美国中学数学（套装共4册）

作者简介

《美国中学数学(套装共4册)(代数+几何)》内容简介：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.

书籍目录

《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）》

编辑推荐

《美国中学数学(套装共4册)(代数+几何)》与麦加菲编写的《美国语文读本》，在半个多世纪里，对美国教育产生了很大影响。两套教材自19世纪以来，被10000多所学校使用，累计销量分别高达1.22亿册，至今仍作为“家庭学校”（Homeschooling）的推荐教材。雷伊数学课本，是一套系统完整的中小学数学教材，从简单的算术开始，到高级的代数与解析几何。在近50年里，雷伊数学课本一直被作为美国标准数学教材，10000多所学校采用,超过一亿的美国孩子用此套数学教材接受教育。直到，现在仍作为学生学习和备考AST的参考用书。对中国学生来说，《美国中学数学(套装共4册)(代数+几何)》能帮助学生用英语学习数学，既提高他们的英语水平，也帮助他们将来更好地适应西方学科考试。《美国中学数学(套装共4册)(代数+几何)》包括：代数课本上下册，附答案一本；几何一册。

前言

呈现于您眼前的这套美国数学课本，是一套在西方流行了近半个世纪、至今仍在使用的经典教材。编者约瑟夫?雷伊教授，1807年出生于美国弗吉尼亚俄亥俄县，从小在当地学校接受教育，成绩优秀。16岁时开始其教师职业生涯。18岁,雷伊来到富兰克林学院跟随乔尔?马丁教授学习医学，此后又进入俄亥俄医学院学习。大学毕业后，他在辛辛那提伍德沃德中学任教，讲授数学。1836年，伍德沃德中学由高中升格为辛辛那提伍德学院，雷伊成为该学院教授。1851年，该校又变为一所公立高中，雷伊一直在此担任校长，直至去世。雷伊一生杰出的成就是他倾心编写的系列数学教材，并以此闻名。这套数学课本与他在伍德学院的同事威廉?麦加菲编写的《美国语文读本》，同时被美国近万所学校作为教材，累计销量均超过1.22亿册，对几代美国人的教育产生了很大影响。直至今日，这两套书仍被当作美国家庭教育（Homeschooling）的推荐教材，也是美国学生准备SAT考试的参考用书。与其他数学书相比，雷伊数学教材至少有以下几个明显特点：第一，强调在“学”中掌握“数”。例如，《小学数学》不完全按难度分册，而是根据其实际应用范围分为四册：初级算术、智力算术、实用算术与高级算术。让学生从对数的认知、运算法则的掌握，延伸到数学在实际生活中的广泛应用，如购物、记账、存款、利息等，并向更高的学术层次过渡。第二，将数学问题融于文字题（Word Problem）之中。即便最简单的加减运算，它也通过讲故事的方式呈现出来。这样孩子们在学习数学时，不仅可以训练其数学思维，语言能力也可以同步提高。第三，将抽象思维具体化。书中的数学题大都结合现实事物表述出来，让孩子们理解他们所学的数学在现实生活中是如何加以应用的。这对低年级学生来说，尤其帮助很大，他们能更快更清楚地理解那些对其年龄来讲过于抽象的数学概念。第四，将不同学科知识融入数学问题中。这种编写方法能让学生从数学应用的不同领域来掌握数学科学，帮助学生从低年级数学步入更复杂的数学应用领域，如几何学与会计学等。孩子们在学习数学的同时，又能接受其他学科知识。如书中有这样一道题：“华盛顿将军出生于公元1732年，他活了67岁，那么他是于哪一年去世？”这么一道简单的计算题,便将历史知识与数学结合起来，一举多得。对于中国孩子来讲，这套数学课本不仅能教孩子学习数学，更是学习英语的很好途径，让他们换个思维学英语。与阅读文学读本相比，这是另一种不同的感觉，或许更能激发孩子学习英语的兴趣。数学的词汇含义固定，也易于理解记忆，孩子在解题的同时也能提高英语水平，可谓一举多得。对于那些将来准备参加出国英语考试的学生来讲，这套书意义更大，对他们将来的求学之路应该大有帮助。最后，我们需向读者特别说明一点，由于这套书涉及数字与数学符号偏多，考虑到重新录入排版会出现一些难免的错误，给读者学习带来极大不便。于是我们采用了原版影印的办法，以保证内容的高度准确性，但文字清晰度与重新录入相比略有缺陷，敬请读者谅解。衷心祝愿天下孩子们快乐成长，并期待您的宝贵意见与建议。

内容概要

编者：（美国）雷伊（Joseph Ray）
Joseph Ray was born on November 25, 1807, in Ohio County, Virginia.
He at tended local schools and quickly proved himself to be an
adept student.By the time he was sixteen, he had begun a careeras a
teacher. In 1825, Ray enrolled in Franklin College in New Athens,
Ohio. While a student at Franklin College, Ray studied medicine
underJoel Martin. Upon graduating from college in1828, Ray enrolled
in the Medical College of Ohio, located in Cincinnati. During the
win terhe attended college, and during the summers, hetaught
school. He graduated in 1831. Ray is most famous for authoring ma
the matical text books. By the end of the nineteenth century,Ray's
texts had become the most widely used math books in the United
States, with sales approaching120 million copies. For a time, they
were the most used textbooks across all disciplines.
WilliamMcGuffey, a colleague of Ray's at Woodward College,
eventually produced a series of Englis hreaders. Ray was a member
of the Ohio State Teachers Association and served as that
organization'spresident in 1853. In 1854, he became an
associateeditor for The Ohio Journal of Education. He died on April
11, 1855, from tuberculosis.

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