The Origins of the Infinitesimal Calculus
Dover Publications, 1987 - 304 páginas
Few among the numerous studies of calculus offer the detailed and fully documented historical perspective of this text, particularly in regard to the geometric techniques and methods developed prior to the work of Newton and Leibniz. Because the contributions of these and other mathematicians arose from a centuries-long struggle to investigate area, volume, tangent, and arc by purely geometric methods, the author begins by establishing background mathematical concepts. Dr. Baron provides 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 offer an illuminating discussion of 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. An Epilogue concludes the text with a brief chronological survey of the early work of Newton and Leibniz, based on material drawn from original manuscripts. Book jacket.
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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 elements equal equation established Euclid example Fermat finite formed by rotating Galileo geometric geometric series 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 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 techniques theorem tion Torricelli treatise triangle Valerio velocity volumes of solids Wallis