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A treatise on algebra

Author: George Peacock
Publisher: Cambridge [England] J. & J.J. Deighton; London, G.F. & J. Rivington, 1842-45.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
Peacock's mathematical work, although not extensive, is significant in the evolution of a concept of abstract algebra. In the textbook, A Treatise on Algebra, he attempted to put the theory of negative and complex numbers on a firm logical basis by dividing the field of algebra into arithmetical algebra and symbolic algebra. In the former the symbols represented positive integers; in the latter the domain of the  Read more...
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Additional Physical Format: Online version:
Peacock, George, 1791-1858.
Treatise on algebra.
Cambridge [Eng.] J. & J.J. Deighton; London, G.F. & J. Rivington, 1842-45
(OCoLC)610134398
Document Type: Book
All Authors / Contributors: George Peacock
OCLC Number: 1246996
Description: 2 volumes 22 cm
Contents: v. 1. Arithmetical algebra.--v. 2. On symbolical algebra and its applications to the geometry of positions.
Responsibility: By George Peacock.

Abstract:

Peacock's mathematical work, although not extensive, is significant in the evolution of a concept of abstract algebra. In the textbook, A Treatise on Algebra, he attempted to put the theory of negative and complex numbers on a firm logical basis by dividing the field of algebra into arithmetical algebra and symbolic algebra. In the former the symbols represented positive integers; in the latter the domain of the symbols was extended by his principle of the permanence of equivalent forms. This principle asserts that rules in arithmetical algebra, which hold only when the values of the variables are restricted, remain valid when the restriction is removed. Although it was a step toward abstraction, Peacock's view was limited because he insisted that if the variables were properly chosen, any formula in symbolic algebra would yield a true formula in arithmetical algebra. Thus a noncommunicative algebra would not be possible.

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