Part I: Antecedents
Chapter 1. From Geometry to Analysis
Chapter 2. The situation in the first half of the 18th century. Euler and continued fractions
Part II: Johann Heinrich Lambert (1728-1777)
Chapter 3. A biographical approach to Johann Heinrich Lambert
Chapter 4. Outline of Lambert's Mémoire (1761/1768)
Chapter 5. An anotated translation of Lambert's Mémoire (1761/1768)
Chapter 6. Outine of Lambert's Vorläufige Kenntnisse (1766/1770)
Chapter 6. An anotated translation of Lambert's Vorläufige Kenntnisse (1766/1770)
Part III: The influence of Lambert's work and the development of irrational numbers
Chapter 8. The state of irrationals until the turn of the century
Chapter 9. Title to be set up.