The Origins of the Infinitesimal Calculus

Download or read book The Origins of the Infinitesimal Calculus written by Margaret E. Baron and published by . This book was released on 1987 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.