《美國中學(xué)代數(shù)(套裝上下冊)》內(nèi)容簡介：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.
作者簡介：
Joseph Ray was born on November 25, 1807, in Ohio County, Virginia. He attended local schools and quickly proved himself to be an adept student. By the time he was sixteen, he had begun a career as a teacher. In 1825, Ray enrolled in Franklin College in New Athens, Ohio. While a student at Franklin College, Ray studied medicine under Joel Martin. Upon graduating from college in 1828, Ray enrolled in the Medical College of Ohio, located in Cincinnati. During the winter he attended college, and during the summers, he taught school. He graduated in 1831.
Ray is most famous for authoring mathematical textbooks. By the end of the nineteenth century, Ray's texts had become the most widely used math books in the United States, with sales approaching 120 million copies. For a time, they were the most used textbooks across all disciplines. William McGuffey, a colleague of Ray's at Woodward College, eventually produced a series of English readers.
Ray was a member of the Ohio State Teachers Association and served as that organization's president in 1853. In 1854, he became an associate editor for The Ohio Journal of Education. He died on April 11, 1855, from tuberculosis.
約瑟夫·雷伊教授于1807年出生于美國弗吉尼亞俄亥俄縣，小時(shí)在地方學(xué)校接受教育，學(xué)業(yè)優(yōu)秀。16歲時(shí)，他就開始步入其教師生涯，1825年到富蘭克林學(xué)院求學(xué)，跟隨喬爾·馬丁教授學(xué)習(xí)醫(yī)學(xué)。1828年畢業(yè)后進(jìn)入俄亥俄醫(yī)學(xué)院學(xué)習(xí)，1831年畢業(yè)。大學(xué)畢業(yè)后，他在辛辛那提的伍德沃德中學(xué)找了份當(dāng)教師的工作，開始教數(shù)學(xué)。1836年，俄亥俄司法當(dāng)局準(zhǔn)許伍德沃德中學(xué)由高中升格為辛辛那提伍德學(xué)院，雷伊成為該學(xué)院的一名教授。1851年，該校以變?yōu)橐凰⒏咧�，雷伊一直在此�?dān)任校長，直至去世。
雷伊最杰出的貢獻(xiàn)是他編寫的系列數(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)院的同事麥加菲編寫的《美國語文讀本》，一同被作為美國學(xué)校的語文和數(shù)學(xué)教材，近50年內(nèi)，美國上萬學(xué)校使用這兩套教材，累計(jì)銷量均超過1.22億冊，對美國教育產(chǎn)生了極大影響。
雷伊教授對俄亥俄州的教師職業(yè)培訓(xùn)也發(fā)揮了很大作用，他幫助建立西部文化中心與職業(yè)教師學(xué)院，將好的教學(xué)技術(shù)與經(jīng)驗(yàn)傳授給老師。他加入俄亥俄州教師協(xié)會成員，并于1853年任其會長，此外還擔(dān)任《俄亥俄教育》雜志社的副總編。
目錄：
�、�.DEFINITIONS1
ADDITION9
SUBTRACTION.11
MULTIPLICATION..17
DIVISION24
Ⅱ.ALGEBRAIC THEOREMS.32
FACTORING.37
GREATEST COMMON DIVISOR41
LEAST COMMON MULTIPLE.47
�、�.ALGEBRAIC FRACTIONS49
�、�.SIMPLE EQUATIONS68
�、�.SUPPLEMENT TO SIMPLE EQUATIONS103
Ⅰ.GENERALIZATION.103
�、�.NEGATIVE SOLUTIONS108
Ⅲ.DISCUSSION OF PROBLEMS110
�、�.PROBLEM OF THE COURIERS.111
Ⅴ.A SIMPLE EQUATION HAS BUT ONE ROOT.117
�、�.EXAMPLES INVOLVING THE SECOND POWER OF THE
UNKNOWN QUANTITY117
Ⅵ.OF POWERS，ROOTS，RADICALS，AND LNEQUALITIES..118
�、�.INVOLUTION，OR FORMATION OF POWERS118
�、�.EXTRACTION OF THE SQUARE ROOT127
�、�.EXTRACTION OF THE CUBE ROOT139
�、�.EXTRACTION OF THE FOURTH ROOT，SIXTH ROOT，NTH
ROOT，ETC148
Ⅴ.RADICAL QUANTITIES151
�、�.THEORY OF FRACTIONAL EXPONENTS.166
�、�.EQUATIONS CONTAINING RADICALS169
�、�.INEQUALITIES.171
�、�.QUADRATIC EQUATIONS176
AFFECTED QUADRATIC EQUATIONS181
TRINOMIAL EQUATIONS.202
SIMULTANEOUS QUADRATIC EQUATIONS CONTAINING TWO
OF MORE UNKNOWN QUANTITIES210
AFFECTED EQUATIONS.214
�、�.RATIO，PROPORTION，AND PROGRESSIONS226
PROPORTION229
GEOMETRICAL PROGRESSION249
�、�.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
�、�.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
�、�.GENERAL THEORY OF EQUATIONS341
TRANSFORMATION OF EQUATIONS.352
LIMITS OF THE ROOTS OF EQUATIONS.363
STURM’S THEOREM.367
ⅩⅢ.RESOLUTION OF NUMERICAL EQUATIONS374
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