
Mathematical Thought from Ancient to Modern Times
Mathematical Thought from Ancient to Modern Times, Volume 1
By: Morris Kline
Paperback | 1 March 1990
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432 Pages
28.3 x 17.1 x 10.1
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| Mathematics in Mesopotamia | p. 3 |
| Where Did Mathematics Begin? | p. 3 |
| Political History in Mesopotamia | p. 4 |
| The Number Symbols | p. 5 |
| Arithmetic Operations | p. 7 |
| Babylonian Algebra | p. 8 |
| Babylonian Geometry | p. 10 |
| The Uses of Mathematics in Babylonia | p. 11 |
| Evaluation of Babylonian Mathematics | p. 13 |
| Egyptian Mathematics | p. 15 |
| Background | p. 15 |
| The Arithmetic | p. 16 |
| Algebra and Geometry | p. 18 |
| Egyptian Uses of Mathematics | p. 21 |
| Summary | p. 22 |
| The Creation of Classical Greek Mathematics | p. 24 |
| Background | p. 24 |
| The General Sources | p. 25 |
| The Major Schools of the Classical Period | p. 27 |
| The Ionian School | p. 28 |
| The Pythagoreans | p. 28 |
| The Eleatic School | p. 34 |
| The Sophist School | p. 37 |
| The Platonic School | p. 42 |
| The School of Eudoxus | p. 48 |
| Aristotle and His School | p. 51 |
| Euclid and Apollonius | p. 56 |
| Introduction | p. 56 |
| The Background of Euclid's Elements | p. 57 |
| The Definitions and Axioms of the Elements | p. 58 |
| Books I to IV of the Elements | p. 60 |
| Book V: The Theory of Proportion | p. 68 |
| Book VI: Similar Figures | p. 73 |
| Books VII, VIII, and IX: The Theory of Numbers | p. 77 |
| Book X: The Classification of Incommensurables | p. 80 |
| Books XI, XII, and XIII: Solid Geometry and the Method of Exhaustion | p. 81 |
| The Merits and Defects of the Elements | p. 86 |
| Other Mathematical Works by Euclid | p. 88 |
| The Mathematical Work of Apollonius | p. 89 |
| The Alexandrian Greek Period: Geometry and Trigonometry | p. 101 |
| The Founding of Alexandria | p. 101 |
| The Character of Alexandrian Greek Mathematics | p. 103 |
| Areas and Volumes in the Work of Archimedes | p. 105 |
| Areas and Volumes in the Work of Heron | p. 116 |
| Some Exceptional Curves | p. 117 |
| The Creation of Trigonometry | p. 119 |
| Late Alexandrian Activity in Geometry | p. 126 |
| The Alexandrian Period: The Reemergence of Arithmetic and Algebra | p. 131 |
| The Symbols and Operations of Greek Arithmetic | p. 131 |
| Arithmetic and Algebra as an Independent Development | p. 135 |
| The Greek Rationalization of Nature | p. 145 |
| The Inspiration for Greek Mathematics | p. 145 |
| The Beginnings of a Rational View of Nature | p. 146 |
| The Development of the Belief in Mathematical Design | p. 147 |
| Greek Mathematical Astronomy | p. 154 |
| Geography | p. 160 |
| Mechanics | p. 162 |
| Optics | p. 166 |
| Astrology | p. 168 |
| The Demise of the Greek World | p. 171 |
| A Review of the Greek Achievements | p. 171 |
| The Limitations of Greek Mathematics | p. 173 |
| The Problems Bequeathed by the Greeks | p. 176 |
| The Demise of the Greek Civilization | p. 177 |
| The Mathematics of the Hindus and Arabs | p. 183 |
| Early Hindu Mathematics | p. 183 |
| Hindu Arithmetic and Algebra of the Period A.D. 200-1200 | p. 184 |
| Hindu Geometry and Trigonometry of the Period A.D. 200-1200 | p. 188 |
| The Arabs | p. 190 |
| Arabic Arithmetic and Algebra | p. 191 |
| Arabic Geometry and Trigonometry | p. 195 |
| Mathematics circa 1300 | p. 197 |
| The Medieval Period in Europe | p. 200 |
| The Beginnings of a European Civilization | p. 200 |
| The Materials Available for Learning | p. 201 |
| The Role of Mathematics in Early Medieval Europe | p. 202 |
| The Stagnation in Mathematics | p. 203 |
| The First Revival of the Greek Works | p. 205 |
| The Revival of Rationalism and Interest in Nature | p. 206 |
| Progress in Mathematics Proper | p. 209 |
| Progress in Physical Science | p. 211 |
| Summary | p. 213 |
| The Renaissance | p. 216 |
| Revolutionary Influences in Europe | p. 216 |
| The New Intellectual Outlook | p. 218 |
| The Spread of Learning | p. 220 |
| Humanistic Activity in Mathematics | p. 221 |
| The Clamor for the Reform of Science | p. 223 |
| The Rise of Empiricism | p. 227 |
| Mathematical Contributions in the Renaissance | p. 231 |
| Perspective | p. 231 |
| Geometry Proper | p. 234 |
| Algebra | p. 236 |
| Trigonometry | p. 237 |
| The Major Scientific Progress in the Renaissance | p. 240 |
| Remarks on the Renaissance | p. 247 |
| Arithmetic and Algebra in the Sixteenth and Seventeenth Centuries | p. 250 |
| Introduction | p. 250 |
| The Status of the Number System and Arithmetic | p. 251 |
| Symbolism | p. 259 |
| The Solution of Third and Fourth Degree Equations | p. 263 |
| The Theory of Equations | p. 270 |
| The Binomial Theorem and Allied Topics | p. 272 |
| The Theory of Numbers | p. 274 |
| The Relationship of Algebra to Geometry | p. 278 |
| The Beginnings of Projective Geometry | p. 285 |
| The Rebirth of Geometry | p. 285 |
| The Problems Raised by the Work on Perspective | p. 286 |
| The Work of Desargues | p. 288 |
| The Work of Pascal and La Hire | p. 295 |
| The Emergence of New Principles | p. 299 |
| Coordinate Geometry | p. 302 |
| The Motivation for Coordinate Geometry | p. 302 |
| The Coordinate Geometry of Fermat | p. 303 |
| Rene Descartes | p. 304 |
| Descartes's Work in Coordinate Geometry | p. 308 |
| Seventeenth-Century Extensions of Coordinate Geometry | p. 317 |
| The Importance of Coordinate Geometry | p. 321 |
| The Mathematization of Science | p. 325 |
| Introduction | p. 325 |
| Descartes's Concept of Science | p. 325 |
| Galileo's Approach to Science | p. 327 |
| The Function Concept | p. 335 |
| The Creation of the Calculus | p. 342 |
| The Motivation for the Calculus | p. 342 |
| Early Seventeenth-Century Work on the Calculus | p. 344 |
| The Work of Newton | p. 356 |
| The Work of Leibniz | p. 370 |
| A Comparison of the Work of Newton and Leibniz | p. 378 |
| The Controversy over Priority | p. 380 |
| Some Immediate Additions to the Calculus | p. 381 |
| The Soundness of the Calculus | p. 383 |
| List of Abbreviations | |
| Index | |
| Table of Contents provided by Ingram. All Rights Reserved. |
ISBN: 9780195061352
ISBN-10: 0195061357
Series: Mathematical Thought from Ancient to Modern Times : Book 1
Published: 1st March 1990
Format: Paperback
Language: English
Number of Pages: 432
Audience: Professional and Scholarly
Publisher: Oxford University Press USA
Country of Publication: GB
Dimensions (cm): 28.3 x 17.1 x 10.1
Weight (kg): 0.5
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