《美国中学代数(套装上下册)》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.
作者简介：
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.
约瑟夫·雷伊教授于1807年出生于美国弗吉尼亚俄亥俄县，小时在地方学校接受教育，学业优秀。16岁时，他就开始步入其教师生涯，1825年到富兰克林学院求学，跟随乔尔·马丁教授学习医学。1828年毕业后进入俄亥俄医学院学习，1831年毕业。大学毕业后，他在辛辛那提的伍德沃德中学找了份当教师的工作，开始教数学。1836年，俄亥俄司法当局准许伍德沃德中学由高中升格为辛辛那提伍德学院，雷伊成为该学院的一名教授。1851年，该校以变为一所公立高中，雷伊一直在此担任校长，直至去世。
雷伊最杰出的贡献是他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麦加菲编写的《美国语文读本》，一同被作为美国学校的语文和数学教材，近50年内，美国上万学校使用这两套教材，累计销量均超过1.22亿册，对美国教育产生了极大影响。
雷伊教授对俄亥俄州的教师职业培训也发挥了很大作用，他帮助建立西部文化中心与职业教师学院，将好的教学技术与经验传授给老师。他加入俄亥俄州教师协会成员，并于1853年任其会长，此外还担任《俄亥俄教育》杂志社的副总编。
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
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