'A remarkably wide-ranging discussion of the language, aims, and methods of geometry from Greek antiquity, via Descartes, up to Weil, Grothendeick, and beyond.' - David Fowler, University of Warwick

• Preface Introduction Part I: The Subject Matter of Geometry in Euclid, Descartes and Hilbert 1. The Opening of The Elements 2. Propositions and Proofs - Theorems and Problems Part II 1. The Contexts of Measurement 2. Number Theory in the 19th Century Appendix Part III Introduction 1. Types of Wholes 2. Generality in Contemporary Mathematics Conclusion

'A remarkably wide-ranging discussion of the language, aims, and methods of geometry from Greek antiquity, via Descartes, up to Weil, Grothendeick, and beyond.' - David Fowler, University of Warwick

• Preface Introduction Part I: The Subject Matter of Geometry in Euclid, Descartes and Hilbert 1. The Opening of The Elements 2. Propositions and Proofs - Theorems and Problems Part II 1. The Contexts of Measurement 2. Number Theory in the 19th Century Appendix Part III Introduction 1. Types of Wholes 2. Generality in Contemporary Mathematics Conclusion

'A remarkably wide-ranging discussion of the language, aims, and methods of geometry from Greek antiquity, via Descartes, up to Weil, Grothendeick, and beyond.' - David Fowler, University of Warwick

• Preface Introduction Part I: The Subject Matter of Geometry in Euclid, Descartes and Hilbert 1. The Opening of The Elements 2. Propositions and Proofs - Theorems and Problems Part II 1. The Contexts of Measurement 2. Number Theory in the 19th Century Appendix Part III Introduction 1. Types of Wholes 2. Generality in Contemporary Mathematics Conclusion