In 1690, Christiaan Huygens (1629-1695) published Traité de la Lumière, containing his renowned wave theory of light. It is considered a landmark in seventeenth-century science, for the way Huygens mathematized the corpuscular nature of light and his probabilistic conception of natural knowledge. This book discusses the development of Huygens' wave theory, reconstructing the winding road that eventually led to Traité de la Lumière. For the first time, the full range of manuscript sources is taken into account. In addition, the development of Huygens' thinking on the nature of light is put in the context of his optics as a whole, which was dominated by his lifelong pursuit of theoretical and practical dioptrics. In so doing, this book offers the first account of the development of Huygens' mathematical analysis of lenses and telescopes and its significance for the origin of the wave theory of light. As Huygens applied his mathematical proficiency to practical issues pertaining to telescopes ¿ including trying to design a perfect telescope by means of mathematical theory ¿ his dioptrics is significant for our understanding of seventeenth-century relations between theory and practice. With this full account of Huygens' optics, this book sheds new light on the history of seventeenth-century optics and the rise of the new mathematical sciences, as well as Huygens' oeuvre as a whole. Students of the history of optics, of early mathematical physics, and the Scientific Revolution, will find this book enlightening.

Chapter 1 Introduction - 'the perfect Cartesian'.- A history of Traité de la Lumière. Huygens' optics. New light on Huygens. Chapter 2 1653 - 'Tractatus'.- 2.1 The Tractatus of 1653. 2.1.1 Ovals to lenses. 2.1.2 A theory of the telescope. The focal distance of a bi-convex lens. Images. Conclusion. 2.2 Dioptrics and the telescope. 2.2.1 Kepler and the mathematics of lenses. Image formation. Lenses. Perspectiva and the telescope. 2.2.2 The use of the sine law. Descartes and the ideal telescope. After Descartes. Dioptrics as mathematics. 2.2.3 The need for theory. The micrometer and telescopic sights. Understanding the telescope. Huygens' position. Chapter 3 1655-1672 - 'De Aberratione'.- 3.1 The use of theory. 3.1.1 Huygens and the art of telescope making. Huygens' skills. Alternative configurations. Experiential knowledge. 3.1.2 Inventions on telescopes by Huygens. 3.2 Dealing with aberrations. 3.2.1 Properties of spherical aberration.- Specilla circularia.- Theory and its applications. 3.2.2 Putting theory to practice. A new design. 3.2.3 Newton's other look and Huygens' response. 3.3 Dioptrica in the context of Huygens' mathematical science. 3.3.1 The mathematics of things. Huygens 'géomètre'. 3.3.2 Huygens the scholar & Huygens the craftsman. The 'raison d'être' of Dioptrica: l'instrument pour l'instrument. Chapter 4 The 'Projet' of 1672.- 'Projet du Contenu de la Dioptrique'. 4.1 The nature of light and the laws of optics. 4.1.1 Alhacen on the cause of refraction. 4.1.2 Kepler on the measure and the cause of refraction. The measure of refraction. True measures. Paralipomena and the seventeenth-century reconfiguration of optics. 4.1.3 The laws of optics in corpuscular thinking. Refraction in La Dioptrique. Epistemic aspects of Descartes' account in historical context. Historian's assessment of Descartes' optics. Reception of Descartes' account of refraction. Barrow's causal account of refraction. 4.2 The mathematics of strange refraction. 4.2.1 Bartholinus and Huygens on Iceland Crystal. Bartholinus' experimenta. Huygens' alternatives. 4.2.2 Rays versus waves: the mathematics of things revisited. The particular problem of strange refraction: waves versus masses. Chapter 5 1677-1679 - Waves of Light.- 5.1 A new theory of waves. 5.1.1 A first EUPHKA. The solution of the 'difficulté' of Iceland Crystal. 5.1.2 Undulatory theory. Explaining strange refraction. 5.1.3 Traité de la Lumière and the 'Projet'. 5.2 Comprehensible explanations. 5.2.1 Mechanisms of light. Hobbes, Hooke and the pitfalls of mechanistic philosophy: rigid waves. 5.2.2 'Raisons de mechanique'. Newton's speculations on the nature of light. The status of 'raisons de mechanique'. 5.3 A second euphka. 5.3.1 Danish objections. Forced innovation. 5.3.2 Hypotheses and deductions. Chapter 6 1690 - Traité de la Lumière.- 6.1 Creating Traité de la Lumière. 6.1.1 Completing 'Dioptrique'. Huygens' dioptrics in the 1680s. 6.1.2 From 'Dioptrique' to Traité de la Lumière. The publication of Traité de la Lumière. 6.2 Traité de la Lumière and the advent of physical optics. Mathematization by extending mathematics. The matter of rays. The mathematics of light. 6.3 Traité de la Lumière and Huygens' oeuvre. 6.3.1 Huygens' Cartesianism. The subtle matter of 1669. Huygens versus Newton. Huygens' self-image. 6.3.2 The reception of Huygens. Chapter 7 Conclusion: Lenses & Waves.- A seventeenth-century Archimedes.- From mathematics to mechanisms.- Huygens and Descartes.- The small Archimedes.- List of figures.- Bibliography.- Index