Treatise on Algebra, Volume I: Arithmetical Algebraby George Peacock
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.
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