The Origins of the Infinitesimal CalculusDover 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. |
Índice
THE TRANSITION TO WESTERN EUROPE | 60 |
SOME CENTRE OF GRAVITY DETERMINATIONS IN | 90 |
INFINITESIMALS AND INDIVISIBLES IN THE EARLY | 108 |
Direitos de autor | |
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algebraic angle Archimedes arithmetic Arithmetica axis Barrow Cavalieri centre of gravity circle circular circular sector concept considered construction correspondence curve cycloid cylinder Descartes determination diameter differential ductus dy/dx equal equation established Euclid example Fermat finite formed by rotating Galileo geometric given Greek mathematics Grégoire Grégoire de Saint-Vincent Gregory Hence Hofmann Huygens hyperbola Ibid idea infinitesimal calculus Isaac Barrow James Gregory Kepler Leibniz Math mathematicians Mersenne motion Newton notation Oeuvres de Fermat ordinate Oresme parabola parallel parallelogram Paris Pascal plane problem 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 Valerio velocity volumes of solids Wallis