Excerpt from Advanced Arithmetic and Elementary Algebra and Mensuration

IN my Advanced Arithmetic I adopted the methods of algebra without using its notation; in the present book I use both its methods and its notation. To make the notation intelligible to students Who have not read algebra, I open With a chapter on literal symbolic representation and such other parts of algebra as are necessary and useful in the generalisation of arithmetical practice and in the solution of equations of the first and second degree. Less than this would be insufficient, and more super ?uous, for nine-tenths of the boys and girls Whose education is to be carried beyond the primary but not to the University stage. My treatment of equations of the second degree may seem to suffer from the omission of exercises in the factorisation of compound algebraic expressions but the method of solving such equations by completing the square is very simple and never fails, and may, I hope, be regarded as adequate in a book that is intended to embrace only those departments of algebra that can be made of real service to arithmetic. In my treatment of decimals I have given great prominence to the significance of index notation. This I have done partly because decimal operations cannot be adequately understood Without a sound knowledge of index notation, and partly that the student may the better understand the nature of logarithms when he comes upon them in the succeeding chapter.

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