Between Tradition and Innovation

Gregorio a San Vicente and the Flemish Jesuit Mathematics School

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Author: Ad J. Meskens
In Between Tradition and Innovation, Ad Meskens traces the profound influence of a group of Flemish Jesuits on the course of mathematics in the seventeenth century. Using manuscript evidence, this book argues that one of the Flemish mathematics school’s professors, Gregorio a San Vicente (1584–1667), had developed a logically sound integration method more than a decade before the Italian mathematician Bonaventura Cavalieri. Although San Vincente’s superiors refused to grant him permission to publish his results, his methods went on to influence numerous other mathematicians through his students, many of whom became famous mathematicians in their own right. By carefully tracing their careers and outlining their biographies, Meskens convincingly shows that they made a number of ground-breaking contributions to fields ranging from mathematics and mechanics to optics and architecture.

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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
All interested in the history of the Jesuits and in the history of mathematics, in particular the early history of infinitesimal calculus.