intervening Moment of Rest a. Marsilius of Inghen b. Galileo Galilei 51. Mathematical Representations of Motion a. Thomas Bradwardine: "Bradwardine's Function" and the Repudiation of Four Opposition Theories on Proportions of Motion b. Nicole Oresme: Extended Application of "Bradwardine's Function" E. ATOMISM 52. The Development and Criticism of Atomism in the Later Middle Ages a. Thomas Bradwardine b. Algazel c. John Duns Scotus d. Henry of Harclay and William of Alnwick F. ON VACUUM 53. Nature Abhors a Vacuum a. Albert of Saxony: A Natural Vacuum Denied b. John Buridan: Experiments Demonstrating that Nature Abhors a Vacuum c. Marsilius of Inghen: Experiments Demonstrating that Nature Abhors a Vacuum d. Galileo Galilei: Experiments Demonstrating that Nature Abhors a Vacuum 54. Nature Does Not Abhor a Vacuum Blaise Pascal 55. Motion in a Hypothetical Void a. St. Thomas Aquinas: A Kinematic Argument for Finite Motion in a Hypothetical Void b. Albert of Saxony: Dynamic Arguments Justifying Motion in a Hypothetical Void c. Galileo Galilei: His Earliest Law of Motion and His Arguments for Finite Velocity in a Void d. Thomas Bradwardine: Unequal Homogeneous Bodies Fall with Equal Velocity in a Vacuum e. Albert of Saxony: Unequal Homogeneous Bodies Fall with Equal Velocity in a Vacuum f. Galileo Galilei: Unequal Homogeneous Bodies Fall with Equal Velocity in a Vacuum 56. On Interstitial Vacua a. Marsilius of Inghen: Explanation of Condensation and Rarefaction, and Denial of Interstitial Vacua b. Nicholas of Autrecourt: The Existence of Interstitial Vacua Affirmed c. Galileo Galilei: The Existence of Interstitial Vacua Affirmed G. MEASUREMENT OF FORCES 57. On Maximum and Minimum Powers John Buridan H. MAGNETISM 58. An Encyclopedist's Description of the Magnet Bartholomew the Englishman 59. The First Systematic Description in Europe of the Properties of the Lodestone Peter Peregrinus I. OPTICS 60. The Encyclopedic Tradition in Optics a. Adelard of Bath: Natural Questions b. Alexander Neckam: Concerning the Natures of Things c. Bartholomew the Englishman: Concerning the Properties of Things 61. Robert Grosseteste and the Revival of Optics in the West 1. Robert Grosseteste: Concerning Lines, Angles, and Figures 2. Robert Grosseteste: On the Rainbow 62. Late Thirteenth-Century Synthesis in Optics a. Roger Bacon: The Nature and Multiplication of Light or Species b. John Pecham: The Nature and Multiplication of Light or Species c. Roger Bacon: The Nature and Multiplication of Light or Species d. Witelo: The Nature and Multiplication of Light or Species e. Witelo: The Speed of Propagation of Light or Species f. Roger Bacon: The Speed of Propagation of Light or Species g. John Pecham: The Structure of the Eye h. Alhazen: The Lens as the Sensitive Organ of the Eye i. Roger Bacon: The Lens as the Sensitive Organ of the Eye j. Witelo: The Lens as the Sensitive Organ of the Eye k. Alhazen: The Act of Sight l. Witelo: The Act of Sight m. John Pecham: The Act of Sight n. Alhazen: The Debate about Visual Rays o. Roger Bacon: The Debate about Visual Rays p. John Pecham: The Debate about Visual Rays q. Witelo: The Debate about Visual Rays r. Roger Bacon: Psychology of Visual Perception s. John Pecham: The Geometry of Reflection t. Witelo: A Problem of Image Formation by Reflection u. Alhazen: Paraboloidal Burning Mirrors v. Witelo: Paraboloidal Burning Mirrors w. Alhazen: Causal Analysis of Reflection x. Roger Bacon: Causal Analysis of Reflection y. Witelo: Causal Analysis of Reflection z. Alhazen: An Instrument for Investigating Refraction aa. Roger Bacon: The Geometry of Refraction bb. Witelo: The Geometry of Refraction cc. John Pecham: Image Formation by Refraction dd. Roger Bacon: Image Formation by Refraction ee. John Pecham: The Burning Glass ff. Roger Bacon: Causal Analysis of Refraction gg. Witelo: Causal Analysis of Refraction 63. Late Medieval Optics a. Henry of Hesse: Questions Concerning Perspective b. Theodoric of Freiberg: On the Rainbow Astronomy, Astrology, and Cosmology A. THE ELEMENTS OF ASTRONOMY 64. The Two Most Popular Medieval Handbooks of the Elements of Astronomy a. John of Sacrobosco: On the Sphere b. Anonymous: The Theory of the Planets 65. Extracts from the Alfonsine Tables and Rules for Their Use John of Saxony B. ASTROLOGY 66. An Attack upon Astrology Nicole Oresme C. COSMOLOGY 67. On the Possible Diurnal Rotation of the Earth a. Introduction Edward Grant b. Ptolemy: The Immobility of the Earth in the Center of the World c. St. Thomas Aquinas: The Immobility of the Earth in the Center of the World d. St. Thomas Aquinas: Heraclides of