美国中学数学·代数（上下册附答案）电子书

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出版前言

CONTENTS

Ⅰ. DEFINITIONS

ADDITION

SUBTRACTION

MULTIPLICATION

DIVISION

Ⅱ. ALGEBRAIC THEOREMS

FACTORING

GREATEST COMMON DIVISOR

LEAST COMMON MULTIPLE

Ⅲ. ALGEBRAIC FRACTIONS

CASE Ⅰ. TO REDUCE A FRACTION TO ITS LOWEST TERMS

CASE Ⅱ. TO REDUCE A FRACTION TO AN ENTIRE OR MIXED QUANTITY

CASE Ⅲ. TO REDUCE A MIXED QUANTITY TO THE FORM OF A FRACTION

CASE Ⅳ. TO REDUCE FRACTIONS OF DIFFERENT DENOMINATORS TO EQUIVALENT FRACTIONS HAVING A COMMON DENOMINATOR

CASE Ⅴ. ADDITION AND SUBTRACTION OF FRACTIONS

CASE Ⅵ. MULTIPLICATION OF FRACTIONS

CASE Ⅶ. DIVISION OF FRACTIONS

Ⅳ. SIMPLE EQUATIONS

DEFINITIONS AND ELEMENTARY PRINCIPLES

SIMPLE EQUATIONS CONTAINING ONE UNKNOWN QUANTITY

AXIOMS

TRANSPOSITION

TO CLEAR AN EQUATION OF FRACTIONS

SOLUTION OF SIMPLE EQUATIONS CONTAINING ONE UNKNOWN QUANTITY

QUESTIONS PRODUCING SIMPLE EQUATIONS, CONTAINING ONE UNKNOWN QUANTITY

TO ELIMINATE BY COMPARISON

TO ELIMINATE BY ADDITION AND SUBTRACTION

GENERAL RULE, FOR ELIMINATION BY ADDITION AND SUBTRACTION

Ⅴ. SUPPLEMENT TO SIMPLE EQUATIONS

GENERALIZATION

RULE, FOR FINDING TWO QUANTITIES, WHEN THEIR SUM AND DIFFERENCE ARE GIVEN

GENERAL PROBLEMS

NEGATIVE SOLUTIONS

DISCUSSION OF PROBLEMS

PROBLEM OF THE COURIERS

CASES OF INDETERMINATION IN SIMPLE EQUATIONS, AND IMPOSSIBLE PROBLEMS

Ⅵ. OF POWERS, ROOTS, AND RADICALS

CASE Ⅰ. TO RAISE A MONOMIAL TO ANY GIVEN POWER

CASE Ⅱ. TO RAISE A POLYNOMIAL TO ANY POWER

CASE Ⅲ. TO RAISE A FRACTION TO ANY POWER

Ⅶ. QUADRATIC EQUATIONS

DEFINITIONS AND ELEMENTARY PRINCIPLES

PURE QUADRATICS

QUESTIONS PRODUCING PURE QUADRATIC EQUATIONS

AFFECTED QUADRATIC EQUATIONS

TO SOLVE AN AFFECTED QUADRATIC EQUATION

Ⅷ. PROGRESSIONS AND PROPORTION

ARITHMETICAL PROGRESSION

GEOMETRICAL PROGRESSION

TO FIND THE SUM OF A GEOMETRICAL SERIES

RATIO AND PROPORTION

PROPORTION

CHAPTER Ⅰ.DEFINITIONS

ADDITION

SUBTRACTION

MULTIPLICATION

DIVISION

CHAPTER Ⅱ.ALGEBRAIC THEOREMS

FACTORING

GREATEST COMMON DIVISOR

LEAST COMMON MULTIPLE

CHAPTER Ⅲ.ALGEBRAIC FRACTIONS

CHAPTER Ⅳ.SIMPLE EQUATIONS

CHAPTER Ⅴ.SUPPLEMENT TO SIMPLE EQUATIONS

Ⅰ.GENERALIZATION

Ⅱ.NEGATIVE SOLUTIONS

Ⅲ.DISCUSSION OF PROBLEMS

Ⅳ.CASES OF INDETERMINATION IN SIMPLE EQUATIONS AND IMPOSSIBLE PROBLEMS

Ⅴ.A SIMPLE EQUATION HAS BUT ONE ROOT

Ⅵ.EXAMPLES INVOLVING THE SECOND POWER OF THE UNKNOWN QUANTITY

CHAPTER Ⅵ.OF POWERS，ROOTS，RADICALS，AND LNEQUALITIES

Ⅰ.INVOLUTION，OR FORMATION OF POWERS

Ⅱ.EXTRACTION OF THE SQUARE ROOT

Ⅲ.EXTRACTION OF THE CUBE ROOT

Ⅳ.EXTRACTION OF THE FOURTH ROOT，SIXTH ROOT，N^T^H ROOT，ETC

Ⅴ.RADICAL QUANTITIES

Ⅵ.THEORY OF FRACTIONAL EXPONENTS

Ⅶ.EQUATIONS CONTAINING RADICALS

Ⅷ.INEQUALITIES

CHAPTER Ⅶ.QUADRATIC EQUATIONS

AFFECTED QUADRATIC EQUATIONS

TRINOMIAL EQUATIONS

SIMULTANEOUS QUADRATIC EQUATIONS CONTAINING TWO OF MORE UNKNOWN QUANTITIES

AFFECTED EQUATIONS

CHAPTER Ⅷ.RATIO，PROPORTION，AND PROGRESSIONS

PROPORTION

GEOMETRICAL PROGRESSION

CHAPTER Ⅸ.PERMUTATIONS，COMBINATIONS，AND BINOMIAL THEOREM

CHAPTER Ⅹ.INDETERMINATE COEFFICIENTS：BINOMIAL THEOREM，GENERAL DEMONSTRATION：SUMMATION ANDINTERPOLATION OF SERIES

THEOREM

BINOMIAL THEOREM

THE DIFFERENTIAL METHOD OF SERIES

PILING OF CANNON BALLS AND SHELLS

INTERPOLATION OF SERIES

INFINITE SERIES

RECURRING SERIES

REVERSION OF SERIES

CHAPTER Ⅺ.CONTINUED FRACTIONS：LOGARITHMS：EXPONENTIAL EQUATIONS：INTEREST，AND ANNUITIES

CONTINUED FRACTIONS

LOGARITHMS

COMPUTATION OF LOGARITHMS

NAPERIAN，OF HYPERBOLIC LOG ARITHMS

SINGLE AND DOUBLE POSITION

EXPONENTIAL EQUATIONS

INTEREST AND ANNUITIES

CHAPTER Ⅻ.GENERAL THEORY OF EQUATIONS

TRANSFORMATION OF EQUATIONS

LIMITS OF THE ROOTS OF EQUATIONS

STURM’S THEOREM

CHAPTER ⅩⅢ.RESOLUTION OF NUMERICAL EQUATIONS

KEY