xii CONTENTS.
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CHAPTER PAGE
XXIX. Problems 258
XXX. Theory of Quadratic Equations 264 Number of the Roots 264 Character of the Roots 265 Relation of Roots and Coefficients 266 Formation of Equations with Given Roots 267 Miscellaneous Theorems 272 Remainder Theorem 272 Symmetry 273
XXXI. Indeterminate Equations of the First Degree 276
XXXII. Inequalities 279 Miscellaneous Examples V 283
XXXIII. Ratio 286 Proportion 291 Transformations that may be made in a Proportion 293 Variation 296
XXXIV. Arithmetical Progression 301 Geometrical Progression 308 Harmonical Progression 313
XXXV. Permutations and Combinations 319
XXXVI. Probability (Chance) 331 Miscellaneous Examples VI 334
XXVII. Binomial Theorem: Proof for Positive Integral Index 338 The General Term 341 Simplest Form of the Binomial Theorem 342 Proof by Mathematical Induction 343 Equal Coefficients 345 Greatest Coefficient 345 Greatest Term 345 Sum of the Coefficients 347 Expansion of Multinomials 347 Application when Index is Negative or Fractional 347
XXVIII. Logarithms 352 Properties of Logarithms 353 Characteristic and Mantissa 354
