简介
《美国中学数学(代数+几何)(英文版)(套装共4册)》包括《美国中学数学·代数（上）》、《美国中学数学·代数（下）》、《美国中学几何》和《美国中学数学·代数（上下册）（答案）》。We
are honored and happy to bring this set of math textbooks by Joseph
Ray. These popular books sold more than any other arithmetic in
America, in fact over 120 million copies and are still used in
modern American schools and families. As you can see, this set of
textbooks is organized in an orderly manner around the discipline
of arithmetic itself.
Ray emphasized critical thinking in his classroom. He believed that
his students needed to learn how to apply what they learned to
real-life situations. Rather than giving his pupils simple problems
to solve, he preferred word problems. Students can increase their
reading comprehension skills, and learn to think.
The science of Algebra, properly taught, stands among the first of
those studies essential to both the great objects of education. In
a course of instruction properly arranged, it naturally follows
Arithmetic, and should be taught immediately after it. The pupil
should acquire both a practical and theoretical knowledge of the
subject While every page is the result of the author's own
reflection, and the experience of many years in the
school-room.
目录
《美国中学数学·代数（上册）》目录：
DEFINITIONS
ADDITION
SUBTRACTION
MULTIPLICATION
DIVISION
ALGEBRAIC THEOREMS
FACTORING
GREATEST COMMON DIVISOR
LEAST COMMON MULTIPLE
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 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
CASEⅦ. DIVISION OF FRACTIONS
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
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
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
QUADRATIC EQUATIONS
DEFINITIONS AND ELEMENTARY PRINCIPLES
PURE QUADRATICS
QUESTIONS PRODUCING PURE QUADRATIC EQUATIONS AFFECTED QUADRATIC EQUATIONS
TO SOLVE AN AFFECTED QUADRATIC EQUATION
PROGRESSIONS AND PROPORTION
ARITHMETICAL PROGRESSION
GEOMETRICAL PROGRESSION
TO FIND THE SUM OF A GEOMETRICAL SERIES
RATIO AND PROPORTION
PROPORTION
《美国中学数学·代数（下册）》目录：
Ⅰ.DEFINITIONS1
ADDITION9
SUBTRACTION.11
MULTIPLICATION..17
DIVISION24
Ⅱ.ALGEBRAIC THEOREMS.32
FACTORING.37
GREATEST COMMON DIVISOR41
LEAST COMMON MULTIPLE.47
Ⅲ.ALGEBRAIC FRACTIONS49
Ⅳ.SIMPLE EQUATIONS68
Ⅴ.SUPPLEMENT TO SIMPLE EQUATIONS103
Ⅰ.GENERALIZATION.103
Ⅱ.NEGATIVE SOLUTIONS108
Ⅲ.DISCUSSION OF PROBLEMS110
Ⅳ.PROBLEM OF THE COURIERS.111
Ⅴ.A SIMPLE EQUATION HAS BUT ONE ROOT.117
Ⅵ.EXAMPLES INVOLVING THE SECOND POWER OF THE
UNKNOWN QUANTITY117
Ⅵ.OF POWERS,ROOTS,RADICALS,AND LNEQUALITIES..118
Ⅰ.INVOLUTION,OR FORMATION OF POWERS118
Ⅱ.EXTRACTION OF THE SQUARE ROOT127
Ⅲ.EXTRACTION OF THE CUBE ROOT139
Ⅳ.EXTRACTION OF THE FOURTH ROOT,SIXTH ROOT,NTH
ROOT,ETC148
Ⅴ.RADICAL QUANTITIES151
Ⅵ.THEORY OF FRACTIONAL EXPONENTS.166
Ⅶ.EQUATIONS CONTAINING RADICALS169
Ⅷ.INEQUALITIES.171
Ⅶ.QUADRATIC EQUATIONS176
AFFECTED QUADRATIC EQUATIONS181
TRINOMIAL EQUATIONS.202
SIMULTANEOUS QUADRATIC EQUATIONS CONTAINING TWO
OF MORE UNKNOWN QUANTITIES210
AFFECTED EQUATIONS.214
Ⅷ.RATIO,PROPORTION,AND PROGRESSIONS226
PROPORTION229
GEOMETRICAL PROGRESSION249
Ⅸ.PERMUTATIONS,COMBINATIONS,AND BINOMIAL
THEOREM259
Ⅹ.INDETERMINATE COEFFICIENTS:BINOMIAL THEOREM,
GENERAL DEMONSTRATION:SUMMATION AND
INTERPOLATION OF SERIES270
THEOREM270
BINOMIAL THEOREM275
THE DIFFERENTIAL METHOD OF SERIES283
PILING OF CANNON BALLS AND SHELLS..288
INTERPOLATION OF SERIES.292
INFINITE SERIES..295
RECURRING SERIES.299
REVERSION OF SERIES.303
Ⅺ.CONTINUED FRACTIONS:LOGARITHMS:EXPONENTIAL
EQUATIONS:INTEREST,AND ANNUITIES.306
CONTINUED FRACTIONS306
LOGARITHMS.314
COMPUTATION OF LOGARITHMS322
NAPERIAN,OF HYPERBOLIC LOG ARITHMS.327
SINGLE AND DOUBLE POSITION331
EXPONENTIAL EQUATIONS333
INTEREST AND ANNUITIES.335
Ⅻ.GENERAL THEORY OF EQUATIONS341
TRANSFORMATION OF EQUATIONS.352
LIMITS OF THE ROOTS OF EQUATIONS.363
STURM’S THEOREM.367
ⅩⅢ.RESOLUTION OF NUMERICAL EQUATIONS374
《美国中学几何》目录：
THE NATURE, DIVISIONS, AND METHOD OF THE SCIENCE
DETERMINATE GEOMETRY
INDETERMINATE GEOMETRY BOOK I PLANE CO-ORDINATES
PART I THE REPRESENTATION OF FORM BY
ANALYTIC SYMBOLS
CHAPTER 1. THE OLDER GEOMETRY: BILINEAR AND
POLAR CO-ORDINATES
THE POINT
THE RIGHT LINE
PAIRS OF RIGHT LINES
THE CIRCLE
THE ELLIPSE
THE HYPERBOLA
THE PARABOLA
LOCUS OF SECOND ORDER IN GENERAL
CHAPTER 2. THE MODERN GEOMETRY: TRILINEAR
AND TANGENTIAL CO-ORDINATES
TRILINEAR CO-ORDINATES
TANGENTIAL CO-ORDINATES
PART II. THE PROPERTIES OF CONICS.
CHAPTER 1. THE RIGHT LINE
CHAPTER 2. THE CIRCLE
CHAPTER 3. THE ELLIPSE
THE CURVE REFERRED TO ITS AXES
THE CURVE REFERRED TO ANY TWO CONJUGATES
THE CURVE REFERRED TO ITS FOCI
AREA OF THE ELLIPSE
EXAMPLES ON THE ELLIPSE
CHAPTER 4. THE HYPERBOLA.
THE CURVE REFERRED TO ITS AXES
THE CURVE REFERRED TO ANY TWO CONJUGATES
THE CURVE REFERRED TO ITS FOCI
THE CURVE REFERRED TO ITS ASYMPTOTES
AREA OF THE HYPERBOLA
EXAMPLES ON THE HYPERBOLA
CHAPTER 5. THE PARABOLA
THE CURVE REFERRED TO ITS AXIS AND VERTEX
THE CURVE IN TERMS OF ANY DIAMETER
THE CURVE REFERRED TO ITS FOCUS
AREA OF THE PARABOLA
EXAMPLES ON THE PARABOLA
CHAPTER 6. THE CONIC IN GENERAL
BOOK II CO-ORDINATES IN SPACE
CHAPTER 1. THE POINT
CHAPTER 2. LOCUS OF FIRST ORDER IN SPACE
CHAPTER 3. LOCUS OF SECOND ORDER IN SPACE
《美国中学数学·代数（上下册）（答案）》
DEFINITIONS
ADDITION
SUBTRACTION
MULTIPLICATION
DIVISION
ALGEBRAIC THEOREMS
FACTORING
GREATEST COMMON DIVISOR
LEAST COMMON MULTIPLE
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 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
CASEⅦ. DIVISION OF FRACTIONS
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
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
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
QUADRATIC EQUATIONS
DEFINITIONS AND ELEMENTARY PRINCIPLES
PURE QUADRATICS
QUESTIONS PRODUCING PURE QUADRATIC EQUATIONS AFFECTED QUADRATIC EQUATIONS
TO SOLVE AN AFFECTED QUADRATIC EQUATION
PROGRESSIONS AND PROPORTION
ARITHMETICAL PROGRESSION
GEOMETRICAL PROGRESSION
TO FIND THE SUM OF A GEOMETRICAL SERIES
RATIO AND PROPORTION
PROPORTION
《美国中学数学·代数（下册）》目录：
Ⅰ.DEFINITIONS1
ADDITION9
SUBTRACTION.11
MULTIPLICATION..17
DIVISION24
Ⅱ.ALGEBRAIC THEOREMS.32
FACTORING.37
GREATEST COMMON DIVISOR41
LEAST COMMON MULTIPLE.47
Ⅲ.ALGEBRAIC FRACTIONS49
Ⅳ.SIMPLE EQUATIONS68
Ⅴ.SUPPLEMENT TO SIMPLE EQUATIONS103
Ⅰ.GENERALIZATION.103
Ⅱ.NEGATIVE SOLUTIONS108
Ⅲ.DISCUSSION OF PROBLEMS110
Ⅳ.PROBLEM OF THE COURIERS.111
Ⅴ.A SIMPLE EQUATION HAS BUT ONE ROOT.117
Ⅵ.EXAMPLES INVOLVING THE SECOND POWER OF THE
UNKNOWN QUANTITY117
Ⅵ.OF POWERS,ROOTS,RADICALS,AND LNEQUALITIES..118
Ⅰ.INVOLUTION,OR FORMATION OF POWERS118
Ⅱ.EXTRACTION OF THE SQUARE ROOT127
Ⅲ.EXTRACTION OF THE CUBE ROOT139
Ⅳ.EXTRACTION OF THE FOURTH ROOT,SIXTH ROOT,NTH
ROOT,ETC148
Ⅴ.RADICAL QUANTITIES151
Ⅵ.THEORY OF FRACTIONAL EXPONENTS.166
Ⅶ.EQUATIONS CONTAINING RADICALS169
Ⅷ.INEQUALITIES.171
Ⅶ.QUADRATIC EQUATIONS176
AFFECTED QUADRATIC EQUATIONS181
TRINOMIAL EQUATIONS.202
SIMULTANEOUS QUADRATIC EQUATIONS CONTAINING TWO
OF MORE UNKNOWN QUANTITIES210
AFFECTED EQUATIONS.214
Ⅷ.RATIO,PROPORTION,AND PROGRESSIONS226
PROPORTION229
GEOMETRICAL PROGRESSION249
Ⅸ.PERMUTATIONS,COMBINATIONS,AND BINOMIAL
THEOREM259
Ⅹ.INDETERMINATE COEFFICIENTS:BINOMIAL THEOREM,
GENERAL DEMONSTRATION:SUMMATION AND
INTERPOLATION OF SERIES270
THEOREM270
BINOMIAL THEOREM275
THE DIFFERENTIAL METHOD OF SERIES283
PILING OF CANNON BALLS AND SHELLS..288
INTERPOLATION OF SERIES.292
INFINITE SERIES..295
RECURRING SERIES.299
REVERSION OF SERIES.303
Ⅺ.CONTINUED FRACTIONS:LOGARITHMS:EXPONENTIAL
EQUATIONS:INTEREST,AND ANNUITIES.306
CONTINUED FRACTIONS306
LOGARITHMS.314
COMPUTATION OF LOGARITHMS322
NAPERIAN,OF HYPERBOLIC LOG ARITHMS.327
SINGLE AND DOUBLE POSITION331
EXPONENTIAL EQUATIONS333
INTEREST AND ANNUITIES.335
Ⅻ.GENERAL THEORY OF EQUATIONS341
TRANSFORMATION OF EQUATIONS.352
LIMITS OF THE ROOTS OF EQUATIONS.363
STURM’S THEOREM.367
ⅩⅢ.RESOLUTION OF NUMERICAL EQUATIONS374
《美国中学几何》目录：
THE NATURE, DIVISIONS, AND METHOD OF THE SCIENCE
DETERMINATE GEOMETRY
INDETERMINATE GEOMETRY BOOK I PLANE CO-ORDINATES
PART I THE REPRESENTATION OF FORM BY
ANALYTIC SYMBOLS
CHAPTER 1. THE OLDER GEOMETRY: BILINEAR AND
POLAR CO-ORDINATES
THE POINT
THE RIGHT LINE
PAIRS OF RIGHT LINES
THE CIRCLE
THE ELLIPSE
THE HYPERBOLA
THE PARABOLA
LOCUS OF SECOND ORDER IN GENERAL
CHAPTER 2. THE MODERN GEOMETRY: TRILINEAR
AND TANGENTIAL CO-ORDINATES
TRILINEAR CO-ORDINATES
TANGENTIAL CO-ORDINATES
PART II. THE PROPERTIES OF CONICS.
CHAPTER 1. THE RIGHT LINE
CHAPTER 2. THE CIRCLE
CHAPTER 3. THE ELLIPSE
THE CURVE REFERRED TO ITS AXES
THE CURVE REFERRED TO ANY TWO CONJUGATES
THE CURVE REFERRED TO ITS FOCI
AREA OF THE ELLIPSE
EXAMPLES ON THE ELLIPSE
CHAPTER 4. THE HYPERBOLA.
THE CURVE REFERRED TO ITS AXES
THE CURVE REFERRED TO ANY TWO CONJUGATES
THE CURVE REFERRED TO ITS FOCI
THE CURVE REFERRED TO ITS ASYMPTOTES
AREA OF THE HYPERBOLA
EXAMPLES ON THE HYPERBOLA
CHAPTER 5. THE PARABOLA
THE CURVE REFERRED TO ITS AXIS AND VERTEX
THE CURVE IN TERMS OF ANY DIAMETER
THE CURVE REFERRED TO ITS FOCUS
AREA OF THE PARABOLA
EXAMPLES ON THE PARABOLA
CHAPTER 6. THE CONIC IN GENERAL
BOOK II CO-ORDINATES IN SPACE
CHAPTER 1. THE POINT
CHAPTER 2. LOCUS OF FIRST ORDER IN SPACE
CHAPTER 3. LOCUS OF SECOND ORDER IN SPACE
《美国中学数学·代数（上下册）（答案）》
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