Reading the Principia: The Debate on Newton's Mathematical Methods for Natural Philosophy from 1687 to 1736
Isaac Newton's Principia is considered one of the masterpieces in the history of science. The mathematical methods employed by Newton in the Principia stimulated much debate among his contemporaries, especially Leibniz, Huygens, Bernoulli and Euler, who debated their merits and drawbacks. Among the questions they asked were: How should natural philosophy be mathematized?; Is it legitimate to use uninterpreted symbols?; Is it possible to depart from the established Archimedean or Galilean/Huygenian tradition of geometrizing nature?; What is the value of elegance and conciseness?; What is the relation between Newton's geometrical methods and the calculus? This book explains how Newton addressed these issues, taking into consideration the values that directed the research of Newton and his contemporaries. This book will be of interest to researchers and advanced students in departments of history of science, philosophy of science, physics, mathematics and astronomy.
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Purpose of this book
The mathematical methods of the Principia
Huygens the Principia and proportion theory
Leibniz not equivalent in practice
accelerated algebra algorithm analysis analytical method Ancients applied area law attraction Bertoloni Meli body Book central forces centripetal force Cohen component conic sections constant Corollary corpuscle Correspondence curvature curve David Gregory Descartes differential calculus differential equations distance dynamics ellipse employed equal Euler fact Fatio finite fluent formula Furthermore geometrical methods geometrical representation given gravitation Halley Hermann Huygens infinitesimal instance intervals inverse cube force inverse problem inverse square force Jacopo Riccati Johann Bernoulli Keill Leibniz Lemma limit magnitudes manuscripts mathematical methods Mathematical Papers mathematicians method of fluxions natural philosophy Newton's geometrical Newton's mathematical Newton's method Newton's Principia Newtonian notation orbit perturbations Phoronomia planetary polygonal Principles problem of central proof proportional Proposition 41 Propositions 11-13 published quadrature quantities reader resisting media Scholium second edition solution symbols synthetic method tangent techniques theorem theory trajectory Translation by Whiteside triangle ultimate ratios Varignon Variorum velocity wrote
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