The Origins of the Infinitesimal Calculus (Dover Classics of Science and Mathematics)

304 Pages Indexed. Previous owner has done underlining, marginal notes, and scribbling throughout with personal comments. The infinitesimal calculus has been the principal tool in the exploitation of the earth's resources, the charting of the heavens and the building of modern technology. Applications occur wherever there exist measurable phenomena: gravitation, heat, light, sound, electricity, magnetism and radio waves. While the importance of calculus as a mathematical tool has produced numerous studies of the subject, few provide the detailed, fully documented historical perspective of the present volume. In particular, it offers a thorough study of the geometric techniques and methods developed in the seventeenth century prior to the work of Newton and Leibniz. Since the contributions of these and other mathematicians arose out of the centuries-long struggle to investigate area, volume, tangent and arc by purely geometric methods, Dr. Baron begins by establishing background mathematical concepts from Greek, Hindu and Arabic sources. It was these concepts which constituted the framework for the development of infinitesimal methods in the 17th century by Kepler, Galileo and Cavalieri. Later 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 the quadrature of curves. The Epilogue consists of a brief chronological survey of the early work of Newton and Leibniz, based on material drawn from original manuscripts. Much of this material has not been available in English before, or has been scattered among research journals and not readily available. This book, now available for the first time in paperback, makes it easily accessible, in the context of a thoroughly mathematical account of the development of infinitesimal methods.