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CONTENTS 



PAGE 
INTRODUCTION 5 

CHAP. 

I. THE GROWTH OF MATHEMATICAL SCIENCE IN 

ANCIENT TIMES ...... 10 

II. THE RISE AND PROGRESS OP MODERN MATHE- 
MATICS ALGEBRA 23 

III. THE RISE AND PROGRESS OP MODERN MATHE- 

MATICS ANALYTICAL GEOMETRY AND THE 
METHOD OP INDIVISIBLES .... 39 

IV. THE BEGINNINGS OF THE APPLICATION OF MATHE- 

MATICS TO NATURAL SCIENCE THE SCIENCE 

OF DYNAMICS 53 

V. THE RISE OF MODERN MATHEMATICS THE IN- 
FINITESIMAL CALCULUS 65 

VI. MODERN VIEWS OF LIMITS AND NUMBERS . . 77 

VII. THE NATURE OF MATHEMATICS .... 83 

BIBLIOGRAPHY ....... 89 

INDEX 90