This book is a detailed study of Gottfried Wilhelm Leibniz's creation of calculus from 1673 to the 1680s. We examine and analyze the mathematics in several of his early manuscripts as well as various articles published in the Acta Eruditorum. It studies some of the other lesser known "calculi" Leibniz created such as the Analysis Situs, delves into aspects of his logic, and gives an overview of his efforts to construct a Universal Characteristic, a goal that has its distant origin in the Ars Magna of the 13th century Catalan philosopher Raymond Llull, whose work enjoyed a renewed popularity in the century and a half prior to Leibniz.This book also touches upon a new look at the priority controversy with Newton and a Kuhnian interpretation of the nature of mathematical change. This book may be the only integrated treatment based on recent research and should be a thought-provoking contribution to the history of mathematics for scholars and students, interested in either Leibniz's mathematical achievement or general issues in the field.
Evolution or Revolution in Mathematics: The Case of Leibniz; Some Issues Raised by Seventeenth Century Mathematics; Isaac Barrow, a Foil to Leibniz; A Young Central European Polymath between the Scholastics and the Moderns; First Steps in Mathematics (1673 - 1675); The Creation of Calculus (1676 - 1686); Logic; The Universal Characteristic; The Baroque Cultural Context; Epilogue; Some Concluding Remarks on Mathematical Change; Appendices: A: A Transmutation Theorem of Leibniz; B: Leibniz's Series Quadrature of a Conic; C: Syllogistic Logic; D: The Vis Viva Controversy; E: Some Applications of Conic Sections, Mechanical Curves and Neusis to Greek Geometry.