## A Treatise on Algebra, Volume 1Peacock'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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arē arith arithmetical algebra arithmetical series coefficient complete quotient consequently considered continued fraction continued product converging fractions corresponding cube denoted determined divided dividend division divisor equal equation equivalent expressed final digit finite number following are examples geometrical given greater identical inasmuch indeterminate equations involve known terms last Article last digit least common multiple less magnitudes means metical minuend modulus multiplicand multiplied number of combinations number of days number of permutations number of terms operation ordinary preceding primary unit primitive problem proposition quadratic quadratic equations quadratic surds quantities ratio recurring decimal reduced replace represent resolvend respectively result rule scale shewn similar manner simultaneous equations square root subordinate units subtract subtrahend surds Symbolical Algebra third tion Transposing unknown numbers unknown symbols whole number zero