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.

• PrefaceAbbreviationsIntroduction: The Low Countries, Spain, and Europe1 The Jesuits in the Netherlands1 The College and Its School of Mathematics1 Schools in Antwerp2 Jesuit Educational Policy3 Mathematics in the Jesuit Curriculum4 The Academy of Mathematics at the Collegio Romano5 The College of Leuven6 The Antwerp College in the Sixteenth Century7 The Antwerp College in the Seventeenth Century8 The School of Mathematics9 Michiel Coignet and the Jesuits2 The Seventeenth Century: The Dawn of a New Era1 Conic Sections2 Squaring the Circle the Archimedean Way3 The Humble Beginnings of Infinitesimal Calculus4 Infinitesimals: The Keplerian Revolution5 Cavalieri’s Indivisibles6 The Jesuits and Indivisibles3 Francisco de Aguilón and Mathematical Optics1 Opticorum libri sex2 Aguilón’s Catoptrica Manuscript4 Gregorio a San Vicente: An Ignored Genius1 A Tragic Life2 Mathematical Oeuvre3 The Mechanics Theses5 The Creative Antwerp–Leuven Period1 Trisection of an Angle2 Mean Proportionals3 Properties of Conic Sections6 Exhaustion: The Road to Infinitesimals1 Sequences and Series2 The Exhaustion Method3 San Vicente’s Use of Infinitesimals4 The Cavalieri Dispute7 Infinitesimal Calculus at Work1 The Hyperbola2 Calculation of the Volume of Ductus Figures3 Lateral Area of the Ungula cylindrica and Relations between Ductus Figures8 Rome and Prague, the Final Discoveries1 The Missives to Rome2 The Chartae Romanae3 San Vicente’s Legacy4 Conclusion9 The Erroneous Circle Quadrature10 Joannes della Faille and the Beginning of Projective Geometry1 An Itinerant Life2 Conic Sections3 De centro gravitatis11 The Antwerp Students1 Philip Nuyts2 Ignatius Derkennis3 Other Students12 The Leuven Students1 Theodorus Moretus2 Jan Ciermans3 Willem Boelmans4 Willem Hesius5 Other Students13 The Later Disciples1 Andreas Tacquet2 Gilles-François de Gottignies3 Alphonse Antonius de Sarasa14 The Jesuit Architects1 Ad maiorem Dei gloria2 Descensus ad inferos15 The Influence of the School of MathematicsAppendix 1: Chronology of San Vicente’s ManuscriptsAppendix 2: Students of the School of Mathematics after 1625BibliographyIndex