Pontus and Aristarchus Mentioned as Proponents of the Earth's Diurnal Rotation e. John Buridan: The Compatibility of the Earth's Diurnal Rotation with Astronomical Phenomena f. Nicole Oresme: The Compatibility of the Earth's Diurnal Rotation with Astronomical Phenomena and Terrestrial Physics g. Nicolaus Copernicus: The Compatability of the Earth's Diurnal Rotation with Astronomical Phenomena and Terrestrial Physics 68. On Saving the Phenomena and the Reality or Unreality of Epicycles and Eccentrics a. Moses Maimonides: The Reality of Epicycles and Eccentrics Denied b. Bernard of Verdun: The Reality of Epicycles and Eccentrics Affirmed c. John Buridan: An Intermediate Position--Epicycles Denied, Eccentrics Affirmed 69. On the Commensurability or Incommensurability of Celestial Motions Nicole Oresme 70. On Comets Albertus Magnus 71. The Possibility of a Plurality of Worlds Nicole Oresme 72. On the Existence of an Imaginary Infinite Void Space Beyond the Finite Cosmos a. Hermes Trismegistus to Asclepius: Void Beyond the Cosmos Lacks Matter but Not Spirit 73. On a God-filled Extramundane Infinite Void Space a. Thomas Bradwardine b. Nicole Oresme c. Jesuit Commentators at the College of Coimbra, Portugal d. Otto von Guericke Alchemy and Chemistry 74. On the Formation of Minerals and Metals and the Impossibility of Alchemy Avicenna 75. Twenty-six Arguments against Alchemy and the Responses Thereto Petrus Bonus 76. A Description of Alchemical Operations, Procedures, and Materials Albertus Magnus 77. How Elements Persist in a Compound a. St. Thomas Aquinas b. Albert of Saxony Geology, Geography, and Oceanography A. GEOLOGY 78. On the Formation of Stones and Mountains Avicenna 79. On the Motion of the Earth's Center of Gravity and the Formation of Mountains John Buridan 80. On the Material, Hardness, and Fissility of Stones Albertus Magnus B. GEOGRAPHY 81. The Image or Representation of the World (Ymago Mundi) Pierre d'Ailly, with the Marginal Comments of Christopher Columbus C. OCEANOGRAPHY 82. On the Causes of the Tides Robert Grosseteste Biology A. ZOOLOGY 83. Descriptions of Animals from a Twelfth-Century Bestiary 84. An Attempt at a Scientific Description of Animals Albertus Magnus 85. On the Structure and Habits of Birds Frederick II of Hohenstaufen 86. Philosophical and Theoretical Zoology Albertus Magnus B. BOTANY 87. Philosophical and Theoretical Botany Albertus Magnus 88. An Illustration of Descriptive Botany: The Oak Tree Albertus Magnus Medicine A. THEORY 89. Early Medieval Medicine Isidore of Seville B. PHYSIOLOGY 90. The Galenic System Joannitius (Hunain ibn Ishaq) 91. Canon Avicenna C. SCIENTIFIC METHOD 92. Commentaries on Galen's Tegni Jacopo da Forli and Haly Rodohan D. ANATOMY 93. On Anatomy Isidore of Seville 94. Anatomical Demonstration at Salerno: The Anatomy of the Pig Anonymous 95. A Scholastic Anatomy: The Anatomy of Master Nicholas Master Nicholas (?) 96. Anatomy Based on Human Dissection: The Anatomy of Mundinus Mondino de' Luzzi 97. A Fifteenth-Century Autopsy Bernard Tornius E. PRACTICE 98. General Instructions for the Practitioner Archimatthaeus F. METHODS OF DIAGNOSIS 99. Interpretation of the Pulse Anonymous 100. Interpretation of the Urine a. Giles of Corbeil b. Arnald of Villanova 101. Interpretation of Particular Symptoms a. Gilbert the Englishman: The Symptoms of Leprosy b. Jordan of Turre (?): The Symptoms of Lepers c. John of Mirfeld: Danger Symptoms G. A METHOD OF MEDICAL PRACTICE 102. A Consilium Ugo Benzi H. TREATMENT OF PARTICULAR AILMENTS 103. Gynecology Trotula 104. How to Combat Spells Preventing Intercourse Constantine the African 105. Diseases of the Skin Theodoric, Bishop of Cervia 106. Smallpox John Gaddesden 107. Bubonic Plague Guy de Chauliac I. TOOLS EMPLOYED IN TREATMENT 108. Diet and Regimen Regimen Sanitatis Salernitanum 109. Drugs: Simple Medicines a. Rufinus: Simple Medicines b. Taddeo Alderotti: The Preparation and Medicinal Use of Alcohol 110. Drugs: Compound Medicines a. Matthaeus Platearius: The Rationalization of Pharmacy b. Antidotarium Nicolai: Traditional Empirical Pharmacy c. Bernard of Gordon: Mathematical Pharmacy J. SURGERY 111. History of Surgery Guy de Chauliac 112. Salernitan Surgery Roger of Salerno 113. Definition and Objectives of Surgery Theodoric, Bishop of Cervia 114. Bloodletting Lanfranc 115. The Treatment of Wounds a. Theodoric, Bishop of Cervia b. Henry of Mondevile c. Guy de Chauliac 116. Plastic Surgery Heinrich von Pfolspeundt BRIEF AUTHOR BIOGRAPHIES INDEX

About the Author

Edward Grant is Professor of History of Science, Emeritus, at Indiana University, Bloomington.