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phere; Gases From Philosophy to Experimentation From 

 Alchemy to Chemistry A False Theory of Combustion; 

 Phlogiston Beginnings of Organic Chemistry Organization 

 of the First Scientific Academies and Societies The New 

 Philosophy : Bacon and Descartes Progress of Natural and 

 Physical Science in the Seventeenth Century. 



CHAPTER XIII 



BEGINNINGS OF MODERN MATHEMATICAL SCIENCE .... 273 

 Mathematical Philosophy; Analytic Geometry: Descartes 



Indivisibles : Cavalieri Projective Geometry : Desargues 

 Theory of Numbers and Probability : P'ermat, Pascal Me- 

 chanics and Optics: Huygens Wallis and Barrow Isaac 

 Newton Optics The Theory of Gravitation ; Principia 

 Newton's Mathematics; Fluxions Leibnitz H alley : Pre- 

 diction of Comets. 



CHAPTER XIV 



NATURAL AND PHYSICAL SCIENCE IN THE EIGHTEENTH CENTURY 304 



Chemistry; Decline of the Phlogiston Theory A New 

 Chemistry : Priestley and Lavoisier The Synthesis of Water 



Beginnings of Modern Ideas of Sound The Beginnings of 

 Modern Ideas of Heat ; Latent and Specific Heat, Calorimetry 



Eighteenth Century Researches on Light Beginnings of 

 Modern Ideas of Electricity and Magnetism Beginnings of 

 Modern Ideas of the Earth Eighteenth Century Progress 

 in Botany, Zoology, etc. Progress in Comparative Anatomy 

 and Physiology The Industrial Revolution ; Inventions ; 

 Power Influence of Science upon the Spirit of the Eighteenth 

 Century. 



CHAPTER XV 



MODERN TENDENCIES IN MATHEMATICAL SCIENCE .... 323 



Mathematics and Mechanics in the Eighteenth Century 

 Progress in Theoretical Mechanics Celestial Mechanics 

 The Perturbation Problem The Nebular Hypothesis Mod- 

 ern Astronomy ; Telescopic Discoveries Mathematical Prog- 

 ress and Physical Science Nineteenth Century Mathematics 



Non-Euclidean Geometry Imaginary Numbers The Dis- 

 covery of Neptune Cosmic Evolution Distance of the Stars 



Mathematical Physics. 



