Cover -- Copyright page -- Title Page -- Introduction -- Contents -- Ancient Mathematics -- Foreword -- Sherlock Holmes in Babylon R. CREIGHTON BUCK -- Words and Pictures: New Light on Plimpton 322 ELEANOR ROBSON -- 1 Introduction -- 2 Turning the tables on generating functions -- 3 Circling round trigonometry -- 4 Words count too: reciprocal pairs -- 4 Words count too:reciprocal pairs -- 4 Words count too:reciprocal pairs -- References -- Mathematics, 600 B.C.-600 A.D. MAX DEHN -- 1 600 B.C.-400 B.C. -- 2 400 B.C.-300 B.C. -- 3 300 B.C.-200 B.C. -- 4 200 B.C.-600 A.D. -- Diophantus of Alexandria J. D. SWIFT -- 1 Introduction -- 2 The Arithmetic -- 3 Notation -- 4 Diophantine algebra -- 5 Indeterminate problems -- 6 An approximation problem -- 7 Transmission of Diophantus -- Bibliography -- Hypatia of Alexandria A. W. RICHESON -- Hypatia and Her Mathematics MICHAEL A. B. DEAKIN -- 1 Introduction -- 2 The historical background -- 3 The primary sources -- 4 Life and legend -- 5 Hypatia's Philosophy -- 6 Hypatia's Mathematics -- 7 Apollonius' Conics -- 8 The Astronomical Canon -- 9 Diophantus' Arithmetic -- 10 The astrolabe -- 11 The Hydroscope -- 12 Assessment -- References -- The Evolution of Mathematics in Ancient China FRANK SWETZ -- 1 Legend and fact -- 2 The systematization of early Chinese mathematics -- 3 Trends in Chinese algebraic thought -- 4 Conclusions -- Notes -- Liu Hui and the FirstGolden Age of Chinese Mathematics PHILIP D. STRAFFIN, JR. -- 1 Introduction -- 2 Chinese calculation in the first century A.D. -- 3 Nine Chapters on the Mathematical Art -- 4 Liu Hui's commentary -- 5 The Sea Island Mathematical Manual -- 6 The calculation of pi -- 7 The volume of pyramids -- 8 The volume of a sphere -- 9 Conclusion -- References -- Number Systems of the North American Indians W. C. EELLS -- 1 Principles of formation.

2 Systems of numeration -- 3 Miscellaneous points -- 4 Notes -- References -- The Number System of the Mayas A. W. RICHESON -- 1 Methods of numeration -- 2 Discussion of the numbers -- 3 Conclusion -- References -- Before The Conquest MARCIA ASCHER -- 1 Introduction -- 2 The Incas -- 3 The Maya -- 4 Conclusion -- References -- Afterword -- Medieval and Renaissance Mathematics -- Foreword -- The Discovery of the Series Formula for pi byLeibniz, Gregory and Nilakantha RANJAN ROY -- 1 Introduction -- 2 Gottfried Wilhelm Leibniz (1646-1716) -- 3 James Gregory (1638-1675) -- 4 Kerala Gargya Nilakantha (c. 1450-c. 1550) -- 5 Independence of these discoveries -- References -- Ideas of Calculus in Islam and India VICTOR J. KATZ -- 1 Introduction -- 2 Sums of integer powers in eleventh-century Egypt -- 3 Trigonometric series in sixteenth-century India -- 4 Conclusion -- References -- Was Calculus Invented in India? DAVID BRESSOUD -- 1 Introduction -- 2 Greek origins of trigonometry -- 3 Trigonometry in classical India -- 4 The power series expansion for sine -- 5 Conclusion -- Bibliography -- An Early Iterative Method for the Determination of sin 1 FARHAD RIAHI -- 1 Background -- 2 Al-Kashi's determination of sin 1 -- References -- Leonardo of Pisa and his Liber Quadratorum R.B. McCLENON -- The Algorists vs. the Abacists: An Ancient Controversy on the Use of Calculators BARBARA E. REYNOLDS -- Sidelights on the Cardan-Tartaglia Controversy MARTIN A. NORDGAARD -- Reading Bombelli's x-purgated Algebra ABRAHAM ARCAVI and MAXIM BRUCKHEIMER -- 1 Bombelli's method -- 2 Bombelli's method and continued fractions -- 3 Bombelli's method in the classroom -- 4 Final comments -- References -- The First Work on Mathematics Printed in the New World DAVID EUGENE SMITH -- 1 General description -- 2 Typical problems not listed under algebra.

