美国中学代数

Ⅰ.DEFINITIONS

ADDITION

SUBTRACTION.

MULTIPLICATION

DIVISION

Ⅱ.ALGEBRAIC THEOREMS

FACTORING.

GREATEST COMMON DIVISOR

LEAST COMMON MULTIPLE.

Ⅲ.ALGEBRAIC FRACTIONS.

Ⅳ.SIMPLE EQUATIONS.

Ⅴ.SUPPLEMENT TO SIMPLE EQUATIONS

Ⅰ.GENERALIZATION

Ⅱ.NEGATIVE SOLUTIONS

Ⅲ.DISCUSSION OF PROBLEMS

Ⅳ.PROBLEM OF THE COURIERS.

Ⅴ.A SIMPLE EQUATION HAS BUT ONE ROOT.

Ⅵ.EXAMPLES INVOLVING THE SECOND POWER OF THE

UNKNOWN QUANTITY

Ⅵ.OF POWERS，ROOTS，RADICALS，AND LNEQUALITIES

Ⅰ.INVOLUTION，OR FORMATION OF POWERS

Ⅱ.EXTRACTION OF THE SQUARE ROOT.

Ⅲ.EXTRACTION OF THE CUBE ROOT

Ⅳ.EXTRACTION OF THE FOURTH ROOT，SIXTH ROOT，NTH

ROOT，ETC.

Ⅴ.RADICAL QUANTITIES.

Ⅵ.THEORY OF FRACTIONAL EXPONENTS.

Ⅶ.EQUATIONS CONTAINING RADICALS.

Ⅷ.INEQUALITIES.

Ⅶ.QUADRATIC EQUATIONS

AFFECTED QUADRATIC EQUATIONS

TRINOMIAL EQUATIONS

SIMULTANEOUS QUADRATIC EQUATIONS CONTAINING TWO

OF MORE UNKNOWN QUANTITIES

AFFECTED EQUATIONS

Ⅷ.RATIO，PROPORTION，AND PROGRESSIONS

PROPORTION

GEOMETRICAL PROGRESSION

Ⅸ.PERMUTATIONS，COMBINATIONS，AND BINOMIAL

THEOREM

Ⅹ.INDETERMINATE COEFFICIENTS：BINOMIAL THEOREM，

GENERAL DEMONSTRATION：SUMMATION AND

INTERPOLATION OF SERIES.

THEOREM

BINOMIAL THEOREM

THE DIFFERENTIAL METHOD OF SERIES

PILING OF CANNON BALLS AND SHELLS

INTERPOLATION OF SERIES

INFINITE SERIES

RECURRING SERIES

REVERSION OF SERIES

Ⅺ.CONTINUED FRACTIONS：LOGARITHMS：EXPONENTIAL

EQUATIONS：INTEREST，AND ANNUITIES

CONTINUED FRACTIONS

LOGARITHMS.

COMPUTATION OF LOGARITHMS.

NAPERIAN，OF HYPERBOLIC LOG ARITHMS.

SINGLE AND DOUBLE POSITION

EXPONENTIAL EQUATIONS

INTEREST AND ANNUITIES.

Ⅻ.GENERAL THEORY OF EQUATIONS

TRANSFORMATION OF EQUATIONS

LIMITS OF THE ROOTS OF EQUATIONS

STURM’S THEOREM

ⅩⅢ.RESOLUTION OF NUMERICAL EQUATIONS

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..