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Symbolical algebra adopts the rules of arithmetical algebra, but removes altogether their restrictions: thus symbolical subtraction differs from the … - George Peacock
" "Symbolical algebra adopts the rules of arithmetical algebra, but removes altogether their restrictions: thus symbolical subtraction differs from the same operation in arithmetical algebra in being possible for all relations of value of the symbols or expressions employed... all the results of arithmetical algebra which are deduced by the application of its rules, and which are general in form, though particular in value, are results likewise of symbolical algebra, where they are general in value as well as in form: thus the product of <math>a^{m}</math> and <math>a^{n}</math>, which is <math>a^{m+n}</math> when <math>m</math> and <math>n</math> are whole numbers, and therefore general in form though particular in value, will be their product likewise when <math>m</math> and <math>n</math> are general in value as well as in form: the series for <math>(a+b)^{n}</math>, determined by the principles of arithmetical algebra, when <math>n</math> is any whole number, if it be exhibited in a general form, without reference to a final term, may be shewn, upon the same principle, to the equivalent series for <math>(a+b)^n</math>, when <math>n</math> is general both in form and value.
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About George Peacock
George Peacock (April 9, 1791 – November 8, 1858) was an English mathematician and author of books on mathematics and a biography of Thomas Young. He became a deacon, then priest, in the Church of England, and later, Vicar of Wymewold and Dean of Ely cathedral, Cambridgeshire. He was also professor of astronomy at the University of Cambridge.
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I Gladly avail myself of the opportunity of inscribing to you, for a second time, a work of mine on Algebra, as a sincere tribute of my respect, affection and gratitude.
I trust that I shall not be considered as derogating from the higher duties which, (in common with you), I owe to my station in the Church, if I continue to devote some portion of the leisure at my command, to the completion of an extensive Treatise, embracing the more important departments of Analysis, the execution of which I have long contemplated, and which, in its first volume I now offer to the public, under the auspices of one of my best and dearest friends.
I assure you that I shall never cease to exert myself to the utmost in the cause of reform, and that I will never decline any office which may increase my power to effect it. I am nearly certain of being nominated to the office of Moderator in the year 1818-1819, and as I am an examiner in virtue of my office, for the next year I shall pursue a course even more decided than hitherto, since I shall feel that men have been prepared for the change, and will then be enabled to have acquired a better system by the publication of improved elementary books. I have considerable influence as a lecturer, and I will not neglect it. It is by silent perseverance only, that we can hope to reduce the many-headed monster of prejudice and make the University answer her character as the loving mother of good learning and science.
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I have separated arithmetical from symbolical algebra, and I have devoted the present volume entirely to the exposition of the principles of the former science and their application to the theory of numbers and of arithmetical processes: the second volume, which is now in the press, will embrace the principles of symbolical algebra: it will be followed, if other and higher duties should allow me the leisure to complete them, by other works, embracing all the more important departments of analysis, with the view of presenting their principles in such a form, as may make them component parts of one uniform and connected system.
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