Treatise on algebra 代数论

This historic 1830 text gave algebra a logical treatment comparable to Euclid's Elements, separating arithmetical from symbolic algebra. Appropriate for upper-level undergraduates and graduate students, this first book of a two-volume set is devoted to the exposition of the principles of arithmetical algebra and their application to the theory of numbers and arithmetical processes.
　　Starting with a survey of the basics of arithmetical algebra, the author proceeds to a discussion of the theory of the fundamental operations in arithmetic and the theory of the extraction of the roots of numbers. Examinations of ratios and proportions, the solution of equations, and arithmetical, geometrical, and harmonical progressions follow. The theory of permutations and combinations and the formation of binomial products and powers receive due consideration, as does the solution, in whole numbers, of indeterminate equations of the first degree. The book concludes with a survey of the symbolical representation and properties of numbers.

PREFACE
CHAPTER Ⅰ.PRINCIPLES of arithmetical algebra
CHAPTER Ⅱ.On the theory of the fundamental operations in arithmetic
CHAPTER Ⅲ.On the theory of the extraction of the roots of numbers, and the properties of surds
CHAPTER Ⅳ.On ratios and proportions
CHAPTER Ⅴ.On the solution of equations
CHAPTER Ⅵ.On arithmetical, geometrical and harmordcal progressions or series
CHAPTER Ⅶ.Theory of combinations and permutations
CHAPTER Ⅷ.On the formation of binomial products and powers
CHAPTER Ⅸ.On the solution, in whole numbers, of indeterminate equations of the first degree
CHAPTER Ⅹ.On the symbolical representation and properties of numbers