The Origins of Infinitesimal Calculus
Elsevier, 09/05/2014 - 312 páginas
The Origins of Infinitesimal Calculus focuses on the evolution, development, and applications of infinitesimal calculus.
The publication first ponders on Greek mathematics, transition to Western Europe, and some center of gravity determinations in the later 16th century. Discussions focus on the growth of kinematics in the West, latitude of forms, influence of Aristotle, axiomatization of Greek mathematics, theory of proportion and means, method of exhaustion, discovery method of Archimedes, and curves, normals, tangents, and curvature. The manuscript then examines infinitesimals and indivisibles in the early 17th century and further advances in France and Italy. Topics include the link between differential and integral processes, concept of tangent, first investigations of the cycloid, and arithmetization of integration methods. The book reviews the infinitesimal methods in England and Low Countries and rectification of arcs.
The publication is a vital source of information for historians, mathematicians, and researchers interested in infinitesimal calculus.
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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 equal equation established Euclid example f Ibid Fermat finite formed by rotating Galileo geom geometric given Greek mathematics Grégoire Grégoire de Saint-Vincent Gregory Hence Hofmann Hudde Huygens hyperbola idea infinite number infinitesimal calculus Isaac Barrow 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 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 techniques theorem tion Torricelli treatise triangle Valerio velocity volumes of solids Wallis