Sherlock Holmes in Babylon

Part I. Ancient Mathematics: Foreword; Sherlock Holmes in Babylon; Words and pictures: new light on Plimpton 322; Mathematics 600 BC–600 AD; Diophantus of Alexandria; Hypatia of Alexandria; Hypatia and her mathematics; The evolution of mathematics in ancient China, Liu Hui and the first golden age of Chinese mathematics; Number systems of the North American Indians; The number systems of the Mayas; Before the conquest; Afterword; Part II. Medieval and renaissance mathematics; Foreword; The discovery of the series formula for π; Ideas of calculus in Islam and India; Was calculus invented in India?; An early iterative method for the determination of sin 1º; Leonardo of Pisa and his liber quadratorum; The algorists vs. the abacists: an ancient controversy on the use of calculators; Sidelights on the Cardan-Tartaglia controversy; Reading Bombelli's x-purgated algebra; The first work on mathematics printed in the New World; Afterword; Part III. The Seventeenth Century: Foreword; An application of geography to mathematics: history of the integral of the secant; Some historical notes on the cycloid; Descartes and problem-solving; Rene Descartes' curve-drawing devices: experiments in the relations between mechanical motion and symbolic language; Certain mathematical achievements of James Gregory; The changing concept of change: the derivative from Fermat to Weierstrauss; The crooked made straight: Roberval and Newton on tangents; On the discovery of the logarithmic series and its development in England up to Cotes; Isaac Newton: man, myth, and mathematics; Reading the master: Newton and the birth of celestial mechanics; Newton as an originator of polar coordinates; Newton's method for resolving affected equations; A contribution of Leibniz to the history of complex numbers; Functions of a curve: Leibniz's original notion of functions and its meaning for the parabola; Afterword; Part IV. The Eighteenth Century: Foreword; Brook Taylor and the mathematical theory of Linear Perspective; Was Newton's calculus a dead end? The continental influence of Maclaurin's treatise of fluxions; Discussion of fluxions: from Berkeley to Woodhouse; The Bernoulli and the harmonic series; Leonhard Euler 1707–1783; The number; Euler's vision of a general partial differential calculus for a generalized kind of function; Euler and the fundamental theorem of algebra; Euler and the differentials; Euler and quadratic reciprocity; Afterword; Index; About the editors.