Contents. Foreword, by Ivor Grattan-Guinness... Preface... Illustrations... History and Geography...
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1 Contents Foreword, by Ivor Grattan-Guinness... v Preface... Illustrations... vii xv History and Geography... xvii 1 Life and Works Biography Lucca Bologna: Studies Pisa Turin The Bologna Affair Catania Parma Afterward Overview of Pieri s Research Algebraic and Differential Geometry, Vector Analysis Foundations of Geometry Arithmetic, Logic, and Philosophy of Science Conclusion Others Foundations of Geometry Historical Context Hypothetical-Deductive Systems Projective Geometry Inversive Geometry Absolute and Euclidean Geometry Point and Motion Point and Sphere Pieri s Point and Sphere Memoir Point and Sphere... I Orthogonality... II Points Internal or External... III Theorems on Rotations... IV Relations Smaller Than and Larger Than... V Parallelism... VI
2 xii Contents 3.7 Products of Isometries... VII Ordering and Senses... VIII Appendix Historical and Critical Remarks Pieri s Point and Motion Monograph Hilbert s Foundations of Geometry Veblen s 1904 System of Axioms Pieri s Point and Sphere Memoir The Definitions The Postulates Building Geometry Other Significant Features Questions Answered New Questions Foundations of Arithmetic Historical Background The Real Number System The Natural Numbers Pieri s Investigation of the Natural Number System Pieri s 1907 Axiomatization Axiomatizing Natural Number Arithmetic Dedekind Peano Padoa Pieri Reception of Pieri s Axiomatization Pieri s Impact Peano and Pieri Peano s Background Peano s Early Career Peano s Ascent Pieri and the Peano School Peano s Decline Pieri and Tarski Foundations of the Geometry of Solids Tarski s System of Geometry What Is Elementary Geometry? Basing Geometry on a Single Undefined Relation Pieri s Legacy Peano and Pieri Pieri and Tarski In the Shadow of Giants In the Future
3 Contents xiii 6 Pieri s Works Differential Geometry Algebraic Geometry Beginnings Tangents and Normals Enumerative Geometry Birational Transformations Vector Analysis Foundations of Geometry Projective Geometry Elementary Geometry Inversive Geometry Arithmetic, Logic, and Philosophy of Science Letters Further Works Translations, Edited and Revised Reviews Lecture Notes Collections Memorials to Pieri Bibliography Permissions Index
4
5 Illustrations Portraits Mario Pieri...frontispiece, 24, 130 Augusto Righi... 9 Silvio Pieri and his daughter... 9 Enrico Betti Luigi Bianchi Ulisse Dini Enrico D Ovidio Federigo Enriques Mario Pieri Eugenio Bertini Luigi Cremona Salvatore Pincherle Vito Volterra Virginia Pieri and Paolo Anastasio Pieri s sister Gemma and her sons Pieri and relatives Angiolina Pieri Beppo Levi Corrado Segre Cesare Burali-Forti Felix Klein Mario Pieri Moritz Pasch Gino Fano Giuseppe Veronese G. K. C. von Staudt Theodor Reye August F. Möbius B. L. van der Waerden Gino Loria David Hilbert Oswald Veblen Hermann Grassmann Richard Dedekind Giuseppe Peano , 339 Bertrand Russell Alfred Tarski (2 portraits) Adolf Lindenbaum
6 xvi Illustrations Maps Some Italian cities... xviii Italy s regions...xix Telescopic projections of the planet Mars: Mario Pieri, Figures Scuola Normale Superiore, Pisa Pieri s doctoral thesis Military Academy, Turin Military Academy personnel, Turin Pieri s first Turin Academy of Sciences paper University of Catania Pieri became an editor of the Gioenia Atti Announcement of Pieri s promotion Pieri s 1922 interment in Lucca Pieri s tomb Pieri s definition of cyclic order Pieri s definitions of collinearity Pieri s definition of betweenness Pieri s Point and Sphere memoir, first page Hilbert s Foundations of Geometry Veblen s System of Axioms for Geometry Peano s Principles of Arithmetic Pieri s On the Axioms of Arithmetic Peano s Formulario
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