Mathematical Thought from Ancient to Modern Times, Vol. 1
Now available in a new three-volume paperback edition, Morris Kline's monumental work presents the major creations in mathematics from its beginnings in Babylonia and Egypt through the first few decades of the twentieth century. Organized around the central ideas of mathematical thought, as well as the men responsible for them, this comprehensive history provides a broad panorama of the development of mathematics, displaying the unity behind the disconnected branches of the discipline today....
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The major creations and developments in mathematics from the beginnings in Babylonia and Egypt through the first few decades of the twentieth century are presented with clarity and precision in this comprehensive historical study.
1Mathematics in Mesopotamia31Where Did Mathematics Begin?32Political History in Mesopotamia43The Number Symbols54Arithmetic Operations75Babylonian Algebra86Babylonian Geometry107The Uses of Mathematics in Babylonia118Evaluation of Babylonian Mathematics132Egyptian Mathematics151Background152The Arithmetic163Algebra and Geometry184Egyptian Uses of Mathematics215Summary223The Creation of Classical Greek Mathematics241Background242The General Sources253The Major Schools of the Classical Period274The Ionian School285The Pythagoreans286The Eleatic School347The Sophist School378The Platonic School429The School of Eudoxus4810Aristotle and His School514Euclid and Apollonius561Introduction562The Background of Euclid's Elements573The Definitions and Axioms of the Elements584Books I to IV of the Elements605Book V: The Theory of Proportion686Book VI: Similar Figures737Books VII, VIII, and IX: The Theory of Numbers778Book X: The Classification of Incommensurables809Books XI, XII, and XIII: Solid Geometry and the Method of Exhaustion8110The Merits and Defects of the Elements8611Other Mathematical Works by Euclid8812The Mathematical Work of Apollonius895The Alexandrian Greek Period: Geometry and Trigonometry1011The Founding of Alexandria1012The Character of Alexandrian Greek Mathematics1033Areas and Volumes in the Work of Archimedes1054Areas and Volumes in the Work of Heron1165Some Exceptional Curves1176The Creation of Trigonometry1197Late Alexandrian Activity in Geometry1266The Alexandrian Period: The Reemergence of Arithmetic and Algebra1311The Symbols and Operations of Greek Arithmetic1312Arithmetic and Algebra as an Independent Development1357The Greek Rationalization of Nature1451The Inspiration for Greek Mathematics1452The Beginnings of a Rational View of Nature1463The Development of the Belief in Mathematical Design1474Greek Mathematical Astronomy1545Geography1606Mechanics1627Optics1668Astrology1688The Demise of the Greek World1711A Review of the Greek Achievements1712The Limitations of Greek Mathematics1733The Problems Bequeathed by the Greeks1764The Demise of the Greek Civilization1779The Mathematics of the Hindus and Arabs1831Early Hindu Mathematics1832Hindu Arithmetic and Algebra of the Period A.D. 200-12001843Hindu Geometry and Trigonometry of the Period A.D. 200-12001884The Arabs1905Arabic Arithmetic and Algebra1916Arabic Geometry and Trigonometry1957Mathematics circa 130019710The Medieval Period in Europe2001The Beginnings of a European Civilization2002The Materials Available for Learning2013The Role of Mathematics in Early Medieval Europe2024The Stagnation in Mathematics2035The First Revival of the Greek Works2056The Revival of Rationalism and Interest in Nature2067Progress in Mathematics Proper2098Progress in Physical Science2119Summary21311The Renaissance2161Revolutionary Influences in Europe2162The New Intellectual Outlook2183The Spread of Learning2204Humanistic Activity in Mathematics2215The Clamor for the Reform of Science2236The Rise of Empiricism22712Mathematical Contributions in the Renaissance2311Perspective2312Geometry Proper2343Algebra2364Trigonometry2375The Major Scientific Progress in the Renaissance2406Remarks on the Renaissance24713Arithmetic and Algebra in the Sixteenth and Seventeenth Centuries2501Introduction2502The Status of the Number System and Arithmetic2513Symbolism2594The Solution of Third and Fourth Degree Equations2635The Theory of Equations2706The Binomial Theorem and Allied Topics2727The Theory of Numbers2748The Relationship of Algebra to Geometry27814The Beginnings of Projective Geometry2851The Rebirth of Geometry2852The Problems Raised by the Work on Perspective2863The Work of Desargues2884The Work of Pascal and La Hire2955The Emergence of New Principles29915Coordinate Geometry3021The Motivation for Coordinate Geometry3022The Coordinate Geometry of Fermat3033Rene Descartes3044Descartes's Work in Coordinate Geometry3085Seventeenth-Century Extensions of Coordinate Geometry3176The Importance of Coordinate Geometry32116The Mathematization of Science3251Introduction3252Descartes's Concept of Science3253Galileo's Approach to Science3274The Function Concept33517The Creation of the Calculus3421The Motivation for the Calculus3422Early Seventeenth-Century Work on the Calculus3443The Work of Newton3564The Work of Leibniz3705A Comparison of the Work of Newton and Leibniz3786The Controversy over Priority3807Some Immediate Additions to the Calculus3818The Soundness of the Calculus383List of AbbreviationsIndex
