Cover -- Half-title -- Series-title -- Title -- Copyright -- Dedication -- Contents -- Preface -- Abbreviations -- GREEK AUTHORS -- ROMAN AUTHORS -- DOCUMENTARY SOURCES -- OTHER ABBREVIATIONS -- NOTE ON GENDER -- The Greek alphabet -- Note on the FIgures -- Introduction -- THE STRUCTURE OF SCIENTIFIC REVOLUTIONS -- THE MODULARITY OF MIND -- PLAN OF THE BOOK -- A specimen of Greek mathematics -- CHAPTER 1 The lettered diagram -- PLAN OF THE CHAPTER -- 1 THE MATERIAL IMPLEMENTATION OF DIAGRAMS -- 1.1 The media available for diagrams -- 1.2 Drawing and looking -- 2 PRACTICES OF THE LETTERED DIAGRAM -- 2.1 The mutual dependence of text and diagram -- 2.1.1 Fixation of reference -- 2.1.2 The role of text and diagram for derivations -- 2.1.3 The diagram organises the text -- 2.1.4 The mutual dependence of text and diagram: a summary -- 2.2 Diagrams as metonyms of propositions -- 2.2.1 Speaking about diagrams -- 2.2.2 Diagrams and the individuation of propositions -- 2.2.3 Diagrams as metonyms of propositions: summary -- 2.3 The semiotic situation -- 2.3.1 The semiotics of letters -- 2.3.2 The semiotics of diagrams -- 2.4 The practices of the lettered diagram: a summary -- 3 CONTEXTS FOR THE EMERGENCE OF THE LETTERED DIAGRAM -- 3.1 Non-mathematical contexts for the lettered diagram -- 3.1.1 Contexts of the diagram -- 3.1.2 Contexts of letters as used in the lettered diagram -- 3.2 Mathematical non-verbal contexts -- 3.2.1 The abacus in Greek mathematics -- 3.2.2 Planetaria in Greek mathematics -- 4 SUMMARY -- CHAPTER 2 The pragmatics of letters -- PLAN OF THE CHAPTER -- 1 THE ORIGINS OF THE PRACTICES -- 1.1 A preliminary description -- 1.2 Quantitative results -- 1.3 Self-regulating conventionality: the suggestion -- 1.4 Self-regulating conventionality -- 2 THE IMPLIMCATIONS OF THE PRACTICES -- 2.1 The role of visualisation.

2.2 The drawing of the diagram -- 2.3 'Memory' and many-lettered names -- 3 SUMMARY -- CHAPTER 3 The mathematical lexicon -- INTRODUCTION AND PLAN OF THE CHAPTER -- 1 DEFINITIONS: WHAT THEY DO AND WHAT THEY DON'T -- 1.1 What is a definition? -- 2.2 How do definitions appear? -- 1.3 What is not defined? -- 1.4 What don't definitions do? -- 1.5 Summary -- 2 THE SHAPE OF THE LEXICON -- 2.1 Description -- 2.2 The one-concept-one-word principle -- 2.3 Holistic nature of the lexicon -- 2.4 Smaller or local lexica -- 2.4.1 Logical connectors -- 2.4.2 On floating bodies -- 2.5 Compartmentalised nature of the lexicon -- 2.6 Summary -- 3 COMPARATIVE REMARKS -- 4 THE SHAPING OF THE LEXICON -- CHAPTER 4 Formulae -- INTRODUCTION AND PLAN OF THE CHAPTER -- 1 THE HOMERIC CASE AS A STARTING-POINT -- 1.1 The problem -- 1.2 The problem of definition -- 2 GREEK MATHEMATICAL FORMULAE: A TYPOLOGY -- 2.1 The taxonomy -- 2.1.1 Object formulae -- 2.1.2 Construction formulae -- 2.1.3 Second-order formulae -- 2.1.4 Argumentation formulae -- 2.1.5 Predicate formulae -- 2.2 Parameters for formulae -- 2.2.1 Markedly repetitive? semantically marked? non-compositional? -- 2.2.2 Hierarchic structure -- 2.2.3 Contextual constraints -- 3 THE BEHAVIOUR OF FORMULAE -- 3.1 The flexibility of formulae -- 3.2 The productivity of formulae -- 3.2.1 Transformations on formulae -- 3.2.2 Ellipsis -- 3.2.3 The variability of formulae - and their origin -- 3.3 The generative grammar of formulae -- 3.4 Quantitative remarks -- 3.5 The Greek mathematical language: recapitulation -- 4 SUMMARY: BACK TO THE HOMERIC CASE -- 4.1 Contexts of formulae -- 4.2 Formulae and cognition -- CHAPTER 5 The shaping of necessity -- PLAN OF THE CHAPTER -- 1 STARTING-POINTS -- 1.2 The necessity of starting-points -- 1.2.1 The diagram and starting-points -- 1.2.2 'Intuition' starting-points -- 2 ARGUMENTS.

2.1 Reference -- 2.2 Diagram -- 2.3 Tool-box -- 2.4 Intuition -- 3 THE STRUCTURE OF PROOFS -- 3.1 Size -- 3.2 Structure of meso-proofs -- 3.2.1 Few backward-looking arguments -- 3.2.2 The absence of recycling -- 3.2.3 No hiatuses -- 3.2.4 The cadenza effect -- 3.2.5 Toutestin -- 3.2.6 Hiatuses and logical structure -- 3.3 Why are proofs the way they are? -- 3.4 How is necessity sustained by proofs? -- 4 THE TOOL-BOX -- 4.1 Definition -- 4.2 Preliminary quantitative description -- 4.3 A close-up on the Elements -- 4.4 Accessing the tool-box -- 5 SUMMARY -- 5.1 The shaping of necessity -- 5.2 On the limits of Greek mathematics -- CHAPTER 6 The shaping of generality -- INTRODUCTION AND PLAN OF THE CHAPTER -- 1 HINTS FOR A SOLUTION -- 1.1 Explicit generalisation -- 1.2 Quantifiers -- 2 THE GREEK SOLUTION TO THE PROBLEM OF GENERALITY: A SUGGESTION -- 2.1 The solution: an outline -- 2.2 The structure of the protasis -- 2.3 The permutations inside the proposition -- 2.4 Pointers to the cognitive background -- 2.5 Conclusion: the generality of arithmetic -- 3 SUMMARY -- CHAPTER 7 The historical setting -- INTRODUCTION AND PLAN OF THE CHAPTER -- 1 THE CRONOLOGY OF GREEK MATHEMATICS -- 1.1 The beginning of Greek mathematics -- 1.2 The emergence of Euclidean-style mathematics -- 2 DEMOGRAPHY -- 2.1 Class -- 2.2 Numbers -- 3 MATHEMATICS WHITHIN GREEK CULTURE -- 3.1 The social-political background: an intersection -- 3.3 A border: mathematics and 'the material' -- 3.4 A border: mathematics and other disciplines -- 4 SUMMARY -- APPENDIX The main Greek mathematicians cited in the book -- APOLLONIUS -- ARCHIMEDES -- ARISTARCHUS -- AUTOLYCUS -- EUCLID -- HERO -- HIPPOCRATES OF CHIOS -- PAPPUS -- PROCLUS -- PTOLEMY -- Bibliography -- Index.