xxxvi CONTENTS. 



BOOK 11. 



NUMBER, VARIETY, AND PROBABILITY. 



CHAPTER VIII. 



9 



PRINCIPLES OF NCMBEK, 

 SECTION PAGE 



1. Principles of Number 153 



2. The Nature of Number 156 



3. Of Numerical Abstraction 158 



4. Concrete and Abstract Number 159 



5. Analogy of Logical and Numerical Terms 160 



6. Principle of Mathematical Infei'ence 162 



7. Reasoning by Inequalities 165 



8. Arithmetical Reasoning 167 



9. Numerically Definite Reasoning 168 



10. Numerical meaning of Logical Conditions 171 



CPIAPTER IX. 



rUE VARIETY OF NATURE, OR THE DOCTRINE OF COMBINATIONS 

 AND PERMUTATIONS. 



1. The Variety of Nature 173 



2. Distinction of Combinations and Permutations 177 



3. Calcuhitioa of Number of Combinations 180 



4. The Arithmetical Triangle 182 



5. Connexion between the Arithmetical Triangle and the Logical 



Alphabet " 189 



6. Possible Variety of Nature and Art 190 



7. Higher Orders of Variety 192 



CHAPTER X. 



THEORY OF PROBABILITY. 



1. Theory of Probability 197 



2. Fundamental Principles of the Theory 200 



3. Rules for the Calculation of Probabilities 203 



4. The Logical Alphabet in questions of Probability 205 



