Mancosu - Philosophy of Mathematical Practice (Oxford, 2008).pdf

78 kenneth mandersThe Euclidean Diagram Due to its already somewhat wide distribution,and its role in guiding subsequent work, I have chosen to give the text in itsoriginal 1995 form that was distributed.BibliographyArtmann, Benno (1999), Euclid: the Creation of Mathematics (Berlin: Springer-Verlag).Ball, W. W.Rouse (1892), Mathematical Recreations and Essays (New York: MacMillan).Behboud, Ali(1994), ‘Greek Geometrical Analysis’, Centaurus, 37, 52–86.Bergren, J.L.andvan Brummelen, Glen(2000), ‘The Role and Development ofGeometric Analysis and Synthesis in Ancient Greece and Medieval Islam.’, in PatrickSuppes, Julius Moravscik, and Henry Mendell (eds.), Ancient and Medieval Traditionsin the Exact Sciences (Stanford: CSLI).Berkeley, George(1710), A Treatise Concerning the Principles of Human Knowledge.Beth, EvertW.(1956), ‘Über Locke’s ‘‘Allgemeines Dreieck’’ ’, Kant-Studien, 48,361–380.Bôcher, Maxime(1901), ‘The Theory of Linear Dependence’, Annals of Mathematics(second series), 2, 81–86.Euclid (anc.), The Thirteen Books of Euclid’s Elements.Goodwin, William (2003), Kant’s Philosophy of Geometry, Ph.D. dissertation, Berkeley.Hahn, Hans(1980), ‘The Crisis in Intuition’, in Empiricism, Logic and Mathematics:Philosophical Papers (Dordrecht: Reidel), 73–102.Harari, Orna(2003), ‘The Concept of Existence and the Role of Constructions inEuclid’s Elements’ in Arch. Hist. Exact Sci., 57, 1–23.Hartshorne, Robin (2000), Geometry: Euclid and Beyond (Berlin: Springer-Verlag).Hilbert, David (1899/1902), Foundations of Geometry (La Salle: Open Court).Hintikka, Jaako (1967), ‘Kant’s mathematical method’, The Monist, 51, 352–375.Lloyd, G.E.R. (1996), Adversaries and Authorities (Cambridge: Cambridge UniversityPress).Macbeth, Danielle (2007), ‘Diagrammatic Reasoning in Euclid’s Elements’, manuscript.Manders, Kenneth (1995), ‘Diagram Contents and Representational Granularity’, inJ. M. Seligman and D. Westerstahl (eds.), Logic, Language and Computation (Stanford:CSLI).(2007), ‘The Euclidean Diagram’, this volume.Miller, Nathaniel (2001), A Diagrammatic Formal System for Euclidean Geometry, Ph.D.thesis, Cornell. (2007), Euclid and his Twentieth Century Rivals. Diagrams in the Logic of EuclideanGeometry (Stanford: CSLI).Mumma, John (2006), Intuition Formalized, Ph.D.thesis,CMU.(2007), Proofs, Pictures and Euclid, manuscript.