The Origins of the Infinitesimal Calculus
Courier Corporation, 01/01/2003 - 304 páginas
Few among the numerous studies of calculus offer the detailed and fully documented historical perspective of this text. It begins with an enlightening view of the Greek, Hindu, and Arabic sources that constituted the framework for the development of infinitesimal methods in the seventeenth century. Subsequent chapters discuss the arithmetization of integration methods, the role of investigation of special curves, concepts of tangent and arc, the composition of motions, and the developing link between differential and integral processes. Significant changes in proof structure and presentation are considered in relation to the formulation of rules for the construction of tangents and quadrature of curves. 1969 edition.
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algebraic angle Archimedes arithmetic Arithmetica axis Barrow base Cavalieri Cavalierian centre of gravity circle circular circular sector concept considered construction correspondence curve cycloid cylinder Descartes determination diameter differential ductus dy/dx edition elements equal equation established Euclid example Fermat finite formed by rotating Galileo geometric given Greek mathematics Gregoire Gregory Hence Hofmann Huygens hyperbola Ibid idea infinite number infinitesimal calculus Isaac Barrow Isaac Newton James Gregory Kepler Leibniz Math mathematicians Mersenne motion Newton notation Oeuvres de Fermat ordinate Oresme parabola parallel parallelogram Paris Pascal perpendicular plane problem processes proof structure Prop quadrature quantity radius rectangle reductio reductio ad absurdum relation Roberval Saint-Vincent Schooten segment seventeenth century Simon Stevin Sluse solid formed solids of revolution space spiral square Stevin straight line surface tangent method theorem tion Torricelli treatise triangle Unabridged republication Valerio velocity volumes of solids Wallis
Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century
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