Mathematizing Space: The Objects of Geometry from Antiquity to the Early Modern Age (Trends in the History of Science)

This book collects the papers of the conference held in Berlin, Germany, 27-29 August 2012, on 'Space, Geometry and the Imagination from Antiquity to the Modern Age'. The conference was a joint effort by the Max Planck Institute for the History of Science (Berlin) and the Centro die Ricerca Matematica Ennio De Giorgi (Pisa). This Book Brings Together Papers Of The Conference On 'space, Geometry And The Imagination From Antiquity To The Modern Age' Held In Berlin, Germany, 27-29 August 2012. Focusing On The Interconnections Between The History Of Geometry And The Philosophy Of Space In The Pre-modern And Early Modern Age, The Essays In This Volume Are Particularly Directed Toward Elucidating The Complex Epistemological Revolution That Transformed The Classical Geometry Of Figures Into The Modern Geometry Of Space. Contributors: Graciela De Pierris Franco Farinelli Michael Friedman Daniel Garber Jeremy Gray Gary Hatfield Andrew Janiak Douglas Jesseph Alexander Jones Henry Mendell David Rabouin Vincenzo De Risi: Introduction -- Henry Mendell: What’s Location Got To Do With It? Place, Space, And The infinite In Classical Greek Mathematics -- Jeremy Gray: A Note On Lines And Planes In Euclid’s Geometry -- Alexander Jones: Theon Of Smyrna And Ptolemy On Celestial Modelling In Two and Three Dimensions -- David Rabouin: Proclus’ Conception Of Geometric Space And Its Actuality -- Franco Farinelli: Subject, Space, Object: The Birth Of Modernity -- Gary Hatfield: On Natural Geometry And Seeing Distance Directly In descartes -- Douglas Jesseph: Hobbes’s Theory Of Space -- Andrew Janiak: Mathematics And Infinity In Descartes And Newton -- Daniel Garber: Leibniz’s Transcendental Aesthetic -- Graciela De Pierris: Hume’s Skepticism And Inductivism Concerning Space And geometry -- Michael Friedman: Kant On Geometry And Experience. Edited By Vincenzo Risi. Front Matter....Pages i-ix Introduction....Pages 1-13 What’s Location Got to Do with It? Place, Space, and the Infinite in Classical Greek Mathematics....Pages 15-63 A Note on Lines and Planes in Euclid’s Geometry....Pages 65-73 Theon of Smyrna and Ptolemy on Celestial Modelling in Two and Three Dimensions....Pages 75-103 Proclus’ Conception of Geometric Space and Its Actuality....Pages 105-142 Subject, Space, Object: The Birth of Modernity....Pages 143-155 On Natural Geometry and Seeing Distance Directly in Descartes....Pages 157-191 Hobbes’s Theory of Space....Pages 193-208 Mathematics and Infinity in Descartes and Newton....Pages 209-230 Leibniz’s Transcendental Aesthetic....Pages 231-254 HumeHume ’s Skepticism and Inductivism Concerning Space and Geometry....Pages 255-274 Kant on Geometry and Experience....Pages 275-309 Back Matter....Pages 311-318