3 Typical problems listed under algebra -- Afterword -- The Seventeenth Century -- Foreword -- An Application of Geography to Mathematics: History of the Integral of the Secant V. FREDERICK RICKEY and PHILIP M. TUCHINSKY -- Some Historical Notes on the Cycloid E. A. WHITMAN -- 1 Introduction -- 2 Early history of the curve -- 3 The work of Roberval -- 4 Construction of the tangent -- 5 Pascal's mathematical contest -- 6 The brachistochrone problem -- References -- Descartes and Problem-Solving JUDITH GRABINER -- Introduction -- A first look at Descartes' Geometry -- The background of Descartes' Geometry -- Descartes' method in action -- Beyond the Greeks -- The power of Descartes' methods: tangents and equations -- Conclusion -- References -- René Descartes' Curve-Drawing Devices: Experiments in the Relations Between Mechanical Motion and Symbolic Language DAVID DENNIS -- 1 Introduction -- 2 Apollonius regained -- 3 Conchoids generalized from hyperbolas -- 4 Conclusion -- References -- Certain Mathematical Achievements of James Gregory MAX DEHN and E. D. HELLINGER -- 1 The ``Taylor's series'' -- 2 The interpolation formula -- 3 The binomial series -- 4 Gregory's Vera Quadratura -- 5 Conclusion -- References -- The Changing Concept of Change: The Derivative from Fermat to Weierstrass JUDITH V. GRABINER -- The seventeenth-century background -- Finding maxima, minima, and tangents -- Tangents, areas, and rates of change -- Differential equations, Taylor series, and functions -- Lagrange and the derivative as a function -- Definitions, rigor, and proofs -- Historical development versus textbook exposition -- References -- The Crooked Made Straight: Roberval and Newton on Tangents PAUL R. WOLFSON -- 1 Introduction -- 2 What Roberval knew -- 3 What Newton thought -- 4 Conclusion -- References.

On the Discovery of the Logarithmic Series and Its Development in England up to Cotes JOSEF EHRENFRIED HOFMANN -- 1 Nicolas Mercator (1620-1687) -- 2 James Gregory (1638-1675) -- 3 Isaac Newton (1642-1727) -- 4 The methodological expansion -- References -- Isaac Newton: Man, Myth, and Mathematics V. FREDERICK RICKEY -- 1 Newton's education and public life -- 2 Newton's mathematical readings -- 3 Newton's works -- 4 Conclusion -- References -- Reading the Master: Newton and the Birth of Celestial Mechanics BRUCE POURCIAU -- Newton as an Originator of Polar Coordinates C. B. BOYER -- Newton's Method for Resolving Affected Equations CHRIS CHRISTENSEN -- Newton's method for approximating roots -- Resolution of affected equations -- Extensions -- Appendix I. Portion of the Epistola prior -- Appendix II. Portion of the Epistola posterior -- References -- A Contribution of Leibniz to the History of Complex Numbers R. B. McCLENON -- Functions of a Curve: Leibniz's Original Notion of Functions and Its Meaning for the Parabola DAVID DENNIS and JERE CONFREY -- Afterword -- The Eighteenth Century -- Foreword -- Brook Taylor and the Mathematical Theory of Linear Perspective P. S. JONES -- Was Newton's Calculus a Dead End? The Continental Influence of Maclaurin's Treatise of Fluxions JUDITH GRABINER -- 1 Introduction -- 2 The standard picture -- 3 The nature of Maclaurin's Treatise of Fluxions -- 4 The social context: The Scottish Enlightenment -- 5 Maclaurin's Continental reputation -- 6 Maclaurin's mathematics and its importance -- 7 Other examples of Maclaurin's mathematical influence -- 8 Why a Treatise of Fluxions? -- 9 Why the traditional view? -- 10 Some final reflections -- References -- Discussion of Fluxions: from Berkeley to Woodhouse FLORIAN CAJORI -- The Bernoullis and the Harmonic Series WILLIAM DUNHAM.

Leonhard Euler 1707-1783 J. J. BURCKHARDT -- 1 The legacy of Euler's writings -- 2 Number theory -- 3 Analysis -- 4 ``Applied'' mathematics (physics) -- 5 Astronomy -- 6 Correspondence -- 7 Postscript -- Reference -- The Number e J. L. COOLIDGE -- 1 The Greek beginning -- 2 Grégoire de St. Vincent -- 3 The introduction of logarithms -- 4 Mercator, Newton, Leibniz -- 5 Leonhard Euler -- References -- Euler's Vision of a General Partial Differential Calculus for a Generalized Kind of Function JESPER LÜTZEN -- 1 The algebraic function concept -- 2 Euler's generalized functions -- 3 Euler's vision of a generalized calculus -- 4 The fate of Euler's vision -- 5 Concluding remarks -- References -- Euler and the Fundamental Theorem of Algebra WILLIAM DUNHAM -- Epilogue -- References -- Euler and Differentials ANTHONY P. FERZOLA -- Euler and the 18th century -- Differentials as absolute zeros -- Computations with elementary functions -- The total differential -- Differentials in multiple integrals -- Conclusion -- References -- Euler and Quadratic Reciprocity HAROLD M. EDWARDS -- Afterword -- Index -- About the Editors.