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Lenses and Waves: Christiaan Huygens and the Mathematical Science of Optics in the Seventeenth Century

Kluwer Academic Publishers
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Date Received: 
Wednesday, September 27, 2006
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Fokko Jan Dijksterhuis
Archimedes 9
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 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

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