This principle, which is thus made the foundation of the operations and results of Symbolical Algebra, has been called "The principle of the permanen… - 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.

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.