美國中學(xué)數(shù)學(xué)（套裝共4冊）

前言

呈現(xiàn)于您眼前的這套美國數(shù)學(xué)課本，是一套在西方流行了近半個世紀(jì)、至今仍在使用的經(jīng)典教材。編者約瑟夫?雷伊教授，1807年出生于美國弗吉尼亞俄亥俄縣，從小在當(dāng)?shù)貙W(xué)校接受教育，成績優(yōu)秀。16歲時開始其教師職業(yè)生涯。18歲,雷伊來到富蘭克林學(xué)院跟隨喬爾?馬丁教授學(xué)習(xí)醫(yī)學(xué)，此后又進入俄亥俄醫(yī)學(xué)院學(xué)習(xí)。大學(xué)畢業(yè)后，他在辛辛那提伍德沃德中學(xué)任教，講授數(shù)學(xué)。1836年，伍德沃德中學(xué)由高中升格為辛辛那提伍德學(xué)院，雷伊成為該學(xué)院教授。1851年，該校又變?yōu)橐凰⒏咧?，雷伊一直在此?dān)任校長，直至去世。雷伊一生杰出的成就是他傾心編寫的系列數(shù)學(xué)教材，并以此聞名。這套數(shù)學(xué)課本與他在伍德學(xué)院的同事威廉?麥加菲編寫的《美國語文讀本》，同時被美國近萬所學(xué)校作為教材，累計銷量均超過1.22億冊，對幾代美國人的教育產(chǎn)生了很大影響。直至今日，這兩套書仍被當(dāng)作美國家庭教育（Homeschooling）的推薦教材，也是美國學(xué)生準(zhǔn)備SAT考試的參考用書。與其他數(shù)學(xué)書相比，雷伊數(shù)學(xué)教材至少有以下幾個明顯特點：第一，強調(diào)在“學(xué)”中掌握“數(shù)”。例如，《小學(xué)數(shù)學(xué)》不完全按難度分冊，而是根據(jù)其實際應(yīng)用范圍分為四冊：初級算術(shù)、智力算術(shù)、實用算術(shù)與高級算術(shù)。讓學(xué)生從對數(shù)的認知、運算法則的掌握，延伸到數(shù)學(xué)在實際生活中的廣泛應(yīng)用，如購物、記賬、存款、利息等，并向更高的學(xué)術(shù)層次過渡。第二，將數(shù)學(xué)問題融于文字題（Word Problem）之中。即便最簡單的加減運算，它也通過講故事的方式呈現(xiàn)出來。這樣孩子們在學(xué)習(xí)數(shù)學(xué)時，不僅可以訓(xùn)練其數(shù)學(xué)思維，語言能力也可以同步提高。第三，將抽象思維具體化。書中的數(shù)學(xué)題大都結(jié)合現(xiàn)實事物表述出來，讓孩子們理解他們所學(xué)的數(shù)學(xué)在現(xiàn)實生活中是如何加以應(yīng)用的。這對低年級學(xué)生來說，尤其幫助很大，他們能更快更清楚地理解那些對其年齡來講過于抽象的數(shù)學(xué)概念。第四，將不同學(xué)科知識融入數(shù)學(xué)問題中。這種編寫方法能讓學(xué)生從數(shù)學(xué)應(yīng)用的不同領(lǐng)域來掌握數(shù)學(xué)科學(xué)，幫助學(xué)生從低年級數(shù)學(xué)步入更復(fù)雜的數(shù)學(xué)應(yīng)用領(lǐng)域，如幾何學(xué)與會計學(xué)等。孩子們在學(xué)習(xí)數(shù)學(xué)的同時，又能接受其他學(xué)科知識。如書中有這樣一道題：“華盛頓將軍出生于公元1732年，他活了67歲，那么他是于哪一年去世？”這么一道簡單的計算題,便將歷史知識與數(shù)學(xué)結(jié)合起來，一舉多得。對于中國孩子來講，這套數(shù)學(xué)課本不僅能教孩子學(xué)習(xí)數(shù)學(xué)，更是學(xué)習(xí)英語的很好途徑，讓他們換個思維學(xué)英語。與閱讀文學(xué)讀本相比，這是另一種不同的感覺，或許更能激發(fā)孩子學(xué)習(xí)英語的興趣。數(shù)學(xué)的詞匯含義固定，也易于理解記憶，孩子在解題的同時也能提高英語水平，可謂一舉多得。對于那些將來準(zhǔn)備參加出國英語考試的學(xué)生來講，這套書意義更大，對他們將來的求學(xué)之路應(yīng)該大有幫助。最后，我們需向讀者特別說明一點，由于這套書涉及數(shù)字與數(shù)學(xué)符號偏多，考慮到重新錄入排版會出現(xiàn)一些難免的錯誤，給讀者學(xué)習(xí)帶來極大不便。于是我們采用了原版影印的辦法，以保證內(nèi)容的高度準(zhǔn)確性，但文字清晰度與重新錄入相比略有缺陷，敬請讀者諒解。衷心祝愿天下孩子們快樂成長，并期待您的寶貴意見與建議。

內(nèi)容概要

　　《美國中學(xué)數(shù)學(xué)(代數(shù)+幾何)(英文版)(套裝共4冊)》包括《美國中學(xué)數(shù)學(xué)·代數(shù)（上）》、《美國中學(xué)數(shù)學(xué)·代數(shù)（下）》、《美國中學(xué)幾何》和《美國中學(xué)數(shù)學(xué)·代數(shù)（上下冊）（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.

作者簡介

編者：（美國）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.

書籍目錄

《美國中學(xué)數(shù)學(xué)·代數(shù)（上冊）》目錄：
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
《美國中學(xué)數(shù)學(xué)·代數(shù)（下冊）》目錄：
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
《美國中學(xué)幾何》目錄：
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
《美國中學(xué)數(shù)學(xué)·代數(shù)（上下冊）（答案）》

章節(jié)摘錄

插圖：

編輯推薦

《美國中學(xué)數(shù)學(xué)(套裝共4冊)(代數(shù)+幾何)》與麥加菲編寫的《美國語文讀本》，在半個多世紀(jì)里，對美國教育產(chǎn)生了很大影響。兩套教材自19世紀(jì)以來，被10000多所學(xué)校使用，累計銷量分別高達1.22億冊，至今仍作為“家庭學(xué)?！保℉omeschooling）的推薦教材。雷伊數(shù)學(xué)課本，是一套系統(tǒng)完整的中小學(xué)數(shù)學(xué)教材，從簡單的算術(shù)開始，到高級的代數(shù)與解析幾何。在近50年里，雷伊數(shù)學(xué)課本一直被作為美國標(biāo)準(zhǔn)數(shù)學(xué)教材，10000多所學(xué)校采用,超過一億的美國孩子用此套數(shù)學(xué)教材接受教育。直到，現(xiàn)在仍作為學(xué)生學(xué)習(xí)和備考AST的參考用書。對中國學(xué)生來說，《美國中學(xué)數(shù)學(xué)(套裝共4冊)(代數(shù)+幾何)》能幫助學(xué)生用英語學(xué)習(xí)數(shù)學(xué)，既提高他們的英語水平，也幫助他們將來更好地適應(yīng)西方學(xué)科考試。《美國中學(xué)數(shù)學(xué)(套裝共4冊)(代數(shù)+幾何)》包括：代數(shù)課本上下冊，附答案一本；幾何一冊。

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