This work... was designed in the first instance to be a second edition of a Treatise on Algebra, published in 1830, and which has been long out of pr… - George Peacock

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.

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.

It is now more than twenty years since I somewhat rashly undertook to write the Life of Dr. Young. For many years, however, after making this engagement, I found myself so much occupied by the duties of a very laborious college office, that I had no leisure to commence the work; and when the possession of leisure would have enabled me to have done so, my health became so seriously deranged that I felt myself unequal to any continued and severe literary labour. The undertaking was consequently abandoned, and it was proposed to transfer it to other hands; but it was not found easy to secure the services of a person who possessed sufficient scientific knowledge to enable him to write the life of an author whose works were so various in their character and not unfrequently so difficult to understand and analyse, as those of Dr. Young.