Further Advances in France and Italyĥ.1 The Arithmetisation of Integration Methodsĥ.6 The Link Between Differential and Integral Processesĥ.7 Evangelista Torricelli : Tangent and QuadratureĬhapter 6. Infinitesimals and Indivisibles in the Early Seventeenth CenturyĤ.4 Grégoire de Saint-Vincent (1584-1667)Ĭhapter 5. Some Centre of Gravity Determinations in the Later Sixteenth CenturyĬhapter 4. The Transition to Western EuropeĢ.4 The Continuum, Indivisibles and InfinitesimalsĢ.7 The Function Concept in the Fourteenth and Fifteenth CenturiesĬhapter 3. Table of Contentsġ.1 The Influence of Greek Mathematics in the Seventeenth Centuryġ.2 A Brief Chronology of Greek Mathematicsġ.3 Early Greek Mathematics and the Physical Worldġ.4 The Axiomatisation of Greek Mathematicsġ.9 Curves, Normals, Tangents and CurvatureĬhapter 2. The publication is a vital source of information for historians, mathematicians, and researchers interested in infinitesimal calculus. The book reviews the infinitesimal methods in England and Low Countries and rectification of arcs. Topics include the link between differential and integral processes, concept of tangent, first investigations of the cycloid, and arithmetization of integration methods. The manuscript then examines infinitesimals and indivisibles in the early 17th century and further advances in France and Italy.

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 publication first ponders on Greek mathematics, transition to Western Europe, and some center of gravity determinations in the later 16th century. GoodReads rates it 3.83, but I’m only giving it two stars.The Origins of Infinitesimal Calculus focuses on the evolution, development, and applications of infinitesimal calculus. I was left rather disappointed with this book. “Infinitely small numbers” greater than zero do not exist, and calculus did not have a rigorous foundation until the work of Cauchy and Weierstrass in the 1800s. And, of course, the critics of Cavalieri and Wallis were actually quite correct. Nor does he explain the link between defending Aristotle and defending the doctrine of Transubstantiation. There is not a word about their struggle with the Dominicans for intellectual leadership of the Catholic Church (although this played a major part in the Galileo saga).

However, Alexander does not fully explain the Jesuits’ actions. There are also some errors, noted by Judith Grabiner in her review for the MAA.Īlexander portrays the Jesuits as the “bad guys,” suppressing the idea of “indivisibles,” even though interesting and useful mathematical results can be obtained by using them. As a history of pre-calculus, that’s rather incomplete. This book concentrates on the “indivisibles” of Bonaventura Cavalieri and the “infinitesimals” of John Wallis (the man who introduced the ∞ symbol). I recently read Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World by Amir Alexander. Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World by Amir Alexander (2014)

Infinitesimals book