Between Tradition and Innovation

Ad Meskens (1962), Ph.D., AP University College Antwerp, is a lecturer on the didactics of mathematics. He has published extensively on the history of mathematics in the Low Countries including Mathematics in a Commercial Metropolis (Springer, 2013). He is an active member of the Flemish Association of Mathematics Teachers.

Preface

Abbreviations



Introduction: The Low Countries, Spain, and Europe

 1 The Jesuits in the Netherlands



1 The College and Its School of Mathematics

 1 Schools in Antwerp

 2 Jesuit Educational Policy

 3 Mathematics in the Jesuit Curriculum

 4 The Academy of Mathematics at the Collegio Romano

 5 The College of Leuven

 6 The Antwerp College in the Sixteenth Century

 7 The Antwerp College in the Seventeenth Century

 8 The School of Mathematics

 9 Michiel Coignet and the Jesuits



2 The Seventeenth Century: The Dawn of a New Era

 1 Conic Sections

 2 Squaring the Circle the Archimedean Way

 3 The Humble Beginnings of Infinitesimal Calculus

 4 Infinitesimals: The Keplerian Revolution

 5 Cavalieri’s Indivisibles

 6 The Jesuits and Indivisibles



3 Francisco de Aguilón and Mathematical Optics

 1 Opticorum libri sex

 2 Aguilón’s Catoptrica Manuscript



4 Gregorio a San Vicente: An Ignored Genius

 1 A Tragic Life

 2 Mathematical Oeuvre

 3 The Mechanics Theses



5 The Creative Antwerp–Leuven Period

 1 Trisection of an Angle

 2 Mean Proportionals

 3 Properties of Conic Sections



6 Exhaustion: The Road to Infinitesimals

 1 Sequences and Series

 2 The Exhaustion Method

 3 San Vicente’s Use of Infinitesimals

 4 The Cavalieri Dispute



7 Infinitesimal Calculus at Work

 1 The Hyperbola

 2 Calculation of the Volume of Ductus Figures

 3 Lateral Area of the Ungula cylindrica and Relations between Ductus Figures



8 Rome and Prague, the Final Discoveries

 1 The Missives to Rome

 2 The Chartae Romanae

 3 San Vicente’s Legacy

 4 Conclusion



9 The Erroneous Circle Quadrature



10 Joannes della Faille and the Beginning of Projective Geometry

 1 An Itinerant Life

 2 Conic Sections

 3 De centro gravitatis



11 The Antwerp Students

 1 Philip Nuyts

 2 Ignatius Derkennis

 3 Other Students



12 The Leuven Students

 1 Theodorus Moretus

 2 Jan Ciermans

 3 Willem Boelmans

 4 Willem Hesius

 5 Other Students



13 The Later Disciples

 1 Andreas Tacquet

 2 Gilles-François de Gottignies

 3 Alphonse Antonius de Sarasa



14 The Jesuit Architects

 1 Ad maiorem Dei gloria

 2 Descensus ad inferos



15 The Influence of the School of Mathematics



Appendix 1: Chronology of San Vicente’s Manuscripts



Appendix 2: Students of the School of Mathematics after 1625

Bibliography

